Design_Handbook_7th_Edition (1) (1).pdf

PCI DESIGN HANDBOOK PRECAST AND PRESTRESSED CONCRETE

7TH EDITION



200 West Adams Street Suite 2100 Chicago, IL 60606 Phone: 312-786-0300 Fax: 312-621-1114 www.pci.org

200 West Adams Street Suite 2100 Chicago, IL 60606 Phone: 312-786-0300 Fax: 312-621-1114 www.pci.org

200 West Adams Street I Suite 2100 I Chicago, IL 60606-5230 Phone: 312-786-0300 I Fax: 312-621-1114 I www.pci.org

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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Copyright © 2010 By Precast/Prestressed Concrete Institute First Edition, first printing, 1971 First Edition, second printing, 1972 Second Edition, first printing, 1978 Second Edition, second printing, 1980 Third Edition, first printing, 1985 Fourth Edition, first printing, 1992 Fifth Edition, first printing, 1999 Sixth Edition, first printing, 2004 Seventh Edition, first printing, 2010 All rights reserved. This book or any part thereof may not be reproduced in any form without the written permission of the Precast/Prestressed Concrete Institute.

Library of Congress Catalog Card Number 2010927089 ISBN 978-0-937040-87-4

Printed in U.S.A.

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PCI DESIGN HANDBOOK/SEVENTH EDITION

PCI DESIGN HANDBOOK PRECAST AND PRESTRESSED CONCRETE

7TH EDITION



PCI Industry Handbook Committee Greg Force, P.E., FPCI, Chairman Neal S. Anderson, P.E., S.E., FACI

Karen Laptas, P.E.

Timothy R. Salmons, P.E., S.E.

Ned M. Cleland, PhD, P.E., FPCI, FACI

David J. Larsen, P.E., S.E.

Kim E. Seeber, P.E., FPCI

Harry A. Gleich, P.E., FPCI, FACI

Jason P. Lien, P.E.

Larbi Sennour, PhD, P.E., FPCI, FACI

Gary A. Householder, P.E.

Rafael A. Magana, P.E.

a

Pat Hynes, P.E., FPCI

Michael I. Owings, P.E., S.E.

Irwin J. Speyer, P.E., FPCI, FACI

Phillip J. Iverson, P.E.

Stephen Pessiki, PhD, FPCI, FACI

Peter G. Troiani, P.E., S.E.

Walter Korkosz, P.E., S.E.

Steven H. Peterson, P.E.

Helmuth Wilden, P.E., FPCI

Jason Krohn, P.E.

Courtney B. Phillips, P.E., S.E.

Charles E. Wynings, P.E.

Fattah Shaikh, PhD, P.E., FPCI

Consulting Members Robert F. Mast, P.E., S.E., FPCI, HACI

Jagdish C. Nijhawan, P.E., FPCI

Editor Helmuth Wilden, P.E., FPCI a. Deceased January 10, 2008

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

J. Robert Norris, P.E.

Dedication This seventh edition of the PCI Design Handbook is dedicated to A. Fattah Shaikh, who passed away on January 10, 2008, at the age of 70. He received his BS in civil engineering from the University of Karachi in Pakistan in 1960, his MS in structural engineering from the University of Hawaii in 1964, and his PhD in structural engineering from the University of Iowa in 1967, at which time his career started at the University of Wisconsin Milwaukee (UWM). Dr. Shaikh served UWM for 36 years as a professor of structural engineering, chairman of the Department of Civil Engineering and Mechanics, and associate dean of Graduate Programs and Research. He retired in 2003. His internationally recognized expertise in the field of structural concrete and his passion for his students and profession earned him the reputation as one of the most popular professors at the university. His contributions to PCI and the precast, prestressed concrete industry were extraordinary. He served on many PCI committees for many years, including the Industry Handbook Committee, for which he was co-editor of the 4th edition and chairman of the committee for the 5th edition, and the Connection Details Committee for which he was editor of the 1988 Connection Details Manual. Fattah was admired by practicing precast engineers throughout the country for his practical application of complicated research. He was the first to compile headed stud research results and recommend a simple design methodology that was used successfully by the industry for many years. He also was an early advocate of using dry connections in high seismic areas with the application of the "specific yielding" principle that has become the standard for the design of precast concrete connections today. All users of precast concrete will forever be indebted to him for his work in moving the industry ahead. He has been honored by PCI with several awards including being inducted in the inaugural class of PCI Fellows in 1994 and given the distinguished Educator Award in 1998. In 2004 Fattah was named one of 50 Titans of the Industry. Those chosen for this distinction have made a positive and industry-altering contribution to the industry in the 50 years preceding 2004 by creating new technology, product innovations, opening new markets, or dramatically changing how the industry manufactures and delivers its products. He was one of only five academics chosen for this honor. His other awards include the AMOCO Distinguished Teacher Award in 1979 and the Orton Spanley Award in 1994 for outstanding long-term contributions to the concrete industry in the areas of education, research, and technical leadership. Fattah was also a Fellow of the American Concrete Institute and the American Society of Civil Engineers. Fattah will be remembered for his sense of humor, his enjoyment of tennis and racquetball, and his compassion and love for his wife Sunja, daughters Aysha and Sabina, son Omar, and five grandchildren. All who knew him are very grateful to Fattah for sharing his knowledge, wisdom, and friendship with us.

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PCI DESIGN HANDBOOK/SEVENTH EDITION

Foreword The Precast/Prestressed Concrete Institute, a non-profit corporation, was founded in 1954 for the purpose of advancing the design, manufacture, and use of structural precast/ prestressed concrete and architectural precast concrete in the United States and Canada. To meet this purpose, PCI continually disseminates information on the latest concepts, techniques, and design data to the engineering and architectural professions through regional and national programs and technical publications. The first edition of the PCI Design Handbook was published in 1971 with a primary focus on structural products and buildings. To fill a void in the design of architectural precast concrete, the PCI Manual for Structural Design of Architectural Precast Concrete was published in 1977. In 1978, the second edition of the PCI Design Handbook was published. In keeping with the tradition of continually updating information, an Industry Handbook Committee was formed in 1979 to develop the third edition, which was published in 1985. That edition provided, in a single source, information on the design of both architectural precast concrete and structural precast/prestressed concrete. The fourth edition, published in 1992; the fifth edition, published in 1999; and the sixth edition, published in 2004 continued to present both architectural and structural products and systems. This emphasis is maintained in the seventh edition. All past editions of the handbook have been intended for the design of buildings. For similar design guidelines for bridges, refer to PCI’s Bridge Design Manual, 2003. Since 2004, the committee has continued to monitor technical advancements within the industry, with particular assistance from the many committees of PCI responsible for a variety of specific topics. This seventh edition is the culmination of those efforts and presents current industry practice. The members of the committee listed on the title page have made significant contributions of their time and expertise. In addition, PCI committees have provided a review of specific areas. Many individuals within the industry have also provided advice and comment. The Institute offers all involved in this process a special note of recognition and appreciation. It is important that the user of the handbook understand the process used by the Industry Handbook Committee in the development of this seventh edition. That process was as follows: • Use the sixth edition as the baseline, with the understanding that ACI 318-05, ASCE 7-05, and IBC 2006 would be the relevant building code references for the seventh edition. • The committee agreed on a new arrangement going from 11 chapters to 15 as described below. • A subgroup was established for each chapter with three to seven members each including a chairperson, with the purpose of detailed review of the existing chapter and exhaustive review of research and publications relevant to the subject material within that chapter subsequent to the previous edition.

• After analysis of the above and discussion regarding improved and/or updated content matter, each subgroup developed a draft of their respective chapters. • Each chapter was then edited by the editor and a committee ballot version was created. • Each chapter was balloted by the committee with resolution of all comments done during meetings of the full committee. This process included fourteen face to face meetings, and at least nine web-based teleconferences over the four-year course of development. • Additional editing was done and a TAC ballot version was created. • Each chapter was balloted by TAC with resolution of all comments by both TAC and the Industry Handbook Committee. • Based on these approved versions, a Blue Ribbon Review version was created and this final review phase consisted of a Blue Ribbon Review Committee, made up of plant engineers, specialty engineers, consulting engineers, academicians, and associate members. Each member of the Blue Ribbon Review Committee is a recognized leader in the analysis and design of precast/prestressed concrete products or expert in a closely related field. After a six-week review period, this group met for three days and offered valuable comments, that were considered by the Industry Handbook Committee. Most were accepted as improving the publication. • A final version of each chapter was then created and reviewed thoroughly by the original chapter subgroup. This resulted in a few corrections and further improvement. In addition, a comprehensive editorial review of the Handbook was carried out by the PCI Production Department led by Emily Lorenz, editor in chief of the PCI Journal. PCI and the Industry Handbook Committee extend its appreciation to all individuals for their invaluable review and input. Several that deserve special recognition include: Chuck Oswald, PhD, P.E., who was retained by PCI to develop the section in Chapter 4 on blast resistant design; Alan Mattock, P.E., PhD, who provided the information to justify the changes in the shear friction design; Gary Klein, P.E., S.E., whose experience with research and design of beams with ledges helped update that material; Roy Reiterman, P.E., FACI, for updating the Design Aids related to welded-wire-reinforcement, Dan Stadig who helped with several design examples as well as John Maher and Dan Sochor who were interns at PCI during the latter stages of development and assisted in reviews of several chapters. Updates to the sixth edition have been made throughout the document. Some of particular importance include:

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

• Updated to the ACI 318-05 building code, other current PCI publications, and publications of other technical associations. • Chapter 1 includes updated photographs that illustrate more current projects. • Chapter 2 is entirely new and includes notation for the entire handbook. • Chapter 3 (Chapter 2 in the sixth edition) includes updated load tables as well as new information for preliminary design of stadium risers, stairs, and non-loadbearing panels. • Chapter 4 (Chapter 3 in the sixth edition) has been reduced in content since the PCI publications Seismic Design of Precast/Prestressed Concrete Structures, 2007 has been published and includes the latest seismic design according to IBC 2006. Examples for shear wall buildings and for precast diaphragms have been updated to clarify diaphragm and collector design procedures. An entirely new section on blast-resistant design has been added. • Chapter 5 (Chapter 4 in the sixth edition) has been updated with significant changes to the use of shear friction and ledge hanger steel design. The asymmetrical components (bleacher seating) section has been expanded and a design example added. Sections on concrete corbel design and sandwich panels have been moved into the chapter from other chapters in the previous edition. New sections have been created covering shear walls, including a design example, point loads on double-tee flanges, and warping of double-tees. • Chapter 6 has been updated to reflect the latest headed stud design criteria, advanced steel component design procedures, and the Instantaneous Center Method of weld analysis. • Chapter 7 is updated and now includes examples for ASCE 7-05 wind design Methods 1 and 2 as well as an expanded seismic load example that was in Chapter 4 of the sixth edition. • Chapter 8 has been revised to include updated information and much of the erection stability information has been deleted because this is better handled by the project designers responsible for this aspect of the construction. • Chapter 9 is a totally new chapter on materials and condenses material covered in several chapters of the

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sixth edition. It also provides new information on other materials used in the industry. Chapter 10 (Section 9.3 of the sixth edition) is now totally devoted to information on fire resistance since this is a major benefit of using precast/prestressed concrete. A new section related to fire endurance of precast parking structures has also been added. Chapter 11 (Sections 9.1 and 9.2 of the sixth edition) has updated information. Chapter 12 (Section 9.7 of the sixth edition) is essentially the same. Chapter 13 (Chapter 8 of the sixth edition) has been updated and is more in line with ACI’s tolerances. Chapter 14 (Chapter 10 of the sixth edition) has been reorganized to place an updated Standard Practice first and also includes an updated Operations Practice. The specifications for both structural and architectural precast concrete are in a Word.doc format on the CD in the front jacket pocket. Chapter 15 (Chapter 11 of the sixth edition) includes updated Design Aids as well as new ones providing bent bar details and standard shear reinforcement for double-tees. The Appendix is totally new and is the result of PCI’s Technical Activities Council directing that the impact of ACI 318-08 be included. A searchable CD is included in the front jacket pocket of the handbook. This CD has the full text of the handbook and many of the cited PCI references.

Substantial effort has been made to ensure that this handbook is accurate. However, PCI cannot accept responsibility for any errors or oversights in the use of material or in the preparation of engineering plans. The designer must recognize that no handbook or code can substitute for experience and engineering judgment. This publication is intended for use by professional personnel competent to evaluate the significance and limitations of its contents and able to accept responsibility for the application of the material it contains. PCI considers each new edition of the handbook to be a living document. The user is encouraged to offer comments to PCI and suggestions for improvements to be incorporated in the next edition. Questions concerning the source or derivation of any material in the handbook should be directed to the PCI Technical Director.

Comment by Chairman Greg Force: I would like to offer my sincere thanks, appreciation, and admiration to my fellow Committee Members, the Editor, the PCI Staff, as well as countless others within the industry whose purpose and intent was to create an invaluable design resource that places precast, prestressed concrete in the vanguard of building system materials.

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PCI DESIGN HANDBOOK/SEVENTH EDITION

Members of the Blue Ribbon Committee Suzanne Aultman, P.E.

Barry N. McKinley, P.E.

Martin A. Cuadra, P.E., S.E.

Alexander G. Mihaylov, P.E., S.E.

Roland Diaz, P.E.

Christopher P. Mosley, P.E.

Mike Dixon, P.E.

Clay J. Naito, PhD, P.E.

Robert J. Frosch, PhD, P.E., FACI

Joseph Retzner, P.E.

Kim R. Hammon, P.E.

Sami H. Rizkalla, PhD, FASCE, FPCI, FACI

J. Blake Hodge, P.E.

David M. Schreffler, P.E.

Keith Holshausen, CEng, FICE

Venkatesh Seshappa, P.E., S.E.

John M. Jacobsen, P.E.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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PCI DESIGN HANDBOOK/SEVENTH EDITION

Table of Contents Chapter 1—Precast and Prestressed Concrete: Applications 1–1 to 1–28 Chapter 2—Notations 2–1 to 2–18 Chapter 3—Preliminary Design of Precast/ Prestressed Concrete Structures 3–1 to 3–64 Chapter 4—Analysis and Design of Precast/ Prestressed Concrete Structures 4–1 to 4–98 Chapter 5—Design of Precast and Prestressed Concrete Components 5–1 to 5–152 Chapter 6—Design of Connections 6–1 to 6–116 Chapter 7—Structural Considerations for Architectural Precast Concrete 7–1 to 7–36 Chapter 8—Component Handling and Erection Bracing 8–1 to 8–28 Chapter 9—Precast and Prestressed Concrete: Materials 9–1 to 9–42 Chapter 10—Design for Fire Resistance of Precast and Prestressed Concrete 10–1 to 10–26 Chapter 11—Thermal and Acoustical Properties of Precast Concrete 11–1 to 11–26 Chapter 12—Vibration Design of Precast/ Prestressed Concrete Floor Systems 12–1 to 12–10 Chapter 13—Tolerances for Precast and Prestressed Concrete 13–1 to 13–34 Chapter 14— Specifications and Standard Practices 14-1 to 14-36 Chapter 15— General Design Information 15–1 to 15–62 Appendix—Impact of ACI 318-08 on this Handbook A–1 to A–22 Index

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

LIST OF EXAMPLES AND DESIGN AIDS CHAPTER 3 PRELIMINARY DESIGN OF PRECAST/ PRESTRESSED CONCRETE STRUCTURES 3.12 Design Aids.......................................................................................................................................................... 3-50 3.12.1 Design Strength Interaction Curves for Precast, Prestressed Concrete Columns................ 3-50 3.12.2 Design Strength Interaction Curves for Precast, Reinforced Concrete Columns................ 3-52 3.12.3 Design Strength Interaction Curves for Precast, Prestressed Double-Tee Wall Panels..... 3-54 3.12.4 Partial Interaction Curves for Prestressed Hollow-Core and Sandwich Wall Panels.......... 3-55 3.12.5 Partial Interaction Curves for Precast, Prestressed Solid and Sandwich Wall Panels......... 3-56 3.12.6 Partial Interaction Curves for Precast, Reinforced Concrete Solid and Sandwich Wall Panels......................................................................................................... 3-57 3.12.7 Recommended Height-to-Thickness Ratio Limits for Precast, Reinforced Solid Non-Load Bearing Wall Panels........................................................................................... 3-58 3.12.8 Section Properties and Allowable Service Loads for Prestressed Concrete Piles.............. 3-59 3.12.9 Section Properties and Allowable Service Loads of Prestressed Sheet Piles...................... 3-60 3.12.10 Recommended Maximum Spans for Precast Concrete Stairs............................................. 3-61 3.12.11 Stadium Riser Allowable Spans.......................................................................................... 3-62

CHAPTER 4 ANALYSIS AND DESIGN OF PRECAST/ PRESTRESSED CONCRETE STRUCTURES Example

4.2.2.1 4.2.3.1 4.2.4.1 4.3.2.1 4.4.1.1 4.4.1.2 4.5.7.1 4.5.11.1 4.5.12.1 4.6.1.1 4.6.3.1 4.6.4.1 4.9.4

Calculation of Snow Load..................................................................................................... 4-6 Use of ASCE 7 Method 1 for Wind-Load Determination..................................................... 4-8 Determination of Base Shear Coefficient CS....................................................................... 4-12 Compliance of a Precast Concrete Structure with Structural Integrity Provisions.............. 4-17 Calculation of Volume-Change Shortening......................................................................... 4-19 Determine Volume-Change Shortening by Design Aids 4.11.18 and 4.11.19.................... 4-20 Design of Unsymmetrical Shear Walls................................................................................ 4-27 Typical Single-Story Industrial Building............................................................................. 4-31 Three-Level Parking Structure............................................................................................ 4-37 Stability Analysis of an Unbraced Frame............................................................................ 4-48 Degree of Fixity................................................................................................................... 4-50 Imaginary Column for Computer Model............................................................................. 4-52 Blast Design Example.......................................................................................................... 4-72

4.11 Design Aids.......................................................................................................................................................... 4-77 4.11.1 Classification of Building and Other Structures for Importance Factors I.......................... 4-77 4.11.2 Ground snow loads.............................................................................................................. 4-78 4.11.3 Snow Loading...................................................................................................................... 4-80 4.11.4 Snow Drifting...................................................................................................................... 4-81 4.11.5 Basic Wind Speed................................................................................................................ 4-82 4.11.6 Factors for Use with ASCE 7 Method 1 Wind Design........................................................ 4-84 4.11.7 Site Classifications and Coefficients................................................................................... 4-85 4.11.8 Design Coefficients and Factors for Precast Concrete Seismic-Force-Resisting System.................................................................................................................................. 4-86 4.11.9 Allowable Story Drifta ........................................................................................................ 4-87 4.11.10 Architectural Components Coefficients.............................................................................. 4-87 4.11.11 Maximum Seasonal Climatic Temperature Change, °F...................................................... 4-88 4.11.12 Annual Average Ambient Relative Humidity..................................................................... 4-88 4.11.13 Creep and Shrinkage Strains................................................................................................ 4-89 4.11.14 Correction Factors for Prestress and Concrete Strength, Creep Only................................. 4-89 4.11.15 Correction Factors for Relative Humidity........................................................................... 4-90 4.11.16 Correction Factors for Volume-to-Surface (V/S) Ratio...................................................... 4-90 4.11.17 Design Temperature Strains................................................................................................ 4-90 4.11.18 Volume-Change Strains for Typical Building Elements. Prestressed Components........... 4-91 4.11.19 Volume-Change Strains for Typical Building Elements. Non-Prestressed Components.... 4-91 First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST, PRESTRESSED CONCRETE STRUCTURES 4.11.20 4.11.21 4.11.22 4.11.23 4.11.24 4.11.25 4.11.26

Length of Structure Without Use of Expansion Joints........................................................ 4-92 Build-Up of Restraint Forces in Beams............................................................................... 4-93 Equivalent Volume-Change Strains for Typical Building Elements................................... 4-94 Equivalent Volume-Change Strains for Typical Building Elements................................... 4-94 Coefficients kf and km for Forces and Moments Caused by Volume-Change Restraint Forces................................................................................................................... 4-95 Use of Design Aid 4.11.24.................................................................................................. 4-96 Shear-Wall Deflection......................................................................................................... 4-97

CHAPTER 5 DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS Example 5.2.1.1 5.2.1.2 5.2.1.3 5.2.1.4 5.2.1.5 5.2.2.1 5.2.2.2 5.2.2.3 5.2.2.4 5.2.2.5 5.2.2.6 5.2.3.1 5.2.3.2 5.2.4.1 5.2.5.1 5.3.1.1 5.3.2.1 5.3.3.1 5.3.4.1 5.3.4.2 5.3.5.1 5.4.1 5.4.2 5.5.1 5.5.6.1 5.6.1 5.6.3.1 5.7.1 5.8.1.1 5.8.3.1 5.8.3.2 5.8.3.3 5.8.3.4 5.8.4.1 5.8.5.1 5.8.5.2 5.9.1.1 5.9.1.2 5.9.2.1 5.9.3.1 5.9.4.1 5.9.4.2

Use of Design Aid 5.14.1 for Determination of Non-Prestressed Reinforcement................ 5-7 Use of Design Aid 5.14.2 for Determination of Prestressing Steel Requirements-Bonded Strand …………………………………………..……..…….……..5-8 Use of Design Aid 5.14.3 Values of fps by Stress-Strain Relationship-Bonded Strand…………………………………………………………………5-9 Use of Design Aid 5.14.3 and Eq. 18-3 (ACI 318-05) for Partially Prestressed Component........................................................................................................ 5-10 Design of Partially Prestressed Flange Section Using Strain Compatibility....................... 5-12 Non-Prestressed Panel Design............................................................................................. 5-17 Calculation of Critical Stresses – Straight Strands Class U Component............................. 5-19 Calculation of Critical Stresses – Single-Point Depressed Strand Class T Component...... 5-21 Tensile Force to Be Resisted by Top Reinforcement.......................................................... 5-23 Transformed Cracked Section Using Reference 4: Example 1........................................... 5-25 Transformed Cracked Section Using Reference 4: Example 2........................................... 5-28 Use of Design Aid 5.14.4 - Design Stress for Underdeveloped Strand.............................. 5-37 Moment Capacity of Component with Debonded Strands in Development Region........... 5-38 Calculation of End Reinforcement to Resist Bursting Stresses........................................... 5-40 Design of Stadium Riser for Bending.................................................................................. 5-42 Design of Shear Reinforcement – Non-Prestressed Component......................................... 5-48 Construction of Applied and Resisting Design Shear Diagrams......................................... 5-50 Use of Design Aids 5.14.5 through 5.14.7 – Graphical Solution of Eq. 5-20 (Code Eq. 11-9)..................................................................................................... 5-53 Minimum Shear Reinforcement by Eq. 5-25 and Design Aid 5.14.8.................................. 5-55 Use of Design Aid 5.14.9 – Shear Reinforcement............................................................... 5-55 Horizontal Shear Design for Composite Beam................................................................... 5-56 Shear and Torsion Design of a Non-Prestressed Component.............................................. 5-61 Shear and Torsion Design of a Prestressed Concrete Component...................................... 5-64 L-Beam End and Ledge Design........................................................................................... 5-71 Design of a Prestressed, Pocketed Spandrel Beam.............................................................. 5-73 Reinforced Bearing for a Rectangular Beam....................................................................... 5-78 Reinforcement for Dapped-End Beam................................................................................ 5-81 Loss of Prestress.................................................................................................................. 5-85 Calculation of Initial Camber.............................................................................................. 5-89 Deflection Calculation Using Bilinear Moment-Deflection Relationship – Example 1..... 5-91 Deflection Calculation Using Bilinear Moment-Deflection Relationship – Example 2..... 5-92 Deflection Calculation Using Effective Moment of Inertia – Example 1........................... 5-93 Deflection Calculation Using Effective Moment of Inertia – Example 2........................... 5-94 Use of Multipliers for Determining Long-Term Cambers and Deflections........................ 5-95 Thermal Bow in a Wall Panel.............................................................................................. 5-97 Thermal Force and Bow in a Roof Component................................................................... 5-98 Construction of Interaction Curve for a Precast, Reinforced Concrete Column............... 5-101 Calculation of Interaction Points for a Prestressed Concrete Compression Component... 5-103 Use of Design Aids 5.14.13 and 5.14.14........................................................................... 5-104 Second-Order Analysis of an Uncracked Component....................................................... 5-107 Reinforced Concrete Corbel (Cantilever Beam Design Method)...................................... 5-111 Reinforced Concrete Corbel (Strut-and-Tie Design Method............................................. 5-113

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

PRELIMINARY DESIGN OF PRECAST, PRESTRESSED CONCRETE STRUCTURES 5.9.6.1 5.9.7.1 5.10.1 5.11.1 5.12.1.1 5.12.2.1

Approximate Section Properties of an Architectural Mullion Panel................................. 5-117 Sheet Pile........................................................................................................................... 5-118 Shear-Wall Analysis.......................................................................................................... 5-119 Section Properties of Sandwich Wall Panels..................................................................... 5-124 Flexural Strength of Double-Tee Flange in Transverse Direction.................................... 5-130 General Case Illustrating Effective Resisting Widths for Concentrated Loads on Hollow-core Decks...................................................................................................... 5-134

5.14 Design Aids........................................................................................................................................................ 5-138 5.14.1 Flexural Resistance Coefficients for Components with Non-Prestressed, Prestressed Reinforcement, or Combinations of Both.......................................................................... 5-138 5.14.2 Coefficients K ‘u for Determining Flexural Design Strength – Bonded Prestressing Steel.5-139 5.14.3 Values of fps by Stress-Strain Relationship – Bonded Strand............................................ 5-140 5.14.4 Design Stress for Underdeveloped Strand......................................................................... 5-140 5.14.5 Shear Design by Eq. 5-20 – Straight Strands.................................................................... 5-141 5.14.6 Shear Design by Eq. 5-20 – Shallow Drape...................................................................... 5-142 5.14.7 Shear Design by Eq. 5-20 – Steep Drape.......................................................................... 5-143 5.14.8 Minimum Shear Reinforcement by Eq. 5-25..................................................................... 5-144 5.14.9 Shear Reinforcement......................................................................................................... 5-145 5.14.10 Camber Equations for Typical Strand Profiles.................................................................. 5-146 5.14.11 Moment of Inertia of Transformed Section – Prestressed Components............................ 5-147 5.14.12 Forces Required to Restrain Bowing................................................................................. 5-148 5.14.13 Use of Design Aid 5.14.14................................................................................................ 5-148 5.14.14 Coefficients kf and km for Determining Moments and Restraining Forces on Eccentrically Loaded Columns Braced against Sidesway................................................. 5-149 5.14.15 Design Strength of Concrete Brackets, Corbels, or Haunches.......................................... 5-150

CHAPTER 6 DESIGN OF CONNECTIONS Example

6.5.4.1 6.5.5.1 6.5.5.2 6.5.5.3 6.5.5.4 6.6.1.1 6.6.3.1 6.6.5.1(a) 6.6.5.1(b) 6.6.7.1 6.6.7.2 6.7.3.1 6.7.4.1 6.8.1 6.9.1 6.9.2 6.11.2.1 6.13.1 6.13.2 6.13.3 6.13.4 6.13.5 6.13.6 6.13.7 6.13.8

Tension Strength of Stud Groups........................................................................................ 6-16 Headed Concrete Anchor Front-Edge Failure Mode........................................................... 6-19 Headed Concrete Anchor Corner-Failure Mode.................................................................. 6-23 Headed Concrete Anchor Side-Edge Failure Mode............................................................ 6-24 Design of Bearing Seat with Headed Concrete Anchors..................................................... 6-26 Plastic Section Modulus of a Built-Up Steel Member......................................................... 6-31 Design of Steel Structural Tube in Torsion......................................................................... 6-33 Unstiffened Connection Angle with Headed Concrete Anchors......................................... 6-36 Unstiffened Connection Angle with Bolts........................................................................... 6-39 Triangular Stiffener Analysis.............................................................................................. 6-44 Triangular Stiffener Design................................................................................................. 6-44 Reinforcing Bar Weld Analysis........................................................................................... 6-47 Strength Analysis of Weld Group........................................................................................ 6-51 Structural Steel Corbel......................................................................................................... 6-59 Design of a Cazaly Hanger.................................................................................................. 6-63 Design of a Loov Hanger..................................................................................................... 6-66 Column Connection – Base Plate and Anchor Bolt Design................................................ 6-72 Cladding Connections – Reference Chapter 7, Examples 7.5.1.1 and 7.5.1.3.................... 6-76 Plate-and-Bar Diaphragm Shear Connection- Reference Fig. 4.8.1.................................... 6-80 Diaphragm-to-Wall Shear Connection – Reference Section 4.5 and 4.6............................ 6-82 Wall-to-Wall Tension Connection – Reference Section 4.5............................................... 6-84 Wall-to-Wall Shear Connection – Reference Section 4.5................................................... 6-86 Wall-to-Wall Shear Connection with Combined Loading – Reference Section 4.5........... 6-91 Ordinary Moment Frame Connection – Reference Section 4.5.......................................... 6-96 Deformed Bar or Reinforcing Bar Connection Plate Supporting Steel Beam..................... 6-97

6.15

Design Aids........................................................................................................................................................ 6-101 6.15.1 Allowable and Design Stress for Fillet and Partial Penetration Welds . ........................... 6-101 First Printing/CD-ROM Edition

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PRELIMINARY DESIGN OF PRECAST, PRESTRESSED CONCRETE STRUCTURES 6.15.2 6.15.3 6.15.4 6.15.5 6.15.6 6.15.7 6.15.8 6.15.9 6.15.10 6.15.11 6.15.12 6.15.13 6.15.14

Strength of Fillet Welds for Building Construction.......................................................... 6-101 Minimum Length of Weld to Develop Full Strength of Bar. Weld Parallel to Bar Length......................................................................................................................... 6-102 Size of Fillet Weld Required to Develop Full Strength of Bar. Butt Weld....................... 6-103 Size of Fillet Weld Required to Develop Full Strength of Bar. Weld Through Hole....... 6-104 Strength of Bolts and Threaded Fasteners......................................................................... 6-105 High-Strength Coil Bolt and Coil Threaded Rod Selection Chart.................................... 6-105 Strength of Connection Angles. Vertical Load.................................................................. 6-106 Strength of Connection Angles. Horizontal Load............................................................. 6-106 Design of Structural Steel Haunches — Concrete Design Strength.................................. 6-107 Design of Structural Steel Haunches — Reinforcement Design Strength........................ 6-108 Column Base-Plate Thickness Requirements.................................................................... 6-109 Strength of Welded Headed Studs Based on Steel Strength.............................................. 6-110 Concrete Tension Strength of Welded Headed-Stud Assemblies..................................... 6-110

CHAPTER 7 STRUCTURAL CONSIDERATIONS FOR ARCHITECTURAL PRECAST CONCRETE Example 7.5.1.1 7.5.2.1 7.5.3.1

Use of ASCE 7 Method 1 for Wind-Load Determination................................................... 7-16 Use of ASCE 7 Method 2 for Wind-Load Determination................................................... 7-18 Architectural Precast Concrete Panel with Earthquake Loading......................................... 7-21

CHAPTER 8 COMPONENT HANDLING AND ERECTION BRACING Example

8.3.1 8.3.2 8.5.1 8.6.1

Design of Wall Panel for Stripping..................................................................................... 8-13 Use of Prestressing in the Wall Panel.................................................................................. 8-17 Panel Shipping..................................................................................................................... 8-20 Erecting Wall Panels............................................................................................................ 8-24

CHAPTER 10 DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE Example

10.5.3.1 10.5.4.1 10.6.3.1 10.8.1

Fire Endurance of a Ribbed Panel....................................................................................... 10-7 Fire Endurance of an Assembly......................................................................................... 10-10 Fire Endurance by Rational Design................................................................................... 10-17 Fire Endurance by Code Tables......................................................................................... 10-22

CHAPTER 11 THERMAL AND ACOUSTICAL PROPERTIES OF PRECAST CONCRETE Example

11.1.4.1 11.1.4.2 11.1.6.1 11.1.7.1

Thermal Resistance of Wall................................................................................................. 11-4 Thermal Resistance of Roof................................................................................................ 11-4 Determination of R-Value for Sandwich Panel................................................................. 11-16 Condensation Prevention................................................................................................... 11-22

CHAPTER 12 VIBRATION DESIGN OF PRECAST, PRESTRESSED CONCRETE FLOOR SYSTEMS Example 12.6.1 12.8.1 12.10

Vibrations Caused by Walking............................................................................................ 12-4 Stadium Seat........................................................................................................................ 12-7 Vibration Isolation............................................................................................................... 12-9

CHAPTER 13 TOLERANCES FOR PRECAST AND PRESTRESSED CONCRETE Example 13.4.1 13.4.2

Clearance Determination – Single-Story Industrial Building............................................ 13-28 Clearance Determination – High-Rise Steel-Frame Structure........................................... 13-31

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CHAPTER 15 GENERAL DESIGN INFORMATION 15.1

Design Information.............................................................................................................................................. 15-2 Design Aid 15.1.1 Dead Weights of Floor, Ceilings, Roofs, and Walls............................................................ 15-2 Design Aid 15.1.2 Recommended Minimum Uniformly Distributed and Concentrated Live Loads............... 15-3 Design Aid 15.1.3 Beam Design Equations and Diagrams............................................................................... 15-5 Design Aid 15.1.4 Camber (Deflection) and Rotation Coefficients for Prestress Force and Loads............... 15-23 Design Aid 15.1.5 Moments in Beams with Fixed Ends................................................................................. 15-25 Design Aid 15.1.6 Torsion Diagrams, Reactions, and Rotations.................................................................... 15-26 Design Aid 15.1.7 Moving Load Placement for Maximum Moment and Shear............................................. 15-27 Design Aid 15.1.8 Moments, Shears, and Deflections in Beams with Overhangs.......................................... 15-28

15.2

Material Properties – Concrete........................................................................................................................... 15-29 Design Aid 15.2.1 Concrete Modulus of Elasticity as Affected by Concrete Density and Strength............... 15-29

15.3

Material Properties – Prestressing Steel............................................................................................................. 15-30 Design Aid 15.3.1 Properties and Design Strengths of Prestressing Strand and Wire.................................... 15-30 Design Aid 15.3.2 Properties and Design Strengths of Prestressing Bars....................................................... 15-31 Design Aid 15.3.3 Typical Design Stress-Strain Curve, 7-Wire Low-Relaxation Prestressing Strand.......... 15-32 Design Aid 15.3.4 Transfer and Development Lengths for 7-Wire Uncoated Strand..................................... 15-33

15.4

Material Properties – Reinforcing Bars.............................................................................................................. 15-34 Design Aid 15.4.1 Reinforcing Bar Data......................................................................................................... 15-34 Design Aid 15.4.2 Typical Bar Bends............................................................................................................. 15-35 Design Aid 15.4.3 Location of Reinforcement Confined by Stirrups or Ties................................................. 15-38 Design Aid 15.4.4 Required Development Lengths,a in., for Reinforcing Bars (Grade 60)............................ 15-39 Design Aid 15.4.5 Bar Area Equivalents in a 1-Foot-Wide Section............................................................... 15-41

15.5

Material Properties – Structural Welded-Wire Reinforcement (WWR)............................................................ 15-42 Design Aid 15.5.1 Nomenclature for Structural Welded-Wire Reinforcement............................................... 15-42 Design Aid 15.5.2 Minimum Requirements of Steel Wires in Welded-Wire Reinforcement......................... 15-42 Design Aid 15.5.3 Wires Used in Structural Welded-Wire Reinforcement................................................... 15-43 Design Aid 15.5.4 Common Styles of Welded-Wire Shear Reinforcement (ASTM A185 Plain WWR) Used in Double-Tee Stems................................................................................................................................. 15-44

15.6

Standard Bolts, Nuts, and Washers.................................................................................................................... 15-45 Design Aid 15.6.1 Dimensions of Nuts and Bolts........................................................................................... 15-45 Design Aid 15.6.2 Dimensions of Standard Washers...................................................................................... 15-47

15.7

Welding Information.......................................................................................................................................... 15-48 Design Aid 15.7.1 Weld Symbols Commonly Used in Precast Concrete Construction.................................. 15-48 Design Aid 15.7.2 Typical Welded Joints in Precast Concrete Construction.................................................. 15-49 Design Aid 15.7.3 Properties of Weld Groups Treated as Lines (tw = 1)........................................................ 15-51

15.8

Section Properties............................................................................................................................................... 15-52 15.8.1 Properties of Geometric Sections...................................................................................... 15-52 15.8.2 Plastic Section Moduli and Shape Factors......................................................................... 15-57

15.9

Metric Conversion.............................................................................................................................................. 15-58 15.9.1 Metric Calculations and Example...................................................................................... 15-58 15.9.2 Conversion from U.S. Customary Units to International System (SI).............................. 15-59 15.9.3 Preferred SI Units and U.S. Customary Equivalents......................................................... 15-61 15.9.4 Concrete Stress Coefficients.............................................................................................. 15-61

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CHAPTER 1 PRECAST AND PRESTRESSED CONCRETE: APPLICATIONS 1.1

General........................................................................................................................................................................1-2 1.1.1 History of Precast, Prestressed Concrete in North America.........................................................................1-2 1.1.2 Features and General Principles....................................................................................................................1-4 1.1.3 Sustainability and LEED Considerations......................................................................................................1-4 1.1.4 Common Products.........................................................................................................................................1-5

1.2

Applications.................................................................................................................................................................1-8 1.2.1 Building Structures.......................................................................................................................................1-8 1.2.1.1 Total-Precast-Concrete Systems..................................................................................................1-8 1.2.1.2 Precast Concrete Cladding..........................................................................................................1-9 1.2.1.3 Residential Buildings.................................................................................................................1-12 1.2.1.4 Justice Facilities.........................................................................................................................1-13 1.2.1.5 Office Buildings........................................................................................................................1-13 1.2.1.6 Warehouses and Industrial Buildings........................................................................................1-14 1.2.1.7 Educational Facilities................................................................................................................1-15 1.2.1.8 Other Building Structures..........................................................................................................1-17 1.2.2 Parking Structures.......................................................................................................................................1-17 1.2.3 Stadiums/Arenas.........................................................................................................................................1-19 1.2.4 Bridges........................................................................................................................................................1-20 1.2.5 Other Structures and Applications..............................................................................................................1-23

1.3

Production Process....................................................................................................................................................1-23 1.3.1 Structural Components versus Architectural Components.........................................................................1-24 1.3.2 Long-Line, Multi-Piece Forms versus Single-Piece Forms........................................................................1-24 1.3.3 Prestressed Components versus Non-Prestressed Components..................................................................1-24 1.3.4 Pretensioned Components versus Post-Tensioned Components................................................................1-25 1.3.5 Production Limitations................................................................................................................................1-26

1.4

References.................................................................................................................................................................1-27

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1.1

General

1.1.1

 istory of Precast, Prestressed H Concrete in North America

The growth of precast and prestressed concrete is a story of the vision and daring of a few notable people. These people took a new idea and maximized its potential by modifying and improving existing methods, conceiving new methods, and inventing new devices, all with a focus on mass production. An excellent portrayal of the beginnings and the growth of precast and pre­stressed concrete in North America and the early pioneers is given in a series of papers1 that were developed to commemorate the 25-year silver jubilee of the founding of the Prestressed Concrete Institute. A similar publication2 was developed at the 50-year golden anniversary of the Institute, which is now known as the Precast/Prestressed Concrete Institute (PCI). The most important event leading to the launching of the precast/prestressed concrete indus­try in North America was the construction in 1950 of the famed Walnut Lane Memorial Bridge in Philadelphia, Pa. (Fig. 1.1.1). From techni­cal and historical perspectives, it is both surprising and fascinating that the Walnut Lane Memorial Bridge was constructed of prestressed con­crete. There was very little published information on the subject and there was a total lack of experience with linear prestressing in this country at that time. Furthermore, the length of the bridge span (the main span of the structure was 160 ft long) involved would have been a daring venture in the late 1940s anywhere in the world. The bridge became a reality through a fortunate sequence of events and the vision, courage,

and persistence of a few extra­ordinary individuals. Following completion of the Walnut Lane Memorial Bridge, American engineers and the construction industry enthusiastically embraced prestressed concrete. While many of the early applications remained in bridge construction, such as the lower Tampa Bay crossing now known as the Sunshine Skyway, American engineers and contractors were simultaneously conceiving new devices, improv­ing techniques, and developing new materials for all types of structures. The 1950s were the years that brought into focus the sevenwire strand, long-line beds (Fig. 1.1.2), admixtures, highstrength concrete, vacuum concrete, steam curing, and many other innovations. With these developments, coupled with the technical and logistical support provided by PCI (chartered in 1954), the industry grew, and the applications of precast and prestressed concrete began to appear in an impressive variety of structures. See chapter 9 for information related to materials used in the precast, prestressed concrete industry. Development of standard products was one of the major activities through the 1950s and the 1960s. Early in the 1960s, the federal government–spon­sored program Operation Breakthrough led to the intro­duction of different high-rise, precast concrete building types for housing. As part of this program, a significant testing program was conducted by the Portland Cement Association to establish design principles to prevent progressive failure and to ensure the safety of highrise precast buildings. These rules were adopted into the ACI 318 building code as early as 1963 and have been expanded upon since. The basis for this handbook is ACI 318-05.3 In the late 1970s, low-relaxation strand was introduced, which reduced the loss of prestress force due to relaxation in

Fig. 1.1.2 Long-line, prestressed, double-tee casting bed is one key to both economy and quality.

Fig. 1.1.1 The Walnut Lane Memorial Bridge was the recipient of the 1978 American Society of Civil Engineer’s Out­standing Civil Engineering Achievement Award.

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PRECAST AND PRESTRESSED CONCRETE: APPLICATIONS the strand, thus allowing more efficient use of prestressing and resulting in longer spans and smaller sections. Larger strand sizes have been made available as well, such as 0.6-in.-diam­ eter strand. In the field of bridges, there was the develop­ment of spliced girders, segmental bridges (Fig. 1.1.3), cable-stayed bridges (Fig. 1.1.4), and cantilevered girder bridges.

CHAPTER 1 During the 1980s, both engineers and owners recognized that durability is an important aspect of a structure. The precast and prestressed concrete industry re­sponded by taking advantage of one of its natural strengths. Plant-cast concrete is more durable than site-cast concrete because it can be cast with lower water–cementitious materials ratios and under controlled conditions. This natural durability was enhanced

Fig. 1.1.3 Precast concrete segmental construction takes advantage of all of the benefits of precast concrete and special erection techniques to create significant bridges for the United States' highway system.

Fig. 1.1.4 Precast concrete proved to be a key element in completing the Arthur Ravenel Jr. (Cooper River) Bridge in Charleston, S.C., in a cost-effective manner. It is the longest cablestayed bridge in North America. Photograph by Rob Thompson/SCDOT.

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CHAPTER 1 with the development of admixtures that make the concrete matrix more impermeable, which inhibits steel corrosion. Pretopped double-tees were developed for parking structures to maximize the benefits of the durability of precast, prestressed concrete at the wearing surface. The past few decades have seen the development of more efficient structural sections and more complex architectural shapes and surface treatments. The increasing demands of owners and architects for quality finishes has led to the development of new surface textures and surface treatments. Thin-set brick and stone-faced panels, as well as textures and colors of infinite variety, have been developed. Emerging material technologies using ultra-high-strength concrete, selfconsolidating concrete, polymers, carbon fibers, and highstrength steels continue to improve the capabilities of the industry. With the consolidation of the model building codes and the incorporation of the National Earthquake Hazard Reduction Program (NEHRP) provisions into the International Building Code and the ASCE 7 load standard, design of precast concrete structures for earthquake loading has become a new priority in much of the United States. PCI and its producer members have met this challenge with a sustained program of seismic research and the development of seismic systems and connections that recognize the unique characteristics of precast construction. 1.1.2

• • • 1–4

•

• • • • • •

Speed of construction resulting from the ability to begin casting components for the superstructure while foundation work is in progress, and being able to erect the superstructure year round without delays caused by harsh weather or additional curing requirements. Design flexibility from the long-span capabilities result in larger open areas in buildings and fewer piers in bridges. Fire resistance, which provides improved safety and reduced insurance premiums. Durability, which allows the material to have a long service life, in some cases more than 100 years, and

reduced life cycle costs. With prestressing, components have greater span-to-depth ratios, enhanced performance, and less material usage. Aesthetic flexibility, achieved by the variety of textures, colors, finishes, and inset options that are available and can mimic granite, limestone, brick, and other materials in virtually any shape and configuration. Acoustical control, which results in pleasant work and living conditions for inhabitants and users. Thermal and energy efficiency, due to the material’s high thermal mass, which can be enhanced further with the use of insulated sandwich panels. Sustainability by efficiently using materials and energy resources to minimize their depletion. Improved quality control resulting from being manufactured under plant-controlled conditions. Modular construction and design capabilities lending well to future reuse of systems for a variety of functions. Ability to design redundancy into the building systems to provide blast resistance and structural integrity.

To fully realize these benefits and gain the most economical and effective use of the material, the following general principles are offered: •

Features and General Principles

Precasting concrete in PCI-Certified Plants ensures the manufacture of high-quality architectural and structural products. Precasting also facilitates pro­duction of a wide variety of shapes and sizes, and the use of prestressing substantially extends the span capability of the products. Similarly, prestress­ing, defined by ACI 318-05 as “concrete in which internal stresses have been introduced to reduce potential tensile stresses in concrete resulting from loads,” can be used to enhance the structural capabilities of a con­crete component. These capabilities enable archi­tects and engineers to achieve highly innovative and eco­nomically competitive buildings and other structures. This handbook serves as the primary reference for the design and use of precast and prestressed concrete structures. This chapter enumerates some of the important and unique features and benefits of precast and pre­stressed concrete. These include the following: •

•

• • • • • • •

Precast concrete is basically a simple-span material. However, continuity can be, and often is, effectively achieved with properly engineered connection details with and without the use of field-cast concrete. Sizes and shapes of components should consider production, hauling, and erection techniques. Concrete is a massive material. This is an advantage for such matters as stability under wind and seismic loads, thermal changes, vibra­tion, and fire resistance. Maximum economy is achieved with maximum repetition. Standard or repetitive sections should be used whenever possible. The most efficient and economical use is largely dependent on an effective structural layout and carefully con­ceived connection details. The effects of volume changes caused by creep, shrinkage, and temperature change and the potential restraint of these effects must be considered in every structure. Architectural precast concrete panels can be used as cladding as well as load-bearing components. They can be used to support both gravity and lateral loads. Prestressing improves the economy and per­formance of precast concrete components, but is usually only economically feasible with standard shapes that are capable of being cast in long-line beds.

1.1.3

Sustainability and LEED Considerations

Precast concrete components can contribute to sustainable designs and in meeting standardized requirements for environment-friendly designs. Sustainability and other terms such as “environmental friendliness” and “green buildings” have become watchwords for owners and architects when

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PRECAST AND PRESTRESSED CONCRETE: APPLICATIONS designing new buildings to attain several of the rating criteria incorporated into the Leadership in Energy and Environmental Design (LEED) standards4 from the U.S. Green Building Council (USGBC). In general, sustainability is considered to mean “development that meets present needs without compromising the ability to meet the needs of future generations.”5 This can be interpreted many ways, but in general most would agree that this translates to reducing the amount of virgin raw materials used and that buildings and components are durable, have long life cycles and are environmentally sensitive. Today’s approach to sustainable design extends beyond the ability to use renewable or recycleable resources to examine all environmental flows (materials and energy requirements) for the entire life cycle of a component or building. This environmental accounting practice (known as life-cycle assessment or LCA) encompasses all the energy and materials necessary to manufacture, deliver, install, and use the product, including fuel to extract materials, finish them, and transport them to the site, for its entire life cycle (cradle to grave). Precast concrete’s inherent durability contributes greatly to its sustainable attributes. For more information, on precast concrete’s contributions to the LEED systems, consult "Sustainability" in PCI's Designer’s Notebook Series.6 1.1.4

CHAPTER 1

Fig. 1.1.5 Prestressed double-tee being stripped from a longline casting bed.

Common Products

While precast and prestressed concrete components can be manufactured in a variety of customized sizes and shapes, maximum economy is achieved by using the common products that have evolved in the industry. Among the more prevalent of these pro­ducts are double-tees (Fig. 1.1.5) and hollow-core slabs (Fig. 1.1.6). Double-tees are efficient for spans in the range of 40 ft to 80 ft using depths of 24 in. to 34 in., respectively, although longer spans are possible with deeper sections. Hollow-core slabs are available in a variety of widths ranging from 16 in. to 12 ft, and are used for spans up to about 40 ft. Figure 1.1.7 shows these and other commonly used products. The I-beam, box beam, and bulb-tee are used in bridge construction. The inverted-tee and ledger beam are used for structural framing to support deck components. Square or rectangular columns, with or without corbels, are an integral part of the precast concrete column-beam-deck framing that makes rapid, all-weather erection possible. Precast concrete piles are manu­factured in a variety of shapes, including round, square, hexagonal, and octagonal, as well as rectangular sheet piles. Channel slabs are used to support

Fig. 1.1.6 Erection of hollow-core deck components provides an instant floor and avoids costly formwork.

heavy floor or roof loads in short and medium span ranges. Stadium riser units (Fig. 1.1.8) and raker beams (Fig. 1.1.9) have gained prominence during the past two decades in stadium/arena construction. These risers are typically cast as single, double, or triple step units and offer spans up to 60 ft, depend­ing on their depth. Precast concrete modular products have also established a strong presence in the construction industry, most noticeably as cell units for correctional facilities (Fig. 1.1.10). Single-, double-, and quad-cell modules

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b

c

d

f

e

g

h

i

Fig. 1.1.7 Beams: a. flat slab; b. hollow-core; c. spandrel; d. ledger beam; e. double-tees; f. inverted-tee; g. bulb-tee; h. AASHTO girder; i. box beam.

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Fig. 1.1.8 The owners of this sports stadium chose a totalprecast-concrete solution after evaluating other systems.

can be manu­factured, finished, and furnished at a precaster’s facility, significantly reducing on-site labor and schedule demands. Additionally, precast concrete pavements have been introduced as a material for rapid construction in transportation systems (Fig. 1.1.11). Quality precast and prestressed products are assured when products are designed in accordance with the latest engineering standards and produced in plants where PCI’s Plant Certification Program is an integral part of plant production. The program assures specifi­ers of a manufacturing plant’s audited capability to produce quality products. A minimum of two unan­nounced plant inspections are performed each year by specially trained engineers of PCI’s independent quality auditing agency to evaluate and grade compli­ance with current performance standards. These perfor­mance standards can be found in PCI quality-control manuals Manual for Quality Control for Plants and Production of Structural Precast Concrete Products (MNL-116-1999)7 and Manual for Quality Control for Plants and Production of Architectural Precast Concrete Products (MNL-117-1996).8 These manuals are considered industry standards for quality assurance and control. A plant that does not achieve a minimum required quality audit score loses certification. Plant certification is a prerequisite for PCI producer membership. Plants in Canada subscribe to a similar plant certification program based on the Cana­dian Standards Association (CSA) A251 Stan­dard. For more information on the PCI Plant Certifi­cation Program, see Section 14.4. The high-quality standard products noted previously form the basis for configuring a wide variety of systems for buildings, bridges, parking structures, and other struc­tures. The following pages provide an overview of some of the applications. For other applications and also for products and practices suitable in different geographical zones, contact with the regional producers is highly recommended. A list of PCI producer mem­bers as well as other information pertinent to the industry can be obtained by contacting PCI or accessing the PCI website at www.pci.org. Design of precast and prestressed concrete products and structures for the building industry is usually based on ACI 318-05.

CHAPTER 1

Fig. 1.1.9 Precast concrete risers, raker beams, columns, and mezzanine floors play a prominent role in speeding stadium construction.

Fig. 1.1.10 The repetitive nature of cell layout and the typical quick occupancy requirements make precast concrete an ideal solution to prison overcrowding.

Fig. 1.1.11 Precast, prestressed concrete is used here as a runway pavement at a large airport.

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the latest research results, and new exper­ience. The long-term objective is to augment ACI 318-05 building code with proven industry prac­tices to develop the best designs that take advantage of the many special features of precast and prestressed concrete. Design of precast and prestressed concrete products and structures for the transportation sector is usually based on the AASHTO LRFD Bridge Design Specifications.9 While these specifications encompass the entire range of substructure and superstructure types, PCI publishes the Bridge Design Manual10 for guidance with examples specific to precast, prestressed concrete systems.

1.2

Applications

The developments in products, materials, and techniques noted in the previous section have made precast/prestressed concrete competitive in a variety of residential, commercial, institutional, industrial, transportation, and other types of structures. A few examples of applications for different types of structures are given in this section. 1.2.1

Fig. 1.2.1 Using precast concrete beams and columns with precast concrete floor slabs quickly provides an economical structure. The addition of an architectural precast concrete facade provides the owner with the cost and schedule advantages of a single source of responsibility for the structure.

Building Structures

Owners, developers, and designers recognize the many inherent qualities of precast and prestressed concrete that make it suitable for many types of building structures. Precast and prestressed concrete building structures, assembled from high-quality, plant-produced products, provide superior flexibility for achieving the required degrees of fire resistance, sound control, energy efficiency, sustainability, and durability. The availability of various materials and finishes makes it possible to render almost any desired aesthetic character. The speed of construction that is possible with precast and prestressed concrete minimizes on-site labor costs and reduces the cost of interim financing, providing important overall economy to the owner and developer. 1.2.1.1 Total-Precast-Concrete Systems

Fig. 1.2.2 Architectural precast concrete panels were used as load-bearing elements for this city municipal center.

Section 1.4 of ACI 318-05 specifically allows variances when analysis, research, or testing demonstrates structural adequacy. PCI publishes "PCI Standard Design Practice," included in Section 14.1 of this handbook, that identifies many of the variations commonly encountered in precast/prestressed concrete construction. This is regularly updated to reflect code changes, 1–8

Total-precast-concrete solutions have been provided by the precast concrete industry for many years. The ability for a building’s structural solution to be completely prefabricated and erected by a single-source precast concrete manufacturer continues to be of more and more value to the owner, the contractor, and the design team in today’s fast-paced environment. Support systems can be typical beam and column framing with double-tee decks (Fig. 1.2.1), precast concrete loadbearing walls, load-bearing architectural precast concrete exterior panels (Fig. 1.2.2), special framing systems, and any combination of these vertical load-bearing components. Floor slabs and roof slabs for total-precast-concrete buildings are typically either double-tees or hollow-core slabs. The single source of responsibility makes project management and construction of these buildings much easier and eliminates the cost and schedule risk created by having many different material suppliers all working on the site at one time. While site work is being performed and foundations are being built, the precast concrete engineering, drawing coordination, and production are simultaneously taking place so that, when the

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Fig. 1.2.3 This total-precast-concrete office building is an example of the beauty and economy that can result when precast con­crete is used. Real savings can be achieved by designing the architectural facade to also perform structurally.

site is ready, the total structure can be erected without interruption. The ability to overlap many of the critical path items makes total-precast-concrete systems one the fastest building systems available. Figures 1.2.3 and 1.2.7 illustrate another example of total-precast-concrete systems. 1.2.1.2 Precast Concrete Cladding Architectural precast concrete cladding, illustrated in several figures in this chapter (Fig. 1.2.4 through 1.2.6), provides significant flexibility for architectural expression with the economy of mass production of precast concrete components. The cladding may serve only as an enclosure for the structure or may be designed to support gravity loads. Cladding may also be designed to contribute to the resistance of lateral loads.11 Architectural precast concrete can be cast in almost any color, form, or texture to meet aesthetic and functional requirements (Fig. 1.2.8 through 1.2.11). Special sculptured effects can provide such visual expressions as strength and massiveness or grace and openness (Fig. 1.2.12). Aesthetic versatility is possible in both color and texture by varying aggregate and matrix color, size of aggre­gates, finishing processes, and depth of aggregate exposure. Architectural precast concrete can also be designed to match existing systems, benefiting historical renovation and expansion projects. PCI has developed a guide to assist designers in selecting colors and textures for architectural precast concrete.12 Additional flexibility of aesthetic expression is achieved by casting various other materials, such as veneers on the face of precast

Fig. 1.2.4 Architectural precast concrete provides a striking facade for the landmark Transamerica Pyramid in San Francisco, Calif.

Fig. 1.2.5 The moldability of architectural precast concrete allows for an infi­nite number of sizes and shapes.

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Fig. 1.2.6 A precast concrete facade provides pleasant aesthetic features.

Fig. 1.2.7 The total-precast-concrete Paramount Building in San Francisco, Calif. is 39 stories tall. At the time of its construction, it was the tallest precast, prestressed concrete framed building in a highseismic region.

Fig. 1.2.8 Repetition of size and shape, which allows multiple use of high-quality formwork, is a key to economy.

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CHAPTER 1 Fig. 1.2.9 (left) Office buildings often utilize precast concrete spandrels to provide both aesthetic and load-bearing capability.

Fig. 1.2.10 Libraries can be constructed using precast concrete to achieve an open and quiet environment.

Fig. 1.2.11 By varying minor details like rustication, architectural precast con­crete exteriors can be made both expressive and economical.

Fig. 1.2.12 Prestressed concrete provides free open space for a multitude of applications.

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Fig. 1.2.14 Precast concrete provides a quieter, safer, and more comfortable and upscale place to live.

Fig. 1.2.13 Precast concrete offers an attractive, long-lasting and safe alternative for residential housing. Thin brick are inset in panels during production.

concrete panels. Natural stone, such as polished and thermalfinished granite, limestone, marble, and clay products, such as brick, tile, and terra-cotta, have been frequently used as veneer materials.13 In addition to the freedom of aesthetic expression achievable with load-bearing or non-load-bearing architectural precast concrete, there are a number of other important functional and construc­tion advantages. Insulated wall panels consist of two concrete wythes with a continuous layer of rigid insulation sandwiched between them. These types of panels contribute substantially to the overall thermal efficiency of a building. In cast-in-place concrete construction, precast concrete cladding panels are sometimes used as permanent concrete formwork, thus becoming an integral part of the structure. Off-site preassembly of all components comprising a total wall system, including window sash and glazing, can also be very cost effective. For more comprehensive information about the possibilities available with architectural precast concrete, see Architectural Precast Concrete, MNL-122-07.13 Glass-fiber-reinforced concrete (GFRC) has been adopted for use in producing strong, thin, light–weight architectural cladding panels. GFRC is a portland cement–based composite reinforced with randomly dispersed, alkali-resistant glass fibers. The fibers serve as reinforcement to enhance flexural, tensile, and impact strength of concrete. A major benefit of GFRC is its light weight, which provides for substantial economy resulting from reduced costs of product handling, transportation, and erection, and also results in lower seismic loads. 1.2.1.3 Residential Buildings

Fig. 1.2.15 High-quality concrete in precast concrete walls and prestressed hollow-core floors provide improved sound resistance, enhanced fire safety, and reduced maintenance cost in justice facilities as well as in multifamily housing.

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Precast and prestressed concrete has broad acceptance in low-rise and mid-rise apartment build­ings (Fig. 1.2.13 and 1.2.14), hotels, motels, condominiums, dormatories, retirement housing, and nursing homes. The supe­rior fire resis-

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Fig. 1.2.17 Using quad (four cells in one unit) modules can also minimize production and erection schedules. Fig. 1.2.16 A precast concrete double-cell module is lifted into place, complete with furnishings installed.

tance and sound-control features are specifically recognized by owners and developers. Two-hour fire containment within each living unit provides a high level of safety for adjacent units. With this type of high-quality precast concrete housing, fire insurance rates are reduced and often higher incomes can be generated because of the safer, more soundproof, higher quality environment and lifestyle offered. 1.2.1.4 Justice Facilities Justice facilities encompass many types of building occupancies. These include jails, prisons, police stations, courthouses, juvenile halls, and spe­cial mental health or drugabuse treatment centers (Fig. 1.2.15). Precast concrete has proven to be the favored system for justice facilities because it has many inherent benefits that are important to these building types. In addition to the benefits noted previously, precast and prestressed concrete is ideal for building in the desired level of physical security coupled with efficient accommodation of security hardware and communication systems. The thickness and reinforcement of typical precast concrete wall and slab systems, when designed for gravity and lateral loads, are sufficient even for maximum security requirements. Typical precast concrete products such as load-bearing insulated wall panels, cell walls, and floor slabs are employed frequently in justice facili­ties. Also, the modular nature of precast and pre­stressed concrete products facilitates pre-installation of necessary security and communication hardware in the plant, greatly simplifying field installation work as well as saving valuable time on the project’s critical path. The use of precast concrete box modules in single-, double- (Fig. 1.2.16), and quad-cell (Fig. 1.2.17) configurations has greatly reduced field labor, erection time, overall construction time, punch list problems, multitrade confusion and, ulti­mately, cost and schedule risk. These units can be quickly

Fig. 1.2.18 Box module cells are often supplied with electric conduit and boxes, furniture, window and door embedments, and mechanical and plumbing chases cast in, reducing costly field work.

stacked and can be substantially completed with outfitted materials (bunks, plumbing, desks, and the like) (Fig. 1.2.18) in the precasting plant requiring little finishing work in the field, thereby enhancing the quality and improving the schedule (Fig. 1.2.19). Given the serious shortage of justice facilities, savings in total project time is often a critical consid­eration in selection of a structural material and sys­tem for these projects. Case histories show that total-precast-concrete projects have resulted in saving one to two years of construction time over the esti­mated schedule for competing systems. These experiences and the other considerations discussed have led to rapid growth in the use of precast and prestressed concrete in justice facilities projects. 1.2.1.5 Office Buildings There are many uses of precast and pre­stressed concrete in office-building construction, from total building systems

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Fig. 1.2.19 Interior finishes of precast concrete prisons are low maintenance, fire resistant, and limit vandalism.

to single products like precast concrete stairs. Precast and prestressed concrete beams, columns, and floors are used in framing systems; shear walls can be used alone or in conjunction with beams and columns to resist lateral loads. Precast concrete stairs, along with being economical, provide immediate safe use of stairwells during construction. Architectural precast concrete is used with all types of framing systems. It provides an economical, fire-resistant, soundproof, durable, maintenance-free cladding that allows the architect much freedom of expression and results in beautiful facades. Architectural precast concrete cladding is discussed more fully in Section 1.2.1.2 and in Chapter 7 of this handbook. Also see Reference 13. Significant time savings in both design and production usually result from the choice of a total-precast-concrete structure. The superstructure is prefabricated while the onsite foundations are being built. Details of this type of construction are shown in Fig. 1.2.1. Potential construction delays are reduced with the complete building system being supplied under one contract. Erection of large, precast concrete components can proceed even during adverse weather conditions to quickly 1–14

enclose the structure. Load-bearing, architectural precast concrete panels provide a finished exterior as the superstructure is erected. The prestressed floors provide an immediate working platform that allows the interior workers to get an early start on the mechanical, electrical, and interior finishing work. The quality finishes and fast production and erection schedules result in early occupancy, increased tenant satisfaction, and reduced financing costs, making precast and prestressed concrete buildings very suitable for office buildings. 1.2.1.6 Warehouses and Industrial Buildings The ability of prestressed concrete to span long distances with shallow depths and carry heavy loads is particularly suitable for warehouses and industrial buildings (Fig. 1.2.20 and 1.2.21). Standard prestressed concrete walls, insulated or non-insulated, are very economical for warehouse and light manufacturing applications. Total-precast-concrete systems with prestressed roof diaphragms and precast concrete shear walls can provide owners with a complete structural package. In heavy industrial projects, prestressed floor units capable of carrying the heavy floor loads typical of industrial facili-

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Fig. 1.2.20 This light, industrial office structure is erected and quickly put into service using insulated precast concrete sandwich wall panels.

ties (Fig. 1.2.22) can be combined with other precast concrete compo­nents to construct versatile, low maintainence, and corrosion-resistant structural systems. The precast and prestressed concrete framing can be designed to accommodate a variety of mechanical systems and to support bridge cranes for industrial uses. High-quality precast concrete provides improved protection against fire, dampness, and resistance to a variety of chemical substances. The smooth surfaces achievable in precast concrete make it ideal for food processing, wet operations, computer-component manufacturing, and many other types of manufacturing and storage operations where cleanliness is a critical concern. Clear spans of 40 ft and 80 ft are possible using hollow-core and double-tees, respectively. Even longer spans to about 150 ft can be obtained with bridge-type girders or special double-tees. 1.2.1.7 Educational Facilities Both students and taxpayers benefit immensely when educational facilities are built using precast/prestressed concrete systems. The natural and inherent benefits of the material are realized as well as many that are unique and of special value to educational facilities (Fig. 1.2.23 through 1.2.25). While fire safety is important in all educational facilities, it is particularly important in elementary schools and middle schools where younger children are present. Precast concrete floors and walls do not burn, and, therefore, do not add fuel to a fire, providing overall improved fire safety. School structures can also be compartmentalized, easily containing a fire to a limited area. Precast concrete contributes significantly to energy conservation and sustainability. Insulated sandwich wall panels provide better overall thermal resistance or a higher R-value for a wall assembly than other materials. The massive nature of precast concrete structures provides a thermal lag that

Fig. 1.2.21 Precast and prestressed concrete flat panels are used to quickly provide warehouse walls. Hollow-core slabs may also be used in this application.

Fig. 1.2.22 Total-precast-concrete structures provide many answers for heavy industrial applications. High-quality, plant-produced concrete pro­vides excellent corrosion resistance and durability. Heavy loads can be easily handled by prestressed concrete beams and slabs.

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Fig. 1.2.23 Total-precast-concrete school construction offers early use, safety, and attractive aesthetics.

Fig. 1.2.24 A variety of architectural finishes provide for a unique school exterior.

Fig. 1.2.25 Use of insulated sandwich panels provides a complete wall system ready for finishing.

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reduces overall heating and cooling expenses and provides a high comfort level for the occupants. Most education facilities need to be completed on a fast track schedule to satisfy opening day. Precast concrete is a perfect material for these tight schedules, since many of the critical path items can be overlapped. Building superstructure components are all cast off-site while upfront coordination, site preparation, and foundations are completed at the same time. Several educational facilities have been confronted with mold that has been deemed dangerous to the occupants, and remedial cleanup procedures have resulted in these facilities being closed for an entire school year. Precast concrete provides water tight, quality vapor barriers and eliminates the water and moisture that contribute to the growth of mold. Precast concrete insulated wall panels, architectural precast concrete exterior walls, and precast concrete floor slabs are also free of the organic material that is required for mold to grow. The density that precast concrete floors and walls inherently have also provides improved acoustical qualities that provides students with a quiet environment that promotes learning.

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Fig. 1.2.26 Erection of precast concrete wall panels is fast and can be per­formed year-round, even in cold climates. Roof diaphragms and supporting beams and columns of precast concrete provide economical building solutions.

1.2.1.8 Other Building Structures The many benefits of precast and prestressed concrete make it suitable for many other types of buildings in addition to residential, justice facilities, office buildings, indus­trial buildings, and educational facilities. Applications abound in commercial buildings such as shopping malls, and public buildings, including hospitals, librar­ies, museums (Fig. 1.2.26) and airport terminals. Precast and prestressed concrete has also been effectively used in numer­ous retrofit projects. 1.2.2

Parking Structures

Architects, engineers, developers, and owners have made precast and prestressed concrete the material of choice for their commercial, municipal, and institutional parking needs. Though classified and constructed as buildings, parking structures are unique; in some ways, they may be compared with bridges with multiple decks. They are subjected to moving loads from automobile traffic, and the roof level of a parking structure is exposed to weather in much the same way as a bridge deck. In addition, they are usually open-air structures and, thus, the entire structure is subjected to ambient weather conditions. Also, exposure to deicing salts in northern climates or to salt-laden atmospheres in coastal regions requires special consideration of durability to ensure long-term performance. The controlled conditions in a precast concrete plant assures the parking-structure owner of both the qual­ity concrete and workmanship that provides long-term durability. The low water–cementitious materials ratio concrete that precast concrete manufacturers use has been proven to increase resistance to deterioration as compared with other materials. Studies14 have also shown that accelerated curing makes precast concrete more resistant to chloride penetration than

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Fig. 1.2.27 Spandrel panels spanning from column to column can be load-bearing or solely architectural. False columns can be added at midspan to modify the visual impact.

field-cured concrete. These inherent, enhanced durability characteristics, along with low-cost, rapid erection in all weather condi­tions, unlimited opportunities for architectural expression, and long clear spans make precast concrete the natural choice for parking structures. Through surveys of existing structures and other experiences, and through PCI-funded and private research and development, significant improvements have been achieved in engineering state-of-the-art parking structures. This accumulated experience and knowledge has been assembled in a comprehensive publication, Precast, Prestressed Parking Structures: Recommended Practice for Design and Con­struc­tion,15 that includes recommendations on planning, design, construction, and maintenance.

Fig. 1.2.28 Stair towers acting as shear walls resist lateral loads and, at the same time, provide architectural features.

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Fig. 1.2.30 Openings in load-bearing walls provide the security of visibility and openness as well as carrying vertical and lateral loads.

Fig. 1.2.29 Long, clear spans make precast, prestressed concrete an economical and aesthetically preferable parking structure solution.

Fig. 1.2.31 Details of a load-bearing, column-beam, doubletee floor building. Spandrels can be load-bearing to improve economy.

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Fig. 1.2.32 An interior L-beam is deep enough to also act as the car stop.

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Fig. 1.2.33 Special erection equipment is available for adding floors to existing parking structures.

Figures 1.2.27 and 1.2.28 show typical precast concrete parking structures. Long-span double-tees are shown in Fig. 1.2.29, and Fig. 1.2.30 shows double-tees bearing on an innovative litewall that adds openness and enhances both the perceived and actual security. Figure 1.2.31 shows a precast, prestressed spandrel beam being erected into pockets of a precast concrete column. This same figure also shows a double-tee bearing on an interior, inverted-tee beam spanning from column to column. Interior spandrel beams can also serve as bumpers for automobile traffic (Fig. 1.2.32). Vertical expansion of precast concrete parking structures can be accomplished with special erection methods that allow for erection of new components over erected decks (Fig. 1.2.33). This erection method also allows precast concrete to be consid­ ered for expansion of non-precast concrete struc­tures. 1.2.3

Long-spans and the ability to eliminate costly field formwork makes precast, prestressed concrete the best choice for many components of stadium construction, especially for seating that can be standardized to take advantage of repeated form utilization. Construction of components that would require tall scaffolding towers to field-form, such as

Stadiums/Arenas

Large stadiums and arenas (Fig. 1.2.34 and 1.2.35) are complex structures that can benefit significantly from the applications of precasting technology. Often these projects are built on tight schedules to accommodate a specific sporting event. Because of both the construction-period advantages and the long-term, low-maintenance characteristics, precast and pre­ stressed concrete has been the overwhelming choice for many of these projects. For the same reasons, precast/prestressed concrete systems are also beneficial for smaller facilities such as high schools and small arenas (Fig. 1.2.36). Mass-produced seating units have been manu­factured in a variety of configurations and spans to provide for quick installation and long-lasting service. Local producers can provide the best advice regarding readily available riser sections.

Fig. 1.2.34 Repetition, simplicity, and multiple form use allow the columns, raker breams, and riser units to be framed economically with total precast concrete.

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Fig. 1.2.35 Special framing is handled easily with precast concrete, eliminating expensive field formwork.

Fig. 1.2.36 Smaller grandstands and huge stadiums all benefit from the use of precast and prestressed concrete.

raker beams and ring beams, can be simplified by precasting these units in a plant, delivering them to the site, and lifting them into place (Fig. 1.1.8 and 1.1.9). Pedestrian ramps, mezzanine floors, concession, toilet, and dressing-room areas can all be efficiently framed and quickly constructed using precast, prestressed concrete components. The technique of post-tensioning precast concrete segments together has made complex cantilever arm and ring beam construction possible, which can efficiently support the roofs of these structures. Post-tensioning can be employed to minimize the depth of precast concrete cantilevered raker beams, which carry the seating and provide unhindered viewing of the playing surface. 1.2.4

Bridges

Bridge construction gave the prestressing industry its start in North America. Precast and pre­stressed concrete is now the dominant structural material for short- to medium-span bridges. With its inherent durability, low maintenance, per1–20

Fig. 1.2.37 Low maintenance, long-term performance, economy, and the ability to span long distances make precast and prestressed concrete the pre­ferred system for bridges of all spans.

formance, and assured quality, precast and prestressed concrete is a natural product for bridge construction. The ability to quickly erect precast concrete components in all types of weather with little disruption of traffic adds to the economy of the project. For short spans (spans to 100 ft), use of box sections and double-tee sections have proven economical. However, the most common product used for short- to medium-spans is the I-girder. Spans to 150 or 160 ft are not uncommon with I-girders and bulb-tees. Spliced girders allow spans as much as 300 ft.16 Even longer spans (300 ft and up) can be achieved using precast concrete box girder segments, which are then post-tensioned together in the field. Using cable stays, the spanning capability of precast and prestressed concrete has been increased to over 1000 ft. An important innovation in bridge construction has been the use of precast concrete in horizontally curved bridges. A study17 commissioned by PCI documents the technical feasibility and the economic viability of this application. Another application of precast and prestressed concrete in bridge construction is the use of precast concrete deck panels.18 Used as stay-in-place forms, the panels reduce field placement of reinforcing steel and concrete, resulting in consider­able savings in both cost and schedule. The panels become composite with the field-placed concrete for live loads. Through PCI’s commitment to provide quality bridges for the transportation infrastructure, the Bridge Design Manual was published to provide guidance to engineers and owners on the design of precast concrete bridges. Precast concrete not only is the choice material for highway bridges, but also finds tremendous use in railway bridges. Figures 1.2.37 through 1.2.42 show some of these applications that have been discussed.

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Fig. 1.2.38 This bridge uses readily available American Association of State Highway and Transportation Officials girders to span from precast concrete pile cap to pile cap, eliminating expensive over-water formwork. Precast and prestressed concrete piling, as well as deck panels, add speed to the project as well as proven durability in a harsh marine environment.

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Fig. 1.2.39 Standard shapes from the American Association of State Highway and Transportation Officials offer immediate availability, economy, durability, and low maintenance over an extended service life.

Fig. 1.2.41 The use of large, hollow edge beams with solid floor slabs and field post-tensioning provided a 110-ft span to meet a 14-in. structure-depth constraint using this throughgirder solution.

Fig. 1.2.40 Standardization allows optimized bridge designs that provide unmatched economy.

Fig. 1.2.42 Precasting this arched culvert and its footings and wing walls allowed quick erection with little site disruption and no field formwork.

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Fig. 1.2.45 These identical water tanks benefit from the durability, economy, and aesthetic capability of precast concrete.

Fig. 1.2.43 Precast and prestressed concrete utility poles provide low maintenance, durable, economical poles capable of carrying heavy line loads.

Fig. 1.2.44 Precast and prestressed concrete has proven to be a viable alter­native to timber for railroad ties.

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Fig. 1.2.46 This large, circular storage tank is under construction. Vertically prestressed, precast concrete wall segments are braced tempo­rarily. Cast-in-place concrete joints and circumferential post-tensioning complete this durable, longlasting structure.

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Fig. 1.2.47 This light-rail system in Monterrey, Nuevo Leon, Mexico, features U-shaped precast concrete girders that allow two rail tracks to be placed between the structure's sides.

1.2.5

Other Structures and Applications

The inherent qualities of precast and prestressed concrete noted in previous sections and the high degree of design flexibility also make it ideal for a wide variety of special applications. Properties such as corrosion resistance, fire resistance, durability, and fast installation have been used to good advantage in the construction of poles (Fig. 1.2.43), piles, railroad ties (Fig. 1.2.44), storage tanks (Fig. 1.2.45 and 1.2.46), monorails (Fig. 1.2.47), retaining walls, highway and runway pavements, and sound barriers (Fig. 1.2.48).19–25 Where repetition and standardization opportunities exist, precasting components can economically provide the quality of plant-manufactured products while eliminating expensive and risky field procedures. Precast, prestressed concrete can also be used efficiently in customized applications, blending function and form to suit any context-sensitive environment. These applications are too numerous to categorize here separately but examples are illustrated in the figures in this chapter.

1.3

Production Process

The methods used to produce precast concrete components vary with the type of component being manufactured. Among the factors influencing the production process are: • Structural components versus architectural components

Fig. 1.2.48 Precast concrete soundwalls provide outstanding aesthetics and protects resi­dential neighborhoods from highway noise.

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Long-line, multipiece forms versus single-piece forms Prestressed components versus non-prestressed components Pretensioned components versus post-tensioned components Production facility limitations

Discussions with regional precasters during project development will allow these factors to be considered in the design of the precast concrete components and structures. See Fig. 1.3.1 through 1.3.5 for various aspects of production. 1.3.1

 tructural Components versus S Architectural Components

Structural precast concrete components are traditionally produced in a process aimed toward high vol­ume and high efficiency. Emphasis is placed on using standard shapes so that forms can be reused multiple times. These forms are usually long steel forms designed to produce a number of components with each casting. Products commonly considered to be structural components include double-tees, bridge girders, interior beams, hollow-core units, and interior walls. Precast concrete producers certified by PCI as structural or commercial fabricators must comply with the requirements of PCI 's MNL-116-99. The flexibility of architectural precast concrete allows designers to incorporate a wide array of shapes, col­ors, and textures into a project’s appear­ance. This demands that the precast producer be capable of constructing complex forms, using a var­iety of concrete mixtures and offering an assortment of surface treatments such as sandblasting, acid etching, or veneers of brick, stone, or other decorative material. Architectural precast concrete components are fab­ricated under the guidelines of PCI's MNL-117-96. Components manufactured in accordance with these guidelines must satisfy stringent dimensional tolerances and offer con­sistent

appear­ances to match finish samples accepted by the architect. These require­ments commonly demand that the product be poured on custom-made forms with special attention given to true, flat surfaces, clean edges and consistent con­crete color and texture. Fiberglass-coated forms are often used to achieve the desired surface quality, and all form joints are sealed to ensure clean edges. Reinforcement is hung from prestressing strands within the component or stiff assemblies spanning across the form. This eliminates the need for reinforcing chairs, which might become visible on the exposed face of the component. Special care must be taken to maintain adequate cover over the reinforce­ment, not only to maintain durability but also to pre­vent reinforcement patterns from shadowing through to the face of the component. In instances where exacting tolerances and ornate shapes are not needed but special surface treatment or colors are desired, consideration should be given to using a PCICertified commercial producer capable of providing such services. These producers are designated with an A suffix on their classification (for example, C3A), and have demonstrated their ability to apply special finishes to their structural products. Additional information regarding plant certification categories can be found in Section 14.4 of this handbook. 1.3.2

When producing large quantities of a standard shaped component, precasters will commonly use a long-line form approach. These long-line forms may be several hundred feet long and are designed to produce a number of pieces with each casting. In most instances, the components produced in this fash­ion are pretensioned, prestressed components. Products such as beams and double-tees use bulkheads at the end of each unit in the form while extruded products such as hollow-core are placed as one continuous piece of concrete and then cut to the prescribed component lengths after curing. Single-piece forms are used with the intent of making one piece with each casting. This type of forming system readily accommodates non-prestressed or post-tensioned products, and is commonly used for architectural precast concrete components. It can also be used to create custom structural and architectural applications. 1.3.3

Fig. 1.3.1 Strand elongation is measured to ensure that the tension is consistent with the design.

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 ong-Line, Multi-Piece Forms versus L Single-Piece Forms

 restressed Components versus NonP Prestressed Components

Where a component’s dimensions and applied loads will allow, a precaster may elect to use reinforcing bars or welded wire to reinforce the product. In these cases, a reinforcing cage or mat is usually assembled and placed in the form. Concrete is then placed and vibrated around the assembly. Care must be taken by the designer to check crack control and deflections when using this type of design. Concrete components are prestressed to achieve higher spanto-depth ratios and provide resistance to cracking. Prestressing is incorporated into a component in the form of pre­tensioned or post-tensioned strands. Prestressing is generally used as the primary reinforcement with reinforcing bars or welded-wire reinforcement serving as secondary reinforcement.

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Fig. 1.3.2 Embeds are shown being placed in a prestressed component on a long-line bed.

1.3.4

 retensioned Components versus P Post-Tensioned Components

In pretensioned components, strands are first ten­sioned, then supplemental reinforcing bars and other items to be embedded in the component are secured and concrete is placed into the form. After the con­crete is allowed to cure and forms a bond with the pre­tensioned strands, the strands are cut (detensioned) and the prestressing force is transferred from the strands to the concrete through bond and mechanical inter­lock. At this point, the components are removed from the form and placed in storage. Post-tensioning is typically tied to a cage or mat of reinforcement, which is then placed into the form. Mechanical anchorages are placed at each end of the tendon and secured to the form or the reinforce­ment. After concrete has been placed and cured within the form, the prestressing force is applied to the post-tensioning strands and held at the mechani­cal anchorages. At this point, the prestress force has been transferred to the component, which can then be stripped out of the mold and placed in storage. Under some circumstances, a combination of pre­tensioning and post-tensioning may be used. This approach may be used

Fig. 1.3.3 Concrete is being placed into the formwork of a prestressed lite-wall.

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CHAPTER 1 where the self-stressing forms or tensioning abutments cannot sustain the full prestressing force. In this case, the majority of the force is applied through pretensioned strands, and post-tensioned tendons are used to introduce the remain­der of design prestressing force after the component is stripped. This approach may also be used in pre­stressed panels that are poured in a flat position but stand in an upright position in service. Occasionally, the full prestress force will cause cracking in the panel while it is flat in the form. This cracking can be avoided by applying a portion of the prestress by posttensioning after the panel is stripped and upright. Thought should be given to space restrictions at the anchorage area and the additional cost of a two-step process.

Fig. 1.3.4 A precast, prestressed component is shown being stripped from the form. Fig. 1.3.5 (below) This double-tee on a truck is ready for shipment to the jobsite.

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1.3.5

Production Limitations

A wide variety of products, in a variety of shapes and sizes, are generally available. Not all products are available in all geographical areas, and, therefore, designers should be aware of these limitations during the project development. Contacting regional precast concrete producers in the project's area is the best way to ensure that the design team takes maximum advantage of precast concrete elements that are readily available. The size of the piece may be limited by the han­dling equipment available in the manufacturing plant or by the transporting and erection equipment avail­able. In most cases, manufacturers are geared to produce standard products that can be transported over the road with a minimum of special permits.  Unusually large pieces can be made, but the special equipment required to handle such pieces can significantly add to the cost. The tensioning capacity of the prestressing beds may be another limitation. Some products, such as deep, long-span bridge girders require massive stressing abut­ments and beds that can handle large hold-down forces for depressed strands. These capabilities are costly and must usually be amortized over a number of projects. For large projects with many pieces, it is sometimes economical to install special facilities that can be written off on the single project. Self-stressing forms, which resist the large forces from the stressing bulkheads with heavy compression members (usually steel) built into the forms, may be another solution. Environmental concerns may also limit the scope of a precaster’s operation. For example, in most cases, operations like sandblasting and acid etching must be contained. The location of the facility related to residences, businesses, streams, and the like may require special noise, dust, or runoff containment.  These are conditions that are confronted by almost all manu­facturing industries, and generally are not restrictions on the design and use of precast concrete products.

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References

 recast/Pre­stressed Concrete Institute (PCI). 1981. P Reflections on the Beginnings of Prestressed Concrete in America. Chicago, IL: PCI.

2.

Schutt, Craig, ed. 2004. PCI 50 Years: Visions Taking Shape. Chicago, IL: Cherbo Publishing Group, Inc.

3.

ACI Committee 318. 2005. Building Code Requirements for Structural Concrete (ACI 318-05), and Commentary (ACI 318R-05). Farmington Hills, MI: American Concrete Institute (ACI).

4.

 .S. Green Building Council (USGBC). "LEED Rating U Systems." USGBC website, February 2009, www .usgbc.org.

5.

 orld Commission on Environment and Development, W “Report on Our Common Future,” Oxford University Press, New, York, NY, 1987.

6. P  recast/Prestressed Concrete Institute (PCI), “Sustainability,” Designer’s Notebook series, PCI, 2006. 7. P  CI Plant Certification Committee. 1999. Manual for Quality Control for Plants and Pro­duction of Structural Precast Concrete Prod­ucts, MNL-116-99. 4th ed. Chicago, IL: PCI. 8. P  CI Architectural Precast Concrete Services Committee and Plant Certification Committee. 1996. Manual for Quality Control for Plants and Pro­duction of Architectural Precast Concrete Products, MNL-117-96. 3rd ed. Chicago, IL: PCI. 9. A  ASHTO. 2007. AASHTO LRFD Bridge Design Specifications. 4th ed. Washington, DC: AASHTO. 10. P  CI. 1997. Bridge Design Manual, MNL-133-97. 1st ed. Chicago, IL: PCI.

CHAPTER 1 17. A  BAM Engineers, Inc. 1988. Precast Prestressed Concrete Horizontally Curved Bridge Beams. PCI Journal, V. 33, No. 5 (September-October). 18. P  CI Bridge Producers Committee. 1988. Recommended Practice for Precast/Prestressed Concrete Composite Bridge Deck Panels. PCI Journal, V. 33, No. 2 (MarchApril). 19. P  CI Committee on Prestressed Concrete Poles. 1997. Full Depth Precast and Precast, Prestressed Concrete Deck Panels. PCI Journal, V. 42, No. 6 (NovemberDecember). 20. E  inea, Amin, Takashi Yamane, and Maher K. Tadros. 1995. Full Depth Precast and Prestressed Concrete Deck Panels. PCI Journal, V. 40, No. 1 (January-February). 21. G  FRC-Recommended Practice-MNL-128-01 Recommended Practice for Glass Fiber Reinforced Concrete. 22. P  CI Committee on Glass-Fiber-Reinforced Concrete Panels. 1981. Recommended Practice for Glass Fiber Reinforced Concrete. PCI Journal, V. 26, No. 1 (January-February). 23. P  CI Committee on Precast, Prestressed Con­crete Tank Construction. 1983. State of the Art of Precast, Prestressed Concrete Tank Construc­tion. PCI Journal, V. 28, No. 4 (July-August). 24. P  CI Committee on Precast, Prestressed Con­crete Storage Tanks. 1987. Recommended Practice for Precast Prestressed Concrete Circular Storage Tanks. PCI Journal, V. 32, No. 4 (July-August). 25. P  CI Bridge Producers Committee 1988. Recommended Practice for Precast Prestressed Concrete Composite Bridge Deck Panels. PCI Journal, V. 33, No. 2 (MarchApril).

11. P  CI. 1990. "Architectural Precast Concrete Cladding — Its Contribution to Lateral Resistance of Build­ings,” Proceedings, SP-CP. Chicago, IL: PCI. 12. P  CI. 2003. Architectural Precast Concrete — Color and Tex­ture Selection Guide. 2nd ed. Chicago, IL: PCI. 13. P  CI Architectural Precast Concrete Committee. 2007. Architectural Precast Concrete, MNL-122-07. 3rd ed. Chicago, IL: PCI. 14. P  feifer, Donald W., J. R. Landgren, and William Perenchio. 1986. Concrete, Chlorides, Cover and Corrosion. PCI Journal, V. 31, No. 4 (July-August). 15. P  CI Committee on Parking Structures. 1997. Precast, Prestressed Parking Structures: Recommended Practice for Design and Con­struc­tion, MNL-129-98. 2nd ed. Chi­cago, IL: PCI. 16. A  bdel-Karim, A. M., and Maher K. Tadros. 1991. Stretched-Out Precast Concrete I-Girder Bridge Spans. Concrete International, V. 13, No. 9, September.

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NOTATIONS

CHAPTER 2

CHAPTER 2 NOTATIONS Introduction The following is a compilation of various notations used in this handbook. For ease of use, it is provided in chapter arrangement. Note that where the definition is the same as ACI 318-05, (ACI) is included after the definition. Where the same notation has more than one definition in the same chapter, the first place that it is used is indicated by referencing the appropriate section number. Units are not shown because they may vary from one application of the notation to another.

Chapter 1 - Precast and Prestressed Concrete: Applications None used

Chapter 3 - Preliminary Design of Precast / Prestressed Concrete Structures A Ag b Class C Class T Class U D DL db f 'c f 'ci fo fpc fpu fse fy h h h1 h2 I IT Ic l L LB Mc Mn Mnb Mu Pn Pnb Po Pu RB S Sb

= cross-sectional area = gross area of concrete section (ACI) = width of compression face of component (ACI) = a prestressed component that is cracked = a prestressed component that is in transition between cracked and uncracked = a prestressed component that is uncracked = dead loads (ACI) = unit dead load of component = nominal diameter of bar, wire, or prestressing strand (ACI) = specified compressive strength of concrete (ACI) = specified compressive strength of concrete at time of initial prestress (ACI) = fundamental natural frequency = compressive stress in concrete (after allowance for all prestress losses) at centroid of cross section resisting externally applied loads (ACI) = specified tensile strength of prestressing steel (ACI) = effective stress in prestressing steel (after allowance for all prestress losses) (ACI) = specified yield strength of reinforcement (ACI) = overall height or thickness of component (ACI) (3.9) = height of stadium riser (see Section 3.3.12) = distance from top of ledge to top of component = ledge height = moment of inertia of section about centroidal axis (ACI) = inverted-tee beam = composite moment of inertia = span length of beam or one-way slab (ACI) = live loads (ACI) = ledge beam = nominal flexural strength with zero axial load = nominal flexural strength at section (ACI) = nominal moment strength of a compression component under balanced conditions = factored moment at section (ACI) = nominal axial strength of a compression component at a given eccentricity (ACI) = nominal axial load strength of a compression component under balanced conditions = nominal axial load strength of a compression component with zero eccentricity (ACI) = factored axial force = rectangular beam = section modulus = section modulus with respect to the bottom fiber of a cross section

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CHAPTER 2 St t Vc Vci Vcw Vu V/S wt yb ycb yt ys δ ρ φ

= section modulus with respect to the top fiber of a cross section = thickness = nominal shear strength provided by concrete (ACI) = nominal shear strength provided by concrete when diagonal cracking results from combined shear and moment (ACI) = nominal shear strength provided by concrete when diagonal cracking results from high principal tensile stress in the web (ACI) = factored shear force at section = volume-to-surface ratio = unit weight = distance from bottom fiber to center of gravity of section = distance from bottom fiber to center of gravity of a composite section = distance from top fiber to center of gravity of section = distance from centroid of prestressed reinforcement to bottom fiber = moment magnification factor = ratio of As to bd (ACI) = strength-reduction factor (ACI)

Chapter 4 - Analysis and Design of Precast / Prestressed Concrete Structures ap A Ab AB Acv Aps As Avf Aw AB b C Cd Ce Cs Ct Ct Cu Cu Cvx Cw D Di DIF e E E Emu Eψ f 'c fdc fdy fy F F Fa Fb 2–2

= component amplification factor = area (with subscripts) = total area of anchor bolts that are in tension = area of base of structure = area of topping slab section = area of prestressing steel in flexural tension zone (ACI) = area of non-prestressed longitudinal tension reinforcement (ACI) = area of shear-friction reinforcement (ACI) = area of shear wall = area of base of structure = width of section or structure (with subscripts) = compressive force = deflection amplification factor as given in Design Aid 4.11.8 = exposure factor as determined from Design Aid 4.11.3 = seismic response coefficient = thermal factor as determined from Design Aid 4.11.3 = factor in calculating approximate fundamental building period (see Section 4.2.4.1) = coefficient from Table 4.2.2 = factored force = vertical distribution factor for level x = calculated factor used in an alternate method to estimate the approximate period of concrete shear wall buildings = dead loads (ACI) = length of shear wall = dynamic increase factor for reinforcing or concrete (see Table 4.9.1) = eccentricity of axial load = load effects of earthquake (ACI) (see Section 4.2.6) = modulus of elasticity of concrete (with subscripts) (ACI) (see Section 4.5.6) = diaphragm seismic force for seismic design categories C and higher = diaphragm earthquake force = specified compressive strength of concrete (ACI) = dynamic concrete compressive strength = dynamic yield strength of reinforcing = specified yield strength of reinforcement (ACI) = horizontal force in shear wall building and in moment-resisting frames (see Section 4.5.7) = pressure of fluids of known density in load combinations (ACI) (see Section 4.2.6) = acceleration-based site coefficient at 0.3-sec period = degree of base fixity (decimal) First Printing/CD-ROM Edition

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NOTATIONS

CHAPTER 2

Fi F i Fi, Fn, Fx Fp F(t) Fv Fx, Fy g g h h hb hc

= lateral force at bay i or in shear wall i = restraining force in multistory columns at level i = portion of seismic base shear V induced at level i, n, or x, respectively = seismic force acting on component of a structure = blast load on component = velocity-based site coefficient at 1.0-sec period = forces in x and y directions, respectively = assumed length over which elongation of anchor bolt takes place = acceleration due to gravity = height of shear wall, height of building (with subscripts) = width of column (see Section 4.6.1) = height of balanced snow load = clear height from top of balanced snow load to (1) closest point on adjacent upper roof, (2) top of parapet, or (3) top of projection on roof hd = height of snow drift hi, hn, hx = height above base level i, n, or x, respectively hs = story height hsx = story height below level x H = loads due to weight and pressure of soil, water in soil, or other materials (ACI) I = importance factor as determined from Design Aid 4.11.1 I = moment of inertia of section about centroidal axis (with subscripts) (ACI) Ieq = approximate moment of inertia that results in flexural deflection equal to combined shear and flexural deflections of wall (see Design Aid 4.11.26) Ig = moment of inertia of gross section about centroidal axis, neglecting reinforcement (ACI) Ip = polar moment of stiffness k = effective length factor of a compression component (ACI) k = c oefficient used to account for the contribution of higher modes to the vertical distribution of equivalent lateral forces (see Section 4.2.4.2) kb, kf, km = coefficients used to determine forces and moments in beams and columns ks = coefficient of subgrade reaction ks = coefficient of subgrade K = stiffness coefficient (with subscripts) Ke = static strength increase factor Kl = constant in determining equivalent volume change KLM = load-mass factor Kr = relative stiffness (see Design Aid 4.11.24) Kt = constant used for calculation of equivalent temperature of shortening Kz = velocity pressure exposure coefficient evaluated at height z Kzt = topographic factor l = length of span (ACI) or structure lu = length of roof for leeward or windward drift lw = length of weld L = live loads (ACI) Lr = roof live load in load combinations M = maximum unfactored moment due to service loads (ACI) M = mass of blast loaded component Mj = moment in multistory columns at point j M T = torsional moment Mu = factored moment at section (ACI) MWFRS = main-wind-force-resisting system n = number of items (ACI); number of panels in shear wall; number of bays in moment-resisting frame; number of floors in building pf = snow load on flat roofs (“flat” = roof slope ≤ 5 deg) pg = ground snow load pn = steel ratio of reinforcement in topping crossing a precast joint pnet30 = net design wind pressure for exposure B at h = 30 ft and I = 1.0 ps = combined windward and leeward net wind pressure ps30 = simplified design wind pressure for exposure B at h = 30 ft and I = 1.0 PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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= vertical load acting at eccentricity e = effective prestress force after all losses = prestress force after transfer losses = factored axial force (ACI) = total unfactored vertical design load at, and above, level x = effect of horizontal seismic (earthquake-induced) forces = rigidity = rain load (ACI) = response modification coefficient as given in Design Aid 4.11.8 = component response modification factor = relative humidity = snow load (ACI) = mapped maximum considered earthquake, 5% damped, spectral response acceleration at a period of 1 sec = site-specific design spectral response acceleration at any period = design, 5% damped, spectral response acceleration at a period of 1 sec = design, 5% damped, spectral response acceleration parameter at short periods = maximum considered earthquake, 5% damped, spectral response acceleration at a period of 1 sec; adjusted for site class effects SMS = maximum considered earthquake, 5% damped, spectral response acceleration at short periods adjusted for site class effects SS = mapped maximum considered earthquake, 5% damped, spectral response acceleration at short periods t = time T = fundamental period of building (see Section 4.2.4) T = tensile force (with subscripts) (see Section 4.3.2) T = cumulative effect of temperature, creep, and shrinkage (ACI) Ta = approximate fundamental period of building TL = long-period transition period between equations for the site-specific design spectral response acceleration Tn = nominal tensile strength To = 0.2SD1/SDS Ts = SD1/SDS Tu = factored tensile force U = required strength to resist factored loads (ACI) V = b asic wind speed obtained from Design Aid 4.11.5 in mph. The basic wind speed corresponds to a 3-sec gust speed at 33 ft above ground in Exposure Category C V = shear (with subscripts) V = total design lateral force or shear at base (see Section 4.2.4.1) Vn = nominal shear strength (ACI) Vu = factored shear force at section (ACI) Vx = seismic design shear in story x V/S = volume-to-surface ratio w = uniform load (with subscripts) w = width of snow drift wi, wn, wx = portion of W that is located at or assigned to levels i, n, or x, respectively W = total gravity dead load (with subscripts) W = wind load (ACI) x = number of shear walls effective in resisting lateral forces in direction under consideration (see Section 4.2.4.1) x = exponent applied to building height in calculation for approximate fundamental period (see Section 4.2.4.1) x1 = distance from face of column to center of anchor bolts x2 = distance from face of column to base plate anchorage x, y = orthogonal distances of individual shear walls from center of rigidity (see Section 4.5.7)  = ratio of shear demand and shear capacity for story between levels x and x–1 (see Section 4.2.4.4)  = ratio of actual shear strength to the shear strength at any given level required by analysis (see Section 4.6.7) γ = flexibility coefficient (with subscripts) γ = snow density δ = volume change shortening (with subscripts) δe = equivalent volume change shortening (with subscripts) δi = elastic displacement at floor i δx = deflection of level x at center of mass at and above level x P Pe Po Pu Px QE r R R Rp RH S S1 Sa SD1 SDS SM1

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NOTATIONS δxe ∆ ∆ ∆ θ λ µs µ ρ φ φ Ω0

CHAPTER 2 = deflection determined from elastic analysis that includes consideration of cracking = design story drift (see Design Aid 4.11.9) = difference of deflections between levels (see Section 4.2.4.4) = total equivalent shortening in a frame (see Section 4.4.3.1) = stability coefficient for P-delta effects = adjustment factor for building height and exposure = static coefficient of friction for soil = ductility ratio for blast design = reliability coefficient based on extent of structural redundancy present in building (see Section 4.2.6) = rotation (with subscripts) = strength-reduction factor (ACI) = amplification factor to account for overstrength of the seismic-force-resisting system (ACI)

Chapter 5 - Design of Precast and Prestressed Concrete Components a a a aw A A1 A2 Acomp Acr Acs A'cs Af Af Ag Ah Al Al An Apl Aps A'ps A'cs, min As A's As, min Ash 5.6.3.3) A'sh At At Atop Atps Ats A'ts Att Av Av Avf Avt Aw Awl Awv

= depth of equivalent rectangular stress block (ACI) = applied load eccentricity (see Fig. 5.5.1) = distance from end of component to strand depression point (see Design Aid 5.14.10) = applied load eccentricity for strut and tie model = cross-sectional area = loaded area (ACI) = a rea of lower base of largest frustum of a pyramid, cone, or tapered wedge contained wholly within the support and having for its upper base the loaded area, and having side slopes of 1 vertical to 2 horizontal (ACI) = cross-sectional area of equivalent rectangular stress block = area of crack interface = area of horizontal shear ties in a composite section = area of topping reinforcement to achieve composite behavior with extended topping = area of flange outside web, in a flanged section = area of reinforcement in bracket or corbel resisting factored moment (ACI); also in extended end of dap = gross area of concrete section (ACI) = shear-friction reinforcement across vertical crack at dapped ends and corbels = total area of longitudinal reinforcement to resist torsion = area of longitudinal reinforcement to resist bending in ledges = area of reinforcement in bracket- or corbel-resisting tensile force (ACI) = area of bearing plate = area of prestressing steel in flexural tension zone (ACI) = area of prestressed reinforcement in compression zone of a component = minimum required horizontal shear reinforcement = area of non-prestressed longitudinal tension reinforcement (ACI) = area of longitudinal compression reinforcement (ACI) = minimum required flexural reinforcement = area of hanger reinforcement for ledge of L beam or inverted-tee beam or dapped ends (see Sections 5.5.4 and = area of extended hanger reinforcement, Ash in a dapped end (see Fig. 5.6.3) = total area of transformed section = area of one leg of closed stirrup resisting torsion within spacing s (ACI) = effective area of cast-in-place composite topping = transformed area of prestressing steel = transformed area of mild tension steel = transfomed area of mild compression steel = total area of transformed compression block = area of diagonal tension reinforcement in dapped end = area of shear reinforcement within spacing s (ACI) = area of shear-friction reinforcement (ACI) = required area of stirrups at end for bursting stresses = area of web in a flanged section = area of steel in longitudinal direction at beam end for torsional equilibrium = area of steel in vertical direction at beam end for torsional equilibrium

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CHAPTER 2 b b bl bse bt bt bte bv bw c cc C C C Class C Class T Class U C1, C2 Cc C'c Cr Ct CR d d' db de dl dna dna dp, d'p ds dt dt dw D D e e' ec ee eo es Ec Eci Eps Es Et ES fb f 'c fc fcds 2–6

= width of compression face of component (ACI) (see Section 5.2.1.2) = dimension of bearing area (see Section 5.6.1) = L beam, width of web and ledge = equivalent width of cast-in-place stem = width of bearing area under concentrated loads on ledges = width of bearing area = equivalent width of topping = width of cross section at contact surface being investigated for horizontal shear (ACI) = web width (ACI) = distance from extreme compression fiber to neutral axis (ACI) = clear cover of reinforcement (ACI) = coefficient as defined in section used (with subscripts) = compressive force (with subscripts to define specific locations) = coefficient of thermal expansion (see Section 5.8.5) = a prestressed component that is cracked = a prestressed component that is in transition between cracked and uncracked = a prestressed component that is uncracked = multipliers used to estimate long-term cambers and deflections = compressive force capacity of composite topping = compression force in the extended part of composite topping = reduction coefficient for bearing of unreinforced section (see Section 5.6.1) = torsion coefficient defined in Section 5.4 = prestress loss due to creep of concrete = distance from extreme compression fiber to centroid of longitudinal tension reinforcement (ACI), but need not be less than 0.8h for prestressed components (dp is used for prestressed components when a distinction from d for non-prestressed reinforcement is relevant) = d istance from extreme compression fiber to centroid of compression reinforcement (ACI), (d'p is used for prestressed components when a distinction from non-prestressed reinforcement is relevant) = nominal diameter of bar, wire, or prestressing strand (ACI) = distance from center of load to end of beam = depth of centroid of reinforcement in L beam ledges = distance from extreme compression fiber to neutral axis of a section = distance from center of gravity of reinforcing to neutral axis of section = distance from extreme compression fiber to centroid of prestressing steel in tension and compression zones, respectively (ACI) = distance from extreme compression fiber to centroid of hanger reinforcement in L beam = distance from extreme compression fiber to centroid of extreme tension steel = extreme depth of component (see Example 5.2.1.5) = depth of reinforcement from outside face of L beam = distance from extreme compression fiber to centroid of tension reinforcement in a dapped end component = dead loads (ACI) = eccentricity of design load or prestressing force parallel to axis measured from centroid of section or reaction = distance between center of gravity of strand at end and center of gravity of strand at lowest point = ec – ee = eccentricity of prestressing force from centroid of section at center of span = eccentricity of prestressing force from centroid of section at end of span = equivalent eccentricity of loads on ledges of an inverted-tee beam = strain in steel = modulus of elasticity of concrete (ACI) = modulus of elasticity of concrete at time of initial prestress = modulus of elasticity of prestressed reinforcement = modulus of elasticity of reinforcement and structural steel (ACI) = adjusted modulus of elasticity to account for temperature lag = prestress loss due to elastic shortening = stress in bottom fiber of cross section (see Example 5.2.2.2) = specified compressive strength of concrete (ACI) = concrete compressive stress = concrete stress at center of gravity of prestressing force due to all permanent (dead) loads not used in computing fcir First Printing/CD-ROM Edition

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NOTATIONS f 'ci fcir fct fcu fd fdc fl fna fpc fpd fpe fpi fps fpu fpy fr f 'r fs f 's fse ft ft ftot fy f 'y fyt fys F Fh Fh Fns Fnt Fu h h h' hf hl hs hs H Hu l lcr le lequiv lext lg lint lt J kf, km K Kt Ku

CHAPTER 2 = specified compressive strength of concrete at time of initial prestress (ACI) = concrete stress at center of gravity of prestressing force immediately after transfer = average splitting tensile strength of lightweight concrete (ACI) = maximum compressive stress in nodal zone of strut and tie method = stress due to service dead load = decompression stress; stress in the prestressing steel when stress is zero in the concrete at the same level as the centroid of the prestressing steel (ACI) = stress due to service live load = stress in concrete at the nuetral axis = compressive stress in concrete (after allowance for all prestress losses) at centroid of cross section resisting externally applied loads (ACI) = stress in prestressed reinforcement limited by strand development = compressive stress in concrete due to effective prestress forces only (after allowance for all prestress losses) at extreme fiber of section where tensile stress is caused by externally applied loads = ratio of initial prestress force to area of prestressing steel = stress in prestressed reinforcement at nominal strength of component (ACI) = specified tensile strength of prestressing steel (ACI) = specified yield strength of prestressing steel (ACI) = modulus of rupture of concrete (ACI) = allowable flexural tension, computed using gross concrete section = calculated tensile stress in reinforcement at service loads (ACI) = stress in compression reinforcement under factored loads (ACI) = effective stress in prestressing steel (after allowance for all prestress losses) (ACI) = stress in top fiber of cross section (see Example 5.2.2.2) = extreme tensile stress at extreme tension in the precompressed tensile zone calculated at service loads (ACI) = final calculated total stress in component = specified yield strength of reinforcement (ACI) = specified yield strength of compression reinforcement = specified yield strength of transverse shear or torsion reinforcement (ACI) = yield strength of Ash reinforcement = fictitious forces on cast-in-place slab (with subscripts) = horizontal shear force = horizontal shear force at interface between precast and cast in place = factored compression force in strut of strut and tie model = factored tension force in tie of strut and tie model = restraining force = overall height or thickness of component (ACI) = depth of component above dap; height of corbel (see Fig. 5.6.3 and 5.9.2) = unsupported length of pile = depth of flange = L beam, depth of ledge = distance between torsional equilibrium reactions = story height = total depth of dapped end component = factored torsional equilibrium reactions = moment of inertia of section about centroidal axis (with subscripts) (ACI) = moment of inertia of cracked section transformed to concrete (ACI) = effective moment of inertia for computation of deflection (ACI) = equivalent constant moment of inertia in components with varying cross sections = moment of inertia of exterior wythe of a sandwich panel = moment of inertia of gross section about centroidal axis, neglecting reinforcement (ACI) = moment of inertia of interior wythe of a sandwich panel = moment of inertia of transformed cracked section = prestress loss coefficient as defined in Section 5.7.3 = coefficients for determining moments and restraining forces on columns braced against sidesway = prestress loss coefficient as defined in Section 5.7.3 (with subscripts) = torsion coefficient as defined in Section 5.4 = design coefficient (see Design Aid 5.14.1)

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CHAPTER 2 K 'u l l1, l2 ld ldh lp lt lvh L m M Ma Mcr Mcre Md ME Mext Mg Mint Ml Mmax Mn Mnb Mnc Mo Msd Msl Mtop Mu n n.a. nps ns N Nc Nu P P P Pc Pe Pe Pi Pn Pnb Po Po Ppd Ps Pu r RE RH s s s S 2–8

= design coefficient (see Design Aid 5.14.2) = length of span (ACI) = dimenisons from forces of a strut and tie model to nodes = development length in tension of deformed bar, deformed wire, plain and deformed welded-wire reinforcement, or pretensioned strand (ACI) = development length in tension of hooked bar (ACI) = horizontal length of a corbel or dap = strand transfer length = horizontal shear length = live loads (ACI) = modification factor for hanger reinforcement design defined in Section 5.5.4 = maximum unfactored moment due to service loads (ACI) = maximum unfactored moment in component at stage deflection is calculated (ACI) = cracking moment (ACI) = moment causing cracking at section due to externally applied loads (ACI) = moment due to service dead load = moment due to earthquake = external moment = unfactored moment due to weight of component = internal moment = moment due to service live load = maximum factored moment at section due to externally applied loads = nominal flexural strength at section (ACI) = nominal moment strength under balanced conditions = moment due to beam self-weight plus dead loads applied before composite action = nominal moment strength of compression component with zero axial load = unfactored moment due to superimposed dead load plus sustained live load = unfactored moment due to superimposed live load = moment due to topping (unfactored) = factored moment at section (ACI) = modular ratio of reinforcing = neutral axis of a section = modular ratio for prestressing steel = modular ratio for mild steel = unfactored axial load = maximum allowable force on a strut = factored horizontal or axial force (ACI) = prestress force (with subscripts) (see Section 5.2.2.2) = force required to restrain bowing (see Section 5.8.5) = force from wheel load on double-tee (see Example 5.12.1.1) = critical buckling load based on Euler’s formula (ACI) = effective prestress force after all losses = equivalent compression force (see Examples 5.2.2.5 and 5.2.2.6) = initial prestress force (jacking force after anchorage loss) = axial load nominal strength of compression component at given eccentricity = axial load nominal strength under balanced conditions = axial load nominal strength of compression component with zero eccentricity (5.9) = prestress force after transfer losses = prestress force limited by strand development = decompression force = factored axial force (ACI) = radius of gyration (ACI) = prestress loss due to relaxation of tendons = average ambient relative humidity = center-to-center spacing of reinforcement, wires, or anchors (ACI) = spacing of concentrated loads on L beam ledge (see Fig. 5.5.1) = distance from face of support to center of loaded area (see Fig. 5.6.1) = section modulus First Printing/CD-ROM Edition

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NOTATIONS Sb Sbc Sext Sint St SH t T1, T2 T T Tc T 'c Tn Tu TL Vc V 'c Vci Vcw Vd VE Vi Vl Vn Vnf Vp Vs Vu V/S w w wc wd wl ws wsd wsl wtop wu wt W x x x1 y y y' y1 yb yna yp ys yt yt ytps

CHAPTER 2 = section modulus with respect to the bottom fiber of a cross section = section modulus with respect to bottom fiber of composite section = section modulus of exterior wythe of a sandwich panel = section modulus of interior wythe of a sandwich panel = section modulus with respect to the top fiber of a cross section = prestress loss due to shrinkage of concrete = thickness (used for various parts of components with subscripts) = outside and inside temperatures, respectively = tensile force, also used with subscripts to define specific locations = torsion = nominal torsion strength of concrete = nominal torsional moment strength under pure torsion = nominal torsional moment strength (ACI) = factored torsional moment at section (ACI) = total prestress loss = nominal shear strength provided by concrete (ACI) = nominal shear strength under pure shear = n ominal shear strength provided by concrete when diagonal cracking results from combined shear and moment (ACI) = nominal shear strength provided by concrete when diagonal cracking results from high principal tensile stress in the web (ACI) = shear force at section due to unfactored dead load (ACI) = shear due to earthquake = factored shear force at section due to externally applied loads occurring simultaneously with Mmax = live load shear (unfactored) = nominal shear strength (ACI) = nominal shear strength across a joint using shear friction = vertical of effective prestress force at section considered = nominal shear strength provided by shear reinforcement = factored shear force at section (ACI) = volume-to-surface ratio = unfactored load per unit length of beam or per unit area of slab = dimension of bearing area (see Fig. 5.6.1) = unit weight (density) of concrete (ACI) = unfactored dead load per unit length = unfactored live load per unit length = 2 times distance from concrete surface to Nc in a strut and tie model = dead load due to superimposed loading plus sustained live load = unfactored superimposed live load per unit of length = unfactored topping load per unit length = factored total load per unit length (ACI) = unit weight = wind load (ACI) = distance from support to point being investigated (see Design Aids 5.14.5, 5.14.6, and 5.14.7) = shorter overall dimension of rectangular part of cross section (ACI) = short side of closed tie = longer overall dimension of rectangular part of cross section (ACI) = distance from center of gravity of section to either extreme surface = distance from top of component to the center of gravity of the compression block = long side of closed tie = distance from bottom fiber to center of gravity of section = d istance from neutral axis of a cracked transformed section to the center of gravity of the cracked transformed section = distance from the applied prestress force to the center of gravity of the cracked section = distance from centroid of prestressed reinforcement to bottom fiber = distance from centroidal axis of gross section to extreme fiber in tension (ACI) = distance from top fiber to center of gravity of section = distance from tension face to center of gravity of transformed prestressing steel

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CHAPTER 2 yts ytt α αt 1 d n s γ γp γt ∆ εc εps, εpd, ε'ps εs εs ε's εsa εse εt εy θ θ λ λ µ µe  ρ ρ' ρp ρv ρw φ φK ω

= distance from tension face to center of gravity of transformed mild steel = distance from bottom of a component to the center of gravity of composite compression area = strain gradient across a panel thickness = torsion coefficient defined in Section 5.4 = factor relating depth of equivalent rectangular compressive stress block to neutral axis depth (ACI) (see Section 5.2.1.1) = ratio used to compute magnified moments in columns due to sustained loads (ACI) = factor to account for the effect of the anchorage of ties on the effective compressive strength of a nodal zone (ACI) (see Section 5.9.4.2.2) = factor to account for the effect of cracking and confining reinforcement on the effective compressive strength of the concrete in a strut (ACI) (see Example 5.9.4.2) f = factor dependent on level of prestress 1 + 10 pc fc' = factor for type of prestressing steel (see ACI 318-05 Section 18.0 for values) = factor used in designing hanger reinforcement as defined in Section 5.5.4 = deflection (with subscripts) = concrete strain = strain in prestressing steel corresponding to fps, fpd, and f 'ps = net tensile strain in extreme tension steel = strain in non-prestressed tension reinforcement = strain in non-prestressed compression reinforcement = strain in prestressing steel caused by external loads = strain in prestressing steel after losses = net tensile strain in extreme layer of longitudinal steel at nominal strength (ACI) = maximum allowable strain in non-prestressed reinforcement = angle of slope for asymmetrical sections (see Section 5.2.5) = angle of possible vertical crack at end of a component (see Fig. 5.6.2) = modification factor for density of concrete (ACI) (see Section 5.3.3) = deflection multiplier to account for long-term behavior (see Section 5.8.4) = coefficient of friction (ACI) (see Table 5.3.6.1) = effective shear-friction coefficient (see Table 5.3.6.1) = time-dependent factor for sustained loads (ACI) = ratio of As to bd (ACI) = ratio of A's to bd (ACI) = ratio of Aps to bd (or bdp) producing balanced strain conditions (ACI) = ratio of tie reinforcement area to area of concrete surface of composite component (ACI) = ratio of As to bwd (ACI) = strength-reduction factor (ACI) = stiffness-reduction factor (ACI) to account for actual component properties ρf A f = tension reinforcement index = ' y = s y' (ACI) fc bdfc

ρ' f y A's f y (ACI) = fc' bdfc'

ω'

= compression reinforcement index =

ω ‒ ωmax

= factor used in Design Aid 5.14.1 = maximum permissible ω A f ρ f = prestressing steel index = p ' ps = ps ps' (ACI) fc bd p fc

ωp ωpu

= factor used in Design Aid 5.14.3

Chapter 6 - Design of Connections a a a a Abrg 2–10

= center of exterior cantilever bearing to center of Cazaly hanger strap (see Fig. 6.9.2) = depth of equivalent rectangular compression stress block (ACI) (see Fig. 6.5.9) = leg size of fillet weld (see Section 6.7.2.1) = height of steel stiffener (see Fig. 6.6.5 and 6.6.7) = bearing area of the head of stud or anchor bolt (ACI) First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

NOTATIONS Ac Ag An AN ANo As Ase Ash At Av Avf Aw − A b b b B BED c C C C1 Cbs Ccrb Ccrb Cn Cu Cu Cx, Cy, Ch, Cev, Cvcr CE d d db de1, de2, de3, de4 dhs do D D e eh ei ev e'N e 'v ev1 ex, ey E f 'c fn fr fut fx fy fy fz

CHAPTER 2 = compression area of a steel element = gross area of a bolt = area of reinforcement required to resist axial tension (ACI) = projected surface area for stud or group of studs = projected surface area of one anchor when not limited by edge distance = area of steel reinforcement = effective cross-sectional area of anchor (ACI) = area of reinforcement in a Loov hanger = tension area of a steel element = area of anchor reinforcement used in a Cazaly hanger = area of shear-friction reinforcement (ACI) = area of structural steel section subjected to shear = area enclosed by centerline of tube walls = dimension (see specific application, with subscripts) = projection of stiffener (see Fig. 6.6.5) = width of compression face of component (ACI) = width of critical section of base plate = distance from back row of studs to front edge = concrete cover to strap of a Cazaly hanger = compressive force (see Example 6.13.3) = factor used for weld design using AISC (see Example 6.7.4.1) = factor used for weld design using AISC = breakout strength coefficient = cracking coefficient (breakout) = cracking coefficient (pullout) = nominal compressive strength of reinforcement = compressive force in bar of a Loov hanger = factored compressive force in anchor bolt = coefficients used in design of shear strength of studs = carbon equivalent = depth of welds in weld group (see Examples 6.5.5.4 and 6.13.6) = distance between rows of studs (see Fig. 6.5.9) = bolt diameter = edge distance from stud group = head diameter of stud = shank diameter of stud or anchor bolt (ACI) = durometer of bearing pad (shore A hardness) (see Fig. 6.10.3) = number of sixteenths of weld size for weld design by AISC (see Example 6.7.4.1) = eccentricity of load = hook projection of an anchor bolt (ACI) = center of bolt to horizontal reaction = eccentricity of vertical load = equivalent eccentricity of tensile force relative to the center of the stud group = distance between resultant group of anchors loaded in shear in the same direction, and the centroid of the group of anchors loaded in shear in the same direction (ACI) = eccentricity from shear load to anchorage centroid = eccentricity of load in x,y directions = modulus of elasticity of concrete (with subscripts) (ACI) = specified compressive strength of concrete (ACI) = nominal stress of weld = resultant stress on weld = specified tensile strength of a stud = combined shear and torsion stress in x direction (see Eq. 6-64) = combined shear and torsion stress in y direction (see Eq. 6-64) = yield strength of headed stud (see Table 6.5.1) = combined shear and torsion stress in z direction (see Eq. 6-64)

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2 

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NOTATIONS

CHAPTER 2 Fb Fcr Fe FEXX Fu Fun Fuv Fy g g G h h hef h 'ef HCA IC Ip Ixx, Iyy JT k k l l lb ld

= bearing stress at outer edge of a stiffener = critical buckling stress = elastic buckling stress = classification strength of weld metal = ultimate tensile strength of base metal = maximum normal stress = maximum shear stress = specified yield strength of structural steel = gage of angle for bolt holes = distance from the face of a component to the edge of bearing in a Cazaly hanger = shear modulus = depth of strap of Cazaly hanger = height of web of a structural steel section = effective embedment depth of an anchor (ACI) = design effective stud embedment length for narrow section = headed concrete anchors = instantaneous center = polar moment of inertia = moment of inertia of weld segment with respect to its own axes = torsional constant = distance from back face of angle to web fillet toe (see Fig. 6.6.2) = effective length factor for compression components (see Example 6.13.1) = length of span (ACI) = length of cantilever (see Section 6.6.3.1) = bearing length = development length in tension of deformed bar, deformed wire, plain and deformed welded wire reinforcement, or pretensioned strand (ACI) le = embedment length ll = angle leg length lp = bearing length of exterior cantilever in hanger connections lw = length of weld L = nominal length of stud M = applied moment (with subscripts) (see Section 6.6.7) Mn = nominal flexural strength at section (ACI) Mp = moment capacity of steel section Mu = factored moment n = number of samples in test data ns = number of studs in back row of group nsides = number of sides that influence stud group capacity nx, ny = number of studs in x and y rows Nb = basic concrete breakout strength in tension of a single anchor in cracked concrete (ACI) Ncb = nominal concrete breakout strength of a single (ACI) (or group) of anchors Nn = nominal tensile strength of stud (ACI) Np = nominal pullout strength of an anchor bolt Nph = nominal pullout strength of stud based on bearing against the head Ns = nominal tensile strength based on steel capacity Nsb = nominal side-face blowout strength for a single stud Nsbg = side-face blowout strength of a group of anchors (ACI) Nu = factored horizontal or axial force P = applied load (with subscripts) Pn = critical buckling force Px, Py, Pz = applied force in x, y, and z directions, respectively r = radius of gyration (ACI) Ro = distance from the center of gravity of a weld group to its instantaneous center s = center-to-center spacing of reinforcement, wires, or anchors (ACI) s = stud spacing corresponding to direction of eccentricity (see Section 6.5.4.1) so = spacing of outer anchors along the edge in the group S = shape factor for bearing pads 2–12

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NOTATIONS Sw SED t tw T Tn Tn Tu Vc Vc3 Vco3 Vcp Vn Vr Vs Vu w wu x x, y x1, x2,… x– y1, y2,… x¯ , y ¯ X,Y Y z Zn Zp σ α α   1 δl ∆ ∆ θ θ κ λ µ µe τu φ ψ ψc ψec,N ψed ψed,N ψy Ω0

CHAPTER 2 = width of strap used in a Cazaly hanger = distance from row of studs farthest from edge to side edge perpendicular to load = thickness (used for various parts of components with subscripts) = effective weld throat = tensile force = nominal torsional moment strength (ACI) = nominal tensile strength (see Example 6.13.2) = factored torsional moment at section (ACI) = nominal shear strength provided by concrete (ACI) = nominal concrete breakout strength for single or multiple-stud connection, accounting for geometry = nominal concrete breakout strength for single or multiple-stud connection unaffected by geometry = nominal concrete pryout strength of a single (ACI) (or group) of stud group of anchors = nominal shear strength (ACI) of connection = additional capacity of structural-steel corbel from reinforcing welded to the embedded section = nominal shear strength of an anchor based on steel capacity = factored shear force at section (ACI) = dimension (see specific application) = uniform load = eccentricity of anchor bolt to critical section = horizontal and vertical distance, respectively (see Example 6.7.4.1) = center-to-center spacing of stud rows in the X direction = sample mean from test data = center-to-center spacing of stud rows in the Y direction = distance of weld to center of gravity to weld group = overall dimensions (width and length) of stud group = depth of bar or hollow structural section used in a Cazaly hanger (see Fig. 6.9.2) = ratio used in stiffener design = shear forces in the Z direction = plastic section modulus of structural steel section = common standard deviation from test data = angle of Ash reinforcement in a Loov hanger = torsion constant used for structural steel sections = torsion constant used for structural steel sections = factor used in weld design = factor relating depth of equivalent rectangular compressive stress block to neutral axis depth (ACI) = differential weld length = design horizontal movement at end of component (see Fig. 6.10.3) = deformation of weld elements (with subscripts) (see Example 6.7.4.1) = rotation due to torsion (see Section 6.6.3.1) = angle of load with respect to the longitudinal axis of the weld element (see Section 6.7.2.1) = coefficient associated with 5% fractile in stud testing = modification factor for density of concrete (ACI) = coefficient of friction (ACI) = effective shear-friction coefficient = torsional shear stress in a structural steel section = strength-reduction factor (ACI) = diaphragm over-strength factor = factor used to modify strength of anchors = factor used to modify tensile strength of anchors based on eccentricity of applied loads (ACI) = factor used to modify stud capacity for multiple-edge distances = factor used to modify tensile strength of anchors based on proximity to edges of concrete component (ACI) = factor used to determine pry-out capacity of stud group = amplification factor to account for overstrength of the seismic-force-resisting system (ACI)

Chapter 7 - Structural Considerations for Architectural Precast Concrete ap CLC

= amplification factor related to type of seismic attachment (see Design Aid 4.11.10) = load combination factor

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NOTATIONS

CHAPTER 2

CSC = seismic cladding factor db = diameter of stone anchor D = dead loads (ACI) DF = distribution factor e = eccentricity of load (with subscripts) E = load effects of earthquake (ACI) Exposures B, C and D = surface roughnesses for use in wind pressure determination f 'c = specified compressive strength of concrete (ACI) Fp = seismic force acting on component of a building FDU = factored gravity design load on element of cladding FPU = factored seismic design load on element of cladding Fw = unfactored wind load on element of cladding FWU = factored wind design load on element of cladding GCp = product of external pressure coefficient and gust-effect factor to be used in determination of wind loads on buildings GCpi = p roduct of internal pressure coefficient and gust-effect factor to be used in determination of wind loads on buildings h = average roof height of structure with respect to the base I = wind importance factor from Design Aid 4.11.1 Ip = seismic component importance factor (see Design Aid 4.11.1) Kd = wind directionality factor (ASCE 7-05 Section 6.5.4.4) Kz = velocity pressure exposure coefficient (ASCE 7-05 Section 6.5.6.6) Kzt = topographic factor at mean roof height (ASCE7-05 Section 6.5.7.2) Method 1 = ASCE 7-05, simplified procedure for wind load determination Method 2 = ASCE 7-05, analytical procedure for wind load determination Method 3 = wind tunnel procedure for wind load determination p = design pressure to be used for determination of wind loads on buildings pnet = net design wind pressure on cladding -pnet30 = net design wind pressure for exposure B, at height = 30 ft and Ι = 1.0 from Fig. 6-3 of ASCE 7-05 and Design Aid 4.11.6(c) q = wind velocity pressure qi = velocity pressure for internal pressure determination qz = wind velocity pressure at height Z Rp = component response modification factor (see Design Aid 4.11.10) SDS = design, 5% damped, spectral response acceleration parameter at short periods t = thickness of stone veneer U = required strength to resist factored loads V = basic wind speed (mph) W = effective seismic weight of component and other dead loads W = wind load (ACI) Wp = component operating weight x = direction in plane of cladding y = direction in vertical direction of cladding z = direction perpendicular to the face of cladding (see Example 7.5.1.1) z = height in structure of point of attachment with respect to the base (see Section 7.5.3) λ = adjustment factor for building height and exposure from Design Aid 4.11.6 (c)

Chapter 8 - Component Handling and Erection Bracing a A As A's b d d e 2–14

= dimension defined in section used = area = area of non-prestressed longitudinal tension reinforcement (ACI) = area of longitudinal compression reinforcement (ACI) = dimension defined in section used = distance from extreme compression fiber to centroid of longitudinal tension reinforcement (ACI) (see Fig. 8.4.4) = distance from center of compression block to center of a swivel plate (see Fig. 8.3.11) = eccentricity of force about center of gravity (see Fig. 8.3.11) First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

NOTATIONS

CHAPTER 2

e = eccentricity of horizontal force and reaction of a swivel plate (see Fig. 8.3.11) Eci = modulus of elasticity of concrete at age other than final fb, ft = stress in bottom and top fiber, respectively f 'c = specified compressive strength of concrete (ACI) f 'ci = specified compressive strength of concrete at time of initial prestress (ACI) fr = modulus of rupture of concrete (ACI) F = multiplication factor to account for sling angle (see Fig. 8.3.4) Fy = specified yield strength of structural steel H = horizontal load on a swivel plate I = moment of inertia of section about centroidal axis (with subscripts) (ACI) l = length of span (ACI) l = length of precast unit (see Fig. 8.6.1) Lc = unbraced length of spreader beam M = bending moment (with subscripts) Mx, My, MZ = bending moment in component (see Fig. 8.3.1, 8.3.2, and 8.3.5) P = axial load P, PH, PZ = components of load at handling (see Fig. 8.3.5) R = reaction (with subscripts) Sb, St = section modulus with respect to bottom and top, respectively t = thickness of panel T = tension load on sling V = vertical load on a swivel plate V = shear in a component w = weight per unit length or area W = total load yb, yc, yt = see Fig. 8.3.5 ymax = instantaneous maximum displacement yt = time dependent displacement (see Section 8.4.2) yt = height of roll axis above center of gravity of beam (see Fig. 8.4.1) ∆ = deflection θ = angle of lift lines in longitudinal directions (sling angle) (see Fig. 8.3.4) θ = angle of roll in long slender components (see Fig. 8.4.1) θ = tilt angle of component in storage (see Fig. 8.4.2) λ = modification factor for density of concrete (ACI) λ = amplification factor due to creep and shrinkage (see Fig. 8.4.3) µ = coefficient of curvature friction for unbonded tendons ρ ' = ratio of A's to bd (ACI)

Chapter 9 - Precast and Prestressed Concrete: Materials None used

Chapter 10 - Design for Fire Resistance of Precast and Prestressed Concrete a aθ Aps As b b b d f 'c fps fpsθ fpu fpuθ fy fyθ

= depth of equivalent rectangular compression stress block (ACI) = depth of equivalent rectangular compression stress block at elevated temperature = area of prestressing steel in flexural tension zone (ACI) = area of non-prestressed longitudinal tension reinforcement (ACI) = width of component at center of gravity of strand (see Fig. 10.6.6) = width of compression face of component (ACI) = minimum width of concrete protection over steel columns (see Fig. 10.9.1) = distance from extreme compression fiber to centroid of longitudinal tension reinforcement (ACI) = specified compressive strength of concrete (ACI) = stress in prestressed reinforcement at nominal strength of component (ACI) = stress in uncoated prestressing steel at nominal strength at elevated temperature θ = specified tensile strength of prestressing steel (ACI) = ultimate tensile strength of uncoated prestressing steel at elevated temperature θ = specified yield strength of reinforcement (ACI) = yield strength of reinforcing bars at elevated temperature θ

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NOTATIONS

CHAPTER 2 H l M Mn Mn+θ Mn- θ R Rt, Rte R1, R2, Rn RB RH s t t te u u– w x0, x1, x2 ys ß1 γp φ ρp

= panel thickness = span length (ACI) = applied gravity load moment = nominal flexural strength at section (ACI) = positive nominal moment strength at elevated temperature θ = negative nominal moment strength at elevated temperature θ = fire endurance of component or composite assembly = fire resistance for respective slab thickness = fire endurance of individual courses = rectangular beam = relative humidity = spacing of ribs in ribbed panels = minimum thickness of ribbed panels (see Fig. 10.5.2) = minimum thickness of steel subjected to fire from both sides (see Fig. 10.9.1) = equivalent thickness of ribbed panel = distance from center of gravity of prestressing steel to fire exposed surface = effective u, average of the distances between the centers of the individual strands or bars and the nearest fireexposed surface = uniform total load per unit of length = horizontal distances as shown in Fig. 10.6.10 = distance from centroid of prestressing steel to bottom fiber = factor relating depth of equivalent rectangular compressive stress block to neutral axis depth (ACI) (see Section 5.2.1.1) = factor for type of prestressing tendon (see ACI 318-05 Section 18.0 for values) = strength-reduction factor (ACI) = ratio of prestressed reinforcement

Chapter 11 - Thermal and Acoustical Properties of Precast Concrete a Ap A'p As A's At Btu C CDD50 d Ez f fi fo Hc Hz HDD65 IIC k kcon kin m M R Ra Rbr Rc Rfi, Rfo Rmaterials Rp 2–16

= thermal conductance of an air space, Btu/[(hr)(ft2 of area)(°F)] = area of perfectly insulated region = ratio of Ap / At = area of solid concrete region = ratio of As / At = total area of panel = British thermal unit = thermal conductance for specified thickness, Btu/[(hr)(ft2 of area)(°F average temperature difference) between two surfaces)] = cooling degree-day base 50 °F = clear cover to ends of metal ties in sandwich panels = size of affected zone around solid concrete = film or surface conductance = film or surface conductance of inside and outside surfaces respectively = heat capacity = a measure of sound wave frequency = heating degree-day base 65 °F = impact insulation class = thermal conductivity, Btu/[(hr)(ft2 of area)(°F)] = concrete conductivity = insulation conductivity = width or diameter of metal ties in sandwich panels = permeance, perms = thermal resistance, (°F)(hr)(ft2 of area)/Btu = thermal resistance of air space = thermal resistance of built up roofing = thermal resistance of ceiling materials = thermal resistances of inside and outside surfaces, respectively = sum of thermal resistance of opaque material layers = thermal resistance of perfectly insulated region First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

NOTATIONS Rs RH STC t tcb tcf ti, to tin ts U Uo W α  µ

CHAPTER 2 = thermal resistance of solid concrete region = relative humidity, % = sound transmission class = concrete thickness = thickness of concrete back wythe, in. = thickness of concrete face wythe, in. = indoor and outdoor temperatures respectively, °F = thickness of insulation, in. = dew-point temperature, room air, at design maximum relative humidity, °F = heat transmittance value Btu/[(hr)(ft2 of surface area)(°F temperature difference)] = overall weighted average heat transmission coefficient of a panel = width of Zone A in sandwich panels (see Section 11.1.6) = a parameter to account for insulation conductivity, kin (see Eq. 11-3) = a parameter to account for concrete conductivity, kcon (see Eq. 11-4) = permeability, permeance of a unit thickness, given material, perm-in.

Chapter 12 - Vibration Design of Precast / Prestressed Concrete Floor Systems ao apk B Ed fdr ff fn f 'c g Hz I kr Kw l ls ln w wp wt Wf αi m ∆f ∆g ∆i ∆j

= acceleration limit = peak acceleration = width of floor affected by load (see Section 12.6.2) = dynamic modulus of elasticity = static modulus per ACI 318-05 × 1.2 = driving frequency of equipment, Hertz (cycles per second) = forcing frequency, Hertz (see Table 12.7.2) = natural frequency of fundamental mode of vibration, Hertz (cycles per sec) = specified compressive strength of concrete (ACI) = acceleration due to gravity, 386 in./sec2 = Hertz (cycles per second) = gross moment of inertia = a dimensionless constant for rythmic activity (1.3 for dancing, 1.7 for lively concert or sports event, 2.0 for aerobics) = a constant for response to walking, given in Table 12.6.1 = length of span (ACI); clear projection of cantilever = span length of side span = natural log = uniform load, per unit length = effective distributed weight of participants per unit area = effective total distributed weight per unit area (weight of participants plus weight of floor system) = unfactored dead load plus some (not full ASCE 7-05) live load on the area being studied (see Section 12.6.2) = dynamic coefficient (see Table 12.7.2) = modal damping ratio (fraction of critical damping)(see Table 12.6.1) = s tatic deflection of floor system caused by weight of equipment, including inertial block, at location of equipment = instantaneous deflection of a supporting girder = static deflection of isolator = instantaneous simple-span deflection of a floor panel due to dead load plus actual (not code) live load

Chapter 13 - Tolerances for Precast and Prestressed Concrete None used

Chapter 14 - Specifications and Standard Practices Refer to Chapter 2 of ACI 318-05 and appropriate chapters of this handbook.

Chapter 15 - General Design Information None used

Appendix - Impact of ACI 318-08 on this Handbook See end of Appendix for notation used PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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CHAPTER 2

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PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

  3

CHAPTER 3 PRELIMINARY DESIGN OF PRECAST/ PRESTRESSED CONCRETE STRUCTURES 3.1

General....................................................................................................................................................................... 3-2

3.2

Preliminary Analysis...................................................................................................................................................3-2 3.2.1 Framing Dimensions.................................................................................................................................... 3-2 3.2.2 Span-to-Depth Ratios....................................................................................................................................3-2 3.2.3 Connection Concepts....................................................................................................................................3-3 3.2.4 Gravity and Lateral-Force-Resisting Systems..............................................................................................3-3 3.2.5 Volume-Change Forces.................................................................................................................................3-8

3.3

Explanation of Load Tables.........................................................................................................................................3-8 3.3.1 Safe Superimposed Loads.............................................................................................................................3-8 3.3.2 Limiting Criteria...........................................................................................................................................3-8 3.3.3 Estimated Cambers and Deflections.............................................................................................................3-9 3.3.4 Design Parameters.........................................................................................................................................3-9 3.3.5 Concrete Strength and Density.....................................................................................................................3-9 3.3.6 Prestressing Strands....................................................................................................................................3-10 3.3.7 Prestress Losses...........................................................................................................................................3-10 3.3.8 Strand Placement.........................................................................................................................................3-10 3.3.9 Columns and Load-Bearing Wall Panels....................................................................................................3-10 3.3.10 Piles.............................................................................................................................................................3-10 3.3.11 Stairs..........................……………………………………………………………………………………..3-11 3.3.12 Stadium Risers.............................………………………………………………………………………...3-11

3.4

Double-Tee Load Tables.......................................................................................................................................... 3-12

3.5

Pretopped Double-Tee Load Tables..........................................................................................................................3-24

3.6

Hollow-Core Load Tables.........................................................................................................................................3-31

3.7

Hollow-Core Section Properties................................................................................................................................3-35

3.8

Solid Flat-Slab Load Tables......................................................................................................................................3-41

3.9

Rectangular Beam Load Tables.................................................................................................................................3-44

3.10

L-Beam Load Tables.................................................................................................................................................3-45

3.11

Inverted-Tee Beam Load Tables...............................................................................................................................3-47

3.12

Design Aids...............................................................................................................................................................3-50

3.13

References.............................………………………………………………………………………………………3-63

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3.1

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

General

This chapter presents data on the shapes that are standard in the precast and prestressed concrete industry. Other shapes and modified standard shapes with depth and width variations are also available in many areas of the country. Designers should contact regional precast concrete manufacturers in the geographic area of the proposed project to determine the properties and dimensions of products available. This section, together with the design methods and aids provided in other chapters of this handbook, will enable the designer to prepare safe and economical designs. The text, figures, and photographs in Chapter 1 illustrate the benefits and advantages of using precast concrete building products. This chapter provides guidelines for preliminary designs to make the most effective use of precast concrete products and systems. Maximizing the efficiency of precast concrete products starts early in the design development stage, when column and wall locations can be configured for maximum spans and standard modular dimensions. The assistance of regional precast concrete manufacturers in early design development will optimize the precast concrete system, provide economic solutions, and ensure the availability of the products being considered in the design. Engineering precast concrete, like most other construction materials, requires consideration of various conditions other than the final in-service condition. The designer needs to consider manufacturing, handling, transportation, and erection of the product in addition to analysis and design for in-service loads. It is not uncommon for one of these temporary conditions to be the controlling factor in the design. While precast concrete can be readily utilized in almost any commercial, residential, and highway construction application, building designs can be optimized by following these general principles: 1. Maximize repetitive and standard product dimensions for plan layout and component dimensions. 2. Use simple spans whenever possible. 3. Standardize size and locations of openings in components. 4. Use standard, regionally available component sizes. 5. Minimize the number of different component types and sizes. 6. Minimize the number of different reinforcing patterns in a particular component type. 7. Minimize the number of different types of connections. 8. Specify general connection types so that specific types preferred by regional manufacturers may be used. 9. Consider the size and weight of components to avoid premium costs associated with producing, shipping, and erecting oversize and overweight pieces. 10. Utilize prestressing in precast concrete components when spans are long, the component depth must be minimized, or the greatest degree of crack control is desired. 3–2

11. Avoid component and connection designs that require close tolerances and workmanship that are not easily achievable by normal operations of producers or erectors. 12. Avoid specifying requirements in excess of what is needed for durable concrete mixture designs, allowable stresses, allowable cambers, deflections, and finishes on reinforcing steel, embedded hardware, and connection hardware. 13. Make use of exterior and interior wall panels as loadbearing components and/or shear walls whenever possible. 14. Configure architectural components to maximize form reuse. 15. Contact a regional producer as early as possible during the design development stage of a project for assistance in applying the above principles.

3.2

Preliminary Analysis

The load tables presented in this chapter are meant to be used for preliminary design. The limiting criteria for these tables are based on ACI’s Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05).1 In addition to the provisions of ACI 318-05, Section 14.1 of Chapter 14 of this handbook, “PCI Standard Design Practice,” has generally been followed. Economy results when the building is laid out to take advantage of the principles discussed previously. The primary considerations when developing a preliminary layout are: • framing dimensions; • span-to-depth ratios; • connection concepts; • gravity and lateral-force-resisting system; • mechanisms to accommodate the effects of volume changes. These five considerations are discussed further in the following sections. 3.2.1

Framing Dimensions

When possible, establish building dimensions by combining the modular dimensions of standard component sizes and by establishing bay sizes based on optimum component spans. Generally, optimum framing dimensions will result when the total number of component pieces is minimized. For example, it is often more economical to cast wall panels and columns in multistory units because of the reduced number of pieces required to produce, ship, and erect. When establishing maximum component sizes, the designer should consider the maximum shipping size and weight along with the producer’s and erector’s crane capacity. 3.2.2

Span-to-Depth Ratios

Typical span-to-depth ratios can be used to determine the approximate required depth of a flexural precast, prestressed concrete component. During preliminary analysis, it is helpful to determine beam or slab depths and the additional space required for other construction elements, including heating, ventilating, and air conditioning (HVAC) equipment accom-

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PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES modation, in order to establish the floor-to-floor (or roof) dimensions of a building. As a general guideline, span-to-depth ratios of flexural precast, prestressed concrete components are: Hollow-core floor slabs 30 to 40 Hollow-core roof slabs 40 to 50 Flat slab 20 to 30 Stemmed floor components 25 to 30 Stemmed roof components 30 to 35 Beams and girders 10 to 20 Stairs Design Aid 3.12.10 Precast concrete walls Design Aid 3.12.7 Stadium risers Design Aid 3.12.11 Note that the function of the component must be considered, and when span-to-depth ratios are high, special attention to camber, deflections, and the potential for vibrations must also be considered. These values are intended as guidelines, not limits. The required depth of beams and slabs is influenced by the magnitude and ratio of live load to total load. Where this ratio is high, deeper sections may be needed. For non-prestressed flexural components, span-to-depth ratios given in ACI 31805 Section 9.5.2.1 may be used as a preliminary guide. 3.2.3

Connection Concepts

The types of connections to be used should be determined during the preliminary analysis, as this may have an effect on

CHAPTER 3

the component dimensions, the overall structural behavior as discussed previously, and on the erection procedure. Also, accommodations for the connection of any planned future expansions should be incorporated. Chapter 6 of this publication and other PCI publications2,3 are devoted entirely to connections. If the designer lacks the experience to specify connection types, assistance may be obtained from regional precast concrete plants or specialty engineers. 3.2.4

 ravity and Lateral-ForceG Resisting Systems

A building system should be selected during the preliminary analysis. The gravity and lateral-force-resisting systems may function separately or they may be combined. Bearing-wall construction (Fig. 3.2.1 and 3.2.3) and beamcolumn framing (Fig. 3.2.2 and 3.2.4) have been used successfully for total-precast concrete buildings of various heights. Resistance to lateral forces can be provided by interior shear walls (Fig. 3.2.5), exterior shear walls (Fig. 3.2.6), moment frames (Fig. 3.2.7), or a combination of these. Limitations of the diaphragm may dictate placement of lateral-force-resisting components. Refer to Chapter 4 for lateral-force-resisting-system analysis and design. It is imperative that the foundation system and the vertical and lateral-force-resisting system that it supports are compatible.

Fig. 3.2.1 Single-story bearing-wall construction. Provides economy by eliminating the need for a structural frame at the perimeter. The wall panels can be selected from a variety of standard sections of flat panels and specially formed architectural precast concrete shapes. Any standard precast concrete deck unit can be used for the roof system. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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Fig. 3.2.2 Multistory beam-column construction. Beam-column framing is suitable for both low- and high-rise buildings. Multistory columns with simple-span beams is the preferred structural system. Key: 1. Ledged spandrel beam 2. Hollow-core slab 3. Rectangular beam 4. Non-load-bearing spandrel beam 5. Staircase and landing 6. Landing support beam 7. Column 8. Wall 9. Double-tee 10. Inverted-tee beam 11. Pocketed spandrel beam

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Fig. 3.2.3 Multistory bearing-wall construction. Precast concrete bearing-wall units can be cast in one-story or multistory units. The units may be started at the second-floor level with the first-floor framing consisting of beams and columns to obtain more open space on the first level.

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Fig. 3.2.4 Single-story, beam-column construction. Any of the standard precast concrete beam and column sections shown in this chapter can be used for single-story structures. Selection of the type of beam to be used depends on considerations such as span length, magnitude of superimposed loads, depth of ceiling construction, and desired architectural expression.

Non-load-bearing spandrel beam

Double-tee

Shear wall

Ledged spandrel beam

Column

Inverted-tee beam

Fig. 3.2.5 Interior shear wall system. Lateral forces are transmitted by floor diaphragms to a structural core of precast concrete shear walls.

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Non-load-bearing wall panel (shear wall)

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Double-tee

Load-bearing wall panel (shear wall)

Column

Inverted-tee beam

Fig. 3.2.6 Exterior shear wall system. In general, the exterior shear wall system permits greater design flexibility than an interior shear wall system because it eliminates the need for a structural core. By combining gravity load-bearing function with lateral-force resistance, the exterior shear wall system is, in general, more economical.

Fig. 3.2.7 Moment-resisting frame system. All lateral forces from the floor diaphragms are transferred to a moment-resisting frame that ties beams and columns together with appropriate connections. The need for shear walls may be eliminated. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

Volume-Change Forces

It is important to consider the effects of volume changes on a structure during the selection of the building system. Use and location of expansion joints, as well as the location of stiff lateral-force-resisting elements, can significantly affect how the structure responds to volume-change strains. A component's length tends to change due to thermal change and shortens due to shrinkage and creep. Restraint of this movement creates forces that must be accounted for or connections designed to provide relief of such forces. Refer to Chapter 4 for recommendations on locating expansion joints and lateral-force-resisting elements.

3.3

Explanation of Load Tables

The load tables on the following pages show dimensions, section properties, and load-carrying capacities of the shapes most commonly used throughout the industry. These shapes include double-tees, hollow-core, and solid flat slabs, beams (girders), columns, piles, wall panels, and stadium risers. The dimensions of the shapes shown in the tables may vary slightly among manufacturers. The variations are usually small and the tables in this section can still be used for preliminary design. In most cases, manufacturers will have their own catalogs with load tables and geometric properties for the components they produce. Hollow-core of different depths, core sizes, and shapes are available in the market under various trade names. Cross sections and section properties of proprietary hollowcore are shown on pages 3-35 through 3-40. Load tables on pages 3-31 through 3-34 are developed for non-proprietary hollow-core sections of depths most commonly used in the industry. Load tables for stemmed deck components, flat deck slabs, and beams show the allowable uniform, superimposed service load; estimated camber at the time of erection; and the estimated long-term camber after the time-dependent deformations have stabilized but before the application of superimposed live load. For deck components, except pretopped double-tees, the upper table gives the information for the component with no topping, and the lower table is for the same component with 2 in. of normalweight concrete topping acting compositely with the precast concrete section. Values in the tables assume a uniform 2 in. topping over the full span length, and assume the component is not shored at the time that the topping is placed. It should be noted that many parking structures use topping thicknesses greater than 2 in. (2.5 in. to 3 in.) to satisfy other design considerations as well as code requirements for seismic diaphragms. Two inches has been used to be on the conservative side and accommodate some building types for which 2 in. is applicable.  Safe loads and cambers shown in the tables are based on the dimensions and section properties shown on the page, and will vary for components with different dimensions. For beams, a single load table is used for several sizes. The values shown are based on sections containing the indicated number of prestressing strands. Regional manufactur3–8

ers should be consulted for stressing capabilities, which may be higher or lower than the number of strands shown in the tables. Capacity can be significantly increased with the use of a composite deck slab. 3.3.1

Safe Superimposed Loads

The values for safe, superimposed, uniform service load are based on the capacity of the component as governed by ACI 318-05 limitations on flexural strength and, in the case of flat deck components, shear strength without shear reinforcement. While ACI 318-05 does not limit tensile stresses, the load tables are based on limits of 12 fc' for double-tees and beams and 7.5 fc' for hollow-core and solid flat slabs. A portion of the safe load shown is assumed to be dead load for the purpose of applying load factors and determining cambers and deflections. For untopped deck components, 10 lb/ft2 of the capacity shown is assumed as superimposed dead load, which is typical for roof components and for deck components in a parking structure. For deck components with composite topping, 15 lb/ft2 of the capacity shown is assumed as superimposed dead load, which is typical for floor components. The capacity shown is in addition to the weight of the topping. For beams, 50% of the capacity shown in the load table is assumed as superimposed dead load. Pretopped double-tees are typically used for parking structures where superimposed dead loads are negligible. Thus, the entire load shown in the tables on pages 3–24 through 3–30 can be considered live load. Example: For an untopped normalweight 8DT24/88-S (page 3–12) with a 52 ft span, the capacity shown is 70 lb/ft2. The double-tee can safely carry superimposed service loads of 10 lb/ft2 dead and 60 lb/ft2 live. 3.3.2

Limiting Criteria

The criteria used to determine the safe superimposed load and strand placement is based on ACI 318-05. For component design procedures, see Chapter 5 of this handbook. A summary of the code provisions used in the development of these load tables is as follows: 1.

Capacity is governed by flexural strength:



Load factors: 1.2D + 1.6L

Strength-reduction factor φ varies linearly from 0.75 to 0.9 between the transfer zone and development length. Calculation of moment assumes simple spans with roller supports. If the strands are fully developed (see Section 5.2.3), the critical moment is assumed at midspan in components with straight strands, and at 0.4l(l = span) in products with strands depressed at midspan. (Note: The actual critical point can be determined by analysis, but will seldom vary significantly from 0.4l.) Flexural strength is calculated using strain compatibility as discussed in Chapter 5.

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PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES 2. Capacity governed by serviceability requirements: Flexural stresses immediately after transfer of prestress:

a)  Compression: 0.7 fci'



b)  Tension:



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of ACI 318-05). For double-tees, if Vu is less than φVc and the end region does not have point loads, shear reinforcement may be omitted with a nominal minimum shear reinforcement provided for 5 ft to 10 ft from the end.4 See Section 14.1, 11.5.6.1 PCI Practice for additional information.

(see Section 14.1)

6 fci' (see Section 14.1)

It is common practice to de-bond some, but not all, straight strands for a short distance at the ends of a pretensioned component to reduce transfer stresses. This causes the critical section for prestress transfer to occur farther from the end of the component. Section 18.3.3 of ACI 318-05 defines three serviceability classes based on the behavior of the component under service loads. Class U is assumed to be uncracked, Class T is a transition between uncracked and cracked, and Class C is assumed to be cracked (Table 5.2.2.1). The load tables limit the double-tees and beams to Class U or Class T. Flat deck components are limited to Class U. Thus, the limiting stresses under service loads are:

Note 1: Except as noted for debonded strands as discussed previously, end transfer stresses are calculated at the theoretical point of full transfer (fse /3)db.

c)  Compression:

Note 4: For flat deck components, values to the right of the vertical line have span-to-depth ratios that exceed 50 for untopped components and 40 for topped components. These values exceed suggested maximums for roof and floor components, and a more detailed analysis should be done.

Extreme fiber stress in compression due to prestress plus sustained loads: 0.45 fc' Extreme fiber stress in compression due to prestress plus total load: 0.60 fc'

d)  Tension:



Double-tees and beams: 12 fc'

(Deflections must be determined based on bilinear moment-deflection relationships; see Section 5.8.3.) Hollow-core and flat deck components: 7.5 fc' 3.

Capacity governed by design shear strength:



Load factors: 1.2D + 1.6L



Strength-reduction factor φ = 0.75 In flat deck components, use of shear reinforcement is generally not feasible; thus, the capacity may be limited by the concrete shear strength. In this case, the safe superimposed load is obtained by equating the corresponding factored shear force Vu to the lesser of φVci and φVcw (see Section 11.4.2 of ACI 318-05 and Section 5.3 of this handbook). For stemmed deck components and beams, the design concrete shear strength is not used as a limiting criterion because shear reinforcement can be readily provided in such components. Shear reinforcement design is illustrated in Section 5.3. In stemmed deck components, minimum shear reinforcement is usually required (see Section 11.5.6

Note 2: Release tension is not used as a limiting criterion for beams. Supplemental top reinforcement may be required as described in Section 5.2.2.2. Note 3: For stemmed deck components, the transverse (flange) flexural and shear strengths are not considered limiting criteria. For heavy uniform loads and/or concentrated loads, these considerations may limit the capacity or require additional transverse reinforcement.

3.3.3

Estimated Cambers and Deflections

Deflections can be calculated using procedures shown in Section 5.8.4 of this handbook and Section 9.5 of ACI 318-05. The estimated cambers shown in this handbook are calculated using multipliers given in Section 5.8.4. These values are estimates and should not be used as absolute values. Attachment of non-structural elements, such as partitions, folding doors, and architectural decoration to prestressed components subject to camber variations should be designed with adequate allowance for these variations. Calculation of topping quantities should also recognize that the values can vary with camber. When choosing components, designs resulting in negative camber under dead load are not recommended. 3.3.4

Design Parameters

The design of prestressed concrete is dependent on many variables. These include concrete strength at release and at 28 days, density of concrete, strand grade and strength, profile and placement of strand, jacking tension, and other factors. The load tables in this handbook are based on commonly used values; somewhat higher allowable loads or longer spans may be achieved by selecting other appropriate sets of conditions. However, in these cases, consultation with regional precast concrete producers is recommended. 3.3.5

Concrete Strength and Density

Twenty-eight-day cylinder strength for precast concrete is assumed to be 5000 psi unless otherwise indicated. Tables for units with composite topping are based on the topping

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concrete being normalweight concrete with a strength of 3000 psi; however, 4000 psi is often recommended for conditions exposed to weather for improved durability. Concrete strength at time of strand tension release is 3500 psi unless the value is shown in the shaded area in the load table, indicating that a cylinder strength greater than 3500 psi is required. No values are shown when the required release strength exceeds 4500 psi. Higher release strengths may be used, but consult with regional precast concrete manufacturers. The concrete strengths used in the load tables are not intended to be limitations or recommendations for actual use. Some precast concrete manufacturers may choose to use higher or lower concrete strengths or aggregates with differing modulus of elasticity, resulting in slightly different load capacities and deflections/camber. For low levels of prestress, the concrete release strength is usually governed by handling stresses. Concrete density is assumed to be 150 lb/ft3 for normalweight and 115 lb/ft3 for lightweight. 3.3.6

Prestress Losses

Prestress losses were calculated in accordance with the recommendations given in Reference 5. This procedure includes consideration of initial stress level (0.7fpu or higher), type of strand, exposure conditions, and type of construction. A lower limit of 30,000 psi for low-relaxation strands was used. This lower limit is reasonable; however, some designers may choose another value based on their experience. Additional information on prestress losses is given in Section 5.7. 3.3.8

Strand Placement

Strand quantity, size, and profile are shown in the load tables under the column headed “strand pattern,” (that is, 88-S). The first digit indicates the total number of strands in the unit, the second digit is the strand diameter in 1/16 in., and the S indicates that the strands are straight. D1 indicates that the strands are depressed at one point at midspan. Some precast concrete producers choose to depress the strand at two points (D2), which provides a somewhat higher flexural capacity. For double-tees and rectangular beams, the distance from 3–10

3.3.9

Prestressing Strands

Prestressing strands are available in diameters from 3/8 in. to 0.6 in. diameter, grades 250 ksi or 270 ksi. While it is not yet recognized by ASTM International, and, therefore, is not included in this handbook, 300 ksi strand may also be available. Many manufacturers also use 1/2-in.-diameter special strand that has a slightly larger area than standard 1 /2-in.-diameter regular strand. The load tables are calculated assuming low-relaxation strand. Stress in the strand at transfer of prestress has been assumed at 90% of the initial stress. In developing the load tables, the stress-strain behavior of the strand was modeled with the curves given in Design Aid 15.2.4. Other stress-strain models are available and could be used in place of the curves used in this handbook; as such, they would be expected to produce allowable loads that differ slightly from those shown. 3.3.7

the centroid of the strand group to the bottom of the component ys at the ends and midspan are shown in the load tables. For straight strand patterns, only one value is shown because the location is uniform from end to end. Strands have been placed so that the stresses at the theoretical transfer point will not exceed those specified previously. For flat deck components, the load table values are based on prestressing strand centered 11/2 in. from the bottom of the slab. Variation in strand placement, typically as low as 7/8 in. to as high as 21/8 in. from the bottom, will change the values shown. The higher strand placements provide improved fire-resistance ratings (Chapter 10 of this handbook provides additional information on fire resistance). The lower strand placement may require higher release strengths or top tension reinforcement at the ends of the component. The designer should contact the regional manufacturer of flat, prestressed concrete deck components for available and recommended strand placement locations.  olumns and Load-Bearing Wall C Panels

Interaction curves for selected precast, prestressed concrete columns; precast concrete reinforced columns; and various types of commonly used wall panels are provided on pages 3-50 to 3-57. These interaction curves are based on strength design for short columns. Appropriate load factors must be applied to the service loads and moments before researching values in the charts. The effect of slenderness must be considered as described in Section 5.9.3. For prestressed columns and wall panels, curves are shown for both partially developed strands, usually appropriate for end-moment capacity, and fully developed strands, usually appropriate for all conditions away from the ends (see Section 5.9). The columns and wall panels that use reinforcing bars assume full development of the reinforcing bars. The curves are terminated at a value of Pu = 0.80Po, the maximum allowable load for tied columns under ACI 318-05. Most of the wall panel curves show the lower portion of the curve only (flexure controlling). Actual design loads will rarely exceed the values shown. The curves for double-tee wall panels are for bending in the direction that causes tension in the stems resulting from both gravity loads and lateral loads. The curves for hollowcore wall panels are based on a generic section as shown, which may result in small variations for sections commonly marketed for wall-panel use. 3.3.10

Piles6

Allowable concentric service loads on prestressed concrete piles, based on the structural capacity of the pile alone, are shown in Design Aid 3.12.8. The ability of the soil to carry these loads must be evaluated separately. Values for concrete strengths up to 10,000 psi are shown. The availability of these concrete strengths should be checked with regional manufacturers. The design of prestressed concrete piles is discussed in Section 5.9.7.

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Section properties and allowable service load bending moments for prestressed concrete sheet pile units are shown in Design Aid 3.12.9. These units are available in some areas for use in earth-retaining structures. 3.3.11

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Stairs

Precast concrete stair units can be produced in many configurations and sizes to provide a variety of riser, tread, and landing geometry. However, shapes that fit existing standard formwork will be more economical than stairs that require new custom forms. Standard forms vary among producers, but most producers can reconfigure typical stairs to match their existing formwork. Design Aid 3.12.10 provides maximum recommended spans for various thicknesses for those commonly used. 3.3.12

Stadium Risers

Due to their asymmetrical shape, stadium riser units behave differently from typical rectangular beams as described in Section 5.2.5. Precast concrete risers are typically produced in single, double, or triple units (Design Aid 3.12.11). Allowable spans are provided for each type of unit with or without stems. Design Aid 3.12.11 is based on a live load of 100 lb/ft2, which is the specified design load for stadium and arena bleachers without fixed seating. For stadiums with fixed seats fastened to the floor, the International Building Code7 specifies a live load of 60 lb/ft2, which will increase the maximum allowable spans indicated in Design Aid 3.12.11. Longer spans can also be achieved with modified shapes, higher concrete strengths, or special reinforcing. These longer spans may require a vibration analysis to ensure appropriate geometry (see Chapter 12). A typical modified shape incorporates a drop riser or stem that increases the riser depth below the underside of the tread. Regional producers should be contacted to determine production capabilities and available forms.

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3.4 Double-Tee Load Tables Strand Pattern Designation

8'-0" × 24" Normalweight Concrete

Number of strand (12) S = straight  D = depressed

128- D1

Section Properties

No Topping



A = 401 I = 20,985 yb = 17.15 yt = 6.85 Sb = 1224 St = 3064 wt = 418 DL = 52 V/S = 1.41

8'-0" Number of depression points Diameter of strand in 16ths

2'-0"

2"

2'-0"

4'-0" 53 4"

2"

Safe loads shown include dead load of 10 lb/ft for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load. 2

24"

2 in. Topping

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

—

27,720 19.27 6.73 1439 4119 618 77

in.4 in. in. in.3 in.3 lb/ft lb/ft2

33 4"

Key 186 – Safe superimposed service load, lb/ft2 0.7 – Estimated camber at erection, in. 0.9 – Estimated long-time camber, in.

fc' = 5000 psi fpu = 270,000 psi

/2-in.-diameter regular strand

1

Check with regional producers for availability.

8DT24 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern

ys (end) ys (center) in.

68-S

4.00 4.00

88-S

5.00 5.00

108-S

6.00 6.00

128-S

7.00 7.00

128-D1

11.67 3.25

148-D1

12.86 3.50

No Topping Span, ft

32

34

36

38

40

42

44

46

48

50

52

186 161 140 122 106 93 81 71 62 55 48 0.7 0.8 0.8 0.9 0.9 1.0 1.0 1.0 1.0 1.0 0.9 0.9 1.0 1.1 1.1 1.1 1.1 1.1 1.1 1.0 0.9 0.8 185 162 143 126 112 99 88 78 70 1.1 1.2 1.3 1.3 1.4 1.4 1.5 1.5 1.5 1.4 1.5 1.6 1.6 1.7 1.7 1.7 1.7 1.6 197 174 155 138 123 110 98 88 1.4 1.5 1.6 1.7 1.7 1.8 1.9 1.9 1.8 1.9 2.0 2.1 2.1 2.1 2.1 2.1 159 142 128 114 101 1.8 1.9 2.0 2.1 2.1 2.3 2.4 2.4 2.5 2.5

54

56

58

42 36 0.8 0.7 0.6 0.4 62 55 1.5 1.4 1.5 1.4 79 71 1.9 1.9 2.1 2.0 90 81 2.2 2.2 2.4 2.4 114 103 2.5 2.6 2.9 2.9

60

62

64

66

68

70

72

74

76

31 27 0.6 0.5 0.1 –0.2 49 43 1.4 1.3 1.2 0.9 64 57 1.9 1.9 1.9 1.8 73 66 2.2 2.2 2.3 2.2 92 83 2.6 2.7 2.9 2.8

38 1.1 0.6 51 1.8 1.6 59 2.2 2.1 74 2.7 2.6

33 29 1.0 0.8 0.3 –0.2 45 39 1.7 1.5 1.3 0.9 53 47 2.1 2.0 1.8 1.6 66 59 2.6 2.6 2.4 2.2 71 3.1 3.0

34 1.3 0.5 42 1.9 1.2 53 2.5 1.8 64 3.1 2.7

29 1.1 0.0 37 1.7 0.8 48 2.3 1.5 58 3.0 2.4

32 27 1.5 1.2 0.3 –0.3 43 39 2.1 1.9 1.1 0.6 52 46 2.9 2.7 2.0 1.6

35 1.6 0.0 42 2.5 1.1

8DT24 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 48-S

ys (end) ys (center) in. 3.00 3.00

68-S

4.00 4.00

88-S

5.00 5.00

108-S

6.00 6.00

128-S

7.00 7.00

128-D1

11.67 3.25

2 in. Normalweight Topping Span, ft

28

30

32

34

36

38

40

169 0.4 0.4

141 0.4 0.4

117 0.5 0.4 189 0.7 0.7

97 0.5 0.4 161 0.8 0.8

81 0.5 0.3 138 0.8 0.8 188 1.1 1.1

67 0.5 0.3 118 0.9 0.7 163 1.1 1.2

55 0.5 0.2 101 0.9 0.7 142 1.3 1.1 176 1.5 1.4

42

46

48

45 36 29 0.5 0.5 0.4 0.0 –0.1 –0.3 87 74 64 1.0 1.0 1.0 0.6 0.6 0.4 124 108 94 1.3 1.4 1.4 1.1 1.1 1.0 155 136 120 1.6 1.7 1.7 1.4 1.4 1.4 160 140 1.8 1.9 1.6 1.6

44

54 1.0 0.2 82 1.5 0.9 104 1.8 1.3 121 2.0 1.6

50

52

54

56

58

60

62

64

66

68

70

45 38 30 1.0 0.9 0.8 0.0 –0.3 –0.6 71 62 52 42 33 1.5 1.5 1.5 1.4 1.4 0.7 0.5 0.3 –0.1 –0.5 90 77 66 56 47 39 31 1.9 1.9 1.9 1.9 1.9 1.9 1.8 1.2 1.0 0.8 0.6 0.3 –0.1 –0.6 104 90 77 67 57 48 41 33 27 2.1 2.1 2.2 2.2 2.2 2.2 2.2 2.1 2.0 1.5 1.3 1.1 0.9 0.6 0.3 –0.1 –0.6 –1.1 105 91 79 68 58 49 40 34 28 2.5 2.6 2.6 2.7 2.7 2.6 2.6 2.5 2.3 1.6 1.4 1.1 0.8 0.4 0.0 –0.6 –1.2 –1.8

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3-8 through 3-11 for explanation. Shaded values require release strengths higher than 3500 psi.

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3.4 Double-Tee Load Tables (cont.) Strand Pattern Designation

8'-0" × 24" Lightweight Concrete

Number of strand (12) S = straight  D = depressed

128- D1

No Topping



2'-0"

2"

2'-0"

4'-0" 53 4"

Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

2 in. Topping

A = 401 I = 20,985 yb = 17.15 yt = 6.85 Sb = 1224 St = 3064 wt = 320 DL = 40 V/S = 1.41

8'-0" Number of depression points Diameter of strand in 16ths

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Section Properties

2" 24"

33 4"

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

—

29,857 19.94 6.06 1497 4927 520 65

in.4 in. in. in.3 in.3 lb/ft lb/ft2

Key 196 – Safe superimposed service load, lb/ft2 1.2 – Estimated camber at erection, in. 1.5 – Estimated long-time camber, in.

fc' = 5000 psi fpu = 270,000 psi

/2-in.-diameter regular strand

1

Check with regional producers for availability.

8LDT24 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern

ys(end). ys(center) in.

68-S

4.00 4.00

88-S

5.00 5.00

108-S

6.00 6.00

128-S

7.00 7.00

128-D1

11.67 3.25

148-D1

12.86 3.50

No Topping Span, ft

32

34

36

196 170 149 1.2 1.3 1.4 1.5 1.6 1.7 194 1.8 2.3

38

40

42

44

46

48

50

52

54

56

58

60

62

64

66

68

70

72

131 115 102 90 80 72 64 1.5 1.6 1.6 1.7 1.8 1.8 1.9 1.8 1.9 1.9 2.0 2.0 2.0 2.0 171 152 135 121 108 97 87 1.9 2.1 2.2 2.3 2.5 2.6 2.7 2.4 2.6 2.7 2.8 2.9 2.9 3.0 183 164 147 132 119 107 2.4 2.5 2.7 2.9 3.0 3.2 3.0 3.2 3.4 3.5 3.6 3.7

57 1.9 1.9 79 2.7 3.0 97 3.3 3.8 110 3.7 4.3

51 1.9 1.8 71 2.8 2.9 87 3.4 3.8 99 3.8 4.4

45 1.9 1.7 64 2.8 2.9 78 3.5 3.8 89 3.9 4.4

40 1.8 1.5 58 2.9 2.8 70 3.6 3.7 80 4.0 4.4

36 1.7 1.2 52 2.9 2.6 64 3.6 3.6 72 4.1 4.3

32 1.6 0.8 47 2.8 2.5 58 3.7 3.5 65 4.2 4.2 83 4.8 5.1

28 1.4 0.4 43 38 2.8 2.6 2.2 1.9 53 48 3.7 3.6 3.3 3.1 59 53 4.2 4.2 4.0 3.8 76 69 4.9 5.0 5.0 4.9

74

35 2.5 1.5 44 3.6 2.8 49 4.2 3.6 62 5.1 4.7

31 2.3 0.9 40 3.5 2.5 44 4.1 3.3 57 5.1 4.4

28 2.0 0.3 36 33 3.3 3.1 2.0 1.5 40 37 4.0 3.9 2.9 2.4 51 46 5.1 5.0 4.0 3.6

76

78

80

29 2.9 0.8 34 3.7 1.9 42 4.9 3.0 51 5.9 4.6

26 2.5 0.0 31 3.5 1.3 38 4.6 2.3 46 5.8 4.1

28 3.2 0.6 34 4.3 1.4 42 5.7 3.4

8LDT24 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern

ys(end) ys(center) in.

48-S

3.00 3.00

68-S

4.00 4.00

88-S

5.00 5.00

108-S

6.00 6.00

128-S

7.00 7.00

128-D1

11.67 3.25

2 in. Normalweight Topping Span, ft

28

30

32

34

36

38

40

42

44

46

48

50

178 150 126 107 90 76 64 54 45 38 31 25 0.6 0.7 0.8 0.8 0.9 0.9 1.0 1.0 1.0 1.0 1.0 0.9 0.6 0.7 0.7 0.7 0.6 0.6 0.5 0.4 0.2 0.0 –0.2 –0.6 198 170 147 127 111 96 84 73 63 55 1.2 1.3 1.4 1.5 1.6 1.7 1.7 1.8 1.9 1.9 1.2 1.2 1.2 1.3 1.2 1.2 1.1 1.0 0.9 0.7 197 172 151 133 117 103 91 80 1.8 1.9 2.1 2.2 2.3 2.5 2.6 2.7 1.8 1.8 1.9 1.9 1.9 1.8 1.7 1.6 186 164 146 129 115 102 2.4 2.5 2.7 2.9 3.0 3.2 2.3 2.3 2.4 2.4 2.3 2.2

52

47 1.9 0.4 71 2.7 1.4 89 3.3 2.1 104 3.7 2.6

54

56

58

40 34 29 1.9 1.9 1.8 0.1 –0.3 –0.8 61 52 45 2.8 2.8 2.9 1.1 0.8 0.5 76 65 56 3.4 3.5 3.6 1.9 1.6 1.3 90 78 68 3.8 3.9 4.0 2.4 2.2 1.9

60

62

64

66

68

70

72

74

37 31 25 2.9 2.8 2.8 0.0 –0.5 –1.1 48 41 34 29 3.6 3.7 3.7 3.7 0.9 0.5 –0.1 –0.7 58 49 42 35 30 4.1 4.2 4.2 4.2 4.2 1.5 1.1 0.5 0.0 –0.7 71 62 53 46 39 32 26 4.8 4.9 5.0 5.1 5.1 5.1 5.0 1.9 1.5 0.9 0.3 –0.5 –1.3 –2.3

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–13

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

  3

3.4 Double-Tee Load Tables (cont.) Strand Pattern Designation

8'-0" in. × 32" Normalweight Concrete

Number of strand (18) S = straight  D = depressed



A = 567 I = 55,464 yb = 21.21 yt = 10.79 Sb = 2615 St = 5140 wt = 591 DL = 74 V/S = 1.79

188- D1

Section Properties

No Topping

Number of depression points Diameter of strand in 16ths

Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

2 in. Topping

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

—

71,886 23.66 10.34 3038 6952 791 99

in.4 in. in. in.3 in.3 lb/ft lb/ft2

Key 192 – Safe superimposed service load, lb/ft2 1.1 – Estimated camber at erection, in. 1.4 – Estimated long-time camber, in.

fc' = 5000 psi fpu = 270,000 psi

/2-in.-diameter regular strand

1

Check with regional producers for availability.

8DT32 Table of safe superimposed service load, lb/ft2, and cambers, in. y (end)

s Strand ys(center) pattern in.

128-S

7.00 7.00

148-S

8.00 8.00

168-S

9.00 9.00

188-S

10.00 10.00

188-D1

14.39 4.00

208-D1

15.50 4.25

No Topping

Span, ft 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 192 173 156 141 1.1 1.2 1.2 1.2 1.4 1.5 1.5 1.5 199 180 163 1.3 1.4 1.4 1.7 1.7 1.7 182 1.5 1.9 192 1.6 2.0

127 1.2 1.5 148 1.4 1.7 165 1.6 1.9 175 1.6 2.0

115 1.2 1.4 134 1.4 1.7 151 1.6 1.9 159 1.7 2.0

104 1.2 1.4 122 1.4 1.7 137 1.6 1.9 144 1.7 2.0 193 2.3 2.9

94 1.2 1.3 111 1.4 1.6 124 1.6 1.8 131 1.7 2.0 176 2.4 2.9

85 1.1 1.2 101 1.4 1.5 113 1.6 1.8 120 1.7 1.9 160 2.4 2.9

77 1.1 1.0 92 1.4 1.4 103 1.6 1.7 109 1.7 1.8 146 2.5 2.9 162 2.7 3.2

69 1.0 0.8 83 1.3 1.3 93 1.5 1.6 99 1.6 1.7 134 2.5 2.8 148 2.7 3.2

62 0.9 0.6 75 1.2 1.1 85 1.4 1.4 90 1.6 1.6 122 2.5 2.8 136 2.8 3.2

56 0.7 0.4 68 1.1 0.8 76 1.3 1.2 82 1.5 1.4 111 2.5 2.7 124 2.8 3.1

50 44 38 33 28 0.6 0.4 0.2 0.0 –0.3 0.1 –0.3 –0.7 –1.1 –1.6 60 53 47 41 35 30 25 1.0 0.8 0.6 0.4 0.1 –0.1 –0.5 0.6 0.2 –0.1 –0.5 –1.0 –1.5 –2.1 68 61 54 48 42 36 31 26 1.2 1.1 0.9 0.7 0.5 0.2 –0.1 –0.4 0.9 0.6 0.3 –0.1 –0.5 –1.0 –1.6 –2.2 74 67 60 53 47 41 36 31 26 1.4 1.2 1.1 0.9 0.7 0.4 0.1 –0.2 –0.6 1.2 0.9 0.6 0.2 –0.3 –0.7 –1.3 –1.9 –2.6 101 92 84 77 71 65 59 54 50 45 40 35 2.4 2.4 2.3 2.1 2.0 1.8 1.6 1.4 1.1 0.8 0.4 0.0 2.5 2.3 2.0 1.8 1.5 1.1 0.7 0.3 –0.2 –0.8 –1.5 -2.2 114 104 95 87 79 72 66 61 56 51 47 43 2.8 2.7 2.7 2.6 2.5 2.3 2.1 1.9 1.7 1.4 1.1 0.7 3.0 2.8 2.6 2.4 2.1 1.7 1.3 0.9 0.5 –0.1 –0.6 –1.3

31 -0.4 -3.1 38 0.3 -2.0

27 -0.9 -4.0 34 30 26 -0.2 -0.7 -1.3 -2.9 -3.9 -4.9

8DT32 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. y (end)

s Strand y (center) pattern s in.

128-S

7.00 7.00

148-S

7.00 7.00

168-S

8.00 8.00

188-S

9.00 9.00

188-D1

14.39 4.00

208-D1

15.50 4.25

2 in. Normalweight Topping Span, ft

52

54

56

58

60

62

270 240 214 190 170 152 1.0 1.0 1.1 1.1 1.2 1.2 1.0 1.1 1.1 1.1 1.0 1.0 289 259 232 208 187 1.3 1.4 1.4 1.5 1.5 1.4 1.4 1.4 1.4 1.4 288 259 233 210 1.4 1.5 1.6 1.7 1.5 1.6 1.6 1.6 282 254 230 1.6 1.6 1.7 1.6 1.7 1.7

42

44

46

48

50

136 1.2 0.9 168 1.6 1.4 190 1.7 1.6 208 1.8 1.7

121 1.2 0.9 152 1.6 1.3 171 1.8 1.5 186 1.8 1.6 233 2.2 2.1

108 1.2 0.8 137 1.7 1.3 155 1.8 1.5 166 1.9 1.6 213 2.2 2.0

97 1.2 0.6 123 1.7 1.2 138 1.8 1.4 148 1.9 1.5 194 2.3 2.0

86 1.2 0.4 111 1.7 1.0 124 1.9 1.3 133 2.0 1.4 175 2.4 1.9

64

66

68

70

72

74

76

78

80

82

84

86

88

90

92

76 67 56 47 38 30 1.1 1.1 1.0 0.9 0.7 0.6 0.2 0.0 –0.3 –0.7 –1.1 –1.5 100 88 77 66 57 47 39 31 1.7 1.6 1.6 1.5 1.4 1.3 1.2 1.0 0.9 0.7 0.5 0.2 –0.2 –0.6 –1.0 –1.5 110 98 87 76 67 57 49 40 33 25 1.9 1.9 1.8 1.8 1.7 1.6 1.5 1.3 1.2 1.0 1.1 1.0 0.7 0.5 0.2 –0.2 –0.6 –1.1 –1.6 –2.2 119 106 94 83 74 65 56 48 40 32 25 2.0 2.0 2.0 1.9 1.9 1.8 1.7 1.6 1.4 1.2 1.0 1.3 1.1 0.9 0.7 0.4 0.1 –0.3 –0.8 –1.3 –1.9 –2.5 157 141 126 113 100 89 78 69 61 54 47 41 35 30 2.4 2.5 2.5 2.5 2.5 2.4 2.4 2.3 2.2 2.0 1.8 1.6 1.4 1.1 1.8 1.7 1.5 1.3 1.1 0.8 0.4 0.0 –0.5 –1.0 –1.5 –2.1 –2.8 –3.6 159 143 129 115 103 92 81 72 63 55 48 42 36 31 2.7 2.7 2.8 2.8 2.8 2.7 2.7 2.6 2.5 2.3 2.1 1.9 1.7 1.4 2.0 1.9 1.7 1.5 1.2 0.9 0.5 0.1 –0.4 –1.0 –1.6 –2.2 –3.0 –3.8

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

3–14

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.4 Double-Tee Load Tables (cont.) Strand Pattern Designation

8'-0" in. × 32" Lightweight Concrete

Number of strand (18) S = straight  D = depressed

No Topping



2 in. Topping

A = 567 I = 55,464 yb = 21.21 yt = 10.79 Sb = 2615 St = 5140 wt = 453 DL = 57 V/S = 1.79

188- D1

  3

Section Properties

Number of depression points Diameter of strand in 16ths

Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

—

77,675 24.52 9.48 3167 8195 653 82

in.4 in. in. in.3 in.3 lb/ft lb/ft2

Key 186 – Safe superimposed service load, lb/ft2 2.0 – Estimated camber at erection, in. 2.4 – Estimated long-time camber, in.

fc' = 5000 psi fpu = 270,000 psi

/2-in.-diameter regular strand

1

Check with regional producers for availability.

8LDT32 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 128-S 148-S

ys(end) ys(center) 50 52 54 in. 186 169 154 7.00 2.0 2.1 2.1 7.00 2.4 2.5 2.6 193 176 8.00 2.3 2.4 8.00 2.9 2.9

168-S

9.00 9.00

188-S

10.00 10.00

188-D1

14.39 4.00

208-D1

15.50 4.25

No Topping Span, ft

56

58

60

62

64

66

68

70

72

74

76

78

80

140 2.2 2.6 161 2.5 3.0 192 175 2.6 2.7 3.2 3.3 185 2.8 3.4

128 2.3 2.6 147 2.6 3.0 159 2.8 3.3 168 2.9 3.5

117 2.3 2.6 134 2.6 3.0 145 2.9 3.4 154 3.0 3.5

107 2.3 2.6 123 2.7 3.1 132 3.0 3.4 140 3.1 3.6

98 2.4 2.6 113 2.7 3.0 120 3.0 3.4 128 3.1 3.6 172 4.1 5.0

90 2.4 2.5 104 2.8 3.0 111 3.0 3.3 117 3.2 3.5 158 4.3 5.1

82 2.3 2.4 95 2.8 2.9 102 3.1 3.3 107 3.2 3.5 146 4.4 5.2

75 2.3 2.3 87 2.7 2.8 94 3.1 3.2 99 3.2 3.4 134 4.5 5.2

69 2.2 2.1 80 2.7 2.7 86 3.0 3.1 91 3.2 3.3 124 4.6 5.2

63 2.1 1.9 74 2.7 2.5 79 3.0 2.9 84 3.2 3.1 114 4.7 5.2

58 2.0 1.6 68 2.6 2.3 73 2.9 2.7 77 3.2 2.9 105 4.8 5.1 117 5.2 5.7

53 1.9 1.3 62 2.5 2.0 67 2.8 2.5 71 3.1 2.7 97 4.8 5.0 108 5.2 5.7

48 1.7 0.9 57 2.3 1.7 62 2.7 2.2 65 3.0 2.4 90 4.8 4.8 100 5.3 5.5

82

94

96

44 40 36 31 28 1.5 1.2 0.9 0.6 0.2 0.4 –0.2 –0.8 –1.4 –2.2 52 47 43 38 34 30 26 2.1 1.9 1.7 1.4 1.0 0.6 0.2 1.3 0.8 0.3 –0.4 –1.1 –1.8 –2.7 57 52 48 44 39 35 31 2.6 2.4 2.2 1.9 1.6 1.2 0.8 1.8 1.4 1.0 0.4 –0.2 –1.0 –1.8 60 55 51 47 43 39 35 2.8 2.7 2.5 2.2 1.9 1.6 1.2 2.1 1.7 1.2 0.7 0.2 –0.5 –1.3 83 76 70 64 59 54 49 4.8 4.7 4.6 4.4 4.2 4.0 3.7 4.5 4.2 3.8 3.4 2.8 2.2 1.5 92 85 79 73 67 62 57 5.3 5.3 5.3 5.2 5.1 4.9 4.7 5.3 5.1 4.8 4.5 4.0 3.5 2.9

84

86

88

90

92

28 0.4 -2.7 31 0.9 -2.1 46 3.4 0.9 52 4.4 2.2

98 100 102 104

28 0.8 -3.1 43 3.0 0.2 48 4.0 1.4

40 2.7 -0.6 43 3.7 0.5

37 2.2 -1.4 40 3.3 -0.3

34 1.7 -2.3 37 2.8 -1.2

8LDT32 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 128-S

ys(end) ys(center) in. 7.00 7.00

148-S

8.00 8.00

168-S

9.00 9.00

188-S

10.00 10.00

188-D1

14.39 4.00

208-D1

15.50 4.25

2 in. Normalweight Topping Span, ft

56

58

183 165 149 134 2.0 2.1 2.1 2.2 1.8 1.8 1.7 1.7 190 172 156 2.3 2.4 2.5 2.1 2.1 2.0 192 174 2.6 2.7 2.3 2.3 186 2.8 2.4

50

52

54

121 2.3 1.6 141 2.6 2.0 156 2.8 2.3 167 2.9 2.4

60

62

64

66

68

70

72

74

76

78

80

82

84

86

88

90

92

94

96

98

109 99 89 81 73 64 56 49 42 35 29 2.3 2.3 2.4 2.4 2.3 2.3 2.2 2.2 2.0 1.9 1.7 1.5 1.3 1.1 0.9 0.6 0.3 –0.1 –0.6 –1.1 –1.7 –2.4 128 115 103 92 82 73 65 57 50 44 38 32 26 2.6 2.7 2.7 2.8 2.8 2.8 2.7 2.7 2.6 2.5 2.3 2.1 1.9 1.9 1.7 1.6 1.4 1.1 0.8 0.4 0.0 –0.5 –1.0 –1.6 –2.3 –3.1 139 124 112 100 90 80 72 64 56 50 43 38 32 27 2.9 3.0 3.0 3.0 3.1 3.1 3.1 3.0 2.9 2.9 2.7 2.6 2.4 2.2 2.2 2.0 1.9 1.7 1.4 1.2 0.8 0.4 0.0 –0.6 –1.1 –1.8 –2.5 –3.4 149 134 120 107 96 86 77 69 61 54 48 42 36 31 26 3.0 3.1 3.1 3.2 3.2 3.2 3.2 3.2 3.2 3.1 3.0 2.8 2.7 2.5 2.2 2.3 2.2 2.0 1.8 1.6 1.3 1.0 0.6 0.2 –0.3 –0.9 –1.5 –2.3 –3.1 –4.0 171 155 140 127 115 104 93 84 75 67 59 52 46 39 34 29 25 4.1 4.3 4.4 4.5 4.6 4.7 4.8 4.8 4.8 4.8 4.7 4.6 4.4 4.2 4.0 3.7 3.4 3.4 3.3 3.2 3.0 2.8 2.5 2.2 1.8 1.3 0.8 0.1 –0.6 –1.5 –2.4 –3.5 –4.5 –5.6 107 96 87 78 70 62 55 49 43 37 31 26 5.2 5.2 5.3 5.3 5.3 5.3 5.2 5.1 5.9 4.7 4.4 4.0 2.8 2.4 2.0 1.5 0.9 0.3 –0.4 –1.3 –2.2 –3.3 –4.5 –5.8

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–15

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

  3

3.4 Double-Tee Load Tables (cont.) Strand Pattern Designation

10'-0" × 24" Normalweight Concrete

Number of strand (12) S = straight  D = depressed

Section Properties

No Topping



A = 449 I = 22,469 yb = 17.77 yt = 6.23 Sb = 1264 St = 3607 wt = 468 DL = 47 V/S = 1.35

128- D1

Number of depression points Diameter of strand in 16ths

Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

2 in. Topping

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

—

29,395 19.89 6.11 1478 4812 718 72

in.4 in. in. in.3 in.3 lb/ft lb/ft2

Key 171 – Safe superimposed service load, lb/ft2 0.6 – Estimated camber at erection, in. 0.8 – Estimated long-time camber, in.

fc' = 5000 psi fpu = 270,000 psi

/2-in.-diameter regular strand

1

Check with regional producers for availability.

10DT24 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 68-S

ys(end) ys(center) in. 4.00 4.00

88-S

5.00 5.00

108-S

6.00 6.00

128-S

7.00 7.00

128-D1

11.67 3.25

148-D1

12.86 3.50

No Topping Span, ft

30

32

34

36

38

40

42

44

46

48

50

52

54

56

58

60

62

64

66

68

70

72

171 146 126 109 94 82 71 62 54 47 0.6 0.7 0.7 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.8 0.9 0.9 1.0 1.0 1.0 1.0 1.0 0.9 0.8 193 167 146 127 112 98 87 77 68 0.9 1.0 1.1 1.1 1.2 1.3 1.3 1.4 1.4 1.2 1.3 1.4 1.4 1.5 1.5 1.5 1.5 1.5 177 156 137 121 108 96 85 1.2 1.3 1.4 1.5 1.6 1.7 1.7 1.6 1.7 1.8 1.9 1.9 2.0 2.0 159 141 125 112 100 1.6 1.7 1.8 1.9 1.9 2.0 2.1 2.2 2.3 2.3

41 0.8 0.7 60 1.4 1.5 76 1.8 2.0 90 2.0 2.3

35 0.8 0.5 53 1.4 1.4 68 1.8 1.9 80 2.0 2.3 100 2.3 2.7

30 0.7 0.3 47 1.3 1.2 61 1.8 1.9 72 2.1 2.2 90 2.4 2.7

26 0.6 0.0 41 1.3 1.0 54 1.8 1.8 64 2.1 2.2 80 2.5 2.6

74

76

78

36 1.2 0.8 48 1.8 1.6 58 2.1 2.1 72 2.5 2.5

32 1.0 0.5 43 1.7 1.4 52 2.1 1.9 64 2.5 2.4

27 0.9 0.1 38 1.6 1.1 46 2.0 1.7 57 2.5 2.2 68 2.9 2.9

33 1.4 0.7 41 1.9 1.4 51 2.4 1.9 61 2.9 2.7

29 1.2 0.3 36 1.8 1.1 46 2.3 1.6 55 2.9 2.5

31 1.6 0.6 41 2.2 1.3 49 2.8 2.2

26 1.4 0.1 37 2.0 0.9 43 2.7 1.8

33 30 26 1.6 1.5 1.2 0.4 -0.2 -0.9 39 36 32 29 2.6 2.4 2.1 1.8 1.4 0.9 0.3 -0.3

10DT24 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 68-S

ys(end) ys(center) in. 4.00 4.00

88-S

5.00 5.00

108-S

6.00 6.00

128-S

7.00 7.00

128-D1

11.67 3.25

148-D1

12.86 3.50

2 in. Normalweight Topping Span, ft

30

32

34

36

38

40

42

44

46

48

50

172 0.6 0.6

145 0.7 0.7 197 0.9 0.9

123 0.7 0.7 169 1.0 1.0

104 0.8 0.7 145 1.1 1.0 180 1.2 1.2

89 0.8 0.6 125 1.1 1.0 156 1.3 1.3

75 0.9 0.6 108 1.2 1.0 136 1.4 1.3 160 1.6 1.5

63 0.9 0.5 93 1.3 0.9 119 1.5 1.3 141 1.7 1.5

56 0.9 0.4 83 1.3 0.9 104 1.6 1.2 124 1.8 1.5

45 0.9 0.2 69 1.4 0.7 91 1.7 1.1 109 1.9 1.4

37 0.9 0.0 60 1.4 0.6 79 1.7 1.0 93 1.9 1.3

30 0.8 –0.3 51 1.4 0.4 68 1.8 0.9 79 2.0 1.2

52

54

56

58

60

43 1.4 0.2 57 1.8 0.7 68 2.1 1.0 92 2.3 1.4

34 1.3 –0.2 48 1.8 0.5 58 2.1 0.8 79 2.4 1.2

40 1.8 0.2 48 2.1 0.5 67 2.5 0.9

31 1.8 –0.2 40 2.1 0.2 57 2.5 0.6

33 2.1 –0.2 47 2.5 0.3

62

64

66

39 2.5 –0.2 53 2.9 0.5

32 2.4 –1.7 44 2.9 0.0

36 2.9 –0.6

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

3–16

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.4 Double-Tee Load Tables (cont.) Strand Pattern Designation

10'-0" × 24" Lightweight Concrete

Number of strand (12) S = straight  D = depressed

No Topping



A = 449 I = 22,469 yb = 17.77 yt = 6.23 Sb = 1264 St = 3607 wt = 359 DL = 36 V/S = 1.35

128- D1

  3

Section Properties

Number of depression points Diameter of strand in 16ths

Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

2 in. Topping

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

—

31,515 20.53 5.47 1535 5761 609 61

in.4 in. in. in.3 in.3 lb/ft lb/ft2

Key 179 – Safe superimposed service load, lb/ft2 1.0 – Estimated camber at erection, in. 1.3 – Estimated long-time camber, in.

fc' = 5000 psi fpu = 270,000 psi

/2-in.-diameter regular strand

1

Check with regional producers for availability.

10LDT24 Table of safe superimposed service load, lb/ft2, and cambers, in. y (end)

s Strand ys(center) pattern in.

68-S

4.00 4.00

88-S

5.00 5.00

108-S

6.00 6.00

128-S

7.00 7.00

128-D1

11.67 3.25

148-D1

12.86 3.50

No Topping Span, ft

36

38

40

42

44

46

48

50

52

54

56

58

60

62

64

66

68

70

72

74

76

78

80

179 155 134 117 1.0 1.1 1.2 1.3 1.3 1.4 1.5 1.6 175 154 1.6 1.7 2.0 2.2 185 2.0 2.5

30

32

34

103 1.4 1.7 136 1.9 2.3 164 2.1 2.7

90 1.5 1.7 120 2.0 2.4 145 2.3 2.9

80 1.6 1.8 107 2.1 2.5 130 2.5 3.0

70 1.6 1.8 95 2.2 2.6 116 2.6 3.2

62 1.7 1.8 85 2.3 2.7 104 2.8 3.3

55 1.7 1.8 76 2.4 2.7 94 2.9 3.4 108 3.2 3.9

49 1.7 1.7 68 2.5 2.7 84 3.1 3.4 98 3.4 4.0

43 1.7 1.6 61 2.6 2.7 76 3.2 3.5 87 3.5 4.0

38 1.7 1.5 55 2.6 2.6 69 3.3 3.4 78 3.7 4.0

34 1.7 1.3 49 2.6 2.5 62 3.3 3.4 70 3.8 4.0

30 1.6 1.0 44 2.6 2.4 56 3.4 3.3 63 3.9 4.0

27 1.5 0.6 40 2.6 2.2 51 3.4 3.2 57 3.9 3.8 72 4.5 4.7

36 2.5 1.9 46 3.4 3.0 51 4.0 3.7 65 4.6 4.6

32 2.4 1.6 42 3.4 2.8 47 4.0 3.5 59 4.7 4.4

29 2.3 1.1 38 3.4 2.5 42 4.0 3.3 53 4.8 4.2

26 2.1 0.6 34 3.3 2.2 39 3.9 3.0 48 4.8 3.9

31 3.1 1.7 35 3.9 2.6 43 4.8 3.5

27 2.9 1.1 32 2.7 2.2 39 4.7 3.0 47 5.6 4.5

29 3.6 1.6 35 4.5 2.4 43 5.6 4.0

26 3.3 1.0 32 4.3 1.7 39 5.5 3.4

29 4.0 1.0 35 5.4 2.8

27 3.7 0.2 31 5.2 2.0

10LDT24 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. y (end)

s Strand ys(center) pattern in.

68-S

4.00 4.00

88-S

5.00 5.00

108-S

6.00 6.00

128-S

7.00 7.00

128-D1

11.67 3.25

2 in. Normalweight Topping Span, ft

30

32

34

36

38

40

42

44

46

48

50

52

54

56

58

60

62

64

66

181 1.0 1.0

154 1.1 1.1

131 1.2 1.1 177 1.6 1.6

113 1.3 1.1 153 1.7 1.6 188 2.0 1.9

97 1.4 1.1 133 1.9 1.7 165 2.1 2.0

83 1.5 1.0 116 2.0 1.7 144 2.3 2.1

72 1.6 1.0 101 2.1 1.6 127 2.5 2.1

62 1.6 0.8 89 2.2 1.6 112 2.6 2.1

53 1.7 0.7 78 2.3 1.5 99 2.8 2.0

45 1.7 0.5 68 2.4 1.3 87 2.9 1.9 102 3.2 2.4

38 1.7 0.2 59 2.5 1.1 75 3.1 1.8 88 3.4 2.2

32 1.7 –0.1 51 2.6 0.8 63 3.2 1.6 76 3.5 2.1

43 2.6 0.5 53 3.3 1.3 65 3.7 1.8

35 2.7 0.1 45 3.3 0.9 55 3.8 1.5

38 3.4 0.6 46 3.9 1.1

32 3.4 0.1 39 3.9 0.6 57 4.5 1.4

33 4.0 0.1 49 4.6 0.9

41 4.7 0.3

34 4.8 –0.4

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–17

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

  3

3.4 Double-Tee Load Tables (cont.) Strand Pattern Designation

10'-0" × 32" Normalweight Concrete

Number of strand (18) S = straight  D = depressed

Section Properties

No Topping



A = 615 I = 59,720 yb = 21.98 yt = 10.02 Sb = 2717 St = 5960 wt = 641 DL = 64 V/S = 1.69

188- D1

2 in. Topping

Number of depression points Diameter of strand in 16ths

Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

—

77,118 24.54 9.46 3143 8152 891 89

in.4 in. in. in.3 in.3 lb/ft lb/ft2

Key 189 – Safe superimposed service load, lb/ft2 1.2 – Estimated camber at erection, in. 1.5 – Estimated long-time camber, in.

fc' = 5000 psi fpu = 270,000 psi

/2-in.-diameter regular strand

1

Check with regional producers for availability.

10DT32 Table of safe superimposed service load, lb/ft2, and cambers, in.

No Topping

y (end)

s Strand ys(center) pattern in.

128-S

7.00 7.00

148-S

8.00 8.00

168-S

9.00 9.00

188-S

10.00 10.00

188-D1

14.39 4.00

208-D1

15.50 4.25

Span, ft 50

52

54

56

58

60

62

64

66

68

70

72

74

76

78

80

82

84

86

88

90

92

94

96

189 169 152 136 1.2 1.2 1.3 1.3 1.5 1.6 1.6 1.7 194 174 157 1.4 1.4 1.5 1.8 1.9 1.9 194 175 1.5 1.6 2.0 2.1 190 1.7 2.2

44

46

48

123 1.4 1.7 142 1.6 2.0 158 1.7 2.1 173 1.7 2.2

110 1.4 1.7 128 1.6 2.0 144 1.7 2.2 157 1.8 2.3

99 1.4 1.7 116 1.7 2.0 130 1.8 2.2 143 1.9 2.3

90 1.5 1.7 105 1.7 2.0 118 1.8 2.2 130 1.9 2.4

81 1.5 1.7 95 1.7 2.0 108 1.9 2.2 118 2.0 2.4

73 1.4 1.6 86 1.7 2.0 98 1.9 2.2 108 2.0 2.4

65 1.4 1.5 78 1.7 1.9 89 1.9 2.2 99 2.0 2.3 132 2.7 3.4

59 1.4 1.4 71 1.7 1.8 81 1.9 2.1 90 2.0 2.3 122 2.8 3.4

53 1.3 1.2 64 1.6 1.7 74 1.9 2.0 82 2.0 2.2 112 2.9 3.4

47 1.2 1.0 58 1.6 1.6 67 1.8 1.9 75 2.0 2.1 103 2.9 3.3

42 1.1 0.8 52 1.5 1.4 61 1.8 1.7 68 1.9 1.9 95 2.9 3.3

37 1.0 0.5 47 1.4 1.1 55 1.7 1.5 62 1.8 1.8 88 2.9 3.2 99 3.2 3.7

33 0.8 0.2 42 1.2 0.8 50 1.6 1.3 57 1.8 1.5 81 2.9 3.0 92 3.3 3.6

29 0.6 –0.2 38 1.1 0.5 45 1.4 1.0 51 1.6 1.3 74 2.9 2.8 85 3.2 3.4

25 0.4 –0.6 34 0.9 0.1 41 1.2 0.6 47 1.5 0.9 68 2.8 2.6 78 3.2 3.2

30 0.7 –0.4 36 1.0 0.2 42 1.3 0.9 63 2.6 2.2 72 3.1 3.0

26 0.4 –0.9 33 0.8 –0.3 38 1.1 0.1 58 2.5 1.9 67 3.1 2.7

29 0.5 –0.8 34 0.8 –0.4 53 2.3 1.5 62 2.9 2.3

26 0.2 –1.4 31 0.5 –1.0 49 2.1 1.1 57 2.7 1.9

27 0.2 –1.7 44 1.9 0.7 52 2.5 1.4

41 1.6 0.2 48 2.3 0.9

37 1.3 –0.4 44 2.0 0.4

34 0.9 –1.1 40 1.7 –0.2

98 100 102

30 0.5 –2.0 37 1.3 –0.9

27 0.0 –2.9 34 31 0.9 0.4 –1.6 –2.5

10DT32 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. ys(end) Strand ys(center) pattern in. 128-S

7.00 7.00

148-S

8.00 8.00

168-S

9.00 9.00

188-S

10.00 10.00

188-D1

14.39 4.00

208-D1

15.50 4.25

2 in. Normalweight Topping Span, ft

50

52

187 166 147 131 1.0 1.1 1.1 1.1 1.0 1.0 1.0 0.9 193 172 153 1.2 1.2 1.3 1.1 1.1 1.1 193 173 1.3 1.4 1.3 1.3 189 1.5 1.3

44

46

48

116 1.2 0.9 137 1.3 1.1 155 1.5 1.2 170 1.5 1.3

54

56

58

60

62

64

66

68

70

72

74

76

78

80

82

84

86

88

103 92 81 72 63 55 47 38 30 1.2 1.2 1.2 1.1 1.1 1.1 1.0 0.9 0.8 0.8 0.7 0.5 0.4 0.2 –0.1 –0.4 –0.7 –1.1 122 109 98 87 78 68 58 49 40 32 25 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.2 1.1 1.0 0.9 1.0 0.9 0.8 0.7 0.5 0.3 0.0 –0.3 –0.7 –1.1 –1.6 139 125 112 100 88 78 68 58 49 41 33 26 1.5 1.5 1.6 1.6 1.6 1.5 1.5 1.4 1.4 1.3 1.1 1.0 1.2 1.1 1.0 0.9 0.7 0.5 0.3 0.0 –0.3 –0.7 –1.2 –1.7 153 137 122 108 96 84 74 64 56 47 39 32 1.6 1.6 1.6 1.7 1.7 1.7 1.6 1.6 1.5 1.4 1.3 1.2 1.3 1.2 1.1 1.0 0.9 0.7 0.5 0.2 –0.1 –0.5 –0.9 –1.4 183 166 151 135 121 107 95 84 74 64 57 50 43 37 32 27 2.1 2.2 2.2 2.3 2.4 2.4 2.4 2.4 2.4 2.3 2.2 2.1 2.0 1.8 1.7 1.5 1.9 1.8 1.8 1.7 1.5 1.4 1.2 0.9 0.6 0.2 –0.2 –0.6 –1.1 –1.7 –2.3 –3.0 136 122 109 97 86 76 67 58 50 44 38 33 28 2.6 2.6 2.7 2.7 2.7 2.7 2.6 2.6 2.5 2.3 2.2 2.0 1.8 1.8 1.7 1.5 1.3 1.0 0.7 0.3 –0.1 –0.6 –1.1 –1.7 –2.4 –3.1

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

3–18

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.4 Double-Tee Load Tables (cont.) Strand Pattern Designation

10'-0" × 32" Lightweight Concrete

Number of strand (18) S = straight  D = depressed





No Topping

A = 615 I = 59,720 yb = 21.98 yt = 10.02 Sb = 2717 St = 5960 wt = 491 DL = 49 V/S = 1.69

188- D1 Number of depression points Diameter of strand in 16ths

Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

  3

Section Properties

2 in. Topping

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

—

83,019 25.40 8.60 3269 9653 741 74

in.4 in. in. in.3 in.3 lb/ft lb/ft2

Key 180 – Safe superimposed service load, lb/ft2 1.7 – Estimated camber at erection, in. 2.2 – Estimated long-time camber, in.

fc' = 5000 psi fpu = 270,000 psi

/2-in.-diameter regular strand

1

Check with regional producers for availability.

10LDT32 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 128-S 148-S

ys(end) ys(center) 46 48 50 in. 180 163 147 7.00 1.7 1.8 1.9 7.00 2.2 2.2 2.3 186 168 8.00 2.1 2.2 8.00 2.6 2.6

168-S

9.00 9.00

188-S

10.00 10.00

188-D1

14.39 4.00

208-D1

15.50 4.25

No Topping Span, ft

52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102

134 2.0 2.4 153 2.3 2.7 186 170 2.3 2.4 2.9 3.0 183 2.5 3.1

122 2.1 2.4 139 2.3 2.8 155 2.5 3.1 166 2.6 3.2

111 2.1 2.5 127 2.4 2.8 142 2.6 3.1 151 2.7 3.3

101 2.2 2.5 116 2.5 2.9 130 2.7 3.2 138 2.8 3.4

92 2.2 2.5 106 2.6 2.9 118 2.8 3.2 125 2.9 3.4

84 2.2 2.4 97 2.6 2.9 107 2.9 3.2 114 3.0 3.4 152 3.9 4.7

77 2.3 2.4 89 2.6 2.8 99 2.9 3.2 104 3.1 3.4 139 4.0 4.8

70 2.2 2.3 82 2.7 2.8 90 3.0 3.2 95 3.1 3.4 128 4.2 4.8

64 2.2 2.1 75 2.7 2.7 83 3.0 3.1 88 3.2 3.3 118 4.3 4.9

58 2.2 2.0 69 2.6 2.6 76 3.0 3.0 81 3.2 3.2 108 4.4 4.9

53 2.1 1.8 63 2.6 2.4 70 2.9 2.8 74 3.2 3.1 100 4.5 4.8 110 4.9 5.4

49 44 2.0 1.9 1.5 1.2 58 53 2.5 2.4 2.2 1.9 65 59 2.9 2.8 2.6 2.4 68 63 3.1 3.1 2.9 2.7 92 85 4.6 4.69 4.8 4.7 102 94 5.0 5.0 5.4 5.3

40 1.7 0.8 49 2.3 1.6 54 2.7 2.1 58 3.0 2.5 78 4.6 4.5 87 5.1 5.2

37 33 30 27 1.5 1.3 1.0 0.7 0.4 –0.2 –0.7 –1.4 45 41 37 33 29 26 2.2 2.0 1.7 1.4 1.1 0.8 1.3 0.8 0.3 –0.3 –1.0 –1.8 50 46 42 38 34 30 27 2.6 2.4 2.2 2.0 1.7 1.4 1.0 1.8 1.4 1.0 0.5 –0.2 –0.9 –1.7 53 49 45 41 38 34 30 27 2.9 2.7 2.6 2.4 2.1 1.8 1.4 1.0 2.1 1.8 1.4 0.9 0.4 –0.3 –1.1 –1.9 72 66 60 55 51 46 43 40 4.6 4.5 4.4 4.3 4.1 3.9 3.7 3.4 4.3 3.9 3.6 3.1 2.6 2.0 1.5 0.9 80 74 68 63 58 53 48 44 5.1 5.1 5.1 5.1 5.0 4.8 4.6 4.3 5.0 0.8 4.6 4.2 3.8 3.3 2.7 2.0

37 34 32 30 3.1 2.7 2.3 1.9 0.2 –0.5 –1.3–2.2 41 38 35 32 4.0 3.7 3.3 2.9 1.2 0.5 –0.3–1.2

10LDT32 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 128-S

ys(end) Span, ft ys(center) 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 in. 199 177 159 142 128 114 103 92 83 74 67 60 53 47 41 35 28 7.00 1.6 1.7 1.8 1.9 2.0 2.1 2.1 2.2 2.2 2.2 2.3 2.2 2.2 2.2 2.1 2.0 1.9 7.00 1.6 1.6 1.6 1.6 1.6 1.5 1.4 1.3 1.2 1.0 0.8 0.5 0.2 –0.2 –0.6 –1.1 –1.7

148-S

8.00 8.00

168-S

9.00 9.00

188-S

10.00 10.00

188-D1

14.39 4.00

208-D1

15.50 4.25

2 in. Normalweight Topping 78

80

82

84

86

88

90

92

183 165 148 134 121 109 98 89 80 72 64 56 49 42 36 31 2.1 2.2 2.3 2.3 2.4 2.5 2.6 2.6 2.6 2.7 2.7 2.6 2.6 2.5 2.4 2.3 1.9 1.9 1.9 1.9 1.8 1.7 1.6 1.4 1.2 1.0 0.7 0.3 –0.1 –0.5 –1.0 –1.6 184 166 150 136 123 112 100 89 79 71 62 55 48 42 36 31 26 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.9 3.0 3.0 3.0 3.0 2.9 2.8 2.7 2.6 2.5 2.1 2.1 2.1 2.1 2.0 1.9 1.7 1.6 1.3 1.1 0.7 0.4 –0.1 –0.6 –1.1 –1.8 –2.5 182 165 149 135 121 107 95 85 76 68 60 53 46 40 34 29 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.1 3.2 3.2 3.2 3.2 3.1 3.0 2.9 2.8 2.3 2.3 2.2 2.2 2.1 1.9 1.7 1.5 1.3 1.0 0.6 0.2 –0.3 –0.8 –1.5 –2.1 149 136 124 112 100 90 80 72 64 56 49 42 36 31 26 3.9 4.0 4.2 4.3 4.4 4.5 4.6 4.6 4.6 4.6 4.5 4.4 4.3 4.1 3.9 3.1 3.0 2.9 2.7 2.5 2.2 1.9 1.5 1.1 0.5 –0.1 –0.9 –1.7 –2.6 –3.6 103 92 83 74 66 59 52 45 39 34 28 4.9 5.0 5.0 5.1 5.1 5.1 5.1 5.1 5.0 4.8 4.6 2.8 2.5 2.1 1.7 1.2 0.7 0.0 –0.7 –1.5 –2.5 –3.5

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–19

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

  3

3.4 Double-Tee Load Tables (cont.) Strand Pattern Designation

12'-0" × 28" Normalweight Concrete

Number of strand (16) S = straight  D = depressed

Section Properties

No Topping



A = 640 I = 44,563 yb = 20.01 yt = 7.79 Sb = 2227 St = 5577 wt = 677 DL = 56 V/S = 1.62

168- D1

Number of depression points Diameter of strand in 16ths

Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

2 in. Topping

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

—

57,323 22.47 7.53 2551 7613 977 81

in.4 in. in. in.3 in.3 lb/ft lb/ft2

Key 133 – Safe superimposed service load, lb/ft2 0.8 – Estimated camber at erection, in. 1.1 – Estimated long-time camber, in.

fc' = 5000 psi fpu = 270,000 psi

/2-in.-diameter regular strand

1

Check with regional producers for availability.

12DT28 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 108-S

ys(end) ys(center) in. 6.00 6.00

128-S

7.00 7.00

148-S

8.00 8.00

168-S

9.00 9.00

168-D1

13.00 3.75

188-D1

14.39 4.00

No Topping Span, ft

40

42

133 0.8 1.1 157 1.0 1.3 178 1.1 1.5 196 1.1 1.6

117 0.9 1.2 139 1.0 1.4 158 1.1 1.5 174 1.2 1.6

44

46

48

50

52

54

56

58

60

62

64

66

68

70

72

74

76

78

80

82

84

102 90 79 70 62 54 47 41 36 0.9 0.9 0.9 0.9 0.9 0.9 0.8 0.7 0.6 1.2 1.3 1.3 1.3 1.2 1.2 1.1 1.0 0.8 123 109 96 86 76 67 60 53 47 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.0 1.0 1.5 1.5 1.5 1.6 1.6 1.6 1.5 1.4 1.3 140 125 11 99 88 79 71 63 56 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.6 1.7 1.7 1.8 1.8 1.8 1.8 1.7 1.7 155 138 123 110 99 89 79 71 64 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.7 1.8 1.9 1.9 1.9 2.0 2.0 1.9 1.9 180 162 146 132 119 108 98 89 1.6 1.7 1.8 1.9 2.0 2.0 2.0 2.0 2.3 2.4 2.5 2.6 2.6 2.7 2.7 2.7 135 122 111 100 2.1 2.2 2.2 2.3 2.9 3.0 3.0 3.0

31 0.5 0.7 41 0.9 1.2 50 1.1 1.5 57 1.3 1.8 80 2.0 2.6 90 2.3 3.0

26 0.4 0.4 36 0.8 1.0 44 1.0 1.4 51 1.2 1.6 72 2.0 2.5 81 2.3 3.0

31 0.6 0.8 39 0.9 1.2 46 1.1 1.5 64 1.9 2.4 73 2.3 2.9

27 0.4 0.5 34 0.7 0.9 40 1.0 1.2 58 1.8 2.3 66 2.2 2.8

30 0.6 0.7 35 0.8 1.0 52 1.7 2.1 59 2.1 2.6

26 0.3 0.3 30 0.6 0.7 47 1.5 1.9 53 2.0 2.4

26 0.3 0.3 42 1.4 1.7 47 1.8 2.2

38 1.2 1.4 43 1.6 1.9

34 0.9 1.1 39 1.4 1.6

30 0.6 0.7 35 1.1 1.3

26 0.3 0.2 31 0.8 0.9

28 0.5 0.4

12DT28 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 108-S

ys(end) ys(center) in. 6.00 6.00

128-S

7.00 7.00

148-S

8.00 8.00

168-S

9.00 9.00

168-D1

13.00 3.75

188-D1

14.39 4.00

2 in. Normalweight Topping Span, ft

40

42

44

46

48

50

52

54

56

58

60

62

64

66

68

70

72

127 0.8 0.8 154 1.0 1.0 177 1.1 1.1 197 1.1 1.2

110 0.9 0.8 134 1.0 1.0 155 1.1 1.2 173 1.2 1.3

95 0.9 0.8 117 1.1 1.0 136 1.2 1.2 152 1.3 1.3 199 1.5 1.7

82 0.9 0.8 102 1.1 1.0 119 1.2 1.2 134 1.3 1.3 177 1.6 1.7

70 0.9 0.7 88 1.1 1.0 105 1.3 1.1 118 1.4 1.3 157 1.7 1.7

60 0.9 0.6 77 1.1 0.9 92 1.3 1.1 104 1.4 1.2 140 1.8 1.8

51 0.9 0.5 66 1.1 0.8 80 1.3 1.0 90 1.4 1.2 125 1.9 1.7 143 2.0 1.9

42 0.8 0.3 57 1.1 0.7 70 1.3 0.9 78 1.4 1.1 111 1.9 1.7 126 2.1 1.9

35 0.8 0.1 49 1.1 0.5 60 1.3 0.8 66 1.4 0.9 97 2.0 1.6 111 2.1 1.9

29 0.7 –0.1 41 1.0 0.3 50 1.2 0.6 56 1.4 0.8 84 2.0 1.5 97 2.2 1.8

32 0.9 0.0 41 1.2 0.3 47 1.3 0.5 72 2.0 1.3 85 2.2 1.7

32 1.1 0.1 39 1.3 0.3 62 2.0 1.1 73 2.3 1.5

31 1.2 0.0 52 1.9 0.8 63 2.3 1.3

43 1.8 0.5 54 2.2 1.0

36 1.8 0.2 45 2.1 0.7

30 1.6 –0.2 37 2.0 0.3

31 1.9 –0.2

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

3–20

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.4 Double-Tee Load Tables (cont.) Strand Pattern Designation

12'-0" × 28" Lightweight Concrete

Number of strand (16) S = straight  D = depressed

Untopped



Topped

A = 640 I = 44,563 yb = 20.01 yt = 7.99 Sb = 2227 St = 5577 wt = 511 DL = 43 V/S = 1.62

168- D1

  3

Section Properties

Number of depression points Diameter of strand in 16ths

Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

—

61,410 23.19 6.81 2648 9018 822 68

in.4 in. in. in.3 in.3 lb/ft lb/ft2

Key 142 – Safe superimposed service load, lb/ft2 1.4 – Estimated camber at erection, in. 1.8 – Estimated long-time camber, in.

fc' = 5000 psi fpu = 270,000 psi

/2-in.-diameter regular strand

1

Check with regional producers for availability.

12LDT28 Table of safe superimposed service load, lb/ft2, and cambers, in. ys(end) Strand y (center) pattern s in. 6.00 108-S 6.00 128-S

7.00 7.00

148-S

8.00 8.00

168-S

9.00 9.00

168-D1

13.00 3.75

188-D1

14.39 4.00

No Topping

Span, ft 40 142 1.4 1.8 167 1.6 2.1 188 1.7 2.3

42 126 1.4 1.9 148 1.7 2.3 167 1.9 2.5 183 1.9 2.6

44 112 1.5 2.0 132 1.8 2.4 150 2.0 2.7 164 2.1 2.8

46 100 1.6 2.1 118 1.9 2.5 134 2.1 2.8 148 2.2 3.0

48 89 1.7 2.2 106 1.9 2.6 121 2.2 2.9 133 2.3 3.1

50 80 1.7 2.3 95 2.0 2.7 109 2.3 3.0 120 2.4 3.2 156 3.0 4.0

52 71 1.7 2.3 86 2.1 2.8 98 2.3 3.1 109 2.5 3.3 141 3.1 4.2

54 64 1.8 2.4 77 2.1 2.8 89 2.4 3.2 98 2.6 3.4 129 3.3 4.4

56 57 1.8 2.4 70 2.2 2.9 80 2.5 3.2 89 2.7 3.5 118 3.4 4.6

58 51 1.7 2.4 63 2.2 2.9 73 2.5 3.3 81 2.7 3.6 107 3.5 4.7

60 46 1.7 2.3 56 2.2 2.9 66 2.5 3.3 74 2.7 3.6 98 3.7 4.9

62 41 1.7 2.2 51 2.1 2.9 60 2.5 3.3 67 2.8 3.6 90 3.8 5.0 100 4.1 5.4

64 36 1.6 2.1 46 2.1 2.8 54 2.5 3.3 61 2.7 3.6 82 3.8 5.0 91 4.2 5.5

66 32 1.4 1.9 41 2.0 2.7 49 2.4 3.2 55 2.7 3.5 74 3.9 5.1 83 4.3 5.6

68 28 1.3 1.7 37 1.9 2.5 44 2.3 3.1 50 2.6 3.4 67 3.9 5.0 76 4.3 5.7

70 25 1.1 1.4 33 1.8 2.4 40 2.2 2.9 45 2.5 3.3 61 3.9 4.9 69 4.4 5.7

72

74

76

78

80

82

84

86

88

90

29 1.6 2.1 36 2.1 2.7 41 2.4 3.1 56 3.8 4.8 63 4.4 5.6

26 1.4 1.7 32 1.9 2.5 37 2.2 2.9 50 3.7 4.6 57 4.4 5.5

29 1.7 2.2 33 2.0 2.6 45 3.6 4.4 52 4.3 5.4

26 1.4 1.8 30 1.8 2.3 41 3.4 4.1 47 4.2 5.1

27 1.5 1.9 37 3.2 3.7 43 4.0 4.8

33 2.9 3.3 39 3.7 4.4

30 2.6 2.9 35 3.5 4.0

28 2.3 2.5 31 3.1 3.4

25 1.9 2.0 28 26 2.8 2.4 2.9 2.3

12LDT28 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. ys(end) Strand y (center) pattern s in. 6.00 108-S 6.00 128-S

7.00 7.00

148-S

8.00 8.00

168-S

9.00 9.00

168-D1

13.00 3.75

188-D1

14.39 4.00

2 in. Normalweight Topping

Span, ft 40

42

44

46

48

50

52

54

56

58

60

62

64

66

68

70

72

74

76

78

137 1.4 1.4 164 1.6 1.7 187 1.8 1.9

120 1.5 1.4 144 1.7 1.7 165 1.9 2.0 183 2.0 2.1

104 1.6 1.4 127 1.8 1.8 146 2.0 2.0 162 2.1 2.2

91 1.6 1.4 111 1.9 1.8 129 2.1 2.1 144 2.2 2.2

80 1.7 1.4 98 2.0 1.8 114 2.2 2.1 128 2.4 2.2

69 1.7 1.3 86 2.1 1.7 101 2.3 2.1 114 2.5 2.2

60 1.8 1.2 76 2.1 1.7 90 2.4 2.0 101 2.6 2.2 135 3.2 3.0

52 1.8 1.1 67 2.2 1.6 80 2.5 1.9 90 2.7 2.2 121 3.3 3.0

45 1.8 0.9 59 2.2 1.4 70 2.5 1.8 78 2.7 2.1 109 3.5 3.0

38 1.8 0.7 51 2.2 1.3 61 2.6 1.7 67 2.8 1.9 98 3.6 3.0

32 1.8 0.5 44 2.2 1.0 52 2.6 1.5 58 2.8 1.7 88 3.7 2.9

27 1.7 0.2 38 2.2 0.8 45 2.6 1.2 50 2.8 1.5 77 3.8 2.8 89 4.1 3.2

31 2.2 0.4 38 2.6 0.9 42 2.8 1.2 68 3.9 2.6 79 4.3 3.0

25 2.1 0.1 31 2.5 0.6 36 2.8 0.9 59 4.0 2.3 69 4.3 2.8

25 2.4 0.1 29 2.8 0.5 51 4.0 2.0 60 4.4 2.6

43 4.0 1.6 52 4.5 2.2

36 3.9 1.1 45 4.5 1.9

30 3.9 0.6 38 4.5 1.4

32 4.5 0.8

26 4.3 0.1

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–21

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

  3

3.4 Double-Tee Load Tables (cont.) Strand Pattern Designation

12'-0" × 32" Normalweight Concrete

Number of strand (20) S = straight  D = depressed

Section Properties

No Topping



A = 690 I = 64,620 yb = 22.75 yt = 9.25 Sb = 2840 St = 6986 wt = 719 DL = 60 V/S = 1.70

208- D1

2 in. Topping

Number of depression points Diameter of strand in 16ths

Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

—

82,413 25.50 8.75 3232 9696 1019 85

in.4 in. in. in.3 in.3 lb/ft lb/ft2

Key 193 – Safe superimposed service load, lb/ft2 0.8 – Estimated camber at erection, in. 1.2 – Estimated long-time camber, in.

fc' = 5000 psi fpu = 270,000 psi

/2-in.-diameter regular strand

1

Check with regional producers for availability.

12DT32 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 128-S 148-S

ys(end) ys(center) 40 42 44 in. 193 171 151 7.00 0.8 0.9 0.9 7.00 1.2 1.2 1.3 196 174 8.00 1.0 1.1 8.00 1.4 1.5

168-S

9.00 9.00

188-S

10.00 10.00

208-D1

15.50 4.25

228-D1

16.41 4.50

No Topping Span, ft

46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96

135 1.0 1.4 156 1.1 1.5 194 174 1.2 1.2 1.6 1.7 189 1.3 1.8

120 1.0 1.4 139 1.2 1.6 156 1.3 1.8 170 1.4 1.8

107 1.0 1.4 125 1.2 1.7 140 1.3 1.8 153 1.4 1.9

96 1.1 1.5 112 1.2 1.7 126 1.4 1.9 138 1.5 2.0

85 1.1 1.5 101 1.3 1.7 114 1.4 1.9 125 1.5 2.0

76 1.1 1.5 90 1.3 1.7 103 1.4 1.9 113 1.5 2.1

68 1.0 1.4 81 1.3 1.7 93 1.4 2.0 102 1.6 2.1

61 1.0 1.4 73 1.3 1.7 84 1.4 2.0 93 1.6 2.1 140 2.3 3.2

54 1.0 1.3 65 1.2 1.7 75 1.4 1.9 84 1.6 2.1 128 2.4 3.2

48 0.9 1.2 59 1.2 1.6 68 1.4 1.9 76 1.5 2.1 117 2.4 3.3

42 0.8 1.1 52 1.1 1.5 61 1.3 1.8 69 1.5 2.0 107 2.5 3.3

37 0.7 0.9 47 1.0 1.4 55 1.3 1.7 62 1.4 1.9 97 2.5 3.3 107 2.7 3.7

33 0.6 0.7 42 0.9 1.2 49 1.2 1.6 56 1.3 1.8 88 2.5 3.3 98 2.7 3.7

28 0.4 0.5 37 0.8 1.0 44 1.0 1.4 51 1.2 1.6 80 2.5 3.2 89 2.8 3.7

33 0.6 0.7 40 0.9 1.1 46 1.1 1.4 73 2.4 3.1 81 2.7 3.6

29 0.4 0.5 35 0.7 0.9 40 0.9 1.2 66 2.3 3.0 74 2.7 3.5

31 0.5 0.6 35 0.7 0.9 59 2.2 2.8 67 2.6 3.4

27 0.3 0.2 31 0.5 0.6 53 2.1 2.5 61 2.6 3.2

26 0.3 0.2 49 1.9 2.3 55 2.4 3.0

44 1.7 2.0 50 2.2 2.7

40 1.5 1.7 45 2.0 2.3

37 1.2 1.4 41 1.8 2.0

33 1.0 1.0 37 1.5 1.6

30 0.6 0.6 33 1.2 1.2

26 0.2 0.0 30 28 0.9 0.5 0.8 0.3

12DT32 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 128-S

ys(end) ys(center) in. 7.00 7.00

148-S

8.00 8.00

168-S

9.00 9.00

188-S

10.00 10.00

208-D1

15.50 4.25

228-D1

16.41 4.50

2 in. Normalweight Topping Span, ft

40

42

44

46

190 167 146 128 0.8 0.9 0.9 1.0 0.9 1.0 1.0 1.0 194 171 151 1.0 1.1 1.1 1.1 1.1 1.2 192 170 1.2 1.2 1.3 1.3 187 1.3 1.4

56

58

113 99 87 76 66 1.0 1.0 1.1 1.1 1.1 1.0 1.0 0.9 0.9 0.8 133 118 104 92 81 1.2 1.2 1.2 1.3 1.3 1.2 1.2 1.1 1.1 1.0 151 135 120 106 94 1.3 1.3 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.2 167 149 133 119 106 1.4 1.4 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4

48

50

52

54

57 1.0 0.7 71 1.3 0.9 84 1.4 1.1 94 1.6 1.3

60

62

64

66

68

49 42 36 30 1.0 1.0 0.9 0.8 0.5 0.3 0.1 –0.2 62 54 47 40 32 1.3 1.2 1.2 1.1 1.0 0.8 0.7 0.5 0.2 –0.1 74 65 56 48 39 1.4 1.4 1.4 1.3 1.3 1.0 0.9 0.7 0.5 0.3 82 71 62 53 45 1.6 1.6 1.5 1.5 1.4 1.2 1.1 0.9 0.7 0.5 132 118 105 93 82 2.3 2.4 2.4 2.5 2.5 2.2 2.1 2.0 1.9 1.8 93 2.7 2.1

70

72

74

76

78

80

82

84

32 1.2 0.0 38 30 1.3 1.2 0.2 –0.1 72 63 2.5 2.5 1.6 1.4 83 73 2.7 2.8 2.0 1.8

54 2.4 1.1 64 2.7 1.5

46 2.3 0.7 55 2.7 1.2

39 32 27 2.2 2.1 1.9 0.3 –0.1 –0.6 48 41 34 28 2.6 2.6 2.4 2.2 0.9 0.5 0.0 –0.5

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

3–22

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.4 Double-Tee Load Tables (cont.) Strand Pattern Designation

12'-0" × 32" Lightweight Concrete

Number of strand (20) S = straight  D = depressed

No Topping



A = 690 I = 64,620 yb = 22.75 yt = 9.25 Sb = 2840 St = 6985 wt = 551 DL = 46 V/S = 1.70

208- D1

  3

Section Properties

Number of depression points Diameter of strand in 16ths

Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

2 in. Topping

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

—

88,305 26.08 7.92 3385 11,149 851 71

in.4 in. in. in.3 in.3 lb/ft lb/ft2

Key 181 – Safe superimposed service load, lb/ft2 1.5 – Estimated camber at erection, in. 2.0 – Estimated long-time camber, in.

fc' = 5000 psi fpu = 270,000 psi

/2-in.-diameter regular strand

1

Check with regional producers for availability.

12LDT32 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 128-S 148-S

ys(end) ys(center) 42 44 46 48 50 52 54 56 in. 181 162 145 131 118 106 96 87 7.00 1.5 1.6 1.6 1.7 1.8 1.9 1.9 2.0 7.00 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.6 185 166 150 135 122 111 101 8.00 1.7 1.9 2.0 2.0 2.1 2.2 2.3 8.00 2.4 2.5 2.6 2.7 2.8 2.9 3.0

168-S

9.00 9.00

188-S

10.00 10.00

208-D1

15.50 4.25

228-D1

16.41 4.50

No Topping Span, ft

58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102

79 71 2.0 2.0 2.7 2.7 92 83 2.3 2.4 3.1 3.1 184 166 151 137 124 113 103 94 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.7 2.9 3.0 3.1 3.3 3.3 3.4 3.5 200 181 164 149 135 123 113 103 2.1 2.2 2.3 2.4 2.6 2.7 2.7 2.8 2.8 3.0 3.1 3.3 3.4 3.5 3.6 3.7

64 2.0 2.7 76 2.4 3.2 86 2.7 3.5 94 2.9 3.8

58 2.0 2.7 69 2.4 3.2 78 2.7 3.6 86 2.9 3.8

53 2.0 2.7 63 2.4 3.2 72 2.7 3.6 79 3.0 3.9

48 2.0 2.6 57 2.4 3.2 66 2.7 3.6 72 3.0 3.9 107 4.4 5.9

43 1.9 2.5 52 2.4 3.1 60 2.7 3.6 66 3.0 3.9 98 4.5 6.0

39 1.8 2.4 47 2.3 3.0 55 2.7 3.5 60 2.9 3.8 91 4.6 6.1

35 1.7 2.2 43 2.2 2.9 50 2.6 3.4 55 2.9 3.7 83 4.7 6.2

31 1.5 2.0 39 2.1 2.7 46 2.5 3.3 51 2.8 3.6 77 4.7 6.2 84 5.2 6.8

28 1.3 1.7 35 1.9 2.6 42 2.4 3.1 46 2.7 3.5 70 4.8 6.2 78 5.2 6.9

32 1.7 2.3 38 2.2 2.9 42 2.5 3.3 65 4.8 6.1 72 5.3 6.8

29 1.5 1.9 34 2.0 2.6 38 2.4 3.0 59 4.8 6.0 66 5.3 6.8

26 1.2 1.5 31 1.8 2.3 35 2.2 2.7 54 4.7 5.8 61 5.2 6.7

28 1.5 1.9 32 1.9 2.4 50 4.5 5.6 56 5.2 6.5

25 1.2 1.4 29 1.6 2.0 45 4.3 5.3 51 5.1 6.3

26 1.3 1.5 44 4.1 4.9 47 5.0 6.1

38 3.9 4.4 43 4.8 5.7

34 3.5 3.9 39 4.5 5.3

31 3.2 3.4 36 4.2 4.8

28 2.8 2.8 32 3.8 4.2

26 2.4 2.2 29 26 3.4 2.9 3.5 2.7

12LDT32 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 128-S

ys(end) ys(center) in. 7.00 7.00

148-S

8.00 8.00

168-S

9.00 9.00

188-S

10.00 10.00

208-D1

15.50 4.25

228-D1

16.41 4.50

2 in. Normalweight Topping Span, ft

42

44

46

48

177 157 139 123 1.5 1.6 1.6 1.7 1.6 1.6 1.7 1.7 181 161 144 1.7 1.9 2.0 1.9 1.9 2.0 181 162 2.0 2.1 2.1 2.2 198 177 2.1 2.2 2.2 2.3

58

60

62

64

66

68

70

72

74

109 97 86 76 68 1.8 1.9 1.9 2.0 2.0 1.7 1.7 1.6 1.6 1.5 128 115 102 92 82 2.0 2.1 2.2 2.3 2.3 2.0 2.0 2.0 1.9 1.9 145 130 117 105 94 2.2 2.3 2.4 2.5 2.6 2.2 2.3 2.3 2.2 2.2 159 143 129 116 105 2.3 2.4 2.6 2.7 2.7 2.4 2.4 2.4 2.4 2.4

50

52

54

56

60 2.0 1.4 73 2.4 1.8 84 2.7 2.1 94 2.8 2.3

53 2.0 1.2 65 2.4 1.7 76 2.7 2.0 83 2.9 2.2

46 2.0 1.0 58 2.4 1.5 67 2.7 1.9 73 2.9 2.1

40 2.0 0.8 51 2.4 1.3 59 2.7 1.7 64 3.0 1.9

35 2.0 0.5 45 2.4 1.1 51 2.7 1.5 56 3.0 1.7 98 4.4 3.6

30 25 1.9 1.8 0.2 –0.2 39 33 2.4 2.3 0.8 0.4 44 38 2.7 2.7 1.2 0.9 49 42 3.0 2.9 1.5 1.2 88 78 4.5 4.6 3.5 3.3

27 2.2 0.0 32 2.6 0.5 36 2.9 0.8 69 4.7 3.1

76

78

80

82

84

86

88

90

27 2.5 0.1 30 25 2.8 2.7 0.4 –0.1 61 54 4.7 4.8 2.8 2.5 71 63 5.2 5.2 3.4 3.1

47 4.8 2.1 56 5.3 2.8

41 4.8 1.6 49 5.3 2.3

35 4.7 1.1 43 5.2 1.9

29 4.5 0.4 37 5.2 1.3

31 26 5.1 5.0 0.7 –0.1

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–23

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

  3

3.5 Pretopped Double-Tee Load Tables Strand Pattern Designation

10'-0" × 26"

Number of strand (12) S = straight  D = depressed

Section Properties

Normalweight



A = 689 I = 30,716 yb = 20.29 yt = 5.71 Sb = 1514 St = 5379 wt = 718 DL = 72 V/S = 2.05

128- D1

Number of depression points Diameter of strand in 16ths

Because these units are pretopped and are typically used in parking structures, safe loads shown do not include any superimposed dead loads. Loads shown are live load. Long-time cambers do not include live load.

Key

Lightweight

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

689 30,716 20.29 5.71 1514 5379 550 55 2.05

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

fc' = 5000 psi

171 – Safe superimposed service load, lb/ft2 0.5 – Estimated camber at erection, in. 0.7 – Estimated long-time camber, in.

fpu = 270,000 psi

/2-in.-diameter regular strand

1

Check with regional producers for availability.

10DT26 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 68-S

ys(end) ys(center) 30 32 34 36 in. 171 143 121 102 4.00 0.5 0.5 0.6 0.6 4.00 0.7 0.7 0.8 0.8

88-S

5.00 5.00

108-S

6.00 6.00

128-S

7.00 7.00

128-D1

11.67 3.25

148-D1

12.86 3.50

196 0.7 1.0

167 0.8 1.1

143 0.8 1.2 180 1.0 1.4

Normalweight — No Topping Span, ft

38

40

42

44

46

48

50

52

54

56

58

60

62

64

66

68

70

72

86 0.6 0.8 123 0.9 1.2 156 1.1 1.5 184 1.3 1.7

72 0.6 0.8 106 0.9 1.3 135 1.2 1.6 161 1.3 1.8 194 1.4 2.0

61 0.6 0.8 91 0.9 1.3 118 1.2 1.7 141 1.4 1.9 171 1.5 2.1

50 0.6 0.8 78 0.9 1.3 103 1.3 1.7 123 1.5 2.0 151 1.6 2.2

42 0.5 0.7 67 0.9 1.3 89 1.3 1.7 108 1.5 2.1 134 1.7 2.3

34 0.4 0.6 57 0.9 1.2 78 1.3 1.8 95 1.5 2.1 119 1.8 2.4

27 0.3 0.4 48 0.8 1.2 67 1.3 1.7 83 1.6 2.1 105 1.8 2.4 127 2.1 2.8

41 0.8 1.0 58 1.2 1.7 73 1.6 2.1 93 1.8 2.4 113 2.1 2.9

34 0.7 0.9 50 1.2 1.6 64 1.5 2.1 82 1.8 2.3 101 2.2 2.9

28 0.5 0.7 43 1.1 1.4 56 1.5 2.0 73 1.7 2.2 89 2.2 2.9

36 0.9 1.2 48 1.4 1.9 64 1.7 21 78 2.2 2.9

30 0.8 1.0 41 1.3 1.7 56 1.6 2.0 68 2.1 2.7

35 1.1 1.4 50 1.4 1.8 59 2.0 2.6

29 0.9 1.1 43 1.3 1.6 52 1.9 2.4

37 1.0 1.3 46 1.7 2.2

31 0.8 0.9 40 1.5 1.9

25 0.5 0.4 36 1.3 1.6

30 1.0 1.1

10LDT26 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 68-S 88-S

ys(end) ys(center) 30 32 34 in. 183 156 133 4.00 0.8 0.9 1.0 4.00 1.1 1.2 1.3 180 5.00 1.3 5.00 1.7

108-S

6.00 6.00

128-S

7.00 7.00

128-D1

11.67 3.25

148-D1

12.86 3.50

Lightweight — No Topping Span, ft

52

54

56

58

60

62

64

66

68

70

72

74

76

115 99 85 73 63 54 46 40 33 1.0 1.1 1.1 1.1 1.2 1.2 1.1 1.1 1.0 1.4 1.4 1.5 1.6 1.6 1.6 1.6 1.5 1.4 156 136 119 104 91 80 70 61 53 1.4 1.5 1.6 1.6 1.7 1.8 1.8 1.8 1.8 1.9 2.0 2.1 2.2 2.3 2.3 2.4 2.4 2.4 192 168 148 130 115 102 90 80 71 1.7 1.8 1.9 2.1 2.2 2.3 2.3 2.4 2.4 2.3 2.5 2.6 2.8 2.9 3.0 3.1 3.1 3.2 196 173 153 136 121 108 96 86 2.0 2.2 2.3 2.5 2.6 2.7 2.8 2.9 2.8 3.0 3.2 3.3 3.5 3.6 3.7 3.8 146 131 118 106 2.8 3.0 3.1 3.2 3.8 4.0 4.1 4.3

36

38

40

42

44

46

48

50

28 0.9 1.2 46 1.8 2.4 63 2.4 3.2 76 2.9 3.8 95 3.3 4.4

78

40 1.7 2.3 55 2.4 3.2 68 3.0 3.9 85 3.4 4.5

35 1.6 2.2 49 2.4 3.2 61 3.0 3.9 76 3.5 4.5 91 4.0 5.4

30 1.4 1.9 43 2.3 3.1 54 2.9 3.9 68 3.4 4.4 81 4.1 5.4

25 1.2 1.6 37 2.2 3.0 48 2.9 3.8 60 3.4 4.3 72 4.2 5.4

33 2.0 2.8 42 2.8 3.7 53 3.3 4.1 65 4.2 5.4

28 1.8 2.4 37 2.7 3.6 46 3.2 3.9 58 4.2 5.3

33 2.5 3.3 41 3.0 3.6 51 4.1 5.1

29 2.2 3.0 36 2.8 3.3 45 3.9 4.8

33 2.5 3.0 40 3.7 4.4

29 2.2 2.6 34 3.4 4.0

26 1.8 2.2 31 27 3.1 2.8 3.5 3.1

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

3–24

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.5 Pretopped Double-Tee Load Tables (cont.) Strand Pattern Designation

10'-0" × 34"

Number of strand (18) S = straight  D = depressed



Normalweight

A = 855 I = 80,780 yb = 25.07 yt = 8.93 Sb = 3222 St = 9046 wt = 891 DL = 89 V/S = 2.32

188- D1

Number of depression points Diameter of strand in 16ths

Because these units are pretopped and are typically used in parking structures, safe loads shown do not include any superimposed dead loads. Loads shown are live load. Long-time cambers do not include live load.

Key

  3

Section Properties

Lightweight

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

855 80,780 25.07 8.93 3222 9046 683 68 2.32

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

fc' = 5000 psi

187 – Safe superimposed service load, lb/ft2 0.8 – Estimated camber at erection, in. 1.2 – Estimated long-time camber, in.

fpu = 270,000 psi

/2-in.-diameter regular strand

1

Check with regional producers for availability.

10DT34 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 128-S 148-S

ys(end) ys(center) 44 46 48 in. 187 166 147 7.00 0.8 0.9 0.9 7.00 1.2 1.2 1.2 193 172 8.00 1.0 1.0 8.00 1.4 1.4

168-S

9.00 9.00

188-S

10.00 10.00

188-D1

14.39 4.00

208-D1

15.50 4.25

Normalweight — No Topping Span, ft

50

52

54

56

58

60

62

64

66

68

70

72

74

76

78

80

82

84

86

88

130 0.9 1.3 153 1.1 1.5 194 174 1.2 1.2 1.6 1.7 192 1.3 1.8

115 0.9 1.3 137 1.1 1.5 156 1.2 1.7 172 1.4 1.8

102 09 1.3 122 1.1 1.5 139 1.3 1.7 155 1.4 1.9

90 0.9 1.2 109 1.1 1.5 125 1.3 1.7 139 1.4 1.9 184 1.8 2.4

79 0.9 1.2 97 1.1 1.5 112 1.3 1.7 125 1.4 1.9 167 1.9 2.5 188 2.0 2.8

70 0.8 1.1 86 1.1 1.5 100 1.3 1.7 113 1.4 1.9 152 1.9 2.5 172 2.1 2.8

61 0.7 1.0 76 1.0 1.4 90 1.2 1.7 101 1.4 1.9 138 1.9 2.5 156 2.1 2.9

53 0.7 0.9 67 0.9 1.3 80 1.2 1.6 91 1.4 1.9 125 1.9 2.5 143 2.2 2.9

46 0.6 0.7 59 0.9 1.2 71 1.1 1.5 82 1.3 1.8 114 1.9 2.5 130 2.2 2.9

40 0.4 0.5 52 0.8 1.0 63 1.0 1.4 73 1.2 1.7 103 1.8 2.4 119 2.2 2.9

34 0.3 0.3 45 0.6 0.8 56 0.9 1.2 65 1.1 1.5 94 1.8 2.3 107 2.1 2.8

28 0.1 0.1 39 0.5 0.6 49 0.8 1.0 58 1.0 1.3 85 1.7 2.2 96 2.1 2.7

34 0.3 0.3 43 0.6 0.8 51 0.9 1.1 77 1.6 2.1 86 2.0 2.5

28 0.1 0.0 37 0.4 0.5 45 0.7 0.8 69 1.5 1.9 78 1.9 2.4

32 0.2 0.2 39 0.5 0.5 63 1.3 1.7 71 1.8 2.2

27 0.0 –0.2 33 0.3 0.2 56 1.2 1.5 65 1.6 2.0

27 0.0 –0.2 50 1.0 1.2 59 1.4 1.8

44 0.7 0.8 53 1.2 1.5

38 0.4 0.4 47 1.0 1.2

32 0.1 –0.1 41 0.7 0.7

90

92

94

27 –0.3 –0.6 35 30 25 0.4 0.0 –0.4 0.2 –0.3 –0.9

10LDT34 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 128-S 148-S

ys(end) ys(center) 46 48 50 in. 181 162 145 7.00 1.5 1.5 1.6 7.00 2.0 2.0 2.1 188 169 8.00 1.8 1.8 8.00 2.4 2.5

168-S

9.00 9.00

188-S

10.00 10.00

188-D1

14.39 4.00

208-D1

15.50 4.25

Lightweight — No Topping Span, ft

52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102

131 1.6 2.2 152 1.9 2.5 189 171 2.0 2.1 2.7 2.8 188 2.3 3.1

117 1.7 2.3 137 2.0 2.6 155 2.2 2.9 170 2.4 3.2

106 1.7 2.3 124 2.0 2.7 141 2.3 3.0 155 2.5 3.3 200 3.0 4.1

95 1.7 2.3 112 2.1 2.8 128 2.3 3.1 141 2.5 3.4 183 3.1 4.2

85 1.7 2.4 102 2.1 2.8 116 2.4 3.2 128 2.6 3.4 167 3.3 4.4 187 3.5 4.8

77 1.7 2.3 92 2.1 2.8 105 2.4 3.2 117 2.7 3.5 154 3.4 4.5 172 3.7 4.9

69 1.7 2.3 83 2.1 2.8 96 2.4 3.2 107 2.7 3.5 141 3.5 4.6 158 3.8 5.1

62 1.7 2.3 75 2.1 2.8 87 2.4 3.2 97 2.7 3.6 129 3.6 4.7 146 3.9 5.2

55 1.6 2.2 68 2.0 2.7 79 2.4 3.2 89 2.7 3.6 119 3.6 4.7 134 4.0 5.3

49 1.5 2.0 61 2.0 2.7 72 2.4 3.1 81 2.7 3.5 109 3.6 4.7 123 4.1 5.4

44 1.4 1.8 55 1.9 2.6 65 2.3 3.1 73 2.6 3.5 101 3.6 4.7 113 4.2 5.4

39 1.2 1.6 49 1.8 2.4 59 2.2 3.0 67 2.6 3.4 92 3.6 4.6 103 4.2 5.4

34 1.0 1.3 44 1.6 2.2 53 2.1 2.8 61 2.5 3.2 83 3.6 4.5 94 4.2 5.4

30 0.8 1.0 39 1.4 1.9 48 2.0 2.6 55 2.3 3.1 76 3.5 4.4 86 4.2 5.3

26 0.6 0.6 35 1.2 1.5 43 1.8 2.3 50 2.2 2.9 69 3.4 4.2 78 4.1 5.1

31 1.0 1.2 38 1.5 2.0 45 2.0 2.6 62 3.2 3.9 71 4.0 4.9

27 0.7 0.7 34 1.3 1.6 40 1.7 2.2 56 3.1 3.6 65 3.8 4.7

30 1.0 1.1 36 1.5 1.8 52 2.9 3.4 58 3.7 4.4

26 0.6 0.6 32 1.1 1.3 48 2.6 3.1 53 3.4 4.0

28 0.8 0.8 44 2.4 2.8 48 3.2 3.7

40 2.1 2.4 44 2.9 3.3

37 1.7 2.0 41 2.6 2.9

33 1.3 1.5 37 2.3 2.5

30 0.9 0.8 34 1.9 2.0

26 0.3 0.0 31 29 1.4 0.9 1.4 0.8

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–25

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

  3

3.5 Pretopped Double-Tee Load Tables (cont.) Strand Pattern Designation

12'-0" × 30"

Number of strand (18) S = straight  D = depressed

Section Properties

Normalweight



A = 928 I = 59,997 yb = 22.94 yt = 7.06 Sb = 2615 St = 8498 wt = 967 DL = 81 V/S = 2.30

188- D1

Number of depression points Diameter of strand in 16ths

Because these units are pretopped and are typically used in parking structures, safe loads shown do not include any superimposed dead loads. Loads shown are live load. Long-time cambers do not include live load.

Lightweight

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

928 59,997 22.94 7.06 2615 8498 741 62 2.30

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

fc' = 5000 psi

Key

fpu = 270,000 psi

158 – Safe superimposed service load, lb/ft2 0.8 – Estimated camber at erection, in. 1.1 – Estimated long-time camber, in.

/2-in.-diameter regular strand

1

Check with regional producers for availability.

12DT30 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 128-S

ys(end) ys(center) in. 7.00 7.00

148-S

8.00 8.00

168-S

9.00 9.00

188-S

10.00 10.00

188-D1

14.39 4.00

208-D1

15.50 4.25

Normalweight — No Topping Span, ft

40

42

44

46

48

50

52

54

56

58

60

62

64

66

68

70

72

74

76

78

80

158 0.8 1.1 182 0.9 1.3

138 0.8 1.2 160 1.0 1.3 178 1.1 1.5 194 1.1 1.6

120 0.9 1.2 140 1.0 1.4 157 1.1 1.5 171 1.2 1.6

105 0.9 1.2 123 1.0 1.4 139 1.2 1.6 152 1.2 1.7

91 0.9 1.2 108 1.0 1.4 122 1.2 1.6 134 1.3 1.7 184 1.6 2.2

79 0.9 1.2 95 1.1 1.5 108 1.2 1.6 119 1.3 1.8 165 1.7 2.3

69 0.8 1.1 83 1.0 1.4 95 1.2 1.6 106 1.3 1.8 148 1.7 2.4 166 1.9 2.6

59 0.8 1.1 73 1.0 1.4 84 1.2 1.6 93 1.3 1.8 132 1.8 2.4 149 2.0 2.7

51 0.7 1.0 63 1.0 1.3 74 1.1 1.6 83 1.3 1.7 119 1.8 2.4 135 2.0 2.7

43 0.6 0.8 55 0.9 1.2 65 1.1 1.5 73 1.2 1.7 107 1.8 2.4 121 2.0 2.7

37 0.5 0.6 47 0.8 1.0 57 1.0 1.3 64 1.1 1.6 96 1.8 2.3 109 2.1 2.7

30 0.4 0.4 41 0.7 0.9 49 0.9 1.2 56 1.0 1.4 86 1.7 2.2 97 2.1 2.7

82

34 0.5 0.6 42 0.8 1.0 49 0.9 1.2 77 1.7 2.1 86 2.0 2.6

29 0.3 0.4 36 0.6 0.7 43 0.8 1.0 68 1.6 2.0 76 1.9 2.4

31 0.4 0.4 36 0.6 0.7 61 1.4 1.9 68 1.8 2.3

29 0.4 0.4 54 1.3 1.7 61 1.7 2.1

48 1.1 1.4 54 1.5 1.9

42 0.9 1.1 48 1.3 1.7

35 0.6 0.7 43 1.1 1.4

29 0.3 0.2 37 0.8 1.0

31 26 0.5 0.1 0.5 –0.1

12LDT30 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 128-S 148-S

ys(end) ys(center) 40 42 44 in. 172 152 134 7.00 1.4 1.4 1.5 7.00 1.8 1.9 2.0 196 174 154 8.00 1.5 1.6 1.7 8.00 2.1 2.2 2.3

168-S

9.00 9.00

188-S

10.00 10.00

188-D1

14.39 4.00

208-D1

15.50 4.25

192 171 1.8 1.9 2.4 2.5 185 2.0 2.6

Lightweight — No Topping Span, ft

46

48

50

52

54

56

58

60

62

64

66

68

70

72

74

76

78

80

82

84

86

119 1.6 2.1 137 1.8 2.4 153 2.0 2.6 166 2.1 2.8

105 1.6 2.2 122 1.9 2.5 136 2.1 2.7 148 2.2 2.9

93 1.7 2.2 109 1.9 2.6 122 2.1 2.8 133 2.3 3.0 179 2.8 3.8

83 1.7 2.3 97 2.0 2.6 109 2.2 2.9 120 2.3 3.1 162 2.9 4.0

73 1.7 2.3 87 2.0 2.7 98 2.2 3.0 108 2.4 3.2 147 3.1 4.1

65 1.7 2.3 77 2.0 2.7 88 2.3 3.0 97 2.5 3.3 133 3.2 4.3

57 1.6 2.2 69 2.0 2.7 79 2.3 3.0 87 2.5 3.3 121 3.3 4.4

51 1.6 2.2 61 2.0 2.7 71 2.3 3.0 78 2.5 3.3 110 3.4 4.4 123 3.7 4.9

45 1.5 2.0 55 1.9 2.6 63 2.2 3.0 70 2.5 3.3 100 3.5 4.5 111 3.8 5.0

39 1.4 1.9 48 1.8 2.5 57 2.2 2.9 63 2.4 3.2 90 3.5 4.5 101 3.8 5.1

34 1.2 1.6 43 1.7 2.3 50 2.1 2.8 57 2.3 3.1 81 3.5 4.5 91 3.9 5.1

29 1.0 1.3 38 1.6 2.1 45 2.0 2.6 51 2.2 3.0 73 3.4 4.4 82 3.9 5.1

88

90

33 1.4 1.8 40 1.8 2.4 45 2.1 2.8 65 3.4 4.2 74 3.9 5.0

29 1.1 1.4 35 1.6 2.1 40 1.9 2.5 58 3.2 4.0 67 3.9 4.9

31 1.3 1.7 36 1.7 2.2 52 3.1 3.7 60 3.8 4.7

27 1.0 1.3 31 1.4 1.8 46 2.9 3.4 53 3.6 4.4

27 1.1 1.3 42 2.7 3.2 48 3.4 4.0

38 2.4 2.8 42 3.1 3.6

35 2.1 2.5 38 2.9 3.3

31 1.8 2.0 35 2.6 2.8

28 1.4 1.5 31 28 26 2.2 1.8 1.3 2.4 1.9 1.3

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

3–26

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.5 Pretopped Double-Tee Load Tables (cont.) Strand Pattern Designation

12'-0" × 34"

Number of strand (18) S = straight  D = depressed

Normalweight



A = 978 I = 86,072 yb = 25.77 yt = 8.23 Sb = 3340 St = 10,458 wt = 1,019 DL = 85 V/S = 2.39

188- D1

Number of depression points Diameter of strand in 16ths

Because these units are pretopped and are typically used in parking structures, safe loads shown do not include any superimposed dead loads. Loads shown are live load. Long-time cambers do not include live load.

  3

Section Properties

Lightweight

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

978 86,072 25.77 8.23 3340 10,458 781 65 2.39

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

fc' = 5000 psi

Key

fpu = 270,000 psi

193 – Safe superimposed service load, lb/ft2 0.7 – Estimated camber at erection, in. 1.0 – Estimated long-time camber, in.

/2-in.-diameter regular strand

1

Check with regional producers for availability.

12DT34 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 128-S 148-S

ys(end) ys(center) 40 42 44 in. 193 169 149 7.00 0.7 0.7 0.8 7.00 1.0 1.0 1.1 197 174 8.00 0.9 0.9 8.00 1.2 1.2

168-S

9.00 9.00

188-S

10.00 10.00

188-D1

14.39 4.00

208-D1

15.50 4.25

Normalweight — No Topping Span, ft

46

48

131 0.8 1.1 154 0.9 1.3 197 174 1.0 1.0 1.4 1.4 192 1.1 1.6

115 0.8 1.1 136 1.0 1.3 155 1.1 1.5 171 1.2 1.6

66

68

70

72

74

76

78

80

82

101 88 77 67 59 51 43 37 31 0.8 0.8 0.8 0.7 0.7 0.6 0.5 0.4 0.3 1.1 1.1 1.1 1.0 09 0.8 0.7 0.5 0.4 120 107 94 83 73 64 56 49 42 1.0 1.0 1.0 1.0 0.9 0.9 0.8 0.7 0.6 1.4 1.4 1.4 1.3 1.3 1.2 1.1 1.0 0.8 138 123 109 97 86 76 67 59 52 1.1 1.1 1.1 1.1 1.1 1.1 1.0 1.0 0.9 1.5 1.6 1.6 1.6 1.5 1.5 1.4 1.3 1.1 153 137 122 109 97 87 77 69 61 1.2 1.3 1.3 1.3 1.3 1.2 1.2 1.1 1.1 1.7 1.7 1.7 1.8 1.7 1.7 1.7 1.6 1.4 180 162 147 132 119 108 97 88 1.6 1.6 1.7 1.7 1.7 1.7 1.6 1.6 2.1 2.2 2.2 2.2 2.2 2.2 2.1 2.1 183 166 150 136 123 112 101 1.8 1.8 1.9 1.9 2.0 2.0 1.9 2.4 2.5 2.6 2.6 2.6 2.6 2.5

50

52

54

56

58

60

62

64

25 0.2 0.1 36 0.5 0.6 45 0.7 1.0 53 1.0 1.3 79 1.5 2.0 92 1.9 2.4

84

30 0.3 0.4 39 0.6 0.8 47 0.8 1.1 71 1.5 1.9 82 1.8 2.3

25 0.1 0.1 34 0.4 0.5 41 0.7 0.8 63 1.4 1.8 74 1.7 2.2

28 0.2 0.2 35 0.5 0.6 57 1.2 1.6 67 1.6 2.1

30 0.3 0.3 50 1.1 1.4 61 1.5 1.9

45 0.9 1.1 55 1.3 1.7

39 0.6 0.7 49 1.1 1.4

34 28 0.4 0.1 0.3 –0.1 43 37 0.9 0.6 1.1 0.7

86

88

31 26 0.3 –0.1 0.2 –0.3

12LDT34 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern 128-S 148-S

ys(end) ys(center) 42 44 46 in. 184 164 146 7.00 1.2 1.3 1.4 7.00 1.6 1.7 1.8 189 169 8.00 1.5 1.6 8.00 2.0 2.1

168-S

9.00 9.00

188-S

10.00 10.00

188-D1

14.39 4.00

208-D1

15.50 4.25

Lightweight — No Topping Span, ft

48

50

52

54

56

58

60

62

64

66

68

70

72

74

76

78

80

82

84

86

88

90

92

94 96

130 1.4 1.9 151 1.6 2.2 189 170 1.8 1.8 2.3 2.5 186 2.0 2.7

116 1.5 2.0 135 1.7 2.3 153 1.9 2.6 168 2.1 2.8

103 1.5 2.0 121 1.8 2.4 137 2.0 2.6 152 2.2 2.9 195 2.6 3.5

92 1.5 2.1 109 1.8 2.4 124 2.1 2.7 137 2.2 3.0 177 2.7 3.7 198 2.9 4.0

82 1.5 2.1 98 1.9 2.5 112 2.1 2.8 124 2.3 3.1 161 2.8 3.8 180 3.1 4.2

73 1.5 2.1 88 1.9 2.5 101 2.1 2.9 112 2.4 3.1 147 3.0 3.9 165 3.2 4.3

65 1.5 2.1 79 1.9 2.5 91 2.2 2.9 102 2.4 3.2 134 3.1 4.1 151 3.3 4.5

58 1.5 2.0 71 1.9 2.5 82 2.2 2.9 92 2.4 3.2 123 3.2 4.2 138 3.4 4.6

52 1.4 2.0 64 1.8 2.5 74 2.2 2.9 83 2.4 3.2 112 3.2 4.2 127 3.6 4.7

46 1.4 1.8 57 1.8 2.4 67 2.1 2.9 76 2.4 3.2 103 3.2 4.2 116 3.6 4.8

40 1.2 1.7 51 1.7 2.3 60 2.1 2.8 68 2.4 3.2 94 3.2 4.2 107 3.7 4.8

35 1.1 1.5 45 1.6 2.2 54 2.0 2.7 62 2.3 3.1 86 3.2 4.1 98 3.8 4.9

31 0.9 1.2 40 1.5 2.0 48 1.9 2.6 56 2.3 3.0 78 3.2 4.0 89 3.8 4.8

26 0.7 0.9 35 1.3 1.7 43 1.8 2.4 50 2.1 2.9 71 3.1 3.9 80 3.7 4.7

31 1.1 1.4 38 1.6 2.1 45 2.0 2.7 64 3.0 3.7 73 3.7 4.6

27 0.9 1.1 34 1.4 1.8 40 1.8 2.4 57 2.9 3.5 66 3.6 4.4

30 1.2 1.5 36 1.6 2.1 53 2.7 3.3 59 3.4 4.2

26 0.9 1.0 32 1.3 1.7 48 2.6 3.1 53 3.3 3.9

28 1.0 1.2 44 2.4 2.9 48 3.1 3.6

40 2.1 2.6 44 2.9 3.4

36 1.8 2.2 41 2.6 3.0

33 1.5 1.8 37 2.3 2.7

29 1.1 1.2 34 2.0 2.3

25 0.6 0.5 31 28 1.6 1.2 1.8 1.2

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–27

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

  3

3.5 Pretopped Double-Tee Load Tables (cont.) Strand Pattern Designation

15'-0" × 26"

Number of strand (20) S = straight  D = depressed



Section Properties

Normalweight

A = 1078 I = 53,280 yb = 19.82 yt = 6.18 Sb = 2688 St = 8618 wt = 1122 DL = 75 V/S = 2.38

208- D1

Number of depression points Diameter of strand in 16ths

Because these units are pretopped and are typically used in parking structures, safe loads shown do not include any superimposed dead loads. Loads shown are live load. Long-time cambers do not include live load.

Key

Lightweight

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

1078 53,280 19.82 6.18 2688 8618 861 57 2.38

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

fc' = 5000 psi

194 – Safe superimposed service load, lb/ft2 0.2 – Estimated camber at erection, in. 0.4 – Estimated long-time camber, in.

fpu = 270,000 psi

/2-in.-diameter regular strand

1

Check with regional producers for availability.

15DT26 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern

ys in.

88-S

7.00

128-S

5.83

168-S

5.69

208-S

5.95

248-S

6.42

Normalweight — No Topping Span, ft

26

28

30

32

34

36

38

40

42

44

46

48

50

52

54

56

58

60

62

64

66

194 159 132 109 90 74 0.2 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 175 150 0.7 0.7 0.9 1.0

61 0.3 0.4 129 0.8 1.0 191 1.2 1.6

49 0.2 0.3 111 0.8 1.1 167 1.2 1.7

40 0.2 0.2 95 0.8 1.1 146 1.3 1.7 192 1.6 2.3

31 0.1 0.1 82 0.8 1.1 128 1.3 1.8 170 1.7 2.4

68

70

70 0.8 1.0 112 1.4 1.9 150 1.8 2.5

60 0.7 1.0 99 1.4 1.9 134 1.9 2.6

51 0.7 0.9 87 1.4 1.9 119 1.9 2.6

43 0.6 0.8 76 1.4 1.9 105 2.0 2.7

36 0.5 0.6 66 1.4 1.9 94 2.0 2.7

29 0.3 0.4 58 1.3 1.8 83 2.0 2.7

50 1.2 1.6 74 2.0 2.7

43 1.1 1.4 65 2.0 2.7

37 0.9 1.2 58 1.9 2.6

31 0.7 0.9 51 1.8 2.4

26 0.5 0.6 44 38 31 1.6 1.5 1.2 2.2 1.9 1.6 45 2.2 2.9

72

74

76

26 1.0 1.2 39 33 27 2.0 1.8 1.5 2.7 2.3 1.9

15LDT26 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern

ys in.

88-S

7.00

128-S

5.83

168-S

5.69

208-S

5.95

248-S

6.42

Lightweight — No Topping Span, ft

28

30

32

34

36

38

40

42

44

46

48

50

52

54

56

58

60

62

64

66

68

70

72

74

76

78

172 145 122 103 0.5 0.5 0.5 0.5 0.6 0.7 0.7 0.8 188 1.1 1.5

87 0.6 0.8 163 1.2 1.6

74 0.6 0.8 142 1.3 1.7

63 0.6 0.8 124 1.3 1.8 180 2.0 2.7

53 0.5 0.7 109 1.4 1.9 159 2.1 2.9

44 0.5 0.7 95 1.5 2.0 141 2.3 3.0

37 0.4 0.6 83 1.5 2.0 126 2.4 3.2

30 0.4 0.5 73 1.5 2.1 112 2.5 3.3

64 1.5 2.1 100 2.6 3.4

56 1.5 2.0 89 2.6 3.4 119 3.4 4.6

49 1.4 2.0 79 2.7 3.5 107 3.6 4.8

42 1.4 1.8 71 2.7 3.5 96 3.7 4.9

36 1.2 1.7 63 2.7 3.5 86 3.7 5.0

31 1.1 1.4 56 2.6 3.5 77 3.8 5.0

27 0.9 1.2 50 2.6 3.4 69 3.8 5.0

44 2.5 3.3 61 3.8 4.9

39 2.4 3.2 55 3.8 4.9

34 2.2 2.9 49 3.7 4.8

30 1.9 2.5 44 3.6 4.7

26 1.6 2.1 40 3.5 4.5 50 5.7 7.1

36 3.3 4.3 46 5.6 6.8

32 3.1 4.0 42 5.4 6.5

28 2.8 3.6 38 5.3 6.2

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

3–28

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.5 Pretopped Double-Tee Load Tables (cont.) Strand Pattern Designation

15'-0" × 30"

Number of strand (20) S = straight  D = depressed

Normalweight



A = 1133 I = 78,625 yb = 22.75 yt = 7.25 Sb = 3457 St = 10,838 wt = 1180 DL = 79 V/S = 2.42

208- D1

Number of depression points Diameter of strand in 16ths

Because these units are pretopped and are typically used in parking structures, safe loads shown do not include any superimposed dead loads. Loads shown are live load. Long-time cambers do not include live load.

Key

  3

Section Properties

Lightweight

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

1133 78,865 22.75 7.25 3457 10,838 905 60 2.42

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2

in.

fc' = 5000 psi

169 – Safe superimposed service load, lb/ft2 0.3 – Estimated camber at erection, in. 0.4 – Estimated long-time camber, in.

fpu = 270,000 psi 1

Check with regional producers for availability.

/2-in.-diameter regular strand 15DT30

Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern

ys in.

88-S

7.00

128-S

5.83

168-S

5.69

208-S

5.95

248-S

6.42

Normalweight — No Topping Span, ft

36

38

40

42

44

46

48

50

52

54

56

58

60

62

64

66

68

70

72

74

76

78

169 141 118 99 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 189 0.6 0.9

30

32

34

83 0.3 0.4 164 0.7 0.9

69 0.3 0.4 142 0.7 1.0

57 0.2 0.3 123 0.7 1.0 184 1.1 1.5

47 0.2 0.3 107 0.7 1.0 163 1.2 1.6

38 0.2 0.2 93 0.7 1.0 144 1.2 1.7 190 1.6 2.2

30 0.1 0.1 81 0.7 1.0 127 1.3 1.7 170 1.7 2.3

80

82

70 0.7 1.0 113 1.3 1.8 152 1.8 2.4

60 0.7 0.9 100 1.3 1.8 136 1.8 2.5

51 0.6 0.8 88 1.3 1.8 122 1.9 2.5

44 0.5 0.7 78 1.3 1.8 109 1.9 2.6

37 0.4 0.6 68 1.3 1.8 98 1.9 2.6

30 0.3 0.4 60 1.2 1.7 87 1.9 2.6

53 1.1 1.5 78 1.9 2.6

46 1.0 1.4 70 1.9 2.6

39 0.9 1.2 62 1.8 2.5

34 0.8 1.0 55 1.8 2.4

29 0.6 0.7 49 1.6 2.2 65 2.4 3.2

43 1.5 2.0 58 2.3 3.1

37 1.3 1.7 53 2.2 3.0

32 1.1 1.3 47 2.1 2.8

26 0.8 0.9 41 35 29 1.9 1.7 1.4 2.6 2.2 1.8

15LDT30 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern

ys in.

88-S

7.00

128-S

5.83

168-S

5.69

208-S

5.95

248-S

6.42

Lightweight — No Topping Span, ft

30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 183 155 132 113 97 83 71 61 52 44 37 31 25 0.4 0.5 0.5 0.5 0.5 0.6 0.6 0.5 0.5 0.5 0.4 0.3 0.2 0.6 0.7 0.7 0.7 0.8 0.8 0.8 0.7 0.7 0.6 0.6 0.4 0.3 177 156 137 121 107 94 83 74 65 57 50 44 1.1 1.2 1.2 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.5 1.6 1.7 1.8 1.8 1.9 1.9 2.0 2.0 1.9 1.9 1.7 198 176 157 141 126 113 102 92 82 74 1.9 2.0 2.1 2.2 2.3 2.4 2.4 2.5 2.5 2.5 2.5 2.7 2.8 2.9 3.0 3.1 3.2 3.2 3.3 3.3 184 166 150 136 123 111 101 2.8 2.9 3.1 3.2 3.3 3.4 3.5 3.8 4.0 4.1 4.3 4.5 4.6 4.7

38 1.2 1.6 66 2.5 3.3 92 3.6 4.7

33 1.1 1.4 59 2.5 3.3 83 3.6 4.8

29 0.9 1.2 53 2.5 3.3 76 3.6 4.8

48 2.4 3.2 68 3.6 4.7

42 2.3 3.1 62 3.6 4.7

37 2.1 2.9 56 3.6 4.6

33 1.9 2.6 51 3.5 4.6

29 1.7 2.2 46 3.4 4.5

25 1.4 1.8 41 37 33 29 3.3 3.1 2.9 2.6 4.3 4.1 3.8 3.4 42 38 4.4 4.2 5.6 5.4

26 2.2 2.9 35 32 29 4.0 3.8 3.5 5.2 4.9 4.5

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–29

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

  3

3.5 Pretopped Double-Tee Load Tables (cont.) Strand Pattern Designation

15'-0" × 34"

Number of strand (20) S = straight  D = depressed

Section Properties

Normalweight



A = 1185 in.2 I = 109,621 in.4 yb = 25.65 in. yt = 8.35 in. Sb = 4274 in.3 St = 13,121 in.3 wt = 1234 lb/ft DL = 82 lb/ft2 V/S = 2.45 in.

208- D1

Lightweight

Number of depression points Diameter of strand in 16ths

Because these units are pretopped and are typically used in parking structures, safe loads shown do not include any superimposed dead loads. Loads shown are live load. Long-time cambers do not include live load.

Key

1185 109,621 22.65 8.35 4274 13,121 946 63 2.45

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2

in.

fc' = 5000 psi

174 – Safe superimposed service load, lb/ft2 0.3 – Estimated camber at erection, in. 0.4 – Estimated long-time camber, in.

fpu = 270,000 psi

/2-in.-diameter regular strand

1

Check with regional producers for availability.

15DT34 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern

Normalweight — No Topping Span, ft

ys in.

32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88

88-S

7.00

128-S

5.83

168-S

5.69

208-S

5.95

248-S

6.42

174 147 124 105 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 198 0.6 0.8

89 0.3 0.4 173 0.6 0.9

75 0.3 0.4 151 0.7 0.9

63 0.2 0.3 132 0.7 0.9 197 1.1 1.4

52 0.2 0.3 116 0.7 1.0 175 1.1 1.5

43 0.2 0.2 101 0.7 1.0 156 1.1 1.6

35 0.1 0.2 89 0.7 1.0 139 1.2 1.6 185 1.6 2.2

27 0.1 0.1 77 0.7 0.9 124 1.2 1.7 167 1.6 2.3

67 0.6 0.9 110 1.2 1.7 150 1.7 2.3

58 0.6 0.8 98 1.2 1.7 135 1.8 2.4

50 0.6 0.7 87 1.2 1.7 122 1.8 2.4

43 0.5 0.6 77 1.2 1.7 110 1.8 2.4

36 0.4 0.5 69 1.2 1.6 99 1.8 2.5

30 0.3 0.3 61 1.1 1.5 89 1.8 2.5

53 1.1 1.4 80 1.8 2.5 105 2.4 3.2

47 1.0 1.3 72 1.8 2.4 95 2.4 3.2

41 0.8 1.1 64 1.7 2.4 86 2.4 3.2

35 0.7 0.9 57 1.7 2.3 78 2.4 3.2

30 0.5 0.6 51 1.6 2.1 71 2.3 3.1

25 0.3 0.3 45 1.4 1.9 64 2.3 3.0

40 1.3 1.6 57 2.2 2.9

35 1.1 1.3 52 2.1 2.8

30 0.8 1.0 46 1.9 2.6

25 0.6 0.6 40 34 29 1.7 1.5 1.2 2.3 1.9 1.5

15LDT34 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand pattern

ys in.

88-S

7.00

128-S

5.83

168-S

5.69

208-S

5.95

248-S

6.42

Lightweight — No Topping

Span, ft 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 188 161 139 120 103 89 77 67 57 49 42 35 30 0.4 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.4 0.4 0.3 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.5 0.4 187 166 147 130 116 103 92 81 72 64 57 50 44 1.0 1.1 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.4 1.5 1.6 1.7 1.7 1.8 1.8 1.8 1.9 1.8 1.8 1.7 1.6 189 170 153 138 125 112 102 92 83 75 1.8 1.9 2.0 2.1 2.2 2.2 2.3 2.3 2.4 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.0 3.1 3.1 3.2 200 181 164 150 136 124 113 103 2.6 2.7 2.8 3.0 3.1 3.2 3.3 3.4 3.5 3.7 3.9 4.0 4.2 4.3 4.4 4.5

39 1.1 1.5 68 2.4 3.2 94 3.4 4.5

34 1.0 1.3 61 2.3 3.1 86 3.5 4.5

29 0.8 1.1 55 2.3 3.1 79 3.5 4.5

25 0.7 0.8 49 2.2 3.0 72 3.5 4.5

44 2.1 2.9 65 3.5 4.5

39 2.0 2.7 60 3.4 4.5

35 1.8 2.4 54 3.4 4.4

31 1.6 2.1 49 3.3 4.3 62 4.5 5.8

27 1.4 1.8 45 3.2 4.2 56 4.5 5.7

40 3.0 4.0 51 4.4 5.6

36 2.9 3.8 47 4.3 5.5

32 2.6 3.4 43 4.2 5.3

29 2.3 3.0 40 4.0 5.2

26 1.9 2.4 36 33 3.8 3.6 4.9 4.6

Strength is based on strain compatibility; bottom tension is limited to 12 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

3–30

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.6 Hollow-Core Load Tables Strand Pattern Designation 76-S

4'-0" × 6" Normalweight Concrete

No Topping



A = I = yb = yt = Sb = St = wt = DL = V/S =

S = straight



Diameter of strand in 16ths Number of strand (7)



Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

fc' = 5000 psi

Capacity of sections of other configurations are similar. For precise values, see local hollow-core manufacturer.

  3

Section Properties 187 763 3.00 3.00 254 254 195 49 1.73

2 in. topping

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

1640 4.14 3.86 396 425 295 74

in.4 in. in. in.3 in.3 lb/ft lb/ft2

fpu = 270,000 psi

Key 290 – Safe superimposed service load, lb/ft2 0.1 – Estimated camber at erection, in. 0.2 – Estimated long-time camber, in.

4HC6 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand designation code 66-S

No Topping

Span, ft 10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

290 0.1 0.2

258 0.2 0.2 302 0.2 0.3 385 0.3 0.3 391 0.3 0.4 435 0.4 0.5

230 0.2 0.2 271 0.2 0.3 345 0.3 0.4 351 0.4 0.5 391 0.4 0.6

206 0.2 0.2 245 0.2 0.3 315 0.3 0.4 316 0.4 0.5 354 0.5 0.6

188 0.2 0.3 223 0.3 0.3 285 0.4 0.5 288 0.5 0.6 324 0.5 0.7

171 0.2 0.3 205 0.3 0.3 262 0.4 0.5 265 0.5 0.7 297 0.6 0.8

157 0.2 0.2 187 0.3 0.3 243 0.4 0.5 245 0.6 0.7 274 0.7 0.8

145 0.2 0.2 172 0.3 0.3 225 0.5 0.6 226 0.6 0.7 254 0.7 0.9

129 0.2 0.2 155 0.3 0.3 201 0.5 0.6 210 0.7 0.8 236 0.8 0.9

114 0.2 0.1 136 0.3 0.3 177 0.5 0.6 197 0.7 0.8 220 0.8 1.0

100 0.2 0.1 120 0.3 0.2 157 0.5 0.5 185 0.7 0.8 203 0.9 1.0

88 0.2 0.0 105 0.3 0.1 139 0.5 0.5 167 0.7 0.8 186 0.9 1.0

77 0.1 –0.1 93 0.3 0.0 124 0.5 0.4 149 0.8 0.7 166 0.9 1.0

68 0.0 –0.3 82 0.2 –0.1 110 0.5 0.3 134 0.8 0.7 148 0.9 0.9

59 –0.1 –0.5 73 0.1 –0.2 99 0.5 0.2 119 0.7 0.6 133 1.0 0.9

52 –0.2 –0.7 65 0.1 –0.4 88 0.4 0.1 107 0.7 0.5 119 0.9 0.8

46 –0.4 –0.9 57 0.0 –0.7 78 0.3 –0.1 95 0.7 0.3 107 0.9 0.7

40 –0.5 –1.2 49 –0.1 –0.9 68 0.3 –0.3 85 0.6 0.2 96 0.9 0.5

33 –0.7 –1.5 42 –0.3 –1.2 60 0.1 –0.6 76 0.5 0.0 86 0.8 0.3

28

76-S 96-S 87-S 97-S

–1.9 36 –0.4 –1.6 53 0.0 –0.9 68 0.4 –0.3 78 0.7 0.1

30

31 –0.6 –2.0 46 –0.1 –1.3 60 0.3 –0.6 70 0.6 –0.2

4HC6 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand designation code 66-S 76-S 96-S 87-S 97-S

2 in. Normalweight Topping

Span, ft 12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

333 0.2 0.2

300 0.2 0.2 357 0.2 0.2

272 0.2 0.2 324 0.3 0.2 418 0.4 0.4 422 0.5 0.5 473 0.5 0.6

248 0.2 0.2 296 0.3 0.2 384 0.4 0.4 388 0.5 0.5 433 0.6 0.6

227 0.2 0.2 272 0.3 0.2 353 0.4 0.4 359 0.6 0.5 400 0.7 0.7

210 02 0.1 248 0.3 0.2 319 0.5 0.4 332 0.6 0.6 371 0.7 0.7

182 0.2 0.1 216 0.3 0.2 279 0.5 0.4 309 0.7 0.6 346 0.8 0.7

158 0.2 0.0 188 0.3 0.1 245 0.5 0.4 288 0.7 0.6 323 0.8 0.7

136 0.2 –0.1 163 0.3 0.1 216 0.5 0.3 258 0.7 0.5 288 0.9 0.7

113 0.2 –0.2 137 0.3 0.0 186 0.5 0.3 224 0.7 0.5 251 0.9 0.7

93 0.1 –0.3 115 0.3 –0.2 160 0.5 0.2 195 0.8 0.4 219 0.9 0.6

75 0.1 –0.5 95 0.2 –0.3 137 0.5 0.1 169 0.8 0.4 192 0.9 0.6

59 0.0 –0.7 78 0.1 –0.5 116 0.5 –0.1 147 0.7 0.2 168 1.0 0.5

46 –0.1 –0.9 63 0.1 –0.7 98 0.4 –0.3 127 0.7 0.1 146 0.9 0.4

34 –0.2 –1.2 50 –0.0 –0.9 82 0.3 –0.5 109 0.7 –0.1 127 0.9 0.2

38 –0.1 –1.2 68 0.3 –0.7 94 0.6 –0.3 110 0.9 0.0

27 –0.3 –1.5 55 0.1 –1.0 80 0.5 –0.5 95 0.8 –0.2

43 0.0 –1.4 67 0.4 –0.8 82 0.7 –0.5

33 –0.1 –1.7 55 0.3 –1.2 70 0.6 –0.8

Strength is based on strain compatibility; bottom tension is limited to 7.5 fc' ; see pages 3–8 through 3–11 for explanation. See item 3, note 4, Section 3.3.2 for explanation of vertical line.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–31

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

  3

3.6 Hollow-Core Load Tables (cont.) Strand Pattern Designation 76-S

4'-0" × 8" Normalweight Concrete

Section Properties

No Topping



A = 215 in.2 I = 1666 in.4 yb = 4.00 in. yt = 4.00 in. Sb = 417 in.3 St = 417 in.3 wt = 224 lb/ft DL = 56 lb/ft2 V/S = 1.92 in.

S = straight





Diameter of strand in 16ths Number of strand (7)

Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load. Capacity of sections of other configurations are similar. For precise values, see local hollow-core manufacturer.

2 in. topping 3071 5.29 4.71 581 652 324 81

in.4 in. in. in.3 in.3 lb/ft lb/ft2

fc' = 5000 psi fpu = 270,000 psi

Key 385 – Safe superimposed service load, lb/ft2 0.1 – Estimated camber at erection, in. 0.2 – Estimated long-time camber, in.

4HC8 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand designation code 66-S 76-S 58-S 68-S 78-S

No Topping

Span, ft 11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

385 0.1 0.2 449 0.2 0.2 422 0.2 0.3 476 0.3 0.3 488 0.3 0.4

345 0.2 0.2 407 0.2 0.2 380 0.2 0.3 430 0.3 0.4 442 0.3 0.5

313 0.2 0.2 367 0.2 0.3 346 0.3 0.4 393 0.3 0.5 402 0.4 0.5

283 0.2 0.3 334 0.2 0.3 316 0.3 0.4 361 0.4 0.5 370 0.5 0.6

260 0.2 0.3 309 0.3 0.3 290 0.3 0.5 332 0.4 0.6 341 0.5 0.7

240 0.2 0.3 285 0.3 0.4 267 0.4 0.5 309 0.5 0.6 318 0.6 0.8

223 0.2 0.3 263 0.3 0.4 247 0.4 0.6 286 0.5 0.7 295 0.6 0.8

204 0.2 0.3 242 0.3 0.4 231 0.5 0.6 269 0.6 0.7 275 0.7 0.9

179 0.3 0.3 213 0.3 0.4 216 0.5 0.6 253 0.6 0.8 259 0.7 1.0

158 0.3 0.3 188 0.3 0.4 202 0.5 0.7 235 0.7 0.8 241 0.8 1.0

140 0.3 0.3 167 0.4 0.4 190 0.5 0.7 223 0.7 0.9 229 0.9 1.1

124 0.3 0.3 149 0.4 0.4 179 0.6 0.7 209 0.7 0.9 215 0.9 1.2

110 0.2 0.2 133 0.4 0.4 169 0.6 0.7 200 0.8 1.0 203 1.0 1.2

98 0.2 0.2 119 0.3 0.3 160 0.6 0.7 180 0.8 1.0 195 1.0 1.2

87 0.2 0.1 106 0.3 0.3 144 0.6 0.7 165 0.8 1.0 180 1.0 1.3

26

27

28

29

30

31

32 33

34

77 69 61 54 48 43 38 33 0.2 0.1 0.0 0.0 –0.1 –0.2 –0.3 –0.5 0.0 –0.1 –0.2 –0.3 –0.5 –0.7 –0.9 95 86 77 69 62 55 50 44 0.3 0.3 0.2 0.2 0.1 0.0 –0.1 –0.2 0.2 0.1 0.0 –0.1 –0.2 –0.4 –0.6 –0.8 130 118 107 97 88 80 72 66 0.6 0.6 0.5 0.5 0.5 0.4 0.3 0.2 0.6 0.6 0.5 0.4 0.3 0.2 0.0 –0.2 153 142 132 121 110 101 92 84 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 1.0 0.9 0.9 0.9 0.8 0.7 0.6 0.4 168 157 144 135 126 118 110 101 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.3 1.3 1.3 1.3 1.2 1.2 1.1 1.0

35

36

37

38

39 40

29 –0.6 –1.4 39 35 31 26 –0.4 –0.5 –0.7 –0.9 –1.1 –1.4 –1.7 –2.0 60 54 48 42 37 32 28 0.1 0.0 –0.4 –0.3 –0.5 –0.7 –0.9 –0.4 –0.6 –0.9 –1.2 –1.6 –2.0 –2.4 77 70 63 56 51 45 40 0.6 0.5 0.4 0.2 0.1 –0.1 –0.3 0.2 0.0 –0.2 –0.5 –0.8 –1.1 –1.5 92 84 77 70 64 58 52 1.0 0.9 0.8 0.7 0.6 0.5 0.3 0.8 0.7 0.5 0.3 0.0 –0.3 –0.7

4HC8 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. Span, ft Strand designation code 66-S 76-S 58-S 68-S 78-S

2 in. Normalweight Topping

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

400 0.2 0.2 474 0.2 0.2 445 0.3 0.3

365 0.2 0.2 435 0.2 0.2 405 0.3 0.3 463 0.4 0.4 472 0.5 0.5

333 0.2 0.2 396 0.3 0.3 374 0.3 0.4 426 0.4 0.5 435 0.5 0.6

308 0.2 0.2 366 0.3 0.3 342 0.4 0.4 393 0.5 0.5 402 0.6 0.6

282 0.2 0.2 340 0.3 0.3 318 0.4 0.4 366 0.5 0.6 375 0.6 0.7

256 0.2 0.2 304 0.3 0.3 298 0.5 0.4 342 0.6 0.6 348 0.7 0.7

224 0.3 0.2 267 0.3 0.3 275 0.5 0.5 319 0.6 0.6 325 0.7 0.8

197 0.3 0.2 235 0.3 0.3 260 0.5 0.5 299 0.7 0.6 305 0.8 0.8

173 0.3 0.1 208 0.4 0.2 243 0.5 0.5 282 0.7 0.7 288 0.9 0.8

153 0.3 0.1 184 0.4 0.2 228 0.6 0.5 267 0.7 0.7 273 0.9 0.9

135 0.2 0.0 164 0.4 0.2 217 0.6 0.4 251 0.8 0.7 257 1.0 0.9

119 0.2 –0.1 146 0.3 0.1 196 0.6 0.3 239 0.8 0.6 245 1.0 0.9

105 0.2 –0.2 130 0.3 0.0 177 0.6 0.3 216 0.8 0.6 232 1.0 0.9

93 0.2 –0.3 116 0.3 –0.1 159 0.6 0.3 195 0.8 0.6 220 1.1 0.8

82 0.1 –0.4 103 0.3 –0.2 143 0.6 0.2 177 0.8 0.5 207 1.1 0.8

68 0.0 –0.6 88 0.2 –0.4 126 0.5 0.1 158 0.8 0.4 186 1.1 0.7

56 –0.0 –0.7 74 0.2 –0.5 110 0.5 –0.1 140 0.8 0.3 167 1.1 0.7

45 –0.1 –0.9 62 0.1 –0.7 95 0.5 –0.2 124 0.8 0.2 149 1.1 0.6

36 –0.2 –1.2 51 –0.0 –0.9 82 0.1 –0.4 110 0.8 0.0 133 1.1 0.4

32

33

34

35

36

37

38

26 –0.3 –1.4 41 31 –0.1 –0.2 –1.2 –1.4 70 59 0.3 0.2 –0.6 –0.9 97 84 0.7 0.7 –0.2 –0.4 119 106 1.1 1.1 0.3 0.1

49 0.1 –1.2 73 0.6 –0.6 94 1.0 –0.1

40 0.0 –1.5 62 0.5 –0.9 83 0.9 –0.3

32 –0.1 –1.8 53 0.4 –1.2 73 0.9 –0.6

44 0.2 –1.6 64 0.7 –0.9

36 0.1 –2.0 55 0.6 –1.3

39

40

28 –0.1 –2.4 46 38 0.5 0.3 –1.7 –2.2

Strength is based on strain compatibility; bottom tension is limited to 7.5 fc' ; see pages 3–8 through 3–11 for explanation. See item 3, note 4, Section 3.3.2 for explanation of vertical line.

3–32

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.6 Hollow-Core Load Tables (cont.) Strand Pattern Designation 48-S

4'-0" × 10" Normalweight Concrete

No Topping



Diameter of strand in 16ths Number of strand (4)



Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

f = 5000 psi ' c

Capacity of sections of other configurations are similar. For precise values, see local hollow-core manufacturer.

2 in. topping

A = 259 in.2 I = 3223 in.4 yb = 5.00 in. yt = 5.00 in. Sb = 645 in.3 St = 645 in.3 wt = 270 lb/ft DL = 68 lb/ft2 V/S = 2.23 in.

S = straight



  3

Section Properties

5328 6.34 5.66 840 941 370 93

in.4 in. in. in.3 in.3 lb/ft lb/ft2

fpu = 270,000 psi

Key 210 – Safe superimposed service load, lb/ft2 0.3 – Estimated camber at erection, in. 0.4 – Estimated long-time camber, in.

4HC10 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand designation code 48-S 58-S 68-S 78-S 88-S

No Topping

Span, ft 20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

210 0.3 0.4 267 0.4 0.5 273 0.5 0.7 282 0.6 0.8 288 0.7 1.0

198 0.3 0.4 249 0.4 0.6 255 0.5 0.7 264 0.7 0.9 270 0.8 1.0

185 0.3 0.4 237 0.4 0.6 243 0.6 0.7 249 0.7 0.9 255 0.8 1.1

174 0.3 0.4 223 0.5 0.6 229 0.6 0.8 235 0.7 1.0 241 0.9 1.2

164 0.3 0.4 211 0.5 0.6 217 0.6 0.8 223 0.8 1.0 229 0.9 1.2

151 0.3 0.4 197 0.5 0.6 206 0.7 0.8 212 0.8 1.1 218 1.0 1.3

136 0.3 0.3 179 0.5 0.6 196 0.7 0.8 202 0.9 1.1 208 1.0 1.3

123 0.3 0.3 162 0.5 0.6 187 0.7 0.9 193 0.9 1.1 199 1.1 1.4

111 0.3 0.2 148 0.5 0.6 176 0.7 0.9 185 0.9 1.1 188 1.1 1.4

100 0.2 0.2 134 0.5 0.5 162 0.7 0.8 174 0.9 1.1 180 1.2 1.4

90 0.2 0.1 122 0.5 0.5 153 0.7 0.8 165 0.9 1.1 174 1.2 1.4

82 0.2 0.0 112 0.4 0.4 141 0.7 0.8 153 1.0 1.1 165 1.2 1.5

74 0.1 –0.1 102 0.4 0.3 129 0.7 0.7 144 1.0 1.1 153 1.2 1.5

66 0.1 –0.2 93 0.4 0.2 118 0.7 0.7 136 1.0 1.1 145 1.2 1.4

60 0.0 –0.3 85 0.3 0.1 109 0.6 0.6 129 0.9 1.0 135 1.2 1.4

54 –0.1 –0.5 77 0.2 0.0 100 0.6 0.5 119 0.9 1.0 128 1.2 1.4

48 –0.2 –0.7 70 0.2 –0.1 92 0.5 0.4 113 0.9 0.9 122 1.2 1.3

43 –0.3 –0.8 64 0.1 –0.3 84 0.5 0.2 104 0.8 0.8 115 1.2 1.2

38 –0.4 –1.1 58 0.0 –0.5 78 0.4 0.1 96 0.8 0.6 106 1.2 1.2

34 –0.6 –1.3 53 –0.1 –0.7 71 0.3 –0.1 89 0.7 0.5 101 1.1 1.0

30 –0.7 –1.3 48 –0.3 –1.0 65 0.2 –0.3 82 0.6 0.3 96 1.1 0.9

26 –0.9 –1.9 43 –0.4 –1.2 60 0.1 –0.6 76 0.5 0.1 91 1.0 0.7

39 –0.6 –1.5 54 –0.1 –0.8 69 0.4 –0.1 84 0.9 0.6

35 –0.7 –1.8 49 –0.2 –1.1 63 0.3 –0.4 77 0.8 0.3

30 –0.9 –2.2 44 –0.4 –1.4 57 0.1 –0.7 71 0.7 0.1

26 –1.2 –2.6 39 –0.6 –1.8 52 0.0 –1.0 65 0.5 –0.2

34 –0.8 –2.2 47 –0.2 –1.3 59 0.3 –0.5

4HC10 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. Span, ft Strand designation code 48-S 58-S 68-S 78-S 88-S

2 in. Normalweight Topping

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

255 0.3 0.3 317 0.4 0.4 326 0.5 0.5 335 0.6 0.7 344 0.7 0.8

238 0.3 0.3 298 0.4 0.4 307 0.5 0.6 313 0.7 0.7 322 0.8 0.8

223 0.3 0.3 282 0.4 0.4 291 0.6 0.6 297 0.7 0.7 306 0.8 0.9

209 0.3 0.2 267 0.5 0.4 273 0.6 0.6 279 0.7 0.8 288 0.9 0.9

197 0.3 0.2 252 0.5 0.4 258 0.6 0.6 267 0.8 0.8 273 0.9 1.0

181 0.3 0.2 237 0.5 0.4 246 0.7 0.6 252 0.8 0.8 258 1.0 1.0

163 0.3 0.1 219 0.5 0.4 234 0.7 0.6 240 0.9 0.8 246 1.0 1.0

146 0.3 0.1 198 0.5 0.3 222 0.7 0.6 228 0.9 0.8 234 1.1 1.0

131 0.3 0.0 180 0.5 0.3 212 0.7 0.5 218 0.9 0.8 221 1.1 1.0

117 0.2 –0.1 163 0.5 0.2 202 0.7 0.5 208 0.9 0.8 211 1.2 1.0

107 0.2 –0.2 148 0.5 0.1 188 0.7 0.4 196 0.9 0.7 202 1.2 1.0

96 0.2 –0.3 134 0.4 0.0 171 0.7 0.4 189 1.0 0.7 195 1.2 1.0

86 0.1 –0.4 120 0.4 –0.1 153 0.7 0.3 181 1.0 0.6 184 1.2 0.9

74 0.1 –0.6 105 0.4 –0.2 137 0.7 0.2 165 1.0 0.5 178 1.2 0.9

63 0.0 –0.8 92 0.3 –0.4 122 0.6 0.0 150 0.9 0.4 172 1.2 0.8

52 –0.1 –1.0 80 0.2 –0.5 108 0.6 –0.1 135 0.9 0.3 158 1.2 0.7

43 –0.2 –1.2 69 0.2 –0.7 96 0.5 –0.3 122 0.9 0.2 144 1.2 0.6

34 –0.3 –1.4 59 0.1 –0.9 84 0.5 –0.5 109 0.8 0.0 130 1.2 0.4

26 –0.4 –1.7 50 0.0 –1.2 74 0.4 –0.7 97 0.8 –0.2 118 1.2 0.3

41 –0.1 –1.5 64 0.3 –0.9 86 0.7 –0.4 107 1.1 0.1

33 –0.3 –1.8 55 0.2 –1.2 76 0.6 –0.6 96 1.1 –0.1

26 –0.4 –2.1 46 0.1 –1.5 67 0.5 –0.9 87 1.0 –0.3

38 –0.1 –1.8 58 0.4 –1.2 77 0.9 –0.6

31 –0.2 –2.2 50 0.3 –1.6 68 0.8 –0.9

42 0.1 –1.9 60 0.7 –1.3

35 0.0 –2.3 52 0.5 –1.6

28 –0.2 –2.8 44 0.3 –2.0

Strength is based on strain compatibility; bottom tension is limited to 7.5 fc' ; see pages 3–8 through 3–11 for explanation. See item 3, note 4, Section 3.3.2 for explanation of vertical line.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–33

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

  3

3.6 Hollow-Core Load Tables (cont.) Strand Pattern Designation 76-S

4'-0" × 12" Normalweight Concrete

Section Properties

No Topping



A = 262 in.2 I = 4949 in.4 yb = 6.00 in. yt = 6.00 in. Sb = 825 in.3 St = 825 in.3 wt = 273 lb/ft DL = 68 lb/ft2 V/S = 2.18 in.

S = straight



Diameter of strand in 16ths Number of strand (4)



Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

f = 5000 psi ' c

Capacity of sections of other configurations are similar. For precise values, see local hollow-core manufacturer.

2 in. topping 7811 7.55 6.45 1035 1211 373 93

in.4 in. in. in.3 in.3 lb/ft lb/ft2

fpu = 270,000 psi

Key 258 – Safe superimposed service load, lb/ft2 0.3 – Estimated camber at erection, in. 0.4 – Estimated long-time camber, in.

4HC12 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand designation code 76-S 58-S 68-S 78-S 88-S

No Topping

Span, ft 20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

258 0.3 0.3 258 0.4 0.5 264 0.4 0.6 273 0.5 0.7 282 0.6 0.8

242 0.3 0.4 242 0.4 0.5 248 0.5 0.6 257 0.6 0.8 266 0.7 0.9

228 0.3 0.4 228 0.4 0.5 234 0.5 0.7 243 0.6 0.8 252 0.7 1.0

215 0.3 0.4 215 0.4 0.6 221 0.5 0.7 230 0.7 0.9 236 0.8 1.0

204 0.3 0.4 204 0.5 0.6 210 0.6 0.8 216 0.7 0.9 225 0.8 1.1

194 0.3 0.4 194 0.5 0.6 200 0.6 0.8 206 0.8 1.0 212 0.9 1.2

175 0.3 0.4 182 0.5 0.6 191 0.6 0.8 197 0.8 1.0 203 0.9 1.2

159 0.3 0.4 174 0.5 0.6 180 0.7 0.9 186 0.8 1.1 192 1.0 1.3

144 0.3 0.4 167 0.5 0.6 173 0.7 0.9 179 0.9 1.1 185 1.0 1.3

131 0.3 0.3 157 0.5 0.6 163 0.7 0.9 169 0.9 1.1 175 1.1 1.4

120 0.3 0.3 151 0.5 0.6 157 0.7 0.9 163 0.9 1.2 169 1.1 1.4

109 0.3 0.3 143 0.5 0.6 149 0.7 0.9 155 1.0 1.2 161 1.2 1.5

99 0.3 0.2 138 0.5 0.6 144 0.7 0.9 150 1.0 1.2 153 1.2 1.5

90 0.2 0.1 128 0.5 0.5 137 0.8 0.9 143 1.0 1.2 149 1.2 1.5

82 0.2 0.1 118 0.5 0.5 133 0.8 0.9 136 1.0 1.2 142 1.3 1.5

75 0.1 0.0 108 05 0.4 127 0.7 0.8 133 1.0 1.2 136 1.3 1.6

68 0.1 –0.1 100 0.4 0.4 121 0.7 0.8 127 1.0 1.2 130 1.3 1.6

62 0.0 –0.2 92 0.4 0.3 112 0.7 0.7 121 1.0 1.1 127 1.3 1.5

56 0.0 –0.3 84 0.3 0.2 106 0.7 0.7 115 1.0 1.1 121 1.3 1.5

51 –0.1 –0.5 78 0.3 0.1 98 0.6 0.6 110 1.0 1.0 116 1.3 1.5

46 –0.2 –0.6 71 0.2 –0.1 93 0.6 0.5 105 1.0 1.0 114 1.3 1.4

41 –0.3 –0.8 66 0.1 –0.2 87 0.5 0.3 98 0.9 0.9 107 1.3 1.4

37 –0.4 –1.0 60 0.1 –0.4 81 0.5 0.2 93 0.9 0.8 102 1.3 1.3

33 –0.5 –1.2 55 0.0 –0.6 75 0.4 0.1 86 0.8 0.7 95 1.2 1.2

30 –0.6 –1.5 51 –0.1 –0.8 69 0.3 –0.1 82 0.7 0.5 91 1.2 1.1

26 –0.8 –1.7 46 –0.3 –1.0 64 0.2 –0.3 78 0.7 0.3 84 1.1 1.0

42 –0.4 –1.2 59 0.1 –0.5 72 0.6 0.2 81 1.1 0.8

4HC12 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand designation code 76-S 58-S 68-S 78-S 88-S

2 in. Normalweight Topping

Span, ft 20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

295 0.3 0.3 292 0.4 0.4 301 0.4 0.5 310 0.5 0.6 319 0.6 0.7

276 0.3 0.3 273 0.4 0.4 282 0.5 0.5 291 0.6 0.6 300 0.7 0.8

258 0.3 0.3 258 0.4 0.4 264 0.5 0.6 273 0.6 0.7 282 0.7 0.8

246 0.3 0.3 243 0.4 0.4 249 0.5 0.6 258 0.7 0.7 267 0.8 0.9

232 0.3 0.3 229 0.5 0.4 235 0.6 0.6 244 0.7 0.8 250 0.8 0.9

217 0.3 0.3 216 0.5 0.5 222 0.6 0.6 231 0.8 0.8 237 0.9 1.0

196 0.3 0.2 205 0.5 0.4 211 0.6 0.6 217 0.8 0.8 226 0.9 1.0

177 0.3 0.2 195 0.5 0.4 201 0.7 0.6 207 0.8 0.8 213 1.0 1.0

160 0.3 0.2 186 0.5 0.4 192 0.7 0.6 198 0.9 0.8 204 1.0 1.1

144 0.3 0.1 175 0.5 0.4 181 0.7 0.6 187 0.9 0.9 193 1.1 1.1

131 0.3 0.1 167 0.5 0.4 173 0.7 0.6 179 0.9 0.9 185 1.1 1.1

118 0.3 0.0 160 0.5 0.3 166 0.7 0.6 172 1.0 0.8 175 1.2 1.1

107 0.3 –0.1 151 0.5 0.3 157 0.7 0.6 163 1.0 0.8 169 1.2 1.1

96 0.2 –0.2 139 0.5 0.2 152 0.8 0.5 158 1.0 0.8 161 1.2 1.1

87 0.2 –0.3 127 0.5 0.1 144 0.8 0.5 150 1.0 0.8 156 1.3 1.1

78 0.1 –0.4 116 0.5 0.0 139 0.7 0.4 142 1.0 0.7 148 1.3 1.0

71 0.1 –0.5 106 0.4 –0.1 132 0.7 0.3 138 1.0 0.6 141 1.3 1.0

63 0.0 –0.7 97 0.4 –0.2 127 0.7 0.2 131 1.0 0.6 137 1.3 0.9

56 0.0 –0.8 89 0.3 –0.3 117 0.7 0.1 128 1.0 0.5 131 1.3 0.9

50 –0.1 –1.0 81 0.3 –0.5 107 0.6 –0.1 122 1.0 0.4 125 1.3 0.8

43 –0.2 –1.2 72 0.2 –0.7 98 0.6 –0.2 116 1.0 0.3 122 1.3 0.7

35 –0.3 –1.4 63 0.1 –0.9 88 0.5 –0.4 113 0.9 0.1 117 1.3 0.6

28 –0.4 –1.7 55 0.1 –1.1 78 0.5 –0.6 102 0.9 –0.1 111 1.3 0.4

47 0.0 –1.3 69 0.4 –0.8 92 0.8 –0.2 106 1.2 0.3

39 –0.1 –1.6 61 0.3 –1.0 83 0.7 –0.5 103 1.2 0.1

32 –0.3 –1.9 53 0.2 –1.3 74 0.7 –0.7 94 1.1 –0.1

26 –0.4 –2.2 46 0.1 –1.6 66 0.6 –0.9 86 1.1 –0.3

Strength is based on strain compatibility; bottom tension is limited to 7.5 fc' ; see pages 3–8 through 3–11 for explanation. Shaded values require release strengths higher than 3500 psi.

3–34

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.7 Hollow-Core Section Properties

  3

Trade name Dynaspan Equipment Manufacturer: Dynamold Corporation, Salina, Kansas

A in.2

yb in.

I in.4

wt lb/ft 2

ycb in.

Ic in.4

wt lb/ft 2

Note: All sections are not available from all producers. Check availability with regional manufacturers.

Trade name Flexicore Licensing Organization: The Flexicore Co., Inc., Dayton, Ohio

A in.2

yb in.

I in.4

wt lb/ft 2

ycb in.

Ic in.4

wt lb/ft 2

Note: All sections are not available from all producers. Check availability with regional manufacturers.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–35

CHAPTER 3

  3

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

3.7 Hollow-Core Section Properties (cont.)

Trade name Echo Represented in North & Latin America: CTI Inc., Green Bay, Wisconsin

A, in.2

yb in.

I in.4

wt lb/ft 2

ycb in.

Ic in.4

wt lb/ft 2

, ,

,

,

,

,

,

, ,

,

Note: All sections are not available from all producers. Check availability with regional manufacturers.

3–36

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.7 Hollow-Core Section Properties (cont.)

  3

Trade name Elematic® Equipment Manufacturer: Elematic Inc., Waukesha, Wisconsin

A in.2

yb in.

I in.4

wt lb/ft 2

ycb in.

Ic in.4

,

,

,

,

,

,

wt lb/ft 2

,

Note: All sections are not available from all producers. Check availability with regional manufacturers.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–37

CHAPTER 3

  3

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

3.7 Hollow-Core Section Properties (cont.)

Trade names: Spancrete, Ultralight Spancrete Licensing Organization: Spancrete Machinery Corporation, Waukesha, Wisconsin

A in.2

yb in.

I in.4

wt lb/ft 2

ycb in.

Ic in.4

,

,

,

,

wt lb/ft 2

Note: All Spancrete hollow-core sections can be produced two at a time on Spancrete’s 96” machine. Note: Spancrete hollow-core is also available in 40 in., 48 in., and 96 in. widths. All sections are not available from all producers. Check availability with regional manufacturers.

3–38

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.7 Hollow-Core Section Properties (cont.)

  3

Trade names: Spancrete®, Ultralight Spancrete® Licensing Organization: Spancrete Machinery Corporation, Waukesha, Wisconsin

A in.2

yb in.

I in.4

wt lb/ft 2

ycb in.

Ic in.4

wt lb/ft 2

, ,

,

, ,

,

Note: Spancrete hollow-core is also available in 40 in., 48 in., and 96 in. widths. All sections are not available from all producers. Check availability with regional manufacturers.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–39

CHAPTER 3

  3

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

3.7 Hollow-Core Section Properties (cont.) Trade name SpanDeck® Licensing Organization: Fabcon, Inc., Savage, Minnesota

A in.2

yb in.

I in.4

wt lb/ft 2

Ic in.4

ycb in.

wt lb/ft 2

, ,

,

Note: All sections are not available from all producers. Check availability with regional manufacturers.

Trade name Ultra-Span Licensing Organization: Ultra-Span Technologies, Inc. Winnepeg, Manitoba, Canada

A in.2

yb in.

I in.4

wt lb/ft 2

ycb in.

Ic in.4

wt lb/ft 2

,

Note: All sections are not available from all producers. Check availability with regional manufacturers.

3–40

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.8 Solid Flat-Slab Load Tables Strand Pattern Designation 76-S

4 in. Thick Normalweight Concrete

No Topping



A = I = yb = yt = Sb = St = wt = DL = V/S =

S = straight



Diameter of strand in 16ths Number of strand (7)



Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

fc' = 5000 psi

Key

  3

Section Properties 192 256 2.00 2.00 128 128 200 50 1.85

2 in. topping

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

763 2.84 3.16 269 242 300 75

in.4 in. in. in.3 in.3 lb/ft lb/ft2

fpu = 270,000 psi

119 – Safe superimposed service load, lb/ft2 0.1 – Estimated camber at erection, in. 0.1 – Estimated long-time camber, in.

FS4 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand designation code 66-S 76-S 58-S 68-S

No Topping

Span, ft 10

11

12

13

14

15

16

17

18

19

20

21

22

119 0.1 0.1 148 0.1 0.1 135 0.2 0.2 169 0.2 0.3

105 0.1 0.1 130 0.1 0.1 120 0.2 0.2 149 0.2 0.3

94 0.1 0.0 116 0.1 0.1 107 0.2 0.2 132 0.2 0.3

86 0.0 0.0 106 0.1 0.0 98 0.2 0.2 120 0.2 0.3

76 0.0 –0.1 93 0.0 –0.1 90 0.1 0.1 110 0.2 0.2

70 –0.1 –0.3 85 0.0 –0.2 82 0.1 0.0 100 0.2 0.2

61 –0.2 –0.4 72 –0.1 –0.3 74 0.0 –0.1 87 0.2 0.1

48 –0.3 –0.6 58 –0.2 –0.5 66 0.0 –0.3 73 0.1 –0.1

38 –0.4 –0.9 47 –0.3 –0.7 61 –0.1 –0.5 62 0.0 –0.3

29 –0.6 –1.2 37 –0.5 –1.0 51 –0.3 –0.8 52 –0.1 –0.5

28 –0.7 –1.4 42 –0.4 –1.1 43 –0.3 –0.8

34 –0.7 –1.5 36 –0.4 –1.2

26 –0.9 –2.0 30 –0.7 –1.6

FS4 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand designation code 66-S 76-S 58-S 68-S

2 in. Normalweight Topping

Span, ft 11

12

13

14

15

16

17

18

19

20

21

22

200 0.1 0.0 250 0.1 0.0

180 0.1 0.0 225 0.1 0.0 210 0.2 0.1

161 0.0 –0.1 200 0.1 –0.1 187 0.2 0.0 228 0.2 0.1

147 0.0 –0.2 177 0.0 –0.1 175 0.1 0.0 215 0.2 0.1

108 –0.1 –0.3 134 0.0 –0.3 154 0.1 –0.1 190 0.2 0.0

76 –0.2 –0.5 99 –0.1 –0.4 146 0.0 –0.3 184 0.2 –0.1

49 –0.3 –0.7 70 –0.2 –0.6 111 0.0 –0.4 146 0.1 –0.3

27 –0.4 –1.0 45 –0.3 –0.9 82 –0.1 –0.7 114 0.0 –0.5

58 –0.3 –0.9 87 –0.1 –0.7

37 –0.4 –1.3 64 –0.3 –1.0

43 –0.4 –1.4

25 –0.7 –1.9

Strength is based on strain compatibility; bottom tension is limited to 7.5 fc' ; see pages 3–8 through 3–11 for explanation. See item 3, note 4, Section 3.3.2 for explanation of vertical line.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–41

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

  3

3.8 Solid Flat-Slab Load Tables (cont.) Strand Pattern Designation 76-S





6 in. Thick Normalweight Concrete

Section Properties

No Topping



A = I = yb = yt = Sb = St = wt = DL = V/S =

S = straight

Diameter of strand in 16ths Number of strand (4)

Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

f = 5000 psi ' c

Key

288 864 3.00 3.00 288 288 300 75 2.67

2 in. topping

in.2 in.4 in. in. in.3 in.3 lb/ft lb/ft2 in.

1834 3.82 4.18 480 439 400 100

in.4 in. in. in.3 in.3 lb/ft lb/ft2

fpu = 270,000 psi

203 – Safe superimposed service load, lb/ft 0.1 – Estimated camber at erection, in. 0.2 – Estimated long-time camber, in.

2

FS6 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand Span, ft designation 11 12 13 14 15 16 17 18 19 20 21 22 code 66-S

203 0.1 0.2

76-S 58-S

180 0.1 0.2 220 0.2 0.2

163 0.2 0.2 198 0.2 0.3 188 0.3 0.4

68-S

148 0.2 0.2 180 0.2 0.3 170 0.3 0.4 213 0.4 0.5

78-S

133 0.2 0.2 165 0.2 0.3 158 0.3 0.4 195 0.4 0.5 230 0.5 0.7

120 0.2 0.1 150 0.2 0.2 143 0.3 0.4 180 0.5 0.6 213 0.6 0.7

110 0.1 0.1 138 0.2 0.2 133 0.4 0.4 165 0.5 0.6 198 0.6 0.8

103 93 79 0.1 0.0 –0.0 0.0 –0.1 –0.2 128 114 96 0.2 0.1 0.0 0.1 0.0 –0.1 120 112 103 0.4 0.3 0.3 0.4 0.3 0.3 155 145 135 0.5 0.5 0.5 0.6 0.6 0.5 185 173 160 0.7 0.7 0.7 0.8 0.8 0.8

68 –0.1 –0.3 80 0.0 –0.2 95 0.3 0.2 125 0.5 0.5 150 0.7 0.7

53 –0.2 –0.5 66 –0.1 –0.4 88 0.2 0.1 118 0.4 0.4 137 0.6 0.6

No Topping 23

24

25

26

27

28

29

42 –0.3 –0.7 54 –0.2 –0.5 77 0.0 –0.2 98 0.3 0.2 119 0.5 0.5

33 –0.5 –1.0 43 –0.3 –0.8 65 –0.1 –0.4 84 0.2 0.0 103 0.4 0.4

34 –0.5 –1.0 54 –0.2 –0.6 71 0.1 –0.2 89 0.4 0.2

26 –0.7 –1.3 44 –0.3 –0.9 60 0.0 –0.4 77 0.3 0.0

35 –0.5 –1.2 50 –0.2 –0.7 66 0.1 –0.3

28 –0.7 –1.6 42 –0.4 –1.1 56 0.0 –0.6

34 –0.6 –1.5 47 –0.2 –0.9

30

31

32

27 –0.9 –1.9 39 32 25 –0.5 –0.7 –1.0 –1.4 –1.8 –2.4

FS6 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand Span, ft designation 13 14 15 16 17 18 19 20 21 code 66-S 76-S 58-S 68-S 78-S

240 0.2 0.1

220 0.2 0.1 265 0.2 0.2

200 0.2 0.1 243 0.2 0.1 230 0.3 0.3

183 0.2 0.0 225 0.2 0.1 210 0.3 0.3

168 0.1 0.0 208 0.2 0.0 195 0.4 0.3 248 0.5 0.4

155 0.1 –0.1 184 0.1 0.0 183 0.3 0.2 228 0.5 0.4 265 0.6 0.5

120 0.0 –0.2 148 0.1 –0.1 168 0.3 0.1 213 0.5 0.4 255 0.7 0.5

92 –0.1 –0.3 118 0.0 –0.2 155 0.3 0.0 200 0.5 0.3 240 0.7 0.5

68 –0.1 –0.5 91 0.0 –0.4 137 0.2 –0.1 179 0.4 0.1 221 0.6 0.4

2 in. Normalweight Topping 22

23

24

25

26

27

28

29

47 –0.2 –0.7 68 –0.1 –0.5 110 0.1 –0.3 148 0.3 0.0 186 0.6 0.3

29 –0.3 –0.9 48 –0.2 –0.7 87 0.0 –0.4 121 0.3 –0.2 156 0.5 0.1

31 –0.3 –1.0 66 –0.1 –0.7 98 0.2 –0.3 130 0.4 0.0

48 –0.2 –0.9 77 0.1 –0.6 107 0.4 –0.2

32 –0.3 –1.2 59 0.0 –0.9 86 0.3 –0.5

42 –0.2 –1.2 68 0.1 –0.8

28 –0.4 –1.5 51 0.0 –1.1

36 –0.2 –1.5

Strength is based on strain compatibility; bottom tension is limited to 7.5 fc' ; see pages 3–8 through 3–11 for explanation. See item 3, note 4, Section 3.3.2 for explanation of vertical line.

3–42

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.8 Solid Flat-Slab Load Tables (cont.) Strand Pattern Designation 76-S

8 in. Thick Normalweight Concrete

No Topping



Diameter of strand in 16ths Number of strand (4)



Safe loads shown include dead load of 10 lb/ft2 for untopped members and 15 lb/ft2 for topped members. Remainder is live load. Long-time cambers include superimposed dead load but do not include live load.

2 in. topping

A = 384 in.2 I = 2048 in.4 yb = 4.00 in. yt = 4.00 in. Sb = 512 in.3 St = 512 in.3 wt = 400 lb/ft DL = 100 lb/ft2 V/S = 3.43 in.

S = straight



  3

Section Properties

f = 5000 psi ' c

3630 4.81 5.19 755 699 500 125

in.4 in. in. in.3 in.3 lb/ft lb/ft2

fpu = 270,000 psi

Key 240 – Safe superimposed service load, lb/ft2 0.1 – Estimated camber at erection, in. 0.2 – Estimated long-time camber, in.

FS8 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand Span, ft designation 13 14 15 16 17 18 19 20 21 22 23 24 25 code 66-S

240 0.1 0.2

76-S

218 0.1 0.2 263 0.2 0.2

198 0.1 0.2 243 0.2 0.2

58-S 68-S

180 165 0.1 0.1 0.2 0.2 223 205 0.2 0.2 0.2 0.2 213 193 0.3 0.3 0.4 0.4 248 0.4 0.5

153 0.1 0.1 190 0.2 0.2 180 0.3 0.4 230 0.4 0.5

78-S

140 0.1 0.1 175 0.2 0.2 168 0.3 0.4 215 0.4 0.6 258 0.6 0.7

128 0.1 0.1 158 0.2 0.2 155 0.3 0.4 200 0.5 0.6 243 0.6 0.7

108 0.1 0.0 134 0.1 0.1 145 0.3 0.3 188 0.5 0.5 228 0.6 0.7

No Topping 30

31

32

33

90 77 65 55 45 35 28 0.0 –0.1 –0.1 –0.2 –0.3 –0.4 –0.5 –0.1 –0.2 –0.3 –0.5 –0.6 –0.8 –1.0 116 100 86 73 62 52 41 32 0.1 0.0 –0.1 –0.1 –0.2 –0.3 –0.4 –0.6 0.0 –0.1 –0.2 –0.3 –0.5 –0.7 –0.9 –1.1 135 125 118 110 92 78 65 54 44 0.3 0.3 0.2 0.2 0.0 –0.1 –0.2 –0.3 –0.4 0.3 0.2 0.2 0.0 –0.1 –0.3 –0.5 –0.7 –0.9 175 165 155 134 117 101 87 74 63 0.5 0.4 0.4 0.3 0.2 0.2 0.1 0.0 –0.1 0.5 0.5 0.4 0.3 0.2 0.0 –0.1 –0.3 –0.5 215 205 183 161 142 124 108 94 81 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.2 0.1 0.7 0.7 0.6 0.5 0.5 0.3 0.2 0.1 –0.1

26

27

28

29

35 –0.6 –1.2 52 –0.3 –0.8 70 0.0 –0.3

27 –0.8 –1.5 43 –0.5 –1.0 59 –0.1 –0.6

34 –0.6 –1.4 50 –0.3 –0.9

34

35

36

27 –0.9 –1.7 41 33 26 –0.5 –0.7 –1.0 –1.2 –1.6 –2.0

FS8 + 2 Table of safe superimposed service load, lb/ft2, and cambers, in. Strand Span, ft designation 15 16 17 18 19 20 21 22 23 24 code 66-S 76-S 58-S 68-S 78-S

263 0.1 0.1

243 0.1 0.1 295 0.2 0.2

223 0.1 0.1 273 0.2 0.2

205 0.1 0.0 255 0.2 0.1 240 0.3 0.3

190 0.1 0.0 235 0.2 0.1 223 0.3 0.3 285 0.4 0.4

163 0.1 –0.1 205 0.2 0.1 208 0.3 0.2 268 0.5 0.4 323 0.6 0.6

139 0.0 –0.1 180 0.1 0.0 195 0.3 0.2 250 0.5 0.4 305 0.6 0.5

119 0.0 –0.2 155 0.1 –0.1 180 0.3 0.1 235 0.5 0.3 300 0.6 0.5

98 –0.1 –0.3 125 0.0 –0.2 170 0.3 0.0 220 0.4 0.3 273 0.6 0.5

75 –0.2 –0.4 99 –0.1 –0.3 147 0.1 –0.1 190 0.3 0.2 234 0.5 0.4

2 in. Normalweight Topping 25

26

27

28

29

30

31

32

33

55 –0.2 –0.6 77 –0.1 –0.5 121 0.1 –0.2 161 0.3 0.1 201 0.5 0.3

37 –0.3 –0.8 57 –0.2 –0.6 98 0.0 –0.3 135 0.2 –0.1 172 0.4 0.2

40 –0.3 –0.8 78 –0.1 –0.5 112 0.2 –0.2 146 0.4 0.1

59 –0.2 –0.7 91 0.1 –0.4 123 0.3 –0.1

43 –0.3 –0.9 72 0.0 –0.6 102 0.2 –0.2

28 –0.4 –1.1 56 –0.1 –0.8 83 0.1 –0.5

40 –0.3 –1.1 66 0.0 –0.7

27 –0.5 –1.4 51 –0.1 –1.0

37 –0.3 –1.3

Strength is based on strain compatibility; bottom tension is limited to 7.5 fc' ; see pages 3–8 through 3–11 for explanation. See item 3, note 4, Section 3.3.2 for explanation of vertical line.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–43

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

  3

3.9 Rectangular Beam Load Tables Normalweight Concrete

b

Section Properties Designation

b in.

h in.

A in.2

12RB16 12RB20 12RB24 12RB28 12RB32 12RB36 16RB24 16RB28 16RB32 16RB36 16RB40

12 12 12 12 12 12 16 16 16 16 16

16 20 24 28 32 36 24 28 32 36 40

192 240 288 336 384 432 384 448 512 576 640

h

fc' = 5000 psi fpu = 270,000 psi

I In.4

yb in.

S in.3

4096 8.00 512 8000 10.00 800 13,824 12.00 1152 21,952 14.00 1568 32,768 16.00 2048 46,656 18.00 2592 18,432 12.00 1536 29,269 14.00 2091 43,691 16.00 2731 62,208 18.00 3456 85,333 20.00 4267

wt lb/ft 200 250 300 350 400 450 400 467 533 600 667

1.  Check local area for availability of other sizes. 2. Safe loads shown include 50% superimposed dead load and 50% live load. 800 psi top tension has been allowed, therefore, additional top reinforcement is required. 3.  Safe loads can be significantly increased by use of structural composite topping.

/2-in.-diameter, low-relaxation strand

1

Key 3550 – Safe superimposed service load, lb/ft 0.4 – Estimated camber at erection, in. 0.2 – Estimated long-time camber, in.

Table of safe superimposed service load, lb/ft, and cambers, in. Designation

Number strand

ys in.

12RB16

5

3.00

12RB20

8

3.00

12RB24

10

3.60

12RB28

12

4.00

12RB32

13

4.77

12RB36

15

5.07

16RB24

13

3.54

16RB28

14

3.71

16RB32

18

4.67

16RB36

20

5.40

16RB40

22

6.00

3–44

Span, ft 22

24

26

28

3550 2770 2210 1790 0.4 0.5 0.6 0.8 0.2 0.2 0.2 0.2 6160 4820 3860 3150 0.4 0.5 0.6 0.7 0.2 0.2 0.3 0.3 8950 7010 5630 4610 0.4 0.4 0.5 0.7 0.2 0.2 0.3 0.3 9780 7860 6440 0.4 0.5 0.6 0.2 0.2 0.3 8320 0.5 0.2

16

18

20

1480 0.9 0.3 2620 0.9 0.4 3830 0.8 0.3 5370 0.7 0.3 6930 0.6 0.3 9010 0.5 0.2 5130 0.8 0.3 7270 0.6 0.2 9340 0.6 0.3

1230 1.0 0.3 2200 1.0 0.4 3230 0.9 0.4 4530 0.8 0.4 5850 0.7 0.3 7620 0.6 0.3 4320 0.9 0.4 6130 0.7 0.3 7890 0.7 0.3 9940 0.6 0.3

1040 1.1 0.3 1860 1.1 0.4 2740 1.0 0.4 3860 0.9 0.4 5000 0.8 0.3 6520 0.7 0.3 3680 1.0 0.4 5230 0.8 0.3 6740 0.8 0.4 5800 0.7 0.3

9390 7540 6170 0.4 0.5 0.6 0.2 0.2 0.3 8730 0.5 0.2

30

32

34

36

40

42

44

46

48

50

52

1600 1.3 0.5 2360 1.1 0.5 3320 1.0 0.5 4310 0.9 0.4 5630 0.8 0.4 3160 1.1 0.5 4510 0.9 0.3 5810 0.9 0.4 7340 0.8 0.4 9120 0.7 0.3

1380 1.4 0.5 2040 1.3 0.5 2890 1.2 0.5 3750 1.0 0.4 4900 0.9 0.4 2730 1.2 0.5 3910 1.1 0.4 5050 1.0 0.5 6390 0.9 0.4 7940 0.8 0.4

1190 1.5 0.5 1780 1.4 0.6 2520 1.3 0.6 3280 1.1 0.4 4290 1.0 0.4 2380 1.4 0.5 3420 1.2 0.4 4420 1.1 0.5 5600 1.0 0.4 6970 0.9 0.4

1040 1.7 0.5 1560 1.5 0.6 2220 1.4 0.6 2890 1.2 0.5 3790 1.1 0.5 2090 1.5 0.5 3010 1.3 0.4 3890 1.2 0.5 4940 1.1 0.5 6160 1.0 0.4

1370 1.6 0.6 1960 1.5 0.7 2560 1.3 0.5 3360 1.2 0.5 1840 1.6 0.6 2660 1.4 0.4 3450 1.3 0.6 4380 1.2 0.5 5470 1.1 0.5

1210 1.8 0.6 1740 1.7 0.7 2270 1.4 0.5 2990 1.3 0.6 1620 1.7 0.6 2360 1.5 0.4 3070 1.5 0.6 3900 1.3 0.5 4880 1.2 0.5

1070 1.9 0.7 1550 1.8 0.7 2030 1.5 0.5 2680 1.4 0.6 1440 1.8 0.6 2100 1.6 0.4 2740 1.6 0.6 3490 1.4 0.6 4370 1.3 0.5

960 2.0 0.6 1380 1.9 0.8 1820 1.6 0.6 2410 1.5 0.6 1280 1.9 0.6 1880 1.7 0.4 2450 1.7 0.7 3130 1.5 0.6 3930 1.4 0.5

1240 2.0 0.8 1630 1.7 0.6 2170 1.6 0.6 1140 2.0 0.6 1680 1.8 0.4 2210 1.8 0.7 2820 1.6 0.6 3550 1.5 0.6

1110 2.1 0.8 1470 1.8 0.6 1960 1.7 0.7 1020 2.1 0.5 1510 1.9 0.4 1990 1.9 0.7 2550 1.7 0.6 3210 1.6 0.6

1000 2.2 0.8 1330 1.9 0.6 1780 1.8 0.7

First Printing/CD-ROM Edition

1360 1.9 0.3 1800 2.0 0.7 2310 1.8 0.6 2910 1.7 0.6

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.10 L-Beam Load Tables 1'-0"

8"

Normalweight Concrete Section Properties

h

1 h

h

2

1'-8"

Designation

h in.

h1/h2 in.

A in.2

I in.4

yb in.

Sb in.3

20LB20 20LB24 20LB28 20LB32 20LB36 20LB40 20LB44 20LB48 20LB52 20LB56 20LB60

20 24 28 32 36 40 44 48 52 56 60

12/8 12/12 16/12 20/12 24/12 24/16 28/16 32/16 36/16 40/16 44/16

304 384 432 480 528 608 656 704 752 800 848

10,160 17,568 27,883 41,600 59,119 81,282 108,107 140,133 177,752 221,355 271,332

8.74 10.50 12.22 14.00 15.82 17.47 19.27 21.09 22.94 24.80 26.68

1163 1673 2282 2971 3737 4653 5610 6645 7749 8926 10,170

St in.3

Wt lb/ft

902 1301 1767 2311 2930 3608 4372 5208 6117 7095 8143

317 400 450 500 550 633 683 733 783 833 883

1.  Check local area for availability of other sizes. 2. Safe loads shown include 50% superimposed dead load and 50% live load. 800 psi top tension has been allowed, therefore, additional top reinforcement is required. 3.  Safe loads can be significantly increased by use of structural composite topping.

fc' = 5000 psi fpu = 270,000 psi

/2-in.-diameter, low-relaxation strand

1

Key 6560 – Safe superimposed service load, lb/ft 0.3 – Estimated camber at erection, in. 0.1 – Estimated long-time camber, in.

Table of safe superimposed service load, lb/ft, and cambers, in. Designation

Number strand

ys in.

20LB20

9

2.44

20LB24

10

2.80

20LB28

12

3.33

20LB32

14

3.71

20LB36

16

4.25

20LB40

18

4.89

20LB44

19

5.05

20LB48

21

5.81

20LB52

23

6.17

20LB56

25

6.64

20LB60

27

7.33

Span, ft 26

28

30

32

34

36

38

40

42

44

46

48

50

6560 5130 4100 3340 2760 2310 0.3 0.4 0.5 0.6 0.7 0.8 0.1 0.2 0.2 0.2 0.2 0.2 9570 7490 6000 4900 4060 3410 0.3 0.3 0.4 0.5 0.5 0.6 0.1 0.1 0.1 0.1 0.1 0.2 8220 6730 5590 4710 0.4 0.4 0.5 0.6 0.1 0.1 0.2 0.2 8940 7440 6280 0.4 0.5 0.5 0.1 0.2 0.2 9450 7980 0.4 0.5 0.2 0.2 9810 0.4 0.2

16

18

20

22

24

1960 0.9 0.3 2890 0.7 0.2 4000 0.6 0.2 5350 0.6 0.2 6820 0.5 0.2 8380 0.5 0.2

1670 1.0 0.3 2470 0.8 0.2 3440 0.7 0.2 4610 0.7 0.2 5880 0.6 0.2 7230 0.6 0.2 8950 0.5 0.2

1430 1.0 0.3 2130 0.9 0.2 2970 0.8 0.2 4000 0.7 0.2 5110 0.7 0.2 6290 0.6 0.2 7800 0.6 0.2 9220 0.5 0.2

1240 1.1 0.3 1850 0.9 0.2 2590 0.9 0.2 3490 0.8 0.2 4470 0.8 0.3 5510 0.7 0.2 6840 0.6 0.2 8100 0.6 0.2 9630 0.6 0.2

1070 1.2 0.2 1610 1.0 0.1 2270 0.9 0.2 3070 0.9 0.3 3940 0.8 0.3 4850 0.8 0.2 6040 0.7 0.2 7150 0.6 0.2 8520 0.6 0.2 9950 0.6 0.2

1410 1.0 0.1 2000 1.0 0.2 2710 1.0 0.3 3480 0.9 0.3 4300 0.8 0.3 5360 0.8 0.2 6360 0.7 0.2 7570 0.7 0.2 8860 0.7 0.2

1240 1.1 0.1 1760 1.1 0.2 2400 1.0 0.3 3100 1.0 0.3 3830 0.9 0.3 4780 0.8 0.2 5670 0.8 0.2 6770 0.7 0.3 7920 0.7 0.3 9080 0.7 0.3

1090 1.1 0.0 1560 1.1 0.2 2140 1.1 0.2 2770 1.1 0.3 3420 1.0 0.3 4280 0.9 0.2 5090 0.8 0.2 6080 0.8 0.3 7120 0.8 0.3 8170 0.7 0.3

969 1.2 0.0 1390 1.2 0.1 1910 1.2 0.2 2480 1.1 0.3 3070 1.0 0.3 3850 0.9 0.2 4580 0.9 0.3 5480 0.9 0.3 6420 0.8 0.3 7380 0.8 0.3

1240 1.2 0.1 1710 1.2 0.2 2230 1.2 0.3 2760 1.1 0.3 3470 1.0 0.2 4140 0.9 0.3 4950 0.9 0.3 5820 0.9 0.3 6680 0.9 0.3

1110 1.2 0.0 1540 1.3 0.2 2010 1.2 0.3 2490 1.1 0.3 3140 1.1 0.2 3750 1.0 0.3 4490 1.0 0.3 5280 1.0 0.3 6080 0.9 0.3

992 1.3 0.0 1380 1.3 0.1 1810 1.3 0.2 2250 1.2 0.3 2850 1.1 0.2 3400 1.1 0.3 4090 1.0 0.3 4810 1.0 0.3 5540 1.0 0.3

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–45

  3

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

  3

3.10 L-Beam Load Tables (cont.) 1'-6"

Normalweight Concrete

8"

Section Properties

h

h

1

h

2

2'-2"

fc' = 5000 psi

Designation

h in.

h1/h2 in.

A in.2

26LB20 26LB24 26LB28 26LB32 26LB36 26LB40 26LB44 26LB48 26LB52 26LB56 26LB60

20 24 28 32 36 40 44 48 52 56 60

12/8 12/12 16/12 20/12 24/12 24/16 28/16 32/16 36/16 40/16 44/16

424 528 600 672 744 848 920 992 1064 1136 1208

I in.4

yb in.

Sb in.3

St in.3

Wt lb/ft

14,298 24,716 39,241 58,533 83,176 114,381 152,104 197,159 250,126 311,586 382,118

9.09 10.91 12.72 14.57 16.45 18.19 20.05 21.94 23.83 25.75 27.67

1573 2265 3085 4017 5056 6288 7586 8986 10,496 12,100 13,810

1311 1888 2568 3358 4255 5244 6351 7566 8879 10,300 11,819

442 550 625 700 775 883 958 1033 1108 1183 1258

1.  Check local area for availability of other sizes. 2. Safe loads shown include 50% superimposed dead load and 50% live load. 800 psi top tension has been allowed, therefore, additional top reinforcement is required. 3.  Safe loads can be significantly increased by use of structural composite topping.

fpu = 270,000 psi

/2-in.-diameter, low-relaxation strand

1

Key 9670 – Safe superimposed service load, lb/ft 0.4 – Estimated camber at erection, in. 0.2 – Estimated long-time camber, in.

Table of safe superimposed service load, lb/ft, and cambers, in. Designation

Number strand

ys in.

26LB20

15

2.67

26LB24

15

2.67

26LB28

18

3.33

26LB32

21

4.00

26LB36

24

4.50

26LB40

27

5.11

26LB44

28

5.29

26LB48

32

5.75

26LB52

35

6.29

26LB56

37

7.00

26LB60

38

7.68

3–46

Span, ft 30

32

34

36

38

40

42

44

9670 7560 6050 4930 4080 3420 2900 2480 0.4 0.5 0.6 0.7 0.8 1.0 1.1 1.2 0.2 0.3 0.3 0.4 0.4 0.5 0.5 0.6 9160 7490 6220 5230 4440 3810 0.5 0.5 0.6 0.7 0.8 0.9 0.2 0.2 0.2 0.2 0.3 0.3 8430 7170 6050 5200 0.6 0.6 0.7 0.8 0.2 0.2 0.3 0.3 9260 7900 6800 0.6 0.7 0.7 0.2 0.3 0.3 8720 0.7 0.3

16

18

20

22

24

26

28

2130 1.4 0.6 3290 1.0 0.3 4510 0.9 0.3 5910 0.8 0.3 7580 0.8 0.3 9370 0.7 0.3

1840 1.5 0.7 2860 1.1 0.3 3930 1.0 0.3 5160 0.9 0.3 6640 0.9 0.3 8210 0.8 0.3

1600 1.6 0.7 2500 1.2 0.3 3450 1.1 0.3 4540 1.0 0.4 5850 0.9 0.4 7240 0.9 0.3 8990 0.8 0.3

1400 1.7 0.7 2190 1.3 0.3 3040 1.2 0.3 4010 1.1 0.4 5180 1.0 0.4 6420 0.9 0.4 7980 0.8 0.3 9630 0.8 0.3

1230 1.8 0.7 1930 1.3 0.3 2690 1.3 0.3 3560 1.2 0.4 4610 1.1 0.4 5720 1.0 0.4 7120 0.9 0.3 8600 0.9 0.4

1080 1.9 0.7 1710 1.4 0.2 2390 1.3 0.3 3180 1.2 0.4 4120 1.2 0.4 5120 1.1 0.4 6380 1.0 0.3 7720 1.0 0.4 9130 0.9 0.4

950 1.9 0.6 1520 1.5 0.2 2130 1.4 0.3 2840 1.3 0.4 3690 1.3 0.4 4600 1.2 0.4 5740 1.0 0.3 6960 1.0 0.4 8240 1.0 0.4 9530 0.9 0.4

First Printing/CD-ROM Edition

46

48

50

1350 1.5 0.1 1900 1.5 0.3 2550 1.4 0.4 3320 1.3 0.4 4140 1.2 0.4 5180 1.1 0.3 6290 1.1 0.4 7450 1.1 0.4 8640 1.0 0.4 9900 0.9 0.3

1200 1.5 0.1 1700 1.5 0.2 2290 1.5 0.3 3000 1.4 0.4 3740 1.3 0.4 4690 1.2 0.3 5700 1.2 0.4 6770 1.1 0.4 7850 1.1 0.4 9000 0.9 0.3

1070 1.5 0.0 1530 1.6 0.2 2060 1.5 0.3 2710 1.5 0.4 3390 1.4 0.4 4260 1.2 0.3 5190 1.3 0.4 6160 1.2 0.5 7150 1.1 0.4 8210 1.0 0.3

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.11 Inverted-Tee Beam Load Tables 8"

1'-0"

Normalweight Concrete

8"

Section Properties

h1 h h2

2'-4"

fc' = 5000 psi

Designation

h in.

h1/h2 in.

A in.2

I in.4

yb in.

Sb in.3

St in.3

Wt lb/ft

28IT20 28IT24 28IT28 28IT32 28IT36 28IT40 28IT44 28IT48 28IT52 28IT56 28IT60

20 24 28 32 36 40 44 48 52 56 60

12/8 12/12 16/12 20/12 24/12 24/16 28/16 32/16 36/16 40/16 44/16

368 480 528 576 624 736 784 832 880 928 976

11,688 20,275 32,076 47,872 68,101 93,503 124,437 161,424 204,884 255,229 312,866

7.91 9.60 11.09 12.67 14.31 15.83 17.43 19.08 20.76 22.48 24.23

1478 2112 2892 3778 4759 5907 7139 8460 9869 11,354 12,912

967 1408 1897 2477 3140 3869 4683 5582 6558 7614 8747

383 500 550 600 650 767 817 867 917 967 1017

1.  Check local area for availability of other sizes. 2. Safe loads shown include 50% superimposed dead load and 50% live load. 800 psi top tension has been allowed, therefore, additional top reinforcement is required. 3.  Safe loads can be significantly increased by use of structural composite topping.

fpu = 270,000 psi

/2-in.-diameter, low-relaxation strand

1

Key 8510 – Safe superimposed service load, lb/ft 0.2 – Estimated camber at erection, in. 0.1 – Estimated long-time camber, in.

Table of safe superimposed service load, lb/ft, and cambers, in. Design- Number ation strand

ys (end) in.

28IT20

9

2.44

28IT24

18

2.73

28IT28

13

3.08

28IT32

15

3.47

28IT36

16

3.50

28IT40

19

4.21

28IT44

20

4.40

28IT48

22

4.55

28IT52

24

5.17

28IT56

26

5.23

28IT60

28

5.57

Span, ft 26

28

30

32

34

36

6510 5070 4040 3280 2710 2260 0.2 0.3 0.4 0.4 0.5 0.5 0.1 0.1 0.1 0.1 0.1 0.1 9610 7500 5990 4880 4030 3370 0.2 0.3 0.3 0.4 0.4 0.5 0.1 0.1 0.1 0.1 0.1 0.1 8350 6820 5650 4750 0.3 0.3 0.4 0.5 0.1 0.1 0.1 0.1 9040 7520 5330 0.3 0.4 0.4 0.1 0.1 0.1 9830 8290 0.3 0.4 0.1 0.1

16

18

20

22

24

1900 0.6 0.0 2850 0.6 0.1 4030 0.5 0.1 5380 0.5 0.1 7070 0.4 0.1 8630 0.4 0.1

1610 0.7 0.0 2420 0.6 0.1 3450 0.6 0.1 4620 0.5 0.1 6090 0.5 0.1 7440 0.5 0.1 9180 0.4 0.1

1380 0.7 0.0 2080 0.7 0.1 2970 0.6 0.1 4000 0.6 0.1 5280 0.5 0.1 6460 0.5 0.1 7980 0.5 0.1 9710 0.4 0.1

1180 0.7 0.0 1790 0.7 0.1 2580 0.7 0.1 3490 0.6 0.1 4610 0.6 0.1 5640 0.6 0.1 6990 0.5 0.1 8520 0.5 0.1 9980 0.5 0.1

1020 0.8 –0.1 1550 0.7 0.0 2250 0.7 0.1 3050 0.7 0.1 4060 0.6 0.1 4960 0.6 0.1 6160 0.6 0.1 7520 0.5 0.1 8820 0.5 0.1

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

38

40

42

44

46

48

50

1350 0.8 0.0 1970 0.8 0.1 2690 0.7 0.1 3580 0.7 0.1 4390 0.7 0.1 5460 0.6 0.1 6670 0.6 0.1 7830 0.6 0.1 9300 0.5 0.2

1170 0.8 –0.1 1730 0.8 0.0 2370 0.8 0.1 3180 0.7 0.1 3890 0.7 0.1 4860 0.7 0.1 5950 0.6 0.1 6990 0.6 0.1 8310 0.6 0.2 9640 0.6 0.2

1020 0.8 –0.2 1530 0.8 0.0 2110 0.8 0.1 2830 0.8 0.1 3470 0.8 0.1 4340 0.7 0.1 5330 0.7 0.1 6270 0.6 0.1 7460 0.6 0.2 8660 0.6 0.2

1350 0.9 –0.1 1870 0.9 0.0 2530 0.8 0.0 3100 0.8 0.1 3890 0.7 0.1 4790 0.7 0.1 5640 0.7 0.1 6730 0.7 0.2 7820 0.7 0.2

1190 0.8 –0.2 1670 0.9 0.0 2270 0.9 0.0 2780 0.8 0.1 3500 0.8 0.1 4320 0.8 0.1 4100 0.7 0.1 6080 0.7 0.2 7080 0.7 0.2

1060 0.8 –0.2 1490 0.9 0.0 2040 0.9 0.0 2500 0.9 0.1 3160 0.8 0.1 3900 0.8 0.1 4610 0.8 0.1 5520 0.8 0.2 6430 0.8 0.2

1330 0.9 –0.1 1830 0.9 –0.1 2250 0.9 0.1 2850 0.8 0.0 3540 0.9 0.1 4190 0.8 0.1 5020 0.8 0.2 5850 0.8 0.2

3–47

  3

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

  3

3.11 Inverted-Tee Beam Load Tables (cont.) 8"

1'-6"

Normalweight Concrete

8"

Section Properties

h

1 h

h

1

2'-10"

fc' = 5000 psi

Designation

h in.

h1/h2 in.

A in.2

I in.4

yb in.

Sb in.3

St in.3

Wt lb/ft

34IT20 34IT24 34IT28 34IT32 34IT36 34IT40 34IT44 34IT48 34IT52 34IT60

20 24 28 32 36 40 44 48 52 60

12/8 12/12 16/12 20/12 24/12 24/16 28/16 23/16 36/16 44/16

488 624 696 768 840 976 1048 1120 1192 1336

16,082 27,825 44,130 65,856 93,616 128,656 171,157 221,906 281,504 439,623

8.43 10.15 11.79 13.50 15.26 16.85 18.58 20.34 22.13 25.78

1908 2741 3743 4878 6135 7635 9212 10,910 12,721 17,053

1390 2009 2722 3560 4514 5558 6733 8023 9424 12,847

508 650 725 800 875 1017 1092 1167 1242 1392

1.  Check local area for availability of other sizes. 2. Safe loads shown include 50% superimposed dead load and 50% live load. 800 psi top tension has been allowed, therefore, additional top reinforcement is required. 3.  Safe loads can be significantly increased by use of structural composite topping.

fpu = 270,000 psi

/2-in.-diameter, low-relaxation strand

1

Key 7820 – Safe superimposed service load, lb/ft 0.4 – Estimated camber at erection, in. 0.1 – Estimated long-time camber, in.

Table of safe superimposed service load, lb/ft, and cambers, in. Designation

Number strand

ys in.

34IT20

14

2.29

34IT24

17

2.59

34IT28

20

3.00

34IT32

23

3.48

34IT36

24

3.50

34IT40

30

4.40

34IT44

30

4.40

34IT48

33

4.73

34IT52

36

5.22

34IT56

39

5.59

34IT60

40

6.00

3–48

Span, ft 16

30

32

34

36

38

40

42

44

46

48

50

7820 6250 5090 4200 3520 2970 2530 0.4 0.5 0.6 0.7 0.7 0.8 0.9 0.1 0.2 0.2 0.2 0.2 0.2 0.2 9220 7520 6230 5220 4430 3780 0.4 0.5 0.6 0.7 0.7 0.8 0.2 0.2 0.2 0.2 0.3 0.3 8640 7270 6180 5300 0.5 0.6 0.7 0.7 0.2 0.2 0.2 0.3 9580 8170 7030 0.5 0.6 0.7 0.2 0.2 0.3 9220 0.6 0.2

18

20

22

24

26

28

2170 1.0 0.2 3260 0.9 0.3 4580 0.8 0.3 6090 0.8 0.3 8010 0.7 0.2 9720 0.6 0.3

1870 1.1 0.2 2820 1.0 0.3 3990 0.9 0.3 5320 0.8 0.3 7010 0.7 0.2 8510 0.7 0.3

1620 1.1 0.2 2460 1.1 0.3 3490 1.0 0.3 4670 0.9 0.3 6170 0.8 0.2 7490 0.8 0.3 9360 0.7 0.2

1410 1.2 0.2 2150 1.1 0.3 3070 1.0 0.3 4120 1.0 0.3 5460 0.9 0.2 6630 0.9 0.3 8300 0.7 0.2

1230 1.2 0.1 1880 1.2 0.2 2710 1.1 0.3 3650 1.0 0.3 4860 0.9 0.2 5900 0.9 0.4 7400 0.8 0.2 8960 0.8 0.3

1080 1.2 0.1 1660 1.2 0.2 2400 1.2 0.3 3250 1.1 0.3 4330 1.0 0.2 5270 1.0 0.4 6630 0.9 0.2 8030 0.8 0.3 9500 0.8 0.3

1460 1.2 0.2 2130 1.2 0.3 2900 1.2 0.3 3880 1.1 0.2 4730 1.1 0.4 5950 0.9 0.2 7230 0.9 0.3 8560 0.9 0.3

1290 1.3 0.1 1900 1.3 0.2 2590 1.2 0.3 3490 1.1 0.2 4250 1.1 0.4 5370 1.0 0.3 6530 1.0 0.3 7740 0.9 0.3

1140 1.3 0.0 1690 1.3 0.2 2320 1.3 0.3 3140 1.2 0.2 3830 1.2 0.4 4850 1.0 0.2 5910 1.0 0.3 7020 1.0 0.3 8260 1.0 0.3 9560 0.8 0.3

1000 1.2 –0.1 1510 1.3 0.1 2090 1.3 0.2 2840 1.2 0.2 3460 1.3 0.4 4400 1.1 0.2 5370 1.1 0.3 6390 1.0 0.3 7530 1.0 0.3 8720 0.9 0.3

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.11 Inverted-Tee Beam Load Tables (cont.) 8"

2'-0"

Normalweight Concrete

8"

Section Properties

h

Designation

h in.

h1/h2 in.

A in.2

I in.4

yb in.

Sb in.3

St in.3

Wt lb/ft

40IT20 40IT24 40IT28 40IT32 40IT36 40IT40 40IT44 40IT48 40IT52

20 24 28 32 36 40 44 48 52

12/8 12/12 16/12 20/12 24/12 24/16 28/16 32/16 36/16

608 768 864 960 1056 1216 1312 1408 1504

20,321 35,136 55,765 83,200 118,237 162,564 216,215 280,266 355,503

8.74 10.50 12.22 14.00 15.82 17.47 19.27 21.09 22.94

2325 3346 4563 5943 7474 9305 11,220 13,289 15,497

1805 2603 3534 4622 5859 7215 8743 10,415 12,233

633 800 900 1000 1000 1267 1367 1467 1567

1 h

h

2

3'-4"

1.  Check local area for availability of other sizes. 2. Safe loads shown include 50% superimposed dead load and 50% live load. 800 psi top tension has been allowed, therefore, additional top reinforcement is required. 3.  Safe loads can be significantly increased by use of structural composite topping.

fc' = 5000 psi fpu = 270,000 psi

/2-in.-diameter, low-relaxation strand

1

Key 8420 – Safe superimposed service load, lb/ft 0.5 – Estimated camber at erection, in. 0.2 – Estimated long-time camber, in.

Table of safe superimposed service load, lb/ft, and cambers, in. Designation

Number strand

ys in.

40IT20

18

2.22

40IT24

22

2.67

40IT28

26

3.08

40IT32

30

3.33

40IT36

32

3.50

40IT40

38

4.32

40IT44

40

4.40

40IT48

44

4.87

40IT52

46

5.05

Span, ft 16

18

32

34

36

38

40

42

44

46

48

50

8420 6870 5680 4760 4030 3440 2960 0.5 0.6 0.7 0.8 0.9 1.0 1.1 0.2 0.2 0.3 0.3 0.3 0.3 0.3 9990 8280 6960 5900 5050 4360 0.5 0.6 0.7 0.8 0.9 1.0 0.2 0.2 0.3 0.3 0.3 0.3 9670 8230 7070 6120 0.6 0.7 0.8 0.9 0.3 0.3 0.3 0.3 9520 8260 0.8 0.8 0.3 0.3

20

22

24

26

28

30

2560 1.2 0.3 3780 1.1 0.3 5330 1.0 0.3 7220 0.9 0.4 9410 0.8 0.3

2220 1.3 0.3 3300 1.2 0.3 4670 1.1 0.4 6350 1.0 0.4 8290 0.9 0.3

1940 1.3 0.3 2890 1.2 0.3 4110 1.2 0.4 5610 1.1 0.4 7340 1.0 0.3 8940 0.9 0.4

1690 1.4 0.2 2540 1.3 0.3 3640 1.2 0.4 4980 1.2 0.4 6530 1.1 0.3 7960 1.0 0.4 9950 0.9 0.3

1490 1.4 0.2 2240 1.4 0.3 3230 1.3 0.4 4440 1.3 0.4 5840 1.1 0.4 7120 1.1 0.4 8910 1.0 0.4

1310 1.5 0.1 1980 1.4 0.3 2870 1.4 0.3 3970 1.3 0.4 5230 1.2 0.4 6390 1.2 0.4 8020 1.1 0.4 9650 1.0 0.4

1150 1.5 0.0 1750 1.4 0.2 2560 1.4 0.3 3560 1.4 0.4 4710 1.3 0.4 5760 1.2 0.4 7230 1.1 0.4 8720 1.1 0.4

1010 1.5 –0.1 1550 1.5 0.1 2290 1.5 0.3 3190 1.5 0.4 4250 1.4 0.3 5200 1.3 0.4 6550 1.2 0.4 7910 1.2 0.4 9490 1.1 0.4

1380 1.5 0.0 2050 1.5 0.3 2880 1.5 0.4 3840 1.4 0.3 4700 1.4 0.4 5940 1.3 0.4 7190 1.2 0.4 8640 1.1 0.4

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

3–49

  3

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

3.12

Design Aids

Design Aid 3.12.1 Design Strength Interaction Curves for Precast, Prestressed Concrete Columns

y

CRITERIA 1. fc' = 5000 psi, normalweight 2. Minimum prestress = 225 psi 3. All strand assumed 1/2 in. diameter, fpu = 270 ksi 4. Curves shown for partial development of strand near member end where fpu ≈ fse 5. Horizontal portion of curve is the maximum for tied columns = 0.80φPo 6. Varies linearly from 0.9 for tension-controlled sections to 0.65 for compression-controlled sections in accordance with ACI 318-05 Section 9.3.2

x

x

y

typical (assumed for design)

USE OF CURVES 1. Enter at left with applied factored axial load Po 2. Enter at bottom with applied magnified factored moment δMu 3. Intersection point must be to the left of curve indicating required concrete strength.

1800

16 x 16 4 strands

1600

strand

NOTATION φPn = design axial strength φMn = design flexural strength φP0 = design axial strength at zero eccentricity Ag = gross area of the column δ = moment magnifier (ACI 318-05, Section 10.11–10.13)

1800

1400

1200

1200

fc' = 10,000 psi f 'c = 9000 psi

fc' = 10,000 psi

1000

f 'c = 9000 psi f 'c = 8000 psi

800

18 x 18 4 Strands

1600

1400

1000

φPn , kip

  3

f 'c = 8000 psi f 'c = 7000 psi

800

f 'c = 7000 psi

600

f 'c = 6000 psi

600

f 'c = 6000 psi f 'c = 5000 psi

400

400

Partial development

Partial Development

200

200 0

f 'c = 5000 psi

Full development

0

50

100

150

200

250

0

300

Full Development

0

50

100

200

250

300

350

400

φMn , kip-ft

φMn , kip-ft

3–50

150

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

Design Aid 3.12.1 Design Strength Interaction Curves for Precast, Prestressed Concrete Columns (cont.)

2600

2600

20 x 20 4 Strands

2400 2200

2200

2000

2000

1800

1800

φ Pn , kip

1600

f c' = 10,000 psi f c' = 9000 psi f c' = 8000 psi

1600 f c' = 10,000 psi

1400

800

f c' = 5000 psi

600

200 0

100

200

Partial development

600

Partial Development

400

f c' = 5000 psi

1000

f c' = 6000 psi

800

f c' = 6000 psi

1200

f c' = 7000 psi

1000

f c' = 7000 psi

1400

f c' = 9000 psi f c' = 5000 psi

1200

0

24 x 24 8 strands

2400

400 Full Development 300 400 500

Full development

200 600

0

0

100

200

300

400

φ M n , kip-ft 4800

28 x 28 8 strands

4400 4000

f c' = 9000 psi

2800

f c' = 8000 psi

2400

f c' = 7000 psi f c' = 6000 psi

2000 1600

4400

f c' = 10,000 psi f c' = 9000 psi

3200

f c' = 8000 psi

2800

f c' = 7000 psi

2400

1200

f c' = 6000 psi f c' = 5000 psi

Partial development

800 Full development

400 400

900 1000

1600

1200 Partial development 800

200

800

32 x 32 12 strands

2000

f c' = 5000 psi

0

700

4800

3600 f c' = 10,000 psi

3200 φ Pn , kip

600

4000

3600

0

500

φ M n , kip-ft

600

800 1000 1200 1400

Full development

400 0

0

200

φ M n , kip-ft

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

400

600

800 1000 1200 1400 1600 1800 2000 φ M n , kip-ft

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PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

Design Aid 3.12.2. Design Strength Interaction Curves for Precast, Reinforced Concrete Columns

y

CRITERIA 1. 2. 3. 4.

Concrete fc' = 5000 psi, normalweight Reinforcement fy = 60,000 psi Curves shown for full development of reinforcement Horizontal portion of curve is the maximum for tied columns = 0.80φPO 5. Varies linearly from 0.9 for tension-controlled sections to 0.65 for compression-controlled sections in accordance with ACI 318-05 Section 9.3.2

x

x

USE OF CURVES

y

1. Enter at left with applied factored axial load Pu 2. Enter at bottom with applied magnified factored moment δMu 3. Intersection point must be to the left of curve indicating required reinforcement.

11/2" Clear to primary steel NOTATION φPn = design axial strength φMn = design flexural strength φPO = design axial strength at zero eccentricity Ag = gross area of the column δ = moment magnifier (ACI 318-05, Section 10.11–10.13)

The interaction curves have been smoothed for plotting purposes. Exact calculated values may be slightly different.

1300

16 x 16 f 'c = 5000 psi

1200

φPn , kip

  3

1300

1100

1100

1000

1000

900

900

800

800

(8) #9,

700 600

= 3.12%

500

400

400

(4) #8, = 1.23%

300

300

200

200

100

100 0

50

100

(4) #11,

= 1.92%

(4)#9,

= 1.23%

600

(4) #10, =1.98%

150

200

250

300

0

0

50

100

φMn , kip-ft

3–52

18 x 18 = 5000 psi

(8) #10,

700

500

0

f 'c

1200

150

200

250

300

= 3.13%

350

400

φMn , kip-ft

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PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

φPn , kip

Design Aid 3.12.2 Design Strength Interaction Curves for Precast, Reinforced Concrete Columns (cont.) 2300 20 x 20 2200 f ' = 5000 psi c 2100 2000 1900 1800 1700 1600 1500 1400 1300 (8) #11, = 3.12% 1200 1100 1000 900 800 700 600 (8) #9, = 2.00% 500 (4) #9, = 1.00% 400 300 200 100 0 0 100 200 300 400 500 600

2300 2200 2100 2000 1900 1800 1700 1600 1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100 0

24 x 24 f c' = 5000 psi

(12) #11,

0

4000

28 x 28

3800

f 'c = 5000 psi

3600

3400 3200

3000

3000

2800

2800 2600 (16) #11,

φPn , kip

2400

= 3.18%

2200

2000

2000

1800

1800

1600

1600

1400

1400

(8) #9,

600

800

= 1.02%

400 200 400

800

(8) #11,

600

200 0

= 2.44%

1000

400 0

(16) #11,

= 3.05%

1200

(16) #9, = 2.04%

800

(20) #11,

2400

2200

1000

f 'c = 5000 psi

3600

3200

2600

32 x 32

3800

3400

1200

= 1.08%

100 200 300 400 500 600 700 800 900 1000 φMn , kip-ft

φMn , kip-ft 4000

= 2.16%

(8) #11,

(4) #11,

= 3.25%

1200

1600

0

0

400

φMn , kip-ft

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

= 1.22%

800

1200

1600

2000

2400

φMn , kip-ft

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CHAPTER 3

3.12.3 Partial interaction curves for prestressed double-tee wallPrecast, panels Prestressed Double-Tee Wall Design Aid 3.12.3 Design Strength Interaction Curves for Panels

t Mark 8DT16 8DT17 10DT16 10DT17 12DT16 12DT17

h

h, in. 16 17 16 17 16 17

Full interaction curve data (flange in compression) Partially Fully developed developed strand force strand force No. t, in. strnd φPo φPnb φMnb φMc φPnb φMnb φMc 2 4 864 619 151 45 591 166 95 3 4 1129 872 178 48 844 195 103 2 4 997 751 161 45 724 176 96 3 4 1328 1071 187 48 1043 204 103 2 4 1130 885 168 46 856 184 97 3 4 1552 1270 194 48 1242 212 103

φ Varies from 0.75 to 0.65 for partially developed strand. φ Varies from 0.9 to 0.65 for fully developed strand.

fc' = 5000 psi, normalweight

Values are applicable for conditions with compression in the flange and tension in the stems.

Strand = 1/2 in. diameter fpu = 270,000 psi Partially developed strand

Fully developed strand

100

100

90

90

8DT16 10DT16

80 70

10DT17 12DT17

40

60

40

30

20

20

10

10

40

70 60 50 φM n , kip-ft per unit

80

8DT17 10DT17 12DT17 8DT17 10DT17 12DT17

50

30

0

3–54

φ Pn , kip per unit

8DT17

50

12DT16

Flange in compression Flange in tension

70

60

8DT16 10DT16

80

12DT16

φ Pn , kip per unit

  3

0

60

First Printing/CD-ROM Edition

8DT16 10DT16 12DT16

100 120 80 φM n , kip-ft per unit

140

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PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

Design Aid 3.12.4 Partial Interaction Curves for Prestressed Hollow-Core and Sandwich Wall Panels

Width varies

Full interaction curve data

h

Partially developed strand force

h, in.

Mark

HC6 6 HC8 8 HC10 10 HC12 12

Curves based on minimum practical prestress no less than 225 psi normalweight concrete

φPo

φPnb

127 145 175 177

Fully developed strand force

φMnb

φMc

φPnb

φMnb

φMc

103

10

2.4

58

10

3.9

128 153

16 22

3.7 5.6

65 78

16 25

6.0 9.1

178

30

6.7

78

32

11.3

Units for φP are kip, units for φM are kip-ft. Values are for 1 ft width.

fc' = 5000 psi, normalweight fpu = 270,000 psi

Width and configuration may vary Load-bearing wythe

Partially developed strand 12

h

HC6

10

6

HC 12

0

HC8

φPn , kip/ft

8

HC1

Partially composite or non-composite

4 2 0

0

2

4

6

8

10

12

14

16

18

16

18

φMn , kip-ft/ft Fully developed strand 12

6

HC 12

HC1 0

HC8

8

HC6

φPn , kip/ft

10

4 2 0

0

2

4

6

8

10

12

14

φMn , kip-ft/ft

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CHAPTER 3

Design Aid 3.12.5 Partial Interaction Curves for Precast, Prestressed Solid and Sandwich Wall Panels







Partially developed strand force

t

t/2

Full interaction curve data



t/2

t, in. 4 6 8 10

Curves based on minimum prestress of 225 psi normalweight concrete f = 5000 psi, normalweight ' c

Fully developed strand force

φPO

φPnb

φMnb

φMc

φPnb

φMnb

φMc

129 194 259

46 69 92

5.3 11.9 21.2

0.9 2.0 3.6

22 33 45

4 9 16

2.2 5.0 9.0

323

115

33

5.6

56

25

14.0

Units for φP are kip, units for φM are kip-ft. Values are for 1 ft width.

fpu = 270,000 psi

Partially developed strand t

12

Fully composite sandwich panel

10

10" t=

t=8 "

6

t = 6"

φPn , kip/ft

t

t = 4"

8

Load-bearing wythe

4

Partially composite or non-composite

2

0 0

6

4

2

8

10

16

20

φMn , kip-ft/ft Fully developed strand 12

10

t=8 "

t = 6"

t = 4"

8

10"

6 t=

φPn , kip/ft

  3

4

2

0 0

4

12

8

φMn , kip-ft/ft 3–56

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PCI DESIGN HANDBOOK/SEVENTH EDITION

PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

Design Aid 3.12.6 Partial Interaction Curves for Precast, Reinforced Concrete Solid and Sandwich Wall Panels

1

t/2

1 /2 t

t

φPo

4 6 8 10

t = 8 in. or 10 in.

t = 4 in. or 6 in.

Full interaction curve data

t, in.

Curves based on minimum vertical reinforcement ρ = 0.10% normalweight concrete fc' = 5000 psi, normalweight fy = 60,000 psi

φPnb

φMnb

φMc

134

67

5.5

0.5

202 269

100 131

12.4 22.6

1.0 1.8

336

164

35.5

2.8

Units for φP are kip, units for φM are kip-ft. Values are for 1 ft width.

t

Fully composite sandwich panel Load-bearing wythe

t = 10"

t = 8"

φPn , kip/ft

t = 4"

Partially composite or non-composite

t = 6"

t

φMn , kip-ft/ft

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PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

Design Aid 3.12.7 Recommended Height-to-Thickness Ratio Limits for Precast, Reinforced Solid Non-Load Bearing Wall Panels

Height versus thickness 60 W = service lateral load 50 2

W

=

20

ft lb/

40 Height, ft (between supports)

  3

2

W

=

20

ft lb/ W

0

=4

30

2

t

f lb/

2

2

0

4 W=

t lb/f

W=

8

2

W=

20

/ft 0 lb

/ft 80 lb

10 Prestressed wall Non-prestressed wall 0

4

6

8 Thickness, in.

10

12

Note: 1. Panel reinforcing must be sized for factored loads and handling. ' 2. fc = 5000 psi, normalweight. 3. Figure applies to non-load-bearing panels only. 4. Deflection of panel must be checked against acceptable limits.

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CHAPTER 3

Design Aid 3.12.8 Section Propertiesa and Allowable Service Loads for Prestressed Concrete Piles

Size

Size

Size

Size

Core diameter Continuous tie Prestressing strand

Square solid

Square hollow 16 turns at 3"

5 turns at 1" 1"

Octagonal solid or hollow 16 turns at 3"

6" pitch

Round 5 turns at 1" 1"

Typical elevation

Size, in.

Core diameter in.

Allowable concentric service load, tonsb

Section properties Area, in.2

Weight, lb/ft

Moment Section of inertia, in.4 modulus, in.3

Radius of gyration, in.

fc' , psi

Perimeter, in.

5000

6000

8000

10,000

4.00 4.67 5.33 6.00 6.67 6.67 8.00 8.00 8.00 8.00 10.00 12.00

105 143 187 236 292 222 420 338 308 291 471 761

129 175 229 290 358 273 515 414 377 357 578 933

176 240 314 397 490 373 705 567 517 488 791 1276

224 305 398 504 622 474 896 720 656 621 1005 1621

3.09 3.60 4.12 4.61 5.15 5.84 5.66 6.53 6.17 7.23

3.31 3.87 4.42 4.97 5.52 5.52 6.08 6.08 6.63 6.63

86 118 154 195 241 172 292 195 348 219

106 145 189 240 296 211 359 240 427 268

145 198 259 328 405 289 491 328 584 368

185 252 330 417 515 367 624 417 742 467

11.10 13.20 15.31 17.41 21.32

9.43 11.00 12.57 14.14 17.28

355 424 493 562 826

436 520 604 689 1013

596 712 827 943 1386

758 904 1050 1198 1759

SQUARE PILES 12 14 16 18 20 20 24 24 24 24 30 36

Solid Solid Solid Solid Solid 11 Solid 12 14 15 18 18

144 196 256 324 400 305 576 463 422 399 646 1042

150 204 267 338 417 318 600 482 439 415 672 1085

1728 3201 5461 8748 13,333 12,615 27,648 26,630 25,762 25,163 62,347 134,815

12 14 16 18 20 20 22 22 24 24

Solid Solid Solid Solid Solid 11 Solid 13 Solid 15

119 162 212 268 331 236 401 268 477 300

125 169 220 280 345 245 420 280 495 315

1134 2105 3592 5705 8770 8050 12,837 11,440 18,180 15,696

36 42 48 54 66

26 32 38 44 54

487 581 675 770 1131

507 605 703 802 1178

60,007 101,273 158,222 233,373 514,027

288 457 683 972 1333 1262 2304 2219 2147 2097 4157 7490

3.46 4.04 4.62 5.20 5.77 6.43 6.93 7.58 7.81 7.94 9.82 11.38

OCTAGONAL PILES 189 301 449 639 877 805 1167 1040 1515 1308

ROUND PILES 3334 4823 6592 8643 15,577

a. Form dimensions may vary with producers with corresponding variations in section properties. b. Allowable loads based on N = Ag(0.33 fc' – 0.27fpc); fpc = 700 psi. Check local producer for available concrete strengths.

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CHAPTER 3

Design Aid 3.12.9 Section Properties and Allowable Service Loads of Prestressed Sheet Piles

Cast-in-place cap

Varies Tie back when required

A

t

Length

Section A 1/ 2-in.-diameter

#3 Varies

  3

Prestressed sheet pile

strand

B 5 gauge wire (typical) Section B

Section properties per foot of width Thickness t in.

Area in.2

Weighta lb/ft2

Moment of inertia in.4

Section modulus in.3

Maximum allowable service load moment,b kip-ft per foot

fc'

= 5000 psi

fc'

= 6000 psi

6c

72

75

216

72

6.0

7.2

8c

96

100

512

128

10.6

12.8

10

120

125

1000

200

16.6

20.0

12

144

150

1728

288

24.0

28.8

16

192

200

4096

512

42.7

51.2 64.8

18

216

225

5832

648

54.0

20

240

250

8000

800

66.7

80.0

24

288

300

13,824

1152

96.0

115.2

a. Normalweight concrete. b. Based on zero tension and maximum 0.4 f c' compression. c. Strand can be placed in a single layer in thin sections. Where site conditions require it, strand may be placed eccentrically.

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CHAPTER 3

Design Aid 3.12.10 Recommended Maximum Spans for Precast Concrete Stairs

  3 h Bearing

h

h

Bearing

 Typical main reinforcing pattern

Thickness h, in.

Span

6

14

8

19

10

23

12

26

, ft

Notes: 1. 2. 3. 4. 5.

Stair reinforcing must be designed for all factored loads. Normalweight concrete. Recommended maximum span  is based on dead weight of stair plus 100 lb/ft2 live load. Minimum concrete 28-day compressive strength is 5000 psi. When deflections are required to be checked in accordance with ACI 318-05 Section 9.5, cracked section properties are required to be used. Top steel may be required to control deflections. 6. Longer spans can be obtained with higher concrete strength or special reinforcing.

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PRELIMINARY DESIGN OF PRECAST / PRESTRESSED CONCRETE STRUCTURES

CHAPTER 3

Design Aid 3.12.11 Stadium Riser Allowable Spans No stem 6"

Double

Single

2'-9"

Triple

Maximum span, ft

1

3 /2"

Stem

h-4"

h

4"

44

Single riser

36

Triple riser

28 Single riser

20

6"

h-4"

12 6

8

10

12

14

16

18

20

22

24

20

22

24

20

22

24

h

6"

1

3 /2"

Rise h, in. 6" stem Double

Triple

52

1

3 /2"

Stem

Single

6"

Maximum span, ft

Double riser

2'-9"

h

h-4"

2'-9"

6"

2'-9"

44

Triple riser

36 Single riser

28 20

1

3 /2"

6

8

10

12

14

16

18

h

Stem

Rise h, in. 1 3 /2"

6"

12" stem Double

Single

Triple riser

Triple

56

Design chart assumptions 2

10 lb/ft superimposed DL 100 lb/ft 2 live load f 'C = 6000 psi, normalweight Midspan step load assumed Fundamental natural frequency f0 > 3.5 Hz under dead load plus 30 lb/ft 2 vertical live load

Maximum span, ft

1

3 /2"

  3

48

Triple riser

40

Single riser

32 6

8

10

12

14

16

Rise h, in.

18

Experience has shown that these diagrams are reasonably accurate for tread dimensions from 2 ft 6 in. to 3 ft 0 in.

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3.13

CHAPTER 3

References

  3

1. A  CI Committee 318. 2005. Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05). Farmington Hills, MI: American Concrete Institute. 2. P  CI Connections Committee. 1988. Design and Typical Details of Connections for Precast and Prestressed Concrete, 2nd ed. Chicago, IL: Precast/Prestressed Concrete Institute (PCI). 3. P  CI Connection Details Committee. 2008. PCI Connections Manual for Precast and Prestressed Concrete Construction, 1st ed. Chicago, IL: PCI. 4. A  swad, A., G. Burnley, N. M. Cleland, D. Orndorff, and C.E. Wynings. 2004. Load Testing of Prestressed Concrete Double-Tees without Web Reinforcement. PCI Journal, V. 49, No. 2 (March-April). 5. Z  ia, P., H. K. Preston, N. L. Scott, and E. B. Workman. 1979. Estimating Prestress Losses. Concrete International, V. 1, No. 6 (June). 6. P  CI Committee on Prestressed Concrete Piling. 1993. Recommended Practice for Design, Manufacture, and Installation of Prestressed Concrete Piling. PCI Journal, V. 38, No. 2 (March-April). 7. I nternational Code Council (ICC). 2006. International Building Code. Country Club Hills, IL: ICC.

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CHAPTER 4 ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES 4.1

Precast Concrete Force-Resisting Systems.................................................................................................................4-3 4.1.1 Emulative Design..........................................................................................................................................4-3 4.1.2 Non-Emulative Design..................................................................................................................................4-5 4.1.3 LFRS Considerations....................................................................................................................................4-5

4.2

Code Requirements for Structural Loads....................................................................................................................4-5 4.2.1 Code References...........................................................................................................................................4-5 4.2.1.1 IBC 2006.....................................................................................................................................4-5 4.2.1.2 ASCE 7-05..................................................................................................................................4-5 4.2.1.3 NEHRP 2000 and 2003..............................................................................................................4-6 4.2.1.4 ACI 318-05.................................................................................................................................4-6 4.2.2 Gravity Loads................................................................................................................................................4-6 4.2.2.1 Dead Loads.................................................................................................................................4-6 4.2.2.2 Live Loads..................................................................................................................................4-6 4.2.2.3 Snow Loads................................................................................................................................4-7 4.2.3 Wind Loads...................................................................................................................................................4-7 4.2.3.1 ASCE 7-05 — Method 1 for Wind Design................................................................................4-7 4.2.4 Earthquake Loads..........................................................................................................................................4-9 4.2.4.1 Base Shear (ASCE 7-05 Section 12.8, Equivalent-Lateral-Force Method).............................4-10 4.2.4.2 Vertical Distribution.................................................................................................................4-13 4.2.4.3 Lateral Distribution and Torsion..............................................................................................4-13 4.2.4.4 Drift Effects..............................................................................................................................4-13 4.2.4.4 Drift Effects..............................................................................................................................4-13 4.2.4.5 P-∆ Effects...............................................................................................................................4-14 4.2.4.6 Redundancy — Seismic Design Categories D, E, and F..........................................................4-14 4.2.5 Lateral Soil Loads.......................................................................................................................................4-14 4.2.6 Load Combinations.....................................................................................................................................4-14 4.2.6.1 Load Factors for Diaphragms...................................................................................................4-15

4.3

Structural Integrity.....................................................................................................................................................4-15 4.3.1 Introduction.................................................................................................................................................4-15 4.3.2 Precast Concrete Structures........................................................................................................................4-16 4.3.3 Large-Panel Bearing-Wall Structures.........................................................................................................4-18 4.3.4 Structures with Mixed Structural Materials................................................................................................4-18

4.4

Volume Changes.......................................................................................................................................................4-18 4.4.1 Axial Volume-Change Strains....................................................................................................................4-21 4.4.2 Expansion Joints.........................................................................................................................................4-21 4.4.2.1 Spacing of Expansion Joints.....................................................................................................4-21 4.4.2.2 Width of Expansion Joints........................................................................................................4-21 4.4.3 Volume-Change Effects in Moment-Resisting Frames..............................................................................4-21 4.4.3.1 Equivalent Volume Change......................................................................................................4-22 4.4.3.2 Calculating Restraint Forces.....................................................................................................4-23

4.5

Shear-Wall Systems...................................................................................................................................................4-23 4.5.1 Introduction.................................................................................................................................................4-23 4.5.2 Principles of Shear-Wall Buildings.............................................................................................................4-23 4.5.3 Code Requirements.....................................................................................................................................4-23

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ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES



4.5.4 4.5.5 4.5.6 4.5.7 4.5.8 4.5.9 4.5.10 4.5.11 4.5.12

4.6

Moment-Resisting Building Frames..........................................................................................................................4-46 4.6.1 Moment Resistance of Column Bases........................................................................................................4-46 4.6.2 Cantilevered Column Systems for Seismic Design....................................................................................4-47 4.6.3 Fixity of Column Bases...............................................................................................................................4-50 4.6.4 Computer Models for Frame Analysis........................................................................................................4-50 4.6.4.1 Modeling Partially Fixed Bases................................................................................................4-50 4.6.5 Classifications for Seismic Considerations.................................................................................................4-52 4.6.6 Analysis and Design — Ordinary Moment Frames....................................................................................4-52 4.6.7 Special Moment Frames for Seismic Design Category C...........................................................................4-53 4.6.8 Special Moment Frames for High Seismic Design Categories...................................................................4-54

4.7

Shear Wall – Frame Interaction.................................................................................................................................4-56

4.8

Diaphragm Design.....................................................................................................................................................4-56



4.8.1

4.9

Blast-Resistant Design of Precast, Prestressed Concrete Components.....................................................................4-65 4.9.1 General........................................................................................................................................................4-65 4.9.2 Blast Loads..................................................................................................................................................4-66 4.9.3 Dynamic Material Properties......................................................................................................................4-67 4.9.4 General Blast-Design Methods...................................................................................................................4-68 4.9.4.1 Single-Degree-of-Freedom Design Method.............................................................................4-69 4.9.4.2 Component Resistance-Deflection Function............................................................................4-70 4.9.4.3 Deformation Limits..................................................................................................................4-71 4.9.5 Additional Design Considerations..............................................................................................................4-74

4.10

References.................................................................................................................................................................4-75

4.11

Design Aids...............................................................................................................................................................4-77

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4.8.2 4.8.3

4.8.4

4.8.5

Design Guidelines for Shear-Wall Structures.............................................................................................4-24 Proportioning Shear Walls..........................................................................................................................4-25 Stiffness Analysis........................................................................................................................................4-25 Distribution of Lateral Loads......................................................................................................................4-26 Coupled Shear Walls...................................................................................................................................4-28 Shear Walls with Large Openings..............................................................................................................4-29 Evaluation of Shear-Wall Systems.............................................................................................................4-29 Example: One-Story Building.....................................................................................................................4-30 Example: Three-Level Parking Structure...................................................................................................4-37

Simple Diaphragm Design — The Horizontal Beam Analogy...................................................................4-57 4.8.1.1 Shear Transfer between Components.......................................................................................4-57 4.8.1.2 Chord Forces.............................................................................................................................4-57 4.8.1.3 Collector Forces........................................................................................................................4-57 Rigid and Flexible Diaphragms..................................................................................................................4-59 4.8.2.1 Defining Rigid or Flexible Diaphragms...................................................................................4-59 4.8.2.2 Behavior and Design Considerations........................................................................................4-60 Diaphragm Design Forces...........................................................................................................................4-61 4.8.3.1 Code-Prescribed Forces............................................................................................................4-61 4.8.3.2 Elastic Design of Diaphragms..................................................................................................4-61 4.8.3.3 Performance-Based Design Alternative...................................................................................4-62 4.8.3.4 Wind and Low Seismic Hazard................................................................................................4-63 Diaphragm Detailing Considerations..........................................................................................................4-63 4.8.4.1 General Detailing Requirements...............................................................................................4-63 4.8.4.2 Moderate Seismic Hazard — Topped and Pretopped Systems................................................4-64 4.8.4.3 Seismic Design Category D and Higher — Topped Systems..................................................4-64 4.8.4.4 Untopped Systems for High Seismic Hazard...........................................................................4-64 Methods of Diaphragm Design...................................................................................................................4-65 4.8.5.1 Strut-and-Tie Modeling............................................................................................................4-65 4.8.5.2 Finite-Element Analysis...........................................................................................................4-65

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4.1

 recast Concrete Force-Resisting P Systems

The design of precast/prestressed concrete structures involves the integration of many considerations. Most of these spatial, functional, and architectural considerations are reviewed in Chapters 1 and 7. This chapter will focus on the design of the entire structural system. Precast/prestressed concrete structures are the integration of the structural system as a whole, the connections, and the individual components. Each aspect of design must consider the others as well as the functional requirements imposed by the building use. It is essential that the design loads be traced from their point of origin to the final support or foundation. Although not always required by code, it is desirable to design the components and their connections to achieve a ductile, rather than a brittle, failure mode. Resistance to gravity loads is largely a matter of component design, which is covered in Chapter 5 of this handbook. In addition to resisting gravity loads, a principal consideration in building design is the lateral-force-resisting system. Methods used to resist lateral forces include: Shear walls. These can be precast concrete, cast-in-place concrete, or masonry. Shear walls are discussed in more detail in Section 4.5. When architectural or structural precast concrete components are used for the exterior cladding, they can often be used as shear walls. Precast concrete box elements have been used effectively in low-rise to high-rise structures. The boxes are created as one complete unit, such as in a precast concrete cell module, or can be created of individual precast concrete walls connected together to create a box unit. Such box units have a much larger stiffness than individual walls and can be important units in a lateral-force-resisting system. Moment-resisting frames. Building function may dictate the use of moment-resisting frames. It is sometimes feasible to provide a moment connection at only one end of a component, allowing the other end to be pinned. When using moment frames, it is important to design for forces created by restraint of volume change resulting from creep, shrinkage, and temperature change. To reduce the number of moment frames required, a combined shear wall/moment-frame system may be used. Moment-resisting frames are discussed in more detail in Section 4.6. H frames are totally precast and form moment-resisting frames where the joints that are resisting moment are completely within the precast concrete unit. Other components tie into the H frame typically using pinned connections. Cantilevered columns. This is usually only feasible in low-rise buildings. Base fixity can be attained by fixing the column to the footing. In this case, a detailed analysis of the footing rotation can be made as described in Section 4.6.3. Although cantilevered column systems are permitted by ASCE 7-05,1 it imposes limitations and requirements for seismic design that significantly reduce their economy. These systems are discussed in more detail in Section 4.6.2.

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Braced frames. X frames can be used in lieu of shear walls and consist of compression struts and tension ties in the form of an X (K frames can also be designed in a similar fashion). The tension ties can consist of structural steel components, while the compression struts are typically precast concrete. Each of these depends on distribution of lateral loads through diaphragm action of the roof and floor systems (see Section 4.8). The required balance in system design is achieved by providing the strength, ductility, and toughness to resist lateral forces with consideration for the effects of concrete creep, shrinkage, and temperature change. These effects are collectively known as volume changes. Details that result in over-restraint of volume changes can be as damaging as any externally applied force. Most buildings will probably never experience the design event that is represented by the requirements for wind or earthquakes, but they will experience the climatic temperature cycle every year. In precast concrete structures, individual components are connected at their joints using a variety of details. These connections may include embedded steel shapes such as plates and angles, with headed concrete anchors or reinforcing bar anchorage; the steel embedments are field bolted or welded. These applications are dry connections. A wet connection consists of reinforcing bars protruding from the precast concrete components with the bars mechanically coupled or spliced. Cast-in-place con­crete or grout at the joint completes this connection. Either dry or wet connections can be used in both moment-resisting frame and shear-wall systems. 4.1.1

Emulative Design

Precast concrete structures have been built in high seismic areas for many years. The building codes have allowed such construction provided that the precast concrete components are connected so they will perform essentially the same as a cast-in-place concrete unit. These designs and details have become known as emulation of cast-in-place concrete. The methods of detailing are described and illustrated in the ACI Committee 550 report, “Guide to Emulating Cast-in-Place Detailing in Precast Concrete Structures.”2 Figure 4.1.1 shows several details excerpted from that report. Emulative design creates construction that either is monolithic at the critical joint locations or provides connections that act as if they are monolithic at those locations. In general, emulative connections involve connecting reinforcing bars across a joint individually by lap splicing, welding, or mechanical couplers. Concrete is made continuous by filling the joint with a high-quality, non-shrink, or fiber-reinforced grout in horizontal joints or a cast-in-place closure pour in vertical joints. Engineering follows the rules for reinforcedconcrete design while taking into account the special circumstances for the connection system chosen, such as maintaining proper cover to mechanical couplers. ACI 318-05,3 while not using the term emulation, has provisions for precast concrete special-moment frames with strong connections (Section 21.6.2), and special structural (shear) walls (Sections 21.8 and 21.13) that follow the principles of emulation.

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Wall panel

Grout full

Optional grouting port Precast concrete floor slab

Lapped splice (lap length according to ACI 318-05) Shim and grout Grout or concrete

Mechanical or welded splice

Bearing strip

Mechanical splice Shim and grout Precast concrete floor slab Mechanical or welded connection Bearing strip

Conduit cast in wall panel

Wall panels and slabs Mechanical welded or lap splice Cast-in-place topping

Double-tee

Inverted tee beam or girder

Bearing pad typical

Prestressed solid slab Mild-steel dowel embedded in prestressed slab Bearing strip Prestressing Mild-steel dowel couplers embedded in double-tee flanges, or lap splice

Slab reinforcement extended into closure pour and mechanically spliced or welded

Bearing strip typically

Seal Bearing strip Prestressed double-tee Inverted tee beam

Deck components and beams (diaphragm connections) Shim and grout

Mechanical splice

Mechanical splice Precast concrete beam Shim and grout

Full grout

Shim and grout Precast concrete beam end

Precast concrete column

Reinforced erection corbel

Columns and beams Fig. 4.1.1 Typical emulation details.2

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ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES 4.1.2

Non-Emulative Design

Many advances have been made in the understanding of the seismic behavior of precast concrete frame structures. ACI 318-05 recognizes acceptance criteria for special moment frames based on validation testing in lieu of emulation.4 Similar criteria for special structural (shear) walls are listed in the 2003 NEHRP provisions.5 ACI 318-086 recognizes the acceptance criteria derived from these resources and published by ACI in ITG 5.1.7 The Precast Seismic Structural Systems (PRESSS) program has researched systems that take advantage of the jointed nature of precast concrete, culminating with the testing of a five-story, 60%-scale building.8 This test structure used precast concrete frames with several different ductile joints in one direction, and precast concrete shear walls in the other direction. Several structures have been constructed using systems resulting from the PRESSS research, including a 39-story hybrid frame system in San Francisco, Calif.9 ACI 318-05 recognizes jointed precast concrete construction for use in seismic areas in Sections 21.6 and 21.13. 4.1.3

LFRS Considerations

Regardless of the system used, it is imperative that lateral load paths and resisting elements be clearly defined. Where significant movement between adjacent components is anticipated, ductile connections must be provided. One advantage of jointed construction is the ease of defining load paths through the connections. Connections can be designed for specific directional resistance while maintaining flexibility in one or more other directions. It is important in a precast concrete structure to develop connections that tie all precast concrete components into the lateral-force-resisting system. Since wind and seismic ground motions are random in direction, a structure that is shaped so as to have sufficient resistance in any direction is necessary. Closed sections (boxes or tubes) are preferred over open sections because they provide more torsional resistance. In structures where openness is important, such as parking structures, shear walls with large openings have been successfully used. Attention must be paid to local flexure and shear in those component sections that surround the openings. To limit damage to non-structural elements, three options are open to the designer. First, the elements can be isolated from the structural system so that these elements are not forced to undergo as much deformation as the supporting structure. Note, however, that if isolated from the structural system, these elements must maintain their own structural integrity. Second, the deflec­tions of the system can be reduced in order to minimize deformation of the non-structural elements. This is typically achieved through the use of shear walls. Third, the connection between individual elements and support components can be designed to sustain large deformations and rotations without failure. Generally, the first or third approach is adopted for non-structural architectural concrete wall panels.

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4.2

 ode Requirements for Structural C Loads

4.2.1

Code References

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With the continuing development of codes and standards, the choice of the correct set of regulations can be confusing. Each jurisdiction, which could be a state or local government, usually adopts a model building code by passing an ordinance or law. The adoption of the model code may include modifications or exceptions appropriate to the local conditions. The model building code, in turn, adopts technical codes and standards by reference, making them part of the legally adopted code. The appropriate codes and standards, then, are made a set that is based on that model code. At the time of the publication of this handbook, the 2006 edition of the International Building Code (IBC 2006)10 has the most widespread adoption by states and localities in the United States, although some states continue to use earlier editions of the IBC. This code is chosen as the basis for the requirements and examples presented in this handbook. IBC 2006 has adopted ASCE 7-05 and ACI 318-05 by reference. To maintain consistency with IBC 2006, these are also used. At printing, the 2009 edition of the IBC and the 2008 edition of ACI 318 have been published. It is not anticipated that the next edition of ASCE 7 will be published until 2010. Although the regulatory process has proceeded in many states, IBC 2009 has not yet been adopted in any. Some states have announced their intention not to adopt IBC 2009. Although the more recent editions of codes and standards may represent the most current technical doctrine, the governing standards are determined by the current model code adopted by the authority having jurisdiction. The acceptability of the use of more current standards should be verified by the authority having jurisdiction. See the Appendix in this handbook for information on the impact of ACI 318-08 on the contents of the handbook. 4.2.1.1 IBC 2006 The IBC is the result of many years of effort to combine the three most commonly adopted codes: the Uniform Building Code (UBC),11 the Standard Building Code (SBC),12 and the National Building Code (BOCA/NBC).13 To have the force of law, any code must be adopted by local jurisdictions such as states, municipalities, towns, and the like. With the publication of the third full version of this unified code, IBC 2006 , adoption of one or another form of IBC has become nearly universal in the United States. Adoption often includes local amendments, so it is important to review the specific code of the local jurisdiction. IBC 2006 load criteria are largely established by direct reference to ASCE 7-05. 4.2.1.2 ASCE 7-05 Minimum Design Loads for Buildings and Other Structures (ASCE 7-05), published by the American Society of Civil Engineers, is a loading standard that is referenced by IBC 2006. It specifies all required design loads, load and resistance factors, and load combinations to be used for the

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EXAMPLE 4.2.2.1 Calculation of Snow Load Given:  flat-roofed office building 450 ft long has A a 50-ft-long, 8-ft-high penthouse centered along the length. The building is located in Milwaukee, Wisconsin. Consider u in Design Aid 4.11.1 = 200 ft. Problem: Determine the roof snow load and drift load. ________________________________________ Solution: From Design Aid 4.11.2: pg = 30 lb/ft2 Assume that within the life of the structure, taller buildings may be built around it. Thus, from Design Aid 4.11.3(b), for Exposure B, sheltered, Ce = 1.2. From Design Aid 4.11.3(c), for a heated building: Ct = 1.0 Importance factor for office buildings, Ι = 1.0 From Eq. 4-1: pf = 0.7CeCt Ipg pf = 0.7(1.2)(1.0)(1.0)(30) = 25.2 lb/ft2 Drifting: From Eq. 4-3: 1.  γ = 0.13pg + 14 = 0.13(30) + 14 = 17.9 lb/ft3 < 30 lb/ft3 OK From Eq. 4-2:

4.2.1.3 NEHRP 2000 and 2003 The National Earthquake Hazards Reduction Program (NEHRP) provisions do not in themselves have the force of a code, but they are in a Federal Emergency Management Agency (FEMA) docu­ment, and are used as the basis for provisions of other codes and standards such as those produced by the IBC and ASCE 7-05. The 2000 edition contained major changes from prior editions that permit precast concrete systems to be designed for high seismic regions, and provide acceptance criteria for non-emulative frames and walls. The 2003 edition included some further modifications. 4.2.1.4 ACI 318-05 Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05) is the basis for concrete design throughout the United States. The 2005 edition includes provisions for the use of precast concrete in seismic regions, and the use of the ASCE 7-05 load and resistance factors. Much of the content of ACI 318-05 includes an implicit assumption that concrete construction is cast-inplace. Section 14.1 of this handbook is a report by the PCI Building Code Com­mittee that identifies provisions in ACI 318-05 that may need special interpretation when related to precast/prestressed concrete structures. Example problems in this handbook typically use ACI 318-05 with the Section 14.1 modifications in the solutions. 4.2.2

hb = pf /γ = 25.2/17.9 = 1.40 ft

Gravity Loads

4.2.2.1 Dead Loads

2.  hc = 8.0 > 0.2 hb 1.40 Drifting must be considered. 3.  From Design Aid 4.11.4(b): For leeward wall, hd = 2.5 ft For windward wall, hd = 3/4(4.8) = 3.6 ft Use hd = 3.6 ft 4.  w = 4(3.6) = 14.4 ft From Eq. 4-4: Snow drift load = 1/2γ hdw = 1/2(17.9)(3.6)(14.4) = 464 lb/ft Applied as a line load at 14.4/3 = 4.8 ft from the projection.

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Load and Resistance Factor Design (LRFD) for buildings. This load standard is usually not adopted directly by local jurisdictions, but may provide the basis for loads that vary with locality such as snow and wind. The earthquake provisions included in ASCE 7-05 were originally derived from NEHRP 2000 and 2003. ASCE 7-05 included a major reorganization that included the separation of the seismic material of Chapter 9 of ASCE 7-02 into thirteen separate chapters.

Dead loads include the self-weight of the structural components plus any materials or elements that are attached to or permanently in place on the component or assembly. Since the dead loads are presumed to be determinable with a reasonable degree of accuracy, the load factor by ASCE 7-05 is 1.2 when combined with live loads. The ultimate factored load, however, may not be less than 1.4D when live loads are low. Weights of commonly used mater­ials encountered in construction (taken from ASCE 7-05) are shown in Chapter 15, Design Aid 15.1.1. 4.2.2.2 Live Loads Live loads are considered variable, transient, and not accurately determinable, so the load factor is higher and is equal to 1.6. In some cases, a maximum live load may be calculated with a high degree of accuracy (for example, fluid pressure), and a lower load factor is then used (see Section 4.2.6). Live loads recom­mended for use by ASCE 7-05 are given in Design Aid 15.1.2.

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ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES 4.2.2.3 Snow Loads Snow loads are treated differently from other live loads by ASCE 7-05 because they are very tran­sient and vary by geographical location and ter­rain. The basic snow load for flat roofs is determined by: pf = 0.7CeCtΙpg



(Eq. 4-1)

limited by: pf ≥ Ιpg where pg ≤ 20 lb/ft2 pf ≥ 20Ι where pg > 20 lb/ft2 where: pf Ce Ct Ι pg

= flat roof snow load, lb/ft2 = exposure factor from Design Aid 4.11.3(b) = thermal factor from Design Aid 4.11.3(c) = importance factor from Design Aid 4.11.1 = ground snow load, lb/ft2, from Design Aid 4.11.2, 4.11.3(a), or as specified by local authorities

Drift effects. Drifting of snow due to roof projections such as penthouses, parapets, and variable roof levels is also required to be taken into account. Drift loads are superimposed on the balanced loads. Design Aid 4.11.3(d) illustrates windward and leeward drifting. Design Aid 4.11.4 illustrates the method speci­fied by Reference 1 for determining the loads caused by snow drifts. 1. Determine height of the balanced snow load:

hb ==



where:

pf γ

(Eq. 4-2)

They are: Method 1 – Simplified procedure Method 2 – Analytical procedure Method 3 – Wind tunnel procedure

  4

Method 1 is applicable for the main wind-force-resisting system for many typical precast concrete structures and is illustrated in Section 4.2.3.1. Method 2 can be used in lieu of Method 1 if desired by the designer. This method is illustrated for a cladding panel in Chapter 7. Method 3 is permitted to be used in lieu of Methods 1 and 2 for any structure. ASCE 7-05 should also be reviewed for more details of these provisions. 4.2.3.1 ASCE 7-05 – Method 1 for Wind Design The limitations on structures for which this method can be used are generally as follows: 1. Height ≤ 60 ft or least lateral dimension. 2. Enclosed building (includes parking structures). 3. Regular shaped. 4. No expansion joints. 5. Fundamental frequency H ≤ 1 Hz. (Nearly all concrete buildings under 60 ft will qualify.) 6. Flat or shallow pitched roof. The following illustrates the procedures required for this simplified analysis: 1. Determine the basic wind speed from Design Aid 4.11.5.

γ = 0.13pg + 14 ≤ 30 lb/ft3



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(Eq. 4-3)

2. If hc /hb ≤ 0.2, drift loads need not be applied. 3. Determine hd from Design Aid 4.11.4(b). • For leeward roofs, lu = length of the higher roof. • For windward roofs, lu = length of the lower roof on either side of the projection, and use threequarters of the value from Design Aid 4.11.4(b) as hd. • Use the larger of these two values.

2. Determine the importance factor Ι from Design Aid 4.11.1. 3. Determine the exposure category that applies to upwind direction. (Note: Reference 1 includes more detailed descriptions and requirements):

4. w = 4hd If hd > hc, w =

4hd2 ≤ 8hc and hd = hc hc

Snow drift load = 1/2γ hdw (Eq. 4-4) applied at w/3 from the face of the projection.

4.2.3

Wind Loads

In many areas of the United States that use IBC 2006, earthquake loading is often more critical than wind, but wind loads should be checked. ASCE 7-05 Chapter 6 provides three procedures for determining wind loads on the main wind-force-resisting system (MWFRS) and cladding.

Width of zone A = the lesser of 20% of the least dimension of the building, or 80% of the mean roof height, but not less than 8% of the least dimension of the building, or 6 ft. Zone A can be on either end, depending on wind direction.

Fig. 4.2.1 Wind pressure zones on typical building elevations.

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EXAMPLE 4.2.3.1 Use of ASCE 7 Method 1 for Wind-Load Determination Given: A 114-ft-wide by 226-ft-long by 54-ft-high hospital building in Memphis, Tennessee. Problem: Determine the design wind load on the main wind-force-resisting system (MWFRS). _________________________________________________________________________________ Solution: Since this is an enclosed building under 60 ft high, method 1 may be used. Step 1: From Design Aid 4.11.5, basic wind speed = 90 mph Step 2: From Design Aid 4.11.1, category IV: Ι = 1.15 Step 3: From Section 4.2.3.1, item 3, exposure category B Step 4: From Fig. 4.2.1: Zone A on long side = 0.2(114) = 22.8 ft or 0.8(54) = 43.2 ft; use 22.8 ft Zone C on long side = 226 – 22.8 = 203.2 ft Zone A on short side = 22.8 ft Zone C on short side = 114 – 22.8 = 91.2 ft Step 5: From Design Aid 4.11.6(c), λ (by interpolation) = 1.18 Step 6: Determine KZT from ASCE 7-05 Section 6.5.7.1, which states that if site conditions do not meet all of the conditions of Section 6.5.7.1 then KZT =1.0, use KZT =1.0. Step 7: Determine ps30 for each zone: From Design Aid 4.11.6(a): Zone A ps30 = 12.8 lb/ft2 Zone C ps30 = 8.5 lb/ft2 Step 8: Determine wind pressures for each zone using Eq. 4-5: ps (A) = λKZTΙps30 = 1.18(1.0)(1.15)(12.8) = 17.4 lb/ft2 ps (C) = 1.18(1.0)(1.15)(8.5) = 11.5 lb/ft2 Step 9: Determine the total forces for each zone on the MWFRS: F1 = bAh[ps(A)] = 22.8(54)(17.4)/1000 = 21.4 kip F2 = bBh[ps(C)] = 203.2(54)(11.5)/1000 = 126.2 kip Total force on length = 21.4 + 126.2 = 147.6 kip Resultant from left =

21.4 ( 22.8 / 2 ) + 126.2 ( 22.8 + 203.2 / 2 ) = 108 ft 147.6

Eccentricity = 226/2 – 108 = 5 ft

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EXAMPLE 4.2.3.1 Use of ASCE 7 Method 1 for Wind-Load Determination (cont.)

C A

F3

F4

  4

F2

F1 A

C

A similar calculation for the short wall results in total force = 78 kip at an eccentricity of 4.2 ft. Note: Zone A can be at either end of the structure or at both ends of the structure, which would result in slightly different total forces on the MWFRS. Also note that these loads are to be applied at a height of half the building height or 27 ft.

• • •

Exposure B: Urban and suburban areas, wooded areas Exposure D: Flat, unobstructed areas outside hurricane-prone regions Exposure C: All others

4. Determine the pressure zones on each side of the building from Fig. 4.2.1. 5. Determine the height and exposure adjustment factor λ from Design Aid 4.11.6(c). 6. Determine topographic factor KZT from ASCE 7-05. 7. Determine the ps30 forces for each zone from Design Aid 4.11.6(a). 8. The pressure on the MWFRS for each zone is then determined from:

ps = λKZTΙps30

(Eq. 4-5)

where: ps = combined windward and leeward net pressures λ = height and exposure adjustment factor Ι = importance factor KZT = topographic factor as defined in Section 6.5.7 of ASCE 7-05

ps30 = wind pressure for exposure B at h = 30 ft 9. The force on the MWFRS is then determined by multiplying the values of ps by their respective zone areas. 4.2.4

Earthquake Loads

Earthquakes generate horizontal and vertical ground movement. When the seismic waves pass beneath a structure, the foundation will tend to move with the ground, while the superstructure will tend to remain in its original position. The lag between foundation and superstructure movement will cause distortions and develop forces in the structure. As the ground moves, changing distortions and forces are produced throughout the height of the structure. The current philosophy for the design of earthquakeresistant structures permits minor damage for moderate earthquakes and accepts major damage for severe earthquakes, provided that the possibility of complete collapse is minimized. The design details often require large, inelastic deformations to occur in order to absorb the inertial forces. This is achieved by providing component and connection ductility. While this ductility can prevent total collapse, the resultant distortions may lead to significant damage to mechanical, electrical, and architectural elements. Seismic damage can be minimized by setting limitations on structural deflections, such as interstory drift.

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Spectral response accelaration Sa

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ings with irregularities in seismic design categories D, E, or F, depending on the nature of the irregularity. The seismic base shear V in a given direction is determined by: SDS

Sa = SD1 T



• T0

Ts

1.0

TL

•

Period T

• •

Fig. 4.2.2 Design response spectrum.

The response of a structure to the ground motion of an earthquake depends on the structural system with its damping characteristics and on the distribution of its mass. With mathematical idealization, a designer can determine the probable response of the structure to an imposed earthquake. ASCE 7-05 requires a dynamic analysis for structures that have highly irregular shapes or framing systems, or are particularly tall in seismic design categories D, E, and F. While ASCE 7-05 allows a dynamic analysis for other structures, most precast buildings are not tall and have structural systems and shapes that are more or less regular. Most designers use the equivalent static force method for these structures. There have been many seismic-related changes including many that address precast concrete construction made to such documents as NEHRP 2000, ASCE 7-05, and ACI 318-05. These changes are based on a significant amount of seismic research and observations from a number of recent earthquakes. Some of these changes are: • •

• • • • •

Recognition of jointed panel construction; Achieving ductile structural behavior by using strong connections that remain elastic while nonlinear action (plastic hinging) occurs in the component away from the connection; Modification of drift computation and limiting drift; Deformation compatibility of structural components and attached non-structural elements; Additional soil type classifications; Special considerations for building sites located near seismic faults; and Special considerations for structures possessing redundancy.

4.2.4.1 B  ase Shear (ASCE 7-05 Section 12.8, Equivalent-Lateral-Force Method) The procedure described is applicable to all buildings in seismic design categories B, C, and to most precast concrete structures in D, E, and F. This method may not apply to build4–10

(Eq. 4-6)

where: Cs = seismic response coefficient W = total dead load of structure plus:

Sa = SD1(TL ) T2

SD1

V = CsW

25% of floor live load in storage areas (live load in parking structures not included). If partition load is included in gravity load, include the actual partition weight or a minimum weight of 10 lb/ft2, whichever is greater. Total weight of permanent operating equipment. 20% of flat-roof snow load where snow load exceeds 30 lb/ft2.

The seismic response coefficient Cs is proportional to the design-response spectrum. The design-response spectrum has two segments: a short-period plateau and a descending curve with lower values for longer building periods. Two coefficients, SS and S1, define these two segments, and they vary with geographical location. Maps of the United States showing contours for SS and S1 are provided in ASCE 7-05 and in IBC 2006. A computer program is also available with IBC 2006 that enables determination of these values by map interpolation from longitude and latitude or zip code of the site. To determine Cs: 1. Determine SS and S1 from the map, computer program, or from local building codes. 2. Determine site classification from soil reports or Design Aid 4.11.7(a). If site soils are not known, use site class D. 3. Calculate response accelerations:

SMS = FaSS

(Eq. 4-7)



SM1 = FvS1

(Eq. 4-8)

where: Fa and Fv are site coefficients from Design Aid 4.11.7(b) and (c), respectively. 4. Calculate the 5% damped design-spectral-response accelerations:

SDS = (2/3)SMS

(Eq. 4-9)



SD1 = (2/3)SM1

(Eq. 4-10)



To = (0.2)SD1/ SDS

(Eq. 4-11)



Ts = SD1/ SDS

(Eq. 4-12)

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ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES 5. Determine the seismic design category from Table 4.2.1. This will sometimes restrict the type of seismicforce-resisting system (SFRS) used (see Design Aid 4.11.8). 6. Determine the fundamental period of the building from:

Ta = Ct hnx



(Eq. 4-13)

where: Ct = 0 .016 for moment-resisting-frame systems of reinforced concrete in which the frames resist 100% of the required seismic forces and are not enclosed or adjoined by more rigid components that prevent that frame from deflecting when subjected to seismic forces = 0.020 for other concrete structural systems hn = distance from base to highest level, ft x = 0.9 for concrete moment-resisting frames = 0.75 for other concrete structural sys­tems

For shear-wall structures, the approximate fundamental period may also be determined from:

Ta =



where:

0.0019 hn Cw

Cw =

100 ⎛ hn ⎞ Ai ∑ 2 ⎜ ⎟ AB i=1 ⎝ hi ⎠ ⎡ ⎛ hi ⎞ ⎤ ⎢1+ 0.83 ⎜ ⎟ ⎥ ⎝ Di ⎠ ⎥⎦ ⎢⎣

Table 4.2.1  Seismic design categories (a) Based on short period response acceleration Occupancy categorya Value of SDS

I or II

III

IV

SDS < 0.167g

A

A

A

0.167g ≤ SDS < 0.33g

B

B

C

0.33g ≤ SDS < 0.50g

C

C

D

b

b

Db

Occupancy categorya Value of SD1

II

III

SD1 < 0.067g

A

A

A

0.067g ≤ SD1 < 0.133g

B

B

C

0.133g ≤ SD1 < 0.20g

C

C

D

b

b

Db

(Eq. 4-15)

Equations 4-13 and 4-14 are considered to provide an approximate period by ASCE 7-05. In some cases, it may be useful to make a more accurate calculation of period from frame analysis. This can be done internally in some advanced stiffness analysis programs, but can be done relatively easily from the load inputs and the displacements using Rayleigh’s formula: n

∑w δ

2 i i

T = 2π



g∑ Fiδ i i=1

where: wi = dead load weight at floor i δi = elastic displacement at floor i

D

0.20g ≤ SD1

D

IV

a. Category in Design Aid 4.11.1. b. Occupancy categories I, II, and III structures located on sites with mapped maximum considered earthquake spectral response acceleration at 1 sec period S1 equal to or greater than 0.75g shall be assigned to seismic design category E, and occupancy category IV structures located on such sites shall be assigned to seismic design category F.

Design spectral response acceleration at 1 sec period SD1

Coefficient CU

≥ 0.4

1.4

0.3

1.4

0.2

1.5

0.15

1.6

≤ 0.1

1.7

AB = area of base of structure, ft2 Ai = web area of shear walls i, ft2 Di = length of shear wall i, ft hi = height of shear wall i, ft x = n umber of shear walls in the building effective in resisting lateral forces in the direction under consideration



D

(b) Based on 1 sec period response acceleration

and

i=1 n

D

0.50g ≤ SDS

Table 4.2.2  Coefficient for upper limit on calculated period

2

x



(Eq. 4-14)

CHAPTER 4

(Eq. 4-16)

Fi = lateral force at floor i g = acceleration of gravity, 386 in./sec2 n = number of floors See Section 4.6.6 for an explanation of the iterative process using this equation. When designing the lateral-force-resisting system for strength, the period used for the calculation for the base shear may not exceed the approximate period by more than a factor Cu, which depends on SD1. The coefficient Cu can be determined from Table 4.2.2. Linear interpolation is permitted for values of SD1 between the values in the table. For shear-wall buildings, the design period factor may be applied to the longer period value of Eq. 4-13 or 4-14. However, as noted above, the period shall not be taken greater than:

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EXAMPLE 4.2.4.1 Determination of Base Shear Coefficient CS Given: A hospital building in Memphis, Tennessee, with plan dimensions of 114 ft × 226 ft and height of 54 ft. The building is a steel-frame building with precast concrete shear walls designed using emulation procedures to perform as special reinforced-concrete shear walls. A soil investigation has determined the site to be class C. Problem: Determine the seismic response coefficient CS. ___________________________________ Solution: 1. From maps found in ASCE 7-05, SS = 1.386 S1 = 0.377; designated site class C 2. Response accelerations:

From Design Aid 4.11.7(b): Fa = 1.0. From Design Aid 4.11.7 (c): Fv = 1.423



Eq. 4-7: SMS = FaSs = 1.0(1.386) = 1.386



Eq. 4-8: SM1 = FvS1 = 1.423(.377) = 0.537

3. 5% damped, design-spectral-response accelerations:

Eq. 4-9: SDS = (2/3)(1.386) = 0.924



Eq. 4-10: SD1 = (2/3)(0.537) = 0.358

4.

Approximate fundamental period:



CT = 0.020



hn = 54 ft



Eq. 4-13: Ta = Ct hnx  = (0.020)(54)0.75 = 0.40 sec

5. From Design Aid 4.11.8. Detail shear walls as special walls. R = 6.

From Design Aid 4.11.1, I = 1.5.

Use lesser of Eq. 4-18 and 4-19 for CS.

From Eq. 4-18: CS =



From Eq. 4-19: CS =



0.924 SDS = = 0.23 (R / Ι ) (6 / 1.5 )

0.358 SD1 = = 0.224 R / Ι T 6 / 1.5 ( ) ( ) (0.40 )

Check Eq. 4-21 CS = 0.044 SDS Ι ≥ 0.01 = 0.044(.924)(1.5) = 0.061 = 0.061 < 0.224 OK

Use CS = 0.224 This is then multiplied by the dead weight of the building to determine the base shear.

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Tmax = CuTa



where Cu is found from Table 4.2.2.

(Eq. 4-17)

7. Determine Cs from the lesser of Eq. 4-18 and 4-19 (or 4-20):

Cs =

SDS (R / I )

where: R = response modification factor from Design Aid 4.11.8 I = importance factor from Design Aid 4.11.1



Fx = CvxV



Cvx ==



Cs =

SD1TL for T > TL T (R / I)

(Eq 4-20)



where: TL = long-period transition period (see ASCE 7-05, Fig. 22-15 to 22-20)

Cs = 0.044SDS Ι ≥ 0.01

In addition, for structures located where S1 ≥ 0.6g, Cs cannot be less than:

Cs =

0.5S1 (R / I )



(Eq. 4-24)

where: Cvx = vertical distribution factor k = 1 for buildings having a period of 0.5 sec or less = 2 for buildings having a period of 2.5 sec or more For buildings with a period between 0.5 and 2.5, determine k by linear interpolation. hi and hx = height from base to level i or x V = base shear wi and wx = portion of total gravity load of building W, assigned to level i or x

(Eq. 4-21)

Equation 4-21 is from ASCE 7-05 Supplement No. 2.



wx hxk n i=1

but cannot be less than:

(Eq. 4-23)

∑w h (Eq. 4-19)



The lateral force at each level is calculated by:

k i i

SD1 for T ≤ TL ( R / I )T

2

assigned results in 11.1% more lateral load for the bearingwall system. If the shear walls are truly incidental to the vertical load frame, then the higher R value is appropriate. It is possible to have different values of R in two orthogonal directions of the same structure. 4.2.4.2 Vertical Distribution

(Eq. 4-18)

Cs =



CHAPTER 4

(Eq. 4-22)

The base shear determined by Eq. 4-6 is a function of Cs, which is calculated using Eq. 4-18 to 4-22. Each of these equations has the term R, the response modification coeffient, which is a function of the lateral-force-resisting system and is provided in Design Aid 4.11.8. In many cases, engineering judgement is required to assign the appropriate R. Systems with walls that carry most of the gravity loads (bearing-wall systems) get lower R factors than systems where structural walls essentially brace complete gravity frames. This reflects the concern for additional safety where structural elements that are resisting lateral forces also support gravity loads. Where there is a gravity system that is independent of the shear walls, but some of the shear walls directly carry vertical loads to the foundation, the engineer must determine if this creates a bearing-wall system, or if the building may be defined as a building-frame system that uses shear walls for lateral-load resistance with the same walls incidentally sharing in part of the vertical support. Such a system with ordinary, reinforced-concrete shear walls is assigned an R of 5. This latter interpretation is implied in the examples given by Ghosh and14 when even a significant portion of the gravity framing is supported by the walls. The distinction is an important one, because the difference in the R values that are

(Note: The denominator of Eq. 4-24 is the sum of the wxhx for all floors. Thus, for example, in a single-story building, the total base shear is assumed to be applied to the roof diaphragm.) 4.2.4.3 Lateral Distribution and Torsion The force Fx as calculated in Section 4.2.4.2 is distributed to the resisting components by the diaphragm as discussed in Section 4.8. Also, actual and accidental torsion must be considered in all buildings that do not have flexible diaphragms. (Note: It is conservative for application of this section to assume the diaphragm is not flexible.) The accidental torsion is calculated by assuming that the center of mass is located a distance of 5% of the plan dimension perpendicular to the applied load on either side of the actual center of mass. The total torsion is the sum of the actual torsion plus the accidental torsion. 4.2.4.4 Drift Effects Seismic design includes requirements not only for strength, but also limits on story drift, calculated as follows:

δx =

Cd δ xe I

(Eq. 4-25)

where: δx = amplified deflection of level x δxe = deflection of level x determined from elastic analysis that includes considera­tion of cracking Cd = deflection amplification factor for structural

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system (Design Aid 4.11.8) Ι = seismic occupancy importance factor (Design Aid 4.11.1) The Cd factor represents an approximation of the post-yield displacement. In the evaluation of the building drift, the limit placed on building period by Eq. 4-17 and on the lower threshold limit Eq. 4-21 or 4-22 do not apply. A separate analysis using reduced lateral loads calculated without these constraints may be used to calculate the deflections used in the drift and stability evaluation. Caution is needed when performing and interpreting the results of elastic analysis for precast concrete moment frames. Designers using linear elastic analysis ordinarily calculate the load distribution and displacements using the load combinations as if the structure is instantly complete. This is usually not accurate. Erection of components and completion of connections is sequential. This sequential erection procedure can result in different actual load distributions and displacements from those a designer might calculate if he/ she did not consider the loading results of sequential erection and instead just analysed the loads and their results as if they were all in place simultaneously. For example, when deck components are placed on simple-span beams and moment connections later make the beam continuous, the deck load does not contribute to the negative moment at the connection. Calculated lateral forces and drifts can be similarly affected in unsymmetrical frames. Also, lateral sway may be taken out during erection as the frame is adjusted to plumb as erection proceeds. The contract drawing should state the assumed sequence of precast concrete construction. Thus, load combinations that include the effect of gravity dead loads as created by sequential erection should be analyzed so that these effects can be subtracted from the seismic-load combinations to accurately reflect the effects of sequential erection. This can substantially reduce the design moments. Similarly, for drift derived from a linear elastic analysis, a load case or combination that includes only the seismic load should be used to separate the seismic deflections from the gravity dead-load effects. A stability coefficient θ must be calculated:

θ=

Px Δ Vx h sxCd

(Eq. 4-26)

θmax =

0.5 ≤ 0.25 β Cd

(Eq. 4-27)

where  = ratio of shear demand to shear capacity between levels x and x–1 4.2.4.5 P-∆ Effects In addition to the inelastic deformation increase, the design story drift must also be increased to account for 1 P-∆ effects by a factor of 1− θ If θ < 0.10, P-∆ effects may be neglected. The allowable story drift limits are shown in Design Aid 4.11.9, which is taken from ASCE 7-05, Table 12.12.1. 4.2.4.6 R  edundancy – Seismic Design Categories D, E, and F In high seismic design categories, ASCE 7-05 requires the consideration of redundancy in the lateral-force-resisting system. This is done by increasing the earthquake force in seismic design categories D, E, and F by a factor ρ. The provisions for redundancy in ASCE 7-05 have been completely changed from earlier versions of the load standard. Under the ASCE 7-05 criteria, ρ is taken as 1.3 unless one of two conditions stated in Section 12.3.4.2 are met. The first condition requires that in each story resisting more than 35% of the base shear in the direction of interest, the loss of moment resistance at the beam-to-column connections at both ends of a single beam in a moment-resisting frame, or the removal of a shear wall not result in more than 33% reduction in story shear nor does the resulting system have an extreme torsional irregularity (Type 1b). This irregularity is not permitted in seismic design categories D, E, and F. The second condition requires that structures that are regular in plan have at least two bays of seismic-force-resisting perimeter framing on each side of the structure in each orthogonal direction at each story resisting more than 35% of base shear. Unless a building has structural irregularities, most practical layouts with precast concrete framing will meet the first condition and will not require the ρ factor to be other than 1.0. 4.2.5

where: Px = total vertical unfactored load at and above level x ∆ = difference of deflections between levels x and x–1 Vx = seismic shear force acting between levels x and x–1 hsx = story height below level x Cd = deflection amplification factor (Design Aid 4.11.8) The stability coefficient is limited to:

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Lateral Soil Loads

Some precast concrete structures require the consider­ ation of lateral soil pressures. Design procedures involving soil loads are beyond the scope of this handbook and can be found in many texts and references. 4.2.6

Load Combinations

References 1 and 3 specify the following load combinations: 1. U = 1.4(D + F)

(Eq. 4-28)

2. U = 1.2(D + F + T) + 1.6(L + H) + 0.5(Lr or S or R) (Eq. 4-29) 3. U = 1.2D +1.6(Lr or S or R) + (1.0 L or 0.8W) (Eq. 4-30)

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(Eq. 4-32)

6. U = 0.9D + 1.6W + 1.6H

(Eq. 4-33)

7. U = 0.9D + 1.0E + 1.6H

(Eq. 4-34)

Except as follows: •

• • •

The load factor on the live load L in Eq. 4-30 to 4-32 shall be permitted to be reduced to 0.5 except for garages, areas occupied as places of public assembly, and all areas where L is greater than 100 lb/ft2. Where wind load W has not been reduced by a directionality factor, it shall be permitted to use 1.3W in place of 1.6W in Eq. 4-31 and 4-33. Where E, the load effects of earthquake, is based on service-level forces, 1.4E shall be used in place of 1.0E in Eq. 4-32 and 4-34. The load factor on H, loads due to weight and pressure of soil, water in soil, or other materials, shall be set equal to zero in Eq. 4-33 and 4-34 if the structural action due to H counteracts that due to W or E. Where lateral earth pressure provides resistance to structural actions from other forces, it shall not be included in H but shall be included in the design resistance.

where: D = dead load F = p ressure of fluids of known density and controlled depths T = effects of temperature, creep, and shrinkage L = live load H = soil load Lr = roof live load S = snow load R = rain load W = wind load E = seismic load IBC 2006 requires that the value of E in Eq. 4-32 and 4-34 be defined by:

ρQE ± 0.2SDSD

(Eq. 4-35)

Note that 0.2SDSD accounts for the vertical acceleration affecting the dead-load contribution. This has the effect of changing those equations to:

U = (1.2 + 0.2SDS)D + ρQE + f1L + 0.2S (Eq. 4-32a)



U = (0.9 – 0.2SDS)D + ρQE + 1.6H

(Eq. 4-34a)

The coefficient ρ is 1.0 for buildings in seismic design categories A, B, and C. See Section 4.2.4.5 for calculation of ρ in high seismic design categories D, E, and F. QE is the horizontal seismic force on the component or system.

CHAPTER 4

4.2.6.1 Load Factors for Diaphragms Although not required by code, recent research into the performance of some precast concrete diaphragms in high seismic areas indicate that the use of special load combinations should be considered. To distinguish the diaphragm overstrength factor from the system overstrength factor, ψ is introduced to represent the diaphragm overstrength factor (see Section 4.8).

U = 1.2D + f1L + Eψ

(Eq. 4-36)



U = 0.9D + Eψ

(Eq. 4-37)

where:

Eψ = QE ± 0.2SDSD

(Eq. 4-38)

For design of the diaphragm in shear-wall buildings, which includes chord reinforcement and shear connections between precast concrete elements, Section 4.8 recommends a diaphragm overstrength factor ψ = 2.0 in the previous equation for seismic design categories D, E, and F. The value for the diaphragm force for any seismic design category should not be less than Fpx calculated by Eq. 4-60 or the largest level seismic force, whichever is greater and still within the limits of 0.25SDSIEFpx ≤ Fpx ≤ 0.4SDSIEWpx. It is recommended that the same force be used for diaphragm design for all levels of the building. Since the diaphragm overstrength factor is not recommended for seismic design categories A, B, and C, it is suggested, based on versions of Reference 5, that perimeter diaphragm reinforcement be designed based on strength-reduction factors φ as follows: For continuous bars, φ = 0.9. For bars spliced with mechanical or welded connections, φ = 0.7. For shear design in diaphragms, φ = 0.60 for shear friction reinforcement and for mechanical connectors in the joints to ensure additional overstrength for shear. For connections from the collectors to the SFRS—shear walls or moment frames—References 1 and 5 require that the equations shown previously be used with Em instead of Eψ in seismic design categories C and higher. Collectors in seismic design catagories A and B do not require any overstrength factor to be applied. The value of Em is determined with Ωo, the system overstrength factor (listed in Design Aid 4.11.8).

4.3

Structural Integrity

4.3.1

Introduction

It is the intent of the structural integrity provisions of ACI 318-05 to improve the redundancy and ductility of structures, thereby reducing the risk of failure or collapse of parts or all of a building due to damage occurring to a relatively small area of a building. ACI 318-05 commentary emphasizes that the overall integrity of the structure can be substantially enhanced by minor changes in the detailing of reinforcement. In the event of damage to a beam, for example, it is important that displacement of its supporting component be minimized, so that other components will not be affected. For this reason, connection

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details that rely solely on friction caused by gravity loads are not permitted. Connections should also be detailed to minimize the potential for cracking due to restraint of volume change forces. 4.3.2

Precast Concrete Structures

For typical precast concrete structures, improved redundancy and ductility are achieved by connecting components to the lateral-force-resisting system and to each other to create a direct load path between components. The load path in the lateral-force-resisting system must be continuous to the foundation. Any individual component may be connected into this load path by several methods. In recognition of the interrelationship between structural integrity and seismic performance, general integrity provisions for even seismic design category A are included in ASCE 7-05. A new provision in Section 12.1.4 provides specific requirements for connections to supports that are more restrictive than previous editions, requiring a connection for a horizontal force parallel to the component, either directly to the supporting component, or to slabs acting as diaphragms. When a beam is connected to the lateral-force-resisting system through direct connections to the diaphragm rather than through a connection to its supporting component, this section requires that the supporting component also have a direct connection to the diaphragm. For example, a load-bearing spandrel could be connected to a diaphragm (part of the lateral-force-resisting system) in more than one way. Structural integrity is typically achieved by connecting the spandrels into all or a portion of the deck components forming the diaphragm, which in turn would be connected to the supporting beams and the beams would be connected to their supporting columns. Section 11.7.4 of ASCE 7-05 imposes an additional requirement for the connections of components to their supports: “A positive connection for resisting a horizontal force acting parallel to the member shall be provided for each beam, girder, or truss either directly to its supporting elements or to slabs designed to act as diaphragms. Where the connection is through a diaphragm, then the member’s supporting element must also be connected to the diaphragm. The connection shall have a minimum design strength of 5% of the dead load plus live load reaction.” This provision is an important change from previous editions. It has been common practice to provide the lateral support and tie of precast concrete columns on the framing perimeter using a load path from the diaphragm through spandrel beams and their torsion connecting rods without a direct connection of the column to the diaphragm. Since forces on these columns in the longitudinal direction of the spandrel beams are usually nominal, the bracing effects provided by tightening the rods to draw the spacers (chloroprene pads) between beam and column partially into the column sleeve, or by the floor flanges or pour strips surrounding the column on three sides, were often taken as sufficient. This section now prescribes a minimum design force for this condition that can only be reliably transferred by adding a direct connection between the column and the diaphragm. Vertical continuity is achieved by providing connections at 4–16

horizontal joints of vertical components. For precast concrete structures, the following provisions will satisfy the requirements of ACI 318-05 Sections 7.13.3 and 16.5. Example 4.3.2.1 demonstrates compliance with these requirements. 1. All components must be connected to the lateralforce-resisting system and to their supporting components and the foundation. Tension ties must be provided in the transverse and longitudinal directions around the perimeter of the structure. 2. Lateral-force-resisting system must be continuous to the foundation. 3. For precast concrete bearing-wall structures three or more stories high, a diaphragm must be provided with connections between diaphragm components, with tension ties around its perimeter, and around openings that significantly interrupt diaphragm action. Section 16.5.2.4 of ACI 318-05 requires perimeter ties to provide a nominal strength of at least 16 kip and to be within 4 ft of the edge. 4. Column splices and column base connections must have a nominal tensile strength not less than 200Ag in pounds, where Ag is the gross area of the column in square inches. For a compression component with a larger cross section than required by consideration of loading, a reduced effective area Ag, not less than one-half of the total area, may be used. 5. Precast concrete walls, other than cladding panels, must be connected across horizontal joints by a minimum of two connections per panel. Each connection is to have a nominal tensile strength of not less than 10 kip. When design forces result in no tension at the base, these connections are permitted to be anchored into an appropriately reinforced slab on grade. If panels are too narrow to accommodate two connections, a single connection is satisfactory, as long as it is connected to adjacent panels. This 10 kip requirement for each of at least two ties per wall panel in Section 16.5.1.3(b) of ACI 318-05 is the numerical equivalent of a common connection that has been used in the precast concrete industry for many years. This is strictly an empirical value, and is intended to only apply to the dimensions of the hardware items in the connections, without including eccentricities in the design.15 An exception to these requirements is appropriate for box modules with four or more walls and a monolithic floor and/or ceiling. Since these modules are monolithic at the corners, it is reasonable to permit a reduction in number and force requirements for the connections. At least four connections should be provided, placed in walls on opposite sides of the module. Where sustained dead load prevents uplift, the nominal shear strength of each connection should not be less than the larger of:

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EXAMPLE 4.3.2.1 Compliance of a Precast Concrete Structure with Structural Integrity Provisions

EXAMPLE 4.3.2.1 Compliance of a Precast Concrete Structure with Structural Integrity Provisions (cont.)

This example uses the design of the one-story building in Example 4.5.11.1 and some of the details shown in Chapter 6 to illustrate methods of compliance with the structural integrity provisions outlined in Section 4.3.2. The numbers used for the structural integrity provisions of this example refer to the same provision numbers used in Section 4.3.2.

Provision 8. “Connections details that rely...” All of the joints in the examples in this handbook show positive connections. In conclusion, the structure of Example 4.5.11.1 with the clarifications noted in this section, satisfies all of the structural integrity provisions outlined in Section 4.3.2.

Provision 1. “Components must be connected...” Compliance is provided by the connections between the roof diaphragm and the walls. Provision 2. “The lateral load resisting...” Compliance is provided by the existence of the exterior shear walls and the connections of these walls to the roof diaphragm and the foundation. Examples 6.13.3 and 6.13.4 show a typical connection detail.

T4

Provision 5. “Precast concrete walls, other than...” There are two shear-wall-to-footing connections per panel. The connections designed to accommodate the loads determined for the wall panels to the foundation must have a minimum tensile strength of 10 kip. Provision 6. “Where precast concrete elements...” The connections between the exterior walls and the roof diaphragm in Example 4.5.11.1 are designed for seismic forces, which exceed these minimum requirements. Provision 7. “To accommodate volume...” The details in Example 4.5.11.1 show how such connections are made.

1 T4

T3

T1

2 3

T4

Provision 3. “A diaphragm must be...” Compliance is provided by the analysis, design, and details of the roof diaphragm. Figure 4.8.2 and Examples 6.13.2 and 6.13.3 show example diaphragm connections. Provision 4. “Column splices and column...” Section 6.11 shows column base plate and anchorage design.

T2

b

T3 T1 T2 T2

Fig. 4.3.1 Recommended forces in precast concrete bearingwall buildings.16

• • •

0.11 times the weight of the module directly above the joint; 140 lb/ft times the largest plan dimension of the module; or 7200 lb.

6. Where precast concrete elements form roof or floor diaphragms, the connections between the diaphragm and those components being laterally supported must have a nominal tensile strength not less than 300 lb/ft. 7. To accommodate volume-change strains (creep, shrinkage, and temperature change) in supported beams, tie connections are typically located at the top of the component, with elastomeric pads used at the bottom bearing surface. Such ties can be accomplished by welding, bolting, placing reinforcing steel in grout joints or bonded topping, or by doweling. 8. Connection details that rely solely on friction caused by gravity loads are not to be used

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Large-Panel Bearing-Wall Structures

Large-panel bearing-wall structures are a special category of precast concrete structures, with respect to structural integrity. Large panel structures are typically constructed with precast concrete walls having a horizontal dimension greater than the vertical dimension, which is generally the height of one story. The panels are stacked for the height of the building and support the floor and roof decks. Criteria have been established for alternate load paths in such buildings three stories or more in height.16 Large-panel wall structures under three stories must meet the requirements of Section 4.3.2. For large-panel bearingwall structures three stories or more in height, minimum tie strength requirements are satisfied by the use of the following forces, illustrated in Fig. 4.3.1.16 It is not intended that these forces replace an analysis of the actual design forces required in the structure or that they be additive to the actual design forces. The required forces are as follows. T1 = n ominal tensile strength equal to 1500 lb/ft of floor or roof span. Ties may be encased in the floor units or in a topping or may be concentrated at the wall. Spacing shall not exceed the spacing of bearing walls. Ties may be positioned in the walls within 2 ft of the plane of the floor or roof. T2 = n ominal tensile strength sufficient to develop diaphragm action, but not less than 16,000 lb, located within the depth of the floor or roof slab and within 4 ft of the edge. Ties may be reinforcing steel in a grout joint or in an edge beam; reinforced spandrels or wall anchored to the floor or roof may also be considered. T3 = n ominal tensile strength not less than 1500 lb/ft of wall. Ties shall be spaced not greater than 10 ft on center. They may project from the precast concrete component or be embedded in grout joints, with sufficient length and cover to develop the specified strength. At end walls, wall reinforcement shall extend into the floor, or mechanical anchorage between floor and wall shall be provided. T4 = n ominal tensile strength not less than 3000 lb per horizontal foot of wall, with a minimum of two ties per wall. These ties shall be continuous from foundation to the top of the wall. 4.3.4

 tructures with Mixed Structural S Materials

The provisions of ACI 318-05 relate to concrete buildings only. Those connections that interface precast concrete components with other structural materials (such as masonry walls, steel, or wood) should provide the same load paths and follow the design philosophy described previously. Since the pre­cast concrete supplier rarely has control over such other materials, the Engineer of Record must design and detail the connections to satisfy structural integrity and include them in the contract drawings. 4–18

4.4

Volume Changes

Creep, shrinkage, and temperature change and the forces caused by restraining these strains affect connections and service-load behavior of precast concrete structures. Consequently, the effect of these strains and forces should not be ignored in the design and detailing. Volume change due to temperature variation can be positive (expansion) or negative (contraction), while volume changes from shrinkage and creep are only negative. Therefore, the critical combination is usually the contraction com­bination of creep, shrinkage, and temperature drop. Design Aids 4.11.13 through 4.11.21 provide data for estimating the amount of shortening that may take place. Use of these aids is shown in Examples 4.4.1.1 and 4.4.1.2. PCI has sponsored a multiyear study of volume-change behavior in precast buildings, with particular focus on parking structures. The objective of this research was twofold: 1) develop a better understanding of volume change movement and forces based on measured performance of precast parking structures and calibration to analytical models, and 2) recommend revised design procedures that reflect this understanding and account for the influence of flexible connections. The primary research tasks included field monitoring and finite element analyses of new parking structures, as well as evaluation of the predictability of volume change forces. The research revealed that deformations of flexible deck and spandrel connections that are typical in most precast structures change the deformation pattern and thereby substantially reduce volume change movement and force at the lowest supported level, where volume change forces are most significant. The study also developed new findings with respect to other volume change parameters, including the thermal expansion coefficient, the design temperature range, the degree of component softening due to creep and microcracking, and the load factor for volume change effects. Design recommendations are provided for qualitative consideration of volume change effects as well as quantitative analysis. A summary paper17 by Klein and Lindenberg has been published, and the research report18 is available from PCI. Properly detailed connections can minimize the effects of volume-change strains. Connections should be detailed so that ductile deformation of one of the components such as the connecting plate or connection bolt assembly can take place. Neglecting the effect of this connection deformation will produce unrealistically high computed restraint forces and can actually have a negative effect if connections are too strong, and inhibit necessary ductility. Problems caused by volume change have appeared when prestressed concrete components were welded to their bearings at both ends. When such components are connected only at the top using a ductile connection, experience has shown that volume changes are adequately accommodated. An excessively strong top connection may also attract high negative moment if compression resistance is encountered at the bearing location. Vertical components such as load-bearing wall panels are also subject to volume-change strains. The approximate mag-

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EXAMPLE 4.4.1.1 Calculation of Volume-Change Shortening

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Given: Heated structure in Denver, Colorado Normalweight concrete beam – 12RB28 Eight 1/2-in.-diameter, 270 ksi, low-relaxation strand Initial tension = 0.75fpu Assume initial prestress loss = 9% Release strength = 4500 psi (accelerated cure) Length = 24 ft Problem: Determine the actual shortening that can be anticipated from casting to erection at 60 days and erection to the end of service life. _________________________________________________________________________________ Solution: From Design Aids 4.11.11 and 4.11.12: Design temperature change = 70 °F Average ambient relative humidity = 55% Aps

= 8(0.153) = 1.224 in.2

Po

= 1.224(270)(0.75)(1 – 0.09) = 225.6 kip

Po /A =

225.6 (1000 ) = 671 psi 12 ( 28 )

Volume-to-surface ratio = a.

12 (28 ) = 4.2 in. 2 (12 ) + 2 (28 )

At 60 days: From Design Aid 4.11.13: Creep strain = 169 × 10–6 in./in. Shrinkage strain = 266 × 10–6 in./in. From Design Aid 4.11.14: Creep correction factor = 0.88 + (71/200)(1.18 – 0.88) = 0.99 From Design Aid 4.11.15: Relative humidity correction (creep) = 1.17 – 0.5(1.17 – 1.08) = 1.13 Relative humidity correction (shrinkage) = 1.29 – 0.5(1.29 – 1.14) = 1.22 From Design Aid 4.11.16: Volume-to-surface ratio correction (creep) = 0.48 – 0.2 (0.48 – 0.36) = 0.46 Volume-to-surface ratio correction (shrinkage) = 0.46 – 0.2 (0.46 – 0.31) = 0.43

(Note: Temperature shortening is not significant for this calculation because the structure is in a controlled environment.) Total strain: Creep = 169 × 10–6 (0.99)(1.13)(0.46) = 87 × 10–6 in./in. Shrinkage = 266 × 10–6 (1.22)(0.43) = 140 × 10–6 in./in. Total strain = 227 × 10–6 in./in. Total shortening = 227 × 10–6 (24)(12) = 0.065 in.

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EXAMPLE 4.4.1.1 Calculation of Volume-Change Shortening (cont.) b.

At final: From Design Aid 4.11.13 Creep strain = 315 × 10–6 in./in. Shrinkage strain = 510 × 10–6 in./in.

Factors from Design Aids 4.11.14 and 4.11.15 are the same as for 60 days. From Design Aid 4.11.16: Volume-to-surface ratio correction (creep): = 0.77 – 0.2(0.77 – 0.74) = 0.76 Volume-to-surface ratio correction (shrinkage): = 0.75 – 0.2(0.75 – 0.64) = 0.73 From Design Aid 4.11.17: Temperature strain = 210 × 10–6 in./in. Total creep and shrinkage strain: Creep = 315 × 10–6 (0.99)(1.13)(0.76) = 268 × 10–6 in./in.

Shrinkage = 510 × 10–6(1.22)(0.73) = 454 × 10–6 in./in.



Total



Difference from 60 days to final = 722 – 227 = 495 × 10–6 in./in.



Total strain



Total shortening = 705 × 10–6(24)(12) = 0.203 in./2 = 0.10 in. per end

= (268 + 722) × 10–6 = 722 × 10–6 in./in.

= 495 + 210 = 705 × 10–6 in./in.

This strain needs to be accommodated by designing connections that will provide for this amount of flexibility and deformation. The behavior of actual structures indicates that reasonable estimates of volume-change characteristics are satisfactory for the design of most structures even though test data relating volume changes to the variables shown in Design Aids 4.11.13 through 4.11.17 exhibit considerable scatter. Therefore, it is possible to reduce the variables and use approximate values as shown in Design Aid 4.11.18 and 4.11.19.

EXAMPLE 4.4.1.2 Determine Volume-Change Shortening by Design Aids 4.11.18 and 4.11.19 Given and Problem: Same as Example 4.4.1.1. _________________________________________________________________________________ Solution: For prestressed, normalweight concrete, in a heated building, use Design Aid 4.11.18. For 55% relative humidity and temperature change of 70 °F, interpolating from Design Aid 4.11.18: Actual strain = 687 × 10–6 in./in. This result is similar to the value of 705 × 10–6 calculated from Design Aids 4.11.13 through 4.11.17.

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ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES nitude can be calculated using Design Aids 4.11.11 through 4.11.17, adding the dead-load strain to any prestress strain. The vertical component effects will only be significant in high-rise structures, and then only the differential movements between supporting columns and facade panels may significantly affect the performance of the components. Such effects can occur, for example, at the exterior of a building where precast concrete panels are connected to a cast-inplace frame. The connections between the precast concrete components and the supporting frames, as well as the connections between panels, must be detailed to accommodate volume changes. Volume-change forces are particularly important in parking structures because of their exposure to the elements. The primary volume change force that must be accommodated is due to temperature change. Connections between precast concrete components and precast concrete components to stiff elements such as shafts must accommodate these strains. 4.4.1

Axial Volume-Change Strains

Design Aids 4.11.11 through 4.11.17 provide the data needed to determine volume-change strains, as shown in Example 4.4.1.1. 4.4.2

Expansion Joints

Expansion joints are placed in structures to limit the magnitude of forces, which result from volume-change deformations (temperature changes, shrinkage, and creep), and to permit movements (volume change and seismic) of structural components. Joints that permit contraction of the structure are needed to relieve the strains typically caused by temperature drop, creep, and shrinkage, which may be additive. Such joints are properly called contrac­tion or control joints but are commonly referred to as expansion joints. Typically, the forces generated by a temperature difference are signifi­cantly greater than shrinkage and creep forces, and a true expansion joint may be needed in long buildings. It is desirable to have as few expansion joints as possible. The purpose of this section is to present guidelines for determining the spacing and width of expansion joints. 4.4.2.1 Spacing of Expansion Joints Recommended expansion-joint spacing for precast concrete buildings is generally based on experience. Evaluation of expansion-joint spacing should consider the types of connections used, the column stiffnesses in simple-span structures, the relative stiffness between beams and columns in framed structures, location of lateral-load-resisting elements, and weather-exposure conditions. Non-heated structures, such as parking structures, are subjected to much greater temperature changes than enclosed structures, so the distance between expansion joints should consider the previously mentioned items. Design Aid 4.11.20 shows expansion-joint spacing as recommended by the Federal Construction Council, and is adapted from Reference 19. The spacings obtained from the graph in Design Aid 4.11.20 should be modified for various

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conditions as shown in the notes below the graph. Values for the design temperature change can be obtained from Design Aid 4.11.11. It should be noted that recent studies on four precast concrete parking structures reveal that there is some relief of force build-up by virtue of the connections, such that the design aids may be somewhat conservative. When expansion joints are required in non-rectangular structures, such as T- or L-shaped structures, they should be located at places where the plan or elevation dimensions change radically. 4.4.2.2 Width of Expansion Joints The width of the expansion joint can be calculated theoretically using a coefficient of expansion of 6  ×  10–6  in./in./°F for normalweight concrete and 5  ×  10–6  in./in./°F for sandlightweight concrete. Since the primary problem in concrete buildings is contraction rather than expansion, expansion joints that are too wide may result in problems with reduced bearing or loss of filler material. The expansion joint width should consider the ambient temperature at the time of erection. Seismic codes also stipulate joint widths to accommodate earthquake movement. Paragraph 12.12.3 of ASCE 7-05 states that “all portions of a structure shall be designed and constructed to act as an integral unit resisting seismic forces unless separated structurally by a distance sufficient to avoid damaging contact under total deflection (δx)…..” which is the elastic displacement determined from analysis, based on strength design procedures, times the deflection amplification factor Cd. Unless an evaluation for the demand of damaging contact is made, this separation may be taken as the sum of the displacements of the structures on either side of the expansion joint. 4.4.3

 olume-Change Effects in MomentV Resisting Frames

The restraint of volume changes in moment-resisting frames causes tension in the girders and deflections, shears, and moments in the columns. The magnitude of the tension, shear, moment, and deflection of a component is dependent on the distance from the center of stiffness of the frame or of several frames if they are connected. The center of stiffness is that point of a frame subject to a uniform unit shortening at which no lateral movement will occur. For frames that are symmetrical with respect to bay sizes, story heights, and component stiffnesses, the center of stiffness is located at the midpoint of the frame, as shown in Design Aid 4.11.21. Tensions in girders are at maximum in the bay nearest the center of stiffness. Deflections and moments in columns are at maximum farthest from the center of stiffness. Thus, in Design Aid 4.11.21: F1 < F2 < F3 ∆1 > ∆2 > ∆3 M1 > M2 > M3 The degree of fixity of the column base as described in Section 4.6.3 has a great effect on the magnitude of the forces and moments caused by volume-change restraint. An assumption

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w

  4

w

F3

F3

Eccentricity

Eccentricity F1

F2

• Center of lateral load

Center of rigidity

F1 Center of rigidity

F3

(a) Frequently occurs in large buildings with large expansion joints

Center of lateral load F3

(b) Frequently occurs in buildings with large door openings

Fig. 4.5.1 Unsymmetrical shear walls.

of a fully fixed base in the analysis of the structure may result in significant overestimation of the restraint forces, whereas assuming a pinned base may have the opposite effect. The degree of fixity used in the volume-change analysis should be consistent with that used in the analysis of the column for other loadings and the determination of slenderness effects. To avoid a build-up of volume-change forces, rather than connecting several frames, it is advisable to create flexible connections between sets of moment frames. 4.4.3.1 Equivalent Volume Change If a horizontal framing component is connected at the ends such that the volume-change shortening is restrained, a tensile force is built up in the component and is transmitted to the supporting elements. However, since the shortening takes place gradually over a period of time, the effect of the shortening on the shears and moments of the support is lessened because of creep and microcracking of the component and its support. For ease of design, the volume-change shortenings can be treated in the same manner as short-term elastic deformations by using a concept of equivalent shortening. Thus, the following relations can be assumed:

(Eq. 4-39)



δ δ es = s K

(Eq. 4-40)

where: δec, δes = equivalent creep and shrinkage shortenings, respectively δc, δs = calculated creep and shrinkage shortenings,

respectively = a constant for design purposes that varies from 4 to 6

The value of Kl will be near the lower end of the range when the components are heavily reinforced and near the upper end when they are lightly reinforced. For most common structures, a value of Kl = 5 is sufficiently conservative. Shortening due to temperature change will be similarly modified. However, the maximum tempera­ture change will usually occur over a much shorter time, probably within 60 to 90 days. Thus,

δet = δt /Kt

(Eq. 4-41)

where: δet, δt = the equivalent and calculated tempera­ture shortening, respectively Kt = a constant; recommended value = 1.5 Total equivalent shortening to be used for design:

δ δ ec = c K

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Kl

Δ = δ ec + δ es + δ et =

δc + δs δt + K Kt

(Eq. 4-42)

When the equivalent shortening is used in frame analysis for determining shears and moments in the supporting components, the actual modulus of elasticity of the components is used, rather than a reduced modulus as used in other methods. Design Aids 4.11.22 and 4.11.23 provide equivalent volume-change strains for typical building frames.

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ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES 4.4.3.2 Calculating Restraint Forces Most plane frame computer-analysis programs allow the input of shortening strains of components from volume changes. The equivalent strains as described in Section 4.4.3.1 can be input directly into such programs.

4.5

Shear-Wall Systems

4.5.1

Introduction

Buildings that use shear walls as the lateral-force-resisting system provide a safe, serviceable, and economical solution for wind and earthquake resistance. Shear walls make up most common lateral-force-resisting systems in the precast/ prestressed concrete industry. The excellent per­formance of shear-wall buildings throughout the world that have been subjected to earthquakes testifies to the effectiveness of this system. Experience in earthquakes shows that, in many cases, shear-wall buildings have been safe to occupy and fully functional immediately after the earthquake. The design of these buildings has typically followed principles used for cast-inplace structures, with modifications made as appropriate for the jointed nature of a precast concrete structural system. Design methods used to achieve successful performance of precast concrete shear-wall structures have been largely left to the ingenuity and judgment of the design engineer. Observations of performance of structures in earthquakes show that where adequate strength and stiffness were provided to limit interstory drift to about 2%, the resulting displace­ments and damage were within acceptable levels. In regions of low and moderate seismicity, dry connections with small grout joints are generally used. In regions of high seismicity, connections to the foundation and between precast concrete walls generally use details that emulate cast-in-place behavior (see Section 4.1.2) and may include post-tensioning. In the few cases where shear-wall buildings have shown poor performance, the problems were generally related to details that were insufficiently ductile and resulted in brittle local failure (such as improper anchoring of embedments). Incomplete load paths, such as improper diaphragm details, were also problematic. Inadequate diaphragm behavior can be caused by inadequate reinforcement for shear and tension within the diaphragm and insufficient ties between the diaphragm and shear walls. 4.5.2

Principles of Shear-Wall Buildings

Shear walls act as vertical cantilever beams, which transfer lateral forces acting parallel to the face of the wall, from the superstructure to the foundation. Shear walls should be oriented to resist lateral loads applied to the building along both principal axes of the building. Ideally, there should be at least two shear walls oriented to resist lateral loads along each principal axis of the building. If only one shear wall is oriented along one principal axis of the building, two shear walls should be provided along the orthogonal axis to resist diaphragm torsion, but only within reasonable limits dictated by the capacity of the diaphragm and drift (Fig. 4.5.1[a]). It is desirable to design shear walls as load-­bearing pan-

CHAPTER 4

els whenever possible. The increased dead load acting on the panel is an advantage because it increases the panel’s resist­ ance to uplift and overturning. The distribution of the total lateral force acting on a building to each individual shear wall is influenced by the following factors: • • • •

Supporting soil and footings Stiffness of the diaphragm Relative flexural and shear stiffnesses of the shear walls, and of connections Eccentricity of the lateral loads to the center of rigidity of the shear walls

Generally, it is common practice to neglect the deformation of the soil and the footings when distributing shear forces among shear walls. If the span-to-depth ratio of a diaphragm is large, the diaphragm will be flexible and may deflect significantly when subjected to lateral loads. Flexible diaphragms distribute shears to each shear wall in proportion to the tributary width of diaphragm loading each shear wall. If the span-to-depth ratio of a diaphragm is small, the diaphragm will be rigid and not deflect as significantly as a flexible diaphragm when subjected to lateral loads. Rigid diaphragms distribute shears to each shear wall in proportion to the shear wall’s relative stiffness. In precast concrete building design, it is common practice to assume that floor and roof diaphragms act as rigid diaphragms. See Section 4.8 for a more complete discussion of precast concrete diaphragms. 4.5.3

Code Requirements

IBC 2006 provisions directly reference ASCE 7-05, which will result in lateral forces that govern most precast concrete building systems. ASCE 7-05 is now consistent with ACI 318-05 and includes design coefficients and factors (R, Ωo, and Cd) for four concrete shear-wall classifications. These are ordinary precast concrete shear walls, ordinary reinforced-concrete shear walls, intermediate precast concrete shear walls, and special reinforced-concrete shear walls. Special reinforced concrete shear walls may be either cast-in-place or precast. ACI 318-05 defines the various types of structural (shear) walls, shown in bold in the following paragraphs. It should be noted that ACI 318-05 uses the term structural wall. In reference to lateral-load resistance, this is the same as a shear wall. This handbook uses the more traditional term shear wall. Ordinary structural (shear) wall  –  “A wall complying with the requirements of Chapters 1 through 18,” that is, one with no special seismic detailing. Intermediate precast concrete structural (shear) wall – “A wall complying with all requirements of Chapters 1 through 18 in addition to 21.13.” Section 21.13 requires that yielding of connections be in steel elements or reinforcement, and that the strength of elements of the connections that are not designed to yield must develop strength 50% greater than the nominal strength of the yielding elements. ASCE 7-05 adds a requirement that the connections designed to yield be capable of maintaining 80% of their design strength at the

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1. Evaluation of building function and applicable precast concrete frame a. In a warehouse type structure, it is common to include the exterior walls as part of the lateralforce- resisting system. b. In parking structures, shear walls can be located at stair and elevator towers, at the perimeter, or ramped bays, at selected locations anywhere in the structure, or any combination of these locations.

Center of rigidity

Rotation

Translation

Center of rigidity

Center of rigidity Shear walls (a)

(b)

Fig. 4.5.2 Translation and rotation of rigid diaphragms.

t

Smaller of 12t or 1/6 height from level under consideration to top of wall t

Fig. 4.5.3 Effective width of wall perpendicular to shear walls.4

deformation induced by design displacement, or be Type 2 mechanical splices. ASCE 7-05 also adds a requirement that wall piers in intermediate precast concrete walls have transverse (shear) reinforcement designed to meet the shear requirements of members of intermediate moment frames. Special precast concrete structural (shear) wall – A precast concrete wall complying with the requirements of ACI 318-05 21.8. In addition, the requirements for ordinary reinforced concrete structural walls and the requirements of ACI 318-05 21.2.2.3, 21.2.3 through 21.2.7, and 21.7 shall be satisfied. This requires precast concrete walls to be designed and detailed like cast-in-place walls (that is, emulative design), in addition to having them meet the connection requirements of ACI 318-05 Section 21.13. 4.5.4

 esign Guidelines for Shear-Wall D Structures

The following are suggested design guidelines for structures that have shear walls as components making up the primary lateral-force-resisting system.

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2. Preliminary development of shear-wall system a. Provide at least three walls, one of which is oriented in a different direction, to ensure torsional as well as direct lateral resistance. b. Overturning will often be the governing criterion. Thus, the first choice is to use shear walls that also function as bearing walls. c. Arrange shear walls so that they minimize restraint due to volume changes. (Locate as close to the center of mass of the structure as is practical.) d. Consider the orientation of walls, whether horizontal or vertical. e. Consider the practicality of shipping and erection when selecting the size of wall panels. f. Balance the design requirements of the shear walls with the design requirements of the associated diaphragms. 3. Determination of vertical and lateral loads a. Determine the vertical gravity loads that are applicable to each shear wall. b. Use the applicable seismic design criteria to determine the magnitude of lateral load at each floor, and compare with wind loading. Choose the critical condition for design. 4. Preliminary load analysis a. Determine the overturning moment, the lateral in plane shear, and the axial load at the base of each of the shear walls. 5. Selection of shear walls a. Review the preliminary choice of shear-wall size and location. b. Modify the number, location, and dimensions of shear walls as necessary to satisfy the requirements at the base of each. 6. Final load analysis a. Based on the final location and dimensions of shear walls, perform the final lateral-load and vertical-load analysis to determine the design load for each of the shear walls. Consider shear stiffness as well as flexural stiffness when distributing lateral loads to the shear walls. 7. Final shear-wall design a. Design the shear-wall reinforcement and the connections to the associated diaphragms.

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ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES b. Where there is insufficient length of shear wall available to accommodate the necessary number of shear connectors, a portion of the collector (drag strut) may be anchored directly into the end of the shear wall (Fig. 4.8.5). c. Consider the additional requirements necessary to satisfy the structural integrity provisions of the code (see Section 4.3). 8. Diaphragm design a. Though not a code requirement, it is recommended that diaphragms be designed to respond elas­tically to applied lateral loads in order to prevent formation of plastic regions in any diaphragm. See Section 4.8 for a more detailed discussion of diaphragm design. b. Design the diaphragms as beams, provide the necessary tensile reinforcement for each chord, and choose shear connectors using design procedures of Chapter 6, or shear reinforcement using shear-friction methods. c. Design the collectors as tension or compression elements, as appropriate, to drag diaphragm loads to shear walls along each line of resistance where the shear walls do not extend the entire dimension of the structure. d. Consider the additional requirements necessary to satisfy the structural integrity provisions of the code (see Section 4.3). Note that larger portions of the return wall can be engaged if the walls are considered special shear walls and special detailing is provided. See ACI 318-05 Section 21.7.5.2. 4.5.5

Proportioning Shear Walls

A rigid diaphragm subjected to lateral load will translate in the direction of the applied load (Fig. 4.5.2[a]). The magnitude of the diaphragm translation is related to the sum of the rigidities of the resisting shear walls. If the center of rigidity is not coincident with the line of action of the applied loads, the diaphragm will tend to rotate about the center of rigidity (Fig. 4.5.2[b]). The location of the center of lateral load can be different for different load cases, such as wind loading and seismic loading. The dimension between the center of rigidity and center of lateral load is the eccentricity of the lateral-force-resisting system. For seismic design, ASCE 7-05 requires that the addition of extra eccentricity of 5% of the perpendicular plan dimension of the structure provide for accidental torsion. It is desirable to design the wall panels as single, uncoupled units. This reduces the cost of connections and the magnitude of volume-change restraint forces that occur when many wall panels are connected together to form one large shear wall. If the overturning moment results in excessive uplift to an individual, uncoupled shear-wall panel, multiple wall panels can be connected together. Connecting individual vertical wall panels greatly increases the shear resistance and reduces uplift of the shear wall. Locate the required panel-to-panel connections near mid-length of the wall to minimize volume-

CHAPTER 4

change restraint forces within the length of the wall. As previously stated, it is desirable to minimize the number of connected wall panels to minimize volume-change forces and the number of connections required. The stiffness of a shear wall may be increased by connecting it to perpendicular walls, which act as flanges. The effective flange width that can be assumed for such walls is illustrated in Fig. 4.5.3, as long as the connections across the joint are sufficient to transfer forces as strong connections. This requirement applies to seismic design categories D, E, and F only. Generally, the use of flanges increases the shear wall’s flexural rigidity, but has little effect on its shear rigidity. In some structures, it may be desirable to connect perpendicular walls to a shear wall to increase its dead load, which increases the shear wall’s resistance to overturning moment caused by lateral loads. Strong and ductile connections for moment-resistant frames are defined in Chapter 21 of ACI 318-05. 4.5.6

Stiffness Analysis

The distribution of lateral loads to shear walls in buildings with rigid diaphragms should be based on an analysis that includes relative rigidities of the shear walls. The total rigidity considers both flexural and shear stiffness. Rigidity of an individual wall is:

r = 1/∆

(Eq. 4-43)

where: ∆ = sum of flexural and shear wall deflections For a structure with rectangular shear walls of the same material, with a wall height-to-length ratio of less than 0.3, the flexural stiffness can be neglected and the distribution made in accordance with the cross-sectional area of the walls. If the height-to-length ratio is greater than about 3.0, the shear stiffness can be neglected and the distribution made in accordance with the moments of inertia, based on the plan dimensions of the wall. When the height-to-length ratio is between 0.3 and 3.0, the effects of both shear and flexural deformations should be considered. In terms of stiffnesses:

1 1 1 = + ∑ K i ∑ K si ∑ K fi

(Eq. 4-44)

where: ΣKi = summation of total stiffnesses at level i ΣKsi = summation of shear stiffnesses at level i ΣKfi = summation of flexural stiffnesses at level i In lieu of preparing a full stiffness analysis for lateral distribution, it may be sufficient to make a reasonable approximation using a simplified cantilevered beam model for the shear walls. If the shear walls are considered as cantilever beams above the base (foundations) with both shear and flexural stiffness, the stiffness term for each wall can be approximated according to Eq. 4-45:

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  4

where Kij hj Ai Ii

K ij 1 = E ⎛ 3h j ⎞ ⎛ h 3j ⎞ ⎜⎝ A ⎟⎠ + ⎜⎝ 3I ⎟⎠ i i

ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES

(Eq. 4-45)

= the stiffness of wall i at level j = height of level j above the base at wall i = the effective shear area of wall i = the moment of inertia of wall i about the axis perpendicular to the strong direction of the wall

An equivalent moment of inertia Ieq can be derived for simplifying the calculation of wall rigidity. Ieq is an approximation of the moment of inertia that would result in a flexural deflection equal to the combined flexural and shear deflections of the wall. Design Aid 4.11.26 compares the deflections and Ieq for several load and restraint conditions, assuming the shear modulus, G = 0.4E. Eq. 4-45 is a combined equation for the first case in Design Aid 4.11.26. The shear resisting area of the walls is not necessarily the total area of the walls. Just as only the web of a flanged beam really resists shear, wall groups perpendicular to the direction of load, or flange walls in wall groups, will not contribute to shear stiffness, and their areas should be discounted. The configuration and assembly of walls or wall groups may, however, have an effect on the bending stiffness and the effective moment of inertia. It has been common practice to make calculations using the assumption that a wall or connected group acts as a combined unit as long as the connections in vertical joints between wall elements develop the required capacity to resist overturning or the VQ/I shear force. Codes now prescribe the evaluation of lateral drift using the deflection amplification factor Cd (Design Aid 4.11.8) to determine P-∆ effects and for comparison with maximum limits. Therefore, there is a need to make a more accurate evaluation of the stiffness properties. For precast concrete shear walls that are stacked and connected across horizontal joints, the use of gross section to determine the moment of inertia is sufficiently accurate for determination of relative stiffness. There is, however, some question about the post-yield behavior at these joints, which suggests that the displacement amplification factor Cd should be increased to more accurately reflect the reduction in stiffness. Walls that are assembled with vertical joints, however, may behave differently. The use of ductile connections across vertical joints may have very beneficial effects as the location of clearly defined sites for inelastic behavior and energy dissipation without collateral damage to the major lateral-forceresisting system. Research into the characteristics of these connections is found in References 8 and 20. The effective deformation characteristics of walls connected in this manner will be different from those of a comparable monolithic wall. Reasonable assumptions based on connection detailing can be made to produce reliable results. Connections in vertical joints may be considered either ductile or strong. Ductile connections are detailed for ductility and are intended to yield during the design event. These connections need to 4–26

retain their load-carrying capacity at deformations consistent with the inelastic demand. They will provide the function of continuing to mobilize dead-load resistance for overturning even after yielding has occurred. When these connections are used in vertical joints, the wall stiffness can conservatively be modeled as if each vertical panel acts independently. After yield, each vertical panel has only its own section for resistance, as a limit. In some cases, it may be necessary or desirable to develop strong connections. These connections are proportioned to continue to carry loads elastically beyond yielding of the primary yield mechanism in the walls. The design forces for this type of connection would be based on VQ/I multiplied by the system overstrength factor sufficiently large to ensure that these connections remain elastic through the design event. This is only required when using special, reinforced shear walls. For this condition, the stiffness of the resulting wall is equivalent to that of a comparable monolithic wall (see Section 4.1.2). The type of connection, then, determines the design dimension of the wall that is modeled as a cantilever beam. The loads are applied level by level, and the effects of displacement from both shear and flexure are accumulated by superposition. Thus, story drift and total lateral displacement are derived. By accumulating the forces, the shear at each level and the overturning moments are calculated. It is possible to use the selection of jointing and connection details to define the post-yield stiffnesses of groups of walls. With this technique, walls can be detailed to accept the loads for which they can develop overturning resistance or shed loads for which such capacity cannot be mobilized. In this way, the designer of precast concrete wall systems can favorably modify the stiffness through detailing. 4.5.7

Distribution of Lateral Loads

Lateral loads are distributed to each shear wall in proportion to its rigidity, if the diaphragm is rigid. A building is typically designed for lateral loads separately in two orthogonal directions. When the shear walls are symmetrical with respect to the center of load application, the force resisted by any shear wall is:

Fi = (ki/Σr)Vx

(Eq. 4-46)

where: Fi = force resisted by an individual shear wall i ki = rigidity of wall i Σr = sum of rigidities of all shear walls Vx = total lateral load The analysis of structures that have shear walls placed asymmetrically with respect to the center of the lateral load must consider the torsional effect in the analysis. Typical examples are shown in Fig. 4.5.1. An approximate method of analysis based on a polar moment of stiffness is simple and direct: Force in the Y direction is distributed to a given wall at a given level due to an applied force in the Y direction at that level:

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EXAMPLE 4.5.7.1 Design of Unsymmetrical Shear Walls

  4

Given: The structure shown below. All walls are 8 ft high and 8 in. thick.

Center of lateral load

Center of rigidity eccentricity

kip/ft Problem: For the load shown in the Y direction, determine the shear in each wall, assuming the floors and roof are rigid diaphragms. Walls D and E are not connected to wall B. _________________________________________________________________________________ Solution: Maximum height-to-length ratio of north-south walls = 8/30 < 0.3. Thus, for distribution of the direct wind shear, neglect flexural stiffness. Since walls are the same thickness and material, distribute in proportion to length. Total lateral load, Vy = 0.20 × 200 = 40 kip Determine center of rigidity: X =

40 ( 75 ) + 30 (140 ) + 40 (180 ) = 130.9 ft from left 40 + 30 + 40

Y = c enter of building, since walls D and E are placed symmetrically about the center of the building in the north-south direction. Torsional moment, MT = 40(30.9) = 1236 kip-ft Section 12.8.4.2 of ASCE 7-05 requires that for diaphragms that are not flexible (therefore rigid), an accidental torsion be added to this. The eccentricity to be used for the accidental torsion is 5% of the building dimension perpendicular to the direction of the applied forces. Then: Accidental eccentricity = (0.05)(200) = 10 ft MT accidental = (10)(40) = 400 kip-ft MT total = 1236 + 400 = 1636 kip-ft

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EXAMPLE 4.5.7.1 Design of Unsymmetrical Shear Walls (cont.) Determine the polar moment of stiffness of the shear wall group about the center of rigidity: Since the height-to-length ratios for the east-west walls are greater than 0.3, the polar moment of inertia should more correctly consider the flexural stiffness of the east-west walls. This is negligible in this example and has been omitted. Ip = Ixx + Iyy Ixx = Σly 2 of east-west walls = 2(15)(15)2 = 6750 ft3 Iyy = Σlx 2 of north-south walls = 40(130.9 – 75)2 + 30(140 – 130.9)2 + 40(180 – 130.9)2 = 223,909 ft3 Ip = 6750 + 223,909 = 230,659 ft3 Shear in north-south walls =

Vy  M T x  + ∑ lp

Wall A =

40 ( 40 ) 1636 (130.9 − 75 ) ( 40 ) = 14.5 + 15.9 = 30.4 kip + 110 230,659

Wall B =

40 ( 30 ) 1636 (130.9 − 140 ) ( 30 ) = 10.9 – 1.9 + 110 230,659

Wall C =

40 ( 40 ) 1636 (130.9 − 180 ) ( 40 ) = 14.5 – 13.9 = 0.6 kip + 110 230,659

Shear in east-west walls =



Fy =

MT y  1636 (15 ) (15 ) = 1.21 kip = lp 230,659

Vy K y exVy ( x ) K y + ∑ K y ∑ K y ( x 2 ) + ∑ K x ( y2 )

(Eq. 4-47)

Force in the X direction is distributed to a given wall at a given level due to an applied force in the Y direction at that level:

Fx =

where: Vy Kx, Ky

exVy ( y ) K x ∑ K y ( x 2 ) + ∑ K x ( y2 )

(Eq. 4-48)

= lateral force at the level being considered = rigidity in the X and Y directions, respectively, of the wall under consideration ΣKx, ΣKy = summation of rigidities of all walls at the level in the X and Y directions, respectively x = distance of the wall from the center of stiffness in the X direction y = distance of the wall from the center of stiffness in the Y direction ex = distance between the cen­ter of the load in the Y direction and the center of stiffness measured in the X direction

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= 9.0 kip

For most single-story buildings subjected to wind loads, a simplified, approximate analysis is commonly used to determine torsion in asym­metrically located shear walls. This type of analysis assumes a unit thickness for all shear walls, as described in Example 4.5.7.1. 4.5.8

Coupled Shear Walls

Two individual shear walls separated by large openings may be connected with structural components that can resist axial and/or flexural loads. The combined stiffness of the two coupled shear walls is greater than the sum of their uncoupled stiffnesses. Coupling shear walls can reduce the lateral deflection (drift) in a building and reduce the magnitude of the moments for which a shear wall must be designed. Figure 4.5.4 shows two examples of coupled shear walls. The effect of coupling is to increase the stiffness by transfer of shear and moment through the coupling beam. The wall curvatures are altered from that of a cantilever because of the frame action that is developed. Figure 4.5.5 shows how the deflected shapes differ in response to lateral loads. Several approaches may be used to analyze the response of coupled shear walls. A simple approach is to ignore the coupling effect by considering the walls as independent cantilevers. This method results in a conservative wall design.

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Coupling beam

Fig. 4.5.4 Coupled shear walls.

However, if the coupling beams are rigidly connected, significant shears and moments will occur in the beams that are difficult to economically resist. To avoid this situation, the beam-to-panel connection can be detailed for little or no rigidity, or the beam can be designed to resist the actual shears and moments. Finite element analysis may be used to determine the distribution of shears and moments within a coupled shear wall. The accuracy of such an analysis is a function of the finite element size used. This method may be suitable for coupled walls or walls with large openings. A plane-frame computer analysis will provide sufficiently accurate results for the great majority of structures. In modeling the coupled shear wall as a frame, the component dimensions must be considered, as a centerline basic analysis may yield inaccurate results. A suggested model is shown in Fig. 4.5.6(a). Either a finite element or frame analysis may be used to determine the deflection of a coupled shear wall and, therefore, its equivalent moment of inertia. This may then be used to determine the distribution of shears in a building that contains both solid and coupled shear walls. Some frame-analysis programs do not calculate shear deformations; if significant, shear deformations may have to be calculated separately. 4.5.9

Shear Walls with Large Openings

As with coupled shear walls, the deflections yielded by computer analysis may be used to determine equivalent stiffness for determining lateral-load distribution. In very tall structures, vertical shear and axial deformations influence the rigidity of panels with large openings, so a more rigorous analysis may be required. 4.5.10

Evaluation of Shear-Wall Systems

Fig. 4.5.5 Response to lateral loads.

1. Resistance to overturning Motr is compared with the overturning moment at the wall base by using Eq. 4-33 for wind loading and Eq. 4-34 for earthquake loads. If the resistance to overturning is exceeded by the overturning moment, it is usually possible to provide a positive hold-down from the wall to the foundation (that is, vertical tie bars, post-tensioning, and the like). The foundation size may need to be increased, or, in some cases, tension piles, ground anchors, or other positive methods of resisting the overturning may need to be used. While the connections in vertical joints may reduce stiffness, they still may be adequate to mobilize overturning resistance. If none of these solutions work, additional shear walls or extension of existing walls may be necessary. 2. The anchorage of the wall to the foundation also includes the transfer of shear. The principles of shearfriction may be applied (see Section 5.3.6). Although one side of the wall may have an opened joint due to flexure, with the anchorage acting in tension, there will be a region of compression that results from the combination of flexure and axial load on the wall. This compression force contributes to the shear transfer if it is a sustained load. Additional connections or mechanically spliced reinforcing bars may be required at the wall/foundation joint to provide additional shear capacity. 3. In addition to the limitations on drift in earthquakes, the walls must be designed for the P-∆ effects caused by the shifting of the point of application of gravity loads in some cases. If the stability coefficient θ exceeds 0.10, P-∆ effects must be considered. This is discussed in Section 4.2.4.4.

Once the forces on the shear walls have been determined, the walls and the structural system must be evaluated. The following are the design con­siderations.

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4. The drift used to evaluate the P-∆ effects is the drift from linear-elastic analysis drift, based on the strength design loads, multiplied by Cd (Design Aid 4.11.8). The drift determined with shear-wall systems is usu4–29

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CHAPTER 4

ally much less than that requiring P-∆ consideration, but it must be checked.

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Coupled walls

Frame model

(a) Model for coupled shear walls

4.5.11

Example: One-Story Building

By taking advantage of walls already present, onestory buildings usually can be designed to resist lateral loads (wind or earthquake) by shear wall and diaphragm action. If this is feasible, it is generally the most economical solution. Example 4.5.11.1 illustrates the procedures. Because all loads must funnel through the connections, gravity and lateral loads must be considered together. Thus, this example shows both gravity and lateral-load connections. The example emphasizes the concepts of free-body diagrams and load paths. This example illustrates one option for shear-wall connections. Equilibrium is attained by balancing uplift tension in one panel with the matching compression couple force in an adjacent panel through simple (and ductile) shear connections across the vertical joints. In this system, tie-down connections may be required. Analysis of a rigidly connected panel group is dependent on a number of factors. Connection stiffness determines whether the group will act monolithically or act as a series of single shear walls. The aspect ratio of the rigidly connected group will affect the stress distribution at the base. While a panel group with a high height-to-length ratio may nearly act as a cantilever beam, a group with a medium-to-low ratio of height to length will act as a deep beam and exhibit nonlinear stress distributions. Determination of tie-down forces, vertical joint forces, and base shear distribution will be a function of the aspect ratio. The shear and flexural stiffness of the individual panels will have a similar effect on force distribution.

Continuous frame

Stacked panels (b) Models for shear walls

Fig. 4.5.6 Computer models – shear walls.

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EXAMPLE 4.5.11.1 Typical Single-Story Industrial Building

VL

Double-tee spans

Problem:  esign components and connections for critical latD eral load. _________________________________________ Solution: 1. Using the simplified procedure of Section 4.2.3.1 for wind design, determine from Design Aids 4.11.6 and 4.11.1: λ = 1.0 Zone A ps30 = 22.8 lb/ft2 Zone C ps30 = 15.1 lb/ft2 Ι = 1.0 KZ = 1.0 (see Example 4.2.3.1) Mean roof height = 19.0 ft

T T 10 ft double-tee roof units

VR

Centerline beam C

C

b = 120'

Given: The single-story manufacturing building shown. The basic wind speed (Design Aid 4.11.5) is 120 mph, exposure B. From seismic maps, Ss = 0.30 and S1 = 0.08, site class D. 10-ft-wide doubletees are used on the roof, weighing 47 lb/ft2. Wall units are 10-ft-wide sandwich panels with a 4-in.thick interior wythe, 2 in. insulation, and a 2-in.thick exterior wythe, weighing an average of 75 lb/ft2. A dead load of 10 lb/ft2 is superimposed on the roof. Soil weight is taken as 100 lb/ft3.

  4

10-ft-wide wall panels

 = 160'

F Plan

Top of parapet

Top of roof Grade Bottom of footing

Elevation

Zone A width = lesser of 0.2(120) = 24 ft or 0.8(19.0) = 15.2 ft. Use 15.2 ft. Zone C width = 160 – 15.2 = 144.8 ft ps(A) = λKZTIps30 = 1.0(1.0)(1.0)(22.8) = 22.8 lb/ft2 ps(C) = 1.0(1.0)(1.0)(15.1) = 15.1 lb/ft2 Wind force to roof: = [15.2(22.8) + 144.8(15.1)](19/2 + 2.5)/1000 = 30.4 kip 2. Determine earthquake force: interpolating from Design Aid 4.11.7, Fa = 1.60, Fv = 2.4. SMS SM1 SDS SD1



= FaSs = 1.6(0.30) = 0.48 = FvS1 = 2.4(0.08) = 0.192 = 2/3(SMS) = 2(0.48)/3 = 0.320 = 2/3(SM1) = 2(0.192)/3 = 0.128

From Table 4.2.1: Seismic design category B Period, Ta = CT(hn)3/4 = 0.020(21.0)3/4 = 0.196 sec From Design Aid 4.11.1, Ι = 1.0 From Design Aid 4.11.8, for a bearing-wall system with ordinary precast concrete shear walls: R = 3 From Eq. 4-18: 2'–2"

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EXAMPLE 4.5.11.1 Typical Single-Story Industrial Building (cont.) Cs =

0.320 SDS = = 0.107 R / Ι 3 / 1.0

From Eq. 4-19: Cs =

0.128 SD1 = = 0.218 R / Ι T 3 / 1.0 ( ) ( ) 0.196

From Eq. 4-21: Minimum  Cs = 0.044 SDSΙ = 0.044(0.320)(1.0) = 0.014 > 0.01 Therefore, minimum  Cs = 0.014 < 0.107.  Use Cs = 0.107 Building weight: Walls = 75(23.5)[2(160) + 2(120)]/1000 = 987 kip (50% goes directly into foundation) Roof = 120(160)(47 + 10)/1000 = 1094 kip Beams and columns (estimated load contribution to roof) = 150 kip  SCE 7-05 Section 12.7.2 requires that 20% of snow load be considered if the snow load is greater A than 30 lb/ft The snow load for this example is considered to be less than 30 lb/ft. W=

987 ++1094 + 150 1094 + 150 = 1738 kip 2

Base shear V = CsW = 0.107(1738) = 186.0 kip 3. In a single-story building, the total base shear acts through the roof diaphragm. For a single-span diaphragm such as this, design is straightforward. For buildings with interior shear walls, it is more complex (see Section 4.8). For seismic forces, note the requirements for torsion analysis in Section 4.2.4.3. (No such requirement exists for wind load.) Assuming no substantial door openings in either shear wall, the center of mass is the center of the building. However, the 5% accidental torsion must be considered.  ccidental torsion = 0.05(160) = 8.0 ft. Thus, assume the center of mass is 88 ft from the left wall and A 72 ft from the right wall.

VR

=

186.0 (88 ) = 102.3 160

 s can be seen in Section 4.2.6, seismic forces thus calculated are factored (load factor = 1.0 for this A seismic category), while a load factor of 1.6 is applied to the wind forces. The wind force is distributed equally to each shear wall: 1.6(30.4/2) = 24.3 kip 102.3 > 24.3 kip, seismic loading is critical.  or the seismic diaphragm design (chord steel and shear connectors between roof tees) for this singleF story building, use Fpx calculated by Eq. 4-60 or the total base shear, whichever is greater: (Note that in the case of a single-story structure, Eq. 4-60 will always yield the total base shear.) Check minimum Fp: Fp = 0.2ΙESDSWP = 0.2(1.0)(0.32)(1738) = 111.2 kip < 186.0 kip (governs)

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EXAMPLE 4.5.11.1 Typical Single-Story Industrial Building (cont.) 4.

  4

Check sliding resistance of the foundation: Dead load on the footing: Wall = 75(23.5)(120) = 211,500 lb 12 in. × 18 in. footing = 1(1.5)(150)(120) = 27,000 lb Assume 2 ft backfill = 100(1.5)(120)(2) = 36,000 lb

Total = 274,500 lb

Assume coefficient of friction against granular soil, µs = 0.5 Sliding resistance = µsN = 0.5(274.5) = 137.2 kip > 102.3 (Note: This analysis is a close approximation. More detailed analysis may be required.)

OK

From Eq. 4-34a: U = (0.9 – 0.2SDS)D – ρQE = [0.9 – 0.2(0.32)]137.2 – 1.0(102.3) = 12.4 > 0

OK

Determine the reinforcement and connection requirements for the diaphragm. a.

Connections from the roof to the walls:  connection similar to that shown in Example 6.13.3 may be used. A That connection has a maximum capacity of VR 102.3 = = 7.7 13.2 kip. On east and west walls, connections required = conn. cap. 13.2 Use maximum spacing of about 10 ft. Approximately ten connections required per side. Use two connections per panel and check that structural integrity requirements are satisfied.

Wall panel T

T

Tension connection T

Roof plan

Wall elevation

T

Tension connection

Alternative placement of chord reinforcement

b.

Shear connections between double-tees: The maximum shear is at first joint (10 ft) from left wall. The left wall is 88 ft from the center of force. Assuming a uniformly distributed lateral force: Shear =

(88 − 10 ) 88

(102.3 )

= 90.7 kip

A connection similar to one of those shown in Fig. 4.8.2 may be used. Note: Most engineers and precasters prefer a maximum connection spacing of about 8 to 15 ft for roof connections. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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EXAMPLE 4.5.11.1 Typical Single-Story Industrial Building (cont.)

Plates Chord steel

Bearing pads Inverted-tee beam

Corbel Section at wall

Section at ledger beam

Structural integrity ties

c. To determine chord reinforcement, the seismic force is assumed to be distributed uniformly across the building width b: Diaphragm moment:

F  186.0 (160 ) = = 3720 kip-ft 8 8 Chord force (see plan): Assume chord reinforcement is located 1 ft in from outside of wall. Since these are seismic forces, they can be considered factored: Tu = Cu =

M 3720 = = 31.5 kip b − 2 120 − 2

 ssume bars will be spliced by welded connections and recommendations of NEHRP 2000 will be folA lowed; φ = 0.7 (Section 4.2.6.1): As =

31.5 Tu = = 0.75 in.2 φfy 0.7 (60 )

 his amount of reinforcement should be placed at the perimeter. The chord force can be transmitted T between components by ties at the roof tees, wall panels, or a combination, as illustrated. These ties and transmission of forces will usually provide the tie requirements for structural integrity outlined in Section 4.3.

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EXAMPLE 4.5.11.1 Typical Single-Story Industrial Building (cont.)

  4

Vi

D

T

d.

D

C

T

C

Wall panel connections:  his shear wall may be designed to act as a series of independent units, without ties between the panT els. The shear force is assumed to be distributed equally among the wall panels (see figure). n = 120/10 = 12 panels V = VR /n = 102.3/12 = 8.53 kip/panel D = 75(10)(23.5)/1000 = 17.62 kip  ote that the engineer responsible for the foundation design must confirm that it is designed to be N compatible with the wall behavior. From Eq. 4-34a, D is multiplied by: (0.9 – 0.2SDS) = [0.9 – 0.2(0.320)] = 0.836 D = 0.836 (17.62) = 14.73 kip Design base connection for 1.0E – (0.9 – 0.2SDS)D T u =

8.53 ( 21) − 14.73 ( 4 ) = 15.0 kip 8

As an alternative, the shear walls may be designed with two or more panels connected together. The following figure illustrates an analysis where tension and compression counteract one another with simple shear connections across the vertical joints. For simplicity, it is assumed that the walls have no openings. Thus, there are interior and exterior (corner) wall panels. Connections are made across the vertical panel joints to take advantage of the fact that compensating forces are generated in the panels. Note: Determining connection forces requires solving classic equations of equilibrium. This will be done using factored loads that assume connection tension. Compression forces are assumed to be no problem, as the joint between the wall panel and the foundations is normally grouted. Considering an interior panel: ΣM about C = 0: V(h) = V1(b – a) + D(b/2 – a) + V1a V1 =

V (h ) D (b / 2 a ) b

ΣV = 0:

C=D

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EXAMPLE 4.5.11.1 Typical Single-Story Industrial Building (cont.) Since this force system can exist for all interior panels, edge shears will balance to zero when all panels have the same dimensions and weight. The only requirement for the connections is a transfer of vertical shear. Therefore, connections that permit horizontal deformations can be used if volume-change restraint is of concern. At the exterior panels, the edge shear V1 from an exterior panel will be applied at one edge only. Because tension and compression base connections are not located at the panel edges, equilibrium may have to be satisfied with tension and compression connections to the foundation or connections to the orthogonal panel that will allow the non-shear wall to contribute additional dead load at the corner. At the tension-side of the exterior panel, equilibrium can be determined by summing moments about the compression force, assuming the tension is taken by a tie-down into the foundation:

b V

V

V

D

D

D V1

V1

h V1

V d

V1

V a C

C

(a) Exterior tension side

(b) Interior

T

V d

a T

a C

(c) Exterior compression side

For this example, locate the foundation connections 1 ft from each side. The pertinent dimensions are: h = 21 ft; b = 10 ft; a = 1 ft; d = 8 ft V = 8.53 kip, D = 14.73 kip Using Eq. 4-34: Vu = 1.0(8.53) = 8.53 kip Factored dead load = 14.73 kip (see p. 4-35) For interior panels with factored loads (Fig. b): V1 =

8.53( 21) 14.73 (5 1) = 12.02 kip 10

C = D For the tension-side of the exterior panel (Fig. a): Tu =

8.53 ( 21) − 14.73( 5 − 1) − 12.02 (1) 8

= 13.52 kip

Cu = Tu + Du + V1 = 13.52 – 14.73 – 12.02

= 16.23 kip

For the compression side exterior panel: Tu =

8.53 ( 21) 14.73 (5 1) 12.02 (10 1) = 1.50 kip 8

Cu = Tu + Du + V1 = 1.50 + 14.73 + 12.02 = 28.25 kip

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 xample: Three-Level Parking E Structure

Over the years, precast concrete parking structures have proven to be a reliable, economical means of providing attractive and secure parking for the public. Since prestressed concrete is capable of long spans, which accommodate ease of traffic circulation, the number of columns is minimized.

CHAPTER 4

The resulting openness requires the designer to consider the lateral load resisting system early on in the planning of the structure. This example shows that a sufficient number of walls can be provided without intruding on the parking and driving space, while allowing adequate security. It should be noted that the structural concept illustrated in this example is also applicable for other structures such as office buildings.

EXAMPLE 4.5.12.1 Three-Level Parking Structure Given:  he three-level parking structure shown. The basic wind speed is given as 110 mph, exposure B. T Seismic criteria are given as: Ss = 0.3, S1 = 0.15. A soil report indicates site class C. Concrete is normalweight with fc' = 5000 psi. Problem: Determine the feasibility of a shear-wall structure in this location.

bays at

N

Elevator

typical

typical

Shear walls

Ramp down

bays at

Ramp up

Stair well

at

levels

Plan

Elevation

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EXAMPLE 4.5.12.1 Three-Level Parking Structure (cont.) Solution: Since the structure must resist moderate seismic forces and hurricane force winds as well as the gravity loads, the magnitude of the forces must first be determined to see which combinations of loads will control the design. By arranging support components to resist both vertical and lateral loads, the goal of maintaining an open structure will be achieved.  or gravity loads, 26-in.-deep, 10-ft-wide pretopped double-tees at 72 lb/ft2 will be used. The total weight of F double-tees, beams, columns, and curbs will be taken as 110 lb/ft2. The code-specified live load is 40 lb/ft2. It is determined that for this magnitude of loading, 30 ft bays with 24 in. square columns, and a 36IT36 girder in the end bays, will support vertical loads. For lateral loads, a check is made to determine whether seismic or wind load will govern the design. Wind analysis: The building height is 3(10.5) + 3.5 = 35 ft. Since it is less than 60 ft high, the ASCE 7-05 Method 1 of Section 6.4 may be used. For a north-south wind: From Eq. 4-5: ps = λKZTΙps30 Zone A width is the lesser of 0.2(180) = 36 ft or 0.8(31.5) = 25.2 ft Zone A width = 25.2 ft Zone C width = 264 – 25.2 = 238.8 ft From Design Aid 4.11.6: Table (c): Interpolate for λ = 1.015 Table (a): ps30 (zone A) = 19.2 lb/ft2 ps30 (zone C) = 12.7 lb/ft2 KZT = 1.0 based on ASCE 7-05 Section 6.5.7.2 From Design Aid 4.11.1: I = 1.0 ps (A) = 1.015(1.0)(1.0)(19.2) = 19.5 lb/ft2 ps (C) = 1.015(1.0)(1.0)(12.7) = 12.9 lb/ft2 (combined windward and leeward pressures) Fw

= [19.5(25.2) + 12.9(238.8)]35/1000 = 125 kip

Factored wind load = 125(1.6) = 200 kip Seismic analysis: Determine Fa and Fv by interpolating from Design Aid 4.11.7(b) and (c). For Ss = 0.3, S1 = 0.15, site class C: F a

= 1.2, Fv

= 1.65

From Eq. 4-7: SMS = FaSs

= 1.2(0.3)

= 0.36

From Eq. 4-8: SM1 = FvS1

= 1.65(0.15) = 0.25

From Eq. 4-9: SDS = (2/3)SMS = (2/3)(0.36) = 0.24

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EXAMPLE 4.5.12.1 Three-Level Parking Structure (cont.)

  4

From Eq. 4-10: SD1

= (2/3)SM1 = (2/3)(0.25) = 0.17

From Table 4.2.1 for occupancy category II, seismic design category is C: From Eq. 4-12, determine the period: Since this is a shear wall building, CT = 0.02 Height to highest level = 3(10.5) = 31.5 ft Ta = CThnx = 0.02(31.5)0.75 = 0.27 sec From Design Aid 4.11.8: R = 4 or 5, depending on whether intermediate precast shear walls or special shear walls are used. For seismic design category C, ordinary precast concrete shear walls are not permitted, and at least intermediate walls must be used. At this point in the analysis, assume intermediate precast shear walls as part of the bearing-wall system. An economic analysis may be made later. For this example, assume R = 4. Use lesser of Eq. 4-17 or 4-18 for Cs: From Eq. 4-17: = CC s s =

0.24 SDS = = 0.06 = 0.06 R / Ι 4 / 1.0

From Eq. 4-18: = CCs s =

0.17 SDS = = = 0.16 0.16 (R / Ι )T ( 4 / 1.0 ) 0.27

From Eq. 4-21: Minimum = 0.044SDS(I) = 0.044(0.24)(1.0) = 0.0106 greater than 0.01 Use Cs = 0.06 Weight of all components

= 110 lb/ft2

Weight per level = 0.110(180)(264)

= 5227 kip

Total weight, W = 3(5227)

= 15,681 kip

Base shear, V = CsW = 0.06(15,681) = 941 kip Since this is much higher than the 200 kip wind load, seismic forces will control all of the design. Substantial shear-resisting components are required. Load-bearing shear walls are chosen, primarily because the vertical gravity load will help resist the overturning moments due to applied lateral loads. It may be more economical to add two columns or pilasters to support the end bay inverted tee beams so that the higher R value = 5 for a building frame could be used. The walls could then be connected to the column to mobilize additional dead load. While the corner stairwells and elevator shafts could be used as part of the lateral-forceresisting-system, this may result in high forces due to restraint of volumetric deformations; consequently, it is decided that the corners will be isolated from the main structure. Alternatively, it might have been decided to use these corner components, and provide connections that are flexible in the direction of volumetric restraint. The torsion is assumed to all be taken by the walls parallel to the direction of the lateral force being considered. The distribution of seismic shears to each level using Eq. 4-22 and 4-23 is shown in the following table.

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EXAMPLE 4.5.12.1 Three-Level Parking Structure (cont.) Lateral force distribution through levels (1) Level

(2) x

(3) hx, ft

(4) wx, kip

(5) (3) × (4) wxhx, kip-ft

(6) (5)/Total (5) cvx

(7) (6) × Vbase Fx, kip

3

3

31.5

5,227

164,650

0.500

471

2

2

21.0

5,227

109,767

0.333

313

1

1

10.5

5,227

54,883

0.167

157

15,681

329,300

Totals

941

For the north-south load-resisting system, try two 8-in.-thick, load-bearing shear walls located at each end of the ramp. These walls support the 36IT36 girder, and may be as long as 30 ft without interfering with the traffic flow; a 20 ft length is used as a first iteration. The figure below illustrates the arrangement and loading. The shear walls are located 90 ft from the center in the east-west direction of the structure, which is the center of the lateral-force-resisting system. However, accidental torsion must be considered (Section 4.2.4.3). The accidental eccentricity = 0.05(264) = 13.2 ft. Summing moments about the shear walls on one side, the force resisted by each pair of shear walls is:

F2w =

941(180 / 2 + 13.2) = 540 kip or 270 kip to each wall (note that 180 ft is the distance between shear 180 walls, not the short dimension of the strucPanels above ture)

The force at each level on the wall can be determined by the values of column 6 in the table. Level 3 F1w Level 2 Level 1

= 0.50(270) = 0.333(270) = 0.167(270)

= 135 kip = 90 kip = 45 kip

kip-ft kip

Overturning moment on the wall: = 135(31.5) + 90(21) + 45(10.5) = 6615 kip-ft

kip

Dead load on each wall (includes all components):

a

= 3(42/2))(60)(0.110) = 416 kip

assumed

From Eq. 4-33a: Elevation

U = (0.9 – 0.2SDS)D + 1.0QE

= (0.9 - (0.2)(0.24)D + 1.0E



= 0.85D + 1.0E

TuT u ==

6615 − 0.85 ( 416 ) (10 ) = 171 kip 18

Note that a more accurate answer results if this dimension is between the tensile force and the center of the compression block. The difference is usually negligible. = AA s s =

171 Tu = = 3.17 in.2 φfy 0.9 ( 60 )

Use (4) #8, As = 3.16 in.2 4–40

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EXAMPLE 4.5.12.1 Three-Level Parking Structure (cont.) The (4) #8 will be centered 2 ft from each end of the wall. The force transfer between the precast concrete shear wall and the foundation can be accomplished by reinforcing bars with grouted sleeves, Type 2 mechanical couplers, or welding. Alternatively, post-tensioning bars could be chosen. The preliminary analysis is completed by examining the capacity of the foundation system to transfer this force to the supporting ground. That analysis is not shown here. For resistance in the east-west direction, 18 individual load-bearing walls located along the length on each side of the interior ramped bay will be used. These 8-in.-thick walls are spaced 10 ft on centers, supporting one 60-ft span double-tee on each side of the wall as shown. Each wall is 6 ft-6 in. wide to accommodate the 5 ft stem spacing of the double-tees, and to allow visibility between the wall units. As in the north-south direction, an accidental eccentricity of 5% must be considered: e

= 0.05(180) = 9 ft

  4

kip-ft

150 kip kip

assumed

Elevation

Total force in walls in one row: FF1ew = 1ew =

941( 60 / 2 + 9 ) = 612 kip, or 612/18 = 34 kip to each wall. The force on each wall: 60

Level 3 Fw = 0.50(34) = 17 kip Level 2 Fw = 0.333(34) = 11 kip Level 1 Fw = 0.167(34) = 6 kip Overturning moment on the wall: = 17(31.5) + 11(21) + 6(10.5) = 830 kip-ft Dead load on each wall = one wall + one tee at each level (three levels): 3[0.1(10.5)(6.5)+0.072(60)(10)] = 150 kip From Eq. 4-33a: U

 = (0.9 – 0.2SDS)D + 1.0(QE) = [0.9 – 0.2(0.24)]D + 1.0E = 0.85D + 1.0E

Tu Tu ==

830 − 0.85 (150 ) ( 3.25 ) = 75.6 kip 5.5

As As ==

Tu 75.6 = 1.40 in.2 = φfy 0.9 ( 60 )

Use (1) #11, centered at 12 in. from each end of wall. As = 1.56 in.2

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EXAMPLE 4.5.12.1 Three-Level Parking Structure (cont.) w3

Diaphragm analysis: The diaphragm is modeled for north-south seismic forces as shown. As discussed in Section 4.8.3.1, the diaphragm force is calculated by Eq. 4-60:

R2

∑F

60'

T3

R2

n

R2

C3

R2

i

i =x n

Fpx =

∑w

180'

w px

w2

w2

i

w1

i =x



 = 471(5227)/5227 = 471 kip Fp = 0.2IESDSwp + Vpx = 0.2(1.0)(0.24)(5227) + 0 = 251 kip, but not less than that shown in the table of lateral force distribution earlier in the example = 471 kip.

It is common practice to assume the forces are distributed uniformly. To simplify the calculation, the force is divided among the three bays, and the flat and ramp areas are analyzed separately. Total uniform load:

471 = 1.78 kip/ft 264

Uniform load on each bay = w1 = w3 =

T1 R1

C1 T1

T2 R1

C2

C2 180' R1

42'

1.784 = 0.59 kip/ft 3

R1

180'

42'

264'

Diaphragm analysis

In the flat area, half of the load of the center bay is assumed taken by each of the north and south bays. w2 = 0.59 + 0.59/2 = 0.89 kip/ft Because the overhanging cantilevers will reduce the stresses in the level area, positive moments are calculated for the ramp, and the results conservatively used for the flat area. Negative moments also calculated. Research19 indicates that in a three-bay structure such as this one, the tee-to-beam joints at the end bays at the four inverted tee beams are particularly vulnerable. The pour strips over these beams should have transverse reinforcement across the joints to improve strength and ductility. 2

2

+Mu =

w1 ( ) 0.59 (180 ) = = 2390 kip-ft 8 8

–Mu =

w 2 ( ) 0.89 ( 42 ) = –785 kip-ft = 2 2

Vu =

0.59 (180 ) = 53 kip 2

2

2

R2  = 53/2 = 27 kip

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EXAMPLE 4.5.12.1 Three-Level Parking Structure (cont.)

  4

Diaphragm moment design: Assuming a 58 ft moment arm: T3u = 2390/58 = 41 kip This tensile force may be resisted by reinforcing bars placed into field-applied concrete topping or curbs located at each end of the double-tees, or by reinforcing steel shop welded to plates cast in the edges of the double-tee flanges. These plates would be connected together in the field across the joint using splice plates and welds. Various suggestions for connections are provided in Chapter 6 of this handbook and in References 21 and 22. For reinforcing in the topping: From Section 4.2.6.1: φ = 0.9: As = T3u /φfy = 41/0.9(60) = 0.76 Use (2) #6, As = 0.88 in.2 For welded connection: From Section 4.2.6.1, φ = 0.7: AA = s s =

Flange of pretopped double-tee

41 T3u = 0.98 in.2 = φfy 0.7 ( 60 )

Use (2) #7, As = 1.2 in.2 Splice plate: Required Apl = 41/(0.7)(36) = 1.63 in.2 Use a plate 6 in. × 6 in. × 5/16 in. Provided Apl = 1.88 in.2

Flange of pretopped double-tee

The required length of a 3/16 in. E70 weld, from Design Aid 6.14.2: lw = 41/4.18 = 9.8 in. use

lw = 10 in.

The arrangement of reinforcement is as shown in the figure. Diaphragm shear design: For simplicity of calculation of the connection to the wall, the entire horizontal force, rather than only the collected portion of the demand, is multiplied by Ωo = 2.5 (see ASCE 7-05, Section 12.10.2). Vu to each wall = (2.5)(27) = 67.5 kip 10 ft of each wall is connected to a tee. Vu = 67.5/10 = 6.8 kip/ft If flange-to-wall connectors are provided 5 ft on centers, required φVn per connector = 6.8(5) = 34 kip. Example 6.13.3 illustrates a connector design. A heavier connector than shown there would be required to resist 34 kip. For the first interior tee-to-tee connection: Vu = 53 – 10(0.59) = 47.1 kip Vu = 47.1/60 = 0.79 kip/ft If flange connectors are provided 5 ft on centers, required φVn per connector = 0.79(5) = 4 kip. See Fig. 4.8.2 for typical flange connections.

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EXAMPLE 4.5.12.1 Three-Level Parking Structure (cont.) Collector element design: When the shear walls do not extend the entire length of the diaphragm, loads are transferred from the diaphragm to the walls through collector elements. For seismic design categories C, D, E, and F, ASCE 7-05 requires that these elements, their splices, and their connections to the resisting elements be designed using the load combinations, which include the overstrength factor for the system. The overstrength factor for shear walls Ωo is 21/2. The maximum total load to each wall at a level calculated previously was 135 kip. The shear walls at the ends of the ramp are connected to the diaphragm on two sides. The demand on the collector elements can be calculated from the diaphragm forces. The diaphragm is separated into independent segments by the center ramp, with each bay having a uniform load w1 of 0.59 kip/ft. The interior ramp bay transfers loads to walls on each side of the bay, but the north and south bays must connect to only half the shear wall. For the 180 ft diaphragm segment between the walls, the reaction at each end of each bay is: R1 = 0.59 kip/ft(180 ft)/2 = 53.1 kip The collector elements must be designed for 2.5 times this reaction, or 133 kip. The length of the shear wall is 20 ft, and with the thickness of the load-bearing wall on lines B and C , the tee-flange length in shear at the wall is approximately 8 ft. The shear strength of a 4 in. flange over this length is:

⎡ ⎛ 5000 ⎞ ⎤ φVn = φ 2 fc' bd = 0.75 ⎢2 ⎜ ⎟ ⎥ ( 4 ) ( 96 ) = 40.7 kip ⎢⎣ ⎝ 1000 ⎠ ⎦⎥

(

)

which is less than 133 kip, so reinforcement in the flange to drag the load to the wall is required. The area of tension reinforcement required at this location is 133 kip/(0.9 × 60 ksi) = 2.46 in2. This is equivalent to about six #6. The bars must extend to a length sufficient for the shear strength in the tee flange. To develop 133 kip in shear requires almost 27 ft of tee flange, and some bars must project for their development length beyond that distance. As the tension in the drag strut increases toward the connection area, staggered cut-off for the bars can be calculated. In addition to satisfying the shear capacity, tensile ties must also be provided using an overstrength factor of 2.5 from the shear wall/double-tee interface to the chord force at the other end of the double-tee. Connections of the diaphragm to the shear wall must also be designed for this force. If commercial slotted inserts with an ultimate shear strength φVn of 15 kip per connection are used, nine connectors would be required in this half of the wall on the inside face. Five connectors would be required on the ramp side of this wall face. On the other side of the shear wall, the uniform diaphragm load w2 = 0.89 kip/ft, and the reaction at the wall face is: R2 = 0.89(42) = 37.4 kip The collector element force is then 2.5 × 37.4 kip = 93.5 kip. The length of the connection area on this side of the wall is twice that of the interior side, so the shear strength of the flange at the interface is larger but still not sufficient for the elimination of drag struts. Note that ASCE 7-05 Section 12.11.2.2.1 requires that drag struts extend from chord to chord of the diaphragm. The required bar areas and lengths, however, will be less. For this side, the connection demand is also less, and the total number of connectors required (assuming 15 kip strength) is reduced to seven.

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EXAMPLE 4.5.12.1 Three-Level Parking Structure (cont.)

  4

bays at

N

Elevator

Drag strut reinforcing

typical

typical

Shear walls

Ramp down

bays at

Ramp up

Critical location at end of wall Stair well

Drag strut design: w1 = 0.59 kip/ft, w2 = 0.89 kip/ft Reaction R per north-south wall = 0.59(180/2) + 0.89(42) = 90.5 kip Tension T in drag strut = [(60-10)/60](90.5) = 75.4 kip at end of shear wall, which is the critical location Ωo = 2.5, therefore, design tension in drag strut = 2.5(75.4) = 188.5 kip As required = (188.5)/(0.9)(60) = 3.49 in.2 Reinforcement must extend from chord to chord; however, it may be reduced linearly as the demand force reduces toward the north side of the structure. Conclusion: The preliminary analysis indicates that the presumed sizes and arrangement of load-resisting elements are reasonable. Refinements as may be architecturally required are then made, and the final analysis performed. Note that drag struts are in both tension, as illustrated above, and in compression, which must also be designed.

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CHAPTER 4

4.6

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ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES

Moment-Resisting Building Frames

x2

Precast, prestressed concrete beams and deck components are usually most economical when they can be designed and connected into a structure as simple-span components. This is because: •

Positive moment-resisting capacity is much easier and less expensive to achieve with pretensioned components than negative moment capacity at supports.

•

Connections that achieve continuity at the supports are usually difficult to achieve.

•

The restraint to volume changes that occurs in rigid connections may cause cracking and unsatisfactory performance and must be considered carefully in design.

x1

Moment Resistance of Column Bases

Buildings without shear walls may depend on the fixity of the column base to resist lateral loads. The ability of a spread footing to resist moments caused by lateral loads is dependent on the rotational characteristics of the base. The total rotation of the column base is a function of rotation between the footing and soil, bending in the base plate, and elongation of the anchor bolts, as shown in Fig. 4.6.1. Additional information on this type of analysis, as well as its use with other types of foundations, is given in Reference 23. The total rotation of the base is:

φb = φf + φbp + φab

(Eq. 4-49)

If the axial load is large enough so that there is no tension in the anchor bolts, φbp and φab are zero, and:

4–46

φb = φf

(Eq. 4-50)

P

g h /2 of development length or depth to hook

1

Unrotated column base

Therefore, it is desirable to design precast/prestressed concrete structures with connections that allow lateral movement and rotation, and to design the structure to achieve lateral stability through the use of floor and roof diaphragms and shear walls. However, in some structures, adequate shear walls interfere with the function of the building or are more expensive than alternative solutions. In these cases, the lateral stability of the structure depends on the moment-resisting capacity of either the column bases, beam-to-column frames, or both. When moment connections between beams and columns are required to resist lateral loads, it is desirable to make the moment connection after most of the dead loads have been applied. This requires careful detailing, specification of the construction process, and inspection. If such details are possible, the moment connections need only resist the negative moments from live load, lateral loads, and volume changes, and will then be less costly. 4.6.1

e

e P

x1 + x2

Point of rotation

φbp φab

Center of compression

h + x1 h + 2x1

T

P+T φf

Rotated column base Fig. 4.6.1 Assumptions used in derivation of rotational coefficients for column bases.

Rotational characteristics can be expressed in terms of flexibility or stiffness coefficients:

φ = γM = M/K

(Eq. 4-51)

where: M = applied moment = Pe e = eccentricity of applied load P γ = flexibility coefficient 1 K = stiffness coefficient = γ If bending of the base plate and strain in the anchor bolts are assumed as shown in Fig. 4.6.1, the flexibility coefficients for the base can be derived, and the total rotation of the base becomes:

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ks value, psi/in

x1 = distance from face of column to the center of the anchor bolts, positive when anchor bolts are outside the column and negative when anchor bolts are inside the column x2 = distance from the face of column to base plate anchorage g = assumed length over which elongation of the anchor bolt takes place = one-half of development length plus projection for anchor bolts made from reinforcing bars, or the length to the hook plus projection for smooth anchor bolts (Fig. 4.6.1)

Note: It is recommended that the k value be confirmed by soil testing prior to final design.

Allowable soil-bearing value, lb/ft 2 Fig. 4.6.2 Approximate relation of allowable soil bearing value and coefficient of subgrade reaction ks.



φb = M(γf + γbp + γab) = Pe(γf + γbp + γab) (Eq. 4-52)



γγf f ==

1 k sI f

⎛ 2e ⎞ −1 ⎝ h + 2x1 ⎟⎠ 6eEsI bp ( h + x1 )

( x1 + x2 )3 ⎜



γbpbp ==



⎛ 2e ⎞ −1 g⎜ ⎝ h + 2x1 ⎟⎠ γ γ abab == 2eE s Ab ( h + x1 )

(Eq. 4-53)

(Eq. 4-54)

(Eq. 4-55)

where: γf = flexibility coefficient of footing/soil interaction γbp = flexibility coefficient of base plate γab = flexibility coefficient of anchor bolts ks = coefficient of subgrade reaction from soil testing or Fig. 4.6.2 If = moment of inertia of footing (plan dimensions) Es = modulus of elasticity of steel Ibp = moment of inertia of base plate (vertical crosssection dimensions) Ab = total area of anchor bolts in tension h = width of column in direction of bending

Rotation of the base may cause an additional eccentricity of the loads on the columns, causing moments that must be added to the moments induced by the lateral loads. Note that in Eq. 4-54 and 4-55, if the eccentricity e is less than h/2 + x1 (inside the center of compression), γbp and γab are less than zero, meaning that there is no rotation between the column and the footing, and only the rotation from soil deformation (Eq. 4-53) need be considered. Note that column base connections must also resist shear loads, which may require welded plate washers at the anchor bolts to account for oversized holes in the base plate. 4.6.2

 antilevered Column Systems for C Seismic Design

In Section 4.6.1, cantilevered column systems were recognized as one of the lateral-force-resisting systems used with precast concrete construction. ASCE 7-05 includes these systems in Table 12.2-1 in special-section G. Three concrete systems recognized in the table are ordinary, intermediate, and special, classifications that correspond to the frame definitions in ACI 318-05, which are discussed in Section 4.6.5. Section 12.2.5.2 of ASCE 7-05 imposed a restriction that the axial load on individual columns, calculated with the load combinations of Section 4.2.6 of this handbook, must not exceed 15% of the design strength of the column to resist only axial load. When cantilevered columns are used, the foundation is not subject to the reduction of foundation overturning of ASCE 7-05, Section 12.13.4, but is required to be designed with an overstrength factor of 1.25 applied to the load combinations. A cantilevered column system constructed as an ordinary moment frame is only permitted in seismic design categories A and B, in accordance with ASCE 7-05, and the height of such structures is limited to 35 ft. A response modification factor R of 1 is assigned. To be used in seismic design category C, the column detailing must conform to ACI 318-05 requirements for intermediate moment frames and an R factor of 1.5 is assigned. If the columns are designed and detailed according to the requirements for special moment frames, the cantilevered column system is permitted in seismic design category A, B, C, and D, but the 35 ft height restriction remains for all categories. This system is assigned an R factor of 2.5 and a deflection amplification factor of 2.5. These limitations and requirements for seismic design may significantly reduce the economy of these systems.

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EXAMPLE 4.6.1.1 Stability Analysis of an Unbraced Frame Given: The column shown (see next page). Soil-bearing capacity = 5000 lb/ft2 P = 80 kip dead load, 30 kip snow load W = 2 kip wind load Problem: Determine the column design loads and moments for stability as an unbraced frame. _________________________________________ Solution: ACI 318-05 requires that the column be designed for the following conditions (Section 4.2.6): Eq. 4-29: 1.2D + 1.6S Eq. 4-30: 1.2D + 1.6S + 0.8W Eq. 4-31: 1.2D + 1.6W + 0.5S Eq. 4-33: 0.9D + 1.6W The maximum eccentricity occurs when Eq. 4-33 is applied. Moment at base of column: M = 2(16) = 32 kip-ft = 384 kip-in. Pu = 0.9D = 0.9(80) = 72 kip Mu = 1.6W = 1.6(384) = 614 kip-in. Eccentricity due to wind load: e=

Mu 614 = = 8.53 in. Pu 72

To determine the moments caused by base rotation, an iterative procedure is required. Estimate eccentricity due to rotation = 0.30 in. e = 8.53 + 0.30 = 8.83 in. Check rotation between column and footing: h/2 + x1 = 20/2 + (–2) = 8 in. < 8.53 in. Thus, rotation between the column and footing must be checked: Eq. 4-54: Since x1 + x2 = (–2)+2 = 0; γbp = 0 Eq. 4-55: Assume g = 15 in. ⎛ 2 (8.83) ⎞ 15 ⎜ − 1⎟ 20 + 2 −2 ( ) ⎝ ⎠ γab = = 0.11(10 −9 ) 2 (8.83) (29 × 106 ) (2 × 0.79 ) ⎡⎣20 + ( −2 )⎤⎦

Eq. 4-53: 4

⎡6 (12 )⎤⎦ ==2.24 If = ⎣ 2.24(10 (1066) in.4 12

From Fig. 4.6.2: ks ≈ 200 psi/in. γf

=

1 = 2.23(10–9) 200 (2.24 × 106 )

Mu = 72(8.83) = 636 kip-in.

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EXAMPLE 4.6.1.1 Stability Analysis of an Unbraced Frame (cont.)

  4

φb = (γab + γf)Mu

= (0.11 + 2.23)(10−9)(636,000) = 0.00149 rad

Eccentricity caused by rotation: φbhs = 0.00149(16)(12) = 0.29 ≈ 0.30 in.

P

W

No further trial is required. Check Eq. 4-30: 1.2D = 1.2(80) = 96 kip 1.6S = 1.6(30) = 48 kip 0.8W = 0.8(384) = 307 kip-in. Eccentricity due to wind load:

M 307 e= u = = 2.13 in. Pu 144

(Column section properties assumed to extend to top of roof)

16'-0"

Estimate eccentricity due to rotation = 0.15 in. e = 2.13 + 0.15 = 2.28 in. Check rotation between column and footing:

h 20 + x1 = + ( −2 ) = 8 in. > 2.28 2 2 Thus, there is no movement between the column and footing.

1'-3"

Mu = 144(2.28) = 328 kip-in.

6'-0" square

φb = γfMu = 2.23(10−9)328,000

Elevation

= 0.00073 rad

Eccentricity caused by rotation: φbhs = 0.00073(16)(12) = 0.14 in. ≈ 0.15 in. No further trial is required. Check Eq. 4-31: 1.2D = 1.2(80) = 96 kip 0.5S = 0.5(30) = 15 kip 1.6W = 1.6(384) = 614 kip-in.

2" typical

DBA attached to baseplate 20" 1" diameter anchor bolts

Eccentricity due to wind load: e=

Mu 614 = = 5.53 in. Pu 111

20" Column and base plate Section A-A

Estimate eccentricity due to rotation = 0.30 in. e = 5.53 + 0.30 = 5.83 in. Check rotation between column and footing:

h 20 + x1 = + ( −2 ) = 8 in. > 5.53 in. 2 2

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CHAPTER 4

  4

EXAMPLE 4.6.1.1 Stability Analysis of an Unbraced Frame (cont.) Thus, there is no movement between the column and footing. Mu = 111(5.83) = 647 kip-in. φb = γfMu = 2.23(10−9)647,000 = 0.00144 rad Eccentricity caused by rotation: φbhs = 0.00144(16)(12) = 0.28 in. ≈ 0.30 in. No further trial is required Summary of column load cases: Eq. 4-29: 1.2D + 1.6S: Pu = 144 kip, Mu = 173 kip-in. (minimum by ASCE 7-05) Eq. 4-30: 1.2D + 1.6S + 0.8W: Pu = 144 kip, Mu = 328 kip-in. Eq. 4-31: 1.2D + 1.6W +0.5S: Pu = 111 kip, Mu = 647 kip-in. Eq. 4-33: 0.9D + 1.6W: Pu = 72 kip, Mu = 636 kip-in.

4.6.3

EXAMPLE 4.6.3.1 Degree of Fixity Determine the degree of fixity of the column base in Example 4.6.1.1

The degree of fixity of a column base is the ratio of the rotational stiffness of the base to the sum of the rotational stiffnesses of the column plus the base:

Fb =

For loads of Eq. 4-33:

Kc =



20 4 = 13,333 in.4 12 4 ⎡⎣ 4.3 (106 ) ⎤⎦ (13,333) 16 (12 )

= 11.94(108)

γb = γab + γf = 0.11(10-9) + 2.23 (10-9) = 2.34 (10-9) Kb =

1 1 = = 4.26(108) γ b 2.35 (10 −9 )

4.26 Fb = = 0.263 4.26 + 11.94 For other load combinations:

4–50

Kb Kb + Kc

(Eq. 4-56)

where: Fb = degree of base fixity, expressed as a decimal

Ec = 4300 ksi Ic =

Fixity of Column Bases

Kb =

1 = 4.48(108) 2.23 (10−9 )

Fb =

4.48 = 0.273 4.48 + 11.94

Kb =

1 γb

Kc =

4Ec lc hs

Ec = modulus of elasticity of the column concrete Ic = moment of inertia of the column hs = column height 4.6.4

Computer Models for Frame Analysis

When precast concrete frames are modeled as sticks, as is usually done with steel frames, the results are often very misleading. For example, the structure as modeled in Fig. 4.6.3(a) will indicate more flexibility than is actually true. Lateral drift will be overestimated, and the moments caused by axial shortening may be underestimated. Figure 4.6.3(b) shows a suggested model, which will better estimate the true condition. 4.6.4.1 Modeling Partially Fixed Bases Many computer programs permit the direct modeling of various degrees of base fixity by the use of spring options. A simple way to model base fixity is to incorporate an imagiFirst Printing/CD-ROM Edition

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Low Iz, Ay ; High Ax

  4

High Iz, Ax , Ay

h/2

h/2 Yb

h/2

h/2

Beam properties

Beam properties

Corbel properties

Column properties

Column properties

Base fixity (see section 4.6.2) Pinned

Fixed (b) Suggested model for lateral loads and volume-change resistant forces

(a) Modeling typically used for gravity loads

Fig. 4.6.3 Computer model.

nary column below the actual column base. If the bottom of the imaginary column is modeled as pinned, then the expression for its rotational stiffness is:

3EciI ci (Eq. 4-57) hci where the subscript ci denotes the properties of the imaginary column (Fig. 4.6.4), and Kci = Kb as calculated in Section 4.6.1, or the degree of base fixity Fb can be determined or estimated, and Kb calculated from Eq. 4-56. For the computer model, either Ici or hci may be varied for

K ci =

different values of Kci, with the other terms left constant for a given problem. It is usually preferable to use Eci = Ec. For the assumptions of Fig. 4.6.4:

Imaginary column

Fig. 4.6.4 Model for partially fixed column base.

3EciI ci K ci

(Eq. 4-58)

l ci =

K ci hci 3Eci

(Eq. 4-59)

or

4.6.5

Actual column

hci =

 lassifications for Seismic C Considerations

The evaluation of equivalent lateral forces for design for earthquake effects was reviewed in Section 4.2.4. The various reductions in equivalent lateral force from the full elastic response of a structure to seismic ground motion, Eq. 4-7 to 4-15, reflect strength, ductility, toughness, redun­dancy, and resonance. The implicit assumption of the code is that structures subject to higher levels of seismic risk should be designed to experience higher degrees of inelastic deformations without collapse. This is reflected by prescriptive require­ments for detailing that become more stringent with higher seismic levels. These requirements are con­sistent with increases in the response modification factors that per-

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mit proportionally lower base shear relative to the ground acceleration. The prescriptive detailing requirements are associated with seismic design categories deter­mined in the model building codes from a combination of short periods and one-secondperiod spectral acceleration and the soil conditions at the site. The lowest seismic design categories are A and B. Concrete frame structures assigned to these categories are permitted to use ordinary moment frames. These are defined as cast-inplace or precast concrete frames meeting the requirements of Chapters 1 through 18 of ACI 318, and include only limited prescriptive requirements for seismic detailing requiring continuous top and bottom reinforcement. This requirement can be met by welding connection plates that splice the continuous bars. To reflect the low ductility and potential for unfavorable failure mechanisms, ordinary concrete moment frames are assigned a low response modification factor R = 3 (Design Aid 4.11.8), resulting in a favorable design. The model codes do not permit ordinary moment frames to be used in seismic design category C structures. They require that concrete frames be at least intermediate moment frames. ACI 318-05 defines an intermediate moment frame as a castin-place frame meeting limited detailing requirements specified in Section 21.12. The rules for intermediate moment frames are intended to develop designs where the post-elastic behavior may result in significant damage, but that would avoid general collapse. The high seismic design categories are D, E, and F. Structures in these categories are not permitted to use ordinary or intermediate moment frames, but must use special moment frames. A special moment frame of precast concrete must comply with ACI 318-05, Sections 21.2 through 21.6. The provisions for the design and detailing of these frames aim to produce structures with strong column–weak beam behavior. Yielding will be concentrated in the beam at the negative moment region of the beam/column interface. The remaining frame elements will be detailed with sufficient flexural and shear strength to maintain capacity through the post-elastic displacement of the frame. These frames are assigned an R of 8. 4.6.6

 nalysis and Design – Ordinary A Moment Frames

When the engineer elects to use a frame and the seismic requirements permit an ordinary moment frame, it is usually economical to develop that frame through connections made within the gravity load system. In this way, the components that are ordinarily required are extended to provide lateral resistance without additional components. The beams used for interior framing may not be suitable since they are economically designed as prestressed with simple spans. Connecting these beams to induce negative moments at the columns is not favorable because these moments are additive to the effects of prestressing and put restraints on the components with the highest creep and shrinkage movements. Deep, precast concrete spandrel beams on the building perimeter are an attractive option. These beams are often deeper than required to provide support for the floor framing for architectural reasons. With this depth, they require only 4–52

EXAMPLE 4.6.4.1 Imaginary Column for Computer Model Given: The column base of Examples 4.6.1.1 and 4.6.3.1 Ec = 4300 ksi fc' = 5000 psi Problem:  etermine the length of an imaginary column to D model the fixity of the column. ___________________________________ Solution: Eci = Ec = 4.3(106) psi Ici = Ic = 13,333 in.4 Kci = Kb = 4.48(108) hci =

3E ci l ci 3 ⎡⎣ 4.3 (106 ) ⎤⎦ (13,333) = K ci 4.48 (108 )

= 384 in. = 32.0 ft

light prestressing. Connections can be made near the top and bottom of the beams with a larger tension/compression couple, which reduces the forces. A detailed design example for an office building using ordinary moment frames is included in PCI manual Seismic Design of Precast/Prestressed Concrete Structures.24 The design procedure for an ordinary moment-frame building will generally follow these steps: 1. Determine the gravity loads for the structure. After calculating uniform dead and live loads and line loads, calculate the gravity loads level by level for each column and wall. This can be facilitated using a spreadsheet set up to collect and accumulate the loads to the foundations. Since one primary use of the total load is for column and foundation design, live-load reductions should be calculated with multistory tributary areas. 2. Calculate the seismic coefficients using the procedures shown in Section 4.2.4. Precast concrete frame buildings often have calculated natural periods longer than the approximate period value and greater than the upper-limit period for strength design, so it may save some iterative effort to use the upper-limit period as an initial condition. 3. Calculate the lateral forces. For regions with low seismicity and high wind speeds, these forces might be governed by wind loads (Section 4.2.3). With the change to ASCE 7-05 load criteria and the larger mass

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ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES in concrete structures, seismic loads will likely govern even in regions of low risk. 4. Define the configuration and structural models of frames for analysis. 5. Calculate a horizontal distribution of the forces to each frame (Section 4.2.4.3) considering the actual center of mass and the required allowance for accidental torsion. 6. Perform the stiffness analysis for the frames. This is usually done using a computer program. Several commercial programs are commonly used by structural engineers. 7. Evaluate the frame displacements as discussed in Section 4.2.4.4. This may involve these steps: • •

•

• •

Check the building period using the elastic displacements. To reflect the post-elastic displacements, increase the elastic displacements by the Cd factor for the system. This value is 21/2 for ordinary moment frames. Check the interstory drift and verify that the results are within the limits prescribed by the code (2% for occupancy categories I and II buildings that fall under the category of “all other buildings”). Check for the potential of P-∆ effects by calculating the value of θ from Eq. 4-26. Evaluate component and connection forces for design feasibility.

If the analysis results are within code limits and acceptable component and connection capacities, proceed to the design of the components and connections. Otherwise, iterate on the structural model and repeat the analysis. 4.6.7

 pecial Moment Frames for Seismic S Design Category C

It is possible to emulate a monolithic, cast-in-place, intermediate moment-frame system with precast concrete components that meets all the requirements of ACI 318-05 Section 21.12, but the result would not be similar to the ordinary moment frame described previously. A precast concrete frame emulating a monolithic, cast-in-place frame will require special considerations for panelization, forming, transportation, and erection. With these measures already taken, it is not a significant step to improve the detailing of these components to achieve the emulation of special moment frames, and thereby achieving an R factor of 8 instead of 5. The reduction in base shear results in less demand for the special framing and may be the more economical alternative. Emulation of cast-in-place concrete is discussed in Section 4.1.1. The most economical framing for precast concrete construction is simple spans. When continuity is introduced into a precast concrete frame, it is important to retain as much

CHAPTER 4

simple-span framing as the system can tolerate, keep field connections easy and fast, and introduce those frames that are required, but no more. In regions of moderate seismic risk, look at options that develop special frames with the monolithic joints fabricated in the plant and field joints with details that meet ACI 318-05 Chapter 21 connection provisions. Use as few field connections as can be made consistent with limitations on shipping weights and sizes. An example showing the design of a special moment-resisting frame for seismic design category C is included in PCI’s Seismic Design of Precast/Prestressed Concrete Structures. When a special moment-resisting frame is used in low and moderate seismic-performance categories, the resulting design may be controlled by considerations of stability rather than strength. It is required to consider P-∆ effects when the stability coefficient θ is greater than 0.10. The coefficient is defined in Eq. 4-26. The maximum of this coefficient is set by Eq. 4-27. For a special moment frame with Cd = 5.5, the limit is:

θ=

0.5 0.5 = 0.091 when  = 1.0 = βCd 5.5

where:  = the ratio of actual shear strength to the shear strength at any given level required by analysis and must be equal to or greater than 1.0. Since the moment in the beams at the face of the column govern the shear strength at a level, this is effectively the excess moment strength provided in the beam at this joint. For special moment frames, then, the P-∆ effect limit for drift is greater than the system limit for drift unless additional strength is provided in the beam-column joint. The stability coefficient needs to be checked at each level. Evaluation of the stability coefficient and drift limits in low and moderate seismic design indicates that even when the drift is low, if the lateral forces determined from actual period calculations are very low in comparison with the gravity loads at a level, additional strength or stiffness will be required to protect the structure. This stiffness can be added by adjusting the columns, the beams, or both. The detailed design of components and connections is covered in Chapters 5 and 6, respectively. The design of the frame components of special moment frames requires detailing considerations that need to be applied to this system. Some of these requirements are: •

• • •

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The negative moments in the beams at the face of the columns are expected to be the trigger for the primary yield mechanism. The reinforcement is determined by the structural analysis. The reinforcement ratio in the flexural components may not exceed 0.025. At least two bars are required to be provided continuously top and bottom. The positive moment strength at the joint face must not be less than half the negative moment strength. 4–53

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CHAPTER 4 •

  4

Transverse reinforcement (stirrups and ties) is prescribed so that the inelastic regions are confined and shear strength is ensured. Column ties must be continued through the joint. The sum of the flexural strength of the columns above and below a joint must be 1.2 times the sum of the beam moment strength at the joint. Ties and stirrups must be detailed with 135 deg hooks. Jointed columns that are part of moment-resisting frames must be connected with mechanically spliced bars using Type 2 splices. These splices can be made with commercially available hardware that has been tested to demonstrate Type 2 capability. When additional continuity between beams must be developed, ACI 318-05 Section 21.6 addresses the requirements for connections in special precast concrete moment frames. This section has provisions for both ductile and strong connections.

• • •

•

4.6.8

 pecial Moment Frames for High S Seismic Design Categories

Precast concrete moment frames in seismic design categories D, E, and F are required to be special moment frames. With the increasing lateral forces from higher accelerations, larger portions of the precast concrete framing must be engaged than are needed in low and moderate seismic design categories. An example for the design of special momentresisting frames for seismic design category D is included in PCI’s Seismic Design of Precast/Prestressed Concrete Structures. Two alternatives might be considered: 1. The strength and stiffness of interior frames can be increased by engaging larger portions of the interior framing as part of the special moment-resisting frames. This might be accomplished by erecting several H frames that are panelized with overhanging beams projecting from both sides. Between these

frames, simple-span, inverted tee beams are erected for the immediate support of the floor. After the floors are set, connections are made at the ends of the dropin beams to create continuity in the overall frame for lateral loads. 2. Develop moment frames on both interior and exterior column lines across the structure. This alternative would place H frames along the outside column lines. The beams in these frames would be similar to the interior bays. The exterior spandrels would then be architectural precast concrete cladding that does not participate in the SFRS. It is not permissible to use the spandrel beams even if they are made monolithic with the columns, because ACI 318-05 Section 21.3.1.2 requires that the clear span of the beam be not less than four times the depth. The intent of this requirement is to provide the opportunity for plastic hinges to form in the beams. When strong connections are used at drop-in beam locations, these connections should be located near the natural inflection points for continuous beams so that the moment demand on the connections will be low and they will be located away from the locations of ductile behavior. This requires that: • • •

Column-to-column connections must develop 1.4 times the probable strength at the yield point. The connection moment strength must be at least 40% of the column moment strength within the story. This points to the use of Type 2 splices in the column-to-column connections.

4.7

(a) Rigid frame shear mode deformation

(b) (c) Interconnected frame Shear wall bending mode and shear wall (equal deflections at each deformation story level

Fig. 4.7.1 Deformation modes.

4–54

The beam span for span-to-depth ratio limitations be the distance between locations of flexural yielding. The design strength of every strong connection be sufficient to develop the probable strength at the nearest location of flexural yielding. The primary longitudinal reinforcement must be made continuous across the connection so that it is developed away from the strong connection and the yield locations.

Shear Wall – Frame Interaction

Rigid frames and shear walls exhibit different responses to lateral loads, which may be important, especially in high-rise structures. This difference is illustrated in Fig. 4.7.1. A frame bends predominantly in a shear mode (Fig. 4.7.1[a]), while a shear wall deflects predominantly in a cantilever-bending mode (Fig. 4.7.1[b]). Elevator shafts, stairwells, and concrete walls normally exhibit this behavior. It is not always easy to differentiate between modes of deformation. For example, a shear wall weakened by a row or rows of openings may tend to act like a frame, and an infilled frame will tend to deflect in a bending mode. Also, the shear deforma­tion of a shear wall can be more important than bending deformation if the height-to-length ratio is small, as discussed in Section 4.5.6.

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ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES If all vertical elements of a structure exhibit the same behavior under load, that is, if they are all frames or all shear walls, the load can be distributed to the units in proportion to their stiffnesses (Section 4.5.7). However, because of the difference in bending modes, the load distribution in structures with both frames and shear walls is considerably more complex. References 23 and 25 through 28 address this issue in detail.

4.8

Diaphragm Design

In structural systems, the framing of floor and roof components provides a function beyond the support of the gravity loads. The horizontal framing is designed as a diaphragm to collect and transmit lateral forces from wind or earthquakes to the vertical components of the lateral-force-resisting system. It also provides lateral bracing to the vertical elements and protects them against abnormal loading. Precast concrete diaphragm systems are as varied as the components that form the horizontal framing. Hollow-core floors may be designed as diaphragms with perimeter reinforcing and grouted joints, or may be the form for reinforced cast-in-place topping. Double-tee systems may include untopped or pretopped tees, pretopped tees with pour strips at the ends, or tees with cast-in-place topping that can be designed as the diaphragm. In many precast concrete structures, the configuration and behavior of the diaphragm may be very simple. Rectangular floors or roofs spanning between precast concrete frames or walls provide connectivity and lateral-load distribution and can easily be modeled as a deep horizontal beam. In other cases, the features of the structure may create more complex conditions. The features may include excessive horizontal spans between the vertical components of the lateral-forceresisting system, large openings or discontinuities, large torsion effects from the eccentricity of the lateral force with respect to the center of stiffness, or lateral transfer requirements due to vertical discontinuities. 4.8.1

 imple Diaphragm Design – S The Horizontal Beam Analogy

The diaphragm is analyzed by considering the roof or floor as a deep horizontal beam, analogous to a plate girder or I-beam. The shear walls making up the components of other lateral-force-resisting systems are the supports for this beam. As in a beam, tension and compression are induced in the chords or flanges of the analogous beam. The shear in the diaphragm is resisted by the web of the analogous beam. A diaphragm model using the beam is shown in Fig. 4.8.1. 4.8.1.1 Shear Transfer between Components In precast concrete floors and roofs without composite topping, the individual components composed of a floor or roof diaphragm must be connected together to act as a single diaphragm. Joints between precast concrete components, which are parallel to the lateral-force-resisting system, must contain connections to resist the diaphragm shear forces as well as chord tension/compression forces at the edges of the dia-

CHAPTER 4

phragm. Joints between the precast concrete components that are perpendicular to the lateral-force-resisting system must contain connections to resist horizontal shear (VQ/I). The types of connections used to connect precast concrete components together to form diaphragms vary depending on the required connection strength, strain capacity to accommodate expected joint movement, and the preference of the precast concrete supplier manufacturing and erecting the precast concrete units. Two commonly used welded connections are shown in Fig. 4.8.2. Connections between components often serve functions in addition to the transfer of shear caused by lateral loads. For example, weld plates in flanged components are often used to distribute concentrated loads and to adjust differential camber. Grout keys may be utilized in the joints to distribute concentrated loads. Precast concrete components may be fabricated with grout keys and connected by grouting the joint. For components connected by grout keys, a conservative value of 80 psi can be used for the design shear strength of the grouted key. If necessary, rein­forcement placed as shown in Fig. 4.8.3 can be used to transfer the shear. This steel is designed by the shearfriction principles discussed in Chapter 5. In floors and roofs with composite topping, the topping itself, or in conjunction with the precast concrete components, can act as the diaphragm if adequately reinforced. Shear reinforcement can be determined by shear-friction analysis. Continuous reinforcement at the diaphragm boundaries is provided to resist chord tension forces. Connections that transfer shear from the diaphragm to the shear walls or other lateral-force-resisting systems should be analyzed in the same manner as the connections between components. For rigid diaphragms, the reaction forces will be determined from the diaphragm design force with consideration of the maximum effects of torsion in the plane. For flexible diaphragms, the reactions are derived based on the tributary spans of the diaphragm between the vertical components. Vertical components that are within 5% of the length of the building perpendicular to their line of action to each other can be considered as the same line of resistance in this analysis. 4.8.1.2 Chord Forces Chord forces are calculated as shown in Fig. 4.8.1. For roofs with intermediate supports as shown, the shear stress is carried across the beam with weld plates or bars in grout keys (section A-A of Fig. 4.8.1). Bars are designed by shear friction. In decks consisting of flanged deck components, the chord tension at the perimeter of the building is usually transferred between components by reinforcement in the topping or pour strips or with tension connections. In all buildings, a minimum amount of perimeter reinforcement is required to satisfy structural integrity requirements (Section 4.3). These minimum requirements may be more than enough to resist the chord tension.

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CHAPTER 4 Maximum shear between components = 2a VL 

  4

Lateral load W = w Shear at wall = VR = VL

Chord force C = M/b

Weld plates designed for shear force

A

A

Shear at interior support = VQ/l

Typical double-tee roof

Section A-A(1) Chord force T = M/b

6VR s1(b – s1)



b3 (s1≤ s2)

Bar in grout key

a

VL = W/ 2 VR = W/ 2

Shear on diaphragm

(reaction)

Beam dowel in grouted end joint Typical hollow-core roof

Section A-A(2)

M = W/ 8 Moment on diaphragm Fig. 4.8.1 Analogous beam design of a diaphragm.

4.8.1.3 Collector Forces Diaphragm forces are distributed throughout the diaphragm based on the distribution of the seismic weight at the level and location under consideration. Thus, there is a requirement to provide a positive load path for these area loads into the components making up the lateral-force-resisting system. This design issue is similar to the design of hanger reinforcement in a dap design; however, only the collected portion of the demand requires drag reinforcement as opposed to using the entire reaction, as in the case of a dap (Fig. 4.8.4). Collector reinforcement should be proportioned based on the area of diaphragm for which loads are being collected. In seismic design categories C and higher, the collector demands must include the overstrength factor Ω0 to ensure elastic behavior under a maximum earthquake event. There is also a requirement that the collector transfers load to the vertical resisting component. The Ω0 only applies to the collector; thus, the transfer of load between the diaphragm and the shear wall only requires Ω0 on the portion of the demand that requires collection. In some instances, there are existing components in the diaphragm that can satisfy this requirement; however, supplemental tension ties typically are necessary. Figure 4.8.5 shows collector (drag) reinforcing into and adjacent to 4–56

a shear wall. While shown in the topping, it can be in the component adjacent to the shear wall. Often, collector and chord forces can be resisted by the same tensile tie since collectors are typically oriented parallel to the applied lateral load and chords are typically perpendicular; they do not tend to be additive demands. 4.8.2

Rigid and Flexible Diaphragms

Since the inception of the precast and prestressed concrete industry, building structures have typically been designed using the assumption that the floor systems serve as rigid diaphragms between the vertical components of the lateralforce-resisting system. A diaphragm is classified as rigid if it can distribute the horizontal forces to the vertical lateralload-resisting elements in proportion to their relative stiffness. Close examination of the effective properties of diaphragms, along with long-span applications, suggest that many precast concrete diaphragms may be flexible. 4.8.2.1 Defining Rigid or Flexible Diaphragms A diaphragm is flexible for the purpose of distribution of story shear when the lateral deflection of the diaphragm under lateral load is more than twice the average story drift of adjoining vertical components of the lateral-force-

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(b) Bent bar a,b

(a) Plate and bar

  4

y

Steel angle Reinforcing bar

Edge of member

Plan

Plan

Section

Section

Note: a. Not suitable for diaphragms in high-seismic areas, pending further research. b. Recommendations for welding of reinforcing bars in Section 6.7.3 must be closely followed. Fig. 4.8.2 Typical flange weld plate details. See Chapter 6 of this handbook for design of welds and connections.

resisting system under equivalent, tributary lateral loads. A rigid diaphragm is one that is not flexible. The distinction between rigid and flexible diaphragms is important not just for diaphragm design but also for the design of the entire lateral-force-resisting system. For structures with rigid diaphragms, the seismic-design story shear is distributed to the various vertical components of the lateral-force-resisting system based on the relative lateral stiffnesses of the vertical resisting elements. The general assumption is that the deformation within the diaphragm is not significant, relative to that of the vertical system. This assumption implies that the diaphragm is capable of carrying loads to extreme points even when there are large differences in stiffness between individual vertical components. It also implies that the deformation in the diaphragm does not have a significant effect on drift, so that gravity components remote from the vertical lateral-force-resisting system are not subject to significantly larger lateral displacements. These assumptions may not be conservative. For flexible diaphragms, the seismic-design story shear is distributed to the various vertical components based on the

area of the diaphragm tributary to each line of resistance. Section 12.3.1.2 of ASCE 7-05 states that diaphragms with an aspect ratio of 3 or less are permitted to be considered rigid. It has been demonstrated in research studies that simply limiting the aspect ratio is not sufficient, since deflection is also a function of the actual span. Research by Fleischman et al29 has defined more precise parameters to identify flexible systems. 4.8.2.2 Behavior and Design Considerations The behavior of diaphragms as rigid or flexible depends on many factors, including span, aspect ratio, jointing, and connections. Consider a precast concrete structure with shear walls at several lines of lateral support. Figure 4.8.6 shows a parking structure layout with stiff end walls and interior cruciform walls. The framing layout includes an interior ramp between grid lines 4 and 9, introducing a large interior discontinuity in the diaphragm. It is not uncommon to use the walls as part of the gravity system so that the dead load of the structure helps resist overturning. Such a design could result in the interior cruciform walls being significantly less stiff than the end walls. For a rigid diaphragm

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CHAPTER 4

  4 Grouted shear key

Fig. 4.8.3 Use of perimeter reinforcement as shear-friction steel.

assumption, the lateral forces can be applied as a combination of uniform and triangularly varying load in the plane to represent the effects of accidental torsional eccentricity. Reactions can be calculated from the lateral distribution with proportional adjustments made for the magnitude of diaphragm loading. The determination of shears and flexure in the statically indeterminate horizontal beams can be made by considering the interior walls as applying counteracting loads rather than as acting as supports. Since the interior wall forces in this example are low because of lower relative stiffness, the moment diagram is close to one of a uniformly loaded beam spanning end to end. This is shown as an overlay to the framing on Fig. 4.8.7. Because the ramp discontinuity separates each bay for most of the length, the bays share the loads as equal but separate beams. The required amount of chord reinforcement for flexure in such a system is excessive. For the same system, the diaphragm may be designed as flexible. In this case, the equivalent beam is a continuous beam on four supports. The reactions to the walls are determined as continuous beam-support reactions. The moment diagram for this assumption is quite different, as illustrated in Fig. 4.8.7. The maximum moments for this approach are considerably less than for the rigid diaphragm assumption. The chord-reinforcement requirement is also much less.

bays at Elevator

Collector force demand

typical

typical

Shear walls

•

Ramp down

bays at

• Ramp up

Stair well

Fig. 4.8.4 Collector force demand diagram for shear walls in a parking garage.

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CHAPTER 4

Shear wall Connection to shear wall

  4 Collector reinforcement in line with shear wall Cast-in-place topping

Collector reinforcement in topping

Double-tee deck

Fig. 4.8.5 Perspective view of shear wall and collectors.

Cruciform wall

Cruciform wall

• Inverted-tee beams

Ramp up

Ramp down

•

End wall

Cruciform wall

Cruciform wall

Shear wall locations Fig. 4.8.6 Typical parking structure plan.

Unfortunately, diaphragm design is not usually as simple as selecting one or the other approach. There is concern for local overloads. Redistribution of forces from overloaded components requires some diaphragm rigidity. Flexibility can reduce the demand on the vertical components and the shear and moments in the diaphragm, but actual rigidity inherent

in the floor layout needed to meet the structure’s function may make this reduction unsafe. If the design includes sufficient chord reinforcement to avoid yielding, the rigid model is safer because redistribution is ensured.

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  4

Rigid diaphragm moment

Flexible diaphragm moment

Fig. 4.8.7 Comparison of rigid and flexible diaphragms.

4.8.3

Diaphragm Design Forces

Part of the challenge in the design of diaphragms is the selection of appropriate force criteria. For wind loads, this is straightforward. The combined windward and leeward wind pressures are considered a uniform load that must be collected at the building perimeter and distributed to the vertical elements of the lateral-force-resisting system. Code-prescribed load factors are applied to ensure sufficient strength. When the design event is an earthquake, however, current code prescription for equivalent lateral forces may fail to adequately address dynamic and system effects under high seismic excitations.

n

∑F

i



i=x n

Fpx =

w px

(Eq. 4-60)

∑ wi i=x

with the limits that: 0.2SDS Iwpx ≤ Fpx ≤ 0.4SDS Iwpx

4.8.3.1 Code-Prescribed Forces For the purpose of design, the lateral-force-resisting system is considered as the combination of vertical components (walls or frames) and the horizontal diaphragms that distribute the loads to those vertical components. The main windforce-resisting system must be designed for vertical and horizontal loads based on the combined windward, leeward, and uplift pressures calculated for appropriate wind speed, exposure, and gust-response factors. The load used for diaphragm design is the same used for the design of the vertical components. For seismic design, the current building codes require separate calculations of diaphragm design forces from those used in the design of the vertical components. The diaphragm 4–60

design force is generally designated as Fp. This force cannot be less than the distributed force calculated in accordance with Section 4.2.4.2. Diaphragm forces must not be less than prescribed by ASCE 7-05 Eq. 12.10-1:

The forces from Eq. 4-60 have been reduced by the response modification factor. 4.8.3.2 Elastic Design of Diaphragms The forces used for design of the lateral-force-resisting system use reduction factors based on the inelastic capacity of the system. Each vertical system is assigned a response modification factor related to its ductility, strength, and toughness. The assumption implicit in this approach is that the energy dissipation and post-yield deformation will be controlled by the characteristics of the vertical system. To then be consistent, the diaphragm components of the system need to have both the strength and the deformation capacity to ensure that the primary inelastic mechanism is developed. This means

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ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES that the diaphragm may need to be designed to remain elastic as it develops and transfers forces to the vertical components. For diaphragms assumed to act rigidly, there is an additional reason to avoid yielding in the floor: This may compromise the load paths that can redistribute loads to stiffer components. The diaphragm must also continue to provide lateral support in the weak directions of vertical system components and for components not part of the lateral-force-resisting system. The code-prescribed diaphragm force pro­visions reviewed previously do not require that elastic behavior in the diaphragm be generally maintained. Through ASCE 7-05 Section 12.4.3.2, the special load combinations are required to be used in the design of collector elements and their splices, as discussed in Section 4.2.6.1. The code provisions appear to address the integrity of the diaphragm only through limits on deflection: “Permissible deflections shall be that deflection up to which the diaphragm and any attached distributing or resisting component will maintain its structural integrity under design load conditions, such that the resisting element will continue to support the design loads without danger to occupants of the structure.”10 It is not clear in the provisions whether these deflections include the inelastic behavior of the diaphragm. If so, no guidance on the deflection amplification is provided for any system. This provision also does not recognize that yielding in the diaphragm might create a failure mechanism without mobilizing the strength and ductility of the vertical elements of the lateral-force-resisting system. The code-prescribed design forces for diaphragms appear to contradict the implicit assump­tions that are their basis. To be consistent with the behavior inherently assumed in the prescribed seismic-system parameters from the code and to ensure the integrity of the system, simple diaphragms might be designed to remain elastic through the design event. Nakaki30 lists additional benefits for providing for elastic design: 1. It eliminates the need to confine the reinforcement in the compression chord. 2. It prevents chord reinforcing from buckling when load is reversed and tension cracks close. 3. It improves bar-splice performance without the need for lateral ties around the splice. 4. It eliminates uncontrolled, inelastic diaphragm deformations. Careful consideration of the function and details of diaphragms in precast concrete systems should reveal that design for elastic behavior is not simply a matter of using elastic design forces. Floors and roofs composed of precast concrete components are invariably jointed. These com­ponents may be doubletees, hollow-core slabs, or solid slabs. When the systems are dry (untopped or pretopped), the jointed nature is obvious. The components are connected to one another and to the sup-

CHAPTER 4

porting structure along the joints. When a cast-in-place topping is used, there is still a strong tendency for the diaphragm to behave in a jointed manner. The joints in precast concrete components below the topping are planes of weakness similar to control joints in monolithic construction. Shrinkage strains tend to accumulate and form cracks in the topping above these joints. This is well recognized in parking structure design, so that joints are tooled in the wet topping above the precast concrete joints to provide a regular line for the crack that can be sealed. These discrete joints, then, control the behavior of the diaphragm because the deformations consist almost entirely of the movements in these joints. With precast concrete diaphragms, it is common to differentiate between web and chord effects in the design of connections or topping reinforcement. With field-topped doubletees or pretopped tees with pour strips, the chord steel may be continuous reinforcing bars laid in the topping or pour strips at the ends of the tees, or welded connections that link continuous reinforcing bars embedded across the tee ends. In pretopped tees without pour strips or untopped tees, the chord might use welded connections with tail bars that lap chord reinforcement in the flanges, but this approach has been penalized with a low capacity-reduction factor (φ = 0.5) in some codes based on older NEHRP recommended provisions. The web or flange connectors, then, are designed to transfer the diaphragm shear as well as to assist in the vertical alignment of the flanges. The most common design practice is that no shear capacity is attributed to the chord steel and no tension capacity is attributed to the flange connectors. As the diaphragm deforms, the opening of the joint is actually resisted by the tension capacity in both the chord and the web connections. This opening translates into tension strain concentrated in the small space of the joint that must be withstood by both types of connections. Web connections with high stiffness but low elastic strength may fail in tension and be unable to transfer loads in shear. Some connections have been designed and tested for their capacity to sustain much of their shear capacity in conjunction with the tension load and strain from joint opening.31 With hollow-core slabs, the chord is frequently made from continuous reinforcing bars placed in a cast-in-place strip beyond the ends of the slab. These bars also provide shearfriction steel to hold the joints together and permit shear transfer through the grouted joint. When cast-in-place topping is used, the same discrete deformation at the precast concrete joints will occur. The diaphragm reinforcement is usually provided as continuous reinforcing bars for the chords and welded-wire reinforcement (WWR) to satisfy minimum shrinkage and temperature steel. The WWR also acts as shear reinforce­ment. As the WWR crosses the joints, there is only the distance between the cross wires (those parallel to the span of the tees) available to sustain the strain that results from the joint opening. In recognition of the vulnerability of this condition, ACI 318-05 includes the requirement that the wires parallel to the span of the precast concrete components not be spaced less than 10 in. on center in order to allow more length to absorb the strain.

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For the diaphragm to remain elastic, the design must consider the yield limits of web connections or reinforcement as well as chord connections and reinforcement. The chord steel may need to be increased beyond calculated moment requirements to limit joint strain to protect the web. Preliminary indications from research suggest that the overstrength factor Ωo used for the system is more conservative than necessary for the diaphragm design. There is also concern that some common and practical configurations of diaphragms are particularly vulnerable at points of inelastic behavior. For these reasons, performance-based design may be more appropriate. 4.8.3.3 Performance-Based Design In an effort to find appropriate levels of force for precast concrete diaphragm design, research has been conducted to evaluate their dynamic characteristics.29,32 These studies have produced important findings that bear directly on appropriate design. An important observation is that the dynamic force distributions produced by the investigated structures can differ significantly from those provided by the equivalent lateral force patterns prescribed by the codes. “For a rigid diaphragm structure following the formation of a base plastic hinge, the instantaneous effective centroid occurs well below the centroid implied by the equivalent lateral force pattern. This downward shift is due to the nature of higher modes in the instantaneous deformation state.”29 The research has also identified vulnerabilities in common precast concrete systems, particularly where there are large discontinuities, such as at parking-structure ramps. The load paths across interior beams in these systems have particularly high force demands. Although design forces are applied in orthogonal directions, real accelerations can come from any direction. Oblique load trials also show some vulnerabilities where combined flexure and shear act on joints. For common precast concrete systems with shear walls, the stiffness of the wall configurations can be significantly higher than the stiffness of the diaphragms. Under these circumstances, it may not be feasible to develop designs for diaphragms that are ensured to remain elastic. It may be appropriate, instead, to establish performance criteria that include: “(1) the achievement of the diaphragm’s elastic limit at life-safety; and (2) the exhaustion of the diaphragm’s available ductility at collapse-prevention.”33 The referenced research papers provide design guidelines that consider the specific parameters and characteristics of a building system and layout. Some general guidelines, however, can be derived from this work: 1. For structures of low and moderate seismic risk, the dynamic effects are less pronounced. If every floor diaphragm is designed for the force at the uppermost level derived from Eq. 4-60, additional load factors are not recommended for elastic diaphragm response under the design earthquake.

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2. In regions of high seismic risk, special moment frames of reinforced concrete are sufficiently flexible to limit the direct transfer of ground acceleration to diaphragms at lower levels or the development of significant higher mode effects. Again, if every floor diaphragm is designed for the force at the uppermost level derived from Eq. 4-60, additional load factors are not recommended. 3. In regions of high seismic risk, shear-wall buildings are most vulnerable to higher accelerations in diaphragms. As the buildings get taller, the effect becomes more severe. For most precast concrete buildings that are less than 80 ft tall, it is recommended to apply a diaphragm load factor ψ = 2.0 to the force at the uppermost level derived from Eq. 4-60, and to design each floor for that force. 4. In calculating diaphragm deflection, it is important to make a reasonable estimate of the effective section properties. A detailed analysis that considers the effects of joints, connections, and chord and web reinforcement may be made. A reasonable, but conservative, estimate can be made by taking the effective section as 10% to 15% of the gross section for topped systems and between 5% and 10% of the gross section for untopped and pretopped systems. 5. Precast concrete floors, topped or untopped, experience the strains of deformation by opening at the joints. These strains cannot be disregarded. Chord reinforcement should be proportioned to limit joint opening to the capacity of the shear reinforcement or connections as well as for strength. Joint reinforcement or flange connections should have sufficient ductility to maintain required capacity while they undergo moderate joint strains. 4.8.3.4 Wind and Low Seismic Hazard For wind load and low seismic hazard (seismic design categories A and B), it is generally sufficient to design diaphragms for the strength requirements imposed by the applied forces. Openings and discontinuities may still require special attention for detailing, but these features are more sensitive to volume-change movement than to lateral forces. 4.8.4

Diaphragm Detailing Considerations

As the analysis of diaphragms for lateral forces most frequently follows the horizontal deep-beam analogy, the design of the diaphragm connections and reinforcement also follow this model. “Diaphragms shall provide for both the shear and bending stresses resulting from these forces.”10 With large areas and depth relative to the spans, the characteristics of deep beams must often be considered in this design. Diaphragms need to have elements to form ties or struts to distribute the anchorage forces into the diaphragm. The collector components must be capable of transferring the seismic forces to the component providing the resistance to those forces.

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ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES 4.8.4.1 General Detailing Requirements The primary reinforcing steel or connection details that carry the diaphragm flexure through a tension/compression couple are in the chords. These may contain continuous reinforcing bars placed in a cast-in-place topping or strips or a continuous series of connections across the joints between components. These elements are placed near the boundaries of the diaphragm to increase the moment arm between the tension and compression forces for more efficient flexural resistance. Capacity-reduction fac­tors φ have varied in previous codes to reflect the reliability and ductility of chord details. Continuous reinforcement is treated as in other flexural elements with a φ of 0.90. For chords formed with connections welded at the joints, the φ factors might be treated more conservatively based on the reliability of the details (Section 4.2.6.1). Shear in the analogous beam is carried through shear capacity along or across the components. The transfer of shear across the joints is carried by connections or reinforcement specifically pro­portioned for the load. These connections may actually be weak in tension. It is important, however, that the shear capacity of a connection part or reinforcement is not reduced below the design requirement when the joint is subject to separation. Even with cast-in-place topping, it is recognized that deformations in diaphragms are concentrated at the joints. The topping experiences reflection cracks above the joints in the precast concrete components, and so is frequently tooled to control the cracking. Joint separation compromises the shear capacity in the concrete, so that all shear transfer is considered to be by shear-friction, dependent on the reinforcement crossing the joints. Movement in the joints places a strain demand on the topping reinforcement or joint connections that must be considered in the detailing. The strain consideration may mean limiting that strain by higher strength and stiffness in the chord steel, accom­modating the strain by providing connections or details that are tolerant, or a combination of the two. In the design of long-span, precast concrete diaphragms, there are issues common to all levels of load. Long spans may be vulnerable to excessive deflections because details may result in a low effective stiffness. It is also important to consider stress concentrations at discontinuities, such as the separation points of ramps or at re-entrant corners near stairs or at the ends of spans. Additional strength or reinforcement may be needed in these locations. Although the primary structural considerations for diaphragm design are strength and deflection control, the internal restraint that can develop must find some relief. Connections in diaphragms with strain capacity will permit small local deformations without distress, so that large restraint forces are not developed.

CHAPTER 4

4.8.4.2 M  oderate Seismic Hazard – Topped and Pretopped Systems Topped, untopped, and pretopped diaphragms are commonly used in regions of moderate seismic risk (seismic design category C). For systems that use concrete walls, including precast concrete, there are special requirements for diaphragm design in ASCE 7-05. In these systems, the diaphragm must include special continuous struts or ties between diaphragm chords for wall anchorage. When these diaphragms use sub-diaphragms, the aspect ratio of the subdiaphragms is limited to 21/2 to 1. In moderate seismic-risk areas or design categories, precast concrete wall systems must conform to the requirements of intermediate precast concrete walls. The collector elements and their connections must be designed for the special load combinations with the overstrength factor Ω0. “The design issues in a hollow-core diaphragm are the design of the connections to get the loads into the diaphragm, the strength and ductility of the slab system to transmit these loads to the lateral-resisting elements, and the design of the connections required to unload the lateral forces from the diaphragm to the lateral-resisting elements.”34 For untopped, hollow-core diaphragms, the chord steel may be added in the bearing areas in grout space outside the slab. This detailing requires some positive ties into grouted cores or keyways. Shear trans­fer can be designed through grouted keyways in the joints. Hollow-core slabs may also be topped, with the diaphragm reinforcement provided in the topping. 4.8.4.3 S  eismic Design Category D and Higher – Topped Systems ACI 318-05 includes specific provisions to address the requirements for cast-in-place topping as diaphragms. These provisions include systems with the topping composite with the precast concrete components and systems with the topping, non-com­posite part acting alone. The composite system re­quire­ments recognize that connections may be part of the design proportioned and detailed to transfer forces. They require that the interface be “clean, free of laitance, and intentionally roughened.”3 The chord reinforcing-steel design is determined from flexural analysis. Shear strength must be based entirely on reinforcement crossing the joint:

Vn = Acvρn fy

(Eq. 4-61)

where Acv is based on the thickness of the topping slab and ρn is the steel ratio of the reinforcement crossing the precast concrete joints. This is equivalent to shear-friction capacity with a µ of 1.0. For diaphragm design in areas of high seismic risk, research suggests that it may not be possible or practical to ensure complete elastic behavior of a diaphragm through the maximum considered earthquake. Some ductility needs to be provided to accommodate the potential for local overloads in the diaphragm. Some redundancy in the field-topped systems can be obtained by using mechanical connections between

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tees and between tees and beams for erection stability that stay in place and add to the capacity provided by reinforcement in the topping. The potential for breaking WWR due to the strain demand across the joints must be considered in the detailing. Reinforcing steel needs to be compatible with the strain demand at the joint. Welded-wire reinforcement with larger wire spacing or the use of reinforcing bars may be needed in some cases. Mesh in the topping must take the entire shear across the joint. Lapping in accordance with the code is necessary to maintain diaphragm integrity. ACI 318-05 includes the requirement that the wires parallel to the span of the precast concrete components not be spaced less than 10 in. on center in order to allow more length to absorb the strain. In long spans with widely spaced joints, it may be necessary to consider the joint-strain demand directly. The φ factor for the shear design of the diaphragm must be no greater than that used in the shear design of the supporting vertical components (columns or walls). This will sometimes result in φ = 0.6 if the φ factor for the shear design of shear walls is modified by Section 9.3.4 of ACI 318-05. With the development of ductile yielding at joints in special moment frames or rocking from flexural yielding at the base of special walls, there are deformation demands placed on the diaphragm that are not addressed by the codes. Detailing of reinforcement in areas that are vulnerable to elongation of beams due to formation of plastic hinges should consider protection against loss of support, increased column displacements, and cracks in the diaphragm topping. 4.8.4.4 U  ntopped Systems for High Seismic Hazard The provisions for precast concrete diaphragms that are included in ACI 318-05 are for topped composite and topped, non-composite diaphragms, so untopped diaphragms are implicitly not recognized. Section 21.2.1.5 of ACI 318-05, however, includes the general alternative clause that permits a system to be used if it is shown by experimental evidence and analysis to be equivalent in strength and toughness to comparable monolithic, cast-in-place systems. Reference 35 describes how these conditions can be met in a high seismicdesign-category building. The comparable monolithic, reinforced-concrete system is the cast-in-place-topping slab diaphragm of Section 21.9.3 of ACI 318-05. This is a cast-in-place topping acting alone, proportioned and detailed to resist the design forces. The use of cast-in-place pour strips at the ends of the untopped tees designed for the tension and compression chord forces essentially provides this cast-in-place topping system for that part of the untopped diaphragm. The shear strength in the untopped system must be comparable with the shear strength required by the steel design from Eq. 21-11 of ACI 318-05. The approach recommended here is to use design forces to achieve a performance level greater than the one prescribed by the code. The use of a diaphragm design-load factor of 2 or higher will ensure that the resulting design will exceed the required strength. 4–64

To satisfy requirements for toughness, some attention needs to be paid to the strain at the joints and the capacity of the connections to provide their required strength through that strain. The joint spread can be checked by analysis. The total diaphragm deflection is calculated from effective section properties, and the associated strains distributed to the joints. This strain can be compared with the connection strain capacity. Chord reinforcement may need to be increased beyond that which is needed for strength to control the width or limit the amount of joint opening. Tests have been run on many prototype flange connectors to determine their strain capacity.31 Although many of the common plant-fabricated connections designed with reinforcing bars butt-welded to the backs of plates failed to show sustained capacity or strain tolerance under reversed cyclic loading, some commercial flange connections, designed specifically to have improved strain capacity, showed that they have sustained shear capacity even with 1/4 in. or more joint opening and under reversed cyclic loading. With the selection of these tested welded connections as the replacement for steel reinforcement where the deformation reflected as joint opening is analyzed and controlled, it is possible to demonstrate equivalency of the untopped system and to provide effective design of untopped diaphragms in high seismic regions. 4.8.5

 lternative Methods of Diaphragm A Design

The use of the horizontal deep-beam analogy is a common and reasonably simple approach to diaphragm design. It can be seen, however, that there are some problems with this model in more complex and demanding configurations. In these cases, the designer may consider alternative analysis methods. 4.8.5.1 Strut-and-Tie Modeling Appendix A of ACI 318-05 provides recommendations for the application of strut-and-tie modeling to concrete structures. The method considers the diaphragm as an idealized truss with compression struts, tension ties, and intersection nodes. “Intermediate beams in the slab can act in a similar manner to stirrups in a beam, with diagonal compression forces being resisted by the concrete topping and the precast units where they are continuous.”33 With the jointed and rectilinear nature of precast concrete layouts, some caution must be exercised in defining diagonal struts that may cross joints unless topping can be reinforced to form these elements. The method as applied to precast concrete is discussed in Reference 36. 4.8.5.2 Finite-Element Analysis Although traditionally perceived as a research tool rather than a design aid, finite-element analysis (FEA) has more recently found a place on the computers in many engineering offices. In some cases, the power and simplicity of finite element modeling may become a practical and useful alternative when the diaphragm problem is not simple. The key to successful diaphragm analysis using finite ele-

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4.9

 last-Resistant Design of Precast, B Prestressed Concrete Components

4.9.1

General

Blast-resistant building components are designed to provide an acceptable level of safety to building occupants in the event of an explosion. Significant damage is usually acceptable as long as the component remains attached to the building and the building remains stable after the explosion. For a given explosion scenario, precast concrete components and their connections to the building should be designed to resist the resulting blast load. Framing members directly supporting precast concrete components need to be designed to resist the dynamic reaction forces from the component. Alternatively, they can be designed to resist the blast load acting over their tributary area. Unlike seismic and wind loads, blast loads have a very short duration (typically milliseconds). Therefore, the large mass associated with overall building response often provides enough inertia so that the building’s lateral-force-resisistng system does not need to be strengthened to resist blast loads. The fact that a blast wave applies positive pressure on all sides of the building also limits the effect on the lateral framing system, although the pressure is much higher on the sides facing the explosive source. The lateral-force-resisting system on smaller one- or two-story buildings should typically be checked to consider the combined effects of overall frame sway and direct blast-load effects on frame members. Conventionally designed foundation systems for large and small buildings almost always have adequate mass and strength to resist the short duration reaction loads from the building

  4

Pressure

ments is in the modeling. When the focus of the analysis is the in-plane behavior, shell elements without transverse loads can be used to create the model. With precast concrete systems, it is important to adequately define and model the joints between adjacent precast concrete components. The size or spacing of the elements should match flange connection spacing so that the nodes can be used as connection sites. The model is then copied or arrayed with spacing that leaves joints between the components. At beam lines, the depth of the beam might be represented by increasing the thickness of the shell element. It is equally important to add connections between the components that adequately model the connection characteristics. Some FEA programs provide component releases that can reduce or eliminate tension forces from beam elements used to model the shear connectors. Some programs also permit the definition of nonlinear springs so that test deformations can be modeled. Simple modeling of planar behavior, as indicated previously, can provide significant results and insight into areas with high load concentrations or deformations. In some cases, the prominence of shear deformation as a large component of deflection is evident. It may also be possible to identify deformation patterns that are more characteristic of tied arch behavior than of beam bending. Chord forces and connection forces are the primary results that can be used in design.

CHAPTER 4

Impulse i

0

td

Time

Fig. 4.9.1 Idealized blast-pressure history typically used for design.

response to the blast load. 4.9.2

Blast Loads

An explosion is a release of energy that occurs so rapidly that there is a local accumulation of energy at the site of the explosion.37 This energy expands as a shock or pressure wave, causing a localized, very short duration rise in air pressure at the wave front followed by a short duration negative pressure, or suction, with a lower magnitude. The pressure rise may be several pounds per square inch, or a much higher magnitude close to the explosive source. Additionally, the energy release may cause groundshock, fragmentation, cratering, thermal radiation, or any combination of these effects. Explosions can be caused by many sources including solid explosives, dust or flammable vapor clouds, pressure vessel bursts, rapid electric-energy discharge in a spark gap, rapid vaporization of a fine wire or thin metal strip, and molten metal contacting liquid. Most often, structural components are designed against accidental or terrorist explosions of solid explosives (also known as high explosives or HE) and accidental industrial explosions from vapor clouds or pressure vessel bursts. Many factors affect the pressures caused by an explosion, including the type of explosion, the explosive charge weight or mass, distance from the explosive source, height of the explosion above ground surface, and level of confinement around the explosion. Simplified blast-prediction methods are available for some explosion scenarios, including the common design case of an external (that is, outside the building) surface burst of HE, where the explosion is near the ground surface relative to its standoff distance to the component of interest and near the structural component of interest relative to any other surrounding buildings. This case is often applicable to a terrorism scenario. The blast loads for this case and other simplified cases can be predicted as described in References 37, 38, and 39. Figure 4.9.1 shows the simplified shape of blast-load histories commonly used for blast design. The blast load rises

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CHAPTER 4

PSO Pressure

  4

Positive impulse is

Ambient PO

tA

PSO tA t=0

Negative impulse is

PS(t ) tA + tO Positive phase

Duration tO

tA + tO + tO

Negative phase Duration tO

PS (t)

Time after explosion

Fig. 4.9.2 Actual shape of blast load from a solid, or high explosive, explosion.

immediately to its peak pressure and then decays linearly to ambient pressure over a duration td. The impulse, which is the shaded area under the pressure-versus-time curve, is a measure of the total energy in the blast load. The blast load must normally be defined in terms of at least two parameters, which are typically the peak pressure and impulse or the peak pressure and equivalent triangular duration td. A design blast pressure may be defined in terms of just the peak pressure only if there is an understanding that the blast-load duration is very long compared with the response time of the building’s structural components. This is the case for some industrial explosions and for nuclear explosions. Figure 4.9.2 shows the actual shape of the blast load, including the negative phase (suction pressure), which has a much lower magnitude but a longer duration than the positive phase (inward pressure). The negative phase is often neglected for design (Fig. 4.9.1), which is generally conservative. The simplified design blast load in Fig. 4.9.1 always preserves the peak pressure and impulse from the actual positive phase blast load in Fig. 4.9.2, which typically causes the equivalent triangular duration td in Fig. 4.9.1 to be less than the actual positive phase blast pressure duration in Fig. 4.9.2. It should be noted that the negative phase can significantly reduce the maximum response of precast concrete components, especially as the span length (and, therefore, natural period) increases.40 It is typically very important to include the negative phase when analyzing test data in order to determine analysis results that are as close as possible to measured values. The negative phase is not typically included for design of new components because there is more uncertainty in the prediction of the negative phase blast load compared with the positive phase blast load. The negative phase load is often included for analysis of existing components when a more accurate result is desired to avoid unnecessary structural upgrades to resist blast loads. Figure 4.9.3 shows the blast load from 100 lb of trinitrotoluene (TNT) on a structural component facing the explosive source at a distance of 50 ft. The initial time is set to zero 4–66

(that is, the blast wave arrive time tA is not shown), as is usually the case for a design blast load. This figure illustrates the very short duration of blast loads. The positive-phase durations of blast pressures from HE explosions are often less than 20 milliseconds, although the duration is a function of the charge weight and standoff and may vary considerably. Even long-duration industrial explosions are almost always less than 300 milliseconds. In many cases, the design blast load on a structural component is specified for the structural engineer in terms of the peak blast pressure and the impulse. The blast-pressure history can be assumed to have the shape shown in Fig. 4.9.1. The design blast load for industrial explosions is often specified in terms of an overpressure or free-field pressure. In this case, the applied blast pressure on structural components must be determined based on the orientation of the building surface containing the structural component of interest relative to the explosive source.37,38,39 4.9.3

Dynamic Material Properties

Blast-load durations are generally in the milliseconds range, causing similarly short component-response times, and, therefore, the effects of dynamic material properties should not be ignored. Under dynamic loads, materials exhibit increased yield strengths due to strain rate effects, which can considerably improve the ultimate load capacities of blast-loaded components. To account for the strain rate effects, a dynamic increase factor (DIF) is used when computing the strength of components, as shown in Eq. 4-62. Typical design values for the DIF are shown in Table 4.9.1 for reinforcing steel and concrete.38,39 Also, the minimum specified yield strength for reinforcing steel fy is typically increased by a static increase factor Ke of 1.1 for blast design to account for the difference between actual reinforcing-steel static yield strengths and the minimum specified values obtained from many tensile tests. Equation 4-63 shows the dynamic concrete compressive strength.

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25

Force, psi

  4

Peak load information Peak pressure = 20.2 psi Positive-phase impulse = 77 psi-msec Peak negative pressure = -2.6 psi Negative-phase impulse = -69 psi-ms

20 15 10 5 0 -5 0

10

20

30

40

50

60

Time, msec

Fig. 4.9.3 Reflected blast load for 100 lb of trinitrotoluene (TNT) at 50 feet.



fdy = fy Ke(DIF)

(Eq. 4-62)

where: fdy fy

= reinforcing-steel dynamic yield stress = minimum specified reinforcing-steel static yield stress Ke = static strength increase factor = 1.1 for conventional reinforcing steel = 1.0 for prestressing strands DIF = applicable dynamic increase factor for reinforcing steel (see Table 4.9.1)

f = f ( DIF )



' dc

' c

(Eq. 4-63)

where:

fdc' = =fc' dynamic ( DIF ) concrete compressive strength = specified concrete compressive strength fdc' = fc' ( DIF ) DIF = applicable dynamic increase factor for concrete (see Table 4.9.1) 4.9.4

General Blast-Design Methods

Rigorous analysis methods, such as dynamic, nonlinear FEAs, may be used to obtain the dynamic response of blast-loaded components. These analyses can consider more complex effects, such as dynamic interaction between cladding and framing, multiple modes excited during frame-sway response, and highly non-uniform blast loading over the area of a component. However, blast loads are usually relatively uniform over individual structural components; it is generally conservative to ignore interaction effects, and higher mode response does not usually affect maximum deflections of blastresistant components when there is significant ductile, plastic response. Also, rigorous FEAs tend to be time consuming

and require users to have a high level of knowledge of the sophisticated software packages. It is generally accepted that blast design of most building components can be performed by modeling the dynamic response of the component with an equivalent single-degree-of-freedom (SDOF) system.38,39 This is referred to as the SDOF method for blast design. It should also be noted that commercially available software for applying FEA to blast design has become much more accessible and user-friendly in recent years, and is being used for more complex blast-design cases. 4.9.4.1 S  ingle-Degree-of-Freedom Design Method The SDOF method idealizes the structural component into a mass-spring system with stiffness and mass related to those in the blast-loaded structural component (Fig. 4.9.4). The equivalent SDOF system is defined such that its deflection at each time step is equal to the maximum deflection of the structural component, assuming its response can be described in terms of a single degree of freedom (that is, the point of Table 4.9.1  Dynamic increase factors for reinforcing bars, concrete, and masonry Dynamic increase factor (DIF) Stress type

Reinforcing barsa

Concrete

fdy /fy

fdu /fu

f d' c /f c'

Flexure

1.17

1.05

1.19

Compression

1.10

1.00

1.12

Diagonal Tension

1.00

1.00

1.00

Direct Shear

1.10

1.00

1.10

Bond

1.17

1.05

1.00

a. Applicable for Grade 40 and Grade 60 reinforcing steel only. DIF for all prestressing steel = 1.0.

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  4 P(t ) Blast load P(t )

K M

Deflection x(t ) x(t )

Fig. 4.9.4 Equivalent spring-mass system representing dynamic response of beam loaded by blast.

maximum deflection) and an assumed shape function that defines motion at all other points on the component relative to the maximum deflection. Figure 4.9.5 shows the shape functions that are usually assumed for a simply supported beam before and after yielding in the maximum moment region. The shape function before yielding is almost always based on the deflected shape of the component from a static load with the same spatialload distribution as the blast load (for example, uniformly distributed). The shape function after yielding is based on a hinge at the yielded moment region. Similar shape functions are defined for other boundary conditions and for two-way spanning components.38,39,41,42 Equation 4-64 shows the equation of motion for the equiv-

alent spring-mass system typically used for blast design. The terms in Eq. 4-64 are related to the mass, stiffness, and load on the structural component by transformation factors (that is, load and mass factors) that are combined into a single load-mass factor. The transformation factors are calculated such that the work energy, strain energy, and kinetic energy of the component expressed in terms of its single degree of freedom (the movement at midspan) and assumed shape functions equal the work, strain, and kinetic energies of the equivalent spring-mass system at each time step.42,43 Table 4.9.2 shows load-mass factors for the case of a simply supported beam during elastic and plastic response with different spatial-load distributions. Load-mass factors for beams and one-way spanning slabs with other boundary conditions

Wo

Wo x

x

/2

/2 Ψ2 (x) = x/(/2) for 0 < x <  /2 Ψ2 (x) = 2(1 – x/) for  /2 < x <  W = Wo φ2 (x)

φ(x) = sinπ(x/), W = Woφ(x)

Prior to yield at maximum moment region

After yield in maximum moment region

Fig. 4.9.5 Deflected shape functions for simply supported beam.

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ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES Table 4.9.2  Load-mass factors for one-way components with simple supports Response range

Load-mass factor KLM

Single point load at mid-span

Elastic

0.49

Plastic

0.33

Two point loads at third-points

Elastic

0.60

Plastic

0.56

Uniformly distributed load

Elastic

0.78

Plastic

0.66

Resistance vs deflection

a

  4

2.5 2 Resistance, psi

Load distribution

CHAPTER 4

1.5 1 0.5

a. For component with uniformly distributed mass

0

and for two-way spanning slabs are available in a number of references.38,39,41,42,43 Damping can also be included in the equation of motion, but is often neglected because the peak response almost always occurs during the first response cycle before the cummulative effect of the damping force becomes significant.

KLMMw''(t) + R(w(t)) = F(t)

(Eq. 4-64)

where: M = mass of blast-loaded component F(t) = blast load on component R(w(t)) = resistance of component based on resistance versus deflection curve and deflection at each time w(t) = deflection of SDOF system = component maximum deflection w''(t) = acceleration of SDOF system KLM = load-mass factor (a function of the deflected shape) t = time Detailed information for calculating the terms in Eq. 4-64 is available in References 38, 39, 41, and 43. These terms are also calculated in the example problem. The equation of motion for the equivalent SDOF system in Eq. 4-64 can be solved in a time-step fashion using any number of available numerical integration techniques to determine the deflection history of the component caused by the blast load. The load-mass factor is determined at each time step based on the assumed deflected shape, taking into account any yielding that has occurred. The resistance is also determined at each time step based on the deflection and the resistancedeflection relationship of the spring in the equivalent SDOF system section. The component must be designed so that the maximum calculated dynamic deflection of its equivalent SDOF system is within acceptable limits. These limits, and the resistance-deflection relationship, are described in the following sections. Simplified maximum-response charts have also been created showing the maximum response of the equivalent SDOF system plotted against key parameters from Eq. 4-64 for a blast load with the simplified shape shown in Fig. 4.9.1.38,39,42

0.2

0.4

0.6

0.8

1

Deflection, in.

Fig. 4.9.6 Resistance-deflection relationship for simply supported precast concrete panel.

4.9.4.2 C  omponent Resistance-Deflection Function The resistance at each time in Eq. 4-64 is based on the deflection at the previous time step and the component resistance versus deflection relationship. The resistance-deflection curve relates the resisted load to the midspan deflection of the blast-loaded component. The resisted load has the same spatial distribution as the applied blast load (typically a uniformly distributed pressure load). The component resistance is always equal and opposite to a statically applied load based on equilibrium requirements, but a dynamic load causes an additional inertial force so that the resistance generally does not equal the applied load (see Eq. 4-64). The resistancedeflection curve for a structural component can be derived with conventional static calculation methods using applicable dynamic material yield strengths. This is illustrated in the example problem. In a ductile reinforced-concrete component, the resisted load, or resistance, increases approximately linearly with deflection until yielding of the reinforcing steel in the maximum moment regions and then the resistance remains relatively constant with increasing deflection until failure. Figure 4.9.6 shows the resistance-deflection curve for a precast concrete component with simple supports. The initial slope is the elastic flexural stiffness of the component using an average moment of inertia. Typically, this is calculated for reinforced-concrete components using an average of the gross moment of inertia and the fully cracked moment of inertia. The stiffness goes to zero when yielding occurs at the maximum moment region. The resistance does not degrade after yielding in Fig. 4.9.6, implying ductile response. It is assumed that the stress in the reinforcing steel remains constant at fdy after yielding, ignoring the small amount of strain hardening that occurs, so that the resisting moment and resistance of the component remain constant with increasing midspan deflection out to a limit deflection.

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ru

ru Resistance

Resistance

  4

ke l

re

kE

l

kep

l ke l

xm

xe

xe xE

xp

xm

Deflection

Deflection

Determinate boundary conditions

Indeterminate boundary conditions

Fig. 4.9.7 Resistance-deflection relationships for determinate and indeterminate boundary conditions.

Yield-line theory is used to determine the ultimate resistance for indeterminate components. These components have multiple yield loads, where the reinforcing steel yields at different maximum moment regions as the resisted load increases, causing multiple non-zero slopes in the resistance-deflection curve (Fig. 4.9.7). The resistance-deflection relationship of an indeterminate component can be simplified as shown in Fig. 4.9.7 using an equivalent stiffness kE and yield deflection xE that cause the simplified resistance-deflection curve, with one non-zero slope, to have the same area under its curve as the actual resistance-deflection curve out to the deflection where the component becomes a mechanism xp. Detailed procedures for determining the resistance-deflection relationships of components are described in References 38 and 39. The component absorbs strain energy during elastic and plastic response that must equal the energy imparted by the blast load or the component will fail. The absorbed strain energy can be measured as the area under the component resistance-deflection curve out to the maximum calculated component deflection, which must be less than the maximum allowable design deflection. Strain energy must be absorbed with either high resistance (that is, high component moment

4.9.4.3 Deformation Limits



θ = Support rotation

-1

where θ = tan

Xm

( ) 2 xm



Fig. 4.9.8 Component support rotation.

4–70

capacity) or a large component-deflection capacity, or by some combination of these two factors. Since the required shear strength and connection capacity for a blast-resistant component is proportional to the maximum component resistance (maximum resisted load) and not to the maximum deflection, a ductile component with a large deflection capacity is more desirable where possible. Typically, a well-designed ductile component will absorb most of the blast-load energy with plastic strain energy that occurs after yielding, but the maximum component deflection will only be one-half or less of the deflection corresponding to failure. Prestressed concrete components have much lower ductility than conventionally reinforced concrete because prestressing strands have a lower failure strain than conventional reinforcing steel. Therefore, prestressed concrete components fail at a lower maximum deflection and must possess a higher ultimate flexural resistance and corresponding dynamic moment capacity to absorb the same strain energy and resist the same blast load as conventionally reinforced concrete components. This also implies they must have higher shear strength and connection strength, which can still be manageable from a practical design viewpoint in some cases. However, conventionally reinforced concrete is generally preferred for blast design compared with prestressed concrete. As mentioned in the previous section, blast design involves allowing component stresses to exceed yield; therefore, allowable design stresses are not used in blast design. Instead, allowable design limits are set on component deflections that generally include a controlled amount of plastic deflection after the component yields at all maximum moment regions and becomes a mechanism. Allowable maximum dynamic deflections for components subject to blast loads are typically specified in terms of two parameters: the support rotation θ and ductility ratio µ. These parameters are illustrated

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8’ 4’ A

3

6”

Concrete floor beam

8’–3”

Spandrel beam 9’–9”

  4

2’ 2.5

Resistance, psi

2’

CHAPTER 4

2

1.5 1

0.5 0

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Deflection, in. A

Section A-A

Fig. 4.9.10 Resistance-deflection curve for example panel.

Fig. 4.9.9. Wall panel designed to resist blast load.

in Fig. 4.9.8 and Eq. 4-65, respectively. The ductility ratio is the ratio of maximum deflection under the applied blast load to the yield deflection. The value xE in Fig. 4.9.7 is typically used as the yield deflection for indeterminate components. The support rotation measures the approximate rotation at the supports and essentially relates the maximum deflection to the span of the component for the small angles that are allowed for blast design.

µ=

xm xe

(Eq. 4-65)

where: µ = ductility ratio xm = maximum component deflection xe = deflection causing yield of determinate component or yield of equivalent elastic slope of indeterminate component (Fig. 4.9.7) Maximum support rotation and ductility ratio values allowed for design are based on guidelines established by government and industry committees that have available blast data showing how these parameters correspond to observed component damage and the desired level of protection for the building. Often, the allowable support rotation and ductility ratio are limited to no more than one-half of the values corresponding to failure for design, implying a safety factor of at least 2.0. Based on testing and analysis, the support rotation correlates much better with failure for conventionally reinforced concrete, while the ductility ratio correlates better with failure for prestressed concrete. Allowable support rotations for blast design of reinforced-concrete components are typically in the range of 2 deg to 4 deg. This corresponds to an allowable maximum dynamic deflection between 2.5 in. and 5.0 in. for a 12 ft span. Allowable ductility ratios for blast design

of prestressed concrete components are typically in the range of 1 to 3. For a 40 ft, prestressed concrete T-beam, this can correspond to an allowable maximum dynamic deflection between approximately 1.3 in. and 4 in., although this varies depending on the yield deflection and, therefore, the beam dimensions and prestressed steel area. Numerous references provide allowable support rotations and/or ductility ratios for design and that correspond to given component damage levels.38,39,44,45 In cases where allowable support rotations and/ or ductility ratios are provided for given component damage levels, a performance-based design approach can be used. Job-specific blast-design specifications also may prescribe the allowable support rotations and/or ductility ratios for given component types (that is, reinforced concrete or prestressed concrete). 4.9.5 Additional Design Considerations In almost all cases, the allowable deformation limits are based on assumed ductile flexural response for the component. Therefore, the shear capacity and connection capacity of blast-loaded components must be designed to exceed the ultimate resistance of the component based on flexural capacity. This is achieved if the component shear and connection capacities exceed the design reaction loads from a static load equal to the ultimate resistance of the component (2.56 psi in Fig. 4.9.10). This causes the required shear and connection capacities to typically be much higher than those required for conventional loads. The required shear capacity may necessitate shear reinforcement, although this is typically not necessary for precast/prestressed concrete slabs. Some government agencies state that shear strength of the component must exceed its design reaction load by 20%, otherwise a prescribed minimum amount of shear reinforcement must be provided. Typically, the component shear capacity is based on the static shear strength with no dynamic impact factor (DIF) and no strength-reduction factor. This is a conservative assump-

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  4

EXAMPLE 4.9.4 Blast Design Example Given: The precast concrete wall panel shown in Fig. 4.9.9 will be designed to resist a given blast load. The 4 ft width of the panel that spans vertically is assumed to carry the blast load from the full 8-ftwide panel, where the opening is covered with a blast-resistant window that transfers the full blast load into the panel on either side. The wall panel is reinforced with #4 Grade 60 vertical reinforcing bars at 12 in. on center at each face. The blast load is shown in Fig. 4.9.3. The design blast pressure will be assumed to have the shape shown in Fig. 4.9.1 with a peak pressure of 20.2 psi and impulse of 85 psi-msec. The minimum specified compression strength for the concrete is 5000 psi. Problem: Calculate the mass, spring stiffness, ultimate resistance, and resistance versus deflection relationship for the equivalent SDOF system in Eq. 4-64 representing the wall panel. Solve the equation of motion for the equivalent SDOF system to determine the deflection history and resistance history for the panel. Determine if the panel response will satisfy a design requirement that the maximum support rotation must not exceed 3 deg. _______________________________________________________________________________________ Solution: a) Calculate the mass per unit of blast-loaded area of the SDOF system m based on concrete weight γ, the thickness t, and the acceleration of gravity g. Conservatively, only include the concrete that spans across the full-loaded span and ignore the weight of the window in the opening. The load-mass factors that are generally available, including those in Table 4.9.2, are only applicable for mass that is uniformly distributed over the span length unless otherwise stated. m=

psi − ms2 γ t ⎛ 4 ⎞ (150 ) ( 0.5 ) ⎛ 4 ⎞ ⎜⎝ ⎟⎠ = ⎜⎝ ⎟⎠ = 674 −6 386e in. g 8 8

b) Calculate the dynamic moment capacity Mdu based on 1) the panel properties and 2) the dynamic yield strengths of the reinforcing steel and concrete from Eq. 4-62 and 4-63. The formula for Mdu is the same as for Mu in Chapter 5 of this handbook and ACI 318-05 using dynamic material strengths. This is also true for prestressed concrete.

fdy  = fyKeDIF = (60,000 psi)(1.1)(1.17) = 77,000 psi



fdc' = fc' DIF = (5000 psi)(1.19) = 5950 psi



Mdu ==

As fdy ⎛ As fdy ⎞ (0.8) (77,000 ) ⎛ ( 0.8) (77,000 ) ⎞ = d− − ⎜5 − = 6254 lb-in./in. b ⎜⎝ 1.7bfdc' ⎟⎠ 48 1.7 ( 48 ) (5950 ) ⎟⎠ ⎝

c) Calculate the ultimate resistance ru of the SDOF system causing the spring to yield. ru is equal to the uniform pressure load causing the applied moment in the example panel to equal Mdu. ru =ru

4–72

8M du 8 ( 6254 ) = 2.55 psi = 2 ( 99 )2

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EXAMPLE 4.9.4 Blast Design Example (cont.) d) Calculate the SDOF system spring stiffness per unit area of blast load K during elastic response to blast load using an average of the gross Ig and cracked moment of inertia Icr. Furthermore, the cracked moment of inertia is conservatively assumed to be negligible compared with the gross moment of inertia. The modulus of elasticity Ec is calculated from fc' as shown in Chapter 4 of this handbook and ACI 318-05.

Only the 4 ft width of the panel that is continuous over the span length provides stiffness. K=

(

' 384E cI avg 384 57,000 fc = 4 5b 4 5 ( 96 ) ( 99 )

) ⎡⎢0.5 ⎛ (48)(6) ⎜ ⎝

⎢⎣

12

3

⎞⎤ psi + 0 ⎟ ⎥ = 17.3 in. ⎠ ⎥⎦

e) Determine the resistance versus deflection relationship for the spring of the equivalent SDOF system representing the panel as shown in Fig. 4.9.10. f) Use a time-stepping numerical solution to the equation of motion (for example, Reference 46) for the equivalent SDOF system representing the panel to the blast load based on the SDOF spring and mass properties calculated previously. The elastic and plastic load-mass factors are 0.78 and 0.66, respectively, based on Table 4.9.2 and the fact that the panel has simple supports and a uniformly applied blast load. Figures 4.9.11 and 4.9.12 show the calculated deflection history and resistance history of the panel, respectively. g) Calculate the maximum support rotation θ based on the maximum component dynamic deflection xm from the deflection history in Fig. 4.9.10, and the span length . As shown in the following, θ = 2.83 < 3.0, and the design is acceptable.

θ = tan−1

2x m (2 ) (2.45 )  = 2.83 = tan−1  99

Displacement history

2.5

Displacement, in.

2 1.5 1 0.5 0 0

50

100

150 Time, msec

200

250

300

350

Fig. 4.9.11 Calculated deflection history for example panel. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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Resistance history

  4

3

Resistance (psi)

2 1 0 -1 -2 -3 0

50

100

150

200

250

300

350

Time, (ms)

Fig. 4.9.12 Calculated resistance history for example panel.

tion because there is some increase in the dynamic factor for shear.45 The capacity of connections for blast-loaded components is generally based on load and resistance factor design (LRFD) including a small DIF for the connection material strength, on the order of 1.05, since connections typically have high-strength steel and the DIF decreases with increasing steel strength.38,39 However, this DIF is often neglected. No load factor is used. The connection capacity for blast loading can also be based on 1.7 times the allowable connection capacity from allowable strength design (ASD), which should be nearly equivalent to the previously discussed loadresistant factor force-based design. These requirements for shear and connection capacity imply that the flexural resistance of blast-loaded components should not be over-designed such that the required shear and connection capacities are expensive or difficult to construct. The more the component relies on ductility or deflection past yield, within the allowable deformation limits to develop the required strain energy capacity to resist the blast load, the more economic and constructible the resulting design will generally be. In cases where these required shear and connection capacities cannot be provided, the ultimate resistance of the component must be based on the lower maximum applied load that can be resisted by the shear or connection capacity, and a significantly lower allowable design criteria may be allowed. Structural components initially respond inward, into the building, from the positive-phase blast load and then rebound out from the building, in a similar manner to a spring rebounding from a short-duration applied load. The negative phase of the blast load can accentuate the rebound response phase. During rebound, there is stress reversal at all maximum stress regions of the component. All compressive stress areas during inbound response become tensile stress regions during rebound and require sufficient reinforcing steel to prevent rebound failure. Also, the connections must have the capacity to resist reaction forces from component rebound response. 4–74

Often the maximum forces and stresses that develop during rebound are on the order of 70% to 80% of those during inbound response, although 100% is also possible. It is typical for blast design to provide equal reinforcing steel (symmetrical reinforcing at each face) and connection capacity for inbound and rebound responses. This implies that prestressed components with prestressing strands at mid-thickness are best for blast design, although draped or non-symmetric prestressing patterns can be used if adequate conventional reinforcing steel is used for rebound. This must be determined based on a dynamic analysis of component response to the blast load that models both inbound and rebound component response with a resistancedeflection relationship that has differing ultimate resistances for inbound and rebound response based on the corresponding dynamic moment capacities.

4.10

References

1. A  merican Society of Civil Engineers (ASCE). 2005. Minimum Design Loads for Buildings and Other Structures, including Supplement No. 2 (SEI/ASCE 7-05). Reston, VA: ASCE. 2. A  CI Committee 550. 2009. Guide to Emulating Castin-Place Detailing in Precast Concrete Structures (ACI 550.1R-09). Farmington Hills, MI: American Concrete Institute (ACI). 3. A  CI Committee 318. 2005. Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05). Farmington Hills, MI: ACI. 4. A  CI. 2001. Acceptance Criteria for Moment Frames Based on Structural Testing (T1.1-01) and Commentary (T1.1R-01). Farmington Hills, MI: ACI. 5. N  ational Earthquake Hazards Reduction Program. 2003. Recommended Provisions for Seismic Regulations for

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PCI DESIGN HANDBOOK/SEVENTH EDITION

ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES New Buildings and Other Structures (NEHRP 2003). Washington, DC: Building Seismic Safety Council. 6. A  CI Committee 318. 2008. Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R-08). Farmington Hills, MI: ACI. 7. A  CI. 2004. Acceptance Criteria for Special Unbonded Post-Tensioned Precast Structural Walls Based on Validation Testing (ITG-5.1-07). Farmington Hills, MI: ACI. 8. P  riestley, M. J., Nigel, S. Sritharan, J. R. Conley, and S. Pampanin. 1999. Preliminary Results and Conclusions from the PRESSS Five-Story Precast Concrete Test Building. PCI Journal, V. 44, No. 6 (November– December). 9. E  nglekirk, Robert E. 2002. Design-Construction of The Paramount — A 39-Story Precast Prestressed Concrete Apartment Building. PCI Journal, V. 47, No. 4 (July– August).

CHAPTER 4

Technical Report No. 65, Federal Construction Council, Building Research Advisory Board, Division of Engineering, National Research Council. Washington, DC: National Academy of Sciences. 20. S  chultz, A. E., and R. A. Magaña. 1996. Seismic Behavior of Connections in Precast Concrete Shear Walls. Mete A. Sozen Symposium, ACI Special Publication SP-162. J. K. Wight and M. E., Kreger, eds. Farmington Hills, MI: ACI. 21. P  recast/Prestressed Parking Structures: Recommended Practice for Design and Construction, MNL-129-98, Precast/Pre­stressed Concrete Institute, Chicago, IL, 1998. 22. D  esign and Typical Details of Connections for Precast and Prestressed Concrete, Second Edition, MNL-12388, Precast/Prestressed Concrete Institute, Chicago, IL, 1988.

10. I nternational Conference of Building Officials. 2006. International Building Code (IBC 2006). Falls Church, VA: International Conference of Building Officials.

23. A  ristizabal-Ochoa, J. Dario. 2002. Moment Restraint and Second-Order Analysis of a Cantilevered Precast Column Supported by an Isolated Footing. PCI Journal, V. 47, No. 6 (November–December).

11. I nternational Conference of Building Officials. 1997. Uniform Building Code (UBC 1997). Falls Church, VA: International Conference of Building Officials.

24. C  leland, Ned and S. K. Ghosh. 2007. Seismic Design of Precast/Prestressed Concrete Structures, MNL-140-07. Chicago, IL: PCI.

12. S  outhern Building Code Congress International. 1999. Standard Building Code (SBC 1999). Birmingham, AL: Southern Building Code Congress International.

25. A  CI. 1973. Response of Multistory Concrete Structures to Lateral Forces, Special Publication SP-36. Farmington Hills, MI: ACI.

13. B  uilding Officials and Code Administrators International. 1999. National Building Code (BOCA 1999). Country Club Hills, IL: Building Officials and Code Administrators International.

26. A  CI Committee 442. 1971. Response of Buildings to Lateral Forces. ACI Journal, V. 68, No. 2 (February).

14. G  hosh, S.K. and A. W. Domel Jr. 1992. Design of Concrete Buildings for Earthquake and Wind Forces. Skokie, IL: Portland Cement Association. 15. P  CA Notes on ACI 318-05 Building Code Requirements for Structural Concrete, with Design Applications; Portland Cement Association, Skokie, IL, 2005 16. S  peyer, Irwin J. 1976. Considerations for the Design of Precast Concrete Bearing Wall Buildings to Withstand Abnormal Loads. PCI Journal, V. 21, No. 2 (March– April). 17. K  lein, G. J. and Lindenberg, R. J. 2009, “Volume Change Response of Precast Buildings,” PCI Journal, V. 54, No. 4 (Fall). 18. K  lein, G. J. and Lindenberg, R. J. 2009. Volume Change Movement and Forces in Precast Concrete Buildings. Research Report, Precast/Prestressed Concrete Institute, Chicago, IL 19. S  tanding Committee on Structural Engineering of the Federal Construction Council, Building Research Advisory Board, Division of Engineering, National Research Council. 1974. Expansion Joints in Buildings,

27. P  ortland Cement Association (PCA). 1965. Design of Combined Frames and Shear Walls, Advanced Engineering Bulletin No. 14. Skokie, IL: Portland Cement Association. 28. F  intel, Mark, ed. 1965. Handbook of Concrete Engineering. 2nd edition. New York, NY: Van Nostrand Reinhold Company. 29. F  leischman, Robert B., K. T. Farrow, and K. Eastman. 2002. Seismic Performance of Perimeter LateralSystem Structures with Highly Flexible Diaphragms. Earthquake Spectra, V. 18, No. 2, May. 30. N  akaki, S. D. 2000. Design Guidelines: Precast and Cast-in-Place Concrete Diaphragms. Sacremento, CA: Earthquake Engineering Research Institute. 31. O  liva, M. G. 2000. Testing of the JVI Flange Connectors for Precast Concrete Double-Tee Systems. Madison, WI: University of Wisconsin. 32. R  odriquez, M. E., J. I. Restrepo, and A. J. Carr. 2002. Earthquake-Induced Floor Horizontal Accelerations in Buildings. Earthquake Engineering and Structural Dynamics, V. 31, no. 3: pp. 693-718.

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33. N  aeim, Farzad. 2001. The Seismic Design Handbook. 2nd Edition. Boston, MA: Kluwer Academic Publishers.

  4

34. P  CI. 1998. Manual for the Design of Hollow-Core Slabs, MNL-126-98. Chicago, IL: PCI. 35. C  leland, N. M., and S. K. Ghosh. 2002. Untopped Precast Concrete Diaphragms in High Seismic Applications. PCI Journal, V. 47, No. 6 (November–December). 36. N  ew Zealand Concrete Society and New Zealand Society for Earthquake Engineering. 1999. Guidelines for the Use of Structural Precast Concrete in Buildings, Second Edition. Christchurch, New Zealand: University of Canterbury. 37. U  .S. Department of Energy. 1992. A Manual for the Prediction of Blast and Fragment Loading on Structures, DOE/TIC 11268. Washington, DC: U.S. Department of Energy. 38. D  epartments of the Army, Navy, and the Air Force. 1969. Structures to Resist the Effects of Accidental Explosions, TM 5‑1300/NAVFAC P‑397/AFM 88‑22. 39. A  SCE. 1997. Design of Blast Resistant Buildings in Petrochemical Facilities. Reston, VA: ASCE. 40. C  ramsey, N., C. Naito. 2007. Analytical Assessment of the Blast Resistance of Precast, Prestressed Concrete Components. PCI Journal, V. 52, No. 6 (NovemberDecember). 41. P  CI Committee on Blast Resistance and Structural Integrity. Blast Design of Precast/Prestressed Components. Document currently in preparation. 42. B  iggs, J. M. 1964. Introduction to Structural Dynamics. New York, NY: McGraw-Hill Book Company. 43. M  orison, C. 2006. Dynamic Response of Walls and Slabs by Single-Degree-of-Freedom Analysis - A Critical Review and Revision. International Journal of Impact Engineering 32, pp. 1214–1247. 44. U  .S. Army Corps of Engineers. 2006. Single Degree of Freedom Structural Response Limits for Antiterrorism Design. Protective Design Center Technical Report PDC-TR 06-08. 45. U  . S. Department of Defense. 2002. Design and Analysis of Hardened Structures to Conventional Weapons Effects, UFC 3-340-01. Washington, DC: U.S. Department of Defense. 46. U  .S. Army Corps of Engineers. 2006. Methodology Manual for the Single Degree of Freedom Blast Effects Design Spreadsheets (SBEDS). Protective Design Center Technical Report PDC-TR 06-02.

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CHAPTER 4

Design Aids

Design Aid 4.11.1 Classification of Building and Other Structures for Importance Factors I a SEISMIC FACTOR

SNOW FACTOR

WIND FACTOR

I

 uildings and other structures that represent a low hazard to human B life in the event of failure including, but not limited to: • Agricultural facilities • Certain temporary facilities • Minor storage facilities

1.00

0.8

0.87c

II

Buildings and other structures except those listed in categories I, III, IV

1.00

1.0

1.00

III

 uildings and other structures that represent a substantial hazard to B human life in the event of failure including, but not limited to: • Buildings and other structures where more than 300 people congregate in one area • Buildings and other structures with elementary school, secondary school, or day-care facilities with a capacity greater than 250 • Buildings and other structures with a capacity greater than 500 for colleges or adult-education facilities • Healthcare facilities with a capacity of 50 or more resident patients but not having surgery or emergency-treatment facilities • Jails and detention facilities • Any other occupancy with an occupant load greater than 5000 • Power-generating stations, water treatment for potable water, wastewater treatment facilities and other public-utility facilities not included in category III • Buildings and other structures not included in category III containing sufficient quantities of toxic or explosive substances to be dangerous to the public if released

1.25

1.1

1.15

IV

 uildings and other structures designated as essential facilities includB ing, but not limited to: • Hospitals and other healthcare facilities having surgery or emergency treatment facilities • Fire, rescue and police stations and emergency vehicle garages • Designated earthquake, hurricane or other emer­gency shelters • Designated emergency preparedness, commun­ication, and operation centers and other facilities required or emergency response • Power-generated stations and other public-utility facilities required as emergency back-up facilities for category III structures • Structures containing highly toxic materials as defined by section 307 where the quantity of the material exceeds the maximum allowable quantity of Table 307.7(2) • Aviation control towers, air-traffic control centers and emergency aircraft hangars • Buildings and other structures having critical national-defense functions • Water-treatment facilities required to maintain water pressure for fire suppression

1.50

1.2

1.15

b

CATEGORY

NATURE OF OCCUPANCY

a. Source: IBC 2006, Table 1604.5 (Information same as SEI/ASCE 7-05, Table 1.1, 6.1, 7.4, 9.1.4). b. In hurricane-prone regions with V > 100 mph, I = 0.77.

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Design Aid 4.11.2 Ground Snow Loads

  4

In CS areas, site-specific class studies are required to establish ground snow loads. Extreme local variations in ground snow loads in these areas preclude mapping at this scale. Numbers in parenthesis represent the upper elevation limits in feet for the ground snow load values presented below. Sitespecific case studies are required to establish ground snow loads at elevations not covered. To convert lb/ft2 to kN/m2, multiply by 0.0479. To convert feet to meters, multiply by 0.3048. 0

100

200

300 miles

GROUND SNOW LOADS, pg FOR THE UNITED STATES (lb/ft2) Source: References 1 and 10.

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Design Aid 4.11.2 Ground Snow Loads (cont.)

  4

GROUND SNOW LOADS, pg FOR THE UNITED STATES (lb/ft2) Source: References 1 and 10.

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Design Aid 4.11.3 Snow Loading

  4

(a) Ground snow load for Alaska locations Pg

Location

Ib/ft2

kN/m2

Adak

30

1.4

Anchorage

50

Angoon

70

Barrow Barter Island

Location

Pg Ib/ft2

kN/m2

Galena

60

2.9

2.4

Gulkana

70

3.4

Homer

40

25

1.2

Juneau

35

1.7

Kenai

Bethel

40

1.9

Big Delta

50

2.4

Cold Bay

25

Cordova

100

Fairbanks Fort Yukon

Location

Pg Ib/ft2

kN/m2

Petersburg

150

7.2

3.4

St. Paul Islands

40

1.9

1.9

Seward

50

2.4

60

2.9

Shemya

25

1.2

70

3.4

Sitka

50

2.4

Kodiak

30

1.4

Talkeetna

120

5.8

Kotzebue

60

2.9

Unalakleet

50

2.4

1.2

McGrath

70

3.4

Valdez

160

7.7

4.8

Nenana

80

3.8

Whittier

300

14.4

60

2.9

Nome

70

3.4

Wrangell

60

2.9

60

2.9

Palmer

50

2.4

Yakutat

150

7.2

(b) Exposure factor Ce Terrain category Exposure B: Urban and suburban areas, wooded areas

Fully exposed

Exposure of roof partially exposed

Sheltered

0.9

1.0

1.2

Exposure C: All others

0.8

0.9

1.0

Exposure D: Flat, unobstructed areas outside hurricane-prone regions

0.9

1.0

1.1

Above the treeline in windswept areas

0.7

0.8

N/A

In Alaska, in areas where trees do not exist within a 2 mile (3 km) radius of the site.

0.7

0.8

N/A

The terrain category and roof exposure condition chosen shall be representative of the anticipated conditions during the life of the structure. An exposure factor shall be determined for each roof of a structure.

(c) Thermal factor Ct Ct

Thermal conditiona All structures except as indicated below

1.0

Structures kept just above freezing and others with cold, ventilated roofs in which the thermal resistance (R-value) between the ventilated space and the heated space exceeds 25(hr × ft2 × °F)/(Btu) (4.4 K m2/W)

1.1

Unheated structures and structures intentionally kept below freezing

1.2

a. These conditions shall be representative of the anticipated conditions during winters for the life of the structure.

(d) Windward and leeward drifting Wind Windward step

Windward drift

Leeward step

Leeward drift

Snow

Source: References 1 and 10.

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Design Aid 4.11.4 Snow Drifting

  4

(a) Confirguration of snow drifts u (leeward)

hc

Drift load

hd

Balanced snow load, pf hb w u (windward)

(b) Determination of drift height hd

hd , drift height (ft)

If u > 600 ft, use equation

u

Windward Ex. 4.2.2.1

Leeward

If u < 25ft, use u = 25 ft hd

pg , ground snow load (lb/ft 2 ) To convert lb/ft 2 to kN/m 2 , multiply by 0.0479 To convert feet to meters, multiply by 0.3048 Source: References 1 and 10.

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Design Aid 4.11.5 Basic Wind Speed, mph (m/s)1

  4

BASIC WIND SPEED

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Design Aid 4.11.5 Basic Wind Speed, mph (m/s)1 (cont.)

  4

Location Hawaii Puerto Rico Guam Virgin Islands American Samos

V mph 105 145 170 145 125

(m/s) (47) (65) (76) (65) (56)

Notes: 1. Values are nominal design 3 second gust wind speeds in miles per hour (m/s) at 33 ft (10 m) above ground for exposure C category 2. Linear interpolation between wind contours is permitted. 3. Islands and coastal areas outside the last contour shall use the last wind speed contour of the coastal area. 4. Mountainous terrain, gorges, ocean promontories, and special wind regions shall be examined for unusual wind conditions.

BASIC WIND SPEED

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Design Aid 4.11.6 Factors for Use with ASCE 7-05 Method 1 Wind Design1 (a) p  s30 for Eq. 4-5

horizontal

Basic wind speed, mph

walls

for

use

in

(c) A  djustment factor λ for building height and exposure

ps30

Mean roof height, H

Exposure B

C

D

15

1.00

1.21

1.47

20

1.00

1.29

1.55

25

1.00

1.35

1.61

Zone A

Zone C

85

11.5

7.6

90

12.8

8.5

100

15.9

10.5

30

1.00

1.40

1.66

1.05

1.45

1.70

110

19.2

12.7

35

120

22.8

15.1

40

1.09

1.49

1.74

45

1.12

1.53

1.78

50

1.16

1.56

1.81

55

1.19

1.59

1.84

60

1.22

1.62

1.87

130

26.8

17.8

140

31.1

20.6

150

35.7

23.7

Zone 4 ASCE 7-05, Fig. 6-3

(b) pnet30 for use in components and cladding

Zone 5 ASCE 7-05, Fig. 6-3

  4

Effective wind area, ft2

Basic wind speed, mph

10

20

50

100

500

85

13.0/–14.1

12.4/–13.5

11.6/–12.7

11.1/–12.2

9.7/–10.8

90

14.6/–15.8

13.9/–15.1

13.0/–14.3

12.4/–13.6

10.9/–12.1

100

18.0/–19.5

17.2/–18.7

16.1/–17.6

15.3/–16.8

13.4/–14.9

110

21.8/–23.6

20.8/–22.6

19.5/–21.3

18.5/–20.4

16.2/–18.1

120

25.9/–28.1

24.7/–26.9

23.2/–25.4

22.0/–24.2

19.3/–21.5

130

30.4/–33.0

29.0/–31.6

27.2/–29.8

25.9/–28.4

22.7/–25.2

140

35.3/–38.2

33.7/–36.7

31.6/–34.6

30.0/–33.0

26.3/–29.3

150

40.5/–43.9

38.7/–42.1

36.2/–39.7

34.4/–37.8

30.2/–33.6

85

13.0/–17.4

12.4/–16.2

11.6/–14.7

11.1/–13.5

9.7/–10.8

90

14.6/–19.5

13.9/–18.2

13.0/–16.5

12.4/–15.1

10.9/–12.1

100

18.0/–24.1

17.2/–22.5

16.1/–20.3

15.3/–18.7

13.4/–14.9

110

21.8/–29.1

20.8/–27.2

19.5/–24.6

18.5/–22.6

16.2/–18.1

120

25.9/–34.7

24.7/–32.4

23.2/–29.3

22.0/–26.9

19.3/–21.5

130

30.4/–40.7

29.0/–38.0

27.2/–34.3

25.9/–31.6

22.7/–25.2

140

35.3/–47.2

33.7/–44.0

31.6/–39.8

30.0/–36.7

26.3/–29.3

150

40.5/–54.2

38.7/–50.5

36.2/–45.7

34.4/–42.1

30.2/–33.6

Source: “Minimum Design Loads for Buildings and Other Structures,” SEI/ASCE 7-05, Fig. 6-2 and 6-3. Note: Method 1 applies only to enclosed buildings ≤ 60 ft in height. See Section 4.2.3 for other restrictions and design procedure. Assume flat roof (pitch < 5 deg).

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Design Aid 4.11.7 Site Classifications and Coefficients1,5,10

  4

(a) Site class definitions Site class

Average properties in top 100 ft, as per section 1615.1.5 Soil profile name

Soil shear wave velocity vs, ft/s

Standard penetration resistance N

Soil undrained shear strength su, lb/ft2

vs > 5,000

Not applicable

Not applicable

A

Hard rock

B

Rock

2,500 ≤ vs ≤ 5,000

Not applicable

Not applicable

C

Very dense soil and soft rock

1,200 ≤ vs ≤ 2,500

N > 50

su ≥ 2,000

D

Stiff soil profile

600 ≤ vs ≤ 1,200

15 ≤ N ≤ 15

1,000 ≤ su ≤ 2,000

E

Soft soil profile

vs > 600

N < 15

su < 1,000

E

F

—

Any profile with more than 10 ft of soil having following characteristics: 1. Plasticity index PI > 20; 2. Moisture content w ≥ 40%, and 3. U  ndrained shear strength su < 500 lb/ft2

—

1. A  ny profile containing soils having one or more of the following characteristics: Soils vulnerable to potential failure or collapse under seismic loading such as liquefiable soils, quick and highly organic clays, collapsible weakly cemented soils 2. Peats and/or highly organic clay (H > 10 ft of peat and/or highly organic clay where H = thickness soil) 3. Very high plasticity clays (H > 25 ft with plasticity index PI > 75) 4. Very thick soft/medium stiff clays (H > 120 ft)

(b) Site coefficient Fa Site class

Mapped spectral response acceleration at short periodsa Ss ≤ 0.25

Ss = 0.50

Ss = 0.75

Ss = 1.00

Ss = 1.25

A

0.8

0.8

0.8

0.8

0.8

B

1.0

1.0

1.0

1.0

1.0

C

1.2

1.2

1.1

1.0

1.0

D

1.6

1.4

1.2

1.1

1.0

E

2.5

1.7

1.2

0.9

0.9

F

Note b

Note b

Note b

Note b

Note b

a. Use straight line interpolation for intermediate values of mapped spectral acceleration at short period Ss. b. Site-specific geotechnical investigation and dynamic site response analyses shall be performed to determine appropriate values.

(c) Site coefficient Fv Site Class

Mapped spectral response acceleration at 1 sec periodsa S1 ≤ 0.1

S1 = 0.2

S1 = 0.3

S1 = 0.4

S1 = 0.5

A

0.8

0.8

0.8

0.8

0.8

B

1.0

1.0

1.0

1.0

1.0

C

1.7

1.6

1.5

1.4

1.3

D

2.4

2.0

1.8

1.6

1.5

E

3.5

3.2

2.8

2.4

2.4

F

Note b

Note b

Note b

Note b

Note b

a. Use straight line interpolation for intermediate values of mapped spectral acceleration at 1 sec period Si. b. Site-specific geotechnical investigation and dynamic site response analyses shall be performed to determine appropriate values.

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Design Aid 4.11.8 Design Coefficients and Factors for Precast Concrete Seismic-Force-Resisting Systems1,5,10

  4 Basic seismic-force-resisting system

Response modification coefficient R

System overstrength factor Ω0

Deflection amplification factor Cd

21/2

5

Structural systems limitations and building height (ft) limitationsa Seismic design category B

C

D

E

F

NL

NL

160

160

160

b

b

40b

Bearing wall systems Special reinforced concrete shear walls

5

Intermediate precast concrete shear walls

4

21/2

4

NL

NL

40

40

Ordinary precast concrete shear walls

3

21/2

3

NL

NP

NP

NP

NP

Special reinforced concrete shear walls

6

21/2

5

NL

NL

160

160

160

Intermediate precast concrete shear walls

5

21/2

41/2

NL

NL

40b

40b

40b

Ordinary precast concrete shear walls

4

21/2

4

NL

NP

NP

NP

NP

Special reinforced concrete moment frames

8

3

51/2

NL

NL

NL

NL

NL

Intermediate reinforced concrete moment frames

5

3

41/2

NL

NL

NP

NP

NP

Ordinary reinforced concrete moment frames

3

3

21/2

NL

NP

NP

NP

NP

Special reinforced concrete shear walls

7

21/2

51/2

NL

NL

NL

NL

NL

Ordinary reinforced concrete shear walls

6

21/2

5

NL

NL

NP

NP

NP

Special reinforced concrete shear walls

61/2

21/2

5

NL

NL

160

100

100

Ordinary reinforced-concrete shear walls

51/2

21/2

41/2

NL

NL

NP

NP

NP

Special reinforced concrete moment frames

21/2

11/4

21/2

35

35

35

35

25

Intermediate reinforced concrete moment frames

11/2

11/4

11/2

35

35

NP

NP

NP

1

11/4

1

35

NP

NP

NP

NP

Building frame systems

Moment frame systems

Dual system with special moment frames capable of resisting at least 25% of prescribed seismic forces

Dual system with intermediate moment frames capable of resisting at least 25% of prescribed seismic forces

Cantilevered column systems

Ordinary concrete moment frames

a. Heights are measured from the base of the structure. b. Increase in height to 45 ft is permitted for single-story warehouse facilities. Note: NL = not limited; NP = not permitted.

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Design Aid 4.11.9 Allowable Story Drift ∆a, in.1,5,10,a Seismic use group

Building

I or II

III

IV

Buildings, other than masonry shear walls or masonry wall frame buildings, four stories or less in height with interior walls, partitions, ceilings, and exterior walls systems that have been designed to accommodate the story drifts

0.025 hsxb

0.020 hsx

0.015 hsx

Masonry cantilever shear wall buildingsc

0.010 hsx

0.010 hsx

0.010 hsx

Other masonry shear wall buildings

0.007 hsx

0.007 hsx

0.007 hsx

Masonry wall frame buildings

0.013 hsx

0.013 hsx

0.010 hsx

All other buildings

0.020 hsx

0.015 hsx

0.010 hsx

  4

a. hsx is the story height below level x. b. There shall be no drift limit for single-story buildings with interior walls, partitions, ceilings, and exterior wall systems that have been designed to accommodate the story drifts. c. Buildings in which the basic structural system consists of masonry shear walls designed as vertical elements cantilevered from their base or foundation support that are so constructed that moment transfer between shear walls (coupling) is negligible.

Design Aid 4.11.10 Architectural Components Coefficients1,5,10 Component Amplification Factor ap

Component Response Modification Factor Rp

a. Plain (unreinforced) masonry walls

1.0

1.5

b. Other walls and partitions

1.0

2.5

a. Parapets and cantilever interior non-structural walls

2.5

2.5

b. Chimneys and stacks when laterally braced or supported by the structural frame

2.5

2.5

a. Parapets

1.0

2.5

b. Chimneys and stacks

1.0

2.5

c.

1.0

2.5

a. Wall element

1.0

2.5

b. Body of wall-panel connections

1.0

2.5

c.

1.25

1.0

a. Limited deformability elements and attachments

1.0

2.5

b. Low deformability elements or attachments

1.0

2.5

6. Penthouses (except when framed by an extension of the building frame)

2.5

3.5

7. Ceilings (see also IBC 2006 Section 1621.2.5)

1.0

2.5

Architectural Component or Element 1. Interior non-structural walls and partitions

2. Cantilever elements (unbraced or braced to structural frame below its center of mass)

3. Cantilever elements (braced to structural frame above its center of mass)

Exterior non-structural walls

4. Exterior non-structural wall elements and connections

Fasteners of the connection system

5. Veneer

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Design Aid 4.11.11 Maximum Seasonal Climatic Temperature Change, °F

  4

Design Aid 4.11.12 Annual Average Ambient Relative Humidity, Percent

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Design Aid 4.11.13 Creep and Shrinkage Strains, Millionths in./in. Concrete release strength = 3500 psi

  4

Average prestress = 600 psi Relative humidity = 70% Volume-to-surface ratio = 1.5 in. Time, days

Creep

Shrinkage

Normalweight

Lightweight

Moist Cure

29

43

16

9

51 65 76 86 90 118 137 150 161 169 177 183 188 193 222 244 273 283 315

76 97 114 127 133 176 204 224 239 252 263 272 280 287 331 363 407 422 468

44 70 93 115 124 204 258 299 329 354 373 390 403 415 477 511 543 549 560

26 43 58 72 78 136 180 215 243 266 286 302 317 329 400 443 486 495 510

1 3 5 7 9 10 20 30 40 50 60 70 80 90 100 200 1 year 3 year 5 year Final

Accelerated Cure

Design Aid 4.11.14 Correction Factors for Prestress and Concrete Strength, Creep Only Average P/A, psi 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000

Release Strength, f c' i (psi) 2500

3000

3500

4000

4500

5000

6000

0.00 0.39 0.79 1.18 1.58 1.97 2.37 2.76

0.00 0.36 0.72 1.08 1.44 1.80 2.16 2.52 2.88 3.24

0.00 0.33 0.67 1.00 1.33 1.67 2.00 2.33 2.67 3.00 3.12

0.00 0.31 0.62 0.94 1.25 1.56 1.87 2.18 2.49 2.81 3.12 3.43 3.74

0.00 0.29 0.59 0.88 1.18 1.47 1.76 2.06 2.35 2.65 2.94 3.23 3.53 3.82

0.00 0.28 0.56 0.84 1.12 1.39 1.67 1.95 2.23 2.51 2.79 3.07 3.35 3.63 3.90 4.18

0.00 0.25 0.51 0.76 1.02 1.27 1.53 1.78 2.04 2.29 2.55 2.80 3.06 3.31 3.56 3.82

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CHAPTER 4

Design Aid 4.11.15 Correction Factors for Relative Humidity (RH)

  4

Average ambient RH (from Design Aid 4.11.12)

Creep

Shrinkage

40

1.25

1.43

50

1.17

1.29

60

1.08

1.14

70

1.00

1.00

80

0.92

0.86

90

0.83

0.43

100

0.75

0.00

Design Aid 4.11.16 Correction Factors for Volume-to-Surface (V/S) Ratio Time, days

Creep

Shrinkage

V/S

V/S

1

2

3

4

5

6

1

2

3

4

5

6

1 3 5 7 9

1.30 1.29 1.28 1.28 1.27

0.78 0.78 0.79 0.79 0.80

0.49 0.50 0.51 0.51 0.52

0.32 0.33 0.33 0.34 0.35

0.21 0.22 0.23 0.23 0.24

0.15 0.15 0.16 0.16 0.17

1.25 1.24 1.23 1.23 1.22

0.80 0.80 0.81 0.81 0.82

0.50 0.51 0.52 0.52 0.53

0.31 0.31 0.32 0.33 0.34

0.19 0.19 0.20 0.20 0.21

0.11 0.11 0.12 0.12 0.12

10 20 30 40 50

1.26 1.23 1.21 1.20 1.19

0.80 0.82 0.83 0.84 0.85

0.52 0.56 0.58 0.60 0.62

0.35 0.39 0.41 0.44 0.46

0.24 0.27 0.30 0.32 0.34

0.17 0.19 0.21 0.23 0.25

1.21 1.19 1.17 1.15 1.14

0.82 0.84 0.85 0.86 0.87

0.53 0.57 0.59 0.62 0.63

0.34 0.37 0.40 0.42 0.44

0.21 0.23 0.26 0.28 0.29

0.13 0.14 0.16 0.17 0.19

60 70 80 90 100

1.18 1.17 1.16 1.16 1.15

0.86 0.86 0.87 0.87 0.87

0.64 0.65 0.66 0.67 0.68

0.48 0.49 0.51 0.52 0.53

0.36 0.37 0.39 0.40 0.42

0.26 0.28 0.29 0.31 0.32

1.13 1.12 1.12 1.11 1.11

0.88 0.88 0.89 0.89 0.89

0.65 0.66 0.67 0.68 0.69

0.46 0.48 0.49 0.50 0.51

0.31 0.32 0.34 0.35 0.36

0.20 0.21 0.22 0.23 0.24

200 1 year 3 year 5 year Final

1.13 1.10 1.10 1.10 1.09

0.90 0.91 0.92 0.92 0.93

0.74 0.77 0.81 0.82 0.83

0.61 0.67 0.73 0.75 0.77

0.51 0.58 0.67 0.70 0.74

0.42 0.50 0.62 0.66 0.72

1.08 1.07 1.06 1.06 1.05

0.92 0.93 0.94 0.94 0.95

0.75 0.79 0.82 0.83 0.85

0.59 0.64 0.71 0.72 0.75

0.44 0.50 0.59 0.61 0.64

0.31 0.38 0.47 0.49 0.54

Design Aid 4.11.17 Design Temperature Strains, Millionths Normalweight

Lightweight

Temperature zone (from Design Aid 4.11.11)

Heated

Unheated

Heated

Unheated

10 20 30

30 60 90

45 90 135

25 50 75

38 75 113

40 50 60

120 150 180

180 225 270

100 125 150

150 188 225

70 80 90 100

210 240 270 300

315 360 405 450

175 200 225 250

263 300 338 375

Note: Based on accepted coefficients of thermal expansion, reduced to account for thermal lag. 1

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CHAPTER 4

Design Aid 4.11.18 Volume-Change Strains for Typical Building Elements (Prestressed Components), Millionths Temperature zone (from map)

Prestressed components (P/A = 600 psi) Normalweight concrete Lightweight concrete Average relative humidity (from map) Average relative humidity (from map) 40 50 60 70 80 40 50 60 70 80 Heated buildings

0 10 20 30 40 50 60 70 80 90 100

548 578 608 638 668 698 728 758 788 818 848

501 531 561 591 621 651 681 711 741 771 801

454 484 514 544 574 604 634 664 694 724 754

0 10 20 30 40 50 60 70 80 90 100

548 593 638 683 728 773 818 863 908 953 998

501 546 591 636 681 726 771 816 861 906 951

454 499 544 589 634 679 724 769 814 859 904

407 437 467 497 527 557 587 617 647 677 707

360 390 420 450 480 510 540 570 600 630 660

581 606 631 656 681 706 731 756 781 806 831

532 557 582 607 632 657 682 707 732 757 782

483 508 533 558 583 608 633 658 683 708 733

434 459 484 509 534 559 584 609 634 659 684

385 410 435 460 485 510 535 560 585 610 635

581 619 656 694 731 769 806 844 881 919 956

532 570 607 645 682 720 757 795 832 870 907

483 521 558 596 633 671 708 746 783 821 858

434 472 509 547 584 622 659 697 734 772 809

385 423 460 498 535 573 610 648 685 723 760

Unheated structures 407 452 497 542 587 632 677 722 767 812 857

360 405 450 495 540 585 630 675 720 765 810

Design Aid 4.11.19 Volume-change Strains for Typical Building Elements (Non-Prestressed Components), Millionths Temperature zone (from map)

Non-prestressed components Normalweight concrete Lightweight concrete Average relative humidity (from map) Average relative humidity (from map) 40 50 60 70 80 40 50 60 70 80 Heated buildings

0 10 20 30 40 50 60 70 80 90 100

294 324 354 384 414 444 474 504 534 564 594

265 295 325 355 385 415 445 475 505 535 565

235 265 295 325 355 385 415 445 475 505 535

0 10 20 30 40 50 60 70 80 90 100

294 339 384 429 474 519 564 609 654 699 744

265 310 355 400 445 490 535 580 625 670 715

235 280 325 370 415 460 505 550 595 640 685

206 236 266 296 326 356 386 416 446 476 506

177 207 237 267 297 327 357 387 417 447 477

294 319 344 369 394 419 444 469 494 519 544

265 290 315 340 365 390 415 440 465 490 515

235 260 285 310 335 360 385 410 435 460 485

206 231 256 281 306 331 356 381 406 431 456

177 202 227 252 277 302 327 352 377 402 427

294 332 369 407 444 482 519 557 594 632 669

265 302 340 377 415 452 490 527 565 602 640

235 273 310 348 385 423 460 498 535 573 610

206 244 281 319 356 394 431 469 506 544 581

177 214 252 289 327 364 402 439 477 514 552

Unheated structures 206 251 296 341 386 431 476 521 566 611 656

177 222 267 312 357 402 447 492 537 582 627

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CHAPTER 4

Design Aid 4.11.20 Length of Structure Without Use of Expansion Joints19

See modification factors below

Length between expansion joints, ft

  4

Rectangular, multifaceted configuration with symmetrical stiffness Non-rectangular configurations

Seasonal temperature change, o F (From Design Aid 4.11.1)

These curves are directly applicable to buildings of beam-and-column construction, hinged at the base, and with heated interiors. When other conditions prevail, the following rules are applicable: (a) If the building will be heated only and will have hinged-column bases, use the length as specified; (b) If the building will ever be air conditioned as well as heated, increase the length by 15% (provided the environmental control system will run continuously); (c) If the building will be unheated, decrease the length by 33%; (d) If the building will have fixed-column bases, decrease the length by 15%; (e) If the building will have substantially greater stiffness against lateral displacement at one end of the plan dimension, decrease the length by 25%. When more than one of these design conditions prevail in a building, the percentile factor to be applied should be the algebraic sum of the adjustment factors of all the various applicable conditions. Note: Design Aid 4.11.20 should be used as a preliminary guideline for the spacing of expansion joints. It should not be used as the absolute, authoritative, or sole means of determining the spacing of expansion joints. The spacing of expansion joints should be determined by the designer, based on analysis or experience, for the structure being considered.

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Design Aid 4.11.21 Build-Up of Restraint Forces in Beams kb

  4 ∆2 = δes2

∆1 = δes1

∆3 = δes3 Center of stiffness F2 F2

F1 F 1 M1

F3 F3 M3

M2 i=1

M1

i=2

F1

i=3 M3

M2

F2 - F1

F3 - F2 s1

s3

s2

Values of kb (see Design Aid 4.11.25) Total number of bays n

Number of bays from end i 1

2

3

4

5

6

7

8

2

1.00

3

1.00

4.00

4

1.00

3.00

5

1.00

2.67

9.00

6

1.00

2.50

6.00

7

1.00

2.40

5.00

16.00

8

1.00

2.33

4.50

10.00

9

1.00

2.29

4.20

8.00

25.00

10

1.00

2.25

4.00

7.00

15.00

11

1.00

2.22

3.86

6.40

11.67

36.00

12

1.00

2.20

3.75

6.00

10.00

21.00

13

1.00

2.18

3.67

5.71

9.00

16.00

49.00

14

1.00

2.17

3.60

5.50

8.33

13.50

28.00

15

1.00

2.15

3.55

5.33

7.86

12.00

21.00

64.00

16

1.00

2.14

3.50

5.20

7.50

11.00

17.50

36.00

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Design Aid 4.11.22 Equivalent Volume-Change Strains for Typical Building Elements (Prestressed Components), Millionths

  4

Temperature zone (from map)

Prestressed components (P/A = 600 psi) Normalweight concrete Lightweight concrete Average relative humidity (from map) Average relative humidity (from map) 40 50 60 70 80 40 50 60 70 80 Heated buildings

0 10 20 30 40 50 60 70 80 90 100

110 130 150 170 190 210 230 250 270 290 310

100 120 140 160 180 200 220 240 260 280 300

91 111 131 151 171 191 211 231 251 271 291

0 10 20 30 40 50 60 70 80 90 100

110 140 170 200 230 260 290 320 350 380 410

100 130 160 190 220 250 280 310 340 370 400

91 121 151 181 211 241 271 301 331 361 391

81 101 121 141 161 181 201 221 241 261 281

72 92 112 132 152 172 192 212 232 252 272

116 133 150 166 183 200 216 233 250 266 283

106 123 140 156 173 190 206 223 240 256 273

97 113 130 147 163 180 197 213 230 247 263

87 104 120 137 154 170 187 204 220 237 254

77 94 110 127 144 160 177 194 210 227 244

116 141 166 191 216 241 266 291 316 341 366

106 131 156 181 206 231 256 281 306 331 356

97 122 147 172 197 222 247 272 297 322 347

87 112 137 162 187 212 237 262 287 312 337

77 102 127 152 177 202 227 252 277 302 327

Unheated structures 81 111 141 171 201 231 261 291 321 351 381

72 102 132 162 192 222 252 282 312 342 372

Design Aid 4.11.23 Equivalent Volume-Change Strains for Typical Building Elements (Non-Prestressed Components), Millionths Temperature zone (from map)

4–94

Non-prestressed components Normalweight concrete Lightweight concrete Average relative humidity (from map) Average relative humidity (from map) 40 50 60 70 80 40 50 60 70 80 Heated buildings

0 10 20 30 40 50 60 70 80 90 100

59 79 99 119 139 159 179 199 219 239 259

53 73 93 113 133 153 173 193 213 233 253

47 67 87 107 127 147 167 187 207 227 247

0 10 20 30 40 50 60 70 80 90 100

59 89 119 149 179 209 239 269 299 329 359

53 83 113 143 173 203 233 263 293 323 353

47 77 107 137 167 197 227 257 287 317 347

41 61 81 101 121 141 161 181 201 221 241

35 55 75 95 115 135 155 175 195 215 235

59 76 92 109 126 142 159 176 192 209 226

53 70 86 103 120 137 153 170 186 203 220

47 64 80 97 114 130 147 164 180 197 214

41 58 75 91 108 125 141 158 175 191 208

35 52 69 85 102 119 135 152 169 185 202

59 84 109 134 159 184 209 234 259 284 309

53 78 103 128 153 178 203 228 253 278 303

47 72 97 122 147 172 197 222 247 272 297

41 66 91 116 141 166 191 216 241 266 291

35 60 85 110 135 160 185 210 235 260 285

Unheated structures 41 71 101 131 161 191 221 251 281 311 341

35 65 95 125 155 185 215 245 275 305 335

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CHAPTER 4

Design Aid 4.11.24 C  oefficients kf and km for Forces and Moments Caused by Volume-Change Restraint Forces

  4

See Design Aid 4.11.25 for notation No. of Stories

Kr ΣEbIb /l ________ ΣEcIc /hs 0.0

0.5

1

1.0

2.0 4.0 or more 0.0

0.5

2

1.0

2.0 4.0 or more 0.0

0.5

3 1.0

or more 2.0 4.0 or more

Base Fixity Fixed

Values of kf F1

F2

3.0

3.0

F3

Values of km F4

2nd floor

Base M1

M2L

3.0

0.0

Pinned

0.0

0.0

0.0

0.0

Fixed

6.0

6.0

4.0

2.0

Pinned

1.2

1.2

0.0

1.2

Fixed

7.5

7.5

4.5

3.0

Pinned

1.7

1.7

0.0

1.7

3rd floor

M2U

M3L

2.6

0.0

Fixed

9.0

9.0

5.0

4.0

Pinned

2.2

2.2

0.0

2.2

Fixed

10.1

10.1

5.4

4.7

Pinned

2.5

2.5

0.0

2.5

Fixed

6.8

9.4

2.6

4.3

2.6

Pinned

0.0

3.0

1.5

0.0

1.5

1.5

0.0

Fixed

8.1

10.7

2.6

4.7

3.4

2.1

0.4

Pinned

1.9

3.4

1.4

0.0

1.9

1.2

0.2

Fixed

8.9

11.2

2.3

4.9

3.9

1.8

0.5

Pinned

2.1

3.4

1.3

0.0

2.1

1.0

0.3

Fixed

9.7

11.6

1.9

5.2

4.5

1.4

0.5

Pinned

2.4

3.4

1.0

0.0

2.4

0.8

0.3

Fixed

10.4

11.9

1.4

5.5

5.0

1.0

0.4

Pinned

2.6

3.4

0.8

0.0

2.6

0.5

0.2

Fixed

7.1

10.6

4.1

4.4

2.8

2.8

0.7

0.70

4th floor

M3U

M4

0.70

0.00

Pinned

1.6

3.6

2.4

0.40

0.0

1.6

1.6

0.4

0.40

0.00

Fixed

8.2

11.1

3.5

0.50

4.7

3.5

2.2

0.7

0.40

0.09

Pinned

1.9

3.6

1.9

0.30

0.0

1.9

1.2

0.4

0.20

0.05

Fixed

8.9

11.4

2.9

0.40

5.0

3.9

1.9

0.7

0.30

0.09

Pinned

2.2

3.5

1.6

0.20

0.0

2.2

1.0

0.4

0.20

0.05

Fixed

9.7

11.7

2.2

0.20

5.2

4.7

1.4

0.6

0.20

0.06

Pinned

2.4

3.5

1.2

0.10

0.0

2.4

0.8

0.3

0.10

0.03

Fixed

10.4

11.9

1.5

0.04

5.5

5.0

1.0

0.5

0.04

0.01

Pinned

2.6

3.4

0.8

0.02

0.0

2.6

0.5

0.2

0.02

0.00

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Design Aid 4.11.25 Use of Design Aid 4.11.24

  4 ∆i

F4 M4 hs

∆i

M3U F3

F3 M3

M3L

hs

∆i

hs M2U

M2U F2 M2L

M2 hs

M2L

hs M1

hs M1

M1 F1

F1

where:

kf , km kb

Ec Ic

4–96

F2

F2

F1

Equivalent unit strain (see Section 4.4) Distance from column to center of stiffness F 1 , F 2 , etc., as shown above Coefficients from Design Aid 4.11.24 n +1 – i ) (or from Design Aid 4.11.21) i ( n +2 – 2i Number of bays As shown in Design Aid 4.11.21 Modulus of elasticity of the column concrete Moment of inertia of the column

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CHAPTER 4

Design Aid 4.11.26 Shear-Wall Deflection Deflection due to

Case



Equivalent moment of Inertia Ieq

Flexure

Shear

Single story

Ph 3 3EI

2.78Ph Aw E

l 8.34l 1+ Aw h 2

l 13.4l 1+ Aw h 2

Not applicable

l 23.6l 1+ Aw h 2

(Aw = lt)

Wh 3 8EI

1.39Wh Aw E

W = wh

W = wh

Ph 3 12EI

2.78Ph Aw E





PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

l 33.4l 1+ Aw h 2

Multistory

Not applicable

4–97

  4

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ANALYSIS AND DESIGN OF PRECAST/PRESTRESSED CONCRETE STRUCTURES

  4

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

CHAPTER 5

  5

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS 5.1

Introduction.................................................................................................................................................................5-3

5.2

Flexure........................................................................................................................................................................ 5-3 5.2.1 Strength Design............................................................................................................................................ 5-3 5.2.1.1 Depth of Stress Block.................................................................................................................5-3 5.2.1.2 Flanged Components..................................................................................................................5-3 5.2.1.3 Strength-Reduction Factors........................................................................................................5-5 5.2.1.4 Limitations on Reinforcement....................................................................................................5-5 5.2.1.5 Critical Section...........................................................................................................................5-5 5.2.1.6 Analysis Using ACI 318-05 Equations.......................................................................................5-6 5.2.1.7 Analysis Using Strain Compatibility..........................................................................................5-6 5.2.1.8 Use of Design Aids.................................................................................................................... 5-6 5.2.2 Service Load Design.................................................................................................................................. 5-16 5.2.2.1 Non-Prestressed Component Design........................................................................................5-16 5.2.2.2 Prestressed Component Design............................................................................................... 5-18 5.2.3 Prestress Transfer and Strand Development.............................................................................................. 5-35 5.2.3.1 Strand Debonding.................................................................................................................... 5-40 5.2.4 End Stresses at Transfer..............................................................................................................................5-40 5.2.5 Bending of Asymmetrical Sections............................................................................................................ 5-41 5.2.5.1 Section Properties ....................................................................................................................5-41 5.2.5.2 Service Load Stresses...............................................................................................................5-41 5.2.5.3 Flexural Design Strength..........................................................................................................5-46

5.3

Shear..........................................................................................................................................................................5-46 5.3.1 Shear Resistance of Non-Prestressed Components.....................................................................................5-46 5.3.2 Shear Resistance of Prestressed Components.............................................................................................5-46 5.3.3 Use of Design Aids.....................................................................................................................................5-52 5.3.4 Shear Reinforcement...................................................................................................................................5-52 5.3.5 Horizontal Shear Transfer in Composite Components...............................................................................5-52 5.3.6 Shear Friction............................................................................................................................................. 5-58

5.4

Torsion.......................................................................................................................................................................5-59

5.5

Beams with Ledges....................................................................................................................................................5-68 5.5.1 Shear Strength of Ledge..............................................................................................................................5-68 5.5.2 Transverse (Cantilever) Bending of Ledge.................................................................................................5-68 5.5.3 Longitudinal Bending of Ledge..................................................................................................................5-69 5.5.4 Attachment of Ledge to Web......................................................................................................................5-69 5.5.5 Out-of-Plane Bending near Beam End........................................................................................................5-70 5.5.6 Pocketed Spandrels.................................................................................................................................... 5-70

5.6

Bearing......................................................................................................................................................................5-77 5.6.1 Bearing on Plain Concrete..........................................................................................................................5-77 5.6.2 Reinforced Concrete Bearing......................................................................................................................5-77 5.6.3 Dapped-End Bearing.................................................................................................................................. 5-79 5.6.3.1 Flexure and Axial Tension in Extended End............................................................................5-79 5.6.3.2 Direct Shear..............................................................................................................................5-79 5.6.3.3 Diagonal Tension at Re-entrant Corner....................................................................................5-83 5.6.3.4 Diagonal Tension in Extended End..........................................................................................5-83

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

  5

5.6.3.5 5.6.3.6

Anchorage of Reinforcement....................................................................................................5-83 Other Considerations............................................................................................................... 5-83

5.7

Loss of Prestress....................................................................................................................................................... 5-83 5.7.1 Sources of Stress Loss.................................................................................................................................5-83 5.7.2 Range of Values for Total Loss..................................................................................................................5-84 5.7.3 Estimating Prestress Loss............................................................................................................................5-84 5.7.4 Critical Locations....................................................................................................................................... 5-87

5.8

Camber and Deflection............................................................................................................................................. 5-87 5.8.1 Initial Camber.............................................................................................................................................5-88 5.8.2 Elastic Deflections......................................................................................................................................5-88 5.8.3 Bilinear Behavior....................................................................................................................................... 5-90 5.8.3.1 Cracked-Section Analysis........................................................................................................ 5-90 5.8.4 Long-Term Camber/Deflection...................................................................................................................5-90 5.8.5 Bowing....................................................................................................................................................... 5-96

5.9

Compression Components........................................................................................................................................ 5-99 5.9.1 Strength Design of Precast Concrete Compression Components...............................................................5-99 5.9.2 Eccentrically Loaded Columns.................................................................................................................5-105 5.9.3 Slenderness Effects in Columns and Wall Panels....................................................................................5-106 5.9.3.1 Second-Order (P-∆) Analysis................................................................................................5-106 5.9.4 Concrete Brackets or Corbels..................................................................................................................5-110 5.9.4.1 Cantilever Beam Design Method........................................................................................... 5-110 5.9.4.2 Strut-and-Tie Design Method................................................................................................ 5-112 5.9.4.2.1 Bearing Area....................................................................................................... 5-112 5.9.4.2.2 Truss Geometry................................................................................................... 5-112 5.9.4.2.3 Horizontal Stirrups.............................................................................................. 5-112 5.9.4.3 Comparison of Corbel Design Methods................................................................................ 5-115 5.9.4.4 Development of Corbel Reinforcement.. ............................................................... 5-115 5.9.5 Effective Width of Wall Panels................................................................................................................5-116 5.9.6 Varying Section Properties of Compression Components........................................................................5-116 5.9.7 Piles...........................................................................................................................................................5-116 5.9.7.1 Service-Load Design..............................................................................................................5-116 5.9.7.2 Strength Design......................................................................................................................5-116 5.9.7.3 Other Considerations.............................................................................................................5-116

5.10

Shear Walls.............................................................................................................................................................5-122

5.11

Sandwich Panels......................................................................................................................................................5-122 5.11.1 General......................................................................................................................................................5-122 5.11.2 Structural Design.......................................................................................................................................5-122 5.11.3 Panel Connections.....................................................................................................................................5-126 5.11.4 Wythe Connectors.....................................................................................................................................5-127 5.11.5 Thermal Bowing.......................................................................................................................................5-128 5.11.6 Typical Details..........................................................................................................................................5-128

5.12

Special Considerations...........................................................................................................................................5-128 5.12.1 Point Loads on Double-Tee Flanges.........................................................................................................5-128 5.12.2 Effective Resisting Widths for Concentrated Loads on Hollow-Core Decks...........................................5-128 5.12.3 Openings through Decks...........................................................................................................................5-128 5.12.4 Openings through Webs............................................................................................................................5-129 5.12.5 Continuity..................................................................................................................................................5-133 5.12.6 Cantilevers................................................................................................................................................5-133 5.12.7 Warping of Deck Components.................................................................................................................5-133

5.13

References...............................................................................................................................................................5-135

5.14

Design Aids............................................................................................................................................................5-138

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

5.1

Introduction

This chapter provides a summary of theory and procedures used in the design of precast and prestressed concrete components. Designs are based on the provisions of Building Code Requirements for Structural Concrete (ACI 31805) and Commentary (ACI 318R-05),1 which is referred to as ACI 318-05 in this handbook. Occasionally, standard design practice may require interpretation of ACI 318-05. This has been done in Section 14.1, “PCI Standard Design Practice,” of this handbook and is used where applicable in this chapter. Two different phases must be considered in designing precast concrete components: the manufacturing through erection phase and the in-service conditions. The designer is referred to Chapter 8 for the first phase. This chapter discusses the in-service conditions. The load tables in Chapter 3 are intended for preliminary design and will not provide all the design data necessary. Whether responsibility for component selection lies with the Structural Engineer of Record or the specialty structural engineer, verification that the selected section is capable of satisfying both strength and serviceability criteria for the intended use is required. This chapter presents procedures to be followed to that end. Consultation with precast concrete producers will ensure compatibility of design with the producers’ production capabilities to ensure quality and economy. There are two critical component design considerations: • •

CHAPTER 5

Design strength must equal or exceed the demand resulting from the appropriate factored load combinations. Serviceability requirements must be satisfied.

5.2

Flexure

Design for flexure in accordance with ACI 318-05 requires that precast and prestressed concrete components be checked for both strength (ACI 318-05 Section 18.7) and serviceability requirements (ACI 318-05 Section 18.4). The spacing of nonprestressed flexural reinforcement shall not exceed that given in ACI 318-05 Section 10.6.4, and for Class C prestressed components with non-prestressed flexural reinforcement, ACI 318-05 Section 18.4.4.1. Also see Section 5.2.2 of this handbook. 5.2.1

0.85f'c d' c

Neutral axis

d dp Mn

Apsfps As fy For equilibrium at nominal resistance: 0.85f'c ba = Apsfps + Asfy − A's f'y Mn = Apsfps(dp − a/2) + Asfy(d − a/2) + A's f'y(a/2 − d' ) Fig. 5.2.1 Nominal flexural resistance.

For components with compression reinforcement, the nominal strength can be calculated by assuming that the compression reinforcement yields. This assumption should be subsequently verified from the strain diagram. The designer will normally choose a section and reinforcement and then determine if it meets the basic design strength requirement: φMn ≥ Mu A flowchart illustrating the calculation of the nominal strength of flexural components is given in Fig. 5.2.2. 5.2.1.1 Depth of Stress Block The depth a of the rectangular stress block is related to the depth to the neutral axis c by the equation: a = 1c where, by ACI 318-05 Section 10.2.7.3: 1

fc' , psi

Strength Design

Strength design is based on solution of the equa­tions of equilibrium, normally using the rectangular stress block in accordance with Section 10.2.7 of ACI 318-05 (Fig. 5.2.1). The stress in the bonded prestressing steel at nominal strength fps can be determined by strain compatibility2 or by the approximate equation given in the code (Eq. 18-3). In carrying out strain compatibility analyses, any stress-strain relationship that accurately represents the behavior of the strand may be used. An example of a stress-strain relationship that has been used successfully for many years is given in Design Aid 15.2.4. When using unbonded prestressing steel, strain compatibility is not valid, and fps should be determined using ACI 318-05 Eq. 18-4 and 18-5 accordingly.

A's f'y 0.85f'c ba

a

3000

0.85

4000

0.85

5000

0.80

6000

0.75

7000

0.70

8000 and higher

0.65

5.2.1.2 Flanged Components The equations for nominal strength given in Fig. 5.2.1 apply to rectangular cross sections and flanged sections in which the stress block lies entirely within the depth of the flange hf. The depth of the stress block a is obtained from the first equation of equilibrium in Fig. 5.2.1:

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

a=

Aps f ps + As f y − A's f y' 0.85 fc' b



(Eq. 5-1) 5–3

  5

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5 Start Yes

  5

Non-prestressed reinforcement only

No No

fse ≥ 0.5fpu

a

Determine fps by strain compatability (Design Aid 5.14.3)

Yes Yes

Span-to-depth ratio ≤ 35

f ps = fse + 10,000 +

f

' c

100 ρ p

f py ≥ f ps ≤ ( fse + 60, 000 )

No

Bonded element

No

d

Yes

f ps = fse + 10,000 +

⎛ γ fps = fpu ⎜ 1− p β1 ⎝

e

f

' c

Determine fps by strain compatabilityc (Design Aid 5.14.3) or

300 ρ p

⎡ fpu d ⎤⎞ ⎢ ρp ' + (ω − ω' ) ⎥⎟ ⎣ fc d p ⎦⎠

f py ≥ f ps ≤ ( fse + 30,000 ) b

A f + As fy − A's fy' a = ps ps 0.85fc' b Acomp = ab

b

No

Flanged section Revise a Af = (b - bw)hf Aw = Acomp - Af a = Aw/bw

Yes No

Design as a rectangular section

Yes

a ≤ hf

c = a/ß1 Yes Yes

c > 3d'

No

No

c/dt > 0.375

fs' < fy φ = 0.9

See Figure 5.2.3

Revise a Yes

Flanged section with a > hf

No

b

a⎞ ⎛ h M n = Aps fps d p + As fy d − A's fs' d ' − 0.85fc' ⎜ Af f + Aw ⎟ ⎝ 2 2⎠

b

a⎞ ⎛ M n = Aps fps ⎜ d p − ⎟ + As fy ⎝ 2⎠

a⎞ a ⎛ ' ' ⎛ ' ⎞ ⎜⎝ d − ⎟⎠ + As fs ⎜⎝ − d ⎟⎠ 2 2

a. This analysis may be based on either actual stress-strain curves or the idealized curve given in Design Aid 15.3.3. The latter results in fps values given in Design Aid 5.14.3. b. These equations assume a rectangular section. For other sections, reasonable approximations may be used. See also Fig. 5.9.1. c. Check strand development length. d, e, f. ACI 318-05 Eq. 18-4, 18-5, and 18-3, respectively.

Fig. 5.2.2 Flowchart of nominal strength calculations for flexure.

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS If a  >  hf, and compression reinforcement is present, use of strain compatibility or reasonable approximations for fps may be made to find the nominal strength. If compression reinforcement is not present, the nominal strength can be found using ACI 318-05 equations shown in Fig. 5.2.2 or by strain compatibility.

5.2.1.4 Limitations on Reinforcement For non-prestressed flexural components, except slabs of uniform thickness, the minimum reinforce­ment required is ACI 318-05 Eq. 10-3:

As ,min = 3

fc' fy

bw d ≥

200bw d fy

(Eq. 5-2)

For T-sections with flanges in tension, As,min is the smaller of that determined by Eq. 5-2, where bw is the width of the flange, or by:

As ,min =

6 fc' b d fy w

(Eq. 5-3)

where: bw = width of the web These limits do not apply if the area of ten­sile reinforcement provided is one-third greater than that required by analysis. For structural slabs of uniform thickness, the minimum flexural reinforcement is that amount required for shrinkage and temperature reinforcement, with a maximum spacing not exceeding three times the slab thickness or 18 in., whichever is smaller. For prestressed flexural components to ensure adequate

φ = 0.57 + 67εt

With spirals 0.90 0.70 0.65

5.2.1.3 Strength-Reduction Factors ACI 318-05 classifies prestressed and non-pre­stressed components as tension or compression con­trolled, and establishes the strength-reduction factor φ on that basis. A compression-controlled section is defined as one having a maximum net tensile strain in the extreme tension steel of 0.002 or less (for grade 60 [fy = 60 ksi] reinforcement and prestressing steel), and a tension-controlled section is defined as one having a maximum tensile strain in the steel of 0.005 or more. (In prestressed components, the strain limits are after the decompression.) Tension steel strains between 0.002 and 0.005 are referrred to as transition sections. The net tensile strain limits of 0.002 and 0.005 may also be expressed in terms of c/dt, where c is the depth to the neutral axis and dt is the distance from the extreme compression fiber to the tension steel farthest from that fiber. Figure 5.2.3 shows φ as a function of εt and c/dt. For the rectangular sections with one layer of tension steel, the net tensile strain limit of 0.005 corresponds to ω = 0.321. For flexural components, it is usually best to design sections of maximum moment to be tension con­trolled, adding compression steel, if necessary, to limit c/dt to 0.375. In the transition zone shown in Fig. 5.2.3, the reduction in φ cancels the benefits of higher amounts of reinforcement without balancing compression steel.

CHAPTER 5

  5 Other

φ = 0.48 + 83εt

φ 0.50 Compression controlled

Transition

Strain, εt = 0.002 c/dt = 0.600

Tension controlled 0.005 0.375

Transition, as function of c/dt Spiral φ = 0.37 + 0.20/(c/dt) other

φ = 0.23 + 0.25/(c/dt)

Fig. 5.2.3 Variation of φ with net tensile strain for Grade 60 reinforce­ment and for prestressing steel.

ductility, the ACI 318-05 requires that the total prestressed and non-prestressed reinforcement be adequate to develop a design strength of at least 1.2 times the cracking moment (φMn ≥ 1.2Mcr). This pro­vision is generally assumed to apply only at critical flexural sections, and is waived for components with shear and flexural strength of at least twice that required by analysis. The cracking moment Mcr may be calculated by:

⎛S ⎞ ⎡P Pe ⎤ M cr = Sbc ⎢ e + e + fr ⎥ − M nc ⎜ bc − 1⎟ (Eq. 5-4) ⎝ ⎠ Sb ⎣ A Sb ⎦

Note that compression components that are prestressed to a minimum level of 225 psi after all losses need not satisfy the Mcr requirement. where: Mnc = moment due to beam self-weight plus dead loads applied before composite action Sb = section modulus with respect to the bottom fiber of the precast concrete section Sbc = section modulus with respect to the bottom fiber of a composite section fr = Modulus of Rupture, for normalweight concrete defined in ACI 318-05 as 7.5 fc' . For other concretes, see ACI 318-05 Section 9.5.2.3 5.2.1.5 Critical Section For simply supported, uniformly loaded, prismatic nonprestressed components, the critical section for flexural design will occur at midspan. To reduce the end stresses at release for uniformly loaded prestressed components, some

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

Uniform load

  5

Uniform Load

Prestressed reinforcement

Prestressed reinforcement Strand development length (Section 5.2.3)

Critical section φMn

Critical section φMn

Debonded length Mu

Mu

(a) Beam with strands depressed at midpoint - uniform load

(b) Beam with straight strands some debonded near end

Fig. 5.2.4 Critical section for flexural design.

strands are often depressed near midspan or debonded for a length near the ends. For strands with a single-point depression, the critical section can usually be assumed at 0.4l. For straight strands, the critical section will be at midspan, but if some strands are debonded near the end, an additional critical section may occur near the end of the debonded length, as shown in Fig. 5.2.4. The presence of concentrated loads or non-prestressed reinforcement may alter the location of the critical section. In such cases, computer programs with the capability of checking the capacity at short intervals along the component length can be used to expedite the analysis. 5.2.1.6 Analysis Using ACI 318-05 Equations Figure 5.2.2 outlines the design procedures using the code equations for prestressed and partially prestressed components. If compression reinforcement is present, the code requires certain checks to ensure that the stress in the compression reinforcement is at its yield strength. When computing fps, if any compression reinforcement is taken into account, the term ⎡ f pu d ⎤ ω − ω' ⎥ ⎢ρp ' + fc d p ⎢⎣ ⎥⎦

(

)

should be taken not less than 0.17 and d' shall be no greater than 0.15dp. Alternatively, the yielding of the compression reinforcement is ensured if Eq. 5-5 is satisfied: Aps f ps + As f y − A's fs' bd



5–6

≥ 0.85β1 fc'

d' d

⎛ 87,000 ⎞ ⎜ ⎟ ⎝ 87,000 − f y ⎠

5.2.1.7 Analysis Using Strain Compatibility Strain compatibility provides a more accurate analysis than the code equations discussed previously. The procedure consists of assuming the location of the neutral axis, computing the strains in the prestressed and non-prestressed reinforcement, and establishing the depth of the stress block. Knowing the stress-strain relationship for the reinforcement, and assuming that the maximum strain in the concrete is 0.003, the forces in the reinforcement and in the concrete are determined and the sum of compression and tension forces is computed. If necessary, the neutral axis location is moved on a trial and adjustment basis until the sum of forces is zero. The moment of these forces is then computed to obtain the nominal strength of the section. 5.2.1.8 Use of Design Aids Design Aids 5.14.1 through 5.14.3 assist in the strength design of flexural components. Design Aid 5.14.1 can be used for components with prestressed or non-prestressed reinforcement or combinations (partial prestressing). Note that to use this aid, it is necessary to determine fps from some other source, such as Eq. 18-3 of ACI 318-05 or Design Aid 5.14.3. Design Aid 5.14.2 is only for use with fully pre­stressed components. The value of fps is determined by strain compatibility in a manner similar to that used in Design Aid 5.14.3. The strength-reduction factor φ is included in the values of K u' . Examples 5.2.1.1 through 5.2.1.4 illustrate the use of these design aids.

(Eq. 5-5)

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.2.1.1 Use of Design Aid 5.14.1 for Determination of Non-Prestressed Reinforcement Given: The ledger beam shown. Applied factored moment, Mu = 1460 kip-ft fc' = 5000 psi, normalweight d = 72 in. fy = 60 ksi

  5

Problem: Find the area of mild-steel reinforcement As required. _________________________________________________________________________________ Solution: Referring to Design Aid 5.14.1: Aps = 0 As' = 0 b = bw = 8 in.

8"

⎛ Mu ⎞ 1460 12,000 ⎜⎝ φ ⎟⎠ 0.9 Ku = ' 2 = = 0.0939 2 fc bd 5000 8 72

(

)

Note: Hanger, shear, and torsion steel not shown

( )( )

For tension controlled sections, ωmax = 0.256 ‒ = 0.10 < ωmax Required ω As =

6'-3" As

ω bdfc' 0.10 ( 8 ) ( 72 ) ( 5 ) = = 4.80 in.2 fy 60

Use (5) #9; As = 5.00 in.2 As,min =

or

3 fc' 3 5000 bw d = 8 72 = 2.04 in. 2 fy 60,000

1'-0"

( )( )

1'-4"

200bw d 200 ( 8 ) ( 72 ) = = 1.92 in. 2 fy 60,000

2.04 in.2 < 5.00 in.2

OK

Note: Detailing of reinforcement must provide for adequate crack control (see Section 5.2.2.1).

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.2.1.2 Use of Design Aid 5.14.2 for Determination of Prestressing Steel Requirements — Bonded Strand

  5

Given: PCI standard rectangular beam 16RB24 Applied factored moment, Mu = 600 kip-ft fc' = 6000 psi, normalweight fpu = 270 ksi, low-relaxation strand b = 16 in. Problem: Find the required area of prestressing steel Aps. _________________________________________________________________________________ Solution: Referring to Design Aid 5.14.2:

φM n =

K u' bd p2 12,000

Required KKu' u' ==

(

M u 12,000 bd

16"

kip-ft

) = 600 (12,000) = 1020 16 ( 21) 2

2 p

dp = 21"

for ωpu = 0.22, K u' = 1006 for ωpu = 0.23, K u' = 1043

24"

Therefore, by interpolation: ωpu

= 0.22 + 1020 − 1006 (0.01) = 0.224 1043 − 1006

Aps

=

ω pubd pfc' fpu

=

( )( ) ( )

0.224 16 21 6 270

= 1.67 in.2

Use (12) 1/2-in.-diameter strands; Aps = 1.84 in.2

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.2.1.3 Use of Design Aid 5.14.3 — Values of fps by Stress-Strain Relationship — Bonded Strand Given: 3 ft-4 in. × 8 in. hollow-core unit Concrete: Use 5000 psi, normalweight

  5

Prestressing steel: (8) 3/8-in.-diameter, 270 ksi, low-relaxation strands Aps = 8(0.085) = 0.68 in.2 Section properties: A = 218 in.2 Sb = 381 in.3 yb = 3.98 in. b = 40 in.

40" dp = 7"

11/4" 8"

Problem: Find design flexural strength φMn. _________________________________________________________________________________ Solution: Determine Cωpu for the section: From table on Design Aid 5.14.3: for fc' = 5000 psi, C = 1.06 Cωpu = C

Apsfpu bd pfc'

+

d ω − ω' dp

(

)

Since ω = ω’ = 0 Cωpu =

(

)( ) = 0.139 40 ( 7 )( 5 )

1.06 0.68 270

Entering Design Aid 5.14.3 with this parameter and an assumed effective stress fse of 170 ksi gives a value of: fps = 266 ksi Determine the flexural strength: ⎛ a⎞ Mn = φ Apsfps ⎜ d p − ⎟ 2⎠ ⎝ Apsfps

a

=



=

a

< flange thickness

c

= a = 1.064 = 1.33 in. β1 0.8

0.85fc' b

( ) = 1.064 in. ( )( )

0.68 266

0.85 5 40

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.2.1.3 Use of Design Aid 5.14.3 — Values of fps by Stress-Strain Relationship — Bonded Strand (cont.)

  5

c 1.33 = = 0.19 < 0.375 dp 7

tension controlled, φ = 0.9 ⎡ ⎛ 1.064 ⎞ ⎤ φMn = 0.9 (0.68 )( 266 ) ⎢ 7 − ⎜ ⎥ = 1053 kip-in. = 87.7 kip-ft ⎝ 2 ⎟⎠ ⎦ ⎣

Check the ductility requirement: φMn > 1.2Mcr Pe = fseAps = 170(0.68) = 116 kip e = 3 in. From Eq. 5-4: ⎛P P e ⎞ 1.2Mcr = 1.2 ⎜ e + e + 7.5 fc' ⎟ Sb ⎝ A Sb ⎠

⎛ 116 116 3 7.5 5000 ⎞ + + 1.2Mcr = 1.2 ⎜ ⎟ 381 = 903 kip-in. = 75.3 kip-ft < 87.7 kip-ft 381 1000 ⎠ ⎝ 218

( )

OK

EXAMPLE 5.2.1.4 Use of Design Aid 5.14.3 and Eq. 18-3 (ACI 318-05) for Partially Prestressed Component Given: PCI standard double-tee 8DT24 + 2 Concrete: Precast: fc' = 5000 psi, normalweight Topping: fc' = 3000 psi, normalweight Reinforcement: (12) 1/2-in.-diameter, 270 ksi, low-relaxation strands (six each stem) Aps = 12(0.153) = 1.84 in.2 As (2)#6 = 0.88 in.2 Problem: Find the design flexural strength of the composite section by the stress-strain relationship, Design Aid 5.14.3, and compare using ACI 318-05 Eq. 18-3. _________________________________________________________________________________

5–10

dp = 22.75"

d = 24.75"

b = 8'-0"

Aps

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2" 2"

24"

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.2.1.4 Use of Design Aid 5.14.3 and Eq. 18-3 (ACI 318-05) for Partially Prestressed Component (cont.)

  5

Solution: Assume fse = 170 ksi Since fse > 0.5fpu, ACI 318-05 equation may be used. Cωpu = C

ω

=

Cωpu =

Apsfpu bd f

' p c

+

d ω − ω' dp

(

)

Asfy 0.88 ( 60 ) = = 0.0074; ω ' = 0 bdfc' 96 ( 24.75 ) ( 3)

( )( ) + 24.75 ( 0.0074 ) = 0.084 22.75 96 ( 22.75 )( 3 )

1.00 1.84 270

From Design Aid 5.14.3: fps

= 268 ksi

a

=

M n

⎡ ⎡ ⎛ ⎛ ⎛ 2.23 ⎞ ⎤ ⎛ 2.23 ⎞ ⎤ a⎞ a⎞ = Apsfps ⎜ d p − ⎟ + Asfy ⎜ d − ⎟ = 1.84 ( 268 ) ⎢ 22.75 − ⎜ ⎥ + 0.88 ( 60 ) ⎢ 24.75 − ⎜ ⎥ ⎟ 2⎠ 2⎠ ⎝ ⎝ ⎝ 2 ⎠⎦ ⎝ 2 ⎟⎠ ⎦ ⎣ ⎣



= 11,917 kip-in. = 993 kip-ft

c

=

a 2.23 = = 2.62 β1 0.85

c dt

=

2.62 = 0.107 24.5

Apsfps + Asfy 0.85f b ' c

=

(

) ( ) 0.85 ( 3 ) (96 )

1.84 268 + 0.88 60

= 2.23 in.

From Fig. 5.2.3, 0.107 < 0.375, therefore, tension controlled, φ = 0.9 φMn = 0.9(993) = 894 kip-ft Note: Because a = 2.23 in. > 2.0 in. = the topping thickness, a more exact analysis requires a revised calculation to account for the higher strength concrete of the double-tee flange. However, such a refinement is expected to produce a negligible difference in the results. In this case, the revised calculation yields a = 2.19 in. versus 2.23 in. and φMn = 895 kip-ft versus 894 kip-ft. Find fps using Eq. 18-3 of ACI 318-05: fps

⎛ γ ⎡ f ⎤⎞ d = fpu ⎜ 1− p ⎢ ρp pu' + ω − ω ' ⎥⎟ β1 ⎢⎣ fc d p ⎥⎦⎠ ⎝

ω’

= 0 in this example

fps

⎛ 0.28 ⎡ 1.84 270 ⎤⎞ 24.75 = 270 ⎜ 1− + 0.0074 ⎥⎟ = 263 ksi (versus 268 ksi from Design Aid 5.14.3) ⎢ ⎥⎦⎠ ⎝ 0.85 ⎢⎣ 96 22.75 3 22.75

(

(

(

)

) )( )

(

)

φMn = 879 kip-ft Note: The ductility provisions φMn ≥ 1.2Mcr should be checked as in Example 5.2.1.3.

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.2.1.5 Design of Partially Prestressed Flange Section Using Strain Compatibility

  5

Given: Inverted-tee beam with 2 in. composite topping as shown.

b = 44" Control joints

Concrete: Precast: fc' = 5000 psi, normalweight Topping: fc' = 3000 psi, normalweight

11/2" 2"

2"

A's

Reinforcement:

10"

(12) 1/2-in.-diameter, 270 ksi, low-relaxation strand Aps = 12 (0.153) = 1.836 in.2 Eps = 28,500 ksi (based on strand data) Es = 29,000 ksi As = (2) #7 = 1.2 in.2 As' = (2) #9 = 2.0 in.2

26" Aps

As

12"

2" 3" 6"

Problem: Find flexural strength, φMn. _______________________________

bw = 12"

6"

Solution: Determine effective flange width b from Section 8.10.2 of ACI 318-05; overhanging width = eight times thickness. (Note: May also be limited by one-quarter span.) b d p d d’

= bw + 2(8t) = 12 + 2(8)(2) = 44 in. = 26 – 3 = 23 in. = 26 – 2 = 24 in. = 11/2 in.

Assume 20% loss of prestress. Strand initially tensioned to 75% of fpu: fse = (1 – 0.2)(0.75)(270) = 162 ksi εse =

fse 162 = = 0.0057 E ps 28,500

Construct a strain diagram (see following page): By proportional triangles:

ε sa + 0.003 0.003 = c dp Therefore:

5–12

ε sa + 0.003 d p and = c 0.003

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.2.1.5 Design of Partially Prestressed Flange Section Using Strain Compatibility (cont.)

εsa =

0.003d p c

− 0.003 =

εps = ε sa + ε se = εs

=

( ) − 0.003 = 0.069 − 0.003

0.003 23 c

( )

0.003 24 0.072 0.003d − 0.003 = − 0.003 = − 0.003 c c c '

=

c

0.069 0.069 − 0.003 + 0.0057 = + 0.0027 c c

ε 's = 0.003 − 0.003d = 0.003 − c εy

  5

fy Es

( ) = 0.003 − 0.0045

0.003 1.5 c

c

60 = 0.0021 29,000

=

Try c = 9 in. εps =

0.069 0.069 + 0.0027 = + 0.0027 = 0.0104 9 c

From the strand stress-strain curve equations in Design Aid 15.2.4: fps = 270 −

0.04 0.04 = 258.2 ksi = 270 − 0.0104 − 0.007 ε ps − 0.007

εs (from previous) =

0.072 − 0.003 = 0.0050 > 0.0021; therefore, fs = 60 ksi 9

0.0045 ε 's (from previous) = 0.003 − = 0.0025 > 0.0021 ; therefore, fs' = 60 ksi 9

C1 = 0.85 fc' C2 = 0.85 f

a b = 0.85(3)(2)(44) = 224.4 kip

(topping) 1

a b = 0.85(3)(2)(12) = 61.2 kip

' c (topping) 2 w

a3 = 1c – 4 in. = (0.85)(9) – 4 = 3.65 in. C3 = 0.85 fc' a3bw = 0.85(5)(3.65)(12) = 186.2 kip C4 = As'fs' = 2.0(60) = 120 kip C

= C1 + C2 + C3 + C4 = 224.4 + 61.2 + 186.2 + 120 = 591.8 kip

T1 = Apsfps = 1.836(258.2) = 474.1 kip T2 = Asfs = 1.2(60) = 72 kip T1 + T2 = 474.1 + 72 = 546.1 kip < 591.8 kip

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.2.1.5 Design of Partially Prestressed Flange Section Using Strain Compatibility (cont.)

  5

44"

0.003

d' = 11/2"

a1 = a2 = 2"

c

d = 24"

a3 12"

C1 C 4 C2 C3

a ε's

dp = 23"

εps εsa

εse

εs

T2

T1

Try c = 8 in. εps =

0.069 0.069 + 0.0027 = + 0.0027 = 0.0113 8 c

From the strand stress-strain curve equations in Design Aid 15.2.4: fps = 270 −

εs

0.04 0.04 = 260.7 ksi = 270 − 0.0113 − 0.007 ε ps − 0.007

(from previous) =

0.072 − 0.003 = 0.0060 > 0.0021; therefore, fs = 60 ksi 8

ε 's (from previous) = 0.003 − C1 = 0.85 fc'

(topping) 1

C2 = 0.85 fc'

(topping) 2 w

0.0045 = 0.0024 > 0.0021 ; therefore, fs' = 60 ksi 8

a b = 0.85(3)(2)(44) = 224.4 kip a b = 0.85(3)(2)(12) = 61.2 kip

a3 = 1c – 4 in. = (0.85)(8) – 4 = 2.8 in. C3 = 0.85 fc' a3bw = 0.85(5)(2.8)(12) = 142.8 kip C4 = As'fs' = 2.0(60) = 120 kip C

= C1 + C2 + C3 + C4 = 224.4 + 61.2 + 142.8 + 120 = 548.4 kip

T1 = Apsfps = 1.836(260.7) = 478.6 kip T2 = Asfs = 1.2(60) = 72 kip T1 + T2 = 478.6 + 72 = 550.6 kip ≈ 548.4 kip Therefore, use c = 8 in. Check reinforcement limits by ACI 318-05: Net tensile strain of extreme depth: In this case, εt = εs εt = 0.0060 > 0.005

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.2.1.5 Design of Partially Prestressed Flange Section Using Strain Compatibility (cont.) Therefore, it is a tension-controlled section and φ = 0.9

  5

Alternatively: Extreme depth dt = 24 in. 8.0 c = 0.333 Vu >

φVc 2

Therefore, minimum shear reinforcement is required. ACI 318-05 (Eq. 5-24) requires a minimum amount of reinforcement be provided as follows: Av = 0.75 fc'

Av

≥ 50bw

bw s 0.75 = fyt

(

) ( )(

5000 8 12

)

65,000

= 0.078 in.2/ft

( )( )

s 50 8 12 = = 0.074 in.2/ft 65,000 fyt

From Design Aid 15.2.11, select a welded-wire reinforcement (WWR) that supplies at least 0.039 in.2/ft per layer transverse, and select a longitudinal wire with area of at least 40% of the area of the transverse wires and with spacing that will meet ACI 318-05 Section 12.13.2.4 requirements for development of single leg WWR used as shear reinforcement: Provide WWR 6 × 12 – W2×W1.4 each face. Av = (2)(0.04) = 0.08 in.2/ft. The figure under the “Problem” section of this example shows this WWR cut with eight longitudinal wires and equal overhangs, as well as the relevant ACI 318-05 Section 12.13.2.4 requirements. Note that this code section might be violated if the overhangs are not equal and the longer overhang is toward the bottom of the beam. Depending on quantity required and local availability, it may be preferable to select a style of WWR (Design Aid 15.2.11) that provides a greater area of steel.

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.3.2.1 Construction of Applied and Resisting Design Shear Diagrams

  5

Given: 2HC8 with span and loadings shown. Section properties: A = 110 in.2 I = 843 in.4 yb = 4.0 in. bw = 6.25 in. d = dp = 5.875 in. h = 8.0 in. (0.8 h = 6.4 in.) wt = 57 lb/ft2 = 114 lb/ft Concrete: fc'

5.875" diameter 8.0" n.a.

d = 5.875" 2.125"

e = 1.875"

4.0" /16" strands 23.875" 7

= 5000 psi, normalweight

Note: n.a. = neutral axis

Problem: Determine shear reinforcement requirement. ______________________________________________________________________________________ Solution: 1. Determine factored loads. Uniform dead load = 1.2(42 + 114) = 187 lb/ft Uniform live load = 1.6(100) = 160 lb/ft Concentrated dead load = 1.2(1500) = 1800 lb

10'-0" wsd = 21 lb/ft = 42 lb/ft

2.

wl = 50 lb/ft 2 = 100 lb/ft

Construct shear diagram. wu = 187 + 160 = 347 lb/ft RL =

ω u  (  / 2 ) + Pu ( x ) 



0.347 (22 ) (11) + 1.8 ( 8 ) 22

==

6" precast concrete wall

4.47 1

3. Construct the shear resistance diagram as described in the previous section.

0.347 Point of maximum moment

Construct line at 2 f bwd = 5.2 kip Construct Vc line by Eq. 5-20: ' c

0.38

Vd ⎞ Vd ⎛ Vc = ⎜ 0.6 fc' + 700 u p ⎟ bw d = 1.56 + 25.7 u p Mu ⎠ Mu ⎝

8'-0"

 = 22'-0"

= 4.47 kip RR = 0.347(22) + 1.8 – 4.47 = 4.96 kip

a. b.

10(75) = 750 lb/ft = 1500 lb

2

2.18 0.347

At 1 ft, 2 ft, and 4 ft from each end: Vu (left) = 4.47 – 0.347x ⎛ 0.347x 2 ⎞ Mu (left) = ⎜ 4.47x − ⎟⎠ 12 2 ⎝

4.47/0.347 = 12.88'

1.12'

1

4.96

8.0'

Vu (right) = 4.96 – 0.347x ⎛ 0.347x 2 ⎞ Mu (right) = ⎜ 4.96x − ⎟⎠ 12 2 ⎝

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.3.2.1 Construction of Applied and Resisting Design Shear Diagrams (cont.)

See table at right.

c.

Construct upper limit line.



Since Eq. 5-20 was used,

upper limit = 5 f bw d = ' c

(

)(

5 5000 6.25 5.875

Point

x ft

Vu kip

Mu kip-in.

1

1

4.12

2

2

3

)

1000

 = 13.0 kip d. Construct diagonal line at transfer zone from 3.5 fc' bwd = 9.1 kip at end of component to 13.0 kip at 50d b = 50(7/16) = 21.9 in. = 1.82 ft (see Note) e.

Construct

Vu diagram: φ

4.47/0.75 0.38/0.75 2.18/0.75 4.96/0.75

= 5.96 = 0.51 = 2.91 = 6.61

It is apparent from these diagrams that no shear reinforcement is required. Note: A  ssumed transfer length. See ACI 318-05, Section 11.4.4.

Vud Mu

Vc kip

51.56

0.470

13.6

3.78

98.95

0.224

7.3

4

3.08

181.25

0.100

4.1

4

1

4.61

57.44

0.472

13.7

5

2

4.27

110.71

0.226

7.4

6

4

3.57

204.77

0.102

4.2

  5

1.82'

13.6 13.0

9.1 7.3 5.96 5.2 4.1

x1 3c 3d 3b x2 3a x3

2 00.51

0 x6

3a

4.2 5.2 6.61 7.4

x5 3b

9.1

3d

3c

13.0 13.7

x4 1.82'

14.0'

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5 5.3.3

  5

Use of Design Aids

Design Aid 5.14.5 through 5.14.9 assist in determining the shear strength of precast, prestressed concrete components. When lightweight concrete is used, the shear equations Eq. 5-18 through 5-23 are modified by substituting λ fc' for fc' . The coefficient λ is defined as follows: ⎛ f ⎞ 1 ≤ 1.0 λ = ⎜ ct ⎟ ⎝ 6.7 ⎠ fc'

Moment diagram 2 lvh

In this equation, fct is the splitting tensile strength determined by test (ASTM C496). For normalweight concrete, λ is equal to 1.0. If the value of fct is not known, λ = 0.85 for sand-lightweight concrete and 0.75 for all-lightweight concrete is used. Design Aids 5.14.5 to 5.14.7 provide separate charts for normalweight and lightweight concrete. In these charts, it is assumed that fct is not known and the material is sand-lightweight, or λ = 0.85. 5.3.4

Simple span component

Shear Reinforcement

Shear reinforcement is required in all concrete components, except as noted in Section 11.5.6, ACI 318-05. Also, a limited exception for double-tees is presented in the “PCI Standard Design Practice” (see Section 14.1) and Reference 9. The minimum area required by ACI 318-05 is determined using Eq. 11-13:

Av = 0.75 fc'

s bw s but not less than 50bw (Eq. 5-24) f yt f yt

or, alternatively for prestressed components only, using ACI 318-05 Eq. 11-14:

A f s d Av = ps pu 80 f yt d bw

(Eq. 5-25)

Design Aid 5.14.8 is a graphic solution for the minimum shear reinforcement by Eq. 5-25. Shear reinforcement requirements are defined in ACI 318-05 by Eq. 11-15, which may be rewritten for vertical reinforcement as:



⎡⎛ Vu ⎞ ⎤ ⎢⎜ ⎟ − Vc ⎥ s ⎝φ⎠ ⎦ Av = ⎣ f yt d

(Eq. 5-26)

Design Aid 5.14.9 may be used to design shear reinforcement by Eq. 5-26 for a given excess shear. Stirrup size, strength, or spacing can be varied. Welded-wire reinforcement may also be used for shear reinforcement in accordance with ACI 318-05 Section 11.5.1; Sections 12.13.2.3 and 12.13.2.4 give development requirements. The value of fyt used in the design of shear reinforcement is limited by ACI 318-05 to 60 ksi for reinforcing bar and to 80 ksi for deformed welded-wire reinforcement.

5–52

vh

2 vh

vh

Continuous component

Fig. 5.3.2 Horizontal shear length.

5.3.5

 orizontal Shear Transfer in H Composite Components

Cast-in-place concrete topping is often used on precast concrete components to develop composite structures. The increased stiffness and strength may be required for gravity loads, for developing a diaphragm to transfer lateral loads, or to achieve a level floor. In order for a precast concrete component with topping to behave compositely, full transfer of horizontal shear forces must be ensured at the interface of the component and the cast-in-place concrete topping. This requires that interface surfaces be clean and free of laitance. In addition, intentional roughening of surfaces and/or horizontal shear ties may also be required depending on the magnitude of shear force to be transferred. ACI 318-05 includes two methods for design of horizontal shear transfer. The following recommended procedure is in ACI 318-05 Section 17.5.4. The horizontal shear force Fh that must be resisted is the total force in the topping; compression in positive moment regions and tension in negative moment regions are shown in Fig. 5.3.3. In a composite component that has an interface surface that is intentionally roughened but does not have horizontal shear ties, or where minimum ties are provided in accordance with ACI 318-05 Section 17.6 but the surface is not inten-

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CHAPTER 5

EXAMPLE 5.3.3.1 Use of Design Aids 5.14.5 through 5.14.7 – Graphical Solution of Eq. 5-20 (ACI 318-05 Eq. 11-9) Given: PCI standard double-tee 10LDT24 + 2 Span = l = 50 ft bw = 9.5 in. d = dp = 21 + 2 = 23 in. For depressed strand patterns d ≥ 0.8h 0.8h = 20.8 in. d = dp (near ends) = 16 in. < 20.8, use 20.8 in. d = dp (near midspan) = 23 in. > 20.8, use 23 in. Concrete: Precast: fc' = 5000 psi, sand-lightweight, λ = 0.85 Topping: fc' = 4000 psi, normalweight Reinforcement: Prestressing steel: 270 ksi strand, 108D1 pattern, Aps = 1.53 in.2 ee = 7.77 in. ec = 14.77 in.

  5

10'-0" 2'-6"

5'-0"

2'-6" 5 /4" 3

2" 2"

Shear reinforcement fyt = 60 ksi Loads: Dead load, wd = 609 lb/ft Live load, wl = 800 lb/ft

24"

33/4"

Problem:

Vu −Vc along the span using Eq. 5-20 for Vc. φ _______________________________________________ Find the value of excess shear force

Solution (see figure at the end of this example): The parameters needed for use of Design Aids 5.14.5 through 5.14.7 are: Strand drape: 14.77 – 7.77 = 7 in., which is approximately equal to d/3, thus a shallow drape.

 50 (12 ) = = 26.1 d 23 ⎛  ⎞ ⎛ 1⎞ Vu at support = (1.2wd + 1.6wl) ⎜ ⎟ ⎜ ⎟ = (1.2 × 609 + 1.6 × 800)(50/2)(1/0.75)(1/1000) = 67.0 kip φ ⎝ 2⎠ ⎝ φ ⎠

The solution (shown in the figure at the end of this example) follows these steps: (a) Draw a line from Vu /φ = 67.0 kip at support to Vu /φ = 0 at midspan. (b) At end of component (conservative to assume support = end of component), d = 20.8 in., fpc = Vp = 0 Prestress transfer length is assumed at 50db in ACI 318-05, Section 11.4.4. 50db = 25 in. = 0.042l At end by Eq. 5-23:

 3.5 (0.85 ) 5000 + 0.3 (0 )  Vcw = 3.5λ fc' + 0.3fpc bw d p +Vp =   (9.5) (20.8 ) + 0 = 41.6 kip 1000  

(

)

5 ( 0.85 ) 5000 ( 9.5 )( 20.8 ) = 59.4 kip 1000 Draw line between these two values. At 50db: Vc = 5λ fc' bw d =

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.3.3.1 Use of Design Aids 5.14.5 through 5.14.7 – Graphical Solution of Eq. 5-20 (ACI 318-05 Eq. 11-9) (cont.)

  5

 = 26.1, where d = 23 in. d (d) Draw a vertical line at h/2 from face of support. (e) The shaded area is the excess shear, Vu /φ – Vc, for which shear reinforcement is required (see Example 5.3.4.2 for design of shear reinforcement). (c)

Draw a curved line at

100

Sand-lightweight concrete, λ = 0.85 shallow drape

d b

80

Vc or Vu /φ

c

67.0 60 40

40 e

20

30

5λ fc' bw d = 59.4 kip

20 15

/d = 10 2λ fc' bw d = 26.3 kip

/d = 50 in. e

0 0

a 0.20

0.10

0.30

0.40

0.50

x/

Positive moment section: C

a

C a

Cast-in-place

C Case 1: C < Cc Fh = C = T

Precast concrete

Case 2: C > Cc Fh = Cc < T

As or Aps

T

T Case 1

T Case 2

Negative moment section: T Cast-in-Place A's or A'ps Precast concrete

a

C

Atop = Effective area of cast-in-place composite topping Cc

= Compressive force capacity of the composite topping = 0.85f'cc Atop

C

= Total compressive force

T

= Total tensile force = Asfs or Apsfps

f'c(topping) = Compressive strength of the topping Fh = T = C

Fh

= Horizontal shear force in composite topping

Fig. 5.3.3 Horizontal shear in composite section

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CHAPTER 5

EXAMPLE 5.3.4.1 Minimum Shear Reinforcement by Eq. 5-25 and Design Aid 5.14.8

EXAMPLE 5.3.4.2 Use of Design Aid 5.14.9 – Shear Reinforcement

Given: Double-tee of Example 5.3.3.1.

Given: Double-tee of Examples 5.3.3.1 and 5.3.4.1.

Shear reinforcement: Try W 2.9 wire each leg.

Problem: Design shear reinforcement for:

Av = 2(0.029) = 0.058 in.2 Problem: Determine the minimum amount of shear reinforcement required by Eq. 5-25 (ACI 318-05 Eq. 11-14). Verify the result from Design Aid 5.14.8. ________________________________________ Solution:

⎛ Vu ⎞ ⎜⎝ φ ⎟⎠ −Vc = 10,000 lb

____________________________________ Solution: Excess shear: ⎡ ⎛ Vu ⎞ ⎢ ⎜ ⎟ −Vc ⎝φ⎠ =⎢ ⎢ d ⎢ ⎣

bwd = 9.5(22) = 209 in.2 Note: As a simplification, d = 22 in. is used as an average value. From Eq. 5-25: Av

=

Apsfpu s 80fyt d p

Av = 0.058 =

  5

⎤ ⎥ ⎥ = ⎛ 10,000 ⎞ = 435 lb/in. ⎥ ⎜⎝ 23 ⎟⎠ ⎥ ⎦

From Design Aid 5.14.9:

dp bw

 se two rows (one row per stem) of U welded-wire reinforcement W2.9, vertical wire spacing = 6 in.

1.53 ⎛ 270 ⎞ ⎛ s ⎞ 22 80 ⎜⎝ 60 ⎟⎠ ⎜⎝ 22 ⎟⎠ 9.5

 hear strength provided by reinforcement S per stem:

thus; solving for s: s = 9.7 in.

= 580 lb/in. > 435 lb/in.

OK

From Design Aid 5.14.8: For: Aps fyt fpu bwd Av

ACI 318-05 Section 17.5.3.3 requires that for an interface surface that is both intentionally roughened to a full amplitude of approximately 1/4 in. and includes minimum horizontal shear ties per ACI 318-05 Section 17.6, Fh is limited to:

= 1.53 in.2 = 60 ksi = 270 ksi = 209 in.2 = 0.075 in.2/ft

corresponding s = 12(0.058)/0.075 = 9.3 in. ≈ 9.7 in. Per ACI 318-05 Section 11.5.5: smax = 3/4h ≤ 24 in. 3 /4h = 0.75(26) = 19.5 in. > 9.7 in.

OK

OK



Fh = φ(260 + 0.6ρv  fyt)λbvlvh



Fh < φ 500bvlvh

For Fh exceeding φ500bvlvh, the area of horizontal shear ties required in length lvh may be calculated by:

tionally roughened, Fh should not exceed φ80bvlvh, where bv is the width of the interface surface and lvh is the horizontal shear length as defined in Fig. 5.3.2. (Note: Experience and tests indicate that normal finishing methods used for precast concrete structural components will qualify as intentionally roughened. Thus, horizontal shear strength of φ80bvlvh may be used for design.)

(Eq. 5-27)

Acs ==

Fh φµe f yt

(Eq. 5-28)

where: Acs = area of horizontal shear ties, in.2 Fh = horizontal shear force, lb fyt = yield strength of horizontal shear ties, psi µe = effective shear-friction coefficient; see Eq. 5-29 φ = 0.75 For composite components, µ = 1.0λ and Acr = bvlvh;

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.3.5.1 Horizontal Shear Design for Composite Beam

  5

Given: Inverted-tee beam with 2 in. composite topping Beam length = 24 ft

b = 44" 11/2"

Tooled control joints

Concrete: Precast: fc' = 5000 psi, normalweight

2" 2"

Topping: f = 4000 psi, normalweight ' c

A's = (2) #9

Prestressing steel: (12) 1/2-in.-diameter, 270 ksi strands Aps = 12 × 0.153 = 1.836 in.2 fps = 260.7 ksi Tie reinforcement: fyt = 60,000 psi

10" 24" Aps 12"

Problem: Determine the requirements to transfer horizontal shear force. ____________________________________

3" bv = 12"

Solution: Atop = b(2) + bw(2) = 2(44) + 2(12) = 112 in.2 C = 0.85 fc' (topping) Atop + A'sfs' = 0.85(4)(112) + 2(60) = 380.8 + 120.0 = 500.8 kip lvh

=

( )

24 12

= 144 in. 2 fps = 260.7 ksi Apsfps = 1.836(260.7) = 478.6 kip < 500.8 kip Therefore, from Fig. 5.3.3: Fh = 478.6 kip

φ 80bv  vh =

λ

0.75 ( 80 ) (12 ) (144 ) = 103.7 kip < 478.6 kip. Therefore, ties are required. (1000 )

= 1.0 (normalweight concrete)

Check maximum by Eq. 5-27:

φ 500bv  vh =

0.75 ( 500 ) (12 ) (144 ) = 648 kip > 478.6 kip. Therefore, design by Eq. 5-27: (1000 )

φ(260 + 0.6ρvfyt)λbvlvh = 478,600 lb φλbvlvh = 0.75(1.0)(12)(144) = 1296 in.2 By transporting values:

ρv =

478,600 − 260 (1296 ) = 0.00304 0.6 (1296 ) ( 60,000 )

Acs = ρvbvlvh = 0.00304(12)(144) = 5.25 in.2

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CHAPTER 5

EXAMPLE 5.3.5.1 Horizontal Shear Design for Composite Beam (cont.) Check minimum requirements: AAcs,min = 0.75 fc' cs ,min =

  5

bw  vh 0.75 ( 70.7 ) (12 ) (144 ) = 1.53 in.2 < 5.25 in.2 = fyt 60,000

Use #4 stirrups, Acs = 2(0.20) = 0.40 in.2 Maximum stirrup spacing = 4(4) = 16 in. < 24 in. For Acs = 5.25 in.2, number of stirrup in length lvh = 5.25/0.4 ≈ 13 Total number of stirrups in the beam = 26 Provide (5) #4 stirrups at 6 in. spacing at each end and the remaining (16) #4 at approximately 12 in. spacing in the middle portion of the beam. In this example, it is assumed that the full flange width of 44 in. is part of the composite section. Control joints in topping, particularly in parking structures, are often located along the joints between ends of double-tees and edges of inverted-tee beams for crack control, as shown in the example figure. This raises the concern that the extended parts of the topping on each side of the inverted-tee beam web (16 in. for this example) may not behave compositely with the rest of the section. Note: It is important that the control joints be tooled rather than saw-cut, as there is a danger of cutting the reinforcement. Determine topping reinforcement to achieve composite behavior of cast-in-place flange. The portion of the total compression force in the extended part of topping: Cc'

=

16 ( 2 ) ( 380.8 ) = 108.8 kip (= Vu for use in calculations below) 112

µ e

=

φ1000λ Acr µ 0.75 (1000 ) (1.0 ) (1.5 ) (144 ) (1.4 ) = = 2.08 < 3.4 , use 2.08 Vu 108,800

' Acs

=

108.8 Vu = = 1.16 in.2 φfy µe 0.75 ( 60 ) ( 2.08 )

' = Acs,min

50 (1.5 ) (144 ) = 0.18 in.2 < 1.16 60,000

Use half span = 24 = 12 ft. 2 '' /ft = A Acs cs / ft =

1.16 0.096 in.2 2//ftft ==0.096 in. 12

Use WWR 6 × 6 – W4.9 × W4-9 ' From Design Aid 15.2.13, Acs = 0.098 in.2/ft

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CHAPTER 5 therefore:

µe ==



  5

φ1000 λ bv  vh ≤ 2.9 Fh

will provide a force normal to the crack. This normal force in combination with friction at the crack interface provides the shear resistance. The shear-friction analogy and shearfriction coefficient µ can be adapted to designs for reinforced concrete bearing, corbels, daps, composite sections, connections of shear walls to foundations, shear connections in precast concrete diaphragms, and other applications. In conditions where load reversal does not occur, an effective shear-friction coefficient µe may be used when the concept is applied to monolithic or concrete with roughened surface interfaces.11 Examples can be found in Sections 5.3.6 (“Horizontal Shear Transfer in Composite Components”), 5.6.3 (“Dapped End Bearing”), and 5.9.4 (“Concrete Brackets and Corbels”). The shear-friction reinforcement nominally perpendicular to the assumed crack plane based on either µ or µe can be determined by ACI 318-05 Eq. 11-25, rearranged as:

(Eq. 5-29)

(See Table 5.3.1) The value of Fh is limited to:  Fh  '  φ  ( max ) = 0.25λ fc bvllvhvh



(Eq. 5-30)

≤ 1000λ bvlvh Section 17.5.4.1 of ACI 318-05 requires that stirrups be placed along the component to approximately reflect the distribution of shear forces in the component. Thus, the horizontal shear ties are usually either an extension of or placed the same as shear reinforcement. Section 17.6.1 of ACI 318-05 also requires that ties, when required, be spaced no more than four times the least dimension of the supported element, nor 24 in., and meet the minimum shear reinforcement requirements of ACI 318-05 Section 11.5.6.3: AAvv == 0.75 fc'



Vu φ fy µ

(Eq. 5-32a)

Or, where permitted,

50bv  vh bv  vh but not less than (Eq. 5-31) f yt f yt



Anchorage of stirrups must satisfy ACI 318-05 Section 17.6.3. Research10 has shown that this requirement can be satisfied by providing a minimum distance of 2.25 in., 2.75 in., and 3.25 in. between the shear transfer interface and the outside ends of standard hooks on #3, #4, and #5 stirrups, respectively. See also Section 14.1 for “PCI Standard Design Practice” regarding ACI 318-05 Section 17.6.3. 5.3.6

Avf =

Avf ==

Vu φ f y µe

(Eq. 5-32b)

where: φ = 0.75 Avf = area of reinforcement nominally perpendicular to the assumed crack plane, in.2 fy = yield strength of Avf, psi (equal to or less than 60,000 psi) Vu = applied factored shear force, parallel to the assumed crack plane, lb (limited by the values given in Table 5.3.1)

Shear Friction

Shear friction is an important tool in the design of precast and prestressed concrete structures. Use of the shear friction theory is recognized by Section 11.7 of ACI 318-05, which states that shear friction is “to be applied where it is appropriate to consider shear transfer across a given plane, such as an existing or potential crack, an interface between dissimilar materials, or an interface between two concretes cast at different times.” A basic assumption used in applying the shear-friction concept is that concrete within the direct shear area being considered will crack in the most undesirable manner. Ductility is achieved by placing reinforcement across this anticipated crack so that the tension developed by the reinforcement



µe =

φ1000 λ Acr µ Vu



(Eq. 5-33)

≤ values in Table 5.3.1 λ = f actor for use with lightweight concrete, see Section 5.3.3 µ = shear-friction coefficient (values in Table 5.3.1) Acr = area of the crack interface, in.2 When net axial tension is present, additional reinforcement area should be provided:

Table 5.3.1  Recommended shear friction coefficients Case

Crack interface condition

µa

Maximum µe

Maximum Vu/φ

1

Concrete to concrete, cast monolithically

1.4λ

3.4

0.30λ fc' Acr ≤ 1000λAcr

2

Concrete to hardened concrete, with roughened surface

1.0λ

2.9

0.25λ fc' Acr ≤ 1000λAcr

3

Concrete placed against hardened concrete not intentionally roughened

0.6λ

Not applicableb

0.20λ fc' Acr ≤ 800λAcr

4

Concrete to steel

0.7λ

Not applicableb

0.30λ fc' Acr ≤ 800λAcr

a. In accordance with ACI 318-05 Section 11.7.4.3. b. The use of µe is not applicable for concrete placed against hardened concrete not intentionally roughened or against steel.

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PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS AAnn ==



Nu φ fy

(Eq. 5-34)

where: An = area of reinforcement required to resist axial tension, in.2 Nu = applied factored tensile force nominally perpendicular to the assumed crack plane, lb. May be taken as 0.2 times the factored sustained parallel load12 φ = 0.75 When self-consolidating concrete (SCC) will be used for horizontally cast components that have corbels or ledges cast on the top surface, care should be exercised in selecting the design interface condition. Due to the fluidity of SCC, these corbels or ledges are sometimes cast after the underlying concrete has at least partially hardened, so the monolithic interface (Table 5.3.1, case 1) should not be assumed for design. Because laitance, which must be removed, will usually be present at the surface of the first cast component, it is logical to specify roughening of the interface and design for case 2. If roughening is not specified, interface case 3 should be used, though the interface still must be free of laitance. All reinforcement, either side of the assumed crack plane, should be properly anchored to develop the design forces. The anchorage may be achieved by extending the reinforcement for the required development length (with or without hooks) or by welding to reinforcing bars, angles, or plates.

5.4

CHAPTER 5

(

where: Tu φ λ fc' x, y γ

(Eq. 5-35)

= factored torsional moment, lb-in. = 0.75 = conversion factor for lightweight concrete = concrete compressive strength, psi = short side and long side, respectively, of a component rectangle, in. = a factor dependent on the level of prestress = 1 +10

f pc fc'

= 1.0 for non-prestressed sections fpc = average prestress after losses In computing Σx2y for a flanged section, the section may be divided into component rectangles such that the quantity Σx2y would be the maximum; however, the overhanging flange width used in design should not be taken greater than three times the flange thickness. If Tu ≤ Tu(min), no torsion reinforcement is required. Torsion design is complete. Step 3: Check to ensure that the required nominal torsional moment and shear strengths do not exceed the following maximum limits to avoid potential compression failures due to over-reinforcing:

Torsion

The torsion provisions in ACI 318-05 are based on models that are relatively compact, unlike most precast concrete sections subjected to torsion. Additionally, precast concrete components do not provide the degree of fixity that is common in cast-in-place concrete structures. The design procedure of ACI 318-05 (and previous editions since 1995) typically requires significantly greater reinforcement than previously used methods (see Section 14.1). This section is based on the Zia and McGee procedure,13 updated by Zia and Hsu.14 The Zia and McGee method is essentially the same as in pre-1995 codes for non-prestressed concrete, but allows the benefits of prestressing to be included. Note that Section 11.6.7 of ACI 318-05 allows an alternate design method when the aspect ratio is three or greater. The following is a step-by-step procedure for torsion design based on this method: Step 1: Determine the design shear Vu and the torsional moment Tu at the critical section. The critical section for shear and torsion by ACI 318-05 Sections 11.1.3, 11.6.2.4, and 11.6.2.5 is d from the face of the support for non-prestressed components, and h/2 for prestressed components. If the load is not located at the top of the component, d is to be measured from the bottom of the component to the point of application of the load. If a concentrated load occurs within these dimensions, the critical section must be reestablished to include the load. Step 2: Determine if torsion can be neglected, that is, is Tu ≤ Tu(min):

)

TTu(min) == φ 0.5λ fc' Σ x 2 y γ u(min)







Tn(max) == n( max )

⎛ 1⎞ ' 2 ⎜⎝ 3 ⎟⎠ Kt λ fc Σ x y

Vn(max ) = Vn(max) =

⎛ KV ⎞ 1+ ⎜ t u ⎟ ⎝ 30Ct Tu ⎠

2

10 λ fc' bw d

⎛ 30Ct Tu ⎞ 1+ ⎜ ⎝ KtVu ⎟⎠

2

≥

≥

Tu φ

Vu φ

(Eq. 5-36)

(Eq. 5-37)

where: ⎛ f ⎞ Kt = γ ⎜ 12 − 10 pc' ⎟ fc ⎠ ⎝

Vu = factored shear force, lb Ct =

bw d Σ x2y

Step 4: If Tu ≤ Tu(max) and Vu ≤ Vn(max), design may be continued. Calculate torsion and shear carried by concrete:

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

TTcc ==

Tc' ⎛ T' / T ⎞ 1 + ⎜ c' u ⎟ ⎝ Vc / Vu ⎠

2



(Eq. 5-38)

5–59

  5

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5 VVcc ==



  5

Vc' ⎛ V' / V ⎞ 1 + ⎜ c' u ⎟ ⎝ Tc / Tu ⎠

2



(Eq. 5-39)

or



where: Tc ,Tc' = nominal torsional moment strength of concrete under combined shear and torsion and under pure torsion, respectively

= 0.8λ fc' Σ x 2 y ( 2.5γ − 1.5)



= Vc as calculated in Section 5.3.2

Vc ,V

' c

Step 5: Provide stirrups for torsional moment in excess of that carried by concrete. Stirrups must be closed and must be spaced not more than 12 in. or (x1 + y1)/4: ⎞ ⎛ Tu ⎜⎝ φ − Tc ⎟⎠ s At = α t x1 y1 f yt

where: At x1 y1 s αt fyt

(Eq. 5-40)

= required area of one leg of closed tie, in.2 = short side of closed tie, in. = long side of closed tie, in. = stirrup spacing ≤ ph /8 or 12 in. = [0.66 + 0.33 y1/x1] < 1.5 = yield strength of transverse reinforcement, psi

(

)

whichever is greater. The value of Al calculated from Eq. 5-43 need not exceed that obtained by substituting

Vc ,Vc' = nominal shear strength of concrete under combined shear and torsion and under pure shear, respectively Tc'

⎡ ⎤ ⎛ ⎞ ⎢ ⎜ T ⎟ 2A ⎥ 400x u ⎜ ⎟ − t ⎥ x1 + y1 (Eq. 5-43) AAt = ⎢ ⎢ fy ⎜ Vu ⎟ s ⎥ ⎢ ⎥ ⎜⎝ Tu + 3C ⎟⎠ t ⎣ ⎦

2 At 50bw ⎛ 12 f pc ⎞ 200bw 1+ ' ⎟ ≤ for f yt ⎜⎝ fc ⎠ f yt s

In many cases, the bars or tendons may not be fully developed at the critical section. Thus, it may be necessary to provide U-bars at the ends of the components lapped with the longitudinal reinforcement. Strands may be used as part of the longitudinal reinforcement. However, they must be developed, or the reduced capacity due to partial development should be used. It should be noted that the design of the connections between the torsional component and its supports to provide adequate reactions is critical; also, the effects of torsion on the overall stability of the frame should be investigated. Guidelines for these design considerations are given in Chapter 6.

Note: The required stirrups for torsion are in addition to those required for shear. A minimum amount of web reinforcement should be provided to ensure reasonable ductility. The minimum area of closed stirrups that should be provided is:

(A

v

)

+ 2At min = 50

bw s γ f yt

( )

2

≤ 200

bw s (Eq. 5-41) f yt

where bw = the web width of the beam Step 6: To resist the longitudinal component of the diagonal tension induced by torsion, longitudinal reinforcement approximately equal in cross sectional area to that of stirrups for torsion and effectively distributed around the perimeter (spaced ≤ 12 in.) should be provided. Prestressing strand may be used to satisfy the longitudinal reinforcement requirement. However, to control diagonal crack width, ACI 318-05 Section 11.6.3.4 must be satisfied). This longitudinal steel for torsion is in addition to that required for flexure. Thus:

5–60

AAt =

(

2At x1 + y1 s

)

(Eq. 5-42)

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.4.1 Shear and Torsion Design of a Non-Prestressed Component Given:

  5

Precast concrete, load-bearing spandrel beam shown. Span = l = 30 ft clear Tributary width of floor = 20 ft fc' = 5000 psi, normalweight Reinforcement fyt = 60,000 psi d = 69 in. Factored loads: Dead load: Precast concrete floor 60 lb/ft2 (20 ft)/1000 = 1.2(1.2) = 1.44 kip/ft Topping (38 lb/ft2)(20 ft)/1000 = 0.76(1.2) = 0.91 kip/ft Superimposed (20 lb/ft2)(20 ft)/1000 = 0.4(1.2) = 0.48 kip/ft Window = 0.05(1.2) = 0.06 kip/ft Spandrel = 0.63(1.2) = 0.76 kip/ft Live load: 50 lb/ft2 × (20 ft)/1000 = 1.00(1.6) = 1.60 kip/ft Total load = 5.25 kip/ft Problem: Determine torsion reinforcement requirements. ________________________________________ Solution: 1. Compute shear Vu and torsion Tu at critical section, located at 24 in. – 3 in. = 1 ft-9 in. from the face of the support, equal to 13.25 ft from midspan (see Section 5.3): wu for shear = 5.25 kip/ft Vu = 5.25(13.25) = 69.6 kip wu for torsion = 1.44 + 0.91 + 0.48 + 1.60 = 4.43 kip/ft

12" Y 8" Hollow-core slab with topping

1" 6" 6"

72"

Note: It is sufficiently accurate in this and most precast concrete sections to use the centroid rather than the shear center to calculate the eccentricity. 8"

Eccentricity = 3/4(8) + 3.29 = 9.29 in. Tu

= wue(15 – 1.75) = 4.43(9.29)(13.25)



= 545 kip-in.

2"

8"

8"

3"

Σx  y = 62(72) + 62(8)(2) + 82(8) = 3680 in.3 2

1.0 5000 λ f = = 0.0707 ksi 1000 ' c

40' span

3.29" Y

2.

Determine if torsion can be neglected: Tu(min) = φ(0.5λ fc' Σx 2y)γ = 0.75(0.5)(0.0707)(3680)(1.0) = 97.6 kip-in. < 545 kip-in.



Therefore, consider torsion.

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24"

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.4.1 Shear and Torsion Design of a Non-Prestressed Component (cont.)

  5

3.

Check maximums by Eq. 5-36 and 5-37 with: Kt = 12 Ct



=

6 ( 69 ) bw d 0.1125 = ==0.1125 Σ x 2 y 3680

Eq. 5-36:

Tn(max) =



⎛ 1⎞ 2 ' ⎜⎝ 3 ⎟⎠ K t λ fc Σ x y ⎛ KV ⎞ 1+ ⎜ t u ⎟ ⎝ 30CtTu ⎠

2

(

Tu = φ

)(

)

⎡ ⎤ 12 69.6 1+ ⎢ ⎥ ⎢⎣ 30 0.1125 545 ⎥⎦

(

(

) )( )

2

= 948 kip-in. >

545 = 727 kip-in. 0.75

Eq. 5-37: 10λ fc' bw d

Vn(max) =

⎛ 30CtTu ⎞ 1+ ⎜ ⎝ K tVn ⎟⎠

4.

≥

⎛ 1⎞ ⎜⎝ 3 ⎟⎠ 12 0.0707 3680

2

≥

Vu = φ

(

)( )( ) ⎡ 30 ( 0.1125 ) ( 545 ) ⎤ 1+ ⎢ ⎥ 12 ( 69.6 ) ⎢⎣ ⎥⎦ 10 0.0707 6 69

2

= 121 kip >



Torsion and shear carried by concrete by Eq. 5-38 and 5-39 with: Tc' = 0.8(0.0707)(3680)(1) = 208 kip-in. Near the support, use Eq. 5-19:



From a separate analysis,(not shown) determine:

69.6 = 92.8 kip 0.75

Flexural reinforcement is (3)#8 By Eq. 5-19, Vc' = 73.9 kip Tc' / Tu = 208/545 = 0.382 Vc' /Vu = 73.9/69.6 = 1.062



Eq. 5-38: Tc =

Tc' ⎛ T ' / Tu ⎞ 1+ ⎜ c' ⎝ Vc / Vu ⎟⎠

2

=

208 ⎛ 0.382 ⎞ 1+ ⎜ ⎝ 1.062 ⎟⎠

2

= 195.7 kip-in.

Eq. 5-39: Vc =

5.

Vc' ⎛ V ' / Vu ⎞ 1+ ⎜ c' ⎝ Tc / Tu ⎟⎠

2

=

73.9 ⎛ 1.062 ⎞ 1+ ⎜ ⎝ 0.382 ⎟⎠

2

= 25.0 kip

Determine transverse reinforcement by Eq. 5-40, assuming 3/4 in. cover to reinforcement: x1 = 4 in.; y1 = 70 in. ⎛ ⎛ 70 ⎞ y ⎞ αt  = ⎜ 0.66 + 0.33 1 ⎟ = 0.66 + 0.33 ⎜ ⎟ ==6.44 6.44≥≥1.5 1.5 x1 ⎠ ⎝ 4 ⎠ ⎝

Use αt = 1.5.

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.4.1 Shear and Torsion Design of a Non-Prestressed Component (cont.)

  5

⎛ Tu ⎞ ⎛ 545 ⎞ − 195.7⎟ ⎜⎝ φ −Tc ⎟⎠ ⎜⎝ ⎠ 0.75 At = = 0.0211 in.2/in. = 0.253 in.2/ft = α x y f 70 60 1.5 4 ( )( )( ) s t 1 1 yt

Stirrups required for shear (each side). ⎛ Vu ⎞ ⎛ 69.6 ⎞ ⎜⎝ φ ⎟⎠ −Vc ⎜⎝ ⎟ − 25.0 Av 0.75 ⎠ = = 0.0082 in.2/in. = 0.098 in.2/ft = 2s 2fyt d 2 ( 60 ) ( 69 )

0.098 + 0.253 = 0.351 in.2/ft (each side)

The minimum area of closed stirrups is:

Av + 2At =

50 ( 6 ) 50bw = (12 ) = 0.06 < (0.351)(2) = 0.702 in.2/ft fyt 60,000

#4 at 7 in. = 0.343 in.2/ft

say OK

 pacing may be increased toward midspan S to a maximum of the lesser of ph /8 or 12 in.

#4 corner bars

6. Determine longitudinal reinforcement requirements by Eq. 5-42 or 5-43:

By Eq. 5-42:

2At ( x 1 + y 1 ) 2 ( 0.0211) ( 4 + 70 ) = s 1 2 = 3.12 in.

Al =

A = #4 at 12" 3

/4" clear typical

or by Eq. 5-43: As required by ledge design

2 ( 0.0211) 2At = 0.042 ==0.042 1 s

As = (3) #8 (by flexural design not shown here)

()

50bw 50 6 = 0.005 ==0.005 fyt 60,000



Av + At = #4 at 7" near support Increase to #4 at 12" maximum

Use 0.042 in Eq. 5-43:

⎡ ⎛ ⎞ ⎢ 400x ⎜ T ⎟ 2At u Al At == ⎢ ⎜ ⎟− V s ⎢ fy ⎜ T + u ⎟ u ⎢⎣ 3Ct ⎠ ⎝

⎤ ⎡ ⎛ ⎞ ⎤ ⎥ ⎢ 400 ( 6 ) ⎜ ⎥ ⎟ 545 ⎥ (x1 + y1) = ⎢ –0.96 in.2 ⎜ ⎟ − 0.042 ⎥ ( 4 + 70 ) == −1 ⎥ ⎢ 60,000 ⎜ 545 + 69.6 ⎟ ⎥ ⎜⎝ ⎥ ⎢ ⎥⎦ 3 (0.1125 ) ⎟⎠ ⎦ ⎣

Therefore, use Al = 3.12 in.2 distributed around perimeter. The maximum spacing is 12 in. Corner bars are required, and the flexural reinforcement not required for flexure can also be counted. Thus, additional #4 bars @ 12 in. is adequate.

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.4.2 Shear and Torsion Design of a Prestressed Concrete Component

  5

Given: Precast, prestressed concrete spandrel beam shown Dead load of deck = 89.5 lb/ft2 Live load = 40 lb/ft2 for a parking structure in this example (check code requirements for other uses) Beam properties: A = 696 in.2 wt = 725 lb/ft fc' = 6000 psi, normalweight fy = fyt = 60 ksi

60' -0"

Connections must be designed to torsionally restrain beam

60' -0"

B A

A

4"

28' -0"

3' -0"

4"

8DT24 + 3

3" topping 6' -3" 2' -0"

8"

B 8DT24 + 3

28' -0"

12"

16" Partial plan 2' -0"

Section A-A

6 at 4' -0" = 24' -0"

2' -0"

Section B-B 2' -0"

5–64

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PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.4.2 Shear and Torsion Design of a Prestressed Concrete Component (cont.) Prestressing: (6) 1/2-in.-diameter, 270 ksi strands Aps = 6(0.153) = 0.918 in.2 d = 72 in.

  5

Problem: Determine shear and torsion reinforcement for the spandrel beam at critical section. _______________________________________________ Solution: 1. Calculate Vu and Tu :

Determine factored loads: Dead load of beam = 1.2(0.725) = 0.87 kip/ft 60 Dead load of deck = 1.2(0.0895) (4) = 12.9 kip/stem 2 Live load of deck = 1.6(0.040)(30)(4) = 7.7 kip/stem



Vu at center of column: = [0.87(28) + 7(12.9 + 7.7)](1/2) = 84.3 kip

Center of support to h/2 = 12/2 + 6 = 12 in.

Since a concentrated load occurs within h/2, the critical section is at face of support. Note: The critical section may also be limited by the height at the ledge.

Vu at face of support: = 84.3 – 0.87(1.0) = 83.4 kip



Torsion eccentricity = 4 in. +

Tu at support:

3 8 = 10 in. 4

( )

= (12.9 + 7.7)(7)(1/2)(10) = 721 kip-in. (same at face of support) 2 .

Determine if Tu ≤ Tu(min) by Eq. 5-35: Tu(min) = φ(0.5λ fc' Σx2y)γ φ = 0.75 λ fc' =

1.0 6000 0.0775 ==0.0775 1000

Σx 2y = [(82)(63) + (122)(16)] = 6336 in.3 Determine fpc at critical section approximately 11 in. from end of component. From Design Aid 5.14.4, strand develops 170 ksi at 28 in. Use approximate linear interpolation: ⎛ 11 ⎞ fpd = ⎜ ⎟ (170 ) = 66.8 ksi ⎝ 28 ⎠ Ppd

= 66.8(0.918) = 61.3 kip

fpc

=

γ

= 1+

Ppd A

=

61.3 = 0.088 ksi 696

10fpc f

' c

= 1+

(

10 0.088 6

) ==1.07 1.07

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5–65

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.4.2 Shear and Torsion Design of a Prestressed Concrete Component (cont.)

  5

Tu(min) = φ(0.5λ fc' Σx 2y)γ = 0.75(0.5)(0.0775)(6336)(1.07) = 197 kip-in. < 721 kip-in.

Therefore consider torsion.

3.

Check maximums by Eq. 5-36 and 5-37:



Kt

⎛ ⎛ 10 0.088 ⎞ 10fpc ⎞ = γ ⎜ 12 − ' ⎟ = 1.07 ⎜ 12 − 12.7 ⎟ ==12.7 fc ⎠ 6 ⎝ ⎝ ⎠

Ct

=

(

)

8 ( 72 ) bw d = ==0.087 0.091 Σ x 2 y 6336

Eq. 5-36: Tn(max) =



⎛ 1⎞ ' 2 ⎜⎝ ⎟⎠ K t λ fc Σ x y 3 ⎛ KV ⎞ 1+ ⎜ t u ⎟ ⎝ 30CtTu ⎠

2

=

⎛ 1⎞ ⎜⎝ ⎟⎠ (12.7 ) ( 0.0775 ) ( 6336 ) 3 ⎛ 12.7 ( 83.4 ) ⎞ 1+ ⎜ ⎝ 30 ( 0.091) ( 721) ⎟⎠

2

= 1830 kip-in. >

721 = 961 kip-in. 0.75

Eq. 5-37: Vn(max) =

4.

⎛ 30CtTu ⎞ 1+ ⎜ ⎝ K tVu ⎟⎠

2

=

10 ( 0.0775 ) ( 8 ) ( 72 ) ⎛ 30 ( 0.091) ( 721) ⎞ 1+ ⎜ ⎝ 12.7 ( 83.4 ) ⎟⎠

2

= 211.5 kip >

83.4 = 111.2 kip 0.75

Calculate torsion and shear carried by concrete: Tc'



10λ fc' bw d

= 0.8λ fc' Σx 2y(2.5 γ – 1.5) = 0.8(0.0775)(6336)[2.5(1.07) – 1.5] = 462 kip-in.

Shear near the support, use Eq. 5-23: Vc'

= (3.5λ fc' + 0.3fpc)bwd = [3.5(0.0775) + 0.3(0.088)](8)(72) = 171.4 kip

Tc' / Tu

= 462/721 = 0.64

V / Vu

= 171.4/ 83.4 = 2.05

' c



From Eq. 5-38: 462 Tc' = Tc = = 441 kip-in. 2 2 ' ⎛ 0.64 ⎞ ⎛ Tc / Tu ⎞ 1+ ⎜ 1+ ⎜ ' ⎝ 2.05 ⎟⎠ ⎝ Vc / Vu ⎟⎠

From Eq. 5-39: Vc

5–66

=

Vc' ⎛ V ' / Vu ⎞ 1+ ⎜ c' ⎝ Tc / Tu ⎟⎠

2

=

171.4 ⎛ 2.05 ⎞ 1+ ⎜ ⎝ 0.64 ⎟⎠

2

= 51.1 kip

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.4.2 Shear and Torsion Design of a Prestressed Concrete Component (cont.) 5.

Determine transverse reinforcement by Eq. 5-40: 11/2"

With 1 in. cover (1.25 in. to center of steel):

  5

8"

x1 = 5.5 in.; y1 = 72.5 in. αt

⎛ y ⎞ = ⎜ 0.66 + 0.33 1 ⎟ ≤ 1.5 ==0.66 0.66++0.33 0.33(72.5/5.5) ( 72.5 / 5.5) x1 ⎠ ⎝



= 5.01

Use αt = 1.5: ⎛ Tu ⎞ ⎛ 721 ⎞ − 441⎟ ⎜⎝ φ −Tc ⎟⎠ ⎜⎝ ⎠ At 0.75 = = 0.014 in.2/in. = αt x 1y 1fyt 1.5 ( 5.5 ) ( 72.5 ) ( 60 ) s  



A = #4 at 12" ±

Av + 2At = #4 at 7" closed stirrups at 8" #4 U-bars at end

= 0.174 in.2/ft

Stirrups required for shear (each side).

⎛ Vu ⎞ ⎜⎝ φ −Vc ⎟⎠ Av = = 2fyt d 2s = 0.083 in.2/ft



#4 closed stirrups at 8" on center

⎛ 83.4 ⎞ − 51.1⎟ ⎜⎝ ⎠ 0.75 = 0.007 in.2/in. 2 ( 60 ) ( 72 )

4"

0.174 + 0.083 = 0.257 in.2/ft per leg

The minimum area of closed stirrups by Eq. 5-41 is: 2

Av + 2At =

Check

50 ( 8 ) (12 ) (1.07 ) 50bw s = 0.09 in.2/ft < 0.257(2) = 0.514 (γ )2 = 60,000 fyt

200bw s 200 ( 8 ) (12 ) = 0.32 in.2/ft < 0.514 = fyt 60,000

Use #4 @ 8 in., As = 0.30 in.2/ft > 0.257 in.2/ft







OK OK OK



Spacing may be increased toward midspan to a maximum of the lesser of ph /8 or 12 in.



Shear and torsion reinforcement is not required where Sections 11.5.6.1 and 11.6.1 of ACI 318-05 are satisfied.

6.

Determine longitudinal reinforcement requirements by Eq. 5-42 or 5-43:



By Eq. 5-42:



(

2At x 1 + y 1

)

Al

=



2 ( 0.0140 ) ( 5.5 + 72.5 ) = 2.18 in.2 1

s

or by Eq. 5-43:

2 ( 0.0140 ) 2At = 0.028 == 0.034 1 s

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.4.2 Shear and Torsion Design of a Prestressed Concrete Component (cont.)

  5

50bw fyt



⎡ ⎛ fpc ⎞ ⎤ 50 ( 8 ) ⎡ ⎛ 0.088 ⎞ ⎤ 0.008 ⎢1+ 12 ⎜ ' ⎟ ⎥ = ⎢1+ 12 ⎜⎝ 6 ⎟⎠ ⎥ == 0.008 f 60,000 ⎝ ⎠ ⎣ ⎦ c ⎣ ⎦

Use 0.028 in Eq. 5-43: ⎡ ⎢ 400x Al At == ⎢ ⎢ fy ⎢⎣

⎤ ⎡ ⎥ 2At ⎢ Tu ⎥− ⎢ ⎢Tu + Vu ⎥ s ⎢⎣ 3Ct ⎥⎦

⎡ ⎤ ⎡ ⎤ ⎤ ⎢ 400 ( 8 ) ⎢ ⎥ ⎥ ⎥ 721 ⎢ ⎥ − 0.028 ⎥ ( 5.5 + 72.5 ) = 0.738 in.2 ⎥ (x1 + y1) = ⎢ ⎢ 60,000 ⎢ 721+ 83.4 ⎥ ⎥ ⎥ ⎢ ⎥ ⎢⎣ ⎥⎦ ⎥⎦ 3 0.091 ( ) ⎣ ⎦

Use Al = 2.18 in.2 distributed around perimeter. The maximum spacing is 12 in. Prestressing strands not required for flexure can also be counted. Thus, additional #4 @ 12 in. is adequate. The transverse and longitudinal reinforcement can be reduced to the interior span side of the first double-tee stem.

5.5

Beams with Ledges

As shown in the previous example, one of the most common occurrences of torsion in precast concrete components is in L-shaped beams (beams with a ledge on one side). Significant torsion may also occur in inverted-tee beams with severely unbalanced loads. This section covers additional design items related to the beam end and the ledge and its attachment to the web. These items are discussed in References 13 through 16 and are shown in Fig. 5.5.1. 5.5.1

Shear Strength of Ledge

The design shear strength of continuous beam ledges supporting concentrated loads can be determined by the lesser of Eq. 5-44 and 5-45: for s > bt + hl

φVn = 3φλ fc' h ⎡⎣ 2 ( b − b ) + bt + h ⎤⎦



φVn = φλ fc' h ⎡⎣ 2 ( b − b ) + bt + h + 2d e ⎤⎦ (Eq. 5-45)

(Eq. 5-44)

For s < bt + hl and equal concentrated loads, use the lesser of Eq. 5-46, 5-47, or 5-48.

φVn = 1.5φλ fc' h ⎡⎣ 2 ( b − b ) + bt + h + s ⎤⎦ (Eq. 5-46)



⎡ ⎤ ⎛b +h ⎞ φVn = φλ fc' h ⎢( b − b ) + ⎜ t  ⎟ + de + s ⎥ ⎝ 2 ⎠ ⎣ ⎦



(Eq. 5-47)

where: φ hl b bl bt s de

= 0.75 = depth of beam ledge, in. = beam web width, in. = width of web and one ledge, in. = width of bearing area, in. = spacing of concentrated loads, in. = distance from center of load to end of beam, in.

If the ledge supports a continuous load or closely spaced concentrated loads, the design shear strength is:

φVn = 24φ h λ fc'

where: φVn

(Eq. 5-48)

= design shear strength, lb/ft

If the applied factored load exceeds the strength as determined by Eq. 5-44, 5-45, or 5-48, the ledge should be designed for shear transfer and diagonal tension in accordance with Sections 5.6.3.2 through 5.6.3.4. 5.5.2

 ransverse (Cantilever) Bending of T Ledge

Transverse (cantilever) bending of the ledge requires flexural reinforcement As, which is computed by Eq. 5-49. Such reinforcement may be uniformly spaced over a width of 6hl on either side of the bearing, but not to exceed half the distance to the next load. Bar spacing should not exceed the ledge depth, hl, or 18 in.

As =

1 φ fy

⎡ ⎛ a⎞ ⎛ h ⎞ ⎤ ⎢Vu ⎜ ⎟ + N u ⎜ ⎟ ⎥ ⎝ d ⎠⎦ ⎣ ⎝ d⎠

(Eq. 5-49)

(See Fig. 5.5.1 for definitions.)

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

de

s

CHAPTER 5

b

B

  5

dw Hu

Aw

h

a Vu

C

C

h

d

bt b + hl de + t 2

U-bar or hook to develop A

bt + h

Ash + Awv

d

B

e

Hu

A

Vu

As

b Section B-B

Elevation Potential shear failure surfaces in beam ledges

b

N*u

Equilibrium and connection reinforcement of ledger beam (Note: Reinforcement required for flexure and internal torsions not shown) *For components on bearing pads, Nu should be taken as at least 0.2 times the factored dead load portion of Vu, unless it can be shown as less by calculation.

b

Hu

Center of gravity of triangular area

Vu hs Section C-C

Hu

Vu

Out-of-plane bending caused by torsional equilibrium reactions

Fig. 5.5.1 Design of beam ledges.

5.5.3

Longitudinal Bending of Ledge

Longitudinal reinforcement, calculated by Eq. 5-50, should be placed in both the top and bottom of the ledge portion of the beam:

Al = 200(bl – b) dl /fy

(Eq. 5-50)

where: dl = design depth of Al reinforcement (See Fig. 5.5.1 for other definitions.) 5.5.4

Attachment of Ledge to Web

Hanger steel Ash computed by Eq. 5-51 is required for attachment of the ledge to the web. Distribution and spacing of Ash reinforcement should follow the same guidelines as for As reinforcement in Section 5.5.2. Ash is not additive to

shear and torsion reinforcement designed in accordance with Sections 5.3 and 5.4.

Ash =

Vu (m ) φ fy

(Eq. 5-51)

where: Vu φ fy m

= applied factored load, lb = 0.75 = yield strength of Ash reinforcement, psi = modification factor computed by Eq. 5‑52, which is derived from Reference 17. 2 ⎡ ( x 2 y) ⎤⎥ ⎛ h ⎞ ⎛ h ⎞ ⎛ b ⎞ ⎢( ds + a ) − ⎜ 3 − 2 ⎟ ⎜ ⎟ ⎜ ⎟ − eγ t h ⎠⎝ h ⎠ ⎝ 2 ⎠ Σ x2 y ⎥ ⎝ ⎢ ⎦ m= ⎣ ds

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(Eq. 5-52) 5–69

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

b

Bar must be developed above and below critical section at top of ledge

  5

V1

b

V1e1 ≤ V2e2

V2 e1

e2

eo =

V2e2 − V1e1 V2 + V1

ao = b + eo − ds 2

Ash e

h

ds

a

Calculate m using Eq. 5-52 with e = eo, b = b and a = ao. Then calculate Ash using Eq. 5-51 with Vu = V1 + V2

b Vu

h

Fig. 5.5.3 Loads on an inverted-tee beam.

Closed ties when required (see Section 5.4)

Terms are as shown in Fig. 5.5.1, Section B-B,

Fig. 5.5.2 Ledge hanger steel geometry.

m ≥ 0.6 for L beams. m ≥ 0 .4 for Inverted-tee beams. where: x, y = shorter and longer sides, respectively, of the component rectangles forming the ledge and the web parts of the beam, in. γt = 0, when closed ties are not used in the ledge γt = 1.0 when closed ties are used in the ledge (See Fig. 5.5.2 for additional definitions.) In the case of an inverted-tee beam calculate m as shown in Fig. 5.5.3. 5.5.5

Out-of-Plane Bending near Beam End

In the Reference 17 study, it was found that when the reaction is not colinear with applied loads, as illustrated in Fig. 5.5.1, the resulting out-of-plane bending may require additional vertical and horizontal reinforcement. These are computed by Eq. 5-53 and provided on the inside face of the beam. This reinforcement is not additive to the reinforcement for internal torsion. The Awl and Awv bars should be evenly distributed over a height and width equal to the distance between the torsion connections hs. See Fig. 5.5.1.

5–70

= Awv == AAwl wt =

Vue 2φ f y d w

where: Vu = factored shear force at critical section, lb e = eccentricity, see Fig. 5.5.1, in. φ = 0.75 (The use of φ = 0.75 instead of 0.90 [flexure] compensates for the use of dw in place of the actual, somewhat smaller, lever arm.) fy = yield strength, psi dw = depth of Awv and Awl reinforcement from outside face of beam, in. Note that if the out-of-plane eccentricity e is very small, then the additional reinforcement may not be required. 5.5.6

Pocketed Spandrels

As an alternative to beams with ledges, pocketed beams may be used to provide support for stemmed components. Because of double-tee erection constraints, pocketed beams can only be used to support one end of the tee. They are frequently used on the exterior line of columns in parking structures. Pocketed beams have the advantages of minimal torsion, more simplified forming, economical production, and a flush interior face. Design procedures for pocketed spandrels is provided in Reference 17 and is illustrated in Example 5.5.6.1.

(Eq. 5-53)

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CHAPTER 5

EXAMPLE 5.5.1 L-Beam End and Ledge Design Given: 8-ft-wide double-tees resting on a standard L beam similar to that shown in Fig. 5.5.1. Layout of tees is irregular so that a stem can be placed at any point on the ledge. Closed stirrups are provided in the ledge (γt = 1.0). V u Nu hl d dl bt bl

= 18 kip/stem = 3 kip/stem = 12 in. = 11 in. = 10 in. = 3 in. = 14 in.

h = 36 in. hs = 30 in. b = 8 in. ds = 6.75 in. s = 48 in. fc' = 5000 psi, normalweight fy = 60 ksi

Problem: Investigate the strength of the ledge and its attachment to the web. Determine required reinforcement. _______________________________________________________________________________________ Solution: Minimum de = bt /2 = 1.5 in. Because s > bt + hl and de < 2(bl – b) + bt + hl, use Eq. 5-45: φVn = φλ fc' hl[2(bl – b) + bt + hl + 2de] = 0.75(1) 5000 (12)[2(14 – 8) + 3 +12 + 2(1.5)] = 19,092 lb

OK

= 19.1 kip > 18 kip

Determine reinforcement for flexure and axial tension: Shear span, a = 3/4(bl – b) + 1.25 = 5.75 in., use 6 in. By Eq. 5-49: 1 φfy

⎡ ⎛ a⎞ ⎛ h ⎞ ⎤ 1 ⎢Vu ⎜ ⎟ + Nu ⎜ ⎟ ⎥ = d d ⎝ ⎠ ⎝ ⎠ 0.75 60 ⎣ ⎦

As

=

6hl

= 6 ft > s/2 = 2 ft

( )

⎡ ⎛ 6⎞ ⎛ 12 ⎞ ⎤ ⎢18 ⎜ ⎟ + 3 ⎜ ⎟ ⎥ = 0.29 in.2 11 ⎝ ⎠ ⎝ 11⎠ ⎦ ⎣

Therefore, distribute reinforcement over s/2 each side of the load. (s/2)(2) = 4 ft Maximum bar spacing = hl = 12 in. Use #3 @ 12 in.; As = 0.44 in.2 for each 4 ft.  lace two additional bars at the beam end to provide equivalent reinforcement for a double-tee stem P placed near the end.

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  5

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.5.1 L-Beam End and Ledge Design (cont.)

  5 m =

2 ⎡ x 2y  ⎛ h ⎞⎛h ⎞ ⎛b ⎞ ⎢ d + a − ⎜ 3 − 2  ⎟ ⎜  ⎟ ⎜  ⎟ − eγ t h ⎠⎝ h ⎠ ⎝ 2 ⎠ Σ x 2y ⎝ ⎢⎣ d

(

(

)

)

⎤ ⎥ ⎥⎦

2 2 ⎡ ⎤ 12 ) (14 ) 8⎞ ( ⎡ ⎛ 12 ⎞ ⎤ ⎛ 12 ⎞ ⎛ 14 ⎞ ⎛ 6.75 + 5.75 − 3 − 2 6 + − 0.75 1.0 ( ) ⎢ ) ( ) ⎟⎠ ( ) ⎢ 2 ⎥ ⎜⎝ ⎟⎠ ⎥ ⎜⎝ ⎟⎠ ⎜⎝ ⎟⎠ ⎜⎝ ( 2 2 36 ⎦ 36 2 ⎣ ⎢⎣ (12 ) (14 ) + ( 8 ) ( 24 ) ⎥⎦ = = 0.87 6.75

By Eq. 5-51: Ash =

18 Vu (m ) = (0.87 ) = 0.35 in.2 over the 4 ft width, or φfy 0.75 ( 60 )

Ash =

0.35 = 0.087 in.2/ft 4

Maximum bar spacing = hl = 12 in. Ash = #3 @ 12 in. = 0.11 > 0.087 in.2/ft



OK

By Eq. 5-50: Al =

200 (b − b ) d  200 (14 − 8 ) (10 ) = 0.20 in.2 = fy 60,000

Use (1) #3 top and (1) #3 bottom; As = 0.22 in.2 By Eq. 5-53: Awv = AAwwtl ==

Vu e 2φfy dw

Assume: Rue = Vue = 820 kip-in. dw = b – 1.5 = 6.5 in. Awv = AAwwtl ==

5–72

820 = 1.40 in.2 (to be distributed over a height and length of hs = 30 in.) 2 0.75 60 6.5

(

) ( )( )

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CHAPTER 5

EXAMPLE 5.5.6.1 Design of a Prestressed, Pocketed Spandrel Beam Given: Precast concrete, pocketed spandrel beam shown. Dead load of deck = 68 lb/ft2 (10DT34 lightweight) Live load on deck = 40 lb/ft2

b = 8"

Beam properties: A = 624 in.2 wt = 650 lb/ft fc' = 6000 psi, normalweight fy = 60 ksi Prestressing: (6) 1/2-in.-diameter, 270 ksi strands Aps = 6(0.153) = 0.918 in.2 fse = 170 ksi Problem: Determine shear, torsion, dap, and pocket reinforcement requirements. The differences between this and the similarly loaded beam of Example 5.4.2 are illustrated. _________________________________ Solution: 1. Calculate Vu and Tu : Determine factored loads: Tee stem: Pu

= Vu

Vu ==

6" 2" Min.

4"

10LDT34

e=

2"

12"

CL Center of gravity of strand in beam

Section CL 2'-6"

5'-0"

21.8K 8"

3" Note:

CL =

CL

30'-0" (column CL) 5'-0" 5'-0" 5'-0"

21.8K

21.8K 21.8K

5'-0" 2'-6"

21.8K

21.8K 1"

A B C C 77.0 kip (Vu - reaction) 76.5 kip (Vu - support face)

Spandrel (8 × 78):

 etermine eccentricity e. Stem load is D conservatively applied at 2 in. from the inside face of the beam:

e

19"

= 21.8 kip/stem

( )

D = 74"

H = 6'-6"

60 ⎛ 10 ⎞ ⎡⎣68 (1.2 ) + 40 (1.6 ) ⎤⎦ ⎜ ⎟ 2 ⎝ 2⎠ 1000

650 1.2 = 0.78 kip/ft 1000

  5

Clear span = 60'-0"

B

29'-6" (reaction CL) centerline; Min. = minimum.

A

3"

Interior Elevation

b − 2 = 8/2 – 2 = 2.0 in. 2

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.5.6.1 Design of a Prestressed, Pocketed Spandrel Beam (cont.)

  5

Reaction at column: 21.8(3) + 0.78(14.917) = 77.0 kip At support face: Vu = 77.0 – 0.78(8/12) = 76.5 kip Tu = 21.8(3)(2.0) = 131 kip-in. 2. Determine ifTu ≤ Tu(min) by Eq. 5-35: Tu(min) = φ(0.5λ fc' Σx 2y )γ φ

= 0.75

λ fc' =

1.0 6000 0.0775 == 0.0775 1000

Σx 2y = (82 × 78) = 4992 in.3 Determine fpc at critical section, which is H/2 from face of support or (7 + 12/2) = 13 in. from the end of the component. From Design Aid 5.14.4, strand develops 170 ksi (fse) at ld = 28 in. fpd Ppd

= (13/28)(170) = 78.9 ksi = 78.9(0.918) = 72.4 kip

fpc

= Ppd = 72.4 = 0.116 ksi A 624

γ

=

1+

10fpc 10 ( 0.116 ) = 1+ ==1.16 1.09 ' 6 fc

Tu(min) = φ(0.5λ fc' Σx 2y)γ = 0.75(0.5)(0.0775)(4992)(1.09) = 158.1 kip-in. > 131 kip-in. Torsion need not be considered. 3. Therefore, design transverse reinforcement for shear only. Vc near end of component = 3.5λ 3.5λ fc'fc'bbwwdd ==

(

)(

)( )

3.5 1.0 6000 8.0 74 1000

= 160.5 kip

At edge of pocket A (approximately 29 in. from end) d above pocket ≈ 45 in. fpc =

170 = 0.272 ksi 624

Vc = (3.5λ fc' + 0.3fpc)bwd = [3.5(0.0775) + 0.3(0.272)](8)(45) = 127.0 kip Vu = 77.0 – 0.78(29/12) = 75.1 kip < 127.0 kip (A more complete shear analysis is shown in Section 5.2.) Vc > Vu > Vc /2 use minimum shear reinforcement. From Section 5.2.4, calculate minimum shear reinforcement: Av = 0.75λ f ' bw = 0.75 1 6000 8 = 0.00775 in.2/in. = 0.093 in.2/ft c 60,000 fy s

()

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CHAPTER 5

EXAMPLE 5.5.6.1 Design of a Prestressed, Pocketed Spandrel Beam (cont.) Alternative: At end:

  5

A f Av = ps pu 80f s yd

( ) ( )( )

0.918 270 d = bw 80 60 74

74 = 0.00212 in.2/in. = 0.025 in.2/ft 8

Over pocket:

( ) 80 (60 )( 45 ) 0.918 270

45 = 0.00272 in.2/in. = 0.033 in.2/ft 8

These requirements are easily met with welded-wire reinforcement (WWR) in each face of the beam.  ongitudinal reinforcement: The code does not require skin reinforcement for prestressed components, unless L it is a Class C member (see ACI 318-05 section 18.4.4.4); however, it is generally considered good practice to provide some horizontal steel. The requirements for out-of-plane bending near the end (Section 5.5.5) must be met (only double-tee-stem loads are eccentric): Awv = AAwwtl ==

3 ( 21.8 ) ( 2.5 ) Vue = 2φfy dw 2 ( 0.90 ) ( 60 ) ( 6 )

= 0.24 in.2 on inside face

6 × 6 – W4 × W4 in each face cut out around pockets would meet all of the requirements 4. Determine hanger reinforcement at beam pockets: Vertical component of each leg of hanger bar: =

21.8 = 10.9 kip 2

Vu (each leg) = Ash (each leg) =

101/4"

10.9 = 12.6 kip cos 30°

4" maximum

12.6 Vu = = 0.28 in.2 φfy ( 0.75 ) ( 60 )

Use (1) #5; Ash = 0.31 in.2 > 0.28 in.2 From Design Aid 15.4.4, ld = 19 in. above pocket top

Pocket

42"

 elect #5 with vertical leg length of 42 in. S minimum.  einforcement at the end of the component R should now be designed in accordance with the step-by-step procedure shown in Section 5.6.3. The result is reinforcement similar to that shown in the following figure.

4" maximum

30°

8" (1) #5 hanger bar

19" inside 20" outside

3" to 9" typical to hanger bar

12" May be reduced at first pocket to clear dap corner by 2 in. Detail

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CHAPTER 5

EXAMPLE 5.5.6.1 Design of a Prestressed Pocketed Spandrel Beam (cont.)

  5

5. Other considerations. a. F  or parking structures, the spandrel beam must be checked for vehicle-barrier load criteria. Most codes require the application of 10,000 lb (factored) applied horizontally 18 in. above the floor. b. Local code requirements for snow loading should be checked in addition to the 40 lb/ft2 live load on the roof decks of parking structures.

1

/2" DBA

(2) #3

3'-4"

(2) #9

60"

(2) #3 U-bars #3 each side of pockets A & B

1'-0"

6'-2" Nu

6'-6"

Vu = 77.0 kip

(2) #5

6"

a = 6 + 11/2+ 11/2 = 9"

A

A

center of gravity (6) 1/2" diameter strands

8"

5'-4"

Note: Beam shear steel not shown for clarity, see below.

Elevation

CL column CL stem 9" Support face WWR 6×6 - W4 × W4

Corbel

1"

1" 8"

Precast concrete column

1'-3" 2'-6"

CL stem

Suggested minimim clear dimension between inside of dap and inside of first pocket 5'-0" Section A-A

Note: CL = centerline; DBA = deformed bar anchor; WWR = welded-wire reinforcement.

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5.6

Bearing

5.6.1

Bearing on Plain Concrete

CHAPTER 5

Plain concrete bearing may be used in situations where the bearing is uniform and the bearing stresses are low, for example, as is typical in hollow-core and solid slabs. In other situations, and in thin-stemmed components where the bearing area is smaller than 20 in.2, a minimum reinforcement equal to Nu /φfy (but not less than (1) #3) is recommended. It is recommended that, when properly designed bearing pads are used, Nu be taken as 0.2 times the sustained load portion of Vu unless otherwise calculated. The design bearing strength of plain concrete may be calculated as:

φVnn == φCr ( 0.85 fc' A1 ) φV



A2 ≤ 1.1 fc' A1 A1

  5 45°

45°

b

w

(Eq. 5-54)

where: φVn = design bearing strength, kip φ = 0.65 Nu

Cr

= ⎛⎜ sw ⎞⎟ Vu ⎝ 200 ⎠

s Nu

2

Section

Reinforced Concrete Bearing

If the applied load Vu exceeds the design bearing strength φVn as calculated by Eq. 5-54, reinforcement is required in the bearing area. This reinforcement can be designed by shearfriction as discussed in Section 5.3.6. Referring to Fig. 5.6.2, the reinforcement Avf + An nominally parallel to the direction of the axial load Nu is determined by Eq. 5-32 through 5-34 with Acr = bh (that is, θ ≈ 0).11 This reinforcement must be appropriately developed by hooks or by welding to an anchor bar, bearing plate, or angle. Vertical reinforcement across potential horizontal cracks can be calculated by: Ash ==

(A

vf

)

+ An f y

µe f ys



1

A2 measured on this plane

See Fig. 5.6.1 for additional definitions.



Load

Vu

Load area A1

= 1.0 when reinforcement is provided in direction of Nu, in accordance with Section 5.6.2 or when Nu is zero. The product sw should not be taken greater than 9.0 in.2 5.6.2

Plan

Fig. 5.6.1 Bearing on plain concrete.

Ash Possible vertical crack θ = 0°

Nu

(Eq. 5-55)

Stirrups or welded-wire reinforcement used for diagonal tension reinforcement can be considered to act as Ash reinforcement. When components are subjected to bearing force in excess of 1.1 fc' A1, confinement reinforcement in all directions may be necessary.

Possible horizontal crack

Avf + An

h

d

w Vu

Keep to b minimum (critical) Plan View Alternative scheme for Avf + An anchorage at bearing not recommended for thin-stemmed members such as double-tees.

Fig. 5.6.2 Reinforced concrete bearing. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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CHAPTER 5

EXAMPLE 5.6.1 Reinforced Bearing for a Rectangular Beam

  5

Given: PCI standard rectangular beam 12RB28 Vu = 94 kip (includes all load factors) Nu = 15 kip (includes all load factors) Bearing pad = 4 in. x 10 in. = 5000 psi, normalweight fc' fy = 60,000 psi (all reinforcement)

28"

Problem: Determine reinforcement requirements for the end of the component. ___________________________________________

Nu = 15 kip

Solution: Acr = b(h) =12(28) = 336 in.2

Vu = 94 kip

Check max Vn from Table 5.3.1. 1000λAcr = 1000(1.0)(336)/1000 = 336 kip OK

Max Vu = 0.75(336) = 252 kip > 94 kip By Eq. 5-33: µe =

φ1000λ Acr µ 0.75 (1000 ) (1) ( 336 ) (1.4 ) 3.75>>3.4 3.4, use 3.4 (from Table 5.3.1) = ==3.75 Vu 94,000

By Eq. 5-32b: Avf =

Vu Vu 94,000 94,000 = = 0.61 in.2 φfyφµfey µ0.75 3.4 60,000 3.4 0.75 60,000 ( ) ( ) ( ) ( ) e

By Eq. 5-34: An =

Nu 15,000 = = 0.33 in.2 φfy 0.75 ( 60,000 )

Avf + An = 0.61 + 0.33 = 0.94 in.2 OK

Use (3) #5; As = 0.93 in.2 Consider Determine ld from Design Aid 15.2.9. for fc' ld Acr Vu

= 5000 psi: = 21 in. = ldb = (21)(12) = 252 in.2 = (Avf + An)fy = 0.94(60,000)

µe

=

φ1000λ Acr µ 0.75 (1000 ) (1) ( 252 ) (1.4 ) (1) 4.7 >>3.4 = == 4.7 3.4 Vu 0.94 ( 60,000 )

Use µe = 3.4 in Eq. 5-55: Ash

=

(A

vf

)

( ) 3.4 (60,000 )

+ An fy 0.94 60,000

µefys

= 0.28 in.2

Use (2) #3 stirrups; As = 0.44 in.2

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS 5.6.3

Dapped-End Bearing

Design of bearing areas that are recessed or dapped into the end of the component requires the investigation of several potential failure modes. These are numbered and shown in Fig. 5.6.3 and listed in this section, as well as the reinforcement required for each consideration. The design equations given in this section are based primarily on References 17 and 18, and are appropriate for cases where shear span-todepth ratio (a/d in Fig. 5.6.3) does not exceed 1.0. Dap reinforcement (Eq. 5-56 through 5-62) should be provided in all cases where any one or more of the following conditions occurs: 1. The depth of the recess exceeds 0.2H or 8 in. 2. The width of the recess (lp in Fig. 5.6.3) exceeds 12 in. 3a. For components less than 8 in. wide, less than one-half of the main flexural reinforcement extends to the end of the component above the dap. 3b. For components 8 in. wide or more, less than one-third of the main flexural reinforcement extends to the end of the component above the dap. These criteria indicate that only short, shallow recesses, having the minimum amount of main reinforcement or more extending into the nib above the dap, do not require all the dap reinforcement. Experience and some unpublished tests verify that, for short, shallow recesses, the hanger reinforcement Ash and Ash' is not necessary. However, in these cases, it is recommended that confinement reinforcement Av and flexural reinforcement Avf + An, in accordance with Section 5.6.2, be provided. The potential failure modes are as follows: 1. Flexure (cantilever bending) and axial tension in the extended end. Provide flexural reinforcement Af plus axial tension reinforcement An. 2. Direct shear at the junction of the dap and the main body of the component. Provide shear-friction reinforcement composed of Avf and Ah, plus axial tension reinforcement An. 3. Diagonal tension emanating from the reentrant corner. Provide shear reinforcement Ash. 4. Diagonal tension in the extended end. Provide shear reinforcement composed of Ah and Av. 5. Diagonal tension in the undapped portion. This is resisted by providing a full development length for As beyond the potential crack.16

CHAPTER 5

5.6.3.1 F  lexure and Axial Tension in Extended End The horizontal reinforcement is determined in a manner similar to that for column corbels (Section 5.9.4). Thus:

As = A f + An =

1 φ fy

⎡ ⎛ a⎞ ⎛ h⎞⎤ ⎢Vu ⎜ ⎟ + N u ⎜ ⎟ ⎥ (Eq. 5-56) d ⎝ ⎠ ⎝ d⎠⎦ ⎣

where: φ = 0.75 a = s hear span, measured from load to center of Ash, in. h = depth of component above dap, in. d = distance from top to center of reinforcement As, in. fy = yield strength of flexural reinforcement, psi Nu = 0.2 times sustained load portion of Vu unless otherwise calculated (when bearing pads are used),11 lb Note: To be exact, Eq. 5-56 should have jud in the denominator. The use of φ = 0.75 instead of 0.90 (flexure) compensates for this approximation. Also, for uniformity, φ = 0.75 is used thoughout Section 5.6 even though φ = 0.90 would be more appropriate and may be used where flexure and direct tension are addressed. 5.6.3.2 Direct Shear The potential vertical crack shown as 2 in 4Fig. 5.6.3 5 is resisted by a combination of As and Ah. This reinforcement can be calculated by Eq. 5-57 through 5-59:

Ass ==

2Vu + An 3φ f y µe

(Eq. 5-57)



Ans == A

Nu φ fy

(Eq. 5-58)



Ah = 0.5(As – An)

(Eq. 5-59)

where: φ = 0.75 fy = yield strength of As, An, Ah, psi µe =

φ1000 λ bhµ ≤ values in Table 5.3.1 Vu

The shear strength of the extended end is limited by the maximum values given in Table 5.3.1.

Each of these potential failure modes should be investigated separately. The reinforcement requirements are not cumulative, that is, As is the greater of that required by 1 or 2, not the sum. Ah is the greater of that required by 2 or 4, not the sum.

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CHAPTER 5

5

3

  5

2

1 11/ " maximum 2

Vua + Nu(h-d)

d

4

2

h

/3d maximum

d

Ah As

Av Nu

a

Ash

H-d

D

H

d

Assh A'

Vu p

Center of gravity of flexure reinforcement H-D

d

Critical, minimize

5

D

H

Ash Critical, minimize

A' Assh

H-D

d

Critical, minimize

Common alternative A'sh anchorage The development of A'sh at the bottom is ensured by the extension of d beyond crack 5

Assh bar anchorage Alternative A' For design of welded bar anchor, see ACI 318-05 Section 11.9.6 (not recommended for thin stems)

Fig. 5.6.3 Potential failure modes and required reinforcement in dapped-end connections.

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.6.3.1 Reinforcement for Dapped-End Beam Given: The 16RB28 beam with a dapped end is shown. Vu = 100 kip (includes all load factors) Nu = 15 kip (includes all load factors) fc' = 5000 psi, normalweight fy = 60 ksi (for all reinforcement)

  5

Problem: Determine the required reinforcements As, Ah, Ash, and Av shown in Fig. 5.6.3. _______________________________________________ Solution: 1. Flexure in extended end: By Eq. 5-56: Assume: Shear span, a = 6 in., d = 15 in. As

2.

=

⎡ ⎛h⎞⎤ ⎛ 6⎞ ⎛ 16 ⎞ ⎤ 1 ⎡ ⎛ a⎞ 1 2 ⎢Vu ⎜ ⎟ + Nu ⎜ ⎟ ⎥ = ⎢100 ⎜ ⎟ + 15 ⎜ ⎟ ⎥ = 1.24 in. φfy ⎣ ⎝ d ⎠ ⎝ d ⎠ ⎦ 0.75 60 ⎣ ⎝ 15 ⎠ ⎝ 15 ⎠ ⎦

=

φ1000λbh µ 0.75 (1000 ) (1) (16 ) (16 ) (1.4 ) = 2.69 < 3.4 Use 2.69 = Vu 100,000

( )

Direct shear: µe

By Eq. 5-57 and 5-58: As

=

2 (100 ) N 15 2Vu + u = + = 0.55 + 0.33 = 0.88 in.2 < 1.24 in.2 3φfy µe φfy 3 ( 0.75 ) ( 60 ) ( 2.69 ) 0.75 ( 60 )

(2) #4

h = 16"

(6) #4 stirrups Ash = (12) #4

(2) #4

5"

(4) #5

5"

2'-4"

Nu = 15 kip /4" deformed anchor bar

d = 15" D = 26" H

Flexure reinforcement

3

(5) #6 Vu = 100 kip

a = 6"

6"

1'-5"

Centroid of flexure reinforcement

2'-3" 2'-10"

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.6.3.1 Reinforcement for Dapped-End Beam (cont.) Therefore As = 1.24 in.2 Use (4) #5, As = 1.24 in.2

  5

By Eq. 5-59: Ah = 0.5(As – An) = 0.5(0.88 – 0.33) = 0.28 in.2 Check shear strength, Table 5.3.1: φVn = φ(1000λbd) = 0.75(1000)(1)(16)(15)/1000 = 180 kip > 100 kip Use (2) #3 U-bars. Ah = 0.44 in.2 (also see step 4) 3.

OK

Diagonal tension at re-entrant corner: By Eq. 5-60: Ash =

Vu 100 = = 2.22 in.2 φfy 0.75 60

( )

Use (6) #4 closed stirrups; As = (12)(0.2) = 2.40 in.2 For A's (minimum area = Ash) Use (5) #6, As = 2.20 in.2 4.

Diagonal tension in the extended end: Concrete capacity = 2λ fc' bd =

()

( )( ) = 33.9 kip

2 1 5000 16 15 1000

By Eq. 5-62: Av

=

1 2fy

⎞ ⎡Vu ⎤ 1 ⎛ 100 ' − 33.9⎟ = 0.83 in.2 ⎢ φ − 2bd λ fc ⎥ = ⎜ ⎠ ⎣ ⎦ 2 60 ⎝ 0.75

( )

Try (2) #4 stirrups; As = 0.80 in.2 say

OK

Check Eq. 5-61: φVn = φ(Avfy + Ahfy + 2λ fc' bwd) φVn = 0.75[0.80(60) + 0.44(60) + 33.9] = 81.2 kip < 100 kip Change Ah to (2) #4 φVn = 97.4 kip ≈ 100 kip say

OK

Check anchorage requirements: As bars: From Design Aid 15.4.4: fy = 60,000 psi fc' = 5000 psi #5 bars ld = 21 in. Extension past dap = H – d + ld = 28 – 15 + 21 = 34 in. Ah bars: From Design Aid 15.4.4, for #4: ld = 17 in. A'sh bars: From Design Aid 15.4.4, for #6: ld = 25 in. Bar length = H – D + ld = 28 – 26 + 25 = 27 in.

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS 5.6.3.3 Diagonal Tension at Re-entrant Corner The reinforcement required to resist diagonal tension cracking starting from the re-entrant corner, shown as crack 3 in Fig. 5.6.3, can be calculated from: V Ash = u φ fy



•

•

(Eq. 5-60)

where: φ = 0.75 Vu = applied factored load, lb Ash = vertical or diagonal bars across potential diagonal tension crack, in.2 fy = yield strength of Ash, psi

•

5.6.3.4 Diagonal Tension in Extended End Additional reinforcement for crack 2 required in the extended end, such that:

(



4 in 5Fig. 5.6.3 is

)

φVn = φ Av f y + Ah f y + 2bd λ fc'

(Eq. 5-61)

At least one-half of the reinforcement required in this area should be placed vertically. Thus: minimum Av =



⎞ 1 ⎛ Vu − 2bd λ fc' ⎟ (Eq. 5-62) ⎜ 2 fy ⎝ φ ⎠

5.6.3.5 Anchorage of Reinforcement With reference to Fig. 5.6.3: • • •

• •

Horizontal bars As should be extended a minimum of ld

2past crack 4 5 and anchored at the end of the beam by

welding to cross bars, plates, or angles. Horizontal bars Ah should be extended a minimum of ld past crack 2 and4 anchored 5 at the end of the beam by hooks or other suitable means. To ensure development of hanger reinforcement Ash, it may be bent and continued parallel to the beam bottom, or separate horizontal reinforcement A'sh ≥ Ash must be provided. The extension of reinforcement at beam bottom must be at least ld beyond 2 crack 4 5. The Ash' reinforcement may be anchored on the dap side by welding it to a plate (Fig. 5.6.3), angle, or cross bar. The beam flexure reinforcement may also be used to ensure development of Ash reinforcement, provided that the flexure reinforcement is adequately anchored on the dap side. Vertical reinforcement Av should be properly anchored by hooks, as required by ACI 318-05. Welded-wire reinforcement in place of bars may be used for reinforcement. It should be anchored in accordance with ACI 318-05.

5.6.3.6 Other Considerations •

The depth of the extended end should not be less than about one-half the depth of the beam, unless the beam is significantly deeper than necessary for other than structural reasons.

CHAPTER 5 The hanger reinforcement Ash should be placed as close as practical to the reentrant corner. This reinforcement requirement is not additive to other shear reinforcement requirements, but should be in addition to torsion steel. If the flexural stress in the full depth section immediately beyond the dap exceeds 7.5 fc' , using factored loads and gross section properties, longitudinal reinforcement should be placed in the beam to develop the required flexural strength. The Reference 19 study found that, due to formation of the critical diagonal tension crack 2 (crack 4 5 in Fig. 5.6.3), it was not possible to develop a full-depth beam shear strength greater than the diagonal tension cracking shear in the vicinity of the dap. It is suggested, therefore, that for a length of the beam equal to the overall depth H of the beam, the nominal shear strength of concrete Vc be taken as the lesser of Vci and Vcw calculated at H/2 from the end of the full-depth web.

5.7

Loss of Prestress

Loss of prestress is the reduction of tensile stress in prestressing tendons (strands) due to shortening of the concrete around the tendons, relaxation of stress within the tendons, and external factors that reduce the total initial force before it is applied to the concrete. ACI 318-05 identifies the sources of loss of prestress listed in Section 5.7.1. Losses have no effect on the ultimate strength of a flexural component unless the tendons are unbonded or if the final stress after losses is less than 0.50fpu. Underestimation or overestimation of losses can affect service conditions such as camber, deflection, and cracking. 5.7.1

Sources of Stress Loss

Anchorage seating loss and friction. Anchorage seating loss and friction loss due to intended or unintended curvature in post-tensioning tendons are two mechanical sources of loss. They represent the difference between the tension applied to the tendon by the jacking unit and the initial tension available for application to the concrete by the tendon. Their magnitude can be determined with reasonable accuracy and, in many cases, they are fully or partially compensated for by overjacking. Elastic shortening of concrete. The concrete around the tendons shortens as the prestressing force is applied to it. Tendons that are already bonded to the concrete shorten with it. Shrinkage of concrete. Loss of stress in the tendon due to shrinkage of the concrete surrounding it is proportional to that part of the shrinkage that takes place after the transfer of prestress force to the concrete. Creep of concrete and relaxation of tendons. Creep of concrete and relaxation of tendons complicate stress-loss calculations. The rate of loss due to each of these factors changes when the stress level changes. Because the stress level is changing constantly throughout the life of the structure, the rates of loss due to creep and relaxation are also constantly changing.

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CHAPTER 5

5.7.3

Table 5.7.1  Values of Kre and J Kre

J

Grade 270, stress-relieved strand or wire

20,000

0.150

Grade 250, stress-relieved strand or wire

18,500

0.140

Grade 240 or 235, stress-relieved wire

17,600

0.130

Grade 270, low- relaxation strand

5000

0.040

Grade 250, low-relaxation wire

4630

0.037

Grade 240 or 235, low-relaxation wire

4400

0.035

Grade 145 or 160, stress-relieved bar

6000

0.050

Type of tendon

  5

Stress-relieved strand or wire

Stress-relieved bar or low-relaxation strand or wire

0.80

1.28

0.79

1.22

0.78

1.16

0.77

1.11

0.76

1.05

0.75

1.45

1.00

0.74

1.36

0.95

0.73

1.27

0.90

0.72

1.18

0.85

0.71

1.09

0.80

0.70

1.00

0.75

0.69

0.94

0.70

0.68

0.89

0.66

0.67

0.83

0.61

0.66

0.78

0.57

0.65

0.73

0.53

0.64

0.68

0.49

0.63

0.63

0.45

0.62

0.58

0.41

0.61

0.53

0.37

0.60

0.49

0.33

5.7.2

TL = ES + CR + SH + RE





(Eq. 5-63)

ES = KesEpsfcir /Eci

(Eq. 5-64)

where: Kes = 1.0 for pretensioned components Eps = modulus of elasticity of prestressing tendons (about 28.5 × 106 psi) Eci = modulus of elasticity of concrete at time prestress is applied, psi fcir = net compressive stress in concrete at center of gravity of prestressing force immediately after the prestress has been applied to the concrete, psi:

⎛ P Pe2 ⎞ M e fcir = K cir ⎜ i + i ⎟ − g lg ⎠ lg ⎝ Ag

(Eq. 5-65)

where: Kcir = 0.9 for pretensioned components Pi = initial prestress force (jacking force after anchorage loss), lb e = eccentricity of center of gravity of tendons with respect to center of gravity of concrete at the cross section considered, in. Ag = area of gross concrete section at the cross section considered, in.2 Ig = moment of inertia of gross concrete section at the cross section considered, in.4 Mg = bending moment due to dead weight of prestressed component and any other permanent loads in place at time of prestressing, in./lb Losses due to creep of concrete are calculated as:

Range of Values for Total Loss

Total loss of prestress in typical components will range from about 25,000 psi to 50,000 psi for normalweight concrete components, and from about 30,000 psi to 55,000 psi for sand-lightweight components. The load tables in Chapter 3 have a lower limit on loss of 30,000 psi. 5–84

This section is based on the report of a task group sponsored by ACI-ASCE Committee 423, Prestressed Concrete.20 The report gives simple equations for estimating losses of prestress that enable the designer to estimate the various types of prestress loss rather than using a lump-sum value. It is believed that these equations, intended for practical design applications, provide fairly realistic values for normal design conditions. For unusual design situations and special structures, more detailed analyses may be warranted. Total losses TL are losses due to elastic shortening ES, creep of concrete CR, shrinkage of concrete SH, and relaxation of tendons RE.

Losses due to elastic shortening are calculated as:

Table 5.7.2  Values of C fpi/fpu

Estimating Prestress Loss

CR = Kcr(Eps /Ec)(fcir – fcds)

(Eq. 5-66)

where: Kcr = 2.0 normalweight concrete = 1.6 sand-lightweight concrete fcds = stress in concrete at center of gravity of prestressing force due to all superimposed, permanent dead loads that are applied to the member after it has been prestressed, psi Ec = modulus of elasticity of concrete at 28 days, psi

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.7.1 Loss of Prestress Given: 10LDT 32 + 2 as shown. Span = l = 70 ft No superimposed dead load except topping RH = 75%

  5

Section properties (untopped): A = 615 in.2 I = 59,720 in.4 Sb = 2717 in.3 V/S = 615/364 = 1.69 in. wt = 491 lb/ft wt of topping = 250 lb/ft

10'-0" 5'-0" 73/4"

2" 2"

Concrete: Precast concrete: Sand-lightweight fc' = 5000 psi Ec = 3.0 × 106 psi fci' = 3500 psi Eci = 2.5 × 106 psi

32"

43/4" Section

Topping: fc' = 5000 psi, normalweight Prestressing steel: (12) 1/2-in.-diameter, 270 ksi, low-relaxation strands Aps = 12(0.153) = 1.836 in.2 Eps = 28.5 × 106 psi Depressed at midspan: ee = 12.81 in. ec = 18.73 in. Problem: Determine total loss of prestress. _______________________________________________

Solution: For depressed strand, critical section is at 0.4l. Determine moments, eccentricity, and prestress force. M at 0.4l =

(

)(

w 0.4 wx  −x =  − 0.4 = 0.12w  2 2 2

(

)

)

Mg = 0.12(0.491)(70)2 = 289 kip-ft Msd = 0.12(0.250)(70)2 = 147 kip-ft e at 0.4l = 12.81 + 0.8(18.73 – 12.81) = 17.55 in. Assume compensation for anchorage seating loss during prestressing. Po = 0.75Apsfpu = 0.75(1.836)(270) = 371.8 kip Determine fcir and fcds: ⎛ 371.8 371.8 (17.55 )2 ⎞ (289 ) (12 ) (17.55 ) ⎛P P e2 ⎞ M e fcir K = cirKcir= ⎜ o + o ⎟ − g = 0.9 ⎜ = 1.251 ksi + ⎟− Ig ⎠ 59,720 59,720 Ig ⎝ Ag ⎝ 615 ⎠

= 1251 psi

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.7.1 Loss of Prestress (cont.)

  5

fcds =

ES =

( ) = 147 (12)(17.55)

M sd e Ig

59,720

=

Eci

E ps Ec

(1) ⎡⎣ 28.5 (10 )⎤⎦ (1251) 2.5 (10 ) 6

K esE psfcir

CR = K cr

= 0.518 ksi = 518 psi

6

= 14,261 psi

28.5 10 ) ( ) 3.0((10 )) (1251− 518) = 11,142 psi 6

(f

cir

− fcds = 1.6

6

⎛V ⎞ SH = (8.2 × 10–6)KshEps(1 – 0.06 ⎜ ⎟ )(100 – RH) ⎝S⎠ –6 6 = (8.2 × 10 )(1)(28.5 × 10 ) × [1 – 0.06(1.69)](100 – 75) = 5250 psi

RE = [Kre – J(SH + CR + ES)]C

From Table 5.7.1: Kre = 5000 J = 0.04



From Table 5.7.2: fpi /fpu = 0.75 C = 1.0 RE = [5000 – 0.04(5250 + 11,142 + 14,261)](1) = 3774 psi TL = ES + CR + SH + RE = 14,261 + 11,142 + 5250 + 3774 = 34,427 psi = 34.4 ksi

Final prestress force = 371.8 – (34.4)(1.836) = 308.6 kip



fcds = Msd(e)/Ig

(Eq. 5-67)

For stress-relieved strand:

where: Msd = moment due to all superimposed, permanent dead load and sustained load applied after prestressing; lb-in. Losses due to shrinkage of concrete are calculated as:

If 0.75 ≥



SH = (8.2 × 10-6)KshEps(1 – 0.06V/S)(100 – RH) (Eq. 5-68) where: Ksh = 1.0 for pretensioned components V/S = volume-to-surface ratio RH = average ambient relative humidity (see Design Aid 4.11.12). Losses due to relaxation of tendons are calculated as:

RE = [Kre – J(SH + CR + ES)]C

≥≥0.70 0.70::

⎛ f ⎞ C = 1 + 9 ⎜ pi − 0.7⎟ ⎝ f pu ⎠

If 0.70 >



f pi f pu

f pi f pu

(Eq. 5-70)

≥ 0.51:

  f pi    f pi    f    f  pu  pu − 0.55 C=  0.19  0.85    

(Eq. 5-71)

(Eq. 5-69)

where: Values for Kre and J are taken from Table 5.7.1. For values of coefficient C (see Table 5.7.2 or calculate using Eq. 5-70 through 5-74.) 5–86

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5.8

⎛ f pi ⎞ ⎜f ⎟ ⎛ f pi ⎞ ⎝ pu ⎠ < 0.51: C = If ⎜ ⎟ f 3.83 ⎝ pu ⎠

⎛ f pi ⎞ ⎜f ⎟ ⎛ f pi ⎞ ⎝ pu ⎠ < 0.51: C = ⎜ f ⎟ 3.83 ⎝ pu ⎠

(Eq. 5-72)

For low-relaxation strand: ⎛ f ⎞ If ⎜ pi ⎟ ≥ 0.54 : ⎝ f pu ⎠

  f pi    f pi     f   f  pu  pu − 0.55 C=  0.21  0.9    





(Eq. 5-73)

⎛ f ⎞ If ⎜ pi ⎟ ≤ 0.54 : ⎝ f pu ⎠

⎛ f pi ⎞ ⎜f ⎟ ⎝ pu ⎠ C= 4.25



(Eq. 5-74)

where: f pipi ==

Pi Aps

fpu = ultimate strength of prestressing steel, psi 5.7.4

Critical Locations

Computations for stress losses due to elastic shortening ES and creep of concrete CR are based on the compressive stress in the concrete at the center of gravity of the prestressing force. For bonded tendons, stress losses are computed at that point on the span where flexural tensile stresses are most critical. In components with straight, parabolic, or approximate parabolic tendons, this is usually midspan. In components with tendons deflected at midspan only, the critical point is generally near the 0.4l point of the span. Because the tendons are bonded, only the stresses at the critical point need to be considered, unless critical sections occur within the development length (see Section 5.2.3). Stresses or stress changes at other points along the component do not affect the stresses or stress losses at the critical point.

CHAPTER 5

Camber and Deflection

Most precast, prestressed concrete flexural components will have a net positive (upward) camber at the time of transfer of prestress, caused by the eccentricity of the prestressing force. This camber may increase or decrease with time, depending on the stress distribution across the component under sustained loads. Camber tolerances are suggested in Chapter 13, Table 13.2.1 of this handbook. Limitations on instantaneous deflections and time-dependent cambers and deflections are specified in ACI 318-05. Table 9.5(b) of ACI 318-05 is reprinted for reference (see Table 5.8.1). It is important to realize that these deflections are not measured from flat, but rather from the position of the component prior to application of the load (and time) being considered. The immediate deflection for comparison with the ℓ/360 and ℓ/180 limits is based on the live load, less any portion that is considered as sustained. The gross moment of inertia is used if the component remains uncracked under full service loads. If the component cracks under service loads, then applicable deflections should be based on bilinear behavior or an effective moment of inertia. Transformed section properties may be used, but generally they provide only small improvement. The long-term deflection for comparison with the ℓ/480 and ℓ/240 limits is more complex for prestressed components than for components reinforced with mild steel. Generally, the net deflection (up or down) at erection is calculated by applying multipliers (1) and (2) of Table 5.8.2 to the selfweight deflection and camber due to prestress. For topped components, the immediate deflection caused by the topping weight is deducted. This is the starting point for the longterm deflection. The long-term deflection due to all sustained loads (including prestress) is calculated using multipliers (3) through (6) of Table 5.8.2. If there are sustained live loads, such as equipment weights, they should be included in the dead-load deflection calculation. The difference between these two values is added to the live-load deflection calculated previously and compared with the relevant limits. The following sections contain suggested methods for computing cambers and deflections. There are many inherent variables that affect camber and deflection, such as concrete mixture, storage method, elapsed time since release of prestress, elapsed time since placement of superimposed loads, relative humidity, and the like. Because of this, calculated long-term values should never be considered anything other than estimates. Non-structural components attached to members that could be affected by camber variations, such as partitions or folding doors, should be placed with adequate allowance for variation. Calculation of topping quantities should also recognize the imprecision of camber calculations. It should also be recognized that camber of precast, prestressed concrete components is a result of the placement of the strands needed to resist the design loads and service-load stresses. While minor adjustments in camber may be achieved by raising or lowering the center of gravity of the prestressing strands, design for ultimate moment capacity and stresses must obviously take precedence in the final design. It is not

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Table 5.8.1  Maximum permissible computed deflections1 Type of member

  5

Deflection to be considered

Deflection limitation

Flat roofs not supporting or attached to nonstructural elements likely to be damaged by large deflections

Immediate deflection due to live load

l/180a

Floors not supporting or attached to nonstructural elements likely to be damaged by large deflections

Immediate deflection due to live load

l/360

That part of the total deflection occurring after attachment of non-structural elements (sum of the long-term deflection due to all sustained loads and the immediate deflection due to any additional live load)b

l/480c

Roof or floor construction supporting or attached to non-structural elements likely to be damaged by large deflections Roof or floor construction supporting or attached to non-structural elements not likely to be damaged by large deflections

l/240d

a. Limit not intended to safeguard against ponding. Ponding should be checked by suitable calculations of deflections, including added deflec-

tions due to ponded water, and considering long-term effects of all sustained loads, camber, construction tolerances, and reliability of provisions for drainage. b. Long-term deflection shall be determined in accordance with Sections 9.5.2.5 or 9.5.4.3 of ACI 318-05, but may be reduced by amount of deflection calculated to occur before attachment of nonstructural elements. This amount shall be determined on the basis of accepted engineering data relating to time-deflection characteristics of members similar to those being considered. c. Limit may be exceeded if adequate measures are taken to prevent damage to supported or attached elements. d. But not greater than tolerance provided for non-structural elements. Limit may be exceeded if camber is provided so that total deflection minus camber does not exceed limit.

practical to alter the forms of the components to produce a desired camber. Therefore, cambers should not be specified. However, camber should be recognized and accounted for in the specification of topping, door openings and placement, partition attachments, and finishes. 2

5.8.1 lcr

Initial camber can be calculated using conventional moment-area equations. Design Aid 15.1.4 has equations for the camber caused by prestress force for the most common strand patterns used in precast, prestressed concrete components. Design Aid 15.1.4 provides deflection equations for typical loading conditions and more general camber equations.

1 Bilinear

Moment

Initial Camber

lg

5.8.2

Elastic Deflections

Calculation of instantaneous deflections of both prestressed and non-prestressed concrete components caused by superimposed service loads follows classical methods of mechanics. Design equations for various load conditions are given in Chapter 15 of this handbook. If the bottom tension in a simple-span component does not exceed the modulus of rupture, the deflection is calculated using the uncracked moment of inertia of the section. The modulus of rupture of concrete is defined in Chapter 9 of ACI 318-05 for normalweight concrete as:

le Calculated Calculated using lcr using lg Calculated using le Deflection 1. Moment that results in bottom tension of fr 2. Moment corresponding to final bottom tension (Note: Prestress effects not included in illustration.)



fr = 7.5 fc'

(Eq. 5-75)

For other concrete densities, multiply by factors from Section 5.2.2.1.

Fig. 5.8.1 Bilinear moment-deflection: effective moment of inertia.

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EXAMPLE 5.8.1.1 Calculation of Initial Camber Given: 8DT24 of Example 5.2.2.3. Section properties: A = 401 in.2 I = 20,985 in.4 yb = 17.15 in. yt = 6.85 in.

  5 Sb = 1224 in.3 St = 3063 in.3 wt = 418 lb/ft superimposed dead load = wsd = 52 lb/ft2

Concrete: fc' = 5000 psi, normalweight (w = 150 lb/ft3)

(

Ec = 33w 1.5 fc' = 33 150

1.5

)

8'-0" 2'-0"

4'-0"

5000 1000

2'-0"

= 4287 ksi

fci' = 3500 psi Eci = 33 150

(

1.5

)

2"

53/4" Neutral axis

17.15"

3500 = 3587 ksi 1000

24"

33/4"

(Note: The values of Ec and Eci could also be read from Design Aid 15.2.1.) Problem: Find the initial camber at time of transfer of prestress. _____________________________________

ee = 5.48" Po

Po = 335 kip e' = 8.42"

Solution: The prestress force at transfer and strand eccentricities are calculated in Example 5.2.2.3 and are shown on the figure. Calculate the upward component using equations given in Design Aid 15.1.4:

 = 70'

2

∆ =

Center of gravity of strand

335 ( 8.42 ) ⎡⎣( 70 ) (12 ) ⎤⎦ Poee  2 Poe'  2 335 ( 5.48 ) ⎡⎣( 70 ) (12 ) ⎤⎦ + = + 8E ci I 12E ci I 8 ( 3587 ) ( 20,985 ) 12 ( 3587 ) ( 20,985 )

2

= 2.15 + 2.20 = 4.35 in. 

Deduct deflection caused by weight of component: 4 ⎛ 0.418 ⎞ ⎡⎣ 70 12 ⎤⎦ 5⎜ ⎟ ⎝ 12 ⎠ 5w  = ∆ = = 3.00 in.  384Eci I 384 3587 20,985 4

(

( )( ) )( )

Net camber at release = 4.35 – 3.00 = 1.35 in. 

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Table 5.8.2  Suggested simple span multipliers to be used as a guide in estimating long-term cambers and deflections for typical prestressed components

  5

Without compos- With composite ite topping topping At erection: (1) D  eflection (downward) component—apply to the elastic deflection due to the component weight at release of prestress

1.85

1.85

(2) C  amber (upward) component—apply to the elastic camber due to prestress at the time of release of prestress

1.80

1.80

(3) D  eflection (downward) component—apply to the elastic deflection due to the component weight at release of prestress

2.70

2.40

(4) C  amber (upward) component—apply to the elastic camber due to prestress at the time of release of prestress

2.45

2.20

(5) Deflection (downward)—apply to elastic deflection due to superimposed dead load only

3.00

3.00

—

2.30

Final:

(6) Deflection (downward)—apply to elastic deflection caused by the composite topping

5.8.3

Bilinear Behavior

5.8.3.1 Cracked-Section Analysis

Section 9.5.4.2 of ACI 318-05 requires that for prestressed concrete flexural components that fall into Class T or Class C (see Section 5.2.2.2), deflection calculations be based on transformed cracked-section analysis, and permits the use of bilinear moment-deflection relationships. This means that the deflection before the component has cracked is calculated using the gross (uncracked) moment of inertia Ig and the additional deflection after cracking is calculated using the moment of inertia of the cracked section. Examples 5.8.3.1 and 5.8.3.2 illustrate the direct application of this principle. As an alternative, the code allows the determination of an effective moment of inertia Ie and the deflection then calculated by substituting Ie for Ig in the deflection calculation, as illustrated in Examples 5.8.3.3 and 5.8.3.4. Figure 5.8.1 illustrates the differences between the two methods.



3 ⎡ ⎛ M ⎞3⎤ ⎛M ⎞ I e = ⎜ cr ⎟ I g + ⎢1 − ⎜ cr ⎟ ⎥ I cr ⎝ Ma ⎠ ⎢⎣ ⎝ M a ⎠ ⎥⎦

⎛f −f ⎞ M cr = 1− ⎜ tot r ⎟ ⎝ fl ⎠ Ma

(Eq. 5-76)

(Eq. 5-77)

where: ftot = final calculated total stress in the component fl = calculated stress due to live load

5–90



(

)

IIcrcr = nAps d p2 1 − 1.6 nρ p

(Eq. 5-78)

may be used to determine the cracked moment of inertia. Design Aid 5.14.11 gives coefficients for use in solving this equation. Iterative procedures used for non-prestressed components that neglect the effects of prestressing are also conservative, but may be adequate for Class T components. For Class C components, however, and for other applications where a more exact analysis may be desired, a method described by Mast,4 summarized in Section 5.2.2.2, may be used. 5.8.4

Long-Term Camber/Deflection

ACI 318-05 provides a multiplier λ applied to initial deflection for estimating the long-term deflection of non-prestressed reinforced concrete components (ACI 318-05 Section 9.5.2.5):

The equation for effective moment of inertia is:

For many applications, particularly Class T components, the conservative empirical relationship:



λ=

ξ 1 + 50 ρ'

(Eq. 5-79)

where  = factor related to length of time ρ' = ratio of compressive reinforcement (There is no corresponding ratio for prestressed concrete in ACI 318-05.) The determination of long-term cambers and deflections in precast, prestressed concrete components is somewhat more complex because of the effect of prestress. The loss of prestress over time, the strength gain of concrete after release of prestress, and the camber or deflection is important not only at the initial and final stages but also at erection, which occurs at some intermediate stage, usually from 30 to 60 days after casting. It has been customary in the design of precast, prestressed concrete components to estimate the camber of a component

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EXAMPLE 5.8.3.1 Deflection Calculation Using Bilinear Moment-Deflection Relationship – Example 1 Given: 8DT24 from Examples 5.2.2.3 and 5.8.1.1.

  5

Problem: Determine the total deflection caused by the specified, uniform live load. ______________________________________________________________________________________ Solution: Determine component classification fr

= 7.5 fci' = 530 psi

From Example 5.2.2.3, the final tensile stress is 766 psi, which is more than 530 psi, but less than 12 fci' . Therefore, it is a Class T component. Determine Icr from Design Aid 5.14.11: Aps =1.836 in.2 (see Example 5.2.2.3) dp at midspan = ec + yt = 13.90 + 6.85 = 20.75 in. (Note: It is within the precision of the calculation method and observed behavior to use midspan dp and to calculate the deflection at midspan, although the maximum tensile stress in this case is assumed at 0.4l.)

ρp =

Aps bd p

=

1.836 = 0.00092 96 20.75

( )(

)

C = 0.0056 Icr = Cbdp3 = 0.0056(96)(20.75)3 = 4803 in.4 Determine the portion of the live load that would result in a bottom tension of 530 psi. 766 – 530 = 236 psi The tension caused by live load alone is 1614 psi; therefore, the portion of the live load that would result in a bottom tension of 530 psi is: 1614 − 236 0.280 = 0.239 kip/ft 1614

(

)

0.280 – 0.239 = 0.041 kip/ft 4 ⎛ 0.239 ⎞ 5⎜ ⎡⎣70 (12 ) ⎤⎦ ⎟ ⎠ ⎝ 5w  12 ∆g = 384E I = 384 ( 4287 ) ( 20,985 ) = 1.44 in. c g 4

4 0.041⎞⎞ 4 ⎛⎛ 0.239 ⎡⎣ 70 70(12 12)⎤⎦ 55⎜⎜ ⎟ 12 ⎠ ⎝⎝ 12 5w  ∆cr = = 1.08 in. = 384E cI g 384 384( 4287 ( 4287)()20,985 ( 4803))

4

Total live-load deflection ∆l = ∆g+ ∆cr = 1.44 + 1.08 = 2.52 in.

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EXAMPLE 5.8.3.2 Deflection Calculation Using Bilinear Moment-Deflection Relationship – Example 2

  5

Given: Rectangular beam from Example 5.2.2.5. Problem: Determine deflection caused by the specified live load. _______________________________________________ Solution: From example: Tension caused by live load =

(

)

M 3000 1000 = 1465 psi = S 2048

From Example 5.2.2.5, stress under full dead load and live load = 879 psi Portion of live load that will result in cracking (581 psi) 879 – 581 = 298 psi 1465 − 298 1.25 = 0.996 kip/ft 1465

(

∆g

∆cr

)

⎛ 0.996 4 4 0.239⎞⎞ 12 40()12 55⎜ )⎤⎦)⎤⎦ ( ⎟⎠ ⎡⎣⎡⎣(70 ⎟ 44 5w  12 ⎝ ⎠ 12 5wI = = = 0.37 in. 384E cI gg 384 384E 384((4287 4696))((20,985 32,768))

⎡ 1.25 − 0.996 ) ⎤ 4 4 ⎞ ⎛ (0.239 55 ⎜⎢ ⎡⎣70 (12⎥)⎡⎣⎤⎦( 40 )(12 ) ⎤⎦ ⎟ ⎠ ⎝⎢ 12 12 5w ⎥⎦ 5wI = ⎣ = = 0.27 in. 384E ) (20,985 ) ) 384EccI crcr 384 ( 4287 384 ( 4696 ) (11,708 44

Total live-load deflection ∆l = ∆g+ ∆cr = 0.37 + 0.27 = 0.64 in. From Table 5.8.1:

l/480 = 40(12)/480 = 1 in.

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Section is satisfactory for all applications.

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EXAMPLE 5.8.3.3 Deflection Calculation Using Effective Moment of Inertia – Example 1 Given: Same section and loading conditions of Examples 5.2.2.3, 5.8.1.1, and 5.8.3.1.

  5

Problem: Determine the deflection caused by live load using the Ie method. _______________________________________________ Solution: From the table of stresses in Example 5.2.2.3: fb = 766 psi (tension) fl = 1614 psi (tension) fr

= 7.5 fc' = 530 psi (tension)

Using Eq. 5-77 M cr ⎛ 766 − 530 ⎞ = 0.854 = 1− ⎜ Ma ⎝ 1614 ⎟⎠ 3

⎛ M cr ⎞ 3 ⎜⎝ M ⎟⎠ = (0.854) = 0.623 a

3

⎛M ⎞ 1− ⎜ cr ⎟ = 1− 0.623 = 0.377 ⎝ Ma ⎠ Inserting into Eq. 5-76 le

∆l

= 0.623(20,985) + 0.377(4803) = 14,884 in.4 4 ⎛ 0.239 0.280 ⎞ 4 70 (12 12) ⎤⎦ 5⎜ 5 ⎡⎣70 ⎟ ⎝ 12 5w 12 ⎠ 5wl = = = 2.37 in. 384E 20,985 ) 384EccI ee 384 384( 4287 4287) (14,884 44

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EXAMPLE 5.8.3.4 Deflection Calculation Using Effective Moment of Inertia – Example 2

  5

Given: The composite section of Example 5.2.2.6: Span = l = 24 ft Ec = 4287 ksi Live load = 4.0 kip/ft Ig = 31,984 in.4 fb = 1298 psi tension Icr = 9770 in.4 fb(total) = 1656 psi tension fr = 7.5 5000 == 530 psi 530 psi Problem: Determine live-load deflection and compare with Table 5.8.1. _____________________________________ Solution: From Eq. 5-76: M cr ⎛f −f ⎞ ⎛ 1656 − 530 ⎞ = 1− ⎜ tot r ⎟ = 1− ⎜ = 0.133 ⎝ 1298 ⎟⎠ Ma ⎝ fl ⎠

From Eq. 5-78: 3 ⎡ ⎛M ⎞3⎤ ⎛ M cr ⎞ I g + ⎢1− ⎜ cr ⎟ ⎥ Icr = 0.133 Ie = ⎜ ⎝ M a ⎟⎠ ⎢ ⎝ Ma ⎠ ⎥ ⎦ ⎣

(

) ( 31,912) + ⎡⎣⎢1− ( 0.133) ⎤⎦⎥ (9770) = 9822 in. 3

3

4

 heck conformance with Table 5.8.1 assuming beam is not supporting or attached to non-structural elements C likely to be damaged by large deflections: Permissible live-load deflection: =

24 (12 )  = 0.80 in. = 360 360 4

5 ( 4.0 ) ( 24 ) (1728 ) 5w  4 Live-load deflection = = 0.71 in. < 0.80 in. = 384E cI e 384 ( 4287 ) ( 9822 )

OK

b = 44" 11/2"

Control joints 2" 2"

A's 10" 24" Aps

As

12"

2"

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12"

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EXAMPLE 5.8.4.1 Use of Multipliers for Determining Long-Term Cambers and Deflections Given:  DT24 for Examples 5.2.2.3, 5.8.1.1, and 5.8.3.1. Non-structural elements are attached, but not likely 8 to be damaged by deflections (light fixtures and the like). Problem: Estimate the camber and deflection and determine if they meet the requirements of Table 9.5(b) of ACI 318-05 (see Table 5.8.1). ______________________________________________________________________________________ Solution: Calculate the instantaneous deflections caused by the superimposed dead and live loads:

∆sd

4 ⎛ 0.080 ⎞ ⎡⎣ 70 12 ⎤⎦ 5⎜ ⎟ 12 ⎝ ⎠ 5w  = = = 0.48 in. 384E c I 384 4287 20,985

( )

4

(

∆l = 2.52 in.

)(

)

(Example 5.8.3.1)

For convenience, a tabular format is used. The estimated critical cambers would then be: At erection of the component: After wsd is applied = 1.80 in. Final long-term camber = 1.12 in. The deflection limitation of Table 5.8.1 for the above condition is l/240.

( )

70 12 240

= 3.50 in.

Total deflection occurring after attachment of non-structural elements: ∆t = (1.80 – 1.12) + 2.52 = 3.20 in. < 3.50

OK

(1) Release

Multiplier

(2) Erection

Multiplier

(3) Final

Prestress

4.35

1.80 × (1)

7.83

2.45 × (1)

10.66

wd

3.00

1.85 × (1)

5.55

2.7 × (1)

8.10

1.35 wsd

2.28

2.56

0.48

3.0 × (2)

1.44

1.80

final camber =

1.12

wl

2.52 final deflection =

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h

  5

T1

∆

T2 

Fig. 5.8.3 Corner separation due to thermal bow. CL

Fig. 5.8.2 Thermal bow of wall panel.

5.8.5 after a period of time by multiplying the initial calculated camber by some factor, usually based on the experience of the designer. To properly use these multipliers, the upward and downward components of the initial calculated camber should be separated in order to take into account the effects of loss of prestress, which only affects the upward component. Table 5.8.2 provides suggested multipliers that can be used as a guide in estimating long-term cambers and deflections for typical components, that is, those components that are within the span-to-depth ratios recommended in this handbook (see Section 3.2.2). Derivation of these multipliers is contained in Reference 21. For components that are made continuous for superimposed dead load and live load, the final multipliers, (3) through (6) in Table 5.8.2, may be reduced. Long-term effects can be substantially reduced by adding non-prestressed reinforcement in prestressed concrete components. The reduction effects proposed in Reference 22 can be applied to the approximate multipliers found in Table 5.8.2 as follows: As Aps C2 = As 1+ Aps C1 +



where: C1 5–96

= multiplier from Table 5.8.2

= revised multiplier = area of non-prestressed reinforcement = area of prestressed reinforcement

C2 As Aps

(Eq. 5-80)

Bowing

A strain gradient between the inside and outside of a wall panel, or between the top and underside of an uninsulated roof component, can cause the component to bow. The theoretical magnitude of bowing (Fig. 5.8.2) can be determined by:

Δ =α

2 8h

(Eq. 5-81)

where: α = strain gradient across panel thickness l = distance between supports h = component thickness For a temperature difference between the inside and outside of a panel:

α = C(T1 – T2)

(Eq. 5-82)

where: C = coefficient of thermal expansion T1, T2 = o utside and inside temperatures, respectively Limited records of temperature measurements indicate that in open structures, such as the roofs of parking decks, the temperature differential seldom exceeds 30 °F to 40 °F. In an insulated sandwich wall panel, the theoretical difference can be higher, but this is tempered by thermal lag due to the mass of the concrete (see Section 11.1). Moisture differences between the inside and outside of an enclosed building can also cause bowing; however, the calcu-

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EXAMPLE 5.8.5.1 Thermal Bow in a Wall Panel Given: A 20-ft-high, 6-in.-thick wall panel as shown. Assume a coefficient of thermal expansion. C = 6 × 10–6 in./in./°F

  5 ∆2

Temperature differential T1 – T2 = 35 °F Ec = 4300 ksi

 — 2

Problem: Determine the potential thermal bow ∆1, the force P required at midheight to restrain the bowing, the stress in the panel caused by the restraint, and the residual bow ∆2. __________________________________________________________

P

∆1

Solution: From Eq. 5-81: ⎡6 (10 −6 ) ⎤⎦ ( 35 ) ⎡⎣ 20 (12 ) ⎤⎦ 2 ∆1 = α = ⎣ 8h 8 (6 )

 — 2

2

= 0.252 in.

From Design Aid 5.14.12 for daily temperature change: Et = 0.75(4300) = 3225 ksi I

=

(bh 3 ) = 12 (6 ) 12

12

CL 3

= 216 in.4/ft

From Design Aid 5.14.12, case 1: P

=

48EtI Δ 48 ( 3225 ) ( 216 ) ( 0.25 ) = 0.605 kip/ft of width = 3 3 ⎡⎣ 20 (12 ) ⎤⎦

M

=

P  0.605 ( 20 ) = 3.02 kip-ft/ft of width = 4 4

Panel stress = My/I

=

3.02 (12,000 ) ( 3) = 503 psi 216

The residual bow can be calculated by adjusting the equation in Design Aid 5.14.12, case 5, to read: ∆2 =

M 2 ; and substituting 16 Et I

( )

l/2 for l: ∆2 =

3.02 (12 ) ⎡⎣10 (12 ) ⎤⎦ 16 ( 3225 ) ( 216 )

2

= 0.047 in.

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EXAMPLE 5.8.5.2 Thermal Force and Bow in a Roof Component

  5

Given: A 30IT24 inverted-tee beam supporting the double-tees of the upper level of a parking deck, as shown, is welded at each end at the bearing to the column and subject to a thermal gradient of 35 °F.  ote: Welding at the bearings of precast concrete components is highly discouraged; see note at the end of N the example. Coefficient of thermal expansion: C = 6 × 10–6 in./in./°F T1 – T2 = 35 °F Ec = 4300 ksi, for the composite section I = 51,725 in.4

24'

Problem: Find the tensile force developed at the support. ______________________________________________ Solution: From Eq. 5-81 and 5-82:

∆=

(

)

C T1 −T2  8h

2

=

d

24" T

( ) ( 35) ⎡⎣ 24 (12)⎤⎦ 8 ( 27 )

6 10

6

2

(Typical)

= 0.081 in.

From Design Aid 5.14.12, case 4: Et = 0.75(4300) = 3225 ksi

(

C

3"

)(

)(

)



M=

8Et ΙΔ 8 3225 51,725 0.081 = 1303 kip-in. = 2 2 ⎡ 24 12 ⎤ ⎣ ⎦



T=

1303 M = d 24 + 1.5

Note: This weld is highly discouraged and is shown here for illustrative purposes only.

( )

(

)

= 51.1 kip

Note: This example illustrates that large forces can occur when roof components are welded at the bearings, and why cracking occurs. The force calculated is an upper-bound value, and does not consider the relieving effects of connection extension, microcracking, and column flexibility. Nevertheless, an alternative method that does not use welding at the bearings is strongly recommended.

lation is much less precise and involves more variables. The exterior layer of the concrete panel absorbs moisture from the atmosphere and periodic precipitation, while the interior layer is relatively dry, especially when the building is heated. This causes the inside layer to shrink more than the outside, causing an outward bow. The outward shrinkage bowing would tend to balance the theoretical inward thermal bowing in cold weather, which is believed to explain the observation that wall panels always bow out. While the magnitude of bowing is usually not very significant, in the case of wall panels, it may cause separation at the corners (Fig. 5.8.3) and possible damage to joint sealants. It may, therefore, be desirable to restrain bowing with one or more connections between panels. As illustrated in Example 5.8.5.1, Design Aid 5.14.12 gives equations for calculating 5–98

the required restraint and the moments this restraint would cause in the panel. The midheight-panel restraining force illustrated in Example 5.8.5.1 can occur in a multistory, load-bearing wall panel. For example, if the wall panel is two stories tall and the intermediate floor is laterally braced against sidesway, a restraining, force-resisting, thermal bowing can develop in a connection between the wall panel and the intermediate floor. The wall panel should be connected to the intermediate floor to avoid loss of floor support when the wall panel bows outward. If the intermediate floor is not braced against sidesway, the P-∆ wall analysis should consider the secondary moment due to the intermediate floor gravity reaction loading the wall panel near or at the point of its maximum bow.

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS If non-structural elements, such as drywall ceilings or interior drywall or masonry partitions, are attached to wall panels unrestrained against bowing, those items should be attached with soft or flexible joints. Differential temperature can cause upward bowing in roof components, especially in open structures such as parking decks. If these components are restrained from rotations at the ends, positive moments (bottom tension) can develop at the support, as shown in cases 4 and 5 of Design Aid 5.14.12. The bottom tension can cause severe cracking. Examination of the equations shows that the thermalinduced positive moments are independent of the span length. (For example, substitute Eq. 5-81 for ∆ in Design Aid 5.14.12, case 4.) Note from Design Aid 5.14.12 that if only one end is restrained, as is sometimes done to relieve axial volumechange force, the restraint moment is doubled. Also note that, because thermal bow occurs with daily temperature changes, the cyclical effects could magnify the potential damage.

5.9

Compression Components

Precast and prestressed concrete columns and load-bearing wall panels are usually proportioned on the basis of strength design. Stresses under service conditions, particularly during handling and erection (especially of wall panels) must also be considered. The procedures in this section are based on Chapter 10 of the ACI 318-05 and on the recommendations of the PCI Committee on Prestressed Concrete Columns (referred to in this section as the recommended practice).23 5.9.1

 trength Design of Precast Concrete S Compression Components

The capacity of a reinforced concrete compression component with eccentric loads is typically determined by constructing a capacity interaction curve. Points on this curve are calculated using the compatibility of strains and solving the equations of equilibrium as prescribed in Chapter 10 of ACI 318-05. Solution of these equations is illustrated in Fig. 5.9.1. ACI 318-05 waives the minimum reinforcement requirements for walls in compression if the concrete is prestressed to at least an average of 225 psi after all losses. Interaction curves for typical prestressed square columns and wall panels are provided in Chapter 3. Construction of an interaction curve usually follows these steps: Step 1: Determine Po for Mn = 0. See Fig. 5.9.1(c). Step 2: Determine the point of maximum moment with compression controlling. For components with non-prestressed reinforcement, this is the balance point, which occurs when the net tensile strain in the extreme tension steel is equal to fy /Es. For symmetrical prestressed components, it is sufficiently precise to assume that the point occurs when the compression block a is one-half the component depth. Step 3: Determine Mo for Pn = 0. This is normally done by neglect-

CHAPTER 5

ing the reinforcement above the neutral axis and determining the moment capacity by one of the methods described in Section 5.2.1. Step 4: Calculate the maximum useable axial resistance specified by the code as 0.80φPo for tied columns and 0.85φPo for spiral columns (see Section 5.9.1). Step 5: For each additional point on the interaction curve, proceed as follows: a. Select a value of c and calculate a = 1c. b. Determine the value of Acomp from the geometry of the section. See Fig. 5.9.1(a). c. Determine the strain in the reinforcement assuming that εc = 0.003 at the compression face of the column. For prestressed reinforcement, add the strain due to the effective prestress εse = fse /Eps. d. Determine the stress in the reinforcement. For nonprestressed reinforcement, fs = εsEs ≤ fy. For prestressed reinforcement, the stress is determined from a stress-strain relationship (see Design Aid 15.2.4). If the maximum factored moment occurs near the end of a prestressed component where the strand is not fully developed, an appropriate reduction in the value of fps should be made, as described in Section 5.2.3. e. Calculate Pn and Mn by statics. f. Calculate φPn and φMn. ACI 318-05 prescribes that for compression-controlled sections (without spiral reinforcement) with net tensile strain εt in the extreme tension steel less than or equal to that at the balance point, φ = 0.65. For Grade 60 reinforcement and for prestressed steel, this occurs when εt ≤ 0.002. For tension-controlled sections in which εt ≥ 0.005, φ = 0.9. For sections in which εt is between these limits, φ = 0.48 + 83εt. For each point plotted on the nominal strength curve, multiply Pn and Mn by φ to obtain the design strength curve. For cross sections that are not rectangular, it is necessary to determine separate curves for each direction of the applied moment. Further, since most architectural precast concrete column cross sections are not rectangular, the a distance only defines the depth of the rectangular concrete stress distribution. Instead of using a/2, as for a rectangular cross section, it is necessary to calculate the actual centroid of the compression area that is indicated as y'. As noted in step 5(d), the flexural resistance is reduced for prestressed concrete components at locations within a distance equal to the strand development length from each end. The flexural resistance of the prestressed reinforcement in this zone can be supplemented by non-prestressed reinforcement that is anchored to end plates or otherwise developed. The interaction curves in Chapter 3 are based on a maximum value of fps = fse. This can be assumed to be at the point where the prestressing force is completely transferred to the

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ε's

0.85f'c

b

  5

d'p dp hd

d'

+

0.003 in./in.

y'

c

yt

Pn

As' f's a

e

Ap' s fp' s

c.g. Apsfps

Centroid of Acomp

Asfs

' +A'sfs' − Asfs − A'psfps − Apsfps ' Mn = Pne = ( Acomp − As − A'ps )( y t − y' ) ( 0.85fc' ) +A'sfs' ( y t − d' ) + Asfs (d − y t ) ' −A'psfps ( y t − d'p ) + Apsfps (d p − y t )

(a) Basic relationships

0.85fc'

b d'p d' dp hd

0.003 in./in. y'

c.g.

yt

Pn

As' fs'

Acomp = A if a > h

Ap' s fp' s

ε's

= (0.003/c)(c – d’)

εs

= (0.003/c)(c – d )

a

c

= (0.003/c)(c – d') εs = (0.003/c)(d – c) ε'ps = fse / E ps − (0.003 / c − d 'p ) ≤ 0.035 εps = fse /Eps + (0.003/c)(dp – c) fs' = ε's Es ≤ fy fs = εsEs ≤ fy fps' from stress-strain diagram ≤ fpu fps from stress-strain diagram ≤ fpu Pn = ( Acomp − A's − A'ps ) ( 0.85fc' )

Apsfps

ε = fse / E ps − (0.003 / c ) (c − d 'p ) ≤ 0.035 ' ps

Asfs

εps

n.a.

= fse /Eps + (0.003/c)(dp – c)

Remaining equations same as in case (a).

(b) Special case with neutral axis outside of the section 0.85f'c

b

0.003 in./in.

d'p d' dp hd

As' fy' Ap' s f'ps Pn

c.g.

Apsfps

Pn

= 0.85fc' ( A − A's − A'ps − Aps − As ) −



(A

' ps

+ Aps )(fse − 0.003E ps ) + ( A's + As ) fy

Asfs (c) Special case when:

Mn = 0, Pn = Po 0.85f'c

b d'p d' dp hd

+

0.003 in./in. y'

c

yt

a

Pn As' f's

e

c.g. Centroid of Acomp

Asfy

dt

= the greater of d and dp 0.003d t == 06d c = 0.6dt t 0.003 + 0.002 Calculate Pn and Mn per case (a).

(d) Special case at compression-controlled limit for members reinforced with prestressing strand and/or Grade 60 reinforcement Fig. 5.9.1 Equilibrium equations for prestressed and non-prestressed compression components. Note: c.g. = center of gravity.

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EXAMPLE 5.9.1.1 Construction of Interaction Curve for a Precast, Reinforced Concrete Column Given: Column cross section shown.

  5

12"

Concrete: fc' = 5000 psi, normalweight

2.5"

Reinforcement: Grade 60 fy = 60,000 psi Es = 29,000 ksi

20" X

Problem: Construct interaction curve for bending about X-X axis. _____________________________________

X

(4) #9

Solution: Determine the following parameters: 1 d d ' yt 0.85 fc' Ag As

= 0.85 – 0.05 = 0.80 (per ACI 318-05 Section 10.2.7.3) = 20 – 2.5 = 17.5 in. = 2.5 in. = 10 in. = 0.85(5) = 4.25 ksi = 12(20) = 240 in.2 = As' = 2.00 in.2

Step 1 Determine Po from Fig. 5.9.1(c): With no prestressing steel, the equation reduces to: Po

= Pn = 0.85fc' ( A − As' − As ) + ( As' + As )fy = 4.25 ( 240 − 2 − 2 ) + ( 2 + 2 ) 60 = 1243 kip

φPo = 0.65(1243) = 808 kip Step 2 Determine Pnb and Mnb from Fig. 5.9.1(d) and (a): dt = d = 17.5 in.; c = 0.6dt = 0.6(17.5) = 10.5 in.; a = 1c = 0.80(10.5) = 8.40 in.

fs'

⎡ ⎤ ⎡ = ε 'sE s = ⎢ 0.003 c − d ' ⎥ E s = ⎢ 0.003 10.5 − 2.5 ⎣ c ⎦ ⎣ 10.5

(

)

(

) ⎤⎥ 29,000 = 66.3 ksi > 60 ksi ⎦

Therefore, f = fy = 60 ksi Acomp = ab = 8.40(12) = 100.8 in.2 ' s

With no prestressing steel:

(

)

Pnb = Acomp − As' (0.85fc' ) + As'fs' = Asfs = (100.8 − 2 ) 4.25 + 2 ( 60 ) − 2 (60 ) = 419.9 kip φPnb = 0.65(419.9) = 273 kip y ' = a/2 = 4.20 in.

(

)

Mnb = Acomp − As' ( y t − y ' )( 0.85fc' ) + As'fs' ( y t − d ' ) + Asfs (d − y t ) = (100.8 – 2)(10 – 4.20)(4.25) + 2(60)(10 – 2.5) + 2(60)(17.5 – 10) = 2435 + 900 + 900 = 4235 kip-in. φMnb = 0.65(4235) = 2752 kip-in. = 229 kip-ft

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CHAPTER 5

EXAMPLE 5.9.1.1 Construction of Interaction Curve for a Precast, Reinforced Concrete Column (cont.)

  5

Step 3 Determine Mo; use conservative solution and neglecting compressive reinforcement: a

=

Asfy 0.85f b ' c

=

( ) = 2.35 in. 4.25 (12 ) 2.0 60

⎛ Mao⎞ = ⎛ 2.35 ⎞ Asfy ⎜ d − ⎟ = 2.0 60 ⎜ 17.5 − = 1959 2⎠ 2 ⎟⎠ ⎝ ⎝ kip-in.

1000

( )( )

See step 1 See step 4

800

c

= a = 2.35 = 2.94 β1 0.8

(

0.003 d − c

φPn, kip

) = 0.0149

εt

=

εt

> 0.005; φ = 0.9

c

646 600 400 200

Actual curve See step 5

Approximation See step 2 See step 3

For φ = 0.9, φMo = 1763 kip-in. = 147 kip-ft Step 4 Calculate maximum design load: = 0.80 φPo = 0.80(808) = 646 kip

0

50

100

150

200

250

300

φMn, kip-ft

To determine intermediate points on the curve: Step 5(a) Set a = 6 in., c =

6 = 7.5 in. 0.80

Step 5(b) Acomp = 6(12) = 72 in.2 Step 5(c) Use Fig. 5.9.1(a):

fs'

⎡ 0.003 ⎤ = 29,000 ⎢ 7.5 − 2.5 ⎥ = 58.0 ksi < fy ⎣ 7.5 ⎦

fs

⎡ 0.003 ⎤ = 29,000 ⎢ 17.5 − 7.5 ⎥ = 116 ksi > fy ⎣ 7.5 ⎦

(

(

)

)

Use fs = fy = 60 ksi Steps 5(d) and 5(e) Pn = (72 – 2)4.25 + 2.0(58) – 2.0(60) = 293.5 kip

0.003 (17.5 − 7.5 ) = 0.004 7.5 φ =(0.48 + 83εt) = 0.81 φPn = 0.81(293.5) = 238 kip φMn = 0.81[(72 – 2)(10 – 3)4.25 + 2.0(60)(17.5 – 10) + 2.0(58)(10 – 2.5)] = 0.81(2082 + 900 + 870) = 3120 kip-in. = 260 kip-ft εt

=

Note: Steps 5(a) to 5(e) can be repeated for as many points as desired. A plot of these points is shown in this example. 5–102

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EXAMPLE 5.9.1.2 Calculation of Interaction Points for a Prestressed Concrete Compression Component Given: Hollow-core wall panel shown: Concrete: fc' = 6000 psi, normalweight A = 204 in.2

2"

12"

4"

4'-0" 12"

4"

12"

2"

11/2" 5" 8" 11/2"

Prestressing steel: fpu = 270 ksi Eps = 28,500 ksi (based on strand data) fse = 150 ksi (6) 3/8-in.-diameter, 270 ksi strands Aps (bottom) = 4(0.085) = 0.340 in.2 = 2(0.085) = 0.170 in.2 A'ps (top) Problem: Calculate a point on the design interaction curve for a = 2 in. _________________________________________________________________________________ Solution: Step 1 1 a

= 0.85 – 2(0.05) = 0.75 (per ACI 318-05 Section 10.2.7.3) = 2 in., cc ==

2 = 2.67 in. 0.75

Step 2 Acomp = 48(1.5) + 12(2 – 1.5) = 78 in.2 ⎛ 1.5 ⎞ 48 1.5 ⎜ + 12 0.5 ⎝ 2 ⎟⎠ = 78

( )

y'

⎞ ( ) ⎛⎜⎝ 1.5 + 0.5 2 ⎟⎠

= 0.83 in.

Step 3 εse

=

150 fse = = 0.00526 in./in. E ps 28,500

Step 4 From Fig. 5.9.1(a):

ε'ps = 0.00526 –

0.003 (2.67 – 1.5) = 0.00536 – 0.00131 = 0.00395 in./in. 2.67

From Design Aid 15.2.4, this strain is on the linear part of the curve:

fps' εt εps φ

= ε 'psE s =0.00395(28,500) = 113 ksi 0.003 = (6.5 – 2.67) = 0.00430 2.67 = 0.00526 + 0.00430 = 0.00956 = 0.48 + 83εt = 0.84

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EXAMPLE 5.9.1.2 Calculation of Interaction Points for a Prestressed Concrete Compression Component (cont.)

  5

From Design Aid 15.2.4, fps = 252 ksi From Fig. 5.9.1(a):

(

)

P n

= Acomp 0.85fc' − A'psfps' − Apsfps = 78(0.85)(6) – 0.170(113) – 0.340(252) = 397.8 – 19.2 – 85.7

φPn Mn φMn

= 292.9 kip = 0.84(292.9) = 246 kip = 397.8(4 – 0.83) – 19.2(4 – 1.5) + 85.7(6.5 – 4) = 1261.0 – 48.0 + 214.2 = 1427.2 kip-in. = 118.9 kip-ft = 0.84(1427.2) = 1199 kip-in. = 99.9 kip-ft

Note: This is for fully developed strand. If the capacity at a point near the end of the transfer zone is desired, then fps ≤ fse = 150 ksi, φ = 0.65 because εt < 0.002. φPn = 0.85(0.65)[397.8 – 19.2 – 0.340(150)] = 181.0 kip φMn = 0.85(0.65)[1261.0 – 48.0 + 0.340(150)(6.5 – 4)] = 740.6 kip-in. = 61.7 kip-ft Note: For compliance with ACI 318-05 Section 18.8.3, cracking moment Mcr must be calculated to verify φMn ≥ 1.2Mcr for both faces of the wall panel, except for flexural components with shear and flexural strength at least twice that required by ACI 318-05 Section 9.2. The effects of prestressing and its eccentricity should be included in calculating Mcr and other aspects of wall-panel behavior, such as deflections.

EXAMPLE 5.9.2.1 Use of Design Aids 5.14.13 and 5.14.14 Given: Beam reactions to column haunch at each level: Dead load = 50 kip Live load = 20 kip Eccentricity e = 14 in. Story height hs = 16 ft Column base is determined to be 65% fixed. Problem: Using Design Aid 5.14.14, determine the maximum restraining force and moment in the lowest story of a three-story frame for: a. An interior column in a multibay frame b. An exterior column

a Fixity

65%

65%

b 65%

_____________________________________ Solution: Factored loads: Dead load = 1.2(50) = 60.0 kip Live load = 1.6(20) = 32.0 kip 92.0 kip 1. For the interior column, the dead-load reaction would be the same on either side; thus, there are no moment results. The live load could occur on any one side at any floor; hence, use the coefficients in the Σ maximum line: Pue = 32.0(14) = 448 kip-in. = 37.3 kip-ft

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EXAMPLE 5.9.2.1 Use of Design Aids 5.14.13 and 5.14.14 (cont.)

To determine the maximum moment at point B: For a pinned base: km = 0.67 For a fixed base: km = 0.77 For 65% fixed: km = 0.67 + 0.65(0.77 – 0.67) = 0.74 Mu



  5

= kmPue = 0.74(37.3) = 27.6 kip-ft

Maximum restraining force at level 2: Fu = kfPue/hs kf = 1.40 + 0.65(1.62 – 1.40) = 1.54 Fu = 1.54(37.3)/16 = 3.59 kip (tension or compression)

2. For the exterior column, the total load is eccentric on the same side of the column; hence, use the coefficients in the Σ one-side line: Pue = 92.0(14) = 1288 kip-in. = 107.3 kip-ft

To determine the maximum moment at point B: For a pinned base: km = 0.40 For a fixed base: km = 0.46 For 65% fixed: km = 0.40 + 0.65(0.46 – 0.40)  = 0.44 Mu = kmPue = 0.44(107.3) = 47.2 kip-ft



Maximum restraining force at level 2: Fu = kfPue /hs kf = –0.60 – 0.65(–0.60 + 0.22) = –0.35 Fu = –0.35(107.3)/16 = –2.34 kip (tension)

concrete. Additional anchored end reinforcement should be supplied that is equivalent to a development length equal to the assumed transfer length. The required area of end reinforcement can be determined by matching interaction curves, or can be approximated by the following equation if the bar locations approximately match the strand locations:

As =

where: As Aps fse fy

Aps fse fy



= required area of reinforcement = area of prestressing steel, in.2 = strand stress after losses, psi = yield strength of bars, psi

(Eq. 5-83)

5.9.2

Eccentrically Loaded Columns

Many precast concrete structures utilize multistory columns with simple-span beams resting on haunches. Design Aids 5.14.13 and 5.14.14 are provided as aids for determining the various combinations of load and moment that can occur with such columns. The following conditions and limitations apply to Design Aids 5.14.13 and 5.14.14. • The coefficients are only valid for columns braced against sidesway. • For partially fixed column bases (see Section 4.8.3), a straight-line interpolation between the coefficients for pinned and fixed bases can be used with small error. • For taller columns, the coefficients for the four-story columns can be used with small error. • The coefficients in the Σ maximum line will yield the maximum-required restraining force Fb and column moments caused by loads (equal at each level) that can occur on either side of the column, for example, live loads on interior columns. The maximum force will not necessarily occur with the same loading pattern that causes the maximum moment.

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The coefficients in the Σ one-side line will yield the maximum moments that can occur if the column is loaded on only one side, such as the end column in a bay.

5.9.3

p

 lenderness Effects in Columns and S Wall Panels

Plate or angle

Sections 10.10 through 10.13 of ACI 318-05 contain provisions for evaluating slenderness effects (buckling) of columns. Additional recommendations are given in the recommended practice section of this handbook (Section 14.1). Slenderness effects can be described as the moments in a component produced when the line of action of the axial force is not coincident with the displaced centroid of the component. These moments, which are not accounted for in the primary analysis, are thus termed secondary moments. These secondary moments arise from changes in the geometry of the structure, and may be caused by one or more of the following: 1. Relative displacement of the ends of the component due to: a. Lateral or unbalanced vertical loads in an unbraced frame, usually labeled as translation or sidesway b. Manufacturing and erection tolerances 2. Deflections away from the end of the component due to: a. End moment due to eccentricity of the axial load b. End moments due to frame action-continuity, fixity, or partial fixity of the ends c. Applied lateral loads, such as wind d. Thermal bowing from differential temperature (see Section 5.8.5) e. Manufacturing tolerances f. Camber due to prestressing Section 10.10.1 of ACI 318-05 describes the use of second-order analysis for slenderness effects. ACI 318-05 Section 10.10.2 also allows the use of an approximate procedure called moment magnification. Precast concrete frames with columns reinforced with non-prestressed reinforcement that meet the requirements for minimum reinforcement may be designed using moment magnification, but prestressed compression components usually have less than the minimum 1% vertical reinforcement. The recommended practice suggests ways to modify the code equations used in moment magnification, but the second-order, or P-∆ , analysis is preferred. 5.9.3.1 Second-Order (P-∆) Analysis The usual procedure for this analysis is to perform an elastic-type analysis using factored loads. While deflections are usually only a concern under service load, the deflections calculated for this purpose are to avoid a stability failure, so it is logical to provide the same safety factor as for strength design. Out-of-plumbness (items 1b and 2e noted in Section 5.9.3) are initially assumed based on experience and/or specified tolerances. The thermal bowing effect is usually neglected in 5–106

1 dh a

Vu

As

Nu 1" h d

2 /3d (max.)

d/2 (min.)

Framing bar

3

Ah

Welded cross bars

2

Alternate anchorage 1. As bars should be extended to the far face of the column. Provide fully developed As bars by selecting the number of bars so that the bar size remains small enough to ensure that the length is provided (Design Aid 15.4.4). 2. Vertical length of a standard 90 deg hook is 12db (Design Aid 15.4.4). The horizontal length of As bar, dh must be provided in order to use a standard 90 deg hook. 3. It may be assumed that the As bar is developed at the outside face of the welded anchor bar when the Ah bars are outside that point. Size of welded cross bar is same as As bar.

Fig. 5.9.2 Design of concrete corbels. Note: max. = maximum; min. = minimum.

columns, but may be significant in exterior wall panels (see Section 5.8.5). At each iteration, the lateral deflection is calculated, and the moments caused by the axial load acting at that deflection are accumulated. After three or four iterations, the increase in deflection should be negligible (convergence). If it is not, the component may be approaching stability failure, and the section dimensions should be reevaluated. If the calculated moments indicate that cracking will occur, this needs to be taken into account in the deflection calculations. The stiffness used in the second-order analysis should represent the stiffness of the component immediately before failure. This may involve iterations within iterations, greatly complicating the procedure. Assuming the panel remains uncracked, EI needs to be modified by a stiffness reduction factor φk and effects of creep should also be included. The most common method is to divide the stiffness EI by the factor 1 + d as specified in the ACI 318-05 moment-magnifi-

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EXAMPLE 5.9.3.1 Second-Order Analysis of an Uncracked Component

Loading assumptions are as follows: 1. Axial load eccentricity = 1.0 in. (at one end) 2. Assume midspan bowing = 1.0 in. outward (production tolerances allow l/360, see Chapter 13) 3. Wind load = 30 lb/ft2 4. Non-sway frame – no joint translation 5. Joints assumed pinned top and bottom Concrete: fc' = 5000 psi, normalweight Ec = 4300 ksi

  5

DL = 10 kip LL = 6 kip (roof)

30'-0" = 360"

Given: An 8-in.-thick, 8-ft-wide prestressed concrete wall panel as shown.

Problem: Determine if standard panel (Design Aid 3.7.5) is adequate. _____________________________________ Solution: Case 1: No wind Pu = 1.2D + 1.6Lr = 1.2(10) + 1.6(6) = 21.6 kip Ig = bh3/12 = 96(8)3/12 = 4096 in.4

8"

Note: The bending stiffness EI is multiplied by a stiffness reduction factor φK = 0.85 per ACI 318-05 Sections 10.11.1 and R10.11.1 to account for variability in the actual component properties and it is divided by (1 + d) to account for sustained load effects. Once the moments are established, the φ factor from Section 9.3.2.2 of ACI 318-05 is used to determine the strength of the cross section. d = factored EIe =

12 DL 0.56 = == 0.56 TL 21.6

φK Ec I g 0.85 ( 4300 ) ( 4096 ) = 9.60 x 106 kip-in.2 = 1+ βd 1.56

Check P-critical using Euler’s formula: Pc =

π 2EI e π 2 ⎡⎣ 9.60 (106 ) ⎤⎦ = 731 kip > 21.6 kip = 2 ( 360)2

OK

Moments on panel: Deflection at midspan due to Pue: 2

P e  2 21.6 (1) ( 360 ) ∆i = u = 0.0182 in. = 16EI e 16 ⎡⎣9.60 (106 ) ⎤⎦ Total midspan deflection including initial bow:

= 1.0 + 0.0182 = 1.018 in.

Deflection due to P-∆ moment at midspan: 2

∆ =

Pu e  2 21.6e ( 360 ) = 0.036e = 8EIe 8 ⎡⎣9.60 (106 ) ⎤⎦

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EXAMPLE 5.9.3.1 Second-Order Analysis of an Uncracked Component (cont.)

  5

First iteration: ∆ = 0.036(1.018) =0.037 in. Pue = 21.6 (1)

Second iteration: e = 1.018 + 0.037 = 1.055 in. ∆ = 0.036(1.055) = 0.038 in. Third iteration: e = 1.018 + 0.038 = 1.056 in. ∆ = 0.036(1.056) = 0.038 in. (convergence)

10.8 kip-in.

or using a geometric series to calculate the midspan deflection in one step: e =

21.6 kip-in.

21.6 kip-in.

Eccentricity

21.6 kip-in.

Initial bow

32.4 kip-in.

Combined

e0 1.022 = 1.056 in. = 0.0221 Δi 1− 1− 0.5 e

Mu at midheight = 10.8 + 21.6(1.056) = 33.6 kip-in. Check for cracking at midheight: Mu y = 33.6(4)(1000)/4096 =  Ig Half-panel weight: [100(15)/(8(12))](1.2) = Prestress = Dead load = 10(1000)(1.2)/[8(96)] = Net stress (compression) =

–33 psi 19 psi 225 psi 16 psi 227 psi

Therefore, the analysis is valid. Using interaction of curve in Design Aid 3.7.5: Pu = 21.6/8 + 1.2(15)0.1 = 4.50 kip/ft Mu = 33.6/[12(8)] = 0.35 kip-ft/ft OK.

Point is below curve, Case 2: Include wind Axial load without wind is: Pu = 1.2D + 1.6L + 0.8W = [1.2(10) + 1.6(6)] = 21.6 kip Deflection due to Pue (see case 1) = 0.0182 in. Additive wind load would be suction = 30 lb/ft2 wu = 30(8)(0.8) = 192 lb/ft When considering wind, d = 0 EIe =

φK Ec I g 0.85 ( 4300 ) ( 4096 ) = 1.50 × 107 kip-in.2 = 1+ βd 1.0

Deflection due to wind:

⎛ 0.192 ⎞ 5⎜ ( 360)4 ⎝ 12 ⎟⎠ 5w u  4 = = 0.23 in. 384EI e 384 ⎡⎣1.50 (107 ) ⎤⎦

5–108

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EXAMPLE 5.9.3.1 Second-Order Analysis of an Uncracked Component (cont.) Total initial midspan bow including eccentricity and wind: e = 1.0 + 0.018 + 0.23 = 1.25 in.

  5

Deflection due to P-∆ moment at midspan with EIeff from case 1 (dead + live): 2

Pu  2 21.6e ( 360 ) = ∆ = = 0.036e 8EI e 8 ⎡9.6 (10 )6 ⎤ ⎣ ⎦

First iteration: ∆ = 0.036(1.25) = 0.045 in. Second iteration: e = 1.25 + 0.045 = 1.295 in. ∆ = 0.036(1.295) = 0.047 in. Third iteration: e = 1.25 + 0.047 = 1.297 in. ∆ = 0.036(1.297) = 0.047 in. (convergence)

Mu

2 ⎛ 0.192 ⎞ ⎟⎠ ( 360 ) ⎜⎝ 21.6 (1) 12 = = 298 kip-in. + 21.6 (1.297 ) + 2 8

Mu y = 298(4)(1000)/4096 Ig

= –291 psi

Panel weight Prestress Dead load

= 19 psi = 225 psi = 16 psi

Net stress (tension)

= –31 psi

fr

= 7.5 fc' = 530 psi > 31 psi. Therefore, the analysis is valid.

Pu = 21.6/8 = 2.7 kip/ft Mu = 298/[(12)(8)] = 3.1 kip-ft/ft By comparison with Design Aid 3.7.5,

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5.9.4

  5

Panel reinforcement

As (main reinforcement) Framing bar

d 2

Ah (stirrup reinforcement)

/3d

h h/2

Nu Anchor bar welded

Vu

There are two methods of analysis for a concrete corbel: cantilever beam and strut-and-tie. The cantilever beam method is described in Chapter 11 of ACI 318-05 and the strut-and-tie method follows Appendix A of ACI 318-05. 5.9.4.1 Cantilever Beam Design Method ACI 318-05 prescribes the design method for corbels, based on References 25 and 26. The equations in this section follow those recommendations, and are subject to the following limitations (Fig. 5.9.2 and 5.9.3): • • • •

Reinforcement

Critical sections

d 2

As (Main reinforcement)

/3d

Vu

Hanger reinforcement

•

h h/2

Nu Anchor bar welded

Panel reinforcement Reinforcement

Concrete Brackets or Corbels

a/d ≤ 1 Nu ≤ Vu Use φ = 0.75 for all calculations. Anchorage at the front face must be provided by welding or other positive means. Concentrated loads on continuous corbels may be distributed similar to a beam ledge, Section 5.5.

The area of primary tension reinforcement As is the greater 2 of Af + An and Avf + An as calculated in Section 5.3.6: 3

Af A=f



An A=n

(

Vu a + N u h − d

φ fy d

)

Nu φ fy

(Eq. 5-84) (Eq. 5-85)

For convenience, the equations can be rewritten so that As is the greater of Eq. 5-86 and 5-87:

Fig. 5.9.3 Wall corbels.

cation method. In unbraced, continuous frames, the joint-translations effect and the frame response are interdependent. Thus, a practical analysis, especially when potential cracking is a parameter, usually will require a more sophisticated approach with the aid of a computer. A good review of second-order analysis, along with an extensive bibliography and an outline of a complete program, is contained in Reference 24. An example of P-∆ calculations for a simple, yet frequently encountered, problem is shown in Example 5.9.3.1. In the following example, only two of the ACI 318-05 load combinations are checked, presuming by engineering judgment that these were the controlling cases.



AAss ==

1 φ fy

⎡ ⎛ a⎞ ⎛ h⎞ ⎤ ⎢Vu ⎜ ⎟ + Nu ⎜ ⎟ ⎥ d ⎝ ⎠ ⎝d⎠⎦ ⎣

(Eq. 5-86)



AAss ==

1 φ fy

⎡ 2Vu ⎤ + Nu ⎥ ⎢ ⎣ 3µ e ⎦

(Eq 5-87)

where (Fig. 5.9.2): a = applied load eccentricity d = depth of tension steel h = height of corbel µe = effective shear-friction coefficient as defined in Section 5.3.6 (satisfies Section 11.7.3 of ACI 318-05) φ = strength-reduction factor = 0.75 fy = yield strength of tension steel Vu and Nu = applied factored loads The minimum required tension steel is:

As ,min = 0.04

fc' bd fy

(Eq. 5-88)

where: b = width of corbel, in. 5–110

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EXAMPLE 5.9.4.1 Reinforced Concrete Corbel (Cantilever Beam Design Method) Given: A concrete corbel similar to that shown. Vu = 80 kip (includes all loads and overload factors) Nu = 15 kip (includes all loads and overload factors) fy = 60 ksi (weldable) fc' = 5000 psi, normalweight Bearing pad – 12 in. x 6 in. b = 14 in. lp = 8 in.

  5 14"

8" 6"

Problem: Find the corbel depth and reinforcement by the cantilever beam method. _____________________________________

Vu = 80 kip Nu = 15 kip

14"

Solution: Try h = 14 in. d = 13 in. a = 3/4lp= 6 in. From Table 5.3.1: Maximum Vu = φ(1000)λAcr =

0.75 (1000 ) (1) (14 ) (14 ) = 147 kip > 80.0 kip (1000 )

By Eq. 5-86:

As=

1 ⎡ ⎛a⎞ 1 ⎡ ⎛ 6⎞ ⎛ h⎞⎤ ⎛ 14 ⎞ ⎤ Vu ⎜ ⎟ + Nu ⎜ ⎟ ⎥ = 80 ⎜ ⎟ + 15 ⎜ ⎟ ⎥ = 1.18 in.2 ⎢ ⎢ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ 13 ⎠ ⎦ φfy ⎣ 13 d d ⎦ 0.75 ( 60 ) ⎣

By Eq. 5-33:

µe =

φ1000λbh µ 0.75 (1000 ) (1) (14 ) (14 ) (1.4 ) = 2.57 < 3.4, use 2.57 = Vu 80,000

By Eq. 5-87:

As =

1 φfy

By Eq. 5-88:

⎛ f' ⎞ ⎛ 5⎞ As,min = 0.04bd ⎜ c ⎟ = 0.04 (14 ) (13 ) ⎜ ⎟ = 0.61 in.2 < 1.18 in.2 ⎝ 60 ⎠ ⎝ fy ⎠

OK

⎡ 2 ( 80 ) ⎤ ⎡ 2Vu ⎤ 1 2 2 ⎢ 3µ + Nu ⎥ = 0.75 60 ⎢ 3 2.57 + 15 ⎥ = 0.79 in. < 1.18 in. ( ) ( ) ⎣ e ⎦ ⎣ ⎦

Provide (2) #7, As = 1.20 in.2 The As reinforcement could also be estimated from Design Aid 5.14.15: For: b = 14 in. lp = 8 in. h = 14 in. The corbel would have a design strength of 78 kip with (2) #7. Note that this is less than 80 kip because the table assumes Nu = 0.20Vu = 16 kip (rather than 15 kip) and d = h – 1.25 = 12.75 in. (rather than 13 in.) Use (2) #7 for Vu = 80 kip Consider OK. By Eq. 5-89:

Ah = 0.5 ( As -An ) =0.5 1.18-

15 0.75 (60)

= 0.42 in.2

Provide (2) #3 closed ties, As = 0.44 in.2, distributed within the upper two-thirds of the corbel.

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Where the corbel depth is larger than required by design, a reduced depth d may be used, provided it is used in all the design equations:

  5



Ah < 0.5(As – An)

1 p

(Eq. 5-89)

aw

Ah should be distributed within 2/3d from the tension side of the corbel. The shear strength of a corbel is limited by the maximum values given in Table 5.3.1. Design Aid 5.14.15 can be used to tabulate values based on the cantilever beam method, suitable for preliminary design. 5.9.4.2

Vu n

1. Determination of bearing-plate dimension and protection for the corner against spalling. 2. Determination of truss geometry (Fig. 5.9.4). 3. Determination of forces in the components of the truss. 4. Design of tension ties. 5. Design of nodal zone. 6. Check for compressive struts. 7. Determine area of surface reinforcement. 8. Consider detailing to ensure design technique. Section 9.3.2.6 of ACI 318-05 requires that the strengthreduction factor φ be 0.75 for “strut and tie models, and struts, ties, nodal zones, and bearing areas in such models.” 5.9.4.2.1 Bearing Area Area required for bearing plate: Apl =

Vu φ 0.85 fc'

(

)

(Eq. 5-90)

Bearing pads should be placed away from the edge to avoid spalling. If the plate is larger than the bearing pad, the plate thickness must also be designed for bending. See Section 5.6 for concrete bearing. 5.9.4.2.2 Truss Geometry The truss geometry has been determined by locating the nodes. According to the flow of stresses, the corbel has a four-node (m, n, o, p) truss geometry as shown in Fig. 5.9.4. Node m is located at the intersection of the tension reinforcement of the column and the tie at the bottom fiber of the corbel. Node n is located at the intersection of the tension bar of 5–112

C

d

T

Appendix A of ACI 318-05 permits strut-and-tie, or truss modeling, of D-regions, defined as “the portion of a component within a distance equal to the member height h or depth d from a force discontinuity or a geometric discontinuity.” One such component is a reinforced concrete corbel. There are eight basic steps for the strut-and-tie method of analysis:



o C

Strut-and-Tie Design Method

Nu

T

m T

cc

T

p

C

Nc

2

h

ws /2

hc

Fig. 5.9.4 Strut and tie geometry.

the column and the upper tension tie of the corbel. Node o is located at the intersection of the resultant of the applied reactions (Vu and Nu) and the upper tension tie of the corbel. Node p is located at the intersection of the longitudinal compression strut of the column and bottom tension tie. The width of the compression strut ws, which is the governing factor to locate node p, is determined by moment equilibrium about m. The maximum compression stress at a nodal zone is given in ACI 318-05 Appendix A.3.2 as:

fcu = 0.85β n fc'

(Eq. 5-91)

where: βn = 1.0 in nodal zones bounded by structural or bearing areas = 0.8 in nodal zones anchoring one tie (for example, p in Fig. 5.9.4) = 0.6 in nodal zones anchoring two or more ties (for example, m in Fig. 5.9.4) 5.9.4.2.3 Horizontal Stirrups While horizontal stirrups corresponding to Ah reinforcement in the cantilever beam method are not required by this strut-and-tie analysis, it is suggested that inclusion of some

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EXAMPLE 5.9.4.2 Reinforced Concrete Corbel (Strut-and-Tie Design Method) Given: Same as Example 5.9.4.1.

  5

Problem: Find corbel depth and reinforcement by the strut-and-tie design method. _____________________________________ Solution: Note: ACI 318-05 Section 9.3.2.6 requires a strengthreduction factor φ of 0.75 for analysis of the model and design of struts, ties, and nodal zones. 1

Step 1 Check the bearing area: Required plate area: From Eq. 5-90:

o

tie

Nu = 15 kip

Vu 80 = = 25.1 in.2 ' φ 0.85 fc 0.75 0.85 5

)

(

)( )

str

tie

d

h

.4°

ut

Use 12 in. × 6 in. plate, area = 72 in.2 > 25.1 in.2

ut

(

str

Apl =

n

Vu = 80 kip

Top of corbel

54

Step 2 Refer to Fig. 5.9.4: To determine compressive force Nc at node p:

∑M

m

m

tie

=0

p Nc

Vu(l1) + Nu(d) – Nc(l2) = 0 (Eq. 1)

2

Nu 15 = = 0.19 tanθR = Vu 80

l1

= (h – d) tanθR + aw + (hc – cc) = 1(0.19) + 6 + (14 – 2.25) =17.94 in.

l 2

= hc − c c −

ws w w = 14 − 2.25 − s = 11.75 − s 2 2 2

⎛ w ⎞ Substituting l1 and l2 into (Eq. 1): 80(17.94) + 15(13) −N c ⎜ 11.75 − s ⎟ = 0 2⎠ ⎝ ⎛ w ⎞ 1630 − Nc ⎜ 11.75 − s ⎟ = 0 (Eq. 2) 2⎠ ⎝

Maximum compressive stress at the nodal zone p (anchors one tie, n = 0.8): From Eq. 5-91: fcu = 0.85n fc' = 0.85(0.8)(5) = 3.4 ksi An = area of the nodal zone = bws = 14ws Maximum allowable force on strut: Nc = φfcuAn = 0.75(3.4)(14ws) ws =

Nc = 0.028N c 0.75 3.4 14

( )( )

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EXAMPLE 5.9.4.2 Reinforced Concrete Corbel (Strut-and-Tie Design Method) (cont.)

  5

Substituting in Eq. 2 and rearranging: 0.014N c2 − 11.75Nc + 1630 = 0 Nc = 175 kip ws = 0.028(175) = 4.90 in. 4.90 l2 = 11.75 − = 9.30 in. 2 With ws determined, the node p has been located and the entire truss geometry has been fixed. Step 3 Solving the truss mnop by statics, the member forces are as follows: Strut op = 96.0 kip (compression) Tie no = 68.2 kip (tension) Strut np = 116.8 kip (compression) Tie mp = 14.9 kip (tension) Tie mn = 95.0 kip (tension) Step 4 Reinforcement requirements For top tension tie: Required As =

Fnt 68.2 = = 1.52 in.2 φfy 0.75 ( 60 )

Provide (2) #8, As = 1.58 in.2 at the top For bottom tension tie mp: As =

14.9 = 0.33 in.2 0.75 (60 )

Provide (1) #4 tie, As = 0.40 in.2 at bottom of corbel Step 5 The width ws of the nodal zone p has been chosen in step 2 to satisfy the stress limit on this zone. The stress at nodal zone o must be checked against the compressive force in strut op and the applied reaction Vu. From the compressive stress flow in struts of the corbel (Fig. 5.9.5), it is obvious that the nodal zone p is under the maximum compressive stress due to force Nc. As it is within the acceptable limit, all nodal zones are acceptable. Step 6 Strut np is the most critical strut at node p. The nominal compressive strength of a strut without compressive reinforcement is: Fns

= fcuAc

where: Ac = width of corbel × width of strut Width of strut np =

5–114

ws 4.90 = 6.03 in. = sin 54.4 sin 54.4

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EXAMPLE 5.9.4.2 Reinforced Concrete Corbel (Strut-and-Tie Design Method) (cont.) From ACI 318-05 Appendix A.3.2: fcu = 0.85s fc' for a bottle-shaped strut (see ACI 318-05 Section A.3.2.2) s = 0.60λ (without reinforcement satisfying ACI 318-05 Section A.3.3) fcu = 0.85(0.60)(1.0)(5) = 2.55 ksi φFns = (0.75)(2.55)(14)(6.03) = 161.5 kip > 116.8 kip

  5 OK

Step 7  ecause the lowest value of s was used, surface reinforcement is not required based on A.3.2.2(b). B

(2) #3

Effective width

Vu = 80 kip Nu = 15 kip Distribute ties over 2d 3 d

(2) #7

6t t

Solid or hollow-core panels

Framing bar

a

Effective width 6t

6t

t

Cantilever beam method design

Ribbed wall panels

Vu = 80 kip Nu = 15 kip

(2) #8

6t

Fig. 5.9.6 Effective width of wall panels. d (1) #4

Framing bar 9.5" Strut-and-tie method design

a. Because of increased top steel requirement, lower ties not required by strut-and-tie method.

• •

Fig. 5.9.5 Comparison of corbel design methods.

stirrups be considered. 5.9.4.3 Comparison of Corbel Design Methods The following general observations can be made regarding the two different design methods (Fig. 5.9.5): • The primary reinforcement required for the strut-andtie design method is typically greater than the cantilever beam method. However, additional horizontal ties are not required since the moment of the applied load

in the strut-and-tie method is effectively taken about the center of compressive force in the column. In the cantilever beam method, it is taken about the face of the column. It should be noted that the cantilever beam method has been verified by tests.25 By using the lower value of s in step 6, no transverse surface reinforcement is required. The strut-and-tie method requires a tension tie at the bottom of the corbel, which is not a requirement of the cantilever beam method. Note that this bar must be anchored.

5.9.4.4 Development of Corbel Reinforcement The development length of each reinforcing bar is based on ACI 318-05. Tension development lengths are measured from the assumed failure plane. Typically, concrete corbels are a part of components (columns or walls) that do not have enough room to develop the bar by embedment, requiring the use of hooked bars. As shown in Fig. 5.9.2 and 5.9.3, the main tension steel within the concrete corbel is usually devel-

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oped at the outer edge of the corbel by welding to a cross bar or bearing plate or angle. For steel corbels, see Section 6.8 of this handbook. 5.9.5

Effective Width of Wall Panels

The recommended practice specifies that the portion of a wall considered as effective for supporting concentrated loads or for determining the effects of slenderness shall be the least of the following: • • • •

The center-to-center distance between loads The width of the loaded portion plus six times the wall thickness on either side (Fig. 5.9.6) The width of the rib (in ribbed wall panels) plus six times the thickness of the wall between ribs on either side of the rib (Fig. 5.9.6) 0.4 times the actual height of the wall

These effective widths only apply to concentrated loads applied at the level under consideration. Loads from higher levels will distribute based on an accumulation of effective widths. 5.9.6

 arying Section Properties of V Compression Components

Axial load φPn, kip 0 100 200 300 400 500 600 700

Architectural precast concrete wall panels will frequently be of a configuration that varies over the unsupported height of the panel. While there are precise methods of determin-

-300 -200 -100

  5

14" solid square pile 6 strands, f'c = 6 ksi

5.9.7

Piles

In this section, procedures are discussed to determine the structural capacity of prestressed concrete piles. It is assumed that the soil is adequate to allow the pile to reach its design strength. The soil capacity must be evaluated by a geotechnical engineer. Experience has shown that in piles subjected to concentric axial loads, the frictional and bearing resistance of the soil may control the design more often than the serviceload stresses and the strength of the pile itself. References 27, 28, and 29 provide additional information. 5.9.7.1 Service-Load Design Except when load factors are much higher than normal, service-load stresses are usually more critical than strength. Stresses are computed by: N M ± A S



f = f pc ±

where: fpc N A M S

= average prestress = unfactored axial load = cross-sectional area = service-load moment = section modulus

(Eq. 5-92)

The allowable stress varies with the code, specification, or guide being used and the type of loading being investigated. 5.9.7.2 Strength Design

25

h'/r = 0

Design strength may be obtained from a straincompatibility analysis similar to that used for columns in Section 5.9.1 (illustrated in Example 5.9.7.1) or from interaction diagrams based on such an analysis. A typical pile-interaction diagram is shown in Fig. 5.9.7. Note that piles may be in tension, hence the lower part of the diagram. A series of interaction curves for most common pile sections has been published by PCI.30 Shear reinforcement is determined by strength design (Section 5.3). Wire spirals are often used for shear reinforcement (see illustration on Design Aid 3.12.8). The most severe conditions a pile will endure usually occur during driving. This is discussed in Reference 29.

50 75

100

125

175 150 200

5.9.7.3 Other Considerations

0

20

40 60 80 100 Bending moment φMn, kip-ft

Fig. 5.9.7 Typical pile interaction curve.

5–116

ing the effects of slenderness for such components, the approximate nature of the analysis procedures used do not warrant such precision. Example 5.9.6.1 illustrates approximate methods for determining section properties used in evaluating slenderness effects.

120

The stress in the reinforcing steel used to transfer the tension load from the foundation or pile cap to the pile is usually limited to 30 ksi service-load tension. When non-prestressed reinforcement is used to transfer tension loads to the pile, it should extend a sufficient length into the pile to develop both the prestressed and non-prestressed reinforcement (see Section 5.2.3). Piles subject to large tension loads in combination with bending may have failure of the pile initiated by rupture of

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EXAMPLE 5.9.6.1 Approximate Section Properties of an Architectural Mullion Panel Center mullion compression member

Solution: One method is to determine a simple-span deflection with a unit uniform load as follows: Using the moment area method, the center or midheight deflection is:

A B

4

4 ⎛ 1⎞ 5 ⎜ ⎟ ⎡⎣10 (12 )⎤⎦ ⎝ 12 ⎠ 5w (  ) = Iequiv = = 4025 in.4 Δo 384E 0.013 ( 384 ) ( 4300 ) 4

A second, more approximate method would be to use a weighted average of the moments of inertia of the two sections. In this case:



5638 ( 3 + 2 ) + 3891( 5 ) = 4764 in.4 10

=

B

12'-0"

4"

Center of gravity 6.01"

5w ( ) ∆o = 384El equiv

l1h1 + l 2h2 h1 + h2

A

24"

∆o = 0.013 in.

Iequiv =

B

 nce an equivalent moment of inertia is deterO mined, slenderness effects are evaluated as described in Section 5.9.3.

Section A-A lg = 3891 in.4

10'-0"

Problem: Determine an approximate moment of inertia for slenderness analysis.

3'-0"

B

5'-0"

Concrete: fc' = 5000 psi, normalweight Ec = 4300 ksi

  5

6t

2'-0"

Given: The load-bearing architectural precast concrete wall panel shown.

14" 2" 12"

64" (72" maximum possible)

4" 14"

Section B-B lg = 5638 in.4

2" 12"

Effective sections

Top l = 5638 in. 3'-0"

4

l = 3891 in.4 l = 5638 in.4 Bottom 5'-0" 2'-0" 10'-0"

Moment of inertia w2 M = ___ 8 10.5 kip-ft 3891 E 10.5 kip-ft 5638 E

3'-0"

CL

12.5 kip-ft 3891 E 8.0 kip-ft 3891 E 8.0 kip-ft 5638 E

5'-0" 10'-0"

2'-0"

M — diagram El Note: CL = centerline

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EXAMPLE 5.9.7.1 Sheet Pile

  5

36"

Given: A I S Concrete: fc'

3"

= 432 in.2 = 5184 in.4 = 5184/6 = 864 in.3

6" 12" 3"

= 6000 psi, normalweight (20) 1/2" diameter, 270 ksi strands

Stress to 75% of fpu; assume 18% loss

Problem: For the 12 in. × 36 in. sheet pile shown, compute allowable moment. ______________________________________________________________________________________ Solution: fse Aps fpc

= 0.75(1 – 0.18)(270) = 166 ksi = 20(0.153) = 3.06 in.2 = fse (Aps)/A =

(

166 3.06

)

432

= 1.176 ksi

Moment capacity: (a)

Service loads For allowable tension of 4 fc' or 0.310 ksi: Allowable moment: = 4 fc' + fpc)S = (0.310 + 1.176)864 = 1284 kip-in. per pile = 428 kip-in./ft

(b)

Strength design Use strain compatibility: Using an iteration procedure, determine the depth of neutral axis c to be 4.33 in. (see Example 5.2.1.5). εse = fseEps = 166/28,500 = 0.00582 in./in.

0.003

0.085f'c

Last iteration: εs1 =

9.00 − 4.33 0.00906 0.003 + 0.00582 ==0.00906 4.33

(

fs1 = 270 −

)

C

a C T2

0.04 = 250.6 ksi 0.00906 − 0.007

T 1

= 250.6(0.153)(10) = 383.4 kip

εs2

=

4.33 − 3.00 0.00490 −0.003 + 0.00582 == 0.00490 4.33

(

)

fs2 = 0.00490 (28,500) = 139.7 ksi es1 T2 = 139.7(0.153)(10) = 213.7 kip T1 + T2 = 383.4 + 213.7 = 597.1 kip a = 1c = 0.75(4.33) = 3.25 in. C = 0.85 fc' ba = 0.85(6)(36)(3.25) = 596.7 kip (close to T1 + T2) Mn = –596.7(3.25/2) + 213.7(3) + 383.4(9) = 3122 kip-in. εt = εs1 – εse = 0.00906 – 0.00582 = 0.00324 φ = 0.48 + 83εt = 0.75 φMn = 0.75(3123) = 2342 kip-in. = 195 kip-ft

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EXAMPLE 5.10.1 Shear-Wall Analysis

  5

30'-0"

Uniform DL

6.0 kip/ft

Uniform DL

6.0 kip/ft

6600

6"

3'-0" (4) at 1'-0" d

ME, kip-ft

7'-0"

7'-0"

500

18000 VE, kip

#10 Bars

450

12000

2'-0" 6"

350

6.0 kip/ft

24.0

12'-0" #10 bars Single layer

DL

18.0

12'-0"

Uniform

50 kip 2nd floor

200

2400 Possible openings

100 kip 3rd floor

12'-0"

6.0 kip/ft

12.0

150 kip 4th floor

6.0

Uniform DL

Cumulative DL at joints

12'-0"

200 kip 5th floor

dcomp Note: DL = Dead Load

Given: A 10-in.-thick, intermediate, precast concrete shear wall (see illustration) has been proportioned to resist lateral earthquake loads. The vertical reinforcement at the base of the wall includes (14) #10 bars, spliced at the horizontal joints using Type 2 mechanical sleeves. The quantity of bars has been reduced at upper floors as the lateral loads diminish. The dead load attributed to each story is 6.0 kip/ft along the length of the wall (includes self-weight) and is given immediately above each horizontal shear wall joint. The joints are grouted solid with non-shrink grout of an appropriate strength. dcomp = 15(12) = 180 in. (distance from extreme compression zone to centroid of axial load) Concrete: fc' = 5000 psi, normalweight fy = 60,000 psi SDS = 0.213 Seismic design category B µ = 0.6

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CHAPTER 5

EXAMPLE 5.10.1 Shear-Wall Analysis (cont.)

  5

Problem: For the load combination U = (0.9 - 0.2Sds) D + E, as required by ASCE 7-05 Section 12.4.2.3, confirm that the reinforcement shown is adequate to resist the loading present at the foundation and fourth floor interfaces only. In lieu of strain compatibility, use an approximate equation for nominal moment capacity, where the depth of the compression block is defined as a = (Asfy + Pu)/(0.85 fc' b). _____________________________________ Solution: A.

At foundation: 1.

Compute factored loads: Pu = [0.9 - 0.2(0.213)](24.0)(30) = 617.3 kip ME = 18,000 kip-ft VE = 500 kip

2. Compute depth of reinforcement used to resist overturning moment (conservatively, consider only the bars to the left of the wall centerline): d = 30.0 – [(0.5+1.5+2.5+3.5+4.5+11.5+13.5)/7 bars] = 24.64 ft ([7] #10 bars) Note that the use of axial load and compression reinforcement increases the moment capacity. 3.

Compute depth of compression block: As = 7(1.27) = 8.89 in.2 a = (Asfy + Pu)/{0.85 fc' b} = {(8.89)(60) + 617.3)}/{.85(5)(10)} = 27.1 in.

4.

Compute nominal moment capacity: φMn = φ[Asfy(d-a/2) + Pu(dcomp-a/2)] = 0.9[(8.89)(60){24.64(12) – (27.1/2)} + 617.3{180 – (27.1/2)}](1/12)

5.

= 18,992.8 kip-ft > ME Compute nominal shear strength across joint using shear friction method: φVnf = µφ(Asfy + Pu) = 0.6(0.75)[14(1.27)(60) + 617.3] = 757.8 kip > VE

OK OK

Check Vn max: < φ(0.2) fc' Acr = 0.75(0.2)(5000)(10)(24.64)(12) = 2218 kip > 757.8



6.

OK

< φ800Acr = 0.75(800)(10)(24.64)(12) = 1774 kip) > 757.8 Compute the nominal shear strength for the wall (away from joints):

OK

Vc = 2 fc' bd = 2 5000 (10)(24.64)(12) = 418 kip Because Vu /φ > 0.5Vc, provide shear reinforcement in accordance with ACI 318-05 Section 11.10.9. Av /s = (Vu /φ – Vc)(fyd) = (500/0.75-418)/[(60)(24.64)(12)] = 0.014 in.2/ft But not less than the minimum shear reinforcing steel as required by Sections 11.10.9.2 through 11.10.9.5. Horizontal reinforcement: ρt = 0.0025, Av(horizontal) = 0.0025(10)(12) = 0.30 in.2/ft, use #4 each face spaced at 16 in. on center. Av(horizontal)prov = (0.2)(12 in./16 in.)(2 faces) = 0.30 in.2/ft. OK

Smax = lw /5, 3b, or 18 in. > 16 in. Vertical reinforcement: 0.0025 ≤ ρ ≤ 0.0025 + 0.5(2.5 – hw / lw)(ρt – 0.0025) Since ρt = ρtmin, ρ = ρt = 0.0025, therefore: Av(vertical) = Av(horizontal) = 0.30 in.2/ft, use #4 Smax = lw /3, 3b, or 18 in. > 16 in. 5–120

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

EXAMPLE 5.10.1 Shear-Wall Analysis (cont.) B.

At fourth floor: 1.

Compute factored loads: Pu = [0.9 – 0.2(0.213)](6.0)(30) = 154.3 kip ME = 2400 kip-ft VE = 200 kip

2.

Compute depth of reinforcement used to resist overturning moment: d = 30.0 – [(0.5+4.5+11.5)/3 bars] = 24.5 ft ((3) #10)

3.

Compute depth of compression block: As = 3(1.27) = 3.81 in.2 a = (Asfy + Pu)/[0.85 fc' b] = [(3.81)(60) + 154.3)] / [0.85(5)(10)] = 9.00 in.

4.

Compute nominal moment capacity: φMn = φ[Asfy(d-a/2) + Pu(dcomp - a/2)] = 0.9{(3.81)(60)[24.5(12) – (9.00/2)] + 154.3[180 – (9.00/2)]}(1/12) = 6994 kip-ft > ME OK

5.

Compute nominal shear strength across joint using shear friction method: φVnf = µφ(Asfy + Pu) = 0.6(0.75){6(1.27)(60) + 154.3} = 275 kip > VE φVn max = φ(0.2) fc' Acr = 0.75(0.2)(5000)(10)(24.5)(12) = 2205 kip) > 275 kip or φVn max ≤ φ800Acr = 0.75(800)(10)(24.5)(12) = 1764 kip) > 275 kip

6.

  5

OK OK

OK

Compute the nominal shear strength for the wall (away from joints): Vc = 2 fc' bd = 2 5000 (10)(24.5)(12) = 416 kip Since Vu /φ > 0.5Vc , provide shear reinforcement in accordance with ACI 318-05 Section 11.10.9. Av /s = (Vu /φ – Vc)(fyd) = (200/0.75-416)/[(60)(24.5)(12)] < 0, therefore; Use the minimum shear reinforcing steel as required by ACI 318-05 Sections 11.10.9.2 through 11.10.9.5 Horizontal reinforcement: ρt = 0.0025, Av(horizontal) = 0.0025(10)(12) = 0.30 in.2/ft, use #4 each face spaced at 16 in. on center. Vertical reinforcement: 0.0025 ≤ ρ ≤ 0.0025 + 0.5(2.5 – hw / lw)(ρt – 0.0025) Since ρt = ρtmin, ρ = ρt = 0.0025, therefore: Av(vertical) = Av(horizontal) = 0.30 in.2/ft, use #4 each face spaced at 16 in. on center.

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the prestressing strands before failure of the concrete in compression. This can be noted in the break of the smooth curve of the interaction diagrams in the diagram tension region. In piles that are subject to tension, with or without bending, the nominal strength of the prestressing strands should be equal to or greater than 1.2 times the cracking load of the pile, based on a modulus of rupture fr = 7.5 fc' . This requirement may be waived if the available steel strength is greater than twice the factored tension plus bending loads. Piles in compression should be designed for the actual calculated moment, but not less than the moment induced by a load eccentricity of 0.05 times the pile diameter or width.

5.10

Shear Walls

Chapter 4 provides information regarding the proportioning and distribution of loads to shear walls in accordance with the code, based on the configuration of the structure, the seismic parameters assigned to the particular building site, and the type of shear-wall system utilized (that is, ordinary precast concrete shear walls, intermediate precast concrete shear walls, or special reinforced concrete shear walls). This section provides a general discussion of the design and detailing requirements for the precast concrete components. Once the forces for which the shear walls must be designed have been determined (Chapter 4), component design must be carried out in accordance with the appropriate sections within ACI 318-05 and as modified by ASCE 7-05. Ordinary precast concrete shear walls that are permitted only in seismic design category B (referred to in ACI 31805 as ordinary reinforced concrete structural walls) must be designed and detailed in accordance with the requirements of ACI 318-05 Chapters 1 through 18. These walls do not have to meet any special requirements pertaining to the types of connections used or to ductility. Intermediate precast concrete shear walls that are permitted in seismic design category B and C with no building height limit and in seismic design category D, E, and F with a building height limit of 40 ft to 45 ft (referred to in ACI 318-05 as intermediate precast structural walls) must be designed and detailed in accordance with the requirements of ACI 318-05 Chapters 1 through 18, and to Section 21.13. These walls may be designed and detailed in the same manner as ordinary precast concrete shear walls, except that the non-yielding parts of the connections (mechanical splice connectors, welds, and the like) shall be designed to develop 1.5 times the yield strength of the reinforcement being connected and maintain 80% of their design strength at the deformations induced by the design displacement. Special reinforced concrete shear walls (for the purposes of this handbook, these walls are referred to in ACI 318-05 as special precast structural walls) must be designed and detailed in accordance with the requirements of ACI 31805 Chapters 1 through 18, and to Sections 21.2.2.3, 21.2.3 through 21.2.7, 21.7, 21.8, and 21.13. In structures such as parking garages, it is common that openings be located through shear walls to enhance visibility and security. When these openings are present, the designer 5–122

should investigate the localized shear and bending occurring within the elements surrounding these openings. The forces proportioned to each element will be consistent with its relative stiffness, such as can be determined by frame analyses or appropriate approximate methods. When these openings occur in special reinforced concrete shear walls (or, special precast concrete structural walls), the elements surrounding and adjacent to these openings may require the reinforcing as special boundary elements and coupling beams. Example 5.10.1 features a commonly seen intermediate precast concrete shear wall with horizontal joints connected using type 2 mechanical splice sleeves, thus satisfying ACI 318-05 Section 21.13.

5.11

Sandwich Panels

5.11.1

General

Insulated wall panels, commonly known as sandwich wall panels, are typically composed of two concrete wythes separated by a layer of insulation. One of the concrete wythes may be a standard shape (Fig. 5.11.1) or any architectural concrete section produced for a single project. In service, sandwich wall panels provide the dual function of transferring load and insulating the structure, and can provide the interior and exterior finished wall surfaces. They may be used only for cladding, or they may act as beams, bearing walls, or shear walls. Insulation properties are shown in Table 5.11.1. 5.11.2

Structural Design

The structural design of sandwich wall panels is the same as the design of other wall panels once the section properties of the panel have been determined. Four different assumptions may be used for the properties, depending on the construction: 1. Non-composite for full life cycle of panel. The two concrete layers act independently (Fig. 5.11.2[a]). The wythes are connected by ties that are flexible enough that they offer insignificant resistance to shrinkage and temperature movement between the wythes in the plane of the panel. Positive steps may be taken to ensure that one wythe does not bond to the insulation. Typical techniques are by placing a sheet of polyethylene or reinforced paper over the insulation before the final concrete wythe is placed, by applying a retarder or form release agent to one side of the insulation, or by placing insulation in two layers One wythe is usually considered to be structural and all loads are carried by that wythe, both during handling and in service, although, when designing for wind loads and slenderness effects, the panel may in some cases be designed as in assumption four below. 2. Composite for full life cycle of panel. The two wythes act as a fully composite unit for the full life of the structure (Fig. 5.11.2[b]). In order to provide for composite behavior, positive measures must be taken to ensure shear transfer between the wythes in the direction of panel span. This may be accomplished

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Structural wythe

Non-structural wythe

Structural wythe Rigid insulation

Structural wythe

Composite ties required

Fig. 5.11.1 Typical precast concrete sandwich wall panels.

Table 5.11.1  Properties of insulation Polystyrene Expanded Density, lb/ft3

1.1– 1.4

1.8

Water absorption, % volume

< 4.0

< 3.0

< 2.0

Compressive strength, psi

5–10

13–15

25

18–25

Linear coefficient of expansion, (in./in./°F) × 10–6

25–40

Shear strength, psi

20–35

Flexural strength, psi

a

Extruded

0.7– 0.9

Tensile strength, psi

Polyisocyanurate

1.3– 1.6

1.8– 2.2

3.0

< 0.3

30–40

50

Thermal conductivity, (Btu-in.)/[(hr) 0.32– 0.28 (ft2 of area)(°F)] at 75 °F

0.26– 0.25

0.23

Maximum use temperature

165 °F

Phenolic

Cellular glass

Unfaced

Faced

2.0–6.0

2.0–6.0

2.0–3.0

6.7–9.2

< 3.0

1.0–2.0

< 3.0

< 0.5

15–25

40–60

100

16–50

16

10–16

65

25

50

105

45–140

500

60

50

30–60

10–20

1.6–4.6

20–100

12

50

25–40

10–25

a

 — 

35

50

40–50

60–75

100

0.20

165 °F

50–210

40–50

25

60

0.18

0.10–0.15

0.16–0.23

0.35

300 °F

900 °F

250 °F

a. Unfaced and felt-faced polyisocyanurates should not be used in sandwich panels due to the expansion caused by moisture absorption.

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EXAMPLE 5.11.1 Section Properties of Sandwich Wall Panels

  5

Given: The sandwich wall panel shown. Problem: Calculate the moment of inertia and section modulus if the section is (a) non-composite and (b) composite. Also find the load distribution for the non-composite case. The lateral load applied to the non-composite panel will be resisted by each wythe in proportion to its stiffness. _____________________________________ Solution: (a) The non-composite properties (per foot width) are as follows: Interior (structural) wythe: lint = bd 3/12 = 12(4)3/12 = 64 in.4/ft width Sint = lint /c = 64/2 = 32 in.3/ft width Exterior (non-structural) wythe: lext = 12(2.5)3/12 = 15.6 in.4/ft Sext = 15.6/1.25 = 12.5 in.3/ft

Exterior 21/2"

Distribution of lateral load: lint + lext = 64 + 15.6 = 79.6 in.4/ft

1"

Lateral load resisted by: Interior: 64(100)/79.6 = 80% Exterior: 15.6(100)/79.6 = 20%

4" Interior

(b) The composite properties are as follows: A

y

Ay

y – yb

Ay 2

I

Interior

48

2.00

96.0

1.63

127.5

64.0

Exterior

30

6.25

187.5

2.62

205.9

15.6

Total

78

333.4

79.6

283.5

yb = 283.5/78 = 3.63 in. lc = 333.4 + 79.6 = 413.0 in.4/ft width

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Ties that provide composite behavior

3

1 1

22

CHAPTER 5

3

22

1-1 2-2

1-1

44

44

Alternate arrangement at top or bottom

Alternate composite action achieved by ties 3 3

1 1

(a) Non-composite panel

  5

(b) Composite panel

Fig. 5.11.2 Non-composite and composite panels.

by rigid ties, longitudinal welded-wire trusses, regions of solid concrete that join both wythes, or other tested methods. Consult with the precast concrete producer for tie performance capabilities. 3. Partially-composite for full life cycle of panel. The two wythes do not act independently nor as a fully composite unit, but rather somewhere in between. In a partially composite panel, the ties provide significant shear transfer between the wythes in the direction of the span. Consult with the precast concrete producer for tie performance capabilities. 4. Composite during handling, but non-composite during service life. Composite action results largely because of early bond between insulation and adjacent wythes, in combination with flexible ties. The bond is considered unreliable for the long term; thus, the panel is considered as non-composite for service-life loads. Wind loads are distributed to each wythe in proportion to wythe stiffness. For effects of slenderness, the sum of the individual moments of inertia may be used (Example 5.11.1). For some machine-produced sandwich wall panels, tests and experience have demonstrated that a degree of composite action can be anticipated for the full life cycle. Manufacturer’s recommendations for these panels should be followed. A composite panel will have a stiffness significantly greater than a non-composite panel or partially composite panel of the same thickness. Thus, a composite panel can span greater heights. Thermal bowing will tend to be greater in composite panels than in non-composite panels due to the inherent restraint

of differential movements between wythes. Panel size is limited only by stresses due to handling and service loads, and slenderness in load-bearing panels, modified by the experience of the precast concrete designer. Wythes should be no thinner than three times the maximum aggregate size, Although panels with 3/4 in. aggregate and 2-in.-thick wythes have been successfully used by some manufacturers. Lifting points should be chosen to limit stresses below the modulus of rupture during stripping and handling so that cracks do not occur (see Chapter 8). Prestressing in the long direction is particularly effective as a method of reducing cracks in panels; cracking due to restrained shrinkage in the short direction of the panel does not usually need to be considered, provided the dimension in that direction does not exceed about 15 ft. Composite panels should be concentrically prestressed. In non-composite or partially composite panels, prestressing should be concentric within each wythe that is stressed. The designer may consider prestressing the non-structural exterior wythe to the same or higher prestress level as the structural wythe in order to counteract panel bowing. In some cases, panel openings are so extensive that an insufficient section modulus is left to keep the applied stresses below the cracking limit. In these cases, the following steps should be followed: • •

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  5

Dotted lines show movement of panel (exaggerated)

Inside

Shear connector Connection (pivot point)

Tie connectors at 24" on center Flat sleeve anchor

Area of prying action

Plan

Caulked joint

Possible spall if shims are placed too close to outside of surface

Section Fig. 5.11.5 Anchorage for stemmed panel.

section properties to ensure stability of the panel and avoid a failure mechanism. Fig. 5.11.3 Restraint at foundation.

The maximum strand diameter that may be used is related to wythe thickness. Satisfactory results have been achieved using 3 /8-in.-diameter strand in 2-in.-thick wythes. A wythe thickness of 3 in. is sufficient when using a 1/2-in.-diameter strand. Transverse reinforcement should be provided at the ends of the panel to limit splitting cracks over the strands during detensioning. With low thickness-to-strand diameter ratios, special attention during production should be given to the asplaced strand location in order to maintain required cover and to minimize the risk of splitting cracks. Reference 31 includes design examples for composite and non-composite sandwich panels used as clad­ding, bearing walls, and shear walls. A design exam­ple for a semicomposite panel (design assumption 4 in this section) is also included.

Bent reinforcing bars

5.11.3

Sleeve anchor

Welded-wire truss

Fig. 5.11.4 Typical shear connectors.

composite using rigid ties, wire trusses, or solid concrete sections. • Consider making the panel thicker or adding a full or partial-height pilaster section to the panel. If none of these options provide an acceptable solution, then the designer can only satisfy the strength criteria (normally accomplished by the use of longitudinal steel reinforcement), and some cracking as well as differential panel deflection is to be expected. In these cases, it is critical that the designer perform a second-order analysis of the panel using cracked5–126

Panel Connections

Analysis and design of panel connections to resist normal and transverse wind and seismic shears as well as gravity and alignment loads are described in Chapters 4 and 6. Consideration must also be given to anticipated bowing, particularly of composite panels (see Section 5.8.5). The effects of differential bowing between adja­cent panels of similar span may be minimized by carefully aligning the panel during erection and pro­viding a sealant on both the inside and outside of panel joints. Where adjacent panels are of signifi­cantly different stiffness, connections should be provided across the adjacent joint to maintain alignment. Such connections should be located in the center third of the span. The connection should provide for anticipated movement to prevent build-up of volumetric restraint forces. Panel embedments may be limited by the wythe thickness, and, therefore, may not be fully effective. Confinement reinforcement should be placed around any embedment. When bowing does occur, it is generally outward. Section 5.8.5 discusses the effects of bowing on connections. Recommenda-

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tions stated should be followed to prevent the opening of joints and the resultant possibility of joint-sealant failure. Special attention should also be paid to panels that are hung from adjacent panels. If a hung panel is supported by full-height panels that are supported on a foundation, the assembly of panels can move as a unit without distress to the panel or joint sealant. However, if the hung panel is also rigidly attached to the structure (such as at a mezzanine level), this restraint may result in differential bowing of the hung panel with respect to the adjacent long panels. A detail to permit the hung panel to move with the adjacent panels should be provided. Attention should be paid to the position of the connection near the bottom of a panel supported on a foundation, in order to minimize the possibility of spalling due to thermal bowing (Fig. 5.11.3).

Insulation core Precast concrete component

(a) Ties, acting in tension, transfer weight of lower wythe

5.11.4 Wythe Connectors When one wythe is non-structural, its weight must be transferred to the structural wythe. This may be accomplished by using shear connectors or solid concrete ribs at only the top or bottom of the panel unless both wythes are shimmed at the base. This permits the non-structural wythe to contract and expand with the least restraint. Shear connectors may include bent reinforcing bars, sleeve anchors, expanded metal, fiber connec­tors, carbon-fiber trusses, or welded-wire trusses (Fig. 5.11.4). For stemmed panels, the shear connector is placed in the stem to ensure proper embedment depth. In non-composite panels, it is preferable to have only one anchoring center. In a panel with two stems, the shear connector can be positioned in either one of the stems, and a flat anchor with the same vertical shear capacity is used in the other stem (Fig. 5.11.5). Because the flat anchor has little or no horizontal shear capacity, restraint of the exterior wythe is mini­mized. In a multi-ribbed panel, the shear connector is placed as near

b-1 b-2 (b) Ties, acting in tension or compression, transfer weight of exterior wythe (b-1) rigid connector transfers weight of exterior wythe by shear and flexure (b-2)

(c) Ties, acting in tension or compression, transfer wind forces

(d) Ties similar to (b), transfer lateral forces applied to one wythe Note: Other proprietory connectors are also available. Consult with local producers.

Fig. 5.11.6 Functional behavior of connectors.

Provide plastic tips to prevent rust stains

Z-tie

Hairpin

Fiber tie

C-tie

Fig. 5.11.7 Tension/compression ties. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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the center of rigidity as is possible, and flat anchors are used in the other stems. To complete the connection, tension/compres­sion ties passing through the insulation are spaced at regular intervals to prevent the wythes from separating. Functions of wythe connectors are shown in Fig. 5.11.6. Typical tie details are shown in Fig. 5.11.7. Wire tie connectors are usually 12 to 14 gauge and preferably of stainless steel. Galvanized metal or plastic ties may also be acceptable. Ties of welded-wire reinforcement and reinforcing bars are sometimes used. Galvanized metal, plastic, or fiber-reinforced polymer ties may also be acceptable. Tension/compression ties should be flexible enough so as not to significantly resist temperature and shrinkage parallel to the panel surface, yet strong enough to resist a lifetime of stress reversals caused by temperature strains. Follow the manufac­turer’s recommendations when available; otherwise, the spacing of ties should be approximately 2 ft on centers. 5.11.5 Thermal Bowing Thermal bowing of exterior composite panels must be considered. Calculation of bow and the forces required to restrain it are discussed in Section 5.8.5. Differential movement between panels is sel­dom a problem, except at corners or where abrupt changes in the building occur. Crazing or cracking is some­times caused by bowing, but will be minimized if the recommendations of Section 5.11.2 are fol­lowed; such cracking is seldom of structural significance. 5.11.6

Typical Details

As with all precast concrete construction, satis­factory performance depends on proper detailing. The typical wall-panel connections and details shown in Chapter 6 are equally applicable to sandwich wall panels. Common details and connections for sandwich wall panels can be found in Reference 31.

5.12

Special Considerations

This section outlines solutions of special situations that may arise in the design of a precast concrete system. Because production methods of products vary greatly, regional producers should be consulted. Also, test data may indicate that the conservative guidelines presented here may be exceeded for specific applications with engineering judgment considered. 5.12.1 Point Loads on Double-Tee Flanges Double-tee flanges are often subject to concentrated point loadings, particularly in parking-structure applications as well as numerous other applications. There are several approaches to performing these designs, which include yield line theory, influence charts, and effective-width approaches. All of these methods appear to be conservative when compared with actual load tests, as seen in Reference 32. When considering concentrated loads on cantilevered flanges, the effectivewidth approach usually produces satisfactory results without the need to additionally refine the analysis. This approach requires the use of an influence angle extending back to the flange to stem interface in order to determine an effective 5–128

resisting section. The flange reinforcement is then designed based on one-way bending of a cantilever. This approach neglects plate behavior, which explains why load tests have shown it to be conservative. However, it typically results in a reasonable design. The research suggests that an influence angle of 60 deg results in an effective width consistent with crack patterns from actual load tests. 5.12.2

 ffective Resisting Widths for E Concentrated Loads on Hollow-Core Decks

Frequently, floors and roofs are subjected to line loads, for example, from walls and concentrated loads. The ability of hollow-core systems to transfer or distribute loads laterally through grouted shear keys has been demonstrated in several published reports,33-35 and many unpublished tests. Based on tests, analysis, and experience, the PCI Hollow-Core Slab Producers Committee recommends that moments and shears created by line and concentrated loads be resisted by an effective section as described in Fig. 5.12.1.36 Use of these resisting sections will result in prediction of peak values for moment and shear. That is, the effective width concept is simply a mechanism used to determine the maximum design moments and shears rather than a depiction of the actual load path through the system. Exception: If the total deck width, perpendicular to the span, is less than the span, modification may be required. Contact regional producers for recommendations. Moment and shear distribution in stemmed components may not necessarily follow the same pattern because of different torsional resistance properties. 5.12.3 Openings through Decks Openings may be provided in precast concrete decks by saw cutting after the deck is installed and grouted, forming (blocking out) or sawing in the plant, or using short units with steel headers or other connections. In hollow-core or solid slabs, structural capacity is least affected by orienting the longest dimension of an opening parallel to a span, or by coring small holes to cut the fewest strands. Openings in stemmed components must not cut through the stem, and for double-tees, should be narrower than the stem spacing less the top stem width less 2 in. The following are reasonable guidelines regarding the design of hollow-core units around openings. Some producers may have data to support different pro­cedures: 1. An opening located near the end of the span and extending into the span less than the lesser of 0.125l or 4 ft may be neglected when designing for flexure in the midspan region. 2. Strand development must be considered on each side of an opening that cuts strand (see Section 5.2.3). 3. Slabs that are adjacent to long openings (l/4 or more) or occur near midspan may be considered to have a free edge for flexural design. 4. Slabs that are adjacent to openings closer to the end than 3l/8 may be considered to have a free edge for shear design.

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  5

0.25 Effective width

Effective width 0.50



Effective width

Effective width 0.25

4'-0" Concentrated load

1'-0"

Interpolate

Interpolate

0.50

0.25

Interior loads

Edge loads

Fig. 5.12.1 Assumed moment and shear distribution widths for hollow-core slabs.

2" minimum

Development length of strand, minimum

4" minimum radius

8" minimum Bearing point

Fig. 5.12.2 Openings through webs.

5.12.4 Openings through Webs In special situations, horizontal openings may be required in stems of structural components. References 37 through 40 summarize research on the subject and include the results of full-scale testing and design recommendations. The principal recom­mendations from those references are:

• • •

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Web openings should be placed outside the strand development area (Fig. 5.12.2). Vertical stirrups should be placed on each side of an opening to control cracks in the vicinity of the openings. The openings should be located in regions of the component with low shear and below the compression block. 5–129

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EXAMPLE 5.12.1.1 Flexural Strength of Double-Tee Flange in Transverse Direction

  5

For flanged sections, in addition to providing adequate flexural strength in the longitudinal direction, the flanges must be designed for bending in the transverse direction. This example illustrates a design for both uniformly distributed loads (part A) and concentrated loads (part B). Fibers, which are sometimes used to control shrinkage cracks, do not transfer loads and, therefore, cannot be used to replace structural reinforcement such as welded-wire reinforcement (WWR). This is particularly important for structural toppings over precast concrete decks. The reinforcement in these toppings cannot be replaced with fibers. Part A Given: PCI standard double-tee of Example 5.2.1.4. Topping is reinforced with WWR, 6 × 6–W1.4 × W1.4 and the flange is reinforced with WWR, 6 × 6–W4.0 × W4.0 Concrete: precast fc' = 5000 psi, normalweight topping fc' = 3000 psi, normalweight fy = 60,000 psi Note: 65,000 psi could be used here if the appropriate size WWR is used. See Design Aid 15.2.11.

d1 = 1"

As2

As1 2'-0"

d2 = 3"

1'-9"

4'-0"

2'-0"

Problem: Find the uniform live load that the flange can support. _______________________________________________________________________________________ Solution: From Design Aid 15.2.10: As1 (WWR in precast concrete) = W4.0 at 6 in. = 0.080 in.2/ft As2 (WWR in topping) = W1.4 at 6 in. = 0.028 in.2/ft The cantilevered flange controls the design since the negative moment over the stem reduces the positive moment between the stems. Construct strain diagram: Try c = 0.25 in.

ε s + 0.003 d = c 0.003

εs 2

Therefore: εs1 =

0.003d 1 − 0.003 c

0.003d 2 εs2 = − 0.003 c

εs1 = εs2 = εy =

5–130

( ) − 0.003 ==0.009 0.009

0.003 1

T2

εs 1

d2 d1

T1 c

a

C

εc = 0.003

0.25

( ) − 0.003 == 0.033 0.033

0.003 3 0.25 fy Es

=

60 = 0.0021< 0.009 29,000

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EXAMPLE 5.12.1.1 Flexural Strength of Double-Tee Flange in Transverse Direction (cont.) Therefore, reinforcement yields at both levels, and fs = fy = 60 ksi a = 1c = 0.80(0.25) = 0.20 in. C = 0.85 fc' ba = 0.85(5)(12)(0.20) = 10.2 kip/ft T1 = As1fy = 0.08(60) = 4.80 kip/ft T2 = As2fy = 0.028(60) = 1.68 kip/ft T1 + T2 = 6.48 < 10.2 kip/ft

  5

Therefore, try a

=

(T +T ) = 6.48 (0.85f b ) ⎡⎣0.85 ( 5)(12)⎤⎦

c

=

0.13 = 0.16 0.80

1

2

' c

= 0.13 in.

Check:

( ) − 0.003 = 0.016 > 0.0021

0.003 1

εs1 =

0.16

Therefore, the reinforcement yields, and the analysis is valid. Determine φ: 0.16 c = = 0.16 1 dt

From Fig. 5.2.3, 0.16 < 0.375 Therefore, tension controls, and φ = 0.9: ⎡ ⎛ ⎡ ⎛ ⎛ 0.13 ⎞ ⎛ a⎞ a⎞⎤ 0.13 ⎞ ⎤ + 1.68 ⎜ 3 − φMn = φ ⎢T1 ⎜ d 1 − ⎟ +T2 ⎜ d 2 − ⎟ ⎥ = 0.9 ⎢ 4.80 ⎜ 1− ⎥ = 8.48 kip-in./ft = 707 ft-lb/ft ⎟ 2⎠ 2⎠ ⎦ ⎝ ⎝ 2 ⎠ ⎝ 2 ⎟⎠ ⎦ ⎣ ⎝ ⎣

Check minimum reinforcement:

d b

=

( )

()

0.028 3 + 0.08 1

0.028 + 0.080 = 12 in.

As,min =

= 1.52 in.

( )(

)

3 5000 12 1.52 3 fc' b d= = 0.064 in.2 fy w 60,000

As provided = 0.028 + 0.080 = 0.108 in.2 > 0.064 in.2

OK

Calculate allowable load: wd (flange self-weight) = 50 lb/ft2 Md = Ml wl =

( )(

)

2

w d  2 50 1.2 1.75 = 91.9 ft-lb/ft = 2 2 = 707 – 91.9 = 615.1 ft-lb/ft

( ) (1.75) (1.6) 615.1 2 2

= 251 lb/ft2

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EXAMPLE 5.12.1.1 Flexural Strength of Double-Tee Flange in Transverse Direction (cont.)

  5

Part B Given: Pretopped double-tee 10DT34 (see Chapter 3) fc' = 5000 psi, normalweight fy = 65,000 psi (WWR) Note: ACI 318-05, Section 3.5.3, allows fy to exceed 60,000 psi if stress corresponds to a strain of 0.35%. Problem:  esign the flange for bending in the transverse direction D for a concentrated live load of 3 kip (typical for parking structures) as shown.

b = 8"

Solution: The following assumptions related to distribution of the concentrated load are typical:

60°

1. Because of the flange-to-flange connection, the 3 kip load may be distributed to two adjacent doubletees (1.5 kip per double-tee).31 2. The load is considered applied over an area of about 20 in.2 with the dimension b equal to 6 in. to 10 in. 3. An angle of 60 deg is a reasonable assumption for distribution of the concentrated load in each doubletee flange. Note: For this example, a 60 degree angle and the dimension b equal to 8 in. results in a distribution width at face of stem of 8.17 ft as shown.

4 150 = 50 lb/ft2 12

(

)

8.17'

60°

Plan P = 3 kip 2" P/2

2.17'

P/2

2.17' 2.5'

Calculate factored moment per foot width: wd (self-weight of flange) =

60°

60°

_____________________________________

2.5'

Section

⎛ 2.17 ⎞ ⎛ 12 ⎞ 1.2w d  2 = 1.2 50 2.17 ⎜ = 1.69 kip-in./ft 2 ⎝ 2 ⎟⎠ ⎜⎝ 1000 ⎟⎠ ⎛P⎞ Ml (factored) = 1.6 ⎜ ⎟  = 1.6 1.5 2.17 12 = 62.50 kip-in. distributed over 8.17 ft ⎝ 2⎠

( )(

Md (factored) =

)

( )(

)( )

62.50 = 7.65 kip-in./ft 8.17

Mu = 1.69 + 7.65 = 9.34 kip-in./ft Calculate design moment strength with trial WWR that has W4 wire at 4 in. on centers. As = 0.12 in.2/ft (see Design Aid 15.5.1) a

=

Asfy 0.85f b ' c

=

( ) 0.85 ( 5 )(12 ) 0.12 65

= 0.15 in.

a⎞ 0.15 ⎞ ⎛ ⎛ φMn = φ Asfy ⎜ d − ⎟ = 0.9 (0.12 ) (65 ) ⎜ 3 − ⎟ = 20.53 kip-in./ft > 9.34 kip-in./ft ⎝ ⎝ 2⎠ 2 ⎠

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CHAPTER 5

EXAMPLE 5.12.1.1 Flexural Strength of Double-Tee Flange in Transverse Direction (cont.) Check ACI 318-05 Sections 10.5.4 and 7.12.2.1 for required minimum reinforcement in topping of thickness t: As (shrinkage and temperature)

⎡ 0.0018 (60 ) ⎤ ⎛ 60 ⎞ =⎢ ⎥ bt = 0.0018 ⎜⎝ ⎟⎠ (12 ) ( 2 ) fy 65 ⎣ ⎦ OK

= 0.04 in.2/ft < 0.12 in.2/ft Use WWR 12×4–W2.0×W4.0 (one layer).

The unsupported corners of double-tees should be reinforced a minimum of (1) #4 L-bar. Because double-tees are prestressed units, the flange does not need to have longitudinal reinforcement to satisfy minimum shrinkage and temperature reinforcement.

•

• •

The component should be subjected to primarily uniformly distributed loads. It is preferable to keep significant concentrated loads completely outside the opening boundary. The minimum distance between the openings should be equal to the height of the opening, but not less than 10 in. Components should be designed so that tensile stresses do not exceed the modulus of rupture.

References 37, 39, and 40 provide design examples and further recommendations. These references should be reviewed before designing or specifying horizontal openings in webs. 5.12.5 Continuity In most applications, precast concrete components are used as part of a simple-span system. In some cases, continuous frames are designed to be part or all of the lateral-forceresisting system (see Chapter 4). In other cases, reinforcement is added in topping or pour strips over deck supports, and a positive com­pression block is constructed at the bottoms of the deck components. This can make an effective continuous structure with the resulting structural efficiency. Such a system is, however, highly dependent on proper design, detailing, and construction, and regional precasters should be contacted before such a system is specified. 5.12.6 Cantilevers The method by which precast, prestressed concrete components resist cantilever moments depends on the method of production, the length and loading requirements of the cantilever, and the size of the project (amount of repetition). If a cantilever is not long enough to fully develop top strands, a reduced value of fps must be used, as discussed in Section 5.2.3. As with reinforcing bars, due to settlement of

concrete, top strands often do not bond as well as the ACI 318-05 de­velop­ment equation indicates, especially in drycast systems. It is often necessary, or at least desirable, to debond the top strands in positive moment regions and the bottom strands in the cantilever. In some cases, it is preferable to design cantilevers as reinforced concrete components using deformed reinforcing bars to provide the negative-moment resistance. In machine-made products, the steel can be placed in grout keys, composite topping, or concreted into cores. Top tension under service loads should be lim­ited to 7.5 fc' , including prestress, so that the section remains uncracked, allowing better prediction of service-load deflections. Consultation with regional producers is recom­mended before choosing a method of reinforcement for cantilevers. Some have developed standard methods that work best with their particular system, and have proven them with tests or experience. 5.12.7 Warping of Deck Components It is a fairly common practice to warp double-tees, especially in parking structures, to obtain desired drainage patterns. Warping occurs when one of the four supports for a double-tee is not in the same plane as the other three. Stated another way, the transverse slope across one end of the double-tee is not the same as across the other end. Two primary concerns when evaluating proposed warping of a double-tee are that it can cause flange cracking and it can result in teetering of the double-tee on only three of the four intended support points. It is important to realize that flange cracking due to warping is rarely a structural concern. If topping is to be applied, crack repair is not necessary. For a pretopped system (that is, no field topping will be placed over the double-tees), the sealing of all cracks, except minor ones, to prevent moisture penetration is recommended if the flange reinforcement is

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CHAPTER 5

EXAMPLE 5.12.2.1 General Case Illustrating Effective Resisting Widths for Concentrated Loads on Hollow-core Decks

5'-6"

P1 w1 P2

6'-0"

SDL = 10 lb/ft 2 w1D = 650 lb/ft LL = 40 lb/ft 2 w1L = 1040 lb/ft Slab wt = 56 lb/ft2

P2 w1 5'-6"

9'-6"

25'-0"

9'-6"

  5

P1

P1D = 500 lb P1L = 1000 lb

P2D = 1000 lb P2L = 3000 lb

Given: An untopped hollow-core floor with 4-ft-wide, 8-in.-deep slabs, and supporting a load-bearing wall and concentrated loads as shown on the next page. Problem: Determine the design loads for the slab supporting the wall and concentrated loads. _____________________________________ Solution: Note: Each step corresponds to a line number in the table shown at the end of this example. 1.

Calculate the shears and moments for the non-distributable (uniform) loads: wu = 1.2(56 + 10) + 1.6(40) = 143 lb/ft2

2.

Calculate the shears and moments for the distributable (concentrated and line) loads: wu = 1.2(650) + 1.6(1040) = 2444 lb/ft P1u = 1.2(500) + 1.6(1000) = 2200 lb P2u = 1.2(1000) + 1.6(3000) = 6000 lb

3.

Calculate the effective width along the span: At the support, width = 4.0 ft At 0.25l (6.25 ft), width = 0.5l = 0.5(25) = 12.5 ft Between x = 0 and x = 6.25 ft Width = 4 + (x/6.25)(12.5 – 4) = 4 + 1.36x

4.

Divide distributable shears and moments from step 2 by the effective widths from step 3.

5.

Add the distributed shear and moment to the non-distributable shear and moment from step 1.

Once the moments and shears are determined, the slabs are designed as described in Sections 5.2, 5.3, and 5.6. This method is suitable for computer solution. For manual calculations, the procedure can be simplified by investigating only critical sections. For example, shear may be determined by dividing all distributable loads by 4 ft, and flexure at midspan can be checked by dividing the distributable loads by 0.5l.

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EXAMPLE 5.12.2.1 General Case Illustrating Effective Resisting Widths for Concentrated Loads on Hollow-core Decks (cont.)

  5

Shear and Moments Distance from support, ft 1. Non-distri­ butable loads 2. Distributable loads 3. Effective width 4. Distributed shears and moments 5. Design shears and moments

0

0.333

1

2

3

4

5

7.5

10

12.5

Vu

1.79

1.74

1.64

1.50

1.36

1.22

1.07

0.72

0.36

0.00

Mu

0.00

0.59

1.72

3.29

4.72

6.01

7.15

9.38

10.73

11.17

Vu

31.42

30.60

28.97

26.53

24.09

21.64

19.20

10.89

0.00

0.00

Mu

0.00

10.33

30.20

57.95

83.26 106.12 126.54 162.50 179.39 179.39

Eff, W

4.00

4.45

5.36

6.72

8.08

9.44

10.80

12.50

12.50

12.50

Vu

7.85

6.88

5.41

3.95

2.98

2.29

1.78

0.87

0.00

0.00

Mu

0.00

2.32

5.63

8.62

10.30

11.24

11.72

13.00

14.35

14.35

Vu

9.64

8.62

7.05

5.45

4.34

3.51

2.85

1.59

0.36

0.00

Mu

0.00

2.91

7.35

11.91

15.02

17.25

18.87

22.38

25.08

25.52

Note: Vu is measured in kip/ft, Mu is measured in kip-ft/ft.

susceptible to corrosion. Reference 41 provides guidelines for determining if a crack may be considered minor or not. A double-tee that does not settle down under its own weight to bear at all four support points should be shimmed as required to obtain bearing at all points. This will likely result in some vertical offset between the edges of adjacent doubletees. These offsets can be accommodated by the topping in a topped system, but in a pretopped system they should be limited to 1/4 in. to avoid a tripping hazard. References 42 and 43 provide information based on testing, analysis, and experience. In general, parking structure double-tees in the 60-ft-span range have successfully been warped about 1/4 in./ft of width for pretopped (4-in.-thick flange) and about 3/8 in./ft for topped (2-in.-thick flange).

5.13

References

1. A  CI Committee 318. 2005. Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05). Farmington Hills, MI: American Concrete Institute (ACI). 2. N  aaman, A. E. 1977. Ultimate Analysis of Pre­ stressed and Partially Prestressed Sections by Strain Compatibility. PCI Journal, V. 22, No. 1 (JanuaryFebruary). 3. N  oppakunwijai, P., M. Tadros, Z. Ma, and R. Mast. 2001. Strength Design of Pretensioned Flexural Concrete Members at Prestress Transfer. PCI Journal, V. 46, No. 1 (January-February). 4. M  ast, Robert F. 1998. Analysis of Cracked Pre­stressed Sections: A Practical Approach. PCI Journal, V. 43, No. 4 (July-August). 5. M  artin, L., and W. Korkosz. 1995. Strength of Pre­ stressed Concrete Members at Sections Where Strands Are Not Fully Developed. PCI Journal, V. 40, No. 5 (September-Octo­ber). 6.

 eterman, Robert J. 2007. The Effects of As-Cast Depth P and Concrete Fluidity of Strand Bond. PCI Journal, V.52, No. 3 (May-June).

7. L  ogan, Donald R. 1997. Acceptance Criteria for Bond Quality of Strand for Pretensioned Pre­stressed Concrete Applications. PCI Journal, V. 42, No. 2 (March-April). PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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CHAPTER 5

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

8. K  elly, John B. and Kenneth Pike. 1973. Design and Production of Prestressed L-Shaped Bleacher Seat Units. PCI Journal, V. 18, No. 5 (September-October).

22. S  haikh, A. F. and D. E. Branson. 1970. Non-Ten­sioned Steel in Prestressed Concrete Beams. PCI Journal, V. 15, No. 1 (February).

9. A  swad, A., G. Burnley, N. Cleland, D. Orndorff, and C. Wynings. 2004. Load Testing of Prestressed Concrete Double-Tees without Web Reinforcement. PCI Journal, V. 49, No. 2 (March-April).

23. P  CI Committee on Prestressed Concrete Columns. 1988. Recommended Practice for the Design of Prestressed Concrete Columns and Walls. PCI Journal, V. 33, No. 4 (July-August).

10. M  arshal, W. T., and A. H. Mattock. 1962. Control of Horizontal Cracking in the Ends of Preten­sioned Prestressed Concrete Girders. PCI Journal, V. 7, No. 5 (October).

24. N  athan, Noel D. 1985. Rational Analysis and Design of Prestressed Concrete Beam Col­umns and Wall Panels. PCI Journal, V. 30, No. 3 (May-June).

11. M  attock, Alan H. 1987. Anchorage of Stirrups in a Thin Cast-in-Place Topping. PCI Journal, V. 32, No. 6 (November-December). 12. S  haikh, A. F. 1978. Proposed Revisions to ShearFriction Provisions. PCI Journal, V. 23, No. 2 (MarchApril). 13. Z  ia, Paul and W. D. McGee. 1974. Torsion Design of Prestressed Concrete. PCI Journal, V. 19, No. 2 (March-April). 14. Z  ia, Paul and T. C. Hsu. 1978. Design for Torsion and Shear in Prestressed Concrete Flexural Members, Preprint 3424, American Society of Civil Engineers, October. Reprinted in revised form in PCI Journal, V. 49, No. 3 (May-June). 15. M  irza, S. A. and R. W. Furlong. 1983. Serviceabil­ity Behavior and Failure Mechanisms of Con­crete Inverted T-Beam Bridge Bentcaps Journal of the American Concrete Institute, V. 80, No. 4 (July-August). 16. M  irza, S. A., and R. W. Furlong. 1983. Strength Criteria for Concrete Inverted T-Girders. ASCE Journal of Structural Engineering, V. 109, No. 8 (August). 17. K  lein, G. J. 1986. Design of Spandrel Beams, PCI Research Project No. 5. Sum­mary paper presented in PCI Journal, V. 31, No. 5 (September-October). 18. P  recast/Prestressed Concrete Institute (PCI). 1988. Design and Typical Details of Connections for Precast and Prestressed Concrete (MNL-123-88). 2nd edition. Chicago, IL: PCI. 19. M  attock, A. H. and T. S. Theryo. 1986. Strength of Precast Prestressed Concrete Members with Dapped Ends, PCI Research Project No. 6. Summary paper presented in PCI Journal, V. 31, No. 5 (SeptemberOctober). 20. Z  ia, Paul, H. K. Preston, N. L. Scott, and E. B. Workman. 1979. Estimating Prestress Losses. Concrete International, V. 1, No. 6 (June). 21. M  artin, L. D. 1977. A Rational Method for Estimat­ing Camber and Deflection of Precast Pre­stressed Members. PCI Journal, V. 22, No. 1 (January-February).

5–136

25. K  riz, L. B. and C. H. Raths. 1965. Connections in Precast Concrete Structures — Strength of Corbels. PCI Journal, V. 10, No. 1 (February). 26. M  attock, A. H. 1976. Design Proposals for Reinforced Concrete Corbels. PCI Journal, V. 21, No. 3 (MayJune). 27. A  CI Committe 543. Design, Manufacture and Installation of Concrete Piles (ACI 543R-00). Farmington Hills, MI: ACI. 28. P  CI Committee on Prestressed Concrete Columns. 1993. Recommended Practice for Design, Manu­facture, and Installation of Prestressed Con­crete Piling. PCI Journal, V. 38, No. 2 (March-April). 29. P  CI Bridge Design Manual Steering Committee. 1997. Bridge Design Manual (MNL-133-97). 2nd edition. Chicago, IL: PCI. 30. P  CI. 2005. Prestressed Concrete Pile Interaction Dia­ gram Spreadsheet. CD-ROM, version 1.0. Chicago, IL: PCI. (Explained by and to be used in con­junction with Chapter 20 of Reference 29). 31. P  CI Committee on Precast Sandwich Wall Panels. 1997. State-of-the-Art of Precast/Pre­stressed Sandwich Wall Panels. PCI Journal, V. 42, No. 2 (March-April), and V. 42, No. 3 (May-June). 32. A  swad, Alex and George Burnley. 1991. Point Load Tests of Double-Tee Flanges. PCI Journal, V. 36, No. 4 (July-August). 33. L  aGue, David J. 1971. Load Distribution Tests on Precast Prestressed Hollow-Core Slab Construction. PCI Journal, V. 16, No. 6 (Novem­ber-December). 34. J ohnson, Ted and Zohair Ghadiali. 1972. Load Distribution Test on Precast Hollow-Core Slabs with Openings. PCI Journal, V. 17, No. 5 (SeptemberOctober). 35. P  feifer, Donald W. and Theodore A. Nelson. 1983. Tests to Determine the Lateral Distribu­tion of Vertical Loads in a Long-Span Hol­low-Core Floor Assembly. PCI Journal, V. 28, No. 6 (November-December). 36. P  CI. 1998. Manual for the Design of HollowCore Slabs, MNL-126-98. Chicago, IL: PCI.

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37. S  avage, J. M., M. K. Tadros, P. Arumugasaamy, and L. G. Fisher. 1996. Behavior and Design of DoubleTees with Web Open­ings. PCI Journal, V. 41, No. 1 (January-February).

  5

38. S  aleh, M. A. 1996. Optimization of Prefabricated Joists. Ph.D diss., University of Nebraska-Lincoln. 39. S  aleh, M. A., P. A. Brady, A. Einea, and M. K. Tadros. April 1997. Design and Performance of Prestressed Precast Reinforced Concrete Double-Tee Beams with Web Openings, USACERL Technical Report 97. Washington, DC: U.S. Army Corps of Engineers. 40. B  arney, George B., W. Gene Corley, John M. Hanson, and Richard A. Parmelee. 1977. Behavior and Design of Prestressed Concrete Beams with Large Web Openings. PCI Journal, V. 22, No. 6 (November-December). 41. P  CI Committee on Parking Structures. 1997. Precast Prestressed Concrete Parking Structures: Recommended Practice for Design and Construction (MNL-129-98). Chicago, IL: PCI. 42. M  ack, P., G. Force, C. Magnesio, and K. Bryan. 2003. The Practice of Warping Double-Tees. PCI Journal, V. 48, No. 1 (January-February). 43. B  anks, G., L. N. Lowes, and J. F. Stanton. 2005. Analysis and Design for End Effects in Twisted DoubleTees. PCI Journal, V. 50, No. 3 (May-June).

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5.14 Design Aids 5.14.1 Flexural Resistance Coefficients for Components with Non-Prestressed, Prestressed Rein­forcement, or Combinations of Both

  5

Procedure: Design:

Analysis: 1. Determine ωω ==

M u / φ − A'sfy' (d − d' ) fc' bd 2

1. Determine Ku =

Apsfps + Asfy − A'sfy' bdfc'

2. Find Ku from table. 3. Determine:

2. Find ω from table. 3. For prestressed reinforcement, estimate fps. 4. Select Aps, As, and A's from:

φM n = φ ⎡⎣K ufc'bd 2 + A'sfy' (d − d' ) ⎤⎦ Basis:

' ' ' ' ' ApsA fpspsf+psA+s fA fyA−'sfA fbdf y s− yω c s= y ω bdf c

Ku = ω (1 – 0.59 ω ) Mu in units of lb-in. ωmax = 0.321

5. Check assumed value of fps.

ωmax for tension controlled section

ω 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30

5–138

' c

f

3000

4000

5000

6000

7000

ωmax

0.272

0.272

0.256

0.240

0.224

0.000

0.001

0.002

Values of Ku 0.003 0.004 0.005

0.0000 0.0099 0.0198 0.0295 0.0391 0.0485 0.0579 0.0671 0.0762 0.0852 0.0941 0.1029 0.1115 0.1200 0.1284 0.1367 0.1449 0.1529 0.1609 0.1687 0.1764 0.1840 0.1914 0.1988 0.2060 0.2131 0.2201 0.2270 0.2337 0.2404 0.2469

0.0010 0.0109 0.0207 0.0304 0.0400 0.0495 0.0588 0.0680 0.0771 0.0861 0.0950 0.1037 0.1124 0.1209 0.1293 0.1375 0.1457 0.1537 0.1617 0.1695 0.1772 0.1847 0.1922 0.1995 0.2067 0.2138 0.2208 0.2277 0.2344 0.2410

0.0020 0.0119 0.0217 0.0314 0.0410 0.0504 0.0597 0.0689 0.0780 0.0870 0.0959 0.1046 0.1132 0.1217 0.1301 0.1384 0.1465 0.1545 0.1625 0.1703 0.1779 0.1855 0.1929 0.2002 0.2074 0.2145 0.2215 0.2283 0.2351 0.2417

0.0030 0.0129 0.0227 0.0324 0.0419 0.0513 0.0607 0.0699 0.0789 0.0879 0.0967 0.1055 0.1141 0.1226 0.1309 0.1392 0.1473 0.1553 0.1632 0.1710 0.1787 0.1862 0.1937 02010 02082 0.2152 0.2222 0.2290 0.2357 0.2423

0.0040 0.0139 0.0237 0.0333 0.0429 0.0523 0.0616 0.0708 0.0798 0.0888 0.0976 0.1063 0.1149 0.1234 0.1318 0.1400 0.1481 0.1561 0.1640 0.1718 0.1794 0.1870 0.1944 0.2017 0.2089 0.2159 0.2229 0.2297 0.2364 0.2430

0.0050 0.0149 0.0246 0.0343 0.0438 0.0532 0.0625 0.0717 0.0807 0.0897 0.0985 0.1072 0.1158 0.1242 0.1326 0.1408 0.1489 0.1569 0.1648 0.1726 0.1802 0.1877 0.1951 0.2024 0.2096 0.2166 0.2366 0.2304 0.2371 0.2437

First Printing/CD-ROM Edition

8000 and up 0.208

0.006

0.007

0.008

0.009

0.0060 0.0158 0.0256 0.0352 0.0448 0.0541 0.0634 0.0726 0.0816 0.0906 0.0994 0.1081 0.1166 0.1251 0.1334 0.1416 0.1497 0.1577 0.1656 0.1733 0.1810 0.1885 0.1959 0.2031 0.2103 0.2173 0.2243 0.2311 0.2377 0.2443

0.0070 0.0168 0.0266 0.0362 0.0457 0.0551 0.0644 0.0735 0.0825 0.0914 0.1002 0.1089 0.1175 0.1259 0.1343 0.1425 0.1505

0.0080 0.0178 0.0275 0.0371 0.0466 0.0560 0.0653 0.0744 0.0834 0.0923 0.1011 0.1098 0.1183 0.1268 0.1351 0.1433 0.1513 0.1593 0.1671 0.1749 0.1825 0.1900 0.1973 0.2046 0.2117 0.2187 0.2256 0.2324 0.2391 0.2456

0.0090 0.0188 0.0285 0.0381 0.0476 0.0569 0.0662 0.0753 0.0843 0.0932 0.1020 0.1106 0.1192 0.1276 0.1359 0.1441 0.1521 0.1601 0.1679 0.1756 0.1832 0.1907 0.1981 0.2053 0.2124 0.2194 0.2263 0.2331 0.2397 0.2463

0.1585 0.1664 0.1741 0.1817 0.1892 0.1966 0.2039 0.2110 0.2180 0.2249 0.2317 0.2384 0.2450

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

Design Aid 5.14.2 Coefficients K u' for Determining Flexural Design Strength – Bonded Prestressing Steel Procedure:

  5

⎛ Aps ⎞ ⎛ fpu ⎞ 1. Determine ω pu = ⎜ ⎟⎜ ⎟ ⎝ bd p ⎠ ⎝ fc' ⎠

a

c

2. Find K 'u from table. 3. Determine φM n = K 'u

dp

bd p2 (kip-ft) 12,000

Basis:

K 'u =

⎡ ⎛ f ⎞⎤ φfpsfc' ω pu ) ⎢1− (0.59ω pu ) ⎜ ps ⎟ ⎥ ( fpu ⎝ fpu ⎠ ⎥⎦ ⎢⎣ Table values are based on a strain compatibility analysis, using a stress-strain curve for prestressing strand similar to that in Design Aid 15.3.3.

Note: K 'u from this table is approximately equivalent to φKu fc' from Design Aid 5.14.1.

Values of K u' fc' , psi

3000

4000

5000

6000

7000

8000

ωpu

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

105 343

131

156

180

205

229

543 618

364 560 619

386 578 620

407 595 621

427 611 621

448 613 622

0.0

0

27

53

79

0.1 0.2 0.3

252 467 614

275 487 615

298 506 616

321 524 617

0.0

0

36

71

106

140

174

207

240

273

305

0.1 0.2 0.3

336 623 818

367 649 820

398 674 821

428 699 823

457 724 824

486 747 825

514 770 826

542 793 827

570 815 828

597 817 829

0.0

0

45

89

132

175

218

259

300

341

381

0.1 0.2 0.3

420 777 979

459 810 981

497 841 983

534 872 985

571 902 986

607 931 988

642 960 990

677 971 991

711 974 992

745 976 993

457

0.0

0

54

107

159

210

261

311

360

0.1 0.2 0.3

504 931 1120

550 969 1123

595 1006 1126

640 1043 1128

684 1078 1131

727 1104 1133

769 1107 1135

811 1111 1136

409 852 1114 1138

892 1117 1139

0.0

0

63

124

185

245

304

363

420

477

532

0.1 0.2 0.3

587 1082 1244

641 1126 1247

694 1169 1251

746 1211 1254

797 1218 1256

847 1223 1258

896 1228 1260

944 1232 1263

991 1236 1265

1037 1240 1267

0.0

0

72

142

212

280

348

414

480

544

608

0.1 0.2 0.3

670 1232 1348

731 1282 1352

792 1305 1,355

851 1312 1358

909 1318 1361

966 1324 1364

1022 1329 1367

1076 1334 1369

1129 1339 1372

1181 1344 1375

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

5–139

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

Design Aid 5.14.3 Values of fps By Stress-Strain Relationship – Bonded Strand

0.0270 0.0170 0.0136 0.0120 0.0110

fps ksi 270

0.0090

Cω pu = C

250

0

' c

f

C

3000 4000 5000 6000 7000 8000

1.00 1.00 1.06 1.13 1.21 1.31

170

230

160

0.0080

120

240

140 150

εps 0.0083

Apsfpu d + (ω − ω ' ) bd pfc' d p

VALUES OF C

260

fse = 0 ksi

  5

∞

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Cωpu

Design Aid 5.14.4 Design Stress for Underdeveloped Strand

300

3

7

1

/8" diameter

fpu = 270 ksi

/16" diameter

/2" diameter

200 fse = 170 ksi fpd, ksi 0.6" diameter 100

Bonded to end of component 0

20

40

60

80

100

0

40

80

120

160

200

Partially debonded

Length from start of bonding, in.

Curves based on ACI 318-05 Section 12.9.1. Note that ACI 318-05 Section 12.9.3 is for strands that are debonded near component ends.

5–140

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PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

Design Aid 5.14.5 Shear Design by Eq. 5-20 – Straight Strands Notes: 1. Applicable to simple-span, uniformly loaded components only. 2. fc' = 5000 psi – Error less than 10% for 4000 psi to 6000 psi.

Steep drape Shallow drape Straight strand

d/3

  5

d

Vu d p ⎞ ⎛ Vc = ⎜ 0.6 fc' + 700 bw d (Eq. 5-20) M u ⎟⎠ ⎝

d/3

x /2

See ACI 318-05 Section 11.4.2.

600 bwd Normalweight Concrete Straight Strands

500 bwd Vc or Vu — φ at support, lb

400 bwd

5λ fc' bw d

300 bwd /d = 50 40 30

200 bwd

20

15

/d = 10 2λ fc' bw d

100 bwd

0

0

0.10

0.20

0.30

0.40

0.50

x/ 600 bwd Sand-Lightweight Concrete λ = 0.85 Straight Strands

500 bwd Vc or Vu — φ at support, lb

400 bwd 5λ fc' bw d

300 bwd

200 bwd

/d = 50 40

30

20

15

/d = 10

2λ fc' bw d

100 bwd

0

0

0.10

0.20

0.30

0.40

0.50

x/

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

5–141

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

Design Aid 5.14.6 Shear Design by Eq. 5-20 – Shallow Drape

  5

Notes: 1. Applicable to simple-span, uniformly loaded components only. 2. fc' = 5000 psi – Error less than 10% for 4000 psi to 6000 psi.

Steep drape Shallow drape Straight strand

d/3 d

Vu d p ⎞ ⎛ Vc = ⎜ 0.6 fc' + 700 bw d (Eq. 5-20) M u ⎟⎠ ⎝

x

d/3

/2

See ACI 318-05 Section 11.4.2.

600 bwd Normalweight Concrete Shallow Drape

500 bwd Vc or Vu — φ At Support, lb

400 bwd

5λ fc' bw d

300 bwd /d = 50 40 30

20

15

/d = 10

200 bwd

2λ fc' bw d

100 bwd

0

0

0.10

0.20

0.30

0.40

0.50

x/ 600 bwd Sand Light-Weight Concrete λ = 0.85 Shallow Drape

500 bwd Vc or Vu — φ At Support, lb

400 bwd 5λ fc' bw d

300 bwd

/d = 50 40 30

200 bwd

20

15

/d = 10 2λ fc' bw d

100 bwd

0

0

0.10

0.20

0.30

0.40

0.50

x/

5–142

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

Design Aid 5.14.7 Shear Design by Eq. 5-20 – Steep Drape Notes: 1. Applicable to simple-span, uniformly loaded components only. 2. fc' = 5000 psi – Error less than 10% for 4000 psi to 6000 psi.

Steep drape Shallow drape Straight strand

d/3

  5

d

Vu d p ⎞ ⎛ Vc = ⎜ 0.6 fc' + 700 bw d (Eq. 5-20) M u ⎟⎠ ⎝

d/3

x /2

See ACI 318-05 Section 11.4.2.

600 bwd Normalweight Concrete Steep Drape

500 bwd Vc or Vu — φ At Support, lb

400 bwd

5λ fc' bw d

300 bwd

200 bwd

30 20 40 /d = 50

15

/d = 10 2λ fc' bw d

100 bwd

0

0.10

0

0.20

0.30

0.40

0.50

x/ 600 bwd Sand-lightweight Concrete λ = 0.85 Steep Drape

500 bwd Vc or Vu — φ At Support, lb

400 bwd 5λ fc' bw d

300 bwd

40 30 20

15

200 bwd

/d = 10

/d = 50

2λ fc' bw d

100 bwd

0

0

0.10

0.20

0.30

0.40

0.50

x/

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

5–143

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

Design Aid 5.14.8 Minimum Shear Reinforcement by Eq. 5-25

  5

Av =

Aps fpus d (Eq. 5-25) 80fyt d bw

See ACI 318-05 Section 11.5.6.4.

Av , in.2

Aps , in.2 6.0

0.075 5.0

0.10 1200 1100 800 600 500 400

4.0

Reference For Example 5.3.4.1

300 250

3.0

200

0.20

0.30

150 fy = Grade 60 fpu = 270 ksi

2.0

120 100

1.53

1.0

bwd = 50 in.2

80 70 60

0

5–144

0.40

0.50

0.60

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

Design Aid 5.14.9 Shear Reinforcement

Av =

(Vu / φ −Vc ) s fyt d

  5

(Eq. 5-26)

Stirrup or wire reinforcement

Note: Other configurations of shear reinforcement may be used to simplify production of precast concrete components.

bw

Vertical deformed bar stirrups Maximum values of Stirrup spacing, in.

(Vu / φ −Vc ) d

(lb/in.) Stirrup spacing, in.

fy = 60,000 psi #3 Av = 0.22

#4 Av = 0.40

#5 Av = 0.62

#3 Av = 0.22

#4 Av = 0.40

#5 Av = 0.62

2.0

6600

12000

18600

1320

2400

3720

10.0

2.5

5280

9600

14880

1200

2182

3382

11.0

3.0

4400

8000

12400

1100

2000

3100

12.0

3.5

3771

6857

10629

1015

1846

2862

13.0

4.0

3300

6000

9300

943

1714

2657

14.0

4.5

2933

5333

8267

880

1600

2480

15.0

5.0

2640

4800

7440

825

1500

2325

16.0

5.5

2400

4364

6764

776

1412

2188

17.0

6.0

2200

4000

6200

733

1333

2067

18.0

7.0

1886

3429

5314

660

1200

1860

20.0

8.0

1650

3000

4650

600

1091

1691

22.0

9.0

1467

2667

4133

550

1000

1550

24.0

Welded-wire reinforcement as shear reinforcement (fyt = 60,000 psi)

Maximum values of Spacing of vertical wire, in.

(Vu / φ −Vc ) d

One row vertical wire

(lb/in.) Two rows vertical wire

Spacing of vertical wire, in.

W7.5 Av = 0.075

W5.5 Av = 0.055

W4 Av = 0.040

W2.9 Av = 0.029

W7.5 Av = 0.150

W5.5 Av = 0.110

W4 Av = 0.080

W2.9 Av = 0.058

2

2250

1650

1200

870

4500

3300

2400

1740

2

3

1500

1100

800

580

3000

2200

1600

1160

3

4

1125

825

600

435

2250

1650

1200

870

4

6

750

550

400

290

1500

1100

800

580

6

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

Design Aid 5.14.10 Camber Equations for Typical Strand Profiles



  5 e

e Po

Po Center of gravity of strand

Center of gravity of section

Straight strands Straight strands

Δ ↑=

Poe  2 8El



Po

ee

Po

e'

Single point depressed

Δ ↑=

Poee  2 Poe'  2 + 8El 12El

 a

Po

a

ee

Po

e'

Two point depressed Two point depressed

Δ ↑=

5–146

Poee  2 Poe' ⎛  2 a 2 ⎞ + ⎜ − ⎟⎠ 8El 6 El ⎝ 8

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

Design Aid 5.14.11 Moment of Inertia of Transformed Section – Prestressed Components lcr = nApsd p2 1− 1.6 n ρp

(

)



= n ρp 1− 1.6 n ρp

) (bd )



= C(from table) × (bd p3 )

(

where: ρp =

  5

Es = 28.5 × 106 psi

3 p

Ec = 33w c1.5 fc' (ACI 318-05 Section 8.5.1) wc = 145 lb/ft3 normalweight concrete wc = 115 lb/ft3 sand-lightweight concrete

Aps E , n = s bd p Ec

Values of coefficient C

Sand-lightweight concrete

Normalweight concrete

ρp

fc' , psi

3000

4000

5000

6000

7000

8000

0.0005 0.0010 0.0015 0.0020 0.0025

0.0041 0.0077 0.0111 0.0143 0.0173

0.0036 0.0068 0.0098 0.0126 0.0153

0.0032 0.0061 0.0089 0.0115 0.0139

0.0029 0.0056 0.0082 0.0106 0.0129

0.0027 0.0052 0.0076 0.0099 0.0120

0.0026 0.0049 0.0072 0.0093 0.0113

0.0030 0.0035 0.0040 0.0045 0.0050

0.0201 0.0228 0.0254 0.0278 0.0300

0.0179 0.0203 0.0226 0.0248 0.0270

0.0163 0.0185 0.0207 0.0227 0.0247

0.0151 0.0172 0.0192 0.0211 0.0230

0.0141 0.0161 0.0180 0.0198 0.0216

0.0133 0.0152 0.0170 0.0188 0.0205

0.0055 0.0060 0.0065 0.0070 0.0075

0.0322 0.0343 0.0362 0.0381 0.0398

0.0290 0.0309 0.0327 0.0345 0.0362

0.0266 0.0284 0.0302 0.0319 0.0335

0.0248 0.0265 0.0282 0.0298 0.0314

0.0233 0.0250 0.0266 0.0281 0.0296

0.0221 0.0237 0.0253 0.0267 0.0282

0.0080 0.0085 0.0090 0.0095 0.0100

0.0415 0.0430 0.0445 0.0459 0.0472

0.0378 0.0393 0.0408 0.0422 0.0435

0.0350 0.0365 0.0380 0.0393 0.0406

0.0329 0.0343 0.0357 0.0370 0.0383

0.0311 0.0325 0.0338 0.0351 0.0364

0.0296 0.0309 0.0323 0.0335 0.0348

0.0005 0.0010 0.0015 0.0020 0.0025

0.0056 0.0105 0.0149 0.0190 0.0228

0.0049 0.0092 0.0132 0.0169 0.0203

0.0044 0.0083 0.0120 0.0153 0.0185

0.0040 0.0077 0.0110 0.0142 0.0172

0.0029 0.0071 0.0103 0.0133 0.0161

0.0036 0.0067 0.0097 0.0125 0.0152

0.0030 0.0035 0.0040 0.0045 0.0050

0.0263 0.0296 0.0326 0.0354 0.0381

0.0235 0.0265 0.0294 0.0320 0.0345

0.0215 0.0243 0.0270 0.0295 0.0319

0.0200 0.0226 0.0252 0.0275 0.0298

0.0187 0.0213 0.0237 0.0260 0.0281

0.0177 0.0201 0.0224 0.0246 0.0267

0.0055 0.0060 0.0065 0.0070 0.0075

0.0405 0.0427 0.0448 0.0466 0.0484

0.0368 0.0390 0.0411 0.0430 0.0447

0.0341 0.0362 0.0382 0.0401 0.0419

0.0320 0.0340 0.0360 0.0378 0.0395

0.0302 0.0322 0.0341 0.0359 0.0376

0.0288 0.0307 0.0325 0.0343 0.0359

0.0080 0.0085 0.0090 0.0095 0.0100

0.0499 0.0513 0.0526 0.0537 0.0547

0.0464 0.0478 0.0493 0.0506 0.0518

0.0435 0.0451 0.0465 0.0479 0.0492

0.0412 0.0428 0.0442 0.0456 0.0469

0.0392 0.0408 0.0422 0.0436 0.0449

0.0375 0.0391 0.0405 0.0419 0.0432

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

Design Aid 5.14.12 Forces Required to Restrain Bowing Intermediate restraint (ends free to rotate)

  5

End restraint

Case 1: Single restraint at midspan P=

Case 4: Both ends restrained

48Et Δ 3

M P



Moment in panel =

M

P 4

 M=

Case 2: Two restraint points

Case 5: One end restrained P=

a P 

8Et l Δ 2

24Et l Δ 3a 2 − 4a 3

M

Moment in panel = Pa



P a M=

16Et l Δ 2

Case 3: Three or more restraint points (approximate uniform continuous restraint)

ΣP = w  = 

P P P P P

77E t l Δ 3

For daily temperature change, use Et = 0.75 Ec

Moment in panel = w2 ⎛⎞ = ΣP ⎜ ⎟ ⎝ 8⎠ 8

For season changes, use Et = 0.50 Ec

Design Aid 5.14.13 Use of Design Aid 5.14.14 F3 e

D C

Ji = kfPe/hs Mj = kmPe where: Fi = restraining force at level i Mj = moment at point j kf km = coefficients from Design Aid 5.14.14 P = vertical load acting at eccentricity e See text for limitations and design example.

P

hs F2

B j=A

Level 3

F1 2-story

e

Level 2

F4 F

P

hs F3

E D

hs Level 1

C B

F1

j=A

Level 3 hs

F2

3-story

F5

Level 4

Level 2 hs Level 1

e

H

P

G

hs F4

F F3

E D C

F2

B j=A

Level 5

Level 4 hs Level 3 hs Level 2 hs

F1

Level 1

4-story

5–148

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DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

Design Aid 5.14.14 Coefficients kf and km for Determining Moments and Restraining Forces on Eccentri­cally Loaded Columns Braced against Sidesway

Pinned

Number P actBase of ing at fixity stories level

Pinned

Fixed

2

Pinned

Fixed

3

Fixed

4

kf at level 1

2

3

km at point 4

5

A

B

C

D

E

3

+0.25 −1.50 +1.25

0 −0.25 +0.25 +1.00

2

−0.50

0 +0.50 +0.50

0 +0.50

F

G

0

Σ max ±0.75 ±1.50 ±1.75

0 ±0.75 ±0.75 ±1.00

Σ one side

−0.25 −1.50 +1.75

0 +0.25 +0.75 +1.00

3

+0.43 −1.72 +1.29

−0.14 −0.29 +0.29 +1.00

2

−0.86 +0.43 +0.43

+0.29 +0.57 +0.43

0

Σ max ±1.29 ±2.15 ±1.72

±0.43 ±0.86 ±0.72 ±1.00

Σ one side

−0.43 −1.29 +1.72

+0.15 +0.28 +0.72 +1.00

4

−0.07 +0.40 −1.60 +1.27

0 +0.07 −0.07 −0.27 +0.27 +1.00

3

+0.13 −0.80 +0.20 +0.47

0 −0.13 +0.13 +0.53 +0.47

0

2

−0.47 −0.20 +0.80 −0.13

0 +0.47 +0.53 +0.13 −0.13

0

Σ max ±0.67 ±1.40 ±2.60 ±1.87

0 ±0.67 ±0.73 ±0.93 ±0.87 ±1.00

Σ one side

−0.41 −0.60 −0.60 +1.61

0 +0.40 +0.60 +0.40 +0.60 +1.00

4

−0.12 +0.47 −1.62 +1.27

+0.04 +0.08 −0.08 −0.27 +0.27 +1.00

3

+0.23 −0.92 +0.23 +0.46

−0.08 −0.15 +0.15 +0.54 +0.46

0

2

−0.81

+0.27 +0.54 +0.46 +0.12 −0.12

0

+0. +0.70 −0.12

  5

H

Σ max ±1.16 ±1.62 ±2.55 ±1.85

±0.38 ±0.77 ±0.69 ±0.92 ±0.85 ±1.00

Σ one side

−0.70 −0.22 −0.69 +1.61

+0.23 +0.46 +0.54 +0.38 +0.62 +1.00

5

+0.02 −0.11 +0.43 −1.61 +1.27

0 −0.02 +0.02 +0.07 −0.07 −0.27 +0.27 +1.00

4

−0.04 +0.22 −0.86 +0.22 +0.46

0 +0.04 −0.04 −0.14 +0.14 +0.54 +0.46

0

3

+0.13 −0.75

0 +0.75 −0.12

0 −0.13 +0.13 +0.50 +0.50 +0.12 −0.12

0

2

−0.46 −0.22 +0.86 −0.22 +0.04

0 +0.46 +0.54 +0.14 −0.14 −0.04 +0.04

0

Σ max ±0.65 ±1.30 ±2.15 ±2.80 ±1.89

0 ±0.64 ±0.72 ±0.86 ±0.86 ±0.97 ±0.89 ±1.00

Σ one side

0 +0.35 +0.65 +0.57 +0.43 +0.35 +0.65 +1.00

−0.35 −0.86 +0.43 −0.86 +1.65

5

+0.03 −0.12 +0.43 −1.61 +1.27 −0.01 −0.02 +0.02 +0.07 −0.07 −0.27 +0.27 +1.00

4

−0.06 +0.25 −0.87 +0.22 +0.46 +0.02 +0.04 −0.04 −0.14 +0.14 +0.54 +0.46

0

3

+0.22 −0.87 +0.03 +0.74 −0.12 −0.07 −0.14 +0.14 +0.51 +0.50 +0.12 −0.12

0

2

−0.80 +0.21 +0.74 −0.18 +0.03 +0.27 +0.54 +0.46 +0.12 −0.12 −0.03 +0.03

0

Σ max ±1.11 ±1.45 ±2.07 ±2.75 ±1.88 ±0.37 ±0.74 ±0.67 ±0.84 ±0.83 ±0.93 ±0.88 ±1.00 Σ one −0.61 −0.53 +0.33 −0.83 +1.64 +0.21 +0.41 +0.59 +0.56 +0.44 +0.36 +0.64 +1.00 side Note: See Design Aid 5.14.13 for explanation of terms. + indicates clockwise moments on columns and compression in the restraining beam.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

5–149

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

Design Aid 5.14.15 Design Strength of Concrete Brackets, Corbels, or Haunches

  5

p = Projection

Design strength by Section 5.9.4.1 – Cantilever Beam Method for following criteria: φVn fc' fy Nu b d φ a λ

a Vu

≤ φ(1.0), λbd, kip = 5000 psi = 60,000 psi = 0.2 Vu = width of bearing, in. = h – 1.25 (h in.) = 0.75 = 3/4p = 1.0 (normalweight concrete)

As

Nu

h

As

h

Nu

a Vu

Notes: 1. This table is suitable for preliminary design.

Vu ≤ φVn

p

Governing Criteria Maximum Vu

Flexure

Shear

Values of φVn, kip p, in. h b AS

6

8

10

6

8

10

6

8

10

12

14

16

18

20

8

10

12

14

16

18

20

10

12

14

16

18

20

2 - #4

15

20

24

28

31

34

37

40

16

20

23

26

29

31

34

17

20

22

25

27

29

2 - #5

23

31

38

43

49

52

54

56

25

31

36

40

45

49

52

26

30

35

38

42

45

2 - #6

27

36

45

54

60

64

67

70

35

43

51

57

63

67

70

36

43

49

55

60

65

2 - #7

27

36

45

54

63

72

80

84

36

45

54

63

72

80

84

45

54

63

72

80

84

2 - #4

15

20

24

28

31

34

37

40

16

20

23

29

29

31

34

17

20

22

25

27

29

2 - #5

23

31

38

43

49

53

58

62

25

31

36

40

45

49

52

26

30

35

38

42

45

2 - #6

33

44

53

62

68

71

75

78

35

43

51

57

63

69

74

36

43

49

55

60

65

2 - #7

36

48

60

72

82

86

90

94

48

59

69

78

86

90

94

50

59

67

74

81

88

2 - #8

36

48

60

72

84

96

106

111

48

60

72

84

96

106

111

60

72

84

96

106

111

2 - #9

36

48

60

72

84

96

108

120

48

60

72

84

96

108

120

60

72

84

96

108

120

2 - #4

15

20

24

28

31

34

37

40

16

20

23

26

29

31

34

17

20

22

25

27

29

2 - #5

23

31

38

43

49

53

58

62

25

31

36

40

45

49

52

26

30

35

38

42

45

2 - #6

33

44

53

62

69

76

81

85

35

43

51

57

63

69

74

36

43

49

55

60

65

2 - #7

45

60

73

84

89

94

99

103

48

59

69

78

87

94

101

50

59

67

74

81

88

2 - #8

45

60

75

90

105

111

116

121

60

75

90

103

111

116

121

65

77

88

98

107

116

2 - #9

45

60

75

90

105

120

134

140

60

75

90

105

120

134

140

75

90

105

120

134

140

5–150

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

Design Aid 5.14.15 Design Strength of Concrete Brackets, Corbels, or Haunches (cont.) Values of φVn, kip p, in. h b AS

12

14

16

6

8

10

6

8

10

12

14

16

18

20

8

10

12

14

16

18

20

10

12

14

16

18

20

2 - #5

23

31

38

43

49

53

58

62

25

31

36

40

45

49

52

26

30

35

38

42

45

2 - #6

33

44

53

62

69

76

82

87

35

43

51

57

63

69

74

36

43

49

55

60

65

2 - #7

45

60

73

84

94

101

106

110

48

59

69

78

87

94

101

50

59

67

74

81

88

2 - #8

54

72

90

106

113

119

125

130

63

78

91

103

114

124

130

65

77

88

98

107

116

2 - #9

54

72

90

108

126

137

144

150

72

90

108

126

137

144

150

83

98

111

124

136

147

3 - #5

35

46

56

65

73

80

87

92

37

46

54

61

67

73

78

39

45

52

58

63

68

3 - #6

50

66

80

93

102

107

112

117

53

65

76

86

95

104

111

55

65

74

82

90

97

3 - #7

54

72

90

108

122

129

135

141

72

89

104

117

129

135

141

75

88

100

112

122

132

3 - #8

54

72

90

108

126

144

159

167

72

90

108

126

144

159

167

90

108

126

144

159

167

3 - #9

54

72

90

108

126

144

162

180

72

90

108

126

144

162

180

90

108

126

144

162

180

2 - #5

23

31

38

43

49

53

58

62

25

31

36

40

45

49

52

26

30

35

38

42

45

2 - #6

33

44

53

62

69

76

82

87

33

43

51

57

63

69

74

36

43

49

55

60

65

2 - #7

45

60

73

84

94

103

112

116

48

59

69

78

87

94

101

50

59

67

74

81

88

2 - #8

59

79

96

111

120

127

133

138

63

78

91

103

114

124

133

65

77

88

98

107

116

2 - #9

63

84

105

126

139

146

153

160

80

98

115

130

144

153

160

83

98

111

124

136

147

3 - #5

35

46

56

65

73

80

87

92

37

46

54

51

67

73

78

39

45

52

58

63

68

3 - #6

50

66

80

93

104

114

119

124

53

65

76

85

95

104

111

55

65

74

82

90

97

3 - #7

63

84

105

122

130

137

144

150

72

89

104

117

130

141

150

75

88

100

112

122

132

3 - #8

63

84

105

126

147

162

170

177

84

105

126

147

162

170

177

98

116

132

147

161

174

3 - #9

63

84

105

126

147

168

189

204

84

105

126

147

168

189

204

105

126

147

168

189

204

2 - #6

33

44

53

62

69

76

82

87

35

43

51

57

63

69

74

36

43

49

55

60

65

2 - #7

45

60

73

84

94

103

112

119

48

59

69

78

87

94

101

50

59

67

74

81

88

2 - #8

59

79

96

111

124

134

140

145

63

78

91

103

114

124

133

65

77

88

98

107

116

2 - #9

72

96

120

137

146

154

162

168

80

98

115

130

144

157

168

83

98

111

124

136

147

3 - #6

50

66

80

93

104

114

123

130

53

65

76

86

95

104

111

55

65

74

82

90

97

3 - #7

68

90

109

126

137

145

152

158

72

89

104

117

130

141

152

75

88

100

112

122

132

3 - #8

72

96

120

144

162

171

179

187

95

117

136

155

171

179

187

98

116

132

147

161

174

3 - #9

72

96

120

144

168

192

206

215

96

120

144

168

192

206

215

120

144

167

186

204

215

4 - #6

66

88

107

123

136

143

150

156

70

87

101

115

127

138

149

73

86

98

109

120

129

4 - #7

72

96

120

144

163

172

181

188

96

118

138

156

172

181

188

99

117

134

149

163

176

4 - #8

72

96

120

144

168

192

213

222

96

120

144

168

192

213

222

120

144

168

192

213

222

4 - #9

72

96

120

144

168

192

216

240

96

120

144

169

192

216

240

120

144

168

192

216

240

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

5–151

  5

DESIGN OF PRECAST AND PRESTRESSED CONCRETE COMPONENTS

CHAPTER 5

Design Aid 5.14.15 Design Strength of Concrete Brackets, Corbels, or Haunches (cont.) Values of φVn, kip

  5

p, in. h b AS

18

20

24

6

8

10

6

8

10

12

14

16

18

20

8

10

12

14

16

18

20

10

12

14

16

18

20

2 - #6

33

44

53

62

69

76

82

87

35

43

51

57

63

69

74

36

43

49

55

60

65

2 - #7

45

60

73

84

94

103

112

119

48

59

69

78

87

94

101

50

59

67

74

81

88

2 - #8

59

79

96

111

124

136

146

152

63

78

91

103

114

124

133

65

77

88

98

107

116

2 - #9

75

100

121

140

153

162

169

176

80

98

115

130

144

157

169

83

98

111

124

136

147

3 - #6

50

66

80

93

104

114

123

131

53

65

76

86

95

104

111

55

65

74

82

90

97

3 - #7

68

90

109

126

141

152

159

165

72

89

104

117

130

141

152

75

88

100

112

122

132

3 - #8

81

108

135

159

170

179

188

196

95

117

136

155

171

186

196

98

116

132

147

161

174

3 - #9

81

108

135

162

189

206

216

226

108

135

162

189

206

216

226

124

147

167

186

204

220

4 - #6

66

88

107

123

138

150

156

163

70

87

101

115

127

138

149

73

86

98

109

120

129

4 - #7

81

108

135

161

171

181

189

197

96

118

138

156

173

188

197

99

117

134

149

163

176

4 - #8

81

108

135

162

189

213

223

233

108

135

162

189

213

223

233

131

154

176

196

215

232

4 - #9

81

108

135

162

189

216

243

268

108

135

162

189

216

243

268

135

162

189

216

243

268

2 - #6

33

44

53

62

69

76

82

87

35

43

51

57

63

69

74

36

43

49

55

60

65

2 - #7

45

60

73

84

94

103

112

119

48

59

69

78

87

94

101

50

59

67

74

81

88

2 - #8

59

79

96

111

124

136

147

157

63

78

91

103

114

124

133

65

77

88

98

107

116

2 - #9

75

100

121

140

157

168

176

183

80

98

115

130

144

157

169

83

98

111

124

136

147

3 - #6

50

66

80

93

104

114

123

131

53

65

76

86

95

104

111

55

65

74

82

90

97

3 - #7

68

90

109

126

141

155

165

172

72

89

104

117

130

141

152

75

88

100

112

122

132

3 - #8

89

118

144

166

177

187

196

204

95

117

136

155

171

186

200

98

116

132

147

161

174

3 - #9

90

120

150

180

204

215

226

235

120

148

173

196

215

226

235

124

147

167

186

204

220

4 - #6

66

68

107

123

138

152

163

169

70

87

101

115

127

138

149

73

86

98

109

120

129

4 - #7

90

120

145

168

179

188

197

205

96

118

138

156

173

188

203

99

117

134

149

163

176

4 - #8

90

120

150

180

210

222

233

243

120

150

180

206

222

233

243

131

154

176

196

215

232

4 - #9

90

120

150

180

210

240

268

280

120

150

180

210

240

268

280

150

180

210

240

268

280

2 - #6

33

44

53

62

69

76

82

87

35

43

51

57

63

69

74

36

43

49

55

60

65

2 - #7

45

60

73

84

94

103

112

119

48

59

69

78

87

94

101

50

59

67

74

81

88

2 - #8

59

79

96

111

124

136

147

157

63

78

91

109

114

124

133

65

77

88

98

107

116

2 - #9

75

100

121

140

157

172

186

196

80

98

115

130

144

157

169

83

98

111

124

136

147

3 - #6

50

66

80

93

104

114

123

131

53

65

76

86

95

104

111

55

65

74

82

90

97

3 - #7

68

90

109

126

141

155

168

179

72

89

104

117

130

141

152

75

88

100

112

122

132

3 - #8

89

118

144

166

186

201

210

218

95

117

136

155

171

186

200

98

116

132

147

161

174

3 - #9

108

144

180

206

220

232

243

253

120

148

173

196

216

236

253

124

147

167

186

204

220

4 - #6

66

88

107

123

138

152

164

175

70

87

101

115

127

138

149

73

86

98

109

120

129

4 - #7

90

120

145

168

189

202

211

220

96

118

138

156

173

188

203

99

117

134

149

163

176

4 - #8

108

144

180

213

226

239

250

261

126

156

182

206

228

248

261

131

154

176

196

215

232

4 - #9

108

144

180

216

252

275

288

301

144

180

216

252

275

288

301

166

195

223

248

272

293

5–152

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS

CHAPTER 6

CHAPTER 6 DESIGN OF CONNECTIONS

  6

6.1

Introduction................................................................................................................................................................6–3

6.2

Loads and Load Factors..............................................................................................................................................6–3 6.2.1 Strength-Reduction Factors (φ)...................................................................................................................6–3 6.2.1.1 Concrete Flexure and Axial Load.............................................................................................. 6–3 6.2.1.2 Anchorages................................................................................................................................ 6–3 6.2.1.3 Steel...........................................................................................................................................6–3 6.2.2 Overload Factors..........................................................................................................................................6–3 6.2.3 Diaphragm Over-Strength Factors (Ψ) and System Over-Strength Factor (Ωo).........................................6–4

6.3

Connection Design Criteria........................................................................................................................................ 6–4

6.4

Connection Hardware and Load-Transfer Devices....................................................................................................6–5 6.4.1 Headed Concrete Anchors or Studs............................................................................................................. 6–5 6.4.2 Steel Shapes................................................................................................................................................. 6–5 6.4.3 Reinforcing Bars..........................................................................................................................................6–5 6.4.3.1 Reinforcing Bars in Conduit...................................................................................................... 6–6 6.4.4 Reinforcing-Bar Couplers and Splice Devices............................................................................................ 6–6 6.4.5 Deformed Bar Anchors................................................................................................................................ 6–7 6.4.6 Bolts and Threaded Connectors................................................................................................................... 6–7 6.4.7 High-Strength Threaded Rods.....................................................................................................................6–7 6.4.8 Specialty Inserts........................................................................................................................................... 6–7 6.4.9 Post-Installed Anchors................................................................................................................................. 6–7 6.4.9.1 Expansion Anchors.................................................................................................................... 6–7 6.4.9.2 Adhesive Anchors......................................................................................................................6–8 6.4.9.3 Grouted Anchors........................................................................................................................6–8

6.5

Headed Concrete Anchor (HCA) Design...................................................................................................................6–8 6.5.1 Steel Materials..............................................................................................................................................6–9 6.5.1.1 Steel Plates and Shapes.............................................................................................................. 6–9 6.5.1.2 Headed Concrete Anchors or Studs........................................................................................... 6–9 6.5.2 Headed Concrete Anchors – Steel Strength................................................................................................. 6–9 6.5.3 Headed Concrete Anchors – Concrete Strength..........................................................................................6–9 6.5.3.1 Supplemental Reinforcement................................................................................................... 6–10 6.5.3.2 Cracked Concrete..................................................................................................................... 6–10 6.5.3.3 The 5% Fractile........................................................................................................................ 6–10 6.5.4 Concrete Tension Strength......................................................................................................................... 6–10 6.5.4.1 Breakout Strength.................................................................................................................... 6–11 6.5.4.2 Pullout Strength....................................................................................................................... 6–15 6.5.4.3 Side-Face Blowout................................................................................................................... 6–15 6.5.5 Concrete Shear Strength............................................................................................................................. 6–15 6.5.5.1 Front Edge (de3)........................................................................................................................6–15 6.5.5.2 Corners..................................................................................................................................... 6–18 6.5.5.3 Side Edge (de1 or de2)................................................................................................................ 6–20 6.5.6 Back Edge (de4)..........................................................................................................................................6–25 6.5.7 In-the-Field................................................................................................................................................. 6–25 6.5.8 Interaction of Tension and Shear.............................................................................................................. 6–25

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6.6

Structural-Steel Design............................................................................................................................................ 6–30 6.6.1 Design Flexural Strength...........................................................................................................................6–30 6.6.1.1 Built-Up Steel Sections............................................................................................................ 6–30 6.6.2 Design Shear Strength................................................................................................................................ 6–30 6.6.3 Design Torsional Strength........................................................................................................................ 6–30 6.6.3.1 Rectangular Solid Plates in Torsion........................................................................................ 6–30 6.6.3.2 Hollow Structural Sections (Structural Tubing) in Torsion.................................................... 6–32 6.6.4 Combined Loading..................................................................................................................................... 6–32 6.6.5 Unstiffened Connection Angles................................................................................................................. 6–32 6.6.6 Triangular Stiffener Design.......................................................................................................................6–35 6.6.7 Non-Triangular Stiffener Design.............................................................................................................. 6–43

6.7

Welding ....................................................................................................................................................................6–43 6.7.1 Corrosion Resistance of Welded Connections........................................................................................... 6–43 6.7.1.1 Hot-Dip Galvanized................................................................................................................. 6–45 6.7.1.2 Stainless Steel.......................................................................................................................... 6–45 6.7.2 Weld Design............................................................................................................................................... 6–46 6.7.2.1 Fillet Welds….......................................................................................................................... 6–46 6.7.2.2 Full-Penetration Welds............................................................................................................ 6–46 6.7.2.3 Partial-Penetration Groove Welds........................................................................................... 6–46 6.7.3 Reinforcing-Bar Welding........................................................................................................................... 6–46 6.7.3.1 Carbon Equivalent................................................................................................................... 6–46 6.7.3.2 Strength of Reinforcing-Bar Weld........................................................................................... 6–47 6.7.4 Cracking in Concrete around Welded Connections................................................................................... 6–49 6.7.5 Design of Group Welds.............................................................................................................................. 6–49 6.7.5.1 Elastic Vector Method............................................................................................................. 6–49 6.7.5.2 Instantaneous Center Method ................................................................................................ 6–50

6.8

Structural-Steel Corbels............................................................................................................................................ 6–56

6.9

Hanger Connections................................................................................................................................................ 6–60 6.9.1 Cazaly Hanger............................................................................................................................................ 6–60 6.9.2 Loov Hanger............................................................................................................................................. 6–64

6.10

Bearing Pads............................................................................................................................................................. 6–64 6.10.1 Design Recommendations......................................................................................................................... 6–67

6.11

Column Bases.......................................................................................................................................................... 6–68 6.11.1 Base Plates................................................................................................................................................. 6–68 6.11.2 Anchor Bolts ............................................................................................................................................ 6–70 6.11.2.1 Embedment Strength of Anchor Bolts in Tension...................................................................... 6–70

6.12

Moment Connections................................................................................................................................................ 6–70

6.13

Typical Connections................................................................................................................................................ 6–70

6.14

References.............................................................................................................................................................. 6–100

6.15

Design Aids........................................................................................................................................................... 6–101

6–2

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CHAPTER 6

Introduction

The design procedures presented in this chapter follow ACI 318-051 and other relevant, national, model buildingcode requirements, except where modified, to reflect current industry practice. The design of connections is one of the most important considerations in the structural design of a precast concrete structure. There are many successful solutions to each connection condition, and the design methods and examples presented in this chapter illustrate just a few successful connections. This chapter is intended for use by those with an understanding of engineering mechanics and structural design, and in no case should it replace good engineering judgment. The purpose of a connection is to transfer load, restrain movement, and/or provide stability. Within any one connection, there may be several load transfers; each one must be designed for adequate strength and ductility and be appropriately detailed. The detailing should take into account allowable tolerances, provide for a good fit between the selected materials, and avoid interference between strand or reinforcing steel and the connection components, such as headed concrete anchors (also referred to as studs in this handbook) or deformed bar anchors. In the sections that follow, different methods of transferring load will be examined separately; it will be shown how some of these are combined in typical connection situations. More information on some aspects of connection design can be found in Reference 2.

6.2

Loads and Load Factors

With noted exceptions, such as bearing pads, the design methods in this chapter are based on strength design relationships. Connections are usually designed with factored loads determined from the building analysis. Starting with the 2002 edition, ACI 318-05 has adopted load factors from ASCE 7-053 as shown in Section 4.2.6. In addition to gravity, wind, and seismic loads, forces resulting from restraint of volume changes, as well as those required for compatibility of deformations, must be considered. For flexural components, it is recommended that bearing connections be designed for a minimum horizontal tensile force, acting parallel to the span, of 0.2 times the factored sustained dead load transferred at the bearing unless a smaller value can be justified by using properly designed bearing pads (see Section 6.10). 6.2.1

Strength-Reduction Factors (φ)

6.2.1.1 Concrete Flexure and Axial Load Except for concrete anchorages and concrete corbels, discussed in Section 5.9.4, φ factors from ACI 318-05 Section 9.3 are used: • C  omponents designed as tension-controlled flexural components.................

φ = 0.90

• Shear and torsion.................................

φ = 0.75

• Bearing.................................................

φ = 0.65

• Strut-and-tie models (Section 6.8.2) and struts, ties, nodal zones, and bearing areas in such models......................

φ = 0.75

6.2.1.2 Anchorages The φ factors for concrete anchorages are specified in Appendix D, Section D.4.4 of ACI 318-05. This section describes two conditions governing concrete strength: • C  ondition A applies where the potential concrete failure surfaces are crossed by supplementary reinforcement (see Example 6.5.4.1 for design of such reinforcement by the shear-friction method), tension or shear loads on cast-in concrete anchors, headed bolts, or hooked bolts.....................................

φ = 0.75

• Condition B applies where such supplementary reinforcement is not provided, or where pullout or pryout strength governs.................................

φ = 0.70

Headed studs governed by steel strength: Tension...............................................

φ = 0.75

Shear....................................................

φ = 0.65

Post-installed anchors (Section 6.4.9) are required to be designed with φ factors that range from 0.45 to 0.75, depending on sensitivity to installation and reliability. Seismic conditions require an additional reduction factor of 0.75 when in seismic design category D, E, and F. 6.2.1.3 Steel The φ factors for steel construction are specified in American Institute of Steel Construction’s (AISC’s) Steel Construction Manual.4 • Structural steel: Tension and shear...........................

φ = 0.90

• Welds...................................................

φ = 0.75

• Bolts and threaded fasteners..................

φ = 0.75

6.2.2

Overload Factors

To ensure the overall safety of the connection, the use of an additional load factor, or overload factor, in the range 1.0 to 1.33 has historically been used by the industry. The need and the magnitude of the additional load factor for a particular connection must depend on the engineer’s judgement and consideration of the following: Mode of failure.  For conditions where the predicted failure mode is non-ductile, such as when using very short studs, it is appropriate to use larger overload factors. Consequences of failure.   If failure of a connection is likely to produce catastrophic results (non-redundancy), the

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CHAPTER 6 Table 6.2.1 Diaphragm over-strength factors

Seismic design category

Ψ factor table design element A

B

C

D

E

F

Bearing-wall systems

1

1

2.5a

2.5a

2.5a

2.5a

Building-frame systems

1

1

2.5a

2.5a

2.5a

2.5a

Moment-resisting systems

1

1

2.5a

3a

3a

3a

Dual system with special moment frames

1

1

2.5a

2.5a

2.5a

2.5a

Dual system with intermediate moment frames

1

1

2.5a

2.5a

2.5a

2.5a

Inverted pendulum system and cantilevered-column systems

1

1

2.5a

2

2

2

1

1

1b

2

2

2

1

1

b

2

2

2

1

b

1

1

1

b

1

1

1

Diaphragm to SFRS connection

  6

Diaphragm chord element Bearing-wall systems

1

Building-frame systems

1

Moment-resisting systems Inverted-pendulum system and cantilevered-column systems

1

1

1

1

1

1

1b

2

2

2

b

2

2

2

Diaphragm joint shear connection Bearing-wall systems Building-frame systems

1

1

1

Moment-resisting systems

1

1

1b

1

1

1

1

b

1

1

1

Inverted-pendulum system and cantilevered-column systems

1

1

a. The tabulated value of the diaphragm over-strength factor Ψ may be reduced by subtracting 0.5 for structures with flexible diaphragms but shall not be taken as less than 2.0 for any structure. b. For seismic design category C diaphragms, it has been assumed that the maximum distributed design force at that level is used.

connection should have a larger overall factor of safety. Sensitivity of connection to tolerances.  Production and erection tolerances, interface tolerances with other trades, as well as movements due to volume changes and applied loads may produce changes in load-transfer positions on the connection. The magnitude of the additional load factor should be consistent with this sensitivity as well as the loadtransfer position considered in design. For example, if the most adverse combination of tolerances is used to establish the load-transfer location, an additional load factor may be unnecessary. 6.2.3

 iaphragm Over-Strength Factors (Ψ) D and System Over-Strength Factor (Ωo)

Diaphragm over-strength factors recommended by PCI are shown in Table 6.2.1. For additional discussion, see Section 4.8 of this handbook. System over-strength factors as required by ASCE 7-05 are shown in Table 6.2.2.

6.3

Connection Design Criteria

Precast concrete connections must meet a variety of design and performance criteria, and not all connections are required to meet the same criteria. These criteria include: Strength.  A connection must have the strength to transfer the forces to which it will be subjected during its lifetime, 6–4

including those caused by restraint of volume change and those required to maintain stability. Ductility.   This is the ability to undergo relatively large, inelastic deformations without failure. In connections, ductility is achieved in design and subsequent detailing so steel devices yield prior to weld failure or concrete failure. Concrete typically fails in a brittle manner unless it is well confined. Volume change accommodation.   Restraint of creep, shrinkage, and temperature-change strains can cause large stresses in precast concrete components and their connections. If these stresses develop due to rigid connections, they must be considered in the design. It is usually better if the connection allows some movement to take place, thereby partially or fully relieving these stresses induced by volumechange strain. Durability.  When a connection is exposed to weather or used in a corrosive environment, steel elements should be adequately covered by concrete, painted, epoxy-coated, or galvanized. Stainless steel may also be used in aggressive environments or where corrosion cannot be tolerated due to limited access. Fire resistance.  Connections, which could jeopardize the structure’s stability if weakened by fire, should be protected to the same degree as required for the components that they connect.

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Table 6.2.2  Seismic over-strength factorsa Seismic design category

Ωo factor table design element ‌

‌

Eb

Fb

Bearing-wall systems

1

1

2.5

2.5

2.5

2.5

Building-frame systems

1

1

2.5

2.5

2.5

2.5

Moment-resisting systems

1

1

3

3

3

3

Dual system with special moment frames Dual system with intermediate moment frames

1

1

2.5

2.5

2.5

2.5

1

1

2.5

2.5

2.5

2.5

Inverted-pendulum system and cantilevered-column systems

1

1

1.25

1.25

1.25

1.25

Bearing-wall systems

1

1

2.5

2.5

2.5

2.5

A

B

Cb

Db

Collectors (drag-ties)

Collectors (drag-tie) transfer to vertical resisting element Building-frame systems

1

1

2.5

2.5

2.5

2.5

Moment-resisting systems

1

1

3

3

3

3

Dual system with special moment frames

1

1

2.5

2.5

2.5

2.5

Dual system with intermediate moment frames

1

1

2.5

2.5

2.5

2.5

Inverted-pendulum system and cantilevered-column systems

1

1

1.25

1.25

1.25

1.25

a. Table shown is condensed from ASCE 7-05, Table 12.2-1. b. The tabulated value of the system over-strength factor Ωo may be reduced by subtracting 0.5 for structures with flexible diaphragms but shall not be taken as less than 2.0 for any structure.

Constructibility.  The following items should be considered when designing connections: • • • • • • • • • • • • • • • •

6.4

Standardize products and connections. Use standard hardware items and as few different sizes as possible. Use repetitive details. Avoid reinforcement and hardware congestion. Check material and size availability. Avoid penetration of forms. Reduce post-stripping work. Be aware of material sizes and requirements. Consider clearances and tolerances of connection materials. Avoid non-standard production and erection tolerances. Plan for the shortest possible hoist hook-up time. Provide accessibility while the component is being placed. Use connections that are not susceptible to damage in handling. Allow for adjustment after the product is unhooked from the crane. Minimize weld heat buildup in the surrounding concrete or allow for expansion. Determine if special inspection is required per the applicable building code for the material and the welding process.

 onnection Hardware and LoadC Transfer Devices

A wide variety of hardware including reinforcing bars, headed concrete anchors (studs), coil inserts, structural-steel

shapes, bolts, threaded rods, and other materials are used in connections. These devices provide load transfer to concrete via anchorage in the concrete by bond, bearing, and pullout or by a shear-cone-resistance mechanism. It is preferable to design for a steel-material failure, typically defined by yielding, to govern the connection strength because such failure modes are more predictable and ductile. In seismic regions, this ductile behavior may be a code requirement. Load transfer should be as direct as possible to reduce the complexity and increase the efficiency of the connection. Before using proprietary devices, consult with the manufacturer. 6.4.1

Headed Concrete Anchors or Studs

A headed concrete anchor is a smooth shaft with an integral head. These devices are typically welded to a plate or other structural-steel shape. The studs may be hand welded, but are more often attached using a stud gun. The design method for these devices can be found in Section 6.5. 6.4.2

Steel Shapes

Steel shapes, such as wide flange sections, structural tubes, channels, and angles, can be used for various load-transfer mechanisms. They can act independently or with other loadtransfer devices. The design method for these devices can be found in Section 6.6. 6.4.3

Reinforcing Bars

Reinforcing bars are usually anchored by bonding to the concrete. When insufficient length is available to anchor the bars by bond alone, supplemental mechanical anchorage is required. This can be accomplished by reinforcing bar hooks, nuts with and without washers, threaded ends with heads, or welded crossbars. Welds, lap splices, or mechanical couplers

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3 in. minimum side cover



  6

fied concrete strength or 5000 psi. 7. The specified grout should be non-shrink. 8. The sleeve should be adequately confined either by concrete or reinforcement to avoid a brittle failure mode such as bond slip between the bar and the grout, bond slip between the sleeve and the surrounding concrete, or a shear-cone failure from the base of the sleeve.

Grade 60 reinforcing bar Flexible metallic conduit



Two bars

e Reinforcing bar or welded-wire reinforcement

Bar size

Bar embedment length, le in.a

3

12

4

12

5

12

6

15

7

21

8

27

a. For grout strengths higher than 5000 psi, multiply table values by 5000 / fc' but not less than 12 in.

Fig. 6.4.1 Anchorage in grouted conduit.5

can achieve load transfer between bars. Required development lengths and standard hook dimensions are given in Chapter 15. 6.4.3.1 Reinforcing Bars in Conduit Reinforcing bars have been shown to develop their yield strength when they are anchored by embedment in flexible, metallic, interlocking conduit using grout, as shown in Fig. 6.4.1.5 The conduit must have sufficient concrete around it for adequate confinement. This scheme can be used to transfer tension, compression, or shear forces and is convenient for certain connections, such as column-to-footing, columnto-column, and shear-wall connections. Note that alternate systems are also available, including a system that uses a plastic sleeve. The following limitations are recommended: 1. For tension, the minimum embedment length for any diameter bar is 12 in. 2. Reinforcing-bar ductility requirements should be met for seismic applications. 3. Care should be taken to prevent water from entering the conduit before grouting, especially during freezing weather. 4. The minimum concrete side cover over the conduit should be 3 in. 5. The conduit should have a minimum thickness of 0.023 in. (24 gauge), and there should be a minimum space of 1/2 in. between the bar and the inside of the sleeve. 6. The grout strength should not be less than the speci6–6

6.4.4

 einforcing-Bar Couplers and Splice R Devices

Proprietary bar-coupling devices are available as an alternative to lap splices or welding. These include clamping, couplers that use CAD-welding, threaded sleeves, and a variety of proprietary grouted systems. (See References 6 and 7 for more detailed information). Some grouted systems used extensively in precast concrete are capable of providing reinforcing-bar tension and compression splice capacities equal to 150% of the specified yield strength of the bars. Therefore, they are especially applicable for moment-resistant connections for columns, shear walls, and beams, and are accepted as a means to emulate monolithically cast concrete (see Section 4.1.1). Some codes may require special inspection when using splicing systems. Depending on the system used, splice devices are available for bar sizes ranging from #4 through #18. The splicing mechanism is typically a cylindrical-shaped steel sleeve with open ends for insertion of the reinforcing bar. Once the bar is in place, a specially formulated, high-early-strength, non-shrink grout is pumped into the sleeve by way of PVC tubes attached to inlet and outlet grouting ports on the sleeves. A variation of the system is a sleeve with internal threads at one end, which allows a threaded reinforcing bar to be securely connected to the sleeve. The opposite end of the steel sleeve is open for bar insertion and grouting. Pre-grouting and post-grouting are commonly used: Pre-grouting.  The grout sleeve is located at the top of the lower precast concrete component to be spliced. The grout is gravity fed into the splice sleeve and the upper component with projecting bar is erected into position while the grout is still flowable. Post-grouting.  The grout sleeves are located in the bottom of the upper component with reinforcing bars projecting out of the top of the lower component. Following the placement of the upper component, grouting is achieved by low pressure pumping, as mentioned previously. The following items require special attention when using reinforcing-bar grout sleeves and grouted anchorages: 1. Use only the grout recommended by the grout-sleeve manufacturer. 2. Refer to the manufacturer’s literature for cold- and hot-weather precautions during grouting. 3. Placement of bars projecting from cast-in-place foundations is critical. These bars must be held securely in position during casting to very close tolerances (see manufacturer’s recommendations). When multiple bars are used, a template is recommended for field placement.

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DESIGN OF CONNECTIONS 4. Add approximately 3 in. or 4 in. to the required projection of dowels cast into cast-in-place foundations and trim the bars to the required elevation prior to starting erection. 5. When grout sleeves are not vertical in the grouting condition, care must be taken to avoid air pockets within the sleeve. 6. Care should be taken to prevent water from entering the sleeve before grouting, especially during freezing weather. 7. The bar embedment requirements may be different for different systems. 8. Consider using oversized sleeves (for example, #11 sleeve for a #9 reinforcing bar) to provide more tolerance. 6.4.5

Deformed Bar Anchors

Deformed bar anchors are usually automatically stud welded to steel plates, similar to headed studs. They are anchored to the concrete by bond and have the same development lengths as equal-sized reinforcing bars, provided the strengths are considered equal. Deformed bar anchors conform to AWS D1.1-088 Table 7.1, Type C studs, which have an ultimate tensile strength fut of 80,000 psi and the yield strength fy of 70,000 psi. Type C studs are cold-worked, deformed steel bars manufactured in conformance with ASTM A496. The development lengths are the same as for Grade 60 reinforcing bars per ACI 318-05. For these bars, which have a specified yield strength fy exceeding 60,000 psi, ACI 318-05 Section R3.5.3.6 permits a higher fy. As such, the fy used should be the stress corresponding to a strain of 0.35% if the yield strength specified in the design exceeds 60,000 psi. In addition, the development-length calculation should recognize this increase in strength. 6.4.6

Bolts and Threaded Connectors

In most connections, bolts are shipped loose and threaded into inserts. The design of embedded inserts for concrete strength is similar to that for studs. Occasionally, a precast concrete component will be cast with a threaded connector projecting from the face. This is generally undesirable because of possible damage during handling. High-strength bolts designed as slip critical are used infrequently in precast concrete connections because it is questionable as to whether the bolt pretension can be maintained when tightened against concrete. When high-strength bolts are used in the snug-tight condition, AISC recommendations should be followed.4 Allowable loads on bolts are shown in Design Aid 6.15.6. 6.4.7

CHAPTER 6 6.4.8

Specialty Inserts

Many specialty inserts are used in the precast concrete industry for both permanent connections and for lifting, handling, and bracing conditions. Several of these inserts have become accepted as industry standards due to their history of satisfactory performance, ease of use, and unique solutions for their particular application. The various threaded-coil inserts for lifting and permanent connections and the slotted inserts for lateral tie-back connections are just a few of many examples. When used as part of a connection assembly designed for factored loads, the φ factors for headed studs (Section 6.2.1) are commonly used. Designers should refer to the valuable technical resources provided by the manufacturers of such specialty products. Because of the proprietary nature of such inserts, manufacturers’ catalogs should be consulted for capacities and design information. Most companies will provide test data confirming their published capacity information. These inserts commonly carry a safety factor of 3 or 4 to 1 against working (unfactored) loads when used for lifting and handling. 6.4.9

Post-Installed Anchors

Anchors used in concrete construction fall into two broad categories: cast-in-place anchors and post-installed anchors. With increasing demand for more flexibility in planning and construction, and for repair and retrofit applications, postinstalled anchors have seen increased use. The International Building Code (IBC)9 requires post-installed anchors to be designed using strength design methods in addition to requiring special inspection. PCI-Certified Plants are approved fabricators, as defined in the model codes, and, thus, work done in the plant and approved by the building official satisfies the special inspection requirements. 6.4.9.1 Expansion Anchors All expansion inserts are proprietary, and design values should be taken from manufacturers’ catalogs. The concrete capacity design (CCD) method provides guidance for calculating these design values and is provided in ACI 318-05 Appendix D. Edge distances for expansion inserts can be more critical than for cast-in inserts. Expanding the insert in

hef

High-Strength Threaded Rods

d e1

Rods with coil threads and specially designed nuts and couplers are frequently used for erection (Chapter 8), and they are sometimes used for permanent connections. Allowable working (service) loads are shown in Design Aid 6.15.7.

d e1> 8d b (torque controlled) or de1 > 4hef

Minimum double the values at left

Fig. 6.4.2 Anchorage of post-installed expansion inserts. See ACI 318-05 Section D.5.2.7 and D.8. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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the direction of the edge should be avoided (Fig. 6.4.2). The performance of expansion inserts when subjected to stress reversal, vibrations, or earthquake loading is not sufficiently known. The designer should carefully consider their use for these load conditions. The designer should note that the anchorage strength depends entirely on the lateral force (wedge action) on the concrete. Thus, the hole size must be carefully controlled and the hole must be clean to achieve the published values for shear, tension, or a combination of both. 6.4.9.2 Adhesive Anchors An adhesive anchor is a threaded rod (all-thread) or reinforcing bar inserted into a hole drilled in hardened concrete. The diameter of the hole should not be greater than 1.5 times the anchor diameter; however, most manufacturers’ catalogs recommend the hole size to be 1/16 in. to 1/8 in. larger than the anchor. It is filled with an adhesive that bonds the steel anchor to the concrete. The adhesive is a reactive compound of chemical components that react and cure when blended together. The adhesive compound is usually formulated from organic polymer compounds, which include, but are not limited to, epoxies, polyurethanes, polyesters, methyl methacrylates, and vinyl esters. The compound is typically characterized by A and B components, one being the catalyst for the chemical reaction. While there are generally accepted guidelines for the design of cast-in-place anchors such as headed studs, comparable information is not available for adhesive anchors. Thus, the designer must rely on manufacturers’ recommendations to determine the anchor capacity. References 10 and 11 relate to the calculation of the tensile and shear strength of adhesive anchors. While this information is limited in scope, the designer should find it useful in correlating with manufacturers’ listed capacities to obtain a better assessment of the actual factor of safety associated with adhesive anchors being considered. The manufacturers’ installation procedures must be followed. Fire endurance may be reduced when some types of adhesive anchor polymers are used, and they may have limited use in other elevated temperature or highly corrosive atmospheres. Welding near the anchor after it is in place should be done with caution. Many factors, such as proper proportioning of the compounds, thoroughness of mixing, varying installation temperatures, and age of the adhesive may affect the anchor strength. Therefore, it is recommended that a certain percent of installations should be proof-tested prior to acceptance. Installation of an adhesive anchor is a multistage process and performance is sensitive to the installation procedures followed in the field. Adhesive anchor manufacturers typically publish detailed, product-specific installation instructions critical to the proper performance of the installed anchor. In general, installation consists of the following steps: 1. Drill hole to proper depth and diameter in the required orientation. 2. Clean hole of concrete dust or other material that might affect bond. (Note: The hole diameter and cleanliness 6–8

will play a significant role in the performance of the anchor and its adhesive. Careful adherence to manufacturer’s guidelines is critical.) 3. Mix the adhesive, which depends on the system used. 4. Install the adhesive in the required orientation. 5. Install the anchor (all-thread, reinforcing bar). Special consideration should be given to adhesive anchors that have a sustained tensile load applied because of potential creep in the adhesive. In addition, anchor installation in an overhead condition will require special installation hardware or devices to ensure that the adhesive remains in the hole until it has cured. Consult the manufacturer for more information on both issues. 6.4.9.3

Grouted Anchors

Conventional headed anchors and deformed bar anchors may be post-installed into hardened concrete using nonshrink, cementitious grout. Holes, typically about three times the anchor shank diameter, are drilled in the hardened concrete and then filled with water and allowed to soak. The holes are blown dry with compressed air and filled with ASTM C1107 grout of a pourable consistency prior to inserting the anchors into the holes. Tests have shown that this method of anchor installation provides comparable capacities to anchors cast into fresh concrete.12 6.5 Headed Concrete Anchor (HCA) Design The CCD method that appears in ACI 318-05 Appendix D is primarily based on post-installed anchor tests with a limited amount of data applicable to headed concrete anchors used in the precast concrete industry. PCI sponsored an extensive research project, conducted by Wiss, Janney, Elstner Associates Inc. (WJE), to study design criteria of headed concrete anchor groups loaded in shear and the combined effects of shear and tension. The research and methods presented in this handbook are primarily for the design of headed concrete anchors; methods for other anchor types should be based on either ACI 318-05 or recommendations of proprietary manufacturers. The shear provisions contained herein are the culmination of this research completed in 2002 while the tension method is a modification of the version found in Section D.4.2 of ACI 318-05. The subject research corroborated the CCD tension model as being a better predictor of concrete breakout capacity. The modifications are basically nomenclature and assumptions that the concrete substrate is uncracked. An important factor in the performance of headed studs when controlled by concrete capacity is the location of the stud relative to the component edges. In shear, design capacity can be increased with confinement reinforcement. In tension, ductility can be provided by reinforcement that crosses the potential failure surfaces. Welded headed studs are designed to resist direct tension, shear, or a combination of the two. The design equations given in this section are applicable to studs welded to steel plates or other structural elements and embedded in unconfined concrete.

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Where feasible, headed stud connections should be designed and detailed such that connection failure is precipitated by failure (typically defined as yielding) of the stud material rather than failure of the surrounding concrete. The in-place capacity should be taken as the smaller of the values based on concrete and steel. 6.5.1

Table 6.5.2  Dimensions of headed studs Nominal length, L tpl

ths

hef

  6

dhs

Steel Materials

do

6.5.1.1 Steel Plates and Shapes Steel plates and shapes used with studs may be any of the structural steels used for welded steel structures. By far the most common conforms to ASTM A36. Stainless-steel usage is discussed in Chapter 9 and Section 6.7.1.2. The minimum plate thickness to which studs are attached should be:

tpl (min) = 1/2do

hef = L + tpl − ths − 1/8"

Shank diameter do, in.

Shank area Ase, in.2

1

/4

0.05

1

3

/8

0.11

3

1

/2

5

/8

3 7

(Eq. 6-1)

Thicker plates may be required for bending resistance or to ensure a more uniform load distribution to the attached studs.

Head Head diameter thickness dhs, in. ths, in. /2

3

/4

9

0.20 0.31

/4 /8

Bearing area Abrg, in.2

/16

0.15

/32

0.33

1

9

/32

0.59

11/4

9

/32

0.92

0.44

1

1 /4

3

/8

0.79

0.60

1 /8

3

/8

0.88

3

6.5.1.2 Headed Concrete Anchors or Studs Table 6.5.1, adapted from AWS D1.1-08 Table 7.1, shows the current minimum tensile and yield strengths for headed studs. Type B studs are the most commonly used in precast concrete construction, although the smaller studs, Type A, may occasionally be appropriate for small loads. Stainless-steel studs can be welded to either stainless steel or mild carbon steel using stainless-steel welding rods. Fully annealed stainless-steel studs are recommended when welding stainless-steel studs to a mild-carbon-steel base metal. Annealed-stud use has been shown to be imperative for stainless-steel studs welded to carbon-steel plates subject to repetitive or cyclic loads. In such cases, stress corrosion failure in the weld can occur, and annealed-stud use minimizes the chance of weld cracking and failure. Consult the supplier of headed studs to obtain additional information on stainless steel stud use and availability.

Table 6.5.1  Minimum mechanical property requirements for headed studsa Property, diameters

Type A, 1 /4 in. and 3/8 in.

Type B, 1 /2 in. to 1 in.

Tensile strength (minimum) fut

61,000 psi

65,000 psi

Yield strength fy (0.2% offset)

49,000 psi

51,000 psi

Elongation (minimum percent in 2 in.)

17%

20%

Reduction of area (minimum)

50%

50%

a. Source: AWS D1.1-08, Table 7.1.

6.5.2

 eaded Concrete Anchors – Steel H Strength

The design tensile or shear strength governed by steel failure is given by:

φVs = φNs = φ(n)(Ase)(fut)

(Eq. 6-2)

where: φ Vs

= steel strength-reduction factor = 0.65 (shear) = 0.75 (tension) = nominal shear strength of an anchorage based on steel capacity Ns = nominal tensile strength of an anchorage based on steel capacity n = number of headed studs in the anchorage assembly Ase = nominal area of the headed-stud shank fut = specified tensile strength of the stud steel in accordance with Table 6.5.1

Table 6.5.3 provides shear and tension capacities for various size studs. 6.5.3

 eaded Concrete Anchors – Concrete H Strength

ACI 318-05 Appendix D, titled “Anchoring to Concrete,” covers all types of concrete anchors, including headed concrete anchors, commonly used in precast concrete connections. In general, these provisions have resulted in more conservative designs than those shown in previous editions of the PCI Design Handbook. While there have been no reported incidences of structural failure resulting from the use of the design methods of previous editions, this edition of the handbook, in general, is based on the code provisions. Several con-

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CHAPTER 6 Table 6.5.3  Shear and pullout strength of headed concrete anchors

φNph

φ Nn φVn

  6

φNpha

locations where cracking is not likely, as is the usual case when used in precast concrete, then uncracked concrete design is appropriate. Examples of where cracking should be considered include the tension zones of non-prestressed components and regions near lifting devices of precast concrete wall panels that may crack during handling. This handbook assumes that the majority of the precast concrete component anchorages are in uncracked regions. This is reasonable because many precast concrete components are prestressed and most of the anchorages designed for precast concrete are located where cracking is unlikely. Therefore, all of the tension and shear design equations in this section are written as uncracked equations. There is an additional cracked concrete factor Ccrb for concrete breakout, or Ccrp for pullout, which reduces the headed-stud capacity due to cracking. Application of this coefficient to the handbook equations will produce the same result as the ACI 318-05 Appendix D equations for tension.

Shank diameter do, in.

φVn, kip

φNn, kip

1

/4

2.0

2.3

5.9

3

/8

4.4

5.0

13.0

6.5.3.3 The 5% Fractile

1

/2

8.5

9.8

23.1

5

/8

13.1

15.1

36.1

3

/4

18.6

21.5

31.0

7

/8

25.4

29.3

34.5

ACI 318-05 Section D.4.2 states, in part: “The nominal strength shall be based on the 5% fractile of the basic individual anchor strength.” This is a statistical concept that, simply stated, means that if a design equation is based on tests, 5% of the tests are allowed to fail. This allows us to say with 90% confidence that 95% of the actual test strengths exceed the equation thus derived. As described in the Appendix D commentary, the determination of the coefficient κ, associated with the 5% fractile κσ, depends on the number of tests (sample population) n used to compute x and σ. The term x is the sample mean and σ is the common standard deviation from data analysis. Example values of κ are:

pullout (fc' = 5000 psi), kip

a. Based on bearing capacity against the head of the stud. Capacity may be limited by φNn.

siderations regarding Appendix D are noted in the following section. 6.5.3.1 Supplemental Reinforcement Section D.4.2.1 of ACI 318-05 discusses the use of supplemental reinforcement to enhance the strength of a concrete anchor. The commentary, Section RD.4.2.1, states: “The addition of supplementary reinforcement in the direction of the load, confining reinforcement, or both can greatly enhance the strength and ductility of the anchor connection. Such enhancement is practical with cast-in anchors such as those used in precast sections.”...“For anchors exceeding the limitations of D.4.2.2, or for situations where the geometric restrictions limit breakout capacity, or both, reinforcement oriented in the direction of load and proportioned to resist the total load within the breakout prism, and fully anchored on both sides of the breakout planes, may be provided instead of calculating breakout capacity.” 6.5.3.2 Cracked Concrete The ACI 318-05 Appendix D equations presume that any anchorage device, including headed studs, will be embedded into cracked concrete. They are written so that the reduction caused by embedding in a crack is included, and adjustment factors are applied if the component is presumed not cracked. The uncracked factors are dependent on the anchor type, reinforcement, and crack-width assumption. By providing design equations for cracked concrete, the code assumes the anchorage is located where concrete cracking is likely. If an anchorage is embedded in a flexural compression zone, a column or other compression component, or other 6–10

n = ∞ n = 40 n = 10

κ = 1.645 κ = 2.010 κ = 2.568

ACI 318-05 Appendix D Section D4.2 and the related commentary RD.4.2 and RD.4.3 clearly permit alternative designs, providing the 5% fractile criterion is met. As a result of extensive research and testing sponsored by PCI,13 the equations in this section are based on: • Tension.   The equations are as shown in ACI 318-05 Appendix D, except for the cracking coefficients as previously stated. • Shear.   The shear provisions are based on the tests in Reference 13. Equations derived from those tests meet the 5% fractile criterion discussed previously. • Combined shear and tension (see Section 6.5.8).  The tests in Reference 13 did not find significant variance from the Appendix D recommendations.

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CHAPTER 6

Concrete Tension Strength

The design tensile strength governed by concrete failure is the minimum of the following three modes: • Breakout φNcb.  This is usually the most critical failure mode and is a function of the failure planes shown in Fig. 6.5.1. • Pullout φNph.  This is a function of bearing on the head of the stud. • Side-face blowout φNsb.   To avoid this failure mode, studs cannot be closer to an edge than 0.4hef. For studs closer than that, see Section D.5.4 of ACI 318-05 Appendix D. It should be noted that this situation is not common practice. Each of these possible modes must be checked when a stud connection is designed. 6.5.4.1 Breakout Strength

Ccrb

= 1.0 for concrete assumed uncracked (most common) = 0.8 for locations likely to become cracked

Edge-distance factor ψed,N = modification for edge distance

⎛d ⎞ = 0.7 + 0.3 ⎜ e,min ⎟ ≤≤1.0 1.0 ⎝ 1.5hef ⎠

where: de,min = minimum dimension of de1, de2, de3, or de4, in. (Fig. 6.5.2) Eccentricity factor It is usually possible to locate headed-stud connections so that the load application can logically be assumed concentric. If not, the following modification should be applied to the breakout strength in Eq. 6-3: ψec,N =

The equation for nominal concrete breakout strength for a group of studs loaded between the studs is:

φNcb = φNcbg = φCbsANCcrbΨed,NΨec,N

(Eq. 6-3)

where: φ Cbs

= strength-reduction factor = 0.70 without confinement steel = 0.75 with confinement steel = breakout strength coefficient N (Note: This coefficient is equivalent to b ψ c of ACI 318-05.) ANo

= 3.33λ

fc' hef

(Eq. 6-5)

1 ≤ 1 ⎛ 2e'N ⎞ ⎜ 1+ 3h ⎟ ⎝ ef ⎠

(Eq. 6-6)

where:

e'N = eccentricity of the tensile force relative to the center of the stud group, in. ≤ s/2 s = stud spacing from out to out corresponding to the direction of eccentricity In the case where eccentric loads exist about two axes, the modification factor ψec,N shall be computed for each axis independently and the product of these factors used as ψec,N in Eq. 6-3.

(Eq. 6-4)

AN = projected surface area for a stud or group of studs, in.2 (Fig. 6.5.1) hef = effective embedment depth, in. For headed studs welded to a plate flush with the surface, it is the nominal length less the head thickness, plus the plate thickness, deducting the stud burnoff lost during the welding process (which may be assumed as ≈ 1/8 in.) (Table 6.5.2). In some cases, anchors may be affected by three or four edges. For example, anchors may be located in an edge of a wall, near the end. If the largest edge distance de,max ≤ 1.5hef, then an embedment depth hef' ≤ de,max /1.5 should be used in Eq. 6-3 through 6-6 (Fig. 6.5.2, cases 5 and 6). For further explanation, see ACI 318-05 Section RD.5.2.3. Cracking factor Cracking can reduce the capacity of the anchorage, and a cracking coefficient (breakout) described in Section 6.5.3.2 is applied as appropriate: PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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DESIGN OF CONNECTIONS

CHAPTER 6 (b)

  6

The critical edge distance for headed studs, headed bolts, expansion anchors, and undercut anchors is 1.5hef. Diagrams apply to rectangular stud patterns with outside dimensions X and Y (Fig. 6.5.3). If stud spacing is ≥ 3hef, single-stud capacity multiplied by number of studs may govern design.

Assumed breakout area AN

1.5hef

AN = (de1 + 1.5hef)(2)(1.5hef) if de1 < 1.5hef

1.5hef

de1 1.5hef

(c) 1.5hef

1.5hef

Assumed breakout area

35°±

hef

Section through failure cone

1.5hef

AN

1.5hef

AN = (de1 + X + 1.5hef)(2)(1.5hef) if de1 < 1.5hef X < 3hef de1

ANo

X

1.5hef

1.5hef

(d) Assumed breakout area

1.5hef

1.5hef

1.5hef

AN

1.5hef

de1 AN = (de1 + X + 1.5hef)(de3 + Y + 1.5hef ) if de1 and de3 < 1.5hef X and Y < 3hef

Y

Plan view ANo = (2)(1.5hef)(2)(1.5hef) = 9(hef ) 2

de3 de1

X

1.5hef

(a) Fig. 6.5.1 Calculation of surface projection for anchors AN. Source: ACI 318-05 Fig. RD.5.2.1.

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Case 1: Not near a free edge

hef

  6

φNcb = φCbs(X + 3hef)(Y + 3hef)Ccrb

Case 2: Free edge on one side

hef

de1

φNcb = φCbs(de1 + X + 1.5hef)(Y + 3hef)(Ψed,N)Ccrb

Case 3: Free edges on two opposite sides

hef

de1

de2

φNcb = φCbs(de1 + X + de2)(Y + 3hef)(Ψed,N)Ccrb Note: Diagrams apply to concentrically loaded rectangular stud patterns with outside dimensions X and Y (Fig. 6.5.3). If stud spacing is ≥ 3hef, single-stud capacity multiplied by number of studs may govern design. Near a free edge implies de1, de2, de3 or de4 < 1.5hef. φ

= 0.75 with confinement reinforcement = 0.70 without confinement reinforcement

Cbs = 3.33λ

fc' hef

Ccrb = 1.0 for uncracked concrete Ccrb = 0.8 for cracked concrete For de,min = least of de1, de2, de3, de4 for each case: Ψed,N = 0.7 + 0.3

d e ,min 1.5hef

Fig. 6.5.2 Design tensile strength of stud groups (breakout strength). PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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Case 4: Free edges on two adjacent sides

hef

  6

de3 de1

φNcb = φCbs(de1 + X + 1.5hef)(de3 + Y + 1.5hef)(Ψed,N)Ccrb

Case 5: Free edges on three sides

Single anchor

Pu

hef

de3 de1

de2

φNcb = φCbs(de1 + X + de2)(de3 + Y + 1.5hef)(Ψed,N)Ccrb

Case 6: Free edges on four sides Pu de4

h'e f

hef

hef Pu

de3 de1

de2

h'e f = hef

φNcb = φCbs(de1 + X + de2)(de3 + Y + de4)(Ψed,N)Ccrb

de,max 1.5 For single and multiple anchors, if three edges are less than 1.5hef, use greater of h'e f or 1 /3 max (x,y).

For studs to behave as a group, rather than as separate shear cones, stud spacing ≤ 3hef φ

= 0.75 with confinement reinforcement = 0.70 without confinement reinforcement

Cbs = 3.33λ

Ccrb = 1.0 for uncracked concrete Ccrb = 0.8 for cracked concrete

fc' hef

For de,min = least of de1, de2, de3, de4 for each case: Ψed,N = 0.7 + 0.3

d e ,min 1.5hef

Fig. 6.5.2 (Cont.) Design tensile strength of stud groups.

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Table 6.5.4  Summary for edge-distance modification factors d e ,min

ψed,N = 0.7 + 0.3 1.5hef de,min

Ψed,N

hef 3

1.25

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

7

8

9

10

12

0.783

0.800

0.833

0.867

0.900

0.933

0.967

1.000

b

b

b

b

b

b

b

b

4

a

a

0.800

0.825

0.850

0.875

0.900

0.925

0.950

0.975

1.000

b

b

b

b

b

6

a

a

a

0.783

0.800

0.817

0.833

0.850

0.867

0.883

0.900

0.933

0.967

1.000

b

b

8

a

a

a

a

a

0.763

0.775

0.813

0.825

0.838

0.850

0.875

0.900

0.925

0.950

1.000

a. de,min < 0.4hef ; thus, side-face blowout governs (see Section D.5.4 of Appendix D, ACI 318-05; handbook Section 6.5.4.3). b. de,min < 1.5hef ; thus, stud group is no longer considered near a free edge (see case 1).

6.5.4.2 Pullout Strength The nominal pullout strength is a function of the bearing of the stud head against the concrete. The strength is:

φNph = φ11.2A f Ccrp φ pullout ' brg c

where: φ Abrg Ccrp

(Eq. 6-7)

= 0.70 = bearing area of the stud head in tension, in.2 = area of the head – area of the shank (values are shown in Table 6.5.2) = cracking coefficient (pullout) = 1.0 for concrete assumed uncracked (most common) = 0.7 for locations likely to become cracked

6.5.4.3 Side-Face Blowout For a single headed stud located close to an edge (de1 < 0.4hef):

φNsb = φ160de1 Abrg

fc' ψ ed

(Eq. 6-8)

where: Nsb = nominal side-face blowout strength de1 = distance to closest edge Abrg = area of head (Table 6.5.2)

For multiple headed anchors located close to an edge (de1 < 0.4hef):

⎛ s0 ⎞ N sbψ φNsbg= φ ⎜ 1 + edge ⎝ 6de1 ⎟⎠

where: so = spacing of the outer anchors along the edge in the group ≤ 6de1 Nsb = value from Eq. 6-8 without ψ ed = 6.5.5

Concrete Shear Strength

The design shear strength governed by concrete failure is based on the testing described in Reference 13. The in-place strength should be taken as the minimum value based on computing both the concrete and steel strength. See Table 6.5.5 for shear strength equations. 6.5.5.1 Front Edge (de3) This condition represents a majority of shear-loaded connections. The shear force is applied perpendicular to the front edge de3. It is not necessary to check the front-edge condition when the front-edge dimension is nonexistent, as in the case of a component fully supported by a foundation or another precast concrete component. Basic strength

Multiple-edge distance modification



If the single headed stud is located at a parallel distance de2, less than 3de1 from an edge, Nsb is multiplied by:

where: φ Vc3



ψ ed

⎛ de2 ⎞ ⎜⎝ 1 + d ⎟⎠ e1 = 4

(Eq. 6-9)

(Eq. 6-10)

where: 1 ≤ de2/ de1 ≤ 3 otherwise Ψed = 1.0

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φVc3 = φVco3(Cx3)(Ch3)(Cev3)(Cvcr)

(Eq. 6-11)

= concrete strength-reduction factor = 0.70 without confinement steel = 0.75 with confinement steel = nominal concrete breakout strength for a single or multiple-stud connection, accounting for member and connection geometry, lb Vco3 = concrete breakout strength for a single stud connection unaffected by connection or component geometry, lb

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DESIGN OF CONNECTIONS

CHAPTER 6 CX3 = coefficient for overall X spacing of a connection with two or more Y rows for a de3-type anchorage Ch3 = coefficient for member thickness h for a de3type anchorage Cev3 = coefficient for eccentric shear force influences for a de3-type anchorage

  6

Cvcr = coefficient for cracking in a component, loaded in shear

Example 6.5.4.1 Tension Strength of Stud Groups Given: A flush-mounted base plate with four headed studs embedded in a corner of a 24-in.-thick foundation slab. Four 3/4-in.-diameter headed studs welded to 1/2-in.-thick plate. Nominal stud length = 8 in. fc' = 4000 psi, normalweight fy = 60,000 psi Problem: Determine the design tension strength of the stud group. Solution: Depth of embedment from Table 6.5.2:

hef = L + tpl – ths – 1/8 in. = 8 + 1/2 – 3/8 – 1/8 = 8 in.

Check for edge effect: For the given problem (see Fig. 6.5.2, case 4) X = 16 in., Y = 8 in., de1 = 4 in., de3 = 6 in. de1 and de3 are both less than 1.5hef = 12 in., edge effects apply de,min = 4 in.

From Eq. 6-5:



Ψed,N = 0.7 + 0.3

⎡ 4 ⎤ d e ,min = 0.7 + 0.3 ⎢ ⎥ = 0.8 1.5hef ⎣ 1.5 (8 ) ⎦

Check strength based on concrete breakout: 4000 fc' = 3.33 = 74.5 8 hef



From Eq. 6-4:

Cbs = 3.33



From Eq. 6-6:

Ψec,N = 1.0



From Eq. 6-3:

Ncbg = φCbs(de1 + X +1.5hef)(de3 + Y +1.5hef)(Ψed,N)(Ψec,N)Ccrb



⎛ 0.8 ⎞ = (0.75)(74.5)(4 + 16 + 12)(6 + 8 + 12) ⎜ (1.0)(1.0) = 37.2 kip ⎝ 1000 ⎟⎠

Check steel strength. From Eq. 6-2 and Tables 6.5.1 and 6.5.2: φNs = φnAsefut φNs = (0.75)(4)(0.44)(65) = 85.8 kip (φ = 0.75, see Section 6.2.1) Check pullout strength. From Eq. 6-7 (φ = 0.70, see Section 6.2.1) From Table 6.5.2: Abrg = 0.79 in.2 x 4 studs = 3.16 in.2 From Eq. 6-7: φNnh = φ(11.2)(Abrg) fc' Ccrp = (0.70)(11.2)(3.16)(4)(1.0) = 99.1 kip

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Example 6.5.4.1 Tension Strength of Stud Groups (cont.) (φ = 0.70, see condition B, Section 6.2.1.3) Check side-face blowout strength: de,min = 4 in. > 0.4hef = 0.4(8) = 3.2 in. Therefore, it is not critical.

  6

Tension strength of the group is 37.2 kip. Design confinement reinforcement around the near-corner stud by shear friction, Section 5.3.6: Area of the crack plane is conservatively 4 in. × 8 in. = 32 in.2

φ1000Acr µ 0.75 (1000 ) ( 32 ) (1.4 ) = 3.61 > 3.4 = 37,200 Vu 4



�e =



37.2 Vu 4 Avf = = 0.06 in.2 < 0.11 in.2 = fy μe 0.75 (60 ) ( 3.4)

Use 3.4

OK



Use (1) #3 L-bar around stud group. These bars should extend ld past the breakout surface. Single-anchor strength Y

X

Vco3 = 16.5λ fc' ( BED )1.33

where: λ

V



de4

BED

y1 Y BED de3



y2 Y rows



x1 x2 X rows

de1

X

(Eq. 6-12)

= modification factor for density of concrete (see Section 5.3.3) = distance from back row of studs to front edge = de3 + ∑ yi = de3 + Y , in. in.

(Eq. 6-13)

de3 = distance from front stud to front edge, in. y1, y2,… = center-to-center spacing of stud rows in Y direction, in. Y = total out-to-out dimension of stud rows, in.

X-spacing factor de2

SED

Fig. 6.5.3 Headed-stud plate-edge variables.

Front edge



CX3 = 0.85 +

X ≤ ns 3BED

(Eq. 6-14)

= 1.0, when X = 0

where: x1, x2,… = center-to-center spacing of stud rows in X direction, in. X = overall, out-to-out dimension of outer most studs in back row of anchorage = Σx, in. ns = number of studs in back row

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DESIGN OF CONNECTIONS

CHAPTER 6 Thickness factor

Ch3 =1.0

where: h



for h > 1.75 BED (Eq. 6-15)



= component thickness, in.

Eccentricity factor

for e'v ≤ Cev3 =

where:

Cvcr = 1.0 for uncracked concrete

For cracked concrete:

h = 0.75 for h ≤ 1.75 BED BED



  6

Cracking factor (see Fig. 6.5.4)

X 2

Cvcr = 0.70 no edge reinforcement or reinforcement less than #4 = 0.85 edge reinforcement equal to or greater than #4 = 1.0 edge reinforcement. equal to or greater than #4 and confined within stirrups with a spacing ≤ 4 in.

6.5.5.2 Corners

1 ≤ 1.0 ⎛ e' ⎞ 1+ 0.67 ⎜ v ⎟ ⎝ BED ⎠

(Eq. 6-16)

X e'v ≤= eccentricity of shear force on a group of 2 anchors; distance between point of shear-force application and geometric centroid of group of anchors resisting shear in direction of applied shear, in.

The corner is considered to be a special case of the frontedge loaded anchorage. If the shear force is applied perpendicular to the front edge, and the anchorage is located close to the corner, a different concrete breakout mode occurs. A corner condition should be considered when:

0.2 ≤

SED ≤ 3.0 BED

(Eq. 6-17)

where the side-edge distance (SED), as shown in Fig. 6.5.3, is defined as: SED = de1 + Σxi = de1 + X, in.

(Eq. 6-18)

Cracked concrete component

#4 or greater edge reinforcement

s ≤ 4 in.

Cvcr = 1.0

Stirrups or other transverse confinement reinforcement Note: See Section 6.5.3 for members for which cracking factor should be applied. SED BED

Cvcr= 0.85 With edge reinforcement > #4 bar between anchor and edge Cvcr = 0.85 Edge reinforcement < #4 bar Cracked concrete component

Fig. 6.5.4 Cracking factors Cvcr .

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.5.5.1 Headed Concrete Anchor Front-Edge Failure Mode Given: Plate with headed studs as shown, placed in a position where cracking is unlikely. The 8-in.-thick panel has a 28-day concrete strength of 5000 psi. The plate is loaded with an in-plane torsional eccentricity of 11/2 in. from the centerline of the stud group. The panel has #5 confinement bars around the perimeter of the panel. Problem: Determine the design shear strength of the stud group. Check for corner condition:

#5 3'-8"

SED 48 + 4 ≥3 = 3.25 ≥ 3 BED 12 + 4 Not a corner condition

φVn 11/2"

4" de3 = 1'-0"

PL 3/8" × 6" × 6" w/(4)1/2" × 6" headed concrete anchor

Solution: 4" 4'-0" Steel capacity: From Table 6.5.1: fut = 65 ksi From Eq. 6-2: φVs = φ(ns)(Ase)(fut) = 0.65(4)(0.20)(65) = 33.8 kip Concrete capacity: From Eq. 6-11: φVc3 From Eq. 6-13: BED From Eq. 6-12: Vco3 X-spacing factor: From Eq. 6-14: Cx3

4'-0"

= φVco3 (Cx3)(Ch3)(Cev3)(Cvcr) = de3 + Y = 12 + 4 = 16 in. 1.33 16.5 (1.0) 5000 (16 ) 1.33 = 16.5λ fc' (BED ) = = 46.6 kip 1000 == 0.85 +

X 4 = 0.85 + = 0.93 ≤ nstuds−back 3BED 3 (16 )

Thickness factor: From Eq. 6-15: Ch3

= 0.75

8 h = 0.75 = 0.53 16 BED

Eccentricity factor: From Eq. 6-16: Cev3 Cracked-concrete factor: Cvcr With confinement steel φ Vco3 Use φVc3 = 16.2 kip

==

1 1 = = 0.94 < 1.0 ' ⎛ e ⎞ ⎛ 1.5 ⎞ 1+ 0.67 ⎜ v ⎟ 1+ 0.67 ⎜ ⎝ BED ⎠ ⎝ 16 ⎟⎠

= 1.0 = 0.75 = φVco 3(Cx3)(Ch3)(Cev3)(Cvcr) = 0.75(46.6)(0.93)(0.53)(0.94)(1.0) = 16.2 kip < 33.8 kip

If higher capacity is desired, use tail bars welded to plate. For example, if (2) #5 tail bars are used: φVc 3 = Asfy = 0.9(2)(0.31)(60) = 33.5 kip  ote: If tail bars are added, they must be N designed for entire load. Bar capacity and stud capacity are not additive.

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6–19

  6

DESIGN OF CONNECTIONS

CHAPTER 6 Basic strength The strength governed by concrete breakout at the corner is given by:

  6

φVc3 = φVco3 (Cc3)(Ch3)(Cev3)(Cvcr)

(Eq. 6-19)

= strength-reduction factor = 0.70 without confinement steel = 0.75 with confinement steel = coefficient for corner influence for a de3-type anchorage Ch3, Cvcr, Cev3 are as previously defined

Basic strength The strength governed by concrete breakout at the side edge is given by:

Corner factor Cc3 = 0.7

( ) SED BED

(Eq. 6-20)

Note that there is no Cx3 factor when computing a corner capacity. For the special case of a large X-spacing stud anchorage located near a corner, such that SED/BED > 3, a corner failure may still result if de1 ≤ 2.5BED (see Fig. 6.5.5). This results from an unzippering effect of the anchorage near the corner. 6.5.5.3 Side Edge (de1 or de2) A connection loaded in shear parallel to a side edge results in a concrete breakout failure different from the front-edge breakout mode. In this case, the shear force is applied parallel to the side edge (de1 in Fig. 6.5.5). The anchorage will likely behave in a side-edge mode if:

Side edge

φVc1 = φVco1 (CX1)(CY1)(Cev1)(Cvcr)

Y

BED = back edge distance

(Eq. 6-22)

where: Vc1 = nominal breakout strength of group φ = strength-reduction factor = 0.70 without confinement steel = 0.75 with confinement reinforcement Vco1 = concrete breakout strength for a single stud connection unaffected by connection or member geometry, lb CX1 = coefficient for overall X spacing of a connection with two or more X rows for a de1type anchorage CY1 = coefficient for overall Y spacing of a connection with two or more Y rows for a de1type anchorage Cev1 = coefficient for in-plane, eccentric shear load for a de1-type anchorage Cvcr = coefficient for cracking in a member, loaded in shear (see previous section)

0.33

≤ 1.0

(Eq. 6-21)

The research13 determined that the corner influence can be quite large, especially in thin panels. If the previously stated ratio is close to the 0.2 value, it is recommended that a corner breakout condition be investigated, as it may still control for large BED values. Note also that minimum distribution rein­ force­ment is required.

where: φ Cc3



SED 0.2 ≤< 0.2 BED



de1 = 2.5 BED X

Corner breakout likely Crack through back studs

SED = 3 BED

de1

Front edge breakout likely

BED

de3 Front edge Member corner

SED = side edge distance

SED

Connection positioned such that SED/BED > 3 but stud at de1 < 2.5 BED may dictate a corner breakout (Cc3 = 1.0 for corner breakout equation)

Fig. 6.5.5 Corner transition to a front-edge breakout.

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DESIGN OF CONNECTIONS

CHAPTER 6

Single-anchor strength

Y-Spacing factor

Vco1 = 87 λ fc' ( de1 )1.33 ( d o )0.75



(Eq. 6-23)

CY1 = 1.0 for ny = 1 (one Y-row)

where: λ = lightweight concrete factor de1 = distance from side stud to side edge, in. do = stud diameter, in.

CY1 =

(n Y )

0.25

y

0.6de1

+ 0.15

ny

for ny > 1.0

X-Spacing factor

where : ny = number of Y-row stud lines Y = out-to-out Y-row spacing = Σyi, in.

For a one-edge connection condition or a single Y-row of studs in a two, parallel edge condition (see Fig. 6.5.6):

nx x + 2 − nsides 2.5de1



CX1 =



where 1 ≤ Cx1 ≤ nx CX1 = 1.0, when x = 0

(Eq. 6-26)

(Eq. 6-24)

Eccentricity factor ⎛ e ⎞ Cev1 = 1.0 − ⎜ v1 ⎟ ≤ 1.0 ⎝ 4de1 ⎠



where: nx = number of X-rows x = individual X-row spacing, in. nsides = number of edges or sides that influence the X direction (1 or 2, that is, 2 for a column in which connection is placed equidistant from each side)

(Eq. 6-27)

where: ev1 = eccentricity from shear load to anchorage centroid, in.

For all multiple Y-row anchorages located adjacent to two parallel edges, such as a column corbel connection, the X-spacing factor for two or more studs in the row: CX1 = nx



(Eq. 6-25)

V

V

V

de2

de1

de1

Cx1 =

de2

de1

nxX + 2 − nsides 2.5de1

nx =2 nsides = 1 ny =2

Panel (one edge)

Cx1 = nx =3 nx nsides = 2 ny =1

nx = 3 ny = 3

Column (two edges)

Column (two edges)

de1 ≈ de2

de1 ≈ de2

Fig. 6.5.6 Conditions for calculations of Cx1, for side edges. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

6–21

  6

DESIGN OF CONNECTIONS

CHAPTER 6 Table 6.5.5  Summary table of HCA group concrete shear strength equations Side-edge shear

Limits

  6

0.2 >

Failure mode subscript

φVc(Failure Mode)

Front-edge shear

SED BED

Corner

SED > 3.0 BED

0.2 ≤

SED ≤ 3.0 BED

1

3

3

φVco1(CX1)(CY1)(Cev1)(Cvcr)

φVco3(Cx3)(Ch3)(Cev3)(Cvcr)

φVco3(Cc3)(Ch3)(Cev3)(Cvcr)

Vco()

1.33

87 ( λ ) fc' (d e1 )

Cx()

1.33

(d o )0.75

16.5 ( λ ) fc' (BED )

nx ( x ) + 2 − nsides 2.5d e1

0.85 +

X ≤ nstuds−back 3BED

1.0 when x = 0

1.0 when x = 0  hen multiple rows nx w are adjacent to free edges (columns)

CY()

1.0 for nY = 1 (one Y-row) 0.25

(n Y ) y

0.6d e1

Cev()

+ 0.15 ≤ ny for nY > 1

1 X ≤ 1.0 when e'v ≤ 2 ⎛ ev' ⎞ 1+ 0.67 ⎜ ⎝ BED ⎟⎠

⎛ e ⎞ 1.0 − ⎜ v 1 ⎟ ≤ 1.0 ⎝ 4d e1 ⎠

Ch()

0.75

h  for h ≤ 1.75BED BED

1.0 for h > 1.75BED

Cc()

Cvcr

6–22

⎛ SED ⎞ 0.7 ⎜ ⎝ BED ⎟⎠

0.33

≤1

Cracked

Uncracked = 1.0

= 0.70, no reinforcement or less than #4 = 0.85, reinforcement equal to or greater than #4  = 1.0, reinforcement equal to or greater than #4 and  stirrups stirrups spaced ≤ 4 in.

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.5.5.2 Headed Concrete Anchor Corner-Failure Mode

  6

#5 confinement bars 2'-8" e'v

φVn 11/2" PL 3/8" × 6" × 6" w/(4) 1/2" × 6" headed concrete anchors

4" 1'-0"

1'-6"

3'-0"

4"

Given: Plate with headed studs as shown, placed in a position where cracking is unlikely. The 8-in.-thick panel has a 28-day concrete strength of 5000 psi. The panel has #5 confinement bars around the perimeter. The plate is loaded with an in-plane torsional eccentricity of 11/2 in. from the centerline of the stud group. Problem: Determine the nominal shear strength of the plate. Check for corner condition by Eq. 6-17:

SED 18 + 4 ≤ 3;  = 1.375 BED 12 + 4



0.2 ≤



Thus, corner breakout is likely.

Solution: Steel strength (same as Example 6.5.5.1):   φVs = 33.8 kip Concrete strength from Eq. 6-19:  φVc3 = φVco3 (Cvcr)(Cev3)(Ch3)(Cc3)

de3 single-anchor capacity (same as Example 6.5.5.1):  Vco3 = 46.6 kip

Thickness factor (same as Example 6.5.5.1):  Ch3 = 0.53

⎛ SED ⎞ Corner-spacing factor from Eq. 6-20: Ch3 = 0.7 ⎜ ⎝ BED ⎟⎠

0.33

⎛ 18 + 4 ⎞ = 0.7 ⎜ ⎝ 12 + 4 ⎟⎠

0.33

= 0.78

Eccentricity factor (same as Example 6.5.5.1): Cev3 = 0.94 < 1.0 Cracked-concrete factor: Cvcr = 1.0 With confinement reinforcement φ = 0.75

φVc3 = φVco3(Ch3)(Cc3)(Cvcr)(Cev3)



= 0.75(46.6)(0.53)(0.78)(1.0)(0.94)



= 13.6 kip

Use φVn = 13.6 kip.

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.5.5.3 Headed Concrete Anchor Side-Edge Failure Mode

  6

Given: Headed-stud plate as shown. The 8-in.-thick, reinforced concrete panel has a 28-day concrete strength of 5000 psi. The panel has #5 confinement bars around the perimeter. It is placed in a position where cracking is unlikely. The plate is loaded with an eccentricity of zero. Problem: Determine the design shear strength of the stud group. Check for corner condition from Eq. 6-17. 6+ 4 SED = 0.13 ≤ 0.2 ≤ 0.2 72 + 4 BED Not a corner condition – solve as side-edge condition. Solution: Steel strength (same as Example 6.5.5.1): φVs = 33.8 kip Concrete strength: φVc1 = φVco1(CX1)(CY1)(Cev1)(Cvcr) de1 single-anchor strength: 1.33

1.33

Vco1 = 87λ f (d e1 ) ' c

(d o )

0.75

87 (1.0) 5000 ( 6 ) = 1000

(0.5)0.75

 = 39.6 kip X-spacing factor: 2 (4) n x + 2 − nsides = + 2 − 1= 1.53 Cx1 = x 2.5 ( 6 ) 2.5d e1

#5 confinement bars 6'-0" φVn

Y-spacing factor: CY1 =

(n Y )

0.25

y

0.6d e1

0.25

⎡ 2 ( 4 ) ⎤⎦ + 0.15 = ⎣ + 0.15 = 0.62 0.6 (6 )

4"

PL 3/8" × 6" × 6" w/(4) 1/2" × 6" headed concrete anchors

Eccentricity factor: Cev1 = 1.0 Cracked-concrete factor: Cvcr = 1.0 φVc1 = φVco1(CX1)(CY1)(Cev1)(Cvcr)

= 0.75(39.6)(1.53)(0.62)(1.0)(1.0)



= 28.2 kip

6'-0"

Use φVn = 28.2 kip.

6–24

6"

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PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS 6.5.6

CHAPTER 6 6.5.8

Back Edge (de4 )

The shear force is applied perpendicular to the back edge illustrated in Fig. 6.5.3. Under a condition of pure shear, the back edge has been found through testing to have no influence on the connection capacity. Proper concrete clear cover from the studs to the edge must be maintained. 6.5.7

For hef /do ≤ 4.5 (in normalweight concrete):

ACI 318-05 Section D.7 prescribes a trilinear interaction as shown in Fig. 6.5.7. This drawing shows that when both tension and shear are applied to a connection with anchors: •

In-the-Field

When a headed-stud anchorage is sufficiently away from all edges, termed in-the-field of the component, the anchorage strength will normally be governed by the steel strength. Pry-out failure is a concrete breakout failure that may occur when short, stocky studs are used.

0.5

where: φ Vcp

= = = =

Ψy =

(Eq. 6-28)

strength-reduction factor 0.70 without confinement reinforce­ment 0.75 with confinement reinforce­ment nominal pry-out shear strength, lb

1.0 for y = 0 y 1.0 for > 20 d0 y = center-to-center spacing of studs in direction of load fc' = specified compressive strength of concrete, psi do = shank diameter of stud hef = effective stud-embedment length

For short studs in lightweight aggregate concrete, the hef /do ratio limit is greater than 4.5. Therefore, this capacity equation should be checked for short studs embedded in lightweight aggregate concrete and in-the-field.

Nu φN n

φNn

•

Nu φN n

5 3

+

+

Vu φVn Vu φVn

If the applied shear Vu is less than or equal to 20% of the shear strength φVn, the shear can be neglected, and the connection designed for tension alone. If the applied tension Nu is less than or equal to 20% of the tensile strength φNn, the tension can be neglected, and the connection designed for shear alone. If Vu > 0.2φVn and Nu > 0.2φNn, then:

Nu V + u ≤ 1.2 φ N n φVn

(Eq. 6-29)

ACI 318-05 Section RD.7 (commentary) also suggests the use of a unity interaction based on exponents of 5/3, which has been used in previous editions of the publication. The interaction curves, shown in Fig. 6.5.7, illustrate that checking both interaction equations may be beneficial, depending on the tension/shear ratios present on the given connection: 5



y y for ≤ 20 4do d

N (tension)

•



φVcp = φ 215ψ y n fc' ( d o )1.5 ( hef )

Interaction of Tension and Shear

5

⎛ N u ⎞ 3 ⎛ Vu ⎞ 3 ⎜⎝ φ N ⎟⎠ + ⎜⎝ φV ⎟⎠ ≤ 1.0 n n

= 1.0

= 1.2

(Eq. 6-30)

Note: It is only required to meet either Eq. 6-29 or Eq. 6-30, not both. There are two solution techniques for groups in interaction as illustrated in Fig. 6.5.8 and 6.5.9: Solution 1: Two rows of pullout for φNn ≥ Nu Two rows of shear for φVn ≥ Vu Equivalent eccentricity e'N =

N u ( ey ) + Vu ( ex ) Nu

Solution 2: One row of pullout for φNn ≥ Nu Using sum of forces in the X and sum of moments, the equivalent tension force acting on the row of studs can be solved.

5 3



One row of shear for φVn ≥

Vu 2

Note that for solution 1, each row of studs shares the applied tension and shear loads. In this case, interaction is checked with the tension and shear capacities determined for the entire group of 4 studs. For solution 2, the shear is shared between the rows but the top row resists all the tension. In this case, interaction is checked with the capacities determined for the top row of 2 studs.

0.2φNn

0.2φVn

φVn

V (shear)

Fig. 6.5.7 Tension-shear interaction. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

6–25

  6

DESIGN OF CONNECTIONS

CHAPTER 6

φTn

φVn φNn

ex

φVn 2

ex

Nu

e'N

  6

Vu

e'v

s

Nu e'v

φVn 2

d

Vu

Vu

Vu

ey

a

ey

b

Compression block = 0.85(f'c )(b) (a)

Fig. 6.5.8 Entire group under combined forces of tension and shear.

Fig. 6.5.9 Partial group under combined forces of tension and shear.

EXAMPLE 6.5.5.4 Design of Bearing Seat with Headed Concrete Anchors 18"

Given: A 1/2-in.-thick plate with headed studs for attachment of a steel bracket to a column as shown at the right.

fc' = 6000 psi, normalweight

6"

6"

6"

6"

Assumed failure surface A

25 kip

λ = 1.0 Eight 1/2-in.-diameter studs

3"

Ase = 0.20 in.2

51/2"

(Table 6.5.2)

Nominal stud length = 6 in.

4 kip 10"

3"

fut = 65,000 psi (Table 6.5.1)

1"

A

Vu = 25 kip Nu = 4 kip (all load factors and overload factors included)

1

/2" studs

6"

10"

Elevation

Section A

Column size: 18 in. x 18 in. Problem: Determine if the studs are adequate for the connection, size the bracket and weld for the applied load. Add tail bars to the headed concrete anchor plate and compare the design strength of each element to the applied load. Vu = 25 kip e = 6"



6–26

Nhu =

Nhu

25 (6 ) Vu e + Nu = + 4 = 19.0 kip 10 dc

Nu = 4 kip

dc = 10"

Solution: The eccentric shear force Vu is resolved by the force couple shown at the right, assuming that the tensile force is resisted by the top two rows of studs, with breakout planes as shown in section A. Note: Assumptions for load distribution are a matter of engineering judgment.

b = 8"

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s

DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.5.5.4 Design of Bearing Seat with Headed Concrete Anchors (cont.) For tension on the top group of 4 studs: Concrete: Provide ties around vertical bars in the column to ensure confinement: φ = 0.75 From Table 6.5.2, hef  = L + tpl – ths – 1/8 in. = 6 + 0.5 – 0.3125 – 0.125 = 6.06 in. 6000 f' = 104.8 From Eq. 6-4: Cbs = 3.33λ c = 3.33(1.0) 6.06 hef From Fig. 6.5.2, case 3: de1 = de2 = 6 in.; X = 6 in.; Y = 3 in. φNcb = φCbs(de1 + X + de2)(Y + 3hef)ψed,N(Ccrb)

  6

6 ψed,N = 0.7 + 0.3 d e ,min = 0.7 + ( 0.3 ) = 0.898 1.5hef 1.5 ( 6.06 )

φNcb = 0.75(104.8)(6 + 6 + 6)(3 + 18.2)(0.898)(1.0)/1000 = 26.9 kip Steel:  rom Eq. 6-2: φNs = φnAsefut = 0.75(4)(0.2)(65) = 39.0 kip > 26.9 (concrete breakout governs) F φNn = 26.9 kip For shear on all studs: Assume that the shear force is distributed equally between the top and bottom shear groups (engineering judgment): Vu /2 = 25/2 = 12.5 kip. Evaluate the top group of studs for combined shear and tension: Concrete: For concrete shear strength, it is apparent that side-edge breakout will be critical: From Fig. 6.5.3: de1 = de2 = 6 in.; X = 6 in.; Y = 3 in. From Eq. 6-22: φVc1 = φVco1(CX1)(CY1)(Cev1)(Cvcr) From Eq. 6-23: Vco1 = 87λ fc' (d e1 )1.33 (d o )0.75 = 87 (1.0 )

(

)

1.33

6000 (6 )

( 0.5 )0.75 / 1000 = 43.4 kip

From Eq. 6-25: CX1 = nx1 = 2 From Eq. 6-26: CY1

(n Y ) =

0.25

y

0.6d e1

0.25

⎡⎣2 ( 3) ⎤⎦ + 0.15 ==0.58 0.58 + 0.15 ; nY = 2, Y = 3 in., CY1 = 0.6 ( 6 )

Cev1 = 1.0; Cvcr = 1.0 φVc = φVc1 = 0.75(43.4)(2.0)(0.58)(1.0)(1.0) = 37.8 kip Steel: For steel shear strength: From Eq. 6-2: φVs = φnAsefut = 0.65(4)(0.2)(65) = 33.8 kip Use φVn = 33.8 kip (steel strength governs) Combined loading: Nhu = 19.0 kip;

φNn = 26.9 kip;

Nhu 19.0 = = 0.71> 0.2 φNn 26.9

Vu = 12.5 kip;

φVn = 33.8 kip;

Vu 12.5 = = 0.37 > 0.2 φVn 33.8

( ) ( )

Nhu Vu 19.00.37 =121.08 .5 < 1.2 + == 0.71+ = 0.71 + 0.37 = 1.08 < 1.2 + φNn φVn 26.9 33.8 5

5

5

5

⎛ N ⎞3 ⎛ V ⎞3 12.5 ⎞ 3 ⎛ 19.0 ⎞ 3 =⎛ 0.76 + 0.19 < 1.0= 0.57 + 0.19 = 0.76 < 1.0 or ⎜ hu ⎟ + ⎜ u ⎟ == 0.57 +⎜ ⎜ ⎟ ⎝ 26.9 ⎠ ⎝ 33.8 ⎟⎠ ⎝ φN n ⎠ ⎝ φVn ⎠ PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.5.5.4 Design of Bearing Seat with Headed Concrete Anchors (cont.) Thus, the stud design is satisfactory by either Eq. 6-29 or 6-30. Only one equation needs to be satisfied.

  6

Check embedded plate for bending between studs: Plate

P  19 ( 3) = 14.25 kip-in. = 4 4

Nhu = 19 kip 2

⎛ bt 2 ⎞ φM n = φFy Z p = 0.9 ( 36 ) ⎜ , where b = 10 in. ⎝ 4 ⎟⎠

Nhu = 19 kip 3"

For φMn ≥ Mu, calculate minimum plate thickness: φMn = φFy Z p = 0.9 ( 36 )

10t 2 = 14.25 kip-in. 4

14.25 ( 4 ) = 0.42 in. Use 1/2-in.-thick plate. 0.9 ( 36 ) (10 )

t=

Bracket design (see Section 6.6.6): Try 3/8 in. stiffener.

b 8 = = 0.80, which is > 0.75 and < 1.0. a 10 Therefore,

250 250 b = = 41.7 must be ≤ 36 Fy t

b 8 = 21.3 < 41.7 = t 0.375

OK

From Eq. 6-47: 2

z =

⎛b⎞ ⎛b⎞ ⎛b⎞ 1.39 − 2.2 ⎜ ⎟ + 1.27 ⎜ ⎟ − 0.25 ⎜ ⎟ ⎝ a⎠ ⎝a⎠ ⎝a⎠

3

= 1.39 – 2.2(0.80) + 1.27(0.80)2 – 0.25(0.80)3 = 0.315

φVn = φFy zbt = 0.85(36)(0.315)(8)(0.375) = 28.9 kip

b

Weld design (see Section 6.7.2): Section properties for weld, assumes both sides of the stiffener are welded. b = 7 in. d = 10 in.

y d

A = 2d + b = 2(10) + 7 = 27 in.2/in. Stop =

d2 102 2bd + d 2 2 (7 ) (10 ) + 102 = 80 in.3/in. y = = 3.70 in.2/in. = = b + 2d 7 + 2 (10 ) 3 3 2

fr

2

2

2

= fy2 + fz2 = ⎛⎜ Vu ⎞⎟ + ⎛⎜ Vue + Nu + N u y ⎞⎟ = ⎛⎜ 25 ⎞⎟ + ⎛ 25 (6 ) + 4 + 4 ( 3.70 ) ⎞ = 2.39 kip/in. ⎝ A⎠ ⎝ S ⎝ 27 ⎠ ⎜⎝ 80 A 80 ⎟⎠ 27 S ⎠

Try a 1/4 in. weld. 6–28



φfn = (0.6FEXX)Aw = 0.75 (0.6 (70 ))

1 1 = 5.57 kip/in. > 2.39 kip/in. 4 2

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.5.5.4 Design of Bearing Seat with Headed Concrete Anchors (cont.) Tail-bar design: Add (2) #6 tail bars and recalculate the capacity based on failure modes Shear capacity based on tail-bar hanger steel:

  6

φVnsh = φAsh fy = 0.90(0.88)60 = 47.5 kip  hear capacity based on headed concrete anchor group. Since the tail bars are added to the plate, S the stud group is only used for tension equilibrium. The maximum shear is then based on the design strength of the stud group in tension. In order to determine the design capacity, it is assumed conservatively that Nu = 0.2Vu

Vu e + Nu = φN n dc Vu e + 0.2Vu = φNn dc

Vu (6 ) + 0.2Vu = 26.9 kip 10

0.8Vu = 26.9 kip φVnHCA = Vu = 33.6 kip

Design strength of the weld group: 2

2

2

N y⎞ ⎛V ⎞ ⎛V e N ⎛ V ⎞ ⎛ V ( 6 ) 0.2Vu 0.2Vu ( 3.70 ) ⎞ + + fy2 + fz2 = ⎜ u ⎟ + ⎜ u + u + u ⎟ = ⎜ u ⎟ + ⎜ u ⎟⎠ ⎝ A⎠ ⎝ S ⎝ 27 ⎠ ⎝ 80 A 27 80 S ⎠ 2

2

2

Vu2 ( 0.037 ) +Vu2 ( 0.0917 ) = 5.57 kip/in.

φVnWeld = Vu =

(5.57 )2 (0.037 )2 + (0.0917 )2

Failure mode

= 56.26 kip

Design shear capacity, kip

Hanger tail bar yielding

47.5

Headed concrete anchor breakout

33.6

Weld

56.3

Stiffener yielding

28.9

Shear capacity based on stiffener (from previous): φVn

= 28.9 kip

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6–29

DESIGN OF CONNECTIONS

CHAPTER 6

6.6

  6

Structural-Steel Design

Structural-steel plates, angles, wide flange beams, channels, tubes, and the like are often used in connections. When designed using factored loads, the AISC Steel Construction Manual is the appropriate design reference. For typical steel sections used in connections, plastic section properties and yield strengths with appropriate strength-reduction factors are used. 6.6.1

Design Flexural Strength

φMp = φFyZp

(Eq. 6-31)

For thin plates bent about their major axis, buckling provisions may govern the design. Typical plastic section properties for various shapes are listed in Chapter 15. 6.6.1.1 Built-Up Steel Sections

Design Shear Strength

The design shear strength of a section is determined by the following equation: φVn = φ(0.6Fy)Aw

(Eq. 6-32)

where: φ = 0.9 Aw = area subjected to shear, typically taken as the web area, in.2 This equation is only valid for sections that conform to the following limits:

h 418 ≤ Fy tw

Torsional strength of a steel member is related to its shear strength, as torsional shear stresses (as calculated by Eq. 6-34) are numerically additive to direct shear stresses. The design of a section subject to torsion must also consider torsional rotation. Equations for torsional rotation of members with various support systems are shown in Design Aid 15.1.6.



(Eq. 6-33)

where: h = height of web or clear distance between flanges, in. tw = thickness of shear web, in. Fy = yield stress of web material, ksi

τu = τ u =

where: τu t h α Tu

Tu α ht 2

(Eq. 6-34)

= torsional shear stress = total material thickness = total material height = constant from Table 6.6.1 = applied torsional moment about the Z axis

The maximum shear stress based on Reference 6 is:

Sections built-up from steel plates are often used in precast concrete structures for such items as beam seats. The design of a typical beam seat is illustrated in Example 6.6.1.1.



Design Torsional Strength

The torsional shear stress is (Fig. 6.6.1):

where: φ = 0.9 Fy = material yield strength Zp = plastic section modulus

6.6.2

6.6.3

6.6.3.1 Rectangular Solid Plates in Torsion

The design flexural strength of a steel section is:

For shear elements with geometries outside this range, see Reference 4.

τmax = φ(0.6Fy)

(Eq. 6-35)

where: φ = 0.9 Fy = yield strength of plate Setting the maximum shear stress equal to the allowable limits yields:

φTn = φ(0.6Fy)αht2

(Eq. 6-36)

Check torsional rotation, which is dependent on loading and the end-support conditions. Equations are given in Design Aid 15.1.6. For example, for a single torsion moment applied to a cantilever: θ θ ==

T GJ T

where: θ = rotation angle in radians l = length of cantilever G = shear modulus (11,600 ksi for steel) JT = torsion constant = ht3 for rectangular plates  = value based on h/t (Table 6.6.1) h = total material height t = total material thickness

Table 6.6.1  Torsion constants α and  For solid rectangular sections (Fig. 6.6.1)

6–30

h t

1.00

1.50

1.75

2.00

2.50

3.00

4.00

6.00

8.00

10.00

∞

α

0.208

0.231

0.239

0.246

0.258

0.267

0.282

0.299

0.307

0.313

0.333



0.141

0.196

0.214

0.229

0.249

0.263

0.281

0.299

0.307

0.313

0.333

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.6.1.1 Plastic Section Modulus of a Built-Up Steel Member Tension At 3

4"

/8"

n.a.

y

Fy

yt d

1"

yc

Compression Ac 3

/8"

  6

T C

h

Fy

Stiffener Section B

Given: The built-up steel member shown. The stiffeners have adequate welds so that the assembly acts monolithically. (Note: This small assembly could be used for the bearing seat of a hanger assembly, spanning just a few inches) Fy = 36 ksi Problem: Determine the nominal plastic moment strength of the plate assembly. ______________________________________________________________________________________ Solution: Let y = distance from the top of the member to the centroid. Assume the tension area is within the flange thickness,that is, y ≤ 3/8 in. ΣFx = 0: T = C; AtFy = AcFy; At = Ac At = 4y Ac = (3/8– y)(4) + 2(3/8)(1) = 2.25 – 4y 4y = 18/8 – 4y 8y = 18/8 φMp y = 18/64 = 0.281 in. Centroids of each area based on y: y 0.281 yt = = = 0.14 in. 2 2

PL 3/8" × 4" B

(2) PL 3/8" × 1" (Stiffener) φMp

B

1⎤ ⎛ 0.375 − y ⎞ ⎡ 2 ⎢0.375 (1) ⎥ + ( 0.375 − y )( 4 ) ⎜ 1+ ⎟⎠ ⎝ 2⎦ 2 yc = Σ Ay = ⎣ 2 ⎡⎣0.375 (1) ⎤⎦ + ( 0.375 − y ) 4 ΣA



1⎤ ⎛ 0.375 − 0.281⎞ ⎡ 2 ⎢ 0.375 (1) ⎥ + ( 0.375 − 0.281) ( 4 ) ⎜ 1+ ⎟⎠ ⎝ 2⎦ 2 ⎣ = = 0.683 in. 2 ⎡⎣0.375 (1)⎤⎦ + (0.375 − 0.281) 4

Plastic section modulus: Zp = Atd = At(h – yt – yc) = [4(0.281)](1.375 – 0.14 – 0.683) = 0.62 in.3 Design strength: φMp = φFyZp = 0.9(36)(0.62) = 20.1 kip-in. Weld requirement: Conservative to transfer full C or T force in flange. AtFy = [4(0.375)]36 = 54 kip 1

/4 in. weld:

φfn = φ (0.6FEXX ) Aw = 0.75 ( 0.6 (70 ))

1 1 = 5.57 kip/in. 4 2

54 = 9.7 in. Use 2.5 in. of weld on both sides of both stiffeners. 5.57 PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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DESIGN OF CONNECTIONS

CHAPTER 6 6.6.3.2 H  ollow Structural Sections (Structural Tubing) in Torsion τθu ==



Tu 2 At

(Eq. 6-37)

where:

  6

t = thickness of tube wall A = area enclosed by centerline of tube walls = wd (see image below)

h 2

Setting the maximum shear stress equal to the allowable limits yields: φTn = φ(0.6Fy)2 A t



h 2 Tu

(Eq. 6-38)

h t t 2 2

t

t

d

w

Fig. 6.6.1 Rectangular section subjected to torsion about the Z axis.

Torsional rotation must also be checked (see Example 6.6.3.1). 6.6.4

Combined Loading

The stresses under factored loads are calculated using elastic analysis, and the stresses due to individual loads are added appropriately to obtain resultant stresses (normal stress due to axial load and bending moment or shear stress due to shear force and torsion). These resultant stresses may be combined to produce maximum (principal) stresses; however, for flexural members (such as wide flange beams, channels, or tube sections) such refinement is not necessary and the resultant stresses are checked with the limit states for yielding. For yielding under normal stress:

φFun = φFy

(Eq. 6-39)

where: φ = 0.9 φFuv = φ(0.6Fy)

(Eq. 6-40)

where: φ = 0.9 6.6.5

Unstiffened Connection Angles

Connection angles used to support small precast concrete components can be designed by principles of mechanics, as shown in Fig. 6.6.2. In addition to the applied vertical and horizontal loads, the design should include all loads induced by restraint of relative movement between the precast concrete component and the supporting component. It can be assumed that the centerline of the compression force is at 0.1(ll – g) for bolted connections and at 0.1ll from 6–32



φPn ≤ φ0.2(ll – g)0.85 fc' b

(Eq. 6-41)

For welded connection: Pu(comp) ≤ φPn

For yielding under shear stress:

the top of the angle for welded connec­tions (Fig. 6.6.2). The compression force is determined using this assumption, then it is verified that there is adequate bearing area for this assumption. (Note: This is a simplified, conservative method of analysis. Other methods, including the one used in Example 6.6.5.1, may be used.) The following procedures are based on flexure in the leg of the angles being critical, which is most often the case. Shear should also be considered. For bolted connection: Pu(comp) ≤ φPn

φPn ≤ φ0.2(ll)0.85 fc' b

(Eq. 6-42)

where: φ = 0.65 fc' = concrete strength b = width of angle leg Welds should be designed in accordance with Section 6.7. The design strength of non-stiffened angles loaded as shown in Fig. 6.6.2 can be determined by:

φVn =

where: φ bn ev t

φ Fy bnt 2 4ev

(Eq. 6-43)

= 0.9 = (length of angle) – (hole diameter) – 1/16 in. = applied eccentricity and construction tolerances = thickness of angle

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.6.3.1 Design of Steel Structural Tube in Torsion Given: A hollow-structural-section (HSS) beam 8 × 6 × 1/2 spans 8.5 ft, and is welded to plates embedded in walls at each end. The beam supports a resultant uniform factored load wu of 3 kip/ft, including overload factors, with a 4 in. resultant eccentricity e. wu d Fy φ

= 3 kip/ft = 7.535 in., w = 5.535 in., t = 0.465 in. = 46 ksi = 0.9 (see Section 6.2.1) CL HSS

Problem: Check shear stress and rotation of the beam. ______________________________________________ Solution: Use Design Aid 15.1.6 (6): Uniform torque Tu = wue = 3.0(4) = 12 kip-in./ft Tu at support

wu

e = 4"

Precast slab

Precast slab

Tu  12 ( 8.5 ) = = 51.0 kip-in. 2 2 Section

Combined direct and torsional shear stresses: Aw = 2(8)(0.465) = 7.44 in.2 A = (5.535)(7.535) = 41.71 in.2

3.0 ( 8.5 ) 51 w u  Tu + = + = 1.71+ 1.31 = 3.02 ksi Aw 2At 2 ( 7.44 ) ( 2 ) ( 41.71) ( 0.465 ) OK

φ(0.6)Fy = 0.9(0.6)(46) = 24.8 ksi > 3.02 ksi Check rotation from Design Aid 15.1.6 (6). Assume uniform service load torque = T = Tu /2 = 12/2 = 6 kip-in./ft = 0.5 kip-in./in. 2

2

2 2 Torsional constant JT = 2tw d = 2 ( 0.465 )( 7.535 ) ( 5.535 )= 123.8 in.4 w +d 7.535 + 5.535

Shear modulus G = 11,600 ksi 2 12 ⎡⎣8.5 (12 ) ⎤⎦ T2 = θ= = 0.0109 rad = 0.623 deg 8GJT 8 (11,600 ) (123.8 )

5" Bearing y 0.026°

An angle of 0.623 deg over a 5 in. bearing distance results in a vertical displacement: y = tan(0.623)5 = 0.054 in. Therefore, rotation is not significant.

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  6

DESIGN OF CONNECTIONS

CHAPTER 6

Table 6.6.2  Minimum edge distance

Pu Vu

 − g 

Pu

g

  6

At sheared edges

Bolt diameter,a in.

0.9( − g)

1

/2

5

/8

3

/8

11/8

7

7

/8

/4

1 /4

1

/8

11/2

11/8

1

13/4

11/4

11/4

21/4

15/8

7

Vu

(a) Bolted

a. When oversized or slotted holes are used, edge distances should be increased to provide the same distance from edge of hole to free edge as given by the tabulated edge distances. Use ASTM F436 washers, or 5/16-in.-thick plate washer.4 All edge distances in this column may be reduced 1/8 in. when the hole is at a point where stress does not exceed 25% of the maximum allowable stress in the element. b. These may be 11/4 in. at the ends of beam connection angles.

0.1 Pu Vu 

/4

1

3

ev

At rolled edges of plates, shapes or bars or gas-cut edgesb

0.9 Pu k ev

Either or both

Table 6.6.3  Normal gauges for angles

Vu

(b) Welded

Fig. 6.6.2 Connection angle design parameters.

Angle leg length, in.

Normal angle gauge g in.

2 21/2 3 31/2 4

11/8 13/8 13/4 2 21/2

5 6 7 8

3 31/2 4 41/2

Pu ei



Pu t

Vu

Concrete insert Surface of precast unit

ev

Vu

g

Connection to structure not shown

Fig. 6.6.3 Shear force on unstiffened angle.

ei Pu



t

Fig. 6.6.4 Normal force on unstiffened angle.

6–34

Pu = Vu



φNn =

g

Connection to structure not shown

g2

Two-hole gauge , in. g1

g2

2 21/4 21/2 3

13/4 21/2 3 3

ev ei

(Eq. 6-44)

For angles loaded axially Nu (Fig. 6.6.4), the design strength of non-gusseted angles can be calculated by:

Low-friction washer Vertical slot

Concrete insert

g1

Note: For welded angles, with the weld oriented as shown in Fig. 6.6.2(b), ev may be taken equal to actual eccentricity minus k, where k is the distance from the back face of angle to web toe of fillet. The tension requirement on the bolt and insert (Fig. 6.6.3) can be calculated by:

Nu (g /ei)

g

Nu

φ Fy t 2 bn ≥ Nu 4g

(Eq. 6-45)

and the design tension requirement for the bolt and insert can be calculated by:

⎛ g⎞ φPn = φ N n ⎜ 1 + ⎟ ≥ Pu ⎝ ei ⎠

(Eq. 6-46)

where: φ = 0.9 g = gauge of angle First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS The minimum edge distance for bolt holes and typical gauges is shown in Tables 6.6.2 and 6.6.3 respectively. These holes may be punched, reamed, or drilled holes. The edge distance is measured from the center of the holes. For connections made by welding instead of bolting, the welds should be designed in accordance with Section 6.7. Example 6.6.5.1(a) illustrates the condition of an angle embedded directly into the precast concrete. While a condition of an angle welded to an embedded plate with studs is similar, consideration must be given to the location of the studs, size of plate, and how it is welded. Example 6.6.5.1(b) illustrates a bolted condition where prying action is considered. It represents the procedure shown in AISC Steel Construction Manual, thirteenth edition, part 9. The notation used in the example is consistent with AISC and is as follows: where: a = distance from the bolt centerline to the edge of the angle, in. a’ = distance from the edge of the hole to the edge of the angle A = area of the angle leg at the hole Ab = n ominal unthreaded body area of bolt or threaded part, in.2 b = distance from the bolt centerline to the centerline of angle leg, in. b’ = distance from the edge of the hole to the center of the angle thickness bn = net length of angle, in. (length of angle - hole diameter - 1/16 in.) B = available tension per bolt, lb db = bolt diameter, in. d’ = width of the hole along the length of the angle, in. ei = d istance from the bolt centerline to the edge of the angle, in. ev = applied eccentricity and construction tolerances, in. Fnt = nominal tensile strength of connector, psi Fnv = nominal shear strength of connector, psi Fu = s pecified minimum tensile strength of connected material, psi Fy = specified minimum yield strength of connected material, psi f ‘c = specified minimum compressive strength of concrete, psi g = gage of angle, in. L = length of angle, in. ll = height of vertical angle leg, in. p = tributary length per pair of bolts for angle which should preferably not exceed the gauge between the pair of bolts g in. Q = ratio dependant on geometry Rnt = nominal tension capacity of bolt Rnv = nominal shear capacity of bolt t = thickness of angle, in. tc = angle thickness required to develop the available strength of the bolt B with no prying action, in.

CHAPTER 6 T = tension force in the bolt V =maximum shear force Z = p lastic section modulus of angle leg at the hole α’ = value of α that either maximizes the bolt’s available tensile strength for a given thickness or minimizes the thickness required for a given bolt2available tensile strength. ⎤ factor ⎤ ⎡ ⎛ t c reduction ⎡ φ 1.0 ⎞ = strength ⎥ ⎢ ⎜⎝ ⎟⎠ − 1⎥ ⎢ = rρatio ) ⎦ ⎢⎣ oft the new ⎥⎦ area at bolt line to gross area ⎣ δ ( 1+ at face of the stem or leg of angle Capacity of angles based on Eq. 6-43 and Eq. 6-45 can be determined from Design Aids 6.15.8 and 6.15.9, respectively. 6.6.6

Triangular Stiffener Design

Yielding along the free edge frequently occurs prior to buckling, and stress redistribution occurs within the system.15 The design normal force φNn is assumed to be resisted by the top line of weld of the bearing seat and has no impact on the design of the stiffener. A ratio z has been established for triangular stiffeners that relates average stress, Vu , to the maximum stress fmax: bt 2



3

⎛ b⎞ ⎛ b⎞ ⎛ b⎞ z = 1.39 − 2.2 ⎜⎝ ⎟⎠ +1.27 ⎜⎝ ⎟⎠ − 0.25 ⎜⎝ ⎟⎠ (Eq. 6-47) a a a

where: (see Fig. 6.6.5) b = projection of stiffener a = height of stiffener The design strength is limited when the free edge reaches the material’s yield strength:

φVn = φFy zbt

(Eq. 6-48)

where: φ = 0.85 Fy = yield strength of the stiffener t = stiffener thickness To ensure yielding along the free edge, limits shown in Fig. 6.6.5 should be satisfied.

Transverse weld along top of seat

Vu < φVn

e

Nu

a

b

Free edge

Fig. 6.6.5 Triangular stiffener.

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  6

DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.6.5.1(a) Unstiffened Connection Angle with Headed Concrete Anchors

  6

Given: Angle with headed studs as shown, placed in a position where cracking is unlikely. The 8-in.-thick panel has a 28-day concrete strength of 5000 psi. The angle is loaded as shown below. The panel has #5 confinement bars around the perimeter of the panel. Material properties: Fy = 36,000 psi fc' = 5000 psi, nomalweight Section properties: b = 12 in. (width of angle) d = 3 in. g = 2 in. t = 0.375 in. Problem: Determine the normal force and shear force capacities without consideration of the effects of prying action versus angle thickness. ______________________________________________ Solution: Normal force capacity: t = 0.375" g = 2"

Nu

φNn d − a/2

d = 3" a



/2

a

Based on angle flexure: φ = 0.9 φFy bt 2 Nu = 4g 2



= 0.9 ( 36,000 ) (12 ) ( 0.375 ) 4 (2)

Nu = 6834 lb

Based on anchor tension: φNn = 9572 lb For cast-in headed concrete anchors as determined from this handbook or ACI 318-05 Appendix D. For post-installed anchors as determined from ACI 318-05 or product literature. φ = 0.75 Applicable phi factor based on tension capacity shown previously.



Initial trial values:

6–36

Nu =

φNn g 1+ d



9572 2 1+ 3

=

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PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.6.5.1(a) Unstiffened Connection Angle with Headed Concrete Anchors (cont.) Nu = 5743 lb 5743 Nu a = = ' 0.85 ( 5000 ) (12 ) 0.85fc b

  6

a = 0.11 in. Given: a =

Nu 0.85fc' b

Nu =

φN n g 1+ g d− 2

Starting with Nu = 5743 lb and a = 0.11 in. either by trials until conversion or solving the quadratic equation, solve for a and Nu. The results are: a = 0.149 in. Nu = 5685 lb Shear force capacity: e = 3" t = 0.375" g = 2"

φNn

Vu

φVn d − a/2

d = 3" a

/2

a

Geometry: e = 3 in.

Based on angle flexure: φ = 0.9 Vu =



φFy bt 2 4e

Based on combined anchor tension and shear: φVn = 8296 lb For cast-in headed concrete anchors as determined from this handbook or ACI 318-05 Appendix D. For post-installed anchors as determined from ACI 318-05 or product literature. φ = 0.75 Applicable phi factor based on tension capacity shown previously.

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.6.5.1(a) Unstiffened Connection Angle with Headed Concrete Anchors (cont.)

  6

Initial trial values: The interaction equation neglecting the effect of a is as follows: 5

5

⎛ Vu ⎞ 3 ⎛ Vu e ⎞ 3 ⎜⎝ φV ⎟⎠ + ⎜⎝ φN d ⎟⎠ < 1 n n

Solving for Vu: 3

⎛ ⎞5 ⎜ ⎟ ⎜ ⎟ 1 Vu = ⎜ 5 5 ⎟ ⎜⎛ 1 ⎞3 ⎛ e ⎞3 ⎟ ⎜⎜ ⎟ + ⎜⎝ φN d ⎟⎠ ⎟ ⎝ ⎝ φVn ⎠ ⎠ n Given: φVn = 8296 lb, φNn = 9572 lb, e = 3 in., d = 3 in. Vu = 5854 lb a =

5854 ( 3) Vue = ' 0.85fc bd 0.85 (5000 ) (12 ) ( 3 )

a = 0.115 in. Including the effect of a, the interaction equation becomes 5

⎛ ⎞3 5 ⎟ ⎛ Vu ⎞ 3 ⎜ Vu e = 11 ⎟ = ⎜⎝ φV ⎟⎠ + ⎜ n ⎜ φN ⎛ d − a ⎞ ⎟ ⎟ ⎜⎝ n ⎜⎝ 2 ⎠ ⎟⎠ The solution will converge for the following values: a = 0.114 in. Vu = 5805 lb

6–38

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.6.5.1(b) Unstiffened Connection Angle with Bolts Unstiffened connection angle with consideration of prying action versus angle thickness Material properties:

  6

A307 bolt: Fnt = 45,000 psi Fnv = 24,000 psi Steel angle: Fy = 36,000 psi Fu = 58,000 psi Concrete: fc' = 5000 psi, normalweight Section properties: A307 bolt: db = 0.5 in. Ab = (π) db 2/4 = [(π)(0.5)2]/4 = 0.196 in.2 Or from Design Aid 6.15.6: Ab = 0.196 in.2 Steel angle: 5 in. × 5 in. × 12 in. long L = 12 in.

ll

= 5 in.

t

= 0.375 in.

d' = db + 0.0625 (Note that 0.0625 is the standard hole size (1/16 in.) larger than the bolt diameter.) = 0.5 + 0.0625 = 0.5625 in. bn = L – d' – 0.0625 = 12 – 0.5625 – 0.0625 = 11.375 in. A Z

= bnt = 11.375(0.375) = 4.27 in.2 b t2 = n 4 2 11.375 ( 0.375 ) = 4 = 0.400 in. 2

Geometry ev = 3 in. g

= 2 in.

Problem: Determine the normal force and shear force capabilities with consideration of the effects of prying action versus angle thickness.

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.6.5.1(b) Unstiffened Connection Angle with Bolts (cont.) Solution: Normal force:

  6

a'

a

q

g T

t

b'

b



B = φRnt = T + q

Based on angle flexure: φ = 0.90 T = φFy Z/g = 0.9(36,000)(0.400)/2 = 6480 lb Based on bolt tension: φ = 0.75 a = ll – g =5–2 = 3 in. b = g – t/2 =2 – (0.375)/2 = 1.813 in. a' = lesser of (a + db /2) or [(1.25)b + db /2]

(a + db /2): = 3 + (0.5)/2 = 3.25 in.



[(1.25)b + db /2]: = 1.25(1.813) + (0.5)/2 = 2.516 in. < 3.25 use 2.516 in.



b' = b – db /2 = 1.813 – (0.5)/2 = 1.563 in.

ρ = b' /a' = 1.563/2.516 = 0.621 p = lesser of L or 2g L = 12 in. 2g = 2(2) = 4 in. < 12 use 4 in.

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.6.5.1(b) Unstiffened Connection ⎡Angle 2 with Bolts (cont.) ⎤ ⎡ 1.0 ⎤ ⎛ t c ⎞ − 1⎥ ⎢ ⎢ = 1ρ – ) ⎥⎦d’⎢⎣⎜⎝/pt ⎟⎠ ⎥⎦ ⎣ δ (1+ = 1 – 0.5625/4 = 0.859

  6

φRnt = φFntAb = 0.75(45,000)(0.196) = 6615 lb B = φRnt = 6615 lb tc =

( 4.44 ) (B ) (b' ) pFu

4.44 ( 6615 ) (1.563) ( 4 ) (58,000 )



=



= 0.445 in.

⎡ 1.0 ⎤ ⎡ ⎛ t c ⎞ 2 ⎤ α’ = ⎢ ⎥ ⎢ ⎜ ⎟ − 1⎥ ⎥⎦ ⎣ δ (1+ ρ ) ⎦ ⎢⎣ ⎝ t ⎠



⎤ ⎡⎛ 0.445 ⎞ 2 ⎤ ⎡ 1.0 = ⎢ ⎥ ⎢⎜ ⎟ − 1⎥ ⎥⎦ ⎣ 0.859 (1+ 0.621) ⎦ ⎢⎣⎝ 0.375 ⎠



= 0.294

Q = 1 for α’ < 0 2 ⎛t ⎞ ' ⎜⎝ t ⎟⎠ ⎡⎣1+ (δ ) (α ) ⎤⎦ for 02 < or = α’ < = 1.0 c ⎤ ⎡ 1.0 ⎤ ⎡ ⎛ t c ⎞ ⎢ ⎜ ⎟ − 1⎥ ⎥ ⎢ 2 ⎠ (t/tc) (1 +⎣ δ )(1+ forρα’ ) ⎦>⎢⎣⎝=t 1.0 ⎥⎦ 2 = (0.375/0.445) [1 + 0.859(0.294)] = 0.889 T = QB = 0.889(6615) =5881 lb < 6480 lb, Capacity = 5881 lb Shear force: (ei − a/2)

V (ei − a/2)



V(ev)

V(ev)

V

t

g

ei

a/2

ev

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.6.5.1(b) Unstiffened Connection Angle with Bolts (cont.) Solution: Based on angle flexure:

  6

φ = 0.90 V = φFy Z /ev = 0.9(36,000)(0.400)/3 = 4320 lb Based on combined bolt tension and shear: φ = 0.75 φRnv = φFnvAb = 0.75(24,000)(0.196) = 3528 lb ei = a = 3 in. 2

⎧ ⎫ ⎪ ⎪ ⎛ V ⎞ Vev ⎪ ⎪ 1 = ⎜ + ⎨ ⎬ ⎟ ⎝ φRnv ⎠ ⎪ ⎡φRnt ⎛ ei − a ⎞ ⎤ ⎪ ⎜⎝ ⎟ ⎪⎩ ⎢⎣ 2 ⎠ ⎥⎦ ⎪⎭ 2

a =

Vev φ 0.85fc' Lei

by iteration: V = 3109 lb < 4320 lb use 3109 lb a = 0.081 in. a =

3109 ( 3) 0.75 ( 0.85 ) ( 5,000 ) (12 ) ( 3) 2

⎛ 3109 ⎞ Check that ⎜ + ⎝ 3534 ⎟⎠

3109 ( 3) ⎛ 3 − 0.081⎞ 6627 ⎜ ⎟⎠ ⎝ 2

2

=1

OK

Capacities: T = 5881 lb V = 3109 lb

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CHAPTER 6

e

Vu

Transverse weld along top of seat

a

0.30

φNn

b 0.20

t = thickness

  6

a

45° maximum

0.10

z=

Vu /bt Maximum stress on free edge

φVn

Range of recommended use 0.5

1.0

1.5

b

2.0

Fig. 6.6.7 Non-triangular stiffener.

b/a

Fig. 6.6.6 Triangular stiffener design limits.

b b 250 ≤ 1.0, then ≤ a t Fy b 250 ⎛ ⎞ ⎝ a⎠ b b if 1.0 ≤ ≤ 2.0, then ≤ If a t Fy if 0.75 ≤ If



6.6.7

(Eq. 6-49)

(Eq. 6-50)

Non-Triangular Stiffener Design

The non-triangular, stiffended beam seat is designed based on the recommendations of Reference 14. The minimum stiffener thickness to ensure yielding along the leading free edge is based on Reference 4, part 4, Local Buckling Criteria:

ts =

b Fy 95



b ⎤b ⎡ φV ⎛ e − ⎞ ⎥ φVn ⎢⎣ n ⎝ 2⎠ ⎦ 2 φ (1.8Fy ) = + 3 ts b ts b / 12

φ (1.8Fy ) ⎛e − b⎞ b 1 ⎝ 2⎠ 2 + 3 t s b t s b / 12

(Eq. 6-52)

where: φ = 0.75  he stiffener thickness required based on an applied load T is:



b⎞ ⎤ ⎡ ⎛ ⎢ 1 6⎝ e − 2 ⎠ ⎥ 1 t s = Vu ⎢ + ⎥ 2 b b φ 1.8F ( y) ⎢ ⎥ ⎢⎣ ⎥⎦

(Eq. 6-53)

(Eq. 6-51)

Using the minimum thickness, the nominal strength of the stiffener may be determined using a combined load analogy. The nominal normal force φNn shown in Fig. 6.6.7 is assumed to be resisted by the top line of weld on the bearing seat and has no impact on the design of the stiffener. According to Reference 4, bearing stress Fb at the outer edge of stiffener must satisfy: P Mc + ≤ φ1.8Fy Fb = A I Therefore:



φVn =

6.7

Welding

Nearly all structural steel used in precast concrete connections conforms to ASTM A36, A500 (tubes), or A992 (shapes) steel. Thus, it is readily weldable with standard equipment and standard welding procedures. 6.7.1

 orrosion Resistance of Welded C Connections

For corrosion resistance, elements of connections exposed to aggressive environments are sometimes hot-dip galvanized or stainless steel. Connections that are covered, patched, or painted or not exposed to weather are typically uncoated steel. The requirements and preparation for welding varies for these two types of steel.

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CHAPTER 6

EXAMPLE 6.6.7.1 Triangular Stiffener Analysis

  6

Given: The stiffened seat connection is shown at right. Stiffener thickness, ts = 3/8 in.; Fy = 36 ksi

6"

Problem: Determine the design shear resistance of the stiffener. _____________________________________________________________

φVn

Solution: 10"

b 8 = = 0.80 which is > 0.75 and < 1.0 a 10 250 250 b = ==41.7 Therefore, must be ≤ 41.7 36 Fy t 8 b ==21.3 = 21.3 0.09 in.2 OK

φ1000λ Acr µ Vu



(0.75 ) (1000 ) (1.0 ) (64 ) (1.4 ) (1.0 ) = 36,000

(Eq. 6-89)

fbu = φ0.85 fc' = 0.55 fc'

(Eq. 6-90)

a=

Cu bfbu

(Eq. 6-91)

where:

= 1.87 < 3.4

Use µe = 1.87

1.33 ( 36 ) 1.33Vu = 0.57 in.2 = φfy µe 0.75 ( 60 ) (1.87 )

⎤ ⎡ ⎢ h − d) ⎥ ( ⎥ Cu = Vu tanα + N u ⎢1+ ⎢ ⎛ d − a⎞ ⎥ ⎜ ⎟ ⎢⎣ ⎝ 2 ⎠ ⎥⎦

(Eq. 6-92)

For most designs, the horizontal reinforcement An is placed very close to the bottom of the steel bar. Thus, the term (h – d) can be assumed as equal to zero, simplifying Eq. 6-89 and 6-92. Tests have indicated a weakness in shear in the vicinity of the hangers, so it is recommended that stirrups in the beam end be designed to carry the total shear.

Use (1) #7 dowel. Avf = 0.60 in.2 OK Check welding requirements. By Design Aid 6.15.3 (E80 electrode): lw = 3 in. Use a double-sided, 3-in.-long, flare-bevel-groove weld.

6–64

Nu ⎛ h−d ⎞ ⎜ 1+ ⎟ φ fy ⎝ d − a / 2 ⎠

The connection should be detailed so that the reaction, the center of compression, and the center of the diagonal bars meet at a common point, as shown in Fig. 6.9.3. The compressive force Cu is assumed to act at a distance a/2 from the top of the bearing plate. Thus:

Acr = 4(16) = 64 in.2

Avf =

An =

where: φ = 0.65

Design bottom dowel: By Eq. 5-33 and Eq. 6-87:



(Eq. 6-88)

The steel bar or tube is proportioned so that the bearing strength of the concrete is not exceeded and to provide sufficient weld length to develop the diagonal bars. Bearing strength is discussed in Section 5.6.

Design top dowel: By Eq. 6-86: 5 Nu = An = = 0.09 in.2 φfy 0.9 (60 )



Vu φ f y cosα

where: φ = 0.90 fy = yield strength of An

Use HSS 4 × 4 × 5/16 × 23 in. long

µ e =

Ash =

where: φ = 0.75 fy = yield strength of Ash

By Eq. 6-85:



Loov Hanger

6.10

Bearing Pads

Bearing pads are used to distribute concentrated loads and reactions over the bearing area and to allow limited horizontal and rotational movements to provide stress relief. Their use has proven beneficial and may often be necessary for satisfactory performance of precast concrete structures. Several materials are commonly used for bearing pads. 1. AASHTO-grade chloroprene pads are made with 100% chloroprene as the only elastomer and conform to the

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b1

Steel bar

b

h

d

Nu α

Outline of concrete

  6

An

Vu

Ash

d (a) Basic components

Cu

a 2 a 2

α

Nu Vu

Vu /cos α (b) Design assumptions

Fig. 6.9.3 Loov hanger.

requirements of the AASHTO Standard Specifications for Highway Bridges,24 Section 18. Inert fillers are used with the chloroprene and the resulting pad is black in color and has a smooth uniform texture. While allowable compressive stresses are somewhat lower than other pad types, these pads allow the greatest freedom in movement at the bearing. It is important to note that chloroprene pads that do not meet the AASHTO specifications are not recommended for use in precast concrete structures. 2. Pads reinforced with randomly oriented fibers have been used successfully for many years. These pads are usually black, and the short reinforcing fibers are clearly visible. Vertical load capacity is increased by the reinforcement, but the capability of rotations and horizontal movement is somewhat less than chloroprene pads. Some randomly oriented fiber pads possess different properties in different directions in the plane of the pad. Therefore, unless proper planning and care is used in their installation, it may be prudent to specify those pads that have been tested to exhibit similar properties in different directions. No national standard specifications for this material exists. Manufacturers have developed appropriate design and performance documentation.

α

3. Cotton duck fabric reinforced pads are generally used where a higher compressive strength is desired. These pads are often yellow-orange in color and are reinforced with closely spaced, horizontal layers of fabric, bonded in the elastomer. The horizontal re­in­force­ment layers are easily observed at the edge of the pad. Section 18.10.2 of the AASHTO Standard Specifications for Bridges and Military Specification, MIL-C-882D, discusses this material.25 4. Chloroprene pads laminated with alternate layers of bonded steel or fiberglass are often used in bridges, but seldom in building construction. The previously discussed AASHTO specifications cover these pads. 5. A multimonomer plastic bearing strip or shim is manufactured expressly for bearing purposes. It is a commonly used material for the bearing support of hollowcore slabs, and is highly suitable for this application. It is also often used for bearing of architectural precast concrete cladding panels. 6. Tempered hardboard (also known as masonite) strips are also used with hollow-core slabs. These pads should be used with caution under moist conditions. In addition to progressive deterioration of the pad, staining of the precast concrete unit may occur. 7. Polytetrafluoroethylene-coated (TFE; also known as

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.9.2 Design of a Loov Hanger

  6

Top of component

Given: Hanger is similar to that shown in Fig. 6.9.3. =5  000 psi, normalweight (both component and fc' support) fy = 60 ksi (reinforcing bars) Fy = 36 ksi (structural steel) Vu = 24 kip (includes all load and overload factors) Nu = 4 kip (includes all load and overload factors) b1 = 6 in. α = 30 deg Problem: Size the hanger connections. ___________________________________________

PL 1" × 2" × 6"

2.52"

Cu 3

21/2 21/2 1

(1) #3 × 1'-6" (or 3/8" DBA) (2) #5

11/2"

/2"

/16"

Vu End of component

30°

Solution: Ash

=

24 Vu = 0.62 in.2 = φfy cosα 0.75 ( 60 ) cos30

DBA = deformed anchor bar

Use (2) #5, Ash = 0.62 in.2 Minimum weld length, #5, E70 electrode (Design Aid 6.15.3) = 21/2 in. Detail An so it is near the bottom of the steel bar.

OK

h–d≈0 4 Nu An = φf = 0.9 60 = 0.07 in.2 ( ) y

Provide end bearing plate as shown: Use (1) #3 dowel. By Eq. 6-90: fbu = 0.85φ fc' = 0.85(0.65)(5) = 2.76 ksi By Eq. 6-92:

⎛ ⎞ h −d ⎟ ⎜ Cu = Vu tanα + Nu ⎜ 1+ a⎟ ⎜⎝ d − ⎟⎠ 2

Although a is a function of Cu, with h – d = 0, the second term becomes:



= 24tan30 + 4(1)



= 17.9 kip

b = 1 in. By Eq. 6-91: a

=

Cu 17.9 = = 6.5 in. bfbu 1( 2.76 )

a/2 = 6.5/2 = 3.25 in.

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Figure 6.10.1 shows a typical bearing detail using TFE, and Fig. 6.10.2 shows the range of friction coefficients that may be used for design. Typical allowable stress is about 1000 psi for virgin TFE and up to 2000 psi for filled material with reinforcing agents such as glass fibers. 6.10.1

Design Recommendations

Bearing pads provide stress relief due to a combination of slippage and pad deformation. In elastomeric bearing pads, research26 has shown that slippage is the more significant factor. This research has also shown that the ratio of shear to compressive stress on the pad reduces significantly under slow cyclic movements, such as those produced by temperature variations. The following recommendations, along with Fig. 6.10.3 and 6.10.4, can be used to select bearing pads: 1. Use unfactored service loads for design. 2. At the suggested maximum uniform com­pressive stress, instantaneous vertical strains of 10% to 20% can be expected. This number may double if the bearing surfaces are not parallel. In addition, time-dependent creep will typically increase the instantaneous strains by 25% to 100%, depending on the magnitude of sustained dead load. 3. For stability of the pad, the length and width of unreinforced pads should be at least five times the thickness. 4. A minimum pad thickness of 3/8 in. is recommended

V

w

t b

Shape factor = S =

Polished sliding surface

Bond

Stainless steel may be provided loose or cast with member

  6

Backing

Polytetrafluoroethylene (TFE)

Fig. 6.10.1 Typical polytetrafluoroethylene (TFE) bearing pad detail.

Static coefficient of friction

Teflon) materials are often used in bearing areas when large horizontal movements are anticipated, such as at expansion joints. TFE is normally reinforced by bonding to an appropriate backing material, such as steel.

Pressure, psi Fig. 6.10.2 Polytetrafluoroethylene (TFE) friction coefficients.

wb 2 (w + b )t

D = durometer (Shore A hardness) ∆ = design horizontal movement at end of component

Durometer D

Recommended minimum thickness,b in.

Recommended maximum rotation,b rad

4DS ≤ 800

50 through 70

1.4∆

0.3t b  or w

Random fiber-reinforced elastomeric

1000 + 100S ≤ 1500

80 ± 10

1.4∆

0.3t b  or w

Cotton duck fabric reinforced

≤ 2500 (uniform) ≤ 4000 (nonuniform)

90 ± 10

2.0∆

0.12t b  or w

Pad material

Unreinforced chloroprene or rubber

Allowablea compressive stress, psi

a. Allowable compressive stresses may be increased based on test data supplied by the bearing-pad manufacturer. b. The values in the table are based on sliding criteria. If sliding is not critical or testing indicates more advantageous conditions, thinner pads may be used. The minimum thickness and maximum rotation values for the cotton duck pad account for the effects of creep.

Fig. 6.10.3 Single-layer bearing pads free to slip. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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DESIGN OF CONNECTIONS

CHAPTER 6

On steel

Resistance to horizontal movement, psi, or contact surface a

  6

On concrete

Cotton duck Random fiber reinforced

Chloroprene

Compressive stress, psi

Fig. 6.10.4 Shear resistance of bearing pads. a. Average values based on tests at 70% shear and slippage strain.

5. 6.

7. 8. 9.

10.

6–68

for all precast concrete components except solid slabs and hollow-core slabs. Figure 6.10.4 may be used to estimate the shear resistance of chloroprene, random fiber reinforced, and cotton duck pads. The portion of pad outside of the covered bearing surface as well as the portion that is not under load because of rotation of component should be ignored in calculating shape factors, pad stresses, stability, and movements. Pads should be centered under the bearing area. Shape factors S for unreinforced pads should be greater than 2 when used under double-tee stems, and greater than 3 under beams (Fig. 6.10.3). The sustained dead load compressive stress on unreinforced chloroprene pads should be limited to the range of 300 psi to 500 psi. The volume-change strains shown in Section 4.4 may be significantly reduced when calculating horizontal movement ∆ because of com­pensating creep and slip in the bearing pad. Certain fiber-reinforced bearing pads are reinforced in one direction only; for these types of pads, orientation in the field may be critical.

6.11

Column Bases

Column bases must be designed for both erection loads and loads which occur in service, the former often being more critical. Two commonly used base plate details are shown in Fig. 6.11.1 although many other details are also used. 6.11.1

Base Plates

If in the analysis for erection loads or temporary construction loads, before grout is placed under the plate, all the anchor bolts are in compression, the base plate thickness required to satisfy bending about line Z-Z is determined from:

t=

where: φ x, B Fy Cu

Cu ( 4 ) x φ ( B ) Fy

(Eq. 6-93)

= 0.90 = dimension as shown in Fig. 6.11.1 = yield strength of base plate = factored force on one anchor bolt

If the analysis indicates the anchor bolts on one or both sides of the column are in tension, the base plate thickness is determined by:

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(a) Base plate larger than column Shims 2" minimum grout space 5" maximum

Z

x

Alternate detail

Z B (b) Flush base plate

Shims

2" minimum 5" maximum

Z Alternate detail

x Z B

Fig. 6.11.1 Typical column base-plate detail. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

6–69

  6

DESIGN OF CONNECTIONS

CHAPTER 6 Base plate



Cbs = 2.22

Grout

fc' h

0.33 ef



(Eq. 6-95)

For hooked anchor bolts (Fig. 6.11.2[c]), the pullout strength may not exceed

  6

Top of foundation

hef

do eh (a) Threaded (b) Headed (c) Hooked rod bolt anchor bolt* *J-bolts not recommended for applications with significant tension Fig. 6.11.2 Typical anchor bolts.



t=

Tu ( 4 ) x φ ( B ) Fy

(Eq. 6-94)

where: φ = 0.90 x, B = dimension as shown in Fig. 6.11.1 Tu = total factored forces on anchor bolts 6.11.2

Anchor Bolts

The anchor bolt diameter is determined by the tension or compression on the stress area of the threaded portion of the bolt. Anchor bolts may be ASTM A307 bolts or, more frequently, threaded rods of ASTM A36 steel. ASTM F1554 may also be used. The requirements for structural integrity in Chapter 4 must also be satisfied. In most cases, both base-plate and anchor-bolt stresses can be significantly reduced by using properly placed shims during erection. When the bolts are near a free edge, as in a pier or wall, the buckling of the bolts before grouting may be a consideration. Confinement reinforcement, as shown in Fig. 6.11.1, should be provided as specified in ACI 318-05 Section 7.10.5.6. 6.11.2.1 Embedment Strength of Anchor Bolts in Tension ACI 318-05 Appendix D procedures for the strength of anchorages are applicable for anchor bolts in tension unless the anchor bolt is fully developed in concrete. The procedure is identical to the procedure for headed studs, and the equations presented in Section 6.5.3 are valid for the design of headed anchor bolts with the following addition: For headed anchor bolts (Fig. 6.11.2[a] and [b]), when 11 in. < hef < 25 in., Eq. 6-95 may be used as an alternative to Eq. 6-4: 6–70



Np = 1.26 fc' ehdoCcrp

(Eq. 6-96)

where: eh = hook projection ≥ 3do do = bolt diameter Ccrp = cracking factor (Section 6.5.4.2)

6.12

Moment Connections

When lateral stability of precast/prestressed concrete structures is achieved by frame action or by a combination of shear wall and frame action, the connections developing frame action must be designed for appropriate moment and shear transfer capabilities. The tension force for the moment resistance within a connection can be resisted by various types of cast-in embedments, such as headed studs and deformed bar anchors. These inserts must be properly anchored to preclude failure of the concrete and, thus, ensure a ductile mode of failure. Post-tensioning can also be used to develop moment resistance at joints between interconnected components. Where a high degree of moment resistance and ductility are required, composite construction is frequently used to achieve connections that are similar to monolithic concrete joints in their behavior. Achieving rigid connections can be costly. In most cases, it may not be desirable to build in a high degree of fixity, since the restraint of volume changes could result in large forces in the connections and the components. It is, therefore, preferable that the design of moment-resisting connections be based on the concept that the desired moment resistance is achieved with some deformation/rotation at the connection. The deformation should be controlled to provide for the desired ductility. A few examples of different types of moment-resisting connections are shown in Fig. 6.12.1. Additional examples can be found in Chapter 4 and Reference 2. Moment-curvature analysis of precast and prestressed concrete components is readily done based on established analytical methods. PCI funded research,27 as well as other research in progress, is leading to improved knowledge of momentresisting connections and improved analytical procedures. Example 6.13.7 illustrates the design of a moment connection.

6.13

Typical Connections

Figures 6.13.1 (a) through (e) demonstrate several typical connection details used in the precast/prestressed concrete industry. Additional details can be found in Reference 2.

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  6

Compression grout Bearing pad

Lap or weld

Note: See Section 6.3 regarding volume change accommodation for rigidly welded connections.

Fig. 6.12.1 Moment connections. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.11.2.1 Column Connection – Base Plate and Anchor Bolt Design

  6

x

Given: 20 in. square column anchored with headed threadedrod anchor bolts into a 36 in. × 36 in. pedestal. The column is designed as pinned at the base; thus, there are no tension requirements other than structural integrity (see Section 4.3).

21/4" 51/4" B 5" 20"

Factored axial load = 500 kip, including overload factors.

51/4"

Concrete: Pedestal fc' = 4000 psi, normalweight Column fc'  = 5000 psi, normalweight

21/4"

Steel: Base plate and anchor bolts: Fy = 36 ksi Deformed bar anchor (DBA): fy = 60 ksi

21/4"

51/4"

5"

51/4"

21/4"

20"

Problem: Determine the required base-plate thickness and DBAs to anchor the plate. Check anchor bolts in the pedestal. ___________________________________________ Solution: Structural integrity requirement (Section 4.3) (φ = 1.0): Tu = 200(Ag) = 0.2(20)2 = 80 kip, or 20 kip per bolt Required base plate thickness,: x =

5.25 = 3.71 in. 2

(

)

B = 2 2.25 2 + 5.25 2 = 13.79 in. t

=

Tu ( 4 ) x 20 ( 4 ) ( 3.71) = = 0.77 in. φBFy 1.0 (13.79 ) ( 36 )

Use 1-in.-thick plate. DBA: As =

80 Tu = 1.33 in.2 = φfy 1.0 ( 60 )

Use eight 1/2-in.-diameter DBA As = 8(0.20) = 1.6 in.2 > 1.33 in.2

OK

Anchor bolt requirements: Steel strength from Design Aid 6.14.6: OK

Use 1-in.-diameter bolts = 4(25.6) = 102.4 kip > 80 kip

If a hooked anchor bolt is chosen (Fig. 6.11.2[c]), the hook projection can be determined by rearranging Eq. 6-96: eh

6–72

=

Np 20 − = 3.97 in. 1.26fc' d oCcrp 1.26 ( 4 ) (1) (1.0 )

Use 4 in. projection.

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EXAMPLE 6.11.2.1 Column Connection – Base Plate and Anchor Bolt Design (cont.) Assume headed bolt with 11 in. minimum embedment. The spacing between anchor bolts is 15.5 in., which is less than 3hef (see notes to Fig. 6.5.2): d 10.25 so use hef = e,max = = 6.83 in. for Eq. 6-3 through 1.5 1.5 Eq. 6-7.

de,max = 101/4" 8"

21/4"

5 1 /4 "

x

8"

Concrete breakout strength, Eq. 6-3: Ncb = CbsANCcrbΨed,N From Eq. 6-4: Cbs = 3.33λ

4000 f = 80.6 = 3.33 (1.0 ) 6.83 hef

Cbs = 80.6

From Fig. 6.5.1: de1 = de2 = de3 = de4 < 1.5hef AN

21/4"

' c

= 36(36) = 1296 in.2

Edge distance factor (Eq. 6-5):

Edge of pedestal

B

Edge of base plate

⎛ 10.25 ⎞ ⎛d ⎞ Ψed,N = 0.7 + 0.3 ⎜ e,min ⎟ = 0.7 + 0.3 ⎜ = 1.00 ⎝ 1.5hef ⎠ ⎝ 1.5 ( 6.83) ⎟⎠ Eccentricity factor (Eq. 6-6): Ψec,N = 1.0 Since this is a corner of a pedestal, corner cracking may occur. Therefore, Ccrb = 0.8. 80.6 φCbsAN Ccrb Ψed,N Ψec,N = (1.0) (1296)(0.8)(1.0)(1.0) = 83.6 kip > 80 kip 1000 (The design is based on the minimum structural integrity tension requirement, φ = 1.0.)

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OK

6–73

  6

DESIGN OF CONNECTIONS

CHAPTER 6

  6

Panel Eq.

Eq. Reinforcing bar Reinforcing bar splice sleeve Precast wall Pump splice sleeve w/ special grout per splice sleeve manufacturer

Reinforcement Projection (per manuf.)

Exit port

x

Spandrel or wall panel

x

per design

DT flange

JT.

Continuous non-shrink non metallic grout (fc' - per design)

JT

Compressible material to keep topping out of the slotted insert Strap plate

Embed plate w/ reinforcing bars

Shim stack (two per wall)

Slotted insert

Reinforcing bar

C.I.P FDN

(a) Precast member reinforcing bar splice connection to foundation

(b) Double-tee flange connection to spandrel or wall panel

JT. Column sleeve

Embed plate w/ studs & hole for coil rod

Pocket

Coil insert

Coil rod w/ coil nuts & washer (peen threads after connection is installed)

Hairpins around insert Spandrel

Column Horseshoe bearing pad

Note: Thread coil rod into spandrel to fully engage coil insert

(c) Spandrel-to-column connection

Fig. 6.13.1 Typical precast concrete connections.

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PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS

CHAPTER 6

Panel As per design

  6

Reinforcing bar Non-shrink grout continuous (f c' = per design)

Shim stack (set next to reinforcing bar)

Joint

Precast concrete panel

Reinforcing bar splice sleeve Precast concrete panel

Fill sleeve w/ special grout per splice sleeve manufacturer

(d) Precast component reinforcing splice connection at joint

Eq. Eq.

Panel Important note: Thread each coil rod halfway into coil coupler

C L of wall

Coil rod Coupler

Shim stack

Note: Coil rod and coil coupler can be replaced w/ reinforcing bars and reinforcing bar coupler

Joint

Coil coupler

Precast concrete panel

Non-shrink grout continuous (f c' - per design) Note: Fill sleeve with non-shrink non-metallic grout (f 'c - per design) before erecting panel

Precast concrete panel

Reinforcing bars as per design requirements Corrugated duct tube

Coil rod

(e) Precast component joint connection with grouted corrugated conduit

Fig. 6.13.1 (cont) Typical precast concrete connections. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

6–75

DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.1 Cladding Connections – Reference Chapter 7, Examples 7.5.1.1 and 7.5.1.3

  6

Given: Cladding tension-compression center tieback connection of Examples 7.5.1.1 and 7.5.1.3. Factored loads – from “Load Combinations on Connections, lb” in Example 7.5.1.3: Seismic (in or out): 4490 lb (connection) 14,033 lb (fastener) Factored Wind: 4114 lb (out) Concrete:

fc' = 5000 psi, normalweight

Steel:

Fy = 36 ksi; Fu = 58 ksi

Weld:

E70

Problem: Size the components for the design loads listed. _______________________________________ Solution:

Component

21" Exterior face of panel Load direction

5" × 5"

Distribution reinforcement Seismic connection factors: Component Component Shear of weld Flexure of angle Buckling of rod Shear of weld Flexure of plate Concrete pull out a

Seismic Mode of failure

Seismic

Load type

3"

Design load 1.50 S 0.48 S 1.50 S 1.50 S 0.48 S 1.50 S

a

Or wind if larger

Wind

Critical

Design load, kip Design load, kip Design load, kip

1

Shear of weld

Fastener

14.0

4.1

14.0

2

Flexure of angle

Connection

4.5

4.1

4.5

3

Buckling of rod

Fastener

14.0

4.1

14.0

4

Shear of weld

Fastener

14.0

4.1

14.0

5

Flexure of plate

Connection

4.5

4.1

4.5

6

Flexure of pullout

Connection

14.0

4.1

14.0

Component ➁: Flexure of angle Try angle 5 in. × 5 in. × 5/8 in. × 6 in. Design shear load = 4.5 kip Shear yielding (Eq. 6-32): φVn = φ(0.6Fy)Aw = 0.9(0.6)(36)(5/8)(6) = 73.0 kip  4.5 kip

OK

Flexure: Moment arm = 3 in. Mu = 4.5(3 – 0.31) = 12.1 kip-in. Zp

bt 2 6 ( 0.625 ) = = 4 4

2

= 0.586 in.3

φMn = φZpFy = 0.9(0.586)(36) = 18.9 kip-in. > 12.1 kip-in. OK _____________________________________________________________________________________ Component ➂: Buckling of rod Cu = Tu = 14 kip Try 7/8 in. A36 All-thread rod. As = 0.60 in.2

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.1 Cladding Connections – Reference Chapter 7, Examples 7.5.1.1 and 7.5.1.3 (cont) From AISC Steel Construction Manual, 13th Edition, Chapter E.3. Where:

  6

Pn = critical buckling force φ = 0.9 Fcr = critical buckling stress r = radius of gyration 0.875 d = b = 4 4 = 0.22 in. Ag = gross area 2 π ( 0.875 ) = 4 = 0.60 in.2 When

E ku ≤ 4.71 Fy r

F ⎡ then Fcr = ⎢0.658 F ⎣

When

ku E > 4.71 r Fy

then Fcr = 0.877Fe

y

e

⎤ ⎥ Fy ⎦

Where: E = modulus of elasticity Fy = specified yield strength = FF e e =

π 2E 2 ⎛ ku ⎞ ⎜⎝ ⎟ v ⎠

k = factor based on curvature of element = 1.0

4.71

29,000 E = 4.71 = 133.7 36 Fy

k  u 1.0 (13.5 ) = = 61.4 r 0.22 61.4 < 133.7 Therefore: F ⎡ ⎤ FcrF cr == ⎢0.658 F ⎥ Fy ⎣ ⎦ y

e

Fe = Elastic buckling stress =

π 2 (29,000 ) π 2E = 75.9 ksi 2 = (61.4 )2 ⎛K ⎞ ⎜⎝ ⎟ r ⎠

36

Fcr = ( 0.658) 75.9 ( 36 ) = 29.5 ksi φPn = (0.9)(29.5)(0.60) = 15.97 kip 15.97 > 14.0 PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

OK 6–77

DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.1 Cladding Connections – Reference Chapter 7, Examples 7.5.1.1 and 7.5.1.3 (cont) Component ➃: Weld between nut and plate

  6

Tu = 14 kip Assumed length of weld is circumference of all thread = πD. Try 1/4 in. fillet weld. ⎛ 1 ⎞ a (π D ) φTn = φ(0.6FEXX)A = φ ( 0.6FEXX ) ⎜ ⎝ 2 ⎟⎠ 1 ⎛ 1 ⎞ ⎛ 1⎞ ⎡ ⎛ 7 ⎞ ⎤ φ (0.6Fexx ) α lw == (0.75 ) ( 0.6 ) ( 70 ) ⎜ π = 15.31 kip > 14 kip OK ⎝ 2 ⎟⎠ ⎜⎝ 4 ⎟⎠ ⎢⎣ ⎜⎝ 8 ⎟⎠ ⎥⎦ 2 _____________________________________________________________________________________

Component ➀: Weld design for angle to beam Tu = 14 kip at eccentricity of 3 in. Using the elastic vector method: Assume two line welds, one at each end of angle welded to structural steel shape. Weld section properties based on a unit weld size: Sy

=

d 2 (5 ) = 3 3

2

= 8.33 in.2

Maximum tension stress at end points: fz

=

Tuer 14 ( 3) = = 5.04 kip/in. Sy 8.33

Maximum shear stress: fx

=

Tw 14 = = 1.4 kip/in. w 5 + 5

Resultant stress: fresult = fx2 + fy2 + fz2 =

(1.4 )2 + ( 0 )2 + ( 5.04 )2

= 5.23 kip/in.

Reduced design strength 1/4 in. fillet weld: φfn

= φ ( 0.6FEXX )

1 (0.25 ) = 0.75 (0.6) (70 ) (0.25 ) = 5.57 kip/in. > 5.23 kip/in. 2 2

OK

_____________________________________________________________________________________ Component ➄: Flexure of plate in pullout Try PL 3/8 × 6 × 6 in. with four 1/2-in.-diameter × 3 in. studs at 4 in. on center. T u

= 4.5 kip

Mu

=

P  4.5 ( 4 ) = 4.5 kip-in. = 4 4

⎛ 6 (0.375 )2 ⎞ ⎛ bd 2 ⎞ = 0.9 ( 36 ) ⎜ φMn = φ (Fy ) Z p = φ (Fy ) ⎜ ⎟ ⎟ = 6.83 kip-in. > 4.5 kip-in. ⎝ 4 ⎠ 4 ⎝ ⎠

6–78

First Printing/CD-ROM Edition

OK

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.1 Cladding Connections – Reference Chapter 7, Examples 7.5.1.1 and 7.5.1.3 (cont.) Component ➅: Concrete pullout of plate with studs Nu = 14 kip

  6

Effective length hef = L + tplate – thead – /8 = 3 + 0.375 – /8 – /8 = 2.875 in. 1

3

1

Assume not near free edge: Cmin ≥ 1.5hef Breakout strength: φNcb = CbsANCcrbΨed,NΨec,N 5000 fc' 138.9 = 3.33 ==138.9 2.875 hef

Cbs

= 3.33

AN

= (s + 3hef)(s + 3hef) = [4 + 3(2.875)][4 + 3(2.875)] = 159.39 in.2

Ccrb = 1.0 Ψed,N = 1.0 Ψec,N = 1.0 Panel reinforcement goes through failure surface: φ = 0.75 φNcb = 0.75(138.9)(159.39)(1.0)(1.0)(1.0) = 16.6 kip > 14 kip

OK

Connection detail:

5 5" × 5" × 5/8" with 1-in.-diameter hole /8 diameter threaded rod /8 diameter nut (typical) Nut type slotted insert

7

7

Note: The embedded plate with the nut welded to it (shown on page 6-76) is for illustration purposes only. The detail using a slotted insert is more typical of what the industry does, and the capacity of the insert should be verified.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.2 Plate-and-Bar Diaphragm Shear Connection – Reference Fig. 4.8.2

  6

Given: Double-tee to double-tee diaphragm shear connection shown in Fig. 4.8.2(a). Concrete fc' = 5000 psi, normalweight Reinforcing bar (ASTM A615) fy = 60 ksi Plate: Fy = 36 ksi; Fu = 58 ksi Welds: E70 - plate to angle E90 - rebar to angle Reinforcing bars fully developed and welds as shown in Design Aid 6.14.3. Problem: Determine the shear strength of the connection.

Steel angle Edge of component

#5

Plan

_______________________________________

Solution: Strength based on tension and compression in the bars: φTn = φAsfy = 0.9(0.31)(60) = 16.7 kip φCn = φAsfy = 0.65(0.31)(60) = 12.1 kip φVn = φTn cos45 + φCn cos45 = 16.7(0.707) + 12.1(0.707) = 20.4 kip Strength based on weld shear through the effective throat with applied eccentricity based on erection plate size and analysis based on erection instantaneous center method from American Institute of Steel Construction’s LRFD Manual of Steel Construction.4 (see also Example 6.7.4.1).

(k  )2 2 (k  ) + 

xl

=

kl

=1

al

=

k=

=

(1)2 2 (1) + 4

= 0.167 in. k= 1"

1 = 0.25 R  ound to 0.2 for 4 conservative results.

3 1.5 − 0.167 − x ; a = = 0.333 2 4

k= 1" x= 0.167"

= 4"

From Reference 4: C = 1.35 C1 = 1.0 D = 4 l =4 Vu = CC1Dl = 1.35(1.0)(4)(4) = 21.6 kip

c.g.

e 3" Plan of weld c.g. = center of gravity

6–80

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PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.2 Plate-and-Bar Diaphragm Shear Connection – Reference Fig. 4.8.2 (cont.) Plate strength: Shear yielding: φVn = φ(0.6Fy)Aw φVn = 0.9(0.6)(36)(0.25)(4) = 19.4 kip

  6

Moment strength: ⎛ bd 2 ⎞ φ (Fy ) ⎜ φ (Fy ) Z p ⎝ 4 ⎟⎠ = φVn = e e 2 2

⎛ 0.25 ( 4 )2 ⎞ 0.9 ( 36 ) ⎜ ⎟ 4 ⎝ ⎠ φVn = = 24.2 kip 3 − 2 ( 0.167 ) 2

Failure mode

PL 1/4 × 4 × 3

Design strength, kip

Reinforcing bar

20.4

Weld

21.6

Plate

24.2

1 /4

1

21/2

/4

1

6

4

Typ. 1

Critical φVn = 20.4 kip.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

6–81

DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.3 Diaphragm-to-Wall Shear Connection – Reference Sections 4.5 and 4.8

  6

Given: The typical diaphragm connection to shear wall shown. Wall thickness: 8 in. Studs: fut = 65 ksi Reinforcing bar Grade 60: fy = 60 ksi Plates ASTM A36: Fy = 36 ksi Weld material: E70 - plate to plate E90 - rebar to plate Concrete: fc' = 5000 psi, normalweight

PL 3/8" × 6" × 6" w/ (4) 1/2" diameter × 6" H.A.S. PL 3/8" × 4" × 4" PL 3/8" × 4" × 6" w/ (2) #5 × 2'-0" /4

4

/4

8

1

1

2 2

4

Problem: Determine the shear capacity in the Z direction. PL 3/8" × 6" × 6" w/ (4) 1/2" diameter × 6" headed concrete anchor PL 3/8" × 4" × 4" φZn

My

φZn

My φZn

PL 3/8" × 4" × 6" w/ (2) #5 × 2'-6"

φZn

_______________________________________ Solution: The flange plate assembly should be detailed so that the lines of the diagonal bars intersect at a point on the face of the wall. If this is done properly, there will theoretically be no moment transferred to the wall. Because of residual moments due to tolerances, the wall and flange plate assemblies should have some moment-resisting capacity. Because of the manner in which the erection plate is welded to the two assemblies, there is a moment in the erection plate and the weld group. The following assumptions are used: 1 • The erection plate is fixed at one end. /4 4 • The eccentricity of the connection is the distance between 2 the centroids of the weld groups. Erection-plate moment strength:

e

⎛b⎞ ⎛ 2⎞ 2b ⎜ ⎟ 2 ( 2 ) ⎜ ⎟ ⎝ 2⎠ ⎝ 2⎠ = center of gravity (c.g.) = = 0.5 in. d + 2b 4 + 2 (2 )

/4

8

4

2

φZn φMn φZn

e = 4 – c.g. = 4 – 0.5 = 3.5 in. φMn ≤ φMp φMn = φZn(e) ⎛ bd 2 ⎞ φMp = φFy Zp = φFy ⎜ ⎝ 4 ⎟⎠ 6–82

1

c.g.

PL 3/8" × 4" × 4"

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.3 Diaphragm-to-Wall Shear Connection – Reference Sections 4.5 and 4.8 (cont.) ⎛ 0.375 ( 4 )2 ⎞ φMp = 0.9(36) ⎜ ⎟ = 48.6 kip-in. 4 ⎝ ⎠ φZn(e) φZn =

≤ φMp = 48.6 kip-in.

  6

1"

48.6 48.6 = 13.9 kip = e 3.5 in.

4"

Erection-plate shear strength:

1"

3 φZn = φ(0.6Fy)Aplate = 0.9(0.6)(36) (4) = 29.2 kip 8 Weld strengths: Wall embed to erection plate, 1/4 in. fillet weld, 4 in. long. From Design Aid 6.14.2: φZn = 4(5.57) = 22.3 kip

4"

1"

PL 3/8" × 6" × 6" with (4) 1/2" diameter × 6" headed concrete anchor

Double-tee embed to erection plate: This C-shaped weld can be designed by either of the methods shown in Section 6.7.5. The LRFD Manual of Steel Construction also contains tabulated values and design aids for determining the shear strength of such welds. Using one of those methods yields: From the LRFD Manual of Steel Construction, Table 8-8: 2 3.5 lw = 4 in., k = = 0.5, a = =0.875 4 4 Shows C = 1.878 φZn = φRn = φ(C)(C1)(lw)(D) = 0.75(1.878)(1)(4)(4) φZn = 22.5 kip Wall plate strength: Steel shear from Eq. 6-2: φZn = φVs = φnAseFut = 0.65(4)(0.20)(65) = 33.8 kip Concrete shear: The connection is far enough from any edge and the plate is considered to fail in steel shear.

C

Double-tee deck plate (see previous example):

45°

φZn

φVn = 20.4 kip Summary: Failure mode

Design strength, kip

Weld on erection plate

22.5

Moment in erection plate

13.9

Shear in erection plate

29.2

C-shaped weld on erection plate

22.4

Wall-plate studs steel shear

33.8

Wall-plate studs concrete shear

28.0

Double-tee deck plate

20.4

#5 × 2'-0"

T

PL 3/8" × 4" × 6

Critical φZn = 13.9 kip. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

6–83

DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.4 Wall-to-Wall Tension Connection – Reference Section 4.5 Given: The typical wall-to-wall tension connection

  6

shown.

6" × 6" × 3/8" × 5" w/ (2) #6 × 3'-0" & (2) 1/2" Dia. × 6" HCA

Wall thickness: 8 in. Deformed bar anchors (DBA): fy = 60 ksi Reinforcing bar Grade 60: fy = 60 ksi Plates ASTM A36: Fy = 36 ksi Weld material: E70 - plates to angle E90 - rebar to angle Concrete: fc' = 5000 psi, normalweight

Y

5

4

/16

Erection plates PL 3/8" × 3" × 4"

Problem: Determine the tension design strength in the Y direction. _______________________________________

X

Z PL 1/2" × 6" × 10" w/ (4) 1/2" Dia. × 24" DBA

Solution: Erection plate tension strength: φYn = φAplFy = 0.9(0.375)(4)(2 plates)(36) = 97.2 kip

/16

5

4

Weld strength: Erection plate to lower plate: From Design Aid 6.14.2: Strength of 5/16 in. fillet weld = 6.96 kip/in. φYn = 6.96(4)(2) = 55.7 kip Erection plate to angle: From Design Aid 6.14.2: φYn = 6.96(4)(2) = 55.7 kip

6" × 6" × 3/8" × 5" w/ (2) #6 × 3'-0" & (2) 1/2" Dia. × 6" HCA

φYn PL 3/8" × 3" × 4" φYn

φYn

φYn

PL 1/2" × 6" × 10" w/ (4) 1/2" Dia. × 24" DBA

Note: Dia. = diameter; HCA = headed concrete anchor; DBA = deformed anchor bar

6–84

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PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.4 Wall-to-Wall Tension Connection – Reference Section 4.5 (cont.) Lower plate capacity – controlled by four 1/2 in. DBAs Assume all four DBAs yield to resist applied force φYn = φAbfy = 0.9(0.20) (4)(60) = 43.2 kip Development length of DBA is the same as reinforcing bars. From Design Aid 15.2.9:

7" 10"

OK

Required ld = 17 in. < 24 in.

  6

11/2"

Pocket angle capacity: Neglect headed studs, strength is controlled by #6 reinforcing bars: φYn = φAbfy = 0.9(2)(0.44)(60) = 47.5 kip From Design Aid 15.2.9: Required length of #6 = 25 in. Development length provided = 32 in.

1"

4" 6"

OK

2" 8"

Summary: Failure mode

8"

Design strength, kip

Weld on erection plate to lower plate

55.7

Weld on erection plate to angle

55.7

Tension in erection plate

97.2

Deformed bar anchor tension

43.2

Angle reinforcing bar

47.5

Note: It is good practice to force the failure mode into the tensile plate. This can be done by putting a hole in the erection plate or using other methods of reducing the area.

31/2"

41/2"

/2" Dia. × 6" HCA

1

6" × 6" × 3/8" × 5" #6 × 3'-0"

5"

/2" Dia. × 6" HCA

1

Critical φYn = 43.2 kip.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

6–85

DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.5 Wall-to-Wall Shear Connection – Reference Section 4.5

  6

Given: The typical wall-to-wall shear connection shown. Wall thickness: 8 in. Deformed bar anchors (DBAs): fy = 60 ksi (see Section 6.4.5) Headed studs (HCAs): fut = 65 ksi Reinforcing bar Grade 60 (ASTM A706): fy = 60 ksi, fut = 90 ksi Plates ASTM A-36: Fy = 36 ksi Weld material: E70 - plate to angle and plate E80 - rebar to angle and plate Concrete: fc' = 5000 psi, normalweight Connection plate is recessed 2 in. Problem: Determine the tension design strength in the Y direction. ___________________________________

Solution: Erection plate shear strength:

PL 1/2" × 4" × 8" w/ (2) #6 × 3'-0"

Y

PL 1/2" × 3" × 5" Erection plates

X

Z

6" × 4" × 3/8" × 8" w/ (2) 1/2"φ × 6" HCA & (3) 5/8"φ × 30" DBA

/16

5

φYn = φApl (0.6Fy) = 0.9(0.5)(5)(0.6)(36) = 48.6 kip

/8

3

8

11/2 5 11/2

5

Weld strength: Erection plate to angle (left side): From Design Aid 6.15.2: φYn

Strength of 3/8 in. fillet weld = 8.35 kip/in. φYn = 8.35 (5) = 41.8 kip Erection plate to plate with #6 (right side): This C-shaped weld can be designed by either of the numerical methods or tabulated method of AISC. Using LRFD Manual of Steel Construction,13th edition, Table 8-8, yields: e = al a=

6–86

e 2.72 = = 0.544  5

PL 1/2" × 3" × 5" φYn φMz φYn

6" × 4" × 3/8" × 8" w/ (2) 1/2"φ × 6" HCA & (3) 5/8"φ × 30" DBA

φMz

φYn

PL 1/2" × 4" × 8" w/ (2) #6 × 3'-0"

kl = 1.5 k =

1.5 = 0.3 5

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.5 Wall-to-Wall Shear Connection – Reference Section 4.5 (cont.) From AISC Table 8-8:

e

C = 2.025 φYn = φRn = φ(C)(C1)(l)(D) = 0.75(2.025)(1)(5)(5)

  6

φYn

φYn = 37.9 kip Erection-plate moment capacity (c.g. = center of gravity):

φMz

⎛b⎞ ⎛ 1.5 ⎞ 2b ⎜ ⎟ 2 (1.5) ⎜ ⎝ 2⎠ ⎝ 2 ⎟⎠ = c.g. = d + 2b 5 + 2 (1.5 ) = 0.28 in.

e

c.g.

φYn

PL 1/2" × 3" × 5"

= 3 – c.g. = 3 – 0.28 = 2.72 in.

⎛ 0.5 ( 5 )2 ⎞ ⎛ bd 2 ⎞ = 0.9 36 φMz = φFy Z p = φFy ⎜ ( ) ⎜ ⎟ = 101.3 kip-in. ⎝ 4 ⎟⎠ 4 ⎠ ⎝

φYn =

φM z 101.25 = 37.2 kip = e 2.72

Angle capacity: The angle strength will be controlled by the shear strength of the studs and the DBAs. Since the connection is not located near a free edge, the steel strength will govern. From Eq. 6-2: φVs = φnAsfy = 0.75(3)(0.31)(60) = 41.9 kip

6" 1"

5" 1" 3"

21/2" 3"

3" 1"

8"

21/2"

(2) 1/2" diameter × 6" HCA 11/4"

23/4"

(3) /8" diameter × 30" DBA 5

4"

6" × 4" × 3/8" × 0'-8"

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

6–87

DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.5 Wall-to-Wall Shear Connection – Reference Section 4.5 (cont.) Embed plate with #6 (right side): Steel shear strength: Assume the bar is developed in the wall. Strength based on combined loading of steel. Moment arm d is equal to distance between reinforcing bars. 2 2 1 ⎡⎛ Vu ⎞ ⎛ M u ⎞ ⎤ ⎢⎜ ⎟ + ⎜ ⎥ ≤ 1.0 φ ⎢⎝ Vn ⎠ ⎝ M p ⎟⎠ ⎥ ⎣ ⎦

e = joint + PL = 5" #6 × 3'-0" T

1 ⎡ ⎛ φYn ⎞ ⎛ φYne ⎞ ⎢ + φ ⎢⎜⎝ 0.6fy Arb ⎟⎠ ⎜⎝ fy Arb d ⎟⎠ ⎣ 2

2

⎤ ⎥ ≤ 1.0 ⎥⎦

φYn

C

⎞ ⎛ φYn (5 ) ⎞ 1 ⎡⎛ φYn ⎢ + 0.9 ⎢⎜⎝ 0.6 ( 60 ) ( 2 )( 0.44 ) ⎟⎠ ⎜⎝ 60 (0.44 ) (6 ) ⎟⎠ ⎣ 2

d = 6"

  6

2

⎤ ⎥ ≤ 1.0 ⎥⎦

PL 1/2" × 4" × 8"

⎡⎛ 1 ⎞ 2 ⎛ 5 ⎞ 2 ⎤ φYn2 ⎢ ⎜ ⎟ + ⎜⎝ ⎟ ⎥ ≤ 0.9 158.4 ⎠ ⎥⎦ ⎢⎣ ⎝ 31.68 ⎠

φYn

φY (0.0020) ≤ 0.9 φYn = 21.2 kip

φMz

2 n

Summary: Failure mode

Design strength, kip

Weld on erection plate

41.8

Moment of erection plate

37.2

Shear of erection plate

48.6

C-shaped weld on erection plate

37.9

Deformed bar anchor

41.9

Wall-plate reinforcing bars

21.2

Critical: φYn = 21.2 kip.

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.5 Wall-to-Wall Shear Connection – Reference Section 4.5 (cont.) Check side-edge capacity per Section 6.5.5.3. Basic capacity (DBAs control with closer de1): 1.33

Vco1 = 87λ fc' (d e1 )

  6

(d )0.75 1.33



= 87 (1.0 ) 5000 (2.75 )



= 16,655 lb = 16.66 kip

(0.625)0.75

φVco1 = (0.75)(16.66) = 12.5 kip Cx1 = 1.0 Cy1 factor ny = 3; Y = 6 in. CY1 =

(n,Y )0.25 + 0.15 ≤ n



=

⎡⎣ 3 ( 6 )⎤⎦ + 0.15 ≤ 3 0.6 ( 2.75 )



= 1.4

0.6d e1

y

0.25

Cev1 = 1.0 no eccentricity Cvcr = 1.0 φVc1 = φVco1(Cx1)(Cy1)(Cev1)(Cvcr)

= (12.5)(1.0)(1.4)(1.0)(1.0)



= 17.5 kip

Basic capacity – studs: 1.33

Vco1 =8.7 87(1.0) 5000 ( 5 )

( 0.5 )0.75 ⎛⎜⎝

1 ⎞ ⎟ 1000 ⎠

= 31.1 kip

φVco1 = (0.75)(31.1) = 23.3 kip Cx1 = 1.0 Cy1 factor ny = 2; Y = 3 in. 0.25

⎡⎣2 ( 3) ⎤⎦ + 0.15 ≤ 2 CY1 = 0.6 ( 5 )

= 0.67

Cev1 = 1.0 no eccentricity Cvcr = 1.0 no cracking at this stage φVc1 = φVco1(Cx1)(Cy1)(Cev1)(Cvcr)

= (23.3)(1.0)(0.67)(1.0)(1.0)



= 15.6 kip

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CHAPTER 6

EXAMPLE 6.13.5 Wall-to-Wall Shear Connection – Reference Section 4.5 (cont.) φVs = φ(n)(Asfut) = (0.65)(2)(0.2)(65)

  6



= 16.9 kip

Development length of a #5: fy Ψt Ψe λ

= 60 = 1.0 = 1.0 = 1.0

⎛ fy ψ t ψ e λ ⎞ ld  d == ⎜ ⎟ db ⎝ 25 fc' ⎠

⎛ 60,000 (1.0 ) (1.0 ) (1.0 ) ⎞ = ⎜ ⎟⎠ 0.625 ⎝ 25 5000



= 21.2 in.; actual length = 30 in.

 he #5 will be developed beyond any postulated failure surface. Thus, the three 5/8 in. diameter × T 2 ft-6 in. DBAs will control capacity after cracking (ACI 318-05, RD.4.2.1) Thus: φVs = φnAsfy = (0.65)(3)(0.31)(60)

= 36.3 kip

where:

6–90

φ = 0.65 for shear (dowel action)

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.6 Wall-to-Wall Shear Connection with Combined Loading – Reference Section 4.5 Given: The typical wall-to-wall shear connection shown. Wall thickness: 8 in. Headed studs (HCAs): fut = 65 ksi Reinforcing bar Grade 60 (ASTM A706): fy = 60 ksi, fut = 90 ksi Plates ASTM A36: Fy = 36 ksi Weld material: E70 - plate to plates E80 - rebar to plate Concrete: fc' = 5000 psi, normalweight Connection plate is recessed 2 in. Assume de1 = 48 in., de3 = 48 in. Assume shear eccentricity on HCA plate is 11/2 in.

  6

Problem:  etermine the interaction tension and shear design strength and create an interaction diagram based on the D potential failure modes. These include: 1. Headed concrete interaction 2. Reinforcing bar shear and tension interaction 3. Erection-plate shear and interaction 4. Linear weld shear and interaction 5. C-shaped weld shear and interaction. ___________________________________ P 3/ " × 6" × 6" w/ (4) 1/ " Dia. × 6" HCA L

8

2

PL 1/2" × 3" × 5" φYn φXn

Solution: Headed stud plate: Vu Vn

5 3

+

φYn

φXn φYn

Nu Nn

5 3

φMz

φXn

φMz

φXn

φYn

= 1.0 PL /2" × 4" × 8" w/ (2) #6 × 3'-0" 1

Shear capacity determination: Steel shear from Eq. 6-2: φVs = φnAsefut = 0.65(4)(0.20)(65) = 33.8 kip Concrete shear: From Eq. 6-11: From Eq. 6-13:

φVc3 = φVco3(Cx3)(Ch3)(Cev3)(Cvcr) BED = de3 + Y = 48 + 4 = 52 in. 1.33

From Eq. 6-12:

Vco3 = 16.5λ fc' (BED )1.33 =

16.5 (1.0) 5000 ( 52 ) 1000

= 223.5 kip

X-spacing factor: From Eq. 6-14:

Cx3

= 0.85 +

Ch3

= 0.75

X 4 = 0.85 + = 0.88 ≤ n nstuds−back s 3BED 3 (52 )

Thickness factor: From Eq. 6-15:

8 h = 0.75 = 0.29 52 BED

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.6 Wall-to-Wall Shear Connection with Combined Loading – Reference Section 4.5 (cont.) Eccentricity factor: From Eq. 6-16:

  6

Cev3 =

1 1 = = 0.98 < 1.0 ' ⎛ e ⎞ ⎛ 1.5 ⎞ 1+ 0.67 ⎜ v ⎟ 1+ 0.67 ⎜ ⎝ BED ⎠ ⎝ 52 ⎟⎠

Cracked-concrete factor: Cvcr = 1.0 With confinement steel φ = 0.75 φVc3 = φVco3(Cx3)(Ch3)(Cev3)(Cvcr) = 0.75(223.5)(0.88)(0.29)(0.98)(1.0) = 41.92 kip > 33.8 kip Use φVn = φVc3 = 33.8 kip (steel governs) Tension capacity determination: Check steel strength. From Eq. 6-2 and Tables 6.5.1 and 6.5.2: φNs = φnAsefut φNs

= 0.75(4)(0.44)(65) = 85.8 kip (φ = 0.75, see Section 6.2.1)

Check concrete strength. 1. Depth of embedment from Table 6.5.2:

hef

2.

Check for edge effect.



X = 4 in., Y = 4 in., de1 = 48 in., de3 = 48 in. de1 and de3 are both greater than 1.5hef = 12 in., edge-effect reduction do not apply



From Eq. 6-5: Ψed,N = 1.0

3.

Check breakout strength.

6–92

5000 fc' = 83.9 = 3.33 7.875 hef



From Eq. 6-4: Cbs

= 3.33



From Eq. 6-3: Ncbg

= φCbs (de1 + X + 1.5hef )(de3 + Y + 1.5hef )(Ψed,N)Ccrb

4.

= L + tpl – ths – 1/8 in. = 8 + 3/8 – 3/8 – 1/8 = 7.875 in.

⎛ 83.9 ⎞ = (0.75) ⎜ (12 + 4 + 12)(12 + 4 + 12)(1.0)(1.0) = 49.3 kip ⎝ 1000 ⎟⎠

Check pullout strength. From Eq. 6-7 (φ = 0.70, see Section 6.2.1)

From Table 6.5.2: Abrg = 0.79 in.2 × 4 studs = 3.16 in.2



From Eq. 6-7: φNph = φ(11.2)(Abrg) fc' Ccrp = 0.70(11.2)(3.16)(4)(1.0) = 99.1 kip



(φ = 0.70, see condition B, Section 6.2.1.2)

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.6 Wall-to-Wall Shear Connection with Combined Loading – Reference Section 4.5 (cont.) 5.

Check side-face blowout strength. de,min = 48 in. > 0.4hef = 0.4(8) = 3.2 in. Therefore, it is not critical. Use φNn = φNcbg =49.3 kip

HCA interaction:

HCA interaction equation

  6

40

 y making the resultant shear and normal force a function B of the applied shear acting at an angle with the horizontal, the interaction equation becomes the following.

5

20 10

φYn(θ) = Vu cos(θ) φXn(θ) = Vu sin(θ)

Shear: Tension:

Shear, kip

30

5

0

⎛ Y ⎞ 3 ⎛ X n (θ ) ⎞ 3 Interaction: n (θ ) + ⎜⎝ φV ⎟⎠ ⎜⎝ φN ⎟⎠ = 1.0 n n

10

20

30

40

Tension, kip

For an angle between 0 deg and 90 deg, one can solve for the largest applied load.

Reinforcing bar interaction: Strength based on combined loading of steel. Assume shear rupture of reinforcing bar is 0.6fut. Moment arm d is equal to distance between reinforcing bars.

1 ⎛ ⎛ Vu ⎞ ⎛ M u ⎞ + ⎜ φ ⎜⎝ ⎜⎝ Vn ⎟⎠ ⎜⎝ M p ⎟⎠ 2

2

⎞ ⎟ ≤ 1.0 ⎟⎠

 gain making the resultant shear and normal force a function of the applied shear acting at an angle A with the horizontal, the reinforcing bar interaction equation becomes 1 ⎡⎛ Yn (θ ) ⎞ ⎛ Yn (θ )e1 + X n (θ )e2 ⎞ ⎢ + ⎟ φ ⎢⎜⎝ 0.6fy Arb ⎟⎠ ⎜⎝ fy Arb d ⎠ ⎣ 2

2

⎤ ⎥ ≤ 1.0 ⎥⎦

Yn (θ ) ⎞ ⎛ Yn (θ ) ( 2.68 ) + X n (θ ) ( 3) ⎞ 1 ⎡⎛ ⎢⎜ + φ ⎢⎝ 0.6 ( 60 ) ( 0.88 ) ⎟⎠ ⎜⎝ (60 ) (0.44 ) (6 ) ⎟⎠ ⎣ 2

1 ⎡ ⎛ Yn (θ ) ⎞ ⎛ Yn (θ ) ( 2.68 ) + X n (θ ) ( 3) ⎞ ⎢ + ⎟ φ ⎢⎜⎝ 31.68 ⎟⎠ ⎜⎝ 158.4 ⎠ ⎣ 2



2

2

⎤ ⎥ ≤ 1.0 ⎥ ⎦

⎤ ⎥ ≤ 1.0 ⎥ ⎦

Shear, kip

e1 = eccentricity of the shear component, measured to the location of the center of gravity of the weld group. From previous examples = 2.68 in Reinforcing bar interaction equation e2 = eccentricity of the tension component, measured from the 30 bottom reinforcing bar = s/2 = 6/2 = 3 in. 20

10

0

20

40

Tension, kip

Erection-plate interaction: One simple method for calculating the erection-plate interaction is based on the AISC combined loading limits. These limits are stated in Eq. 6-39 and 6-40. For yielding under normal stress: φfun = φFy For yielding under shear stress: φfuv = φ(0.6Fy) where: φ = 0.9

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.6 Wall-to-Wall Shear Connection With Combined Loading – Reference Section 4.5 (cont.) Between these limits, the material follows a Mohr’s circle with limits of shear maximum stress:

  6

2



ft ⎞ ⎛ 2 ⎜⎝ ft − ⎟⎠ + fv ≤ fv _ max 2

fv_max = φ(0.6Fy) = 19.44 ksi

Tension maximum stress: 2



ft f ⎞ ⎛ + ⎜ ft − t ⎟ + fv2 ≤ ft _ max ⎝ 2 2⎠

ft_max = φ(Fy) = 32.4 ksi

 reating the relationship between the shear stress and normal stress limits as functions of the applied C load and angle, the following interaction diagram can be developed. Normal stress:



ft =

Yn (θ )e

+

S

X n (θ ) A

Shear stress:



=

Yn(θ ) 2.68 X n (θ ) Yn θ 2.68 X n (θ ) = () + + 2.5 0.5 ( 5 ) 2.5 0.48 1 (0.5 ) (53 ) 12

⎡ ⎛ 5⎞⎤ ⎢ ⎛ 5⎞ ⎜ 2 ⎟ ⎥ Yn (θ ) ⎢0.5 ⎜ ⎟ ⎜ ⎟ ⎥ ⎢ ⎝ 2⎠ ⎜ 2 ⎟ ⎥ Yn θ 1.56 Yn (θ )q ⎝ ⎠⎦ ⎣ ft = = = () 5.21( 0.5 ) lt ⎡1 3 ⎤ ⎢⎣ 12 ( 0.5 ) ( 5 ) ⎥⎦ ( 0.5 )

The strength level limits: The extreme limits for maximum tension: φTn = φFy Apl =(0.9)(36)(0.5)(5) = 81 kip The extreme limits for maximum shear is based on the plastic moment of the plate:



φMp = M = Ve

φFy

bd 4

2

Erection-plate interaction equation

= Ve

⎛ 0.5 ( 5 ) ⎞ bd 2 0.9 ( 36 ) ⎜ ⎟ 4 ⎠ ⎝ 4 = 2.68 e 2

φFy



φVn =



= 37.8 kip

Shear, kip



30 20 10

0

20

40

60

80

Tension, kip

It is evident that the elastic analysis is conservative for determining the maximum applied shear force since the plastic moment strength is 37.8 kip compared to about 21 kip using an elastic method.

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.6 Wall-to-Wall Shear Connection With Combined Loading – Reference Section 4.5 (cont.) Linear weld strength: Using the strength increase as a function of applied load angle:

φRn (θ ) = φ (0.6FEXX )

1 Aw 2

φRn (θ ) = 0.75 (0.6 ( 70 ))

  6

3 ⎛ ⎞ ⎜⎝ 1.0 + 0.5sin (θ ) 2 ⎟⎠

3 3 1 (0.25) (5 ) ⎛⎜⎝ 1.0 + 0.5sin (θ )2 ⎞⎟⎠ = ( 27.8 kip ) ⎛⎜⎝ 1.0 + 0.5sin (θ )2 ⎞⎟⎠ 2

Linear-weld interaction equation

Shear, kip

40 30 20 10 0

20

10

Tension, kip

C-shaped weld strength:  he C weld is in plane; thus, the solution can be made up of specific points using the instantaneous T center method. Since software is readily available for elastic analysis, the interaction curve is based on an elastic analysis with load angles in increments of 10 deg, from 0 deg to 90 deg.

Shear, kip

C-weld interaction equation

10

5

0

10

20

30

Tension, kip

Combining all interaction curves, and highlighting the capacity region.

Shear, kip

Connection interaction HCA power interaction Reinforcing bar interaction Erection-plate interaction Linear-weld interaction C-weld interaction

40 30 20 10 0

20

40

60

80

Tension, kip

Note: It may be preferable to increase the weld size to ensure ductility of the connection. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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DESIGN OF CONNECTIONS

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EXAMPLE 6.13.7 Ordinary Moment Frame Connection – Reference Section 4.5

  6

Given: The spandrel-to-column ordinary moment-frame connection is shown. Assume the spandrel and column reinforcement is adequate to resist gravity loads. The connection is not required to resist out-of-plane forces caused by spandrel beam rotation. Reinforcing bar Grade 60 (ASTM A706): fy = 60 ksi Plates ASTM A36: Fy = 36 ksi Weld material: E70 - plate to plate E80 - rebar to plates Concrete: fc' = 5000 psi, normalweight Problem: Determine the tension capacity in the X direction. ___________________________________ Solution: Plate tension capacity: φXn = φFy Apl = 0.9(36)(0.5)(7) = 113.4 kip Weld capacity from Design Aid 6.14.2: φXn = 8.36(16) = 133.8 kip Reinforcement strength (4) #7: φAsfy = 0.9(4)(0.60)(60) = 129.6 kip  rom Design Aid 6.14.3, provide 31/4 in. of weld F each side of bar to 1/2-in.-thick plate.  rom Design Aid 15.2.9, a minimum of 25 in. of F development length is required. Limiting strength is plate tension = 113.4 kip Note: To ensure yielding in the plate, the length between welds should be 1.2 times the width of the plate. Note: These connections are susceptible to restraint forces caused by creep, shrinkage, and temperature change in the connecting spandrel. Creep strains are greater in prestressed concrete components than in non-prestressed components. Design and detailing should take these forces into consideration.

41/2" /8"

3

PL 1/2" × 6" × 0'-9" w/ (4) #7

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16"

7" 41/2"

PL 1/2" × 7" × 0'-10" PL 1/2" × 6" × 0'-9" w/ (4) #7

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.8 Deformed Bar or Reinforcing Bar Connection Plate Supporting Steel Beam

40 kip 1"

6" 4"

  6

/16" 3 /16" 3

1"

11"

3"

1'-4" 2" 2" 4" 4" 4"

Given: Vu = 40 kip (ultimate) fc' = 5000 psi, normalweight, λ = 1.0 Deformed bar anchor (DBA): fy = 60 ksi DBA: fut = 80 ksi Embed plate and single plate: Fy = 36 ksi Embed plate and single plate: Fut = 58 ksi E70 electrodes: FEXX = 70 ksi

/4" × 6" × 1'-4" Plate w/(8) 5/8"φ × 24" DBA

3

3"

W16 /4" Plate w/(4) 11/2" 3/4"φ A325 - N bolts 1

Problem: Check the design of the embed plate and singleplate connection. _______________________________________ Solution: 1.

Check steel strength of deformed bar anchors. Assume all (eight) anchors carry shear. Conservatively assume top (two) anchors carry tension. a. Shear strength Vu /anchor = 40 kip/8 anchors = 5.0 kip From Eq. 6-2: φVs = φnAsefut = 0.65(0.31)(80) = 16.1 kip 16.1 kip > 5.0 kip

OK

b. Tensile strength Nu /anchor =

40 ( 3) = 10 kip/2 = 5 kip/anchor 12

From Eq. 6-2: φNs = φnAsefut = 0.75(0.31)(80) = 18.6 kip/anchor 18.6 kip > 5.0 kip c. Interaction Vu Check interaction limits for shear and tension φV

s

5 = 0.31≥ 0.2 16.1 From Eq. 6-29:

≥ 0.2

5 = 0.27 ≥ 0.2 must use interaction based on both shear and tension. 18.6 Vu N + u ≤ 1.2 φVs φN s

0.31 + 0.27 = 0.58 < 1.2 2.

OK

OK

Check concrete strength. Use shear friction for vertical shear – assume all (eight) anchors resist shear loads. Conservatively assume top (two) anchors carry tension due to eccentric vertical load. a. Steel required for direct shear

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CHAPTER 6

EXAMPLE 6.13.8 Deformed Bar or Reinforcing Bar Connection Plate Supporting Steel Beam (cont.) From Eq. 5-32: Avf =

  6

Vu φfy µ

Acr = plate area = (6)(16) = 96 in.2 For concrete to steel interface use µ = 0.7λ (bar cast monolithically) Required Avf =

40

(0.75 ) (60 ) (0.7 )

= 1.27 in.2

Avf per DBA= 1.27/8= 0.16 in.2 Check max Vn = 0.2λ fc' Acr < 800λAcr

= 0.2(1.0)(5)(96) = 96 kip > 800(1.0)(96)/1000 = 76.8 kip use 76.8 kip 76.8 kip > 40 kip

OK

b. Steel required for direct tension From Eq. 5-34: An =

Nu 5 = = 0.11 in.2 φfy (0.75)( 60 )

Required anchor area (governed by top row) = Avf + An Avf + An = 0.16 in.2 + 0.11 in.2 = 0.27 in.2 / anchor OK

Area provided by 5/8 in. φ DBA = 0.31 in.2 > 0.27 in.2 c. Check bar development length ld Per Design Aid 15.2.9, for fc' = 5000 psi, ld = 21 in. use 24-in.-long DBAs 3.

Check embed-plate thickness.  tep 2 assumed only top two anchors resist tension. Therefore, use 4 in. effective embed-plate width to S resist bending (this is conservative)

Mu =

P  10 ( 4 ) = 10 kip-in. = 4 4

From Eq. 6-31; 10 = 0.9 ( 36 )

φMp = φFy Zp where Z p =

bt 2 4

     2 ( 4 )t min

4 OK

tmin = 0.56 in< 0.75 in. 4.

Check weld. Because plate is welded on both sides, determine if base metal or weld-strength governs. Base metal: φRn = φ(0.6Fu)t = 0.75(0.6)(58)(0.25) = 6.5 kip/in. Single weld: φRn = φ(0.6Fu)tw = 0.75(0.6)(70)(3/16)(0.707) = 4.18 kip/in. Both welds: φRn = 2(4.18) = 8.36 kip/in. 6.5 < 8.36; therefore, base metal controls, Multiply values from weld analyses by 6.5/8.36 = 0.78

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DESIGN OF CONNECTIONS

CHAPTER 6

EXAMPLE 6.13.8 Deformed Bar or Reinforcing Bar Connection Plate Supporting Steel Beam (cont.) a. Elastic vector analysis weld = 2(11.5 in.) = 23 in.

  6

From Design Aid 15.7.3: 2

Sweld =

d 2 (11.5 ) = 44.1 in.3/in. = 3 3

Resultant weld stress: 2

2

2

⎛ V ⎞ ⎛ M ⎞ ( 3) ⎞ ⎞ ⎛V ⎛V fr = ⎜ u ⎟ + ⎜ u ⎟ = ⎜ u max ⎟ + ⎜ u max ⎠ ⎝ 23 ⎝  weld ⎠ ⎝ Sweld ⎠ ⎝ 44.1 ⎟⎠ 2

( 3) ⎞ ⎛V ⎞ ⎛V 4.18 (0.78 ) = ⎜ u max ⎟ + ⎜ u max ⎝ 23 ⎠ ⎝ 44.1 ⎟⎠ Vu max =



2

2

( 3.26 )2 2

⎛ 1⎞ ⎛ 3 ⎞ ⎜⎝ ⎟⎠ + ⎜⎝ ⎟ 23 44.1⎠

2

Vumax = 40.4 kip > 40 kip OK

b. Instantaneous center method From LRFD Manual of Steel Construction, Table 8-4, using k =0: C = 3.27 by interpolation: C1 = 1.0 for E70 electrodes,  = 11.5 in., D = 3 (sixteenths of fillet weld) φRnw = φCC1D Using reduction for plate thickness, φRnw = 0.75(3.27)(1.0)(3)(11.5)(0.78) = 66 kip Note: There is a significant increase in weld strength by using instantaneous center method. If plate is near a free bottom edge, vertical reinforcing welded to the plate to carry the entire reaction or hairpins around the anchors (hanger steel) may be required (see following figure).

(2) #5 hairpins around studs

Free edge

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6.14

References

1. A  CI Committee 318. 2005. Building Code Require­ments for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05). Farmington Hills, MI: American Concrete Institute (ACI).

  6

2. P  CI Connection Details Committee. 2008. PCI Connections Manual for Precast and Prestressed Concrete Construction. 1st ed. Chicago, IL: Precast/ Prestressed Concrete Institute (PCI). 3. A  merican Society of Civil Engineers (ASCE). 2005. ASCE 7-05 Standard, Minimum Design Loads for Buildings and Other Structures. Reston, VA: American Society of Civil Engineers. 4. A  merican Institute of Steel Construction (AISC). 2005. Steel Construction Manual. 13th ed. Chicago, IL: AISC. 5. C  oncrete Technology Associates. 2000. Ductile Pullout Connections. CTA Technical Bulletins, Vol. II. Chicago, IL: Precast/Prestressed Concrete Institute. See also PCI Journal, V. 44, No. 5 (September-October). 6. C  oncrete Reinforcing Steel Institute. 1990. Reinforcement, Anchorages, Lap Splices and Connections. Schaumburg, IL: Concrete Reinforcing Steel Institute. 7. A  CI Committee 439. 1983. Mechanical Connections of Reinforcing Bars. Concrete International, V. 5, No. 1, January. 8. A  merican Welding Society (AWS). 2008. Structural Welding Code — Steel, AWS D1.1-08. Miami, FL: AWS. 9. I nternational Code Council (ICC). 2006. International Building Code 2006. Country Club Hills, IL: ICC. 10. B  ickel, T. S., and A. F. Shaikh. 2002. Shear Strength of Adhesive Anchors. PCI Journal, V. 47, No. 5 (September-October). 11. C  ook, R. A., J. Kunz, W. Fuchs, and R. C. Konz. 1998. Behavior and Design of Single Adhesive Anchors under Tensile Load in Uncracked Concrete. ACI Structural Journal, V. 95, No. 1 (January-February). 12. S  almons, J. R. 1998. Plates with Anchors Post-Installed with Non-Shrink Grout. PCI Journal, V. 43, No. 3 (MayJune).

16. S  pecialty Steel Industry of North America (SSINA). 1995. Design Guidelines for the Selection and Use of Stainless Steel, Designer’s Handbook. Washington, DC: SSINA. 17. A  WS. 1998. Welding Handbook — Materials and Appli­ cations. 8th ed. Miami, FL: AWS. 18. C  hambers, H. A. 2001. Principles and Practices of Stud Welding. PCI Journal, V. 46, No. 5 (SeptemberOctober). 19. A  WS. 2002. Structural Welding Code  —  Reinforcing Steel, AWS D1.4-02. Miami, FL: AWS. 20. B  lodgett, Omer W. 1976. Design of Welded Structures. 8th printing. Cleveland, OH: The James F. Lincoln Arc Welding Foundation. 21. M  arcakis, K., and D. Mitchell. 1980. Precast Concrete Connections with Embedded Steel Members. PCI Journal, V. 25, No. 4 (July-August). 22. C  azaly, L., and M. W. Huggins. 1996. Canadian Prestressed Concrete Institute Handbook. 3rd ed. Ottawa, ON, Canada: Canadian Prestressed Concrete Institute. 23. L  oov, Robert. 1968. A Precast Beam Connection Designed for Shear and Axial Load. PCI Journal, V. 13, No. 3 (May-June). 24. A  merican Association of State Highway and Transportation Officials (AASHTO). Standard Specifications for Highway Bridges. 17th ed. Washington DC: AASHTO. 25. A  ASHTO. Standard Specifications for Bridges and Military Specification, MIL-C-882D. 17th ed. Washington, DC: AASHTO. 26. I verson, J. K., and D. W. Pfeifer. 1985. Criteria for Design of Bearing Pads, Technical Report, TR-4-85. PCI Journal, V. 30, No. 5 (September-October). 27. S  tanton, J. F., R. G. Anderson, D. W. Dolan, and D. E. McCleary. Moment Resistant Connections and Simple Connections, Research Project No 1/4. Chicago, IL: PCI.

13. A  nderson, Neal S., and D. F. Meinheit. 2000. Design Criteria for Headed Stud Groups in Shear: Part 1 — Steel Capacity and Back Edge Effects. PCI Journal, V. 45, No. 5 (September-October). 14. S  almon, Charles G., and J. E. Johnson. 1996. Steel Structures: Design and Behavior. 4th ed. New York, NY: Harper and Collins. 15. T  he Lincoln Electric Company. 1999. The Procedure Handbook of Arc Welding. 14th ed. Cleveland, OH: The Lincoln Electric Company.

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DESIGN OF CONNECTIONS

CHAPTER 6

6.15 Design Aids Design Aid 6.15.1 Allowable and Design Stress for Fillet and Partial Penetration Weldsa Electrode

Allowableb working stress, ksi

Designc strength, ksi

E70

21

31.5

E80d

24

36.0

E90d

27

40.5

E100d

30

45.0

  6

a. For partial penetration welds loaded in shear parallel to the axis of the weld. b. Based on AISC Steel Construction Manual.4 c. Based on AISC Steel Construction Manual. Includes φ = 0.75. d. Refer to AWS D1.1 Table 3.1 – Prequalified Base Metal – Filler Material Combinations for Matching Strength.

Design Aid 6.15.2 Strength of Fillet Welds for Building Construction Filleta weld size

E70 Electrode Allowable stress design, kip/in.

Designb strength, kip/in.

1

/8

1.86

2.78

/16

2.78

4.18

1

/4

3.71

5.57

/16

4.64

6.96

3

/8

5.57

8.35

/16

6.50

9.74

1

/2

7.42

11.14

/16

8.35

12.53

/8

9.28

13.92

3

5

7

9

5

a. Assumes 45 deg fillet. b. Based on AISC Steel Construction Manual.4 Includes φ = 0.75.

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Design Aid 6.15.3 M  inimum Length of Weld to Develop Full Strength of Bar. Weld Parallel to Bar Lengtha,b,c

  6

db

tw = 0.2db

0.2db 0.2db

w

Electrode

E80d

E90d

Bar size, #

Plate thickness in.

3 4 5 6 7 8 9 10 11 3 4 5 6 7 8 9 10 11

tw = 0.3db

db

15° maximum

Splice

Minimum length of weld, in.a /2

Min. splice length, in.

11/4

11/4

1

1 /4

3

1 /4

3

1 /4

3

1 /4

11/4

21/4

21/4

21/4

21/4

21/4

11/2

2 /4

2 /2

2 /2

2 /2

2 /2

13/4

/8

7/16

11/4

11/4

3

1 /4

3

1/4

5/16

11/4

3

1

3

1

1

1

1

33/4

3

3

3

3

2

5

4

31/2

31/2

31/2

21/4

61/4

5

41/4

33/4

33/4

21/2

8

61/4

51/4

41/4

41/4

3

3

9 /4

3

7 /4

1

6 /2

1

5 /2

3

4 /4

31/4

11/4

11/4

11/4

11/4

11/4

1

1

1 /2

1

1 /2

1

1 /2

1

1 /2

1

1 /2

1

2

2

2

2

2

11/4

23/4

21/4

21/4

21/4

21/4

11/2

33/4

3

23/4

23/4

23/4

13/4

5

4

1

3 /4

3

3

2

1

6 /4

5

1

4 /4

3

3 /4

1

3 /2

21/4

8

61/4

51/4

41/2

4

21/2

9 /4

7 /4

6 /2

5 /2

5

23/4

3

3

1

1

a. Lengths above the heavy line are governed by weld strength. Lengths below the heavy line are governed by plate shear. Basis: bar fy = 60 ksi; plate Fy = 36 ksi; shear on plate limited to 0.9(0.6)(36) = 19.44 ksi. b. Weld length listed is the required effective length of weld. Engineer should consider whether weld at start and stop is fully effective. c. Refer to Design Aid 15.4.2 for specifications of flare bevel groove welds. d. Refer to AWS D1.1 Table 3.1 – Prequalified Base Metal – Filler Material Combinations for Matching Strength and AWS D1.4 Table 5.1 Matching Filler Metal Requirements. Use E80 Electrodes for ASTM A706 rebar; use E90 electrodes for ASTM A615 rebar.

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PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS

Design Aid 6.15.4

CHAPTER 6

Size of Fillet Weld Required to Develop Full Strength of Bar. Butt Weld.

BAR PERPENDICULAR TO PLATE, WELDED ONE SIDE ⎛

db

a

a⎞



lw = π ⎜ d b + ⎟ ⎝ 2⎠



Plate = Fy = 36 ksi



Plate area = π(db + 2a)tpl

  6

Weld size

tpl

Grade 40 bar E80 electrodea

E70 electrode Bar size, #

Weld size,b in.

3

3

4

1

5 6

5

7 8

7

9

7

10 11

9

Minimum plate thickness,c in.

Weld size,b in.

E90 electrodea

Minimum plate thickness,c in.

Weld size,b in.

Minimum plate thicknessc tpl, in.

/16

1

/4

3

/16

1

/4

3

/16

1

/4

/4

1

/4

3

/16

1

/4

3

/16

1

/4

1

/4

1

/4

1

/4

1

/4

1

/4

1

/4

/16

1

/4

1

/4

1

/4

1

/4

1

/4

3

/8

5

/16

5

/16

5

/16

5

/16

5

/16

5

/16

1

/8

5

/16

5

/16

1

/8

/16

1

/8

7

/16

1

/8

1

/8

1

/8

1

/2

1

/8

7

/16

7

/16

7

/16

7

/16

7

/16

1

/2

7

/16

7

/16

1

/2

/16

1

/4

/4

1

/4

/16

5

/16 /16

/16

/16

Grade 60 bard 3

3

4 5

5

6 7

7

8 9

9

10

5

11

11

/16

1

/4

3

1

/4

1

/4

1

/16

1

/4

5

3

/8

5

/16

3

/8

5

/16

3

/8

3

/8

3

1

/2

7

/16

7

/16

7

/16

1

/2

1

/2

1

/8

1

/2

9

/16

9

/16

9

/16

5

/8

5

/8

/16 /2

/16 /8

a. Refer to AWS D1.1 Table 3.1 – Prequalified Base Metal – Filler Material Combinations for Matching Strength and AWS D1.4 Table 5.1 Matching Filler Metal Requirements. Use E80 Electrodes for ASTM A706 rebar; use E90 electrodes for ASTM A615 rebar. b. A minimum of 3/16 in. weld size is suggested. c. Theoretical thickness for shear stress on base metal = 0.9(0.6)(36) ksi. A more practical thickness might be taken as 1/2 db as used with headed studs. A minimum of 1/4 in. plate thickness is suggested. d. E70 electrodes are not permitted for grade 60 reinforcement.

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DESIGN OF CONNECTIONS

CHAPTER 6

Design Aid 6.15.5 Size of Fillet Weld Required to Develop Full Strength of Bar. Weld Through Hole. BAR PERPENDICULAR TO PLATE, WELDED BOTH SIDES

  6

db

a Weld size

2



a⎤ ⎡ lw = π ⎢d b + ⎥ 2⎦ ⎣ Plate = Fy = 36 ksi Plate area = π(db + 2a)tpl

tpl

Grade 40 bar E80 electrodea

E70 electrode Bar size, #

Weld size,b in.

3

3

4

3

5

3

6

3

7

3

8

Minimum plate thickness,c c in.

Weld size,b in.

E90 electrodea

Minimum plate thickness,c in.

Weld size,b in.

Minimum plate thickness,c in.

/16

1

/4

3

/16

1

/4

3

/16

1

/4

/16

1

/4

3

/16

1

/4

3

/16

1

/4

/16

1

/4

3

/16

1

/4

3

/16

1

/4

/16

5

/16

3

/16

5

/16

3

/16

5

/16

3

/8

3

/16

3

/8

3

/16

3

1

/4

3

/8

3

/16

7

/16

3

/16

7

/16

9

1

/4

7

/16

1

/4

7

/16

3

/16

7

/16

10

5

/16

1

/2

1

/4

1

/2

1

/4

1

11

5

/16

9

/16

5

/16

9

/16

1

/4

9

/4

3

/16

1

/16

3

/16

5

/8

3

/16

3

/16

3

/16

7

/2

1

/4

1

/16

1

/4

9

/16 /8

/2

/16

Grade 60 bard 3

3

4

3

5

3

6

1

7 8

5

9

5

10

3

11

3

/16

1

/4

/16

5

/16

3

/4

7

1

/4

1

/16

9

/16

5

/8

5

/16

5

/8

/8

11

/16

5

/16

11

/16

/8

3

/4

3

/8

3

/4

/16 /8

/16 /2

/16

a. Refer to AWS D1.1 Table 3.1 – Prequalified Base Metal – Filler Material Combinations for Matching Strength and AWS D1.4 Table 5.1 Matching Filler Metal Requirements. Use E80 Electrodes for ASTM A706 rebar; use E90 electrodes for ASTM A615 rebar. b. A minimum of 3/16 in. weld size is suggested. c. Theoretical thickness for shear stress on base metal = 0.9(0.6)(36) ksi. A more practical thickness might be taken as 1/2 db as used with headed studs. A minimum of 1/4 in. plate thickness is suggested. d. E70 electrodes are not permitted for grade 60 reinforcement.

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DESIGN OF CONNECTIONS

CHAPTER 6

Design Aid 6.15.6 Strength of Bolts and Threaded Fastenersa Bolt diameter, in.

Nominal area A, in.2

/2

A36 Fu = 58 ksi Tension

A307 Fu = 60 ksi Shear

Tension

Shear

Design

Service

Design

Service

Design

Service

Design

Service

0.196

6.4

3.8

3.4

1.9

6.6

3.9

3.5

2.0

/8

0.307

10.0

5.9

5.3

3.0

10.4

6.1

5.5

3.1

/4

0.442

14.4

8.5

7.7

4.4

14.9

8.8

8.0

4.4

/8

0.601

19.6

11.5

10.5

5.9

20.3

12.0

10.8

6.0

1

0.785

25.6

15.0

13.7

7.7

26.5

15.7

14.1

7.9

1

1 /2

1.227

40.0

23.5

21.3

12.1

41.4

24.5

22.1

12.3

1

1 /2

1.767

57.6

33.8

30.7

17.4

59.6

35.3

31.8

17.7

2

3.142

102.4

60.1

54.7

31.0

106.0

62.8

56.6

31.4

Bolt diameter, in.

Nominal area A, in.2

/2

1 5 3 7

ASTM A193 Grade B5 Fu = 100 ksi Tension

ASTM A193 Grade B7 Fu = 125 ksi

Shear

Tension

Shear

Design

Service

Design

Service

Design

Service

Design

Service

0.196

11.0

6.5

5.9

3.3

13.8

8.1

7.4

4.2

/8

0.307

17.3

10.1

9.2

5.2

21.6

12.7

11.5

6.5

/4

0.442

24.9

14.6

13.3

7.5

31.1

18.2

16.6

9.4

/8

0.601

33.8

19.8

18.0

10.2

42.3

24.8

22.5

12.8

1

0.785

44.2

25.9

23.6

13.3

55.2

32.4

29.4

16.7

11/4

1.227

69.0

40.5

36.8

20.9

86.3

50.6

46.0

26.1

11/2

1.767

99.4

58.3

53.0

30.0

124.2

72.9

66.3

37.5

2

3.142

176.7

103.7

94.3

53.4

220.9

129.6

117.8

66.8

1 5 3 7

a. Source: American Institute of Steel Construction, Steel Construction Manual, 13th edition.4 See this manual for shear-tension interaction.

Design Aid 6.15.7 High-Strength Coil Bolt and Coil Threaded Rod Selection Chart Coil rod diameter, in.

Safe working loada Tension, lb

Shear, lb

Minimum root area, in.2

Tensile strength, psi

Yield strength, psi

Minimum coil penetration, in.

1

/2b

9,000

6,000

0.1385

130,000

110,000

2

3

/4b

18,000

12,000

0.3079

117,000

100,000

21/4

1b

38,000

25,300

0.5410

140,000

120,000

21/2

11/4b

56,000

37,500

0.9161

123,000

105,000

21/2

11/2

68,000

45,300

1.3892

98,000

85,000

3

a. Factor of safety is approximately 2 to 1. b. Strength requirements similar to ASTM A325-09, Standard Specification for Structural Bolts, Steel, Heat Treated, 120/105 ksi Minimum Tensile Strength.

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6–105

  6

DESIGN OF CONNECTIONS

CHAPTER 6

Design Aid 6.15.8 Strength of Connection Angles. Vertical Load.

  6

φFy bnt 2 (Eq. 6-43) 4ev = 0.90 = net length of angle, in. = yield strength of angle steel = 36,000 psi



φVn =



φ bn Fy

g

Angle strength only – insert pullout must be checked.

t ev

φVn

φVn, lb per in. of length of angle Angle thickness t, in.

ev = 2 in.

ev = 3 in.

ev = 4 in.

ev = 5 in.

ev = 6 in.

/8

570

380

285

228

190

/2

1013

675

506

405

338

/4

2278

1519

1139

911

759

1

4050

2700

2025

1620

1350

3 1 3

Design Aid 6.15.9

Strength of Connection Angles. Horizontal Load.

φFy bnt 2 (Eq. 6-45) 4g = 0.90 = net length of angle, in. = yield strength of angle steel = 36,000 psi



φNn =



φ bn Fy

 g

Angle strength only – insert pullout must be checked.

t φNn

φNn, lb per in. of length of angle Angle thickness t, in.

t = 5 in. g = 3 in.

t = 6 in. g = 31/2 in.

t = 7 in.

t = 8 in. g = 41/2 in.

/8

380

325

285

/2

675

579

506

/4

1519

1302

1139

1

2700

2314

2025

253 450 1013 1800

3 1 3

6–106

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g = 4 in.

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS

CHAPTER 6

Design Aid 6.15.10 Design of Structural Steel Haunches — Concrete Design Strength e

a

e

a

Values are for design strength of concrete by Eq. 6-75 for following criteria:

Vu

Vu

fc' = 5000 psi; for other strengths multiply values by

  6

fc' 5000 Adequacy of strucural-steel section should be checked.

As' Steel shape

Steel shape As

Additional design strength φVr can be obtained with reinforcing bars; see Design Aid 6.15.11. Vu = φ(Vc + Vr) φ = 0.75

e − 3"

Values of φVc, kip

Shear span a, in.

2

4

6

8

Effective width of section, in.

Embedment e, in.

6

7

8

9

10

11

12

13

14

15

16

17

6 8 10 12 14 16 18 20 22 6 8 10 12 14 16 18 20 22 6 8 10 12 14 16 18 20 22 6 8 10 12 14 16 18 20 22

29 41 54 68 81 94 108 121 135 22 33 45 57 70 83 96 109 122 18 28 39 50 62 74 86 99 111 15 24 34 44 55 67 78 90 102

33 48 63 79 94 110 126 141 157 26 39 53 67 82 96 112 127 142 21 32 45 58 72 86 100 115 130 18 28 39 51 64 78 91 105 119

38 55 72 90 108 126 143 161 179 29 44 60 77 93 110 128 145 162 24 37 51 67 82 98 115 131 148 20 32 45 59 74 89 104 120 137

43 62 81 101 121 141 161 182 202 33 50 68 86 105 124 143 163 183 27 42 58 75 92 111 129 148 167 23 36 51 66 83 100 117 135 154

48 69 91 113 135 157 179 202 224 37 55 75 96 117 138 159 181 203 30 46 64 83 103 123 143 164 185 25 40 56 74 92 111 130 150 171

53 76 100 124 148 173 197 222 247 40 61 83 105 128 152 175 199 223 33 51 71 91 113 135 158 181 204 28 44 62 81 101 122 143 165 188

57 83 109 135 162 188 215 242 269 44 67 90 115 140 165 191 217 244 36 56 77 100 123 147 172 197 223 30 48 67 88 110 133 156 180 205

62 90 118 146 175 204 233 262 292 48 72 98 124 152 179 207 235 264 39 60 84 108 134 160 186 214 241 33 52 73 96 119 144 170 195 222

67 96 127 158 189 220 251 282 314 51 78 105 134 163 193 223 254 284 42 65 90 116 144 172 201 230 260 35 56 79 103 129 155 183 210 239

72 103 136 169 202 235 269 303 336 55 83 113 143 175 207 239 272 304 45 70 96 125 154 184 215 246 278 38 60 84 110 138 166 196 226 256

77 110 145 180 215 251 287 323 359 59 89 120 153 186 221 255 290 325 48 74 103 133 164 197 230 263 297 40 64 90 118 147 177 209 241 273

81 117 154 191 229 267 305 343 381 63 94 128 163 198 234 271 308 345 51 79 109 141 175 209 244 279 315 43 68 95 125 156 188 222 256 290

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

6–107

DESIGN OF CONNECTIONS

CHAPTER 6

Design Aid 6.15.11 Design of Structural Steel Haunches — Reinforcement Design Strength

e

a

Values are for additional design strength of concrete obtained from reinforcement by Eq. 6-76 for following criteria: As = two bars welded to steel shape A's = As Reinforcement anchored in only one direction.

Vu

  6

When reinforcement As and A's is anchored both above and below steel shape, it can be counted twice (values may be doubled).

As' Steel shape As

For design strength of concrete, φVc – see Design Aid 6.15.10. Vu ≤ φVn = φ(Vc + Vr)

e − 3" Values of φVr, kip Shear span a, in.

2

4

6

8

6–108

Embedment e, in. 6 8 10 12 14 16 18 20 22 6 8 10 12 14 16 18 20 22 6 8 10 12 14 16 18 20 22 6 8 10 12 14 16 18 20 22

Reinforcing bar size fy = 60 ksi

Reinforcing bar size fy = 40 ksi #4 5 7 9 9 10 10 11 11 11 4 6 7 8 9 9 10 10 10 3 5 6 7 8 9 9 9 10 3 4 6 7 7 8 8 9 9

#5 8 11 13 15 16 16 17 17 17 6 9 11 13 14 15 15 16 16 5 8 10 11 12 13 14 15 15 4 7 9 10 11 12 13 14 14

#6 12 16 19 21 22 23 24 24 25 9 13 16 18 20 21 22 22 23 7 11 14 16 18 19 20 21 21 6 10 12 14 16 17 18 19 20

#7 16 22 26 28 30 31 32 33 34 12 18 22 25 27 28 29 30 31 10 15 19 22 24 26 27 28 29 8 13 17 20 22 23 25 26 27

#8 21 29 34 37 40 41 43 44 45 16 24 29 32 35 37 39 40 41 13 20 25 29 31 34 36 37 38 11 17 22 26 29 31 33 34 36

#9 26 37 43 47 50 52 54 55 56 20 30 36 41 44 47 49 51 52 16 25 32 36 40 43 45 47 49 14 22 28 33 36 39 42 44 45

#4 8 11 13 14 15 16 16 17 17 6 9 11 12 13 14 15 15 16 5 8 9 11 12 13 14 14 15 4 7 8 10 11 12 12 13 14

First Printing/CD-ROM Edition

#5 12 17 20 22 23 24 25 26 26 9 14 17 19 21 22 23 24 24 8 12 15 17 19 20 21 22 23 6 10 13 15 17 18 19 20 21

#6 17 24 28 31 33 35 36 37 37 13 20 24 27 29 31 32 34 34 11 17 21 24 26 28 30 31 32 9 14 18 21 24 26 27 29 30

#7 24 33 39 43 45 47 49 50 51 18 27 33 37 40 42 44 46 47 15 23 28 33 36 38 41 42 44 12 20 25 29 33 35 37 39 41

#8 31 44 51 56 59 62 64 66 67 24 36 43 49 53 56 58 60 62 19 30 37 43 47 51 53 56 57 16 26 33 39 43 46 49 52 54

#9 39 55 65 71 75 78 81 83 85 30 45 55 62 67 71 74 76 78 24 38 47 54 60 64 68 70 73 20 33 42 49 54 59 62 65 68

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS

CHAPTER 6

Design Aid 6.15.12 Column Base-Plate Thickness Requirements Thickness required for concrete bearing fbu, psi

x0 = 3 in.

500

5

1000

3

x0 = 4 in.

/8

x0 = 5 in.

/4

/8

3

7

/4

1

1 /4

1500

1

11/4

15/8

2000

11/8

11/2

13/4

2500

11/4

15/8

2

3000

3

1 /8

3

1 /4

21/4

3500

11/2

17/8

23/8

4000

1 /2

2

21/2

1

  6

1

Plate Fy = 36 ksi

xc xt

xc or xt

b

xo

External anchor bolts

Internal anchor bolts

Thickness required for bolt loading Tension on external anchor bolts Number and diameter of A-36 or A-307 anchor bolts per side b, in.

2 – 3/4 in. 2 – 3/4 in. 2 – 1 in. 2 – 1 in. 2 – 13/4 in. 2 – 11/4 in. 2 – 11/2 in. 2 – 11/2 in. xt = 3.75 in. xt = 4.25 in. xt = 3.75 in. xt = 4.25 in. xt = 3.75 in. xt = 4.25 in. xt = 3.75 in. xt = 4.25 in.

12

11/8

11/8

11/2

11/2

17/8

2

21/8

21/4

14

1

1

1 /8

3

1 /8

1

1 /2

3

1 /4

3

1 /4

2

21/8

1

1

11/4

13/8

13/8

15/8

17/8

2

/8

1

1

1 /4

1

1 /4

1

1 /2

5

1 /8

13/4

17/8

/8

1

11/8

11/4

13/8

11/2

13/4

13/4

/8

11/8

11/8

13/8

11/2

15/8

13/4

/8

1

1

1 /8

1

1 /4

3

1 /8

1

1 /2

15/8

/8

1

11/8

11/4

13/8

11/2

15/8

/4

1

1

1 /8

1 /4

1

1 /2

11/2

16 18

7

20

7

22

7

24

3

26

3

28

3

/8

7

/4

7

/4

7

/4

3

1

1

Compression on anchor bolts or tension on internal anchor bolts Number and diameter of A-36 or A-307 anchor bolts per side b, in.

2 – 3/4 in. xc = 1.5 in.

12

3

14

3

16

3

18

3

20

3

22

3

24

3

26

3

28

3

2 – 3/4 in. xc = 2.0 in.

/4

7

/4

3

/8

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

2 – 1 in. xc = 1.5 in.

2 – 1 in. xc = 2.0 in.

2 – 13/4 in. xc = 1.5 in.

2 – 13/4 in. xc = 2.0 in.

2 – 11/2 in. xc = 1.5 in.

2–11/2 in. xc = 2.0 in.

1

11/8

11/4

11/8

13/8

15/8

/8

1

1

1 /8

1

1 /4

1

1 /4

11/2

1

1

11/8

11/4

11/8

/8

1

1

1 /8

1

1 /8

11/8

/8

1

11/8

11/4

/8

1

1

11/4

/8

1

1

11/8

1

11/8

/8

11/8

/4

7

/4

7

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

/8 /4

7

/4

7

/4

7

/4

3

/4

3

/4

3

/8

7

/8

7

/4

7

/4

7

/4

3

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

/8

7

/4

7

/8 /8

7

6–109

DESIGN OF CONNECTIONS

CHAPTER 6

Design Aid 6.15.13 Strength of Welded Headed Studs Based on Steel Strength Stud diameter, in.

  6

/4

1

3

/8

1

/2

5

/8

3

/4

7

/8

Tension strength, kip

2.25

5.05

9.57

14.96

21.54

29.31

Shear strength, kip

1.95

4.38

8.30

12.96

18.67

25.41

Design Aid 6.15.14 Concrete Tension Strength of Welded Headed-Stud assemblies CASE 1: Not near a free edge Applies to rectangular stud patterns with outside dimensions X and Y. See Fig. 6.5.2. If stud spacing is ≥ 3hef, single-stud capacity multiplied by number of studs may govern design. φNcb = Cbs (X + 3hef )(Y + 3hef )Ccrb

Y

Assumptions: φ = 0.7 (No confinement reinforcement – multiply Table A values by 0.75/0.7 when confinement reinforcement is used.) Ccrb = 1.0 (Uncracked concrete – multiply Table A values by 0.8 when concrete may be cracked.) Cbs = 3.33 (fc' / hef ) (Normalweight concrete – multiply Table A values by λ when lightweight concrete is used.) fc' = 5000 psi (Multiply Table A values by fc' / 5000 for other concrete strengths.) hef = Ls + tp – ths – 1/8 in. (for stud burnoff during welding.) tp (plate thickness) = 3/8 in. ths (stud-head thickness) = 3/8 in.

X

hef

X Y 0

3

2 4 6 8 10 12 14

0

4

2 4 6 8 10 12 14

0

6

2 4 6 8 10 12 14 16

0

8

6–110

2 4 6 8 10 12 14 16

2

4

6

8

9.4 11.5 13.6 15.7 17.8 19.9 22.0 24.1 13.8 16.2 18.5 20.8 23.1 25.4 27.7 30.0 24.2 26.9 29.6 32.3 35.0 37.7 40.4 43.1 45.8 36.4 39.4 42.4 45.5 48.5 51.5 54.5 57.6 60.6

11.1 13.6 16.1 18.6 21.0 23.5 26.0 28.5 15.8 18.5 21.1 23.7 26.4 29.0 31.6 34.3 26.6 29.6 32.6 35.5 38.5 41.5 44.4 47.4 50.3 39.2 42.4 45.7 49.0 52.2 55.5 58.7 62.0 65.3

12.8 15.7 18.6 21.4 24.3 27.1 30.0 32.8 17.8 20.8 23.7 26.7 29.7 32.6 35.6 38.6 29.1 32.3 35.5 38.8 42.0 45.2 48.4 51.7 54.9 42.0 45.5 49.0 52.4 55.9 59.4 62.9 66.4 69.9

14.6 17.8 21.0 24.3 27.5 30.7 34.0 37.2 19.8 23.1 26.4 29.7 33.0 36.3 39.6 42.9 31.5 35.0 38.5 42.0 45.5 49.0 52.5 56.0 59.5 44.8 48.5 52.2 55.9 59.7 63.4 67.1 70.9 74.6

Table A: Design tensile strength, φNcb, kip 10 12 14 16 18 20 22 16.3 19.9 23.5 27.1 30.7 34.4 38.0 41.6 21.8 25.4 29.0 32.6 36.3 39.9 43.5 47.1 33.9 37.7 41.5 45.2 49.0 52.8 56.5 60.3 64.1 47.6 51.5 55.5 59.4 63.4 67.4 71.3 75.3 79.3

18.0 22.0 26.0 30.0 34.0 38.0 42.0 46.0 23.7 27.7 31.6 35.6 39.6 43.5 47.5 51.4 36.3 40.4 44.4 48.4 52.5 56.5 60.6 64.6 68.6 50.3 54.5 58.7 62.9 67.1 71.3 75.5 79.7 83.9

19.7 24.1 28.5 32.8 37.2 41.6 46.0 50.3 25.7 30.0 34.3 38.6 42.9 47.1 51.4 55.7 38.8 43.1 47.4 51.7 56.0 60.3 64.6 68.9 73.2 53.1 57.6 62.0 66.4 70.9 75.3 79.7 84.1 88.6

21.4 26.2 30.9 35.7 40.4 45.2 50.0 54.7 27.7 32.3 36.9 41.5 46.2 50.8 55.4 60.0 41.2 45.8 50.3 54.9 59.5 64.1 68.6 73.2 77.8 55.9 60.6 65.3 69.9 74.6 79.3 83.9 88.6 93.2

23.1 28.3 33.4 38.5 43.7 48.8 54.0 59.1 29.7 34.6 39.6 44.5 49.4 54.4 59.3 64.3 43.6 48.4 53.3 58.1 63.0 67.8 72.7 77.5 82.4 58.7 63.6 68.5 73.4 78.3 83.2 88.1 93.0 97.9

First Printing/CD-ROM Edition

24.8 30.4 35.9 41.4 46.9 52.4 58.0 63.5 31.6 36.9 42.2 47.5 52.7 58.0 63.3 68.6 46.0 51.1 56.3 61.4 66.5 71.6 76.7 81.8 86.9 61.5 66.7 71.8 76.9 82.1 87.2 92.3 97.4 102.6

26.6 32.5 38.4 44.3 50.2 56.1 62.0 67.9 33.6 39.2 44.8 50.4 56.0 61.6 67.2 72.9 48.4 53.8 59.2 64.6 70.0 75.4 80.7 86.1 91.5 64.3 69.7 75.1 80.4 85.8 91.1 96.5 101.9 107.2

24

26

28

30

28.3 34.5 40.8 47.1 53.4 59.7 65.9 72.2 35.6 41.5 47.5 53.4 59.3 65.3 71.2 77.1 50.9 56.5 62.2 67.8 73.5 79.1 84.8 90.4 96.1 67.1 72.7 78.3 83.9 89.5 95.1 100.7 106.3 111.9

30.0 36.6 43.3 50.0 56.6 63.3 69.9 76.6 37.6 43.8 50.1 56.4 62.6 68.9 75.2 81.4 53.3 59.2 65.1 71.1 77.0 82.9 88.8 94.7 100.7 69.9 75.8 81.6 87.4 93.2 99.1 104.9 110.7 116.6

31.7 38.7 45.8 52.8 59.9 66.9 73.9 81.0 39.6 46.2 52.7 59.3 65.9 72.5 79.1 85.7 55.7 61.9 68.1 74.3 80.5 86.7 92.9 99.1 105.2 72.7 78.8 84.8 90.9 97.0 103.0 109.1 115.2 121.2

33.4 40.8 48.2 55.7 63.1 70.5 77.9 85.4 41.5 48.5 55.4 62.3 69.2 76.1 83.1 90.0 58.1 64.6 71.1 77.5 84.0 90.4 96.9 103.4 109.8 75.5 81.8 88.1 94.4 100.7 107.0 113.3 119.6 125.9

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS

CHAPTER 6

Design Aid 6.15.14 Concrete Tension Strength of Welded Headed-Stud Assemblies (cont.) CASE 2: Near one free edge Applies to rectangular stud patterns with outside dimensions X and Y. See Fig. 6.5.2. If stud spacing is ≥ 3hef, single-stud capacity multiplied by number of studs may govern design. φNcb = φN'cb Ψed,N (φN'cb from Table A; Ψed,N from Table 6.5.4)

Y

Assumptions for Table A: φ = 0.7 (No confinement reinforcement – multiply Table A values by 0.75/0.7 when confinement reinforcement is used.) Ccrb = 1.0 (Uncracked concrete – multiply Table A values by 0.8 when concrete may be cracked.) Cbs = 3.33 (fc' / hef ) (Normalweight concrete – multiply Table A values by λ when lightweight concrete is used.) fc' = 5000 psi (Multiply Table A values by fc' / 5000 for other concrete strengths.) hef = Ls + tp – ths – 1/8 in. (for stud burnoff during welding.) tp (plate thickness) = 3/8 in. ths (stud-head thickness) = 3/8 in.

de1

X b = de1 + X

Table A: φN c' b = φCbs(de1 + X + 1.5hef)(Y + 3hef)Ccrb hef

3

4

6

8

b Y 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

5.6 6.8 8.0 9.3 10.5 11.8 13.0 14.2 7.9 9.2 10.5 11.9 13.2 14.5 15.8 17.1 13.3 14.8 16.3 17.8 19.2 20.7 22.2 23.7 25.2 19.6 21.2 22.8 24.5 26.1 27.7 29.4 31.0 32.6

7.3 8.9 10.5 12.1 13.8 15.4 17.0 18.6 9.9 11.5 13.2 14.8 16.5 18.1 19.8 21.4 15.7 17.5 19.2 21.0 22.7 24.5 26.2 28.0 29.7 22.4 24.2 26.1 28.0 29.8 31.7 33.6 35.4 37.3

9.0 11.0 13.0 15.0 17.0 19.0 21.0 23.0 11.9 13.8 15.8 17.8 19.8 21.8 23.7 25.7 18.2 20.2 22.2 24.2 26.2 28.3 30.3 32.3 34.3 25.2 27.3 29.4 31.5 33.6 35.7 37.8 39.9 42.0

10.7 13.1 15.5 17.8 20.2 22.6 25.0 27.4 13.8 16.2 18.5 20.8 23.1 25.4 27.7 30.0 20.6 22.9 25.2 27.5 29.7 32.0 34.3 36.6 38.9 28.0 30.3 32.6 35.0 37.3 39.6 42.0 44.3 46.6

12.4 15.2 17.9 20.7 23.5 26.2 29.0 31.7 15.8 18.5 21.1 23.7 26.4 29.0 31.6 34.3 23.0 25.6 28.1 30.7 33.2 35.8 38.4 40.9 43.5 30.8 33.3 35.9 38.5 41.0 43.6 46.2 48.7 51.3

14.1 17.3 20.4 23.6 26.7 29.8 33.0 36.1 17.8 20.8 23.7 26.7 29.7 32.6 35.6 38.6 25.4 28.3 31.1 33.9 36.7 39.6 42.4 45.2 48.0 33.6 36.4 39.2 42.0 44.8 47.6 50.3 53.1 55.9

15.8 19.4 22.9 26.4 29.9 33.4 37.0 40.5 19.8 23.1 26.4 29.7 33.0 36.3 39.6 42.9 27.9 31.0 34.0 37.1 40.2 43.3 46.4 49.5 52.6 36.4 39.4 42.4 45.5 48.5 51.5 54.5 57.6 60.6

17.6 21.5 25.4 29.3 33.2 37.1 41.0 44.9 21.8 25.4 29.0 32.6 36.3 39.9 43.5 47.1 30.3 33.6 37.0 40.4 43.7 47.1 50.5 53.8 57.2 39.2 42.4 45.7 49.0 52.2 55.5 58.7 62.0 65.3

19.3 23.6 27.8 32.1 36.4 40.7 45.0 49.2 23.7 27.7 31.6 35.6 39.6 43.5 47.5 51.4 32.7 36.3 40.0 43.6 47.2 50.9 54.5 58.1 61.8 42.0 45.5 49.0 52.4 55.9 59.4 62.9 66.4 69.9

21.0 25.6 30.3 35.0 39.6 44.3 49.0 53.6 25.7 30.0 34.3 38.6 42.9 47.1 51.4 55.7 35.1 39.0 42.9 46.8 50.7 54.6 58.5 62.4 66.3 44.8 48.5 52.2 55.9 59.7 63.4 67.1 70.9 74.6

22.7 27.7 32.8 37.8 42.9 47.9 53.0 58.0 27.7 32.3 36.9 41.5 46.2 50.8 55.4 60.0 37.5 41.7 45.9 50.1 54.2 58.4 62.6 66.8 70.9 47.6 51.5 55.5 59.4 63.4 67.4 71.3 75.3 79.3

24.4 29.8 35.3 40.7 46.1 51.5 57.0 62.4 29.7 34.6 39.6 44.5 49.4 54.4 59.3 64.3 40.0 44.4 48.9 53.3 57.7 62.2 66.6 71.1 75.5 50.3 54.5 58.7 62.9 67.1 71.3 75.5 79.7 83.9

26.1 31.9 37.7 43.5 49.3 55.1 61.0 66.8 31.6 36.9 42.2 47.5 52.7 58.0 63.3 68.6 42.4 47.1 51.8 56.5 61.2 65.9 70.7 75.4 80.1 53.1 57.6 62.0 66.4 70.9 75.3 79.7 84.1 88.6

27.8 34.0 40.2 46.4 52.6 58.8 64.9 71.1 33.6 39.2 44.8 50.4 56.0 61.6 67.2 72.9 44.8 49.8 54.8 59.8 64.7 69.7 74.7 79.7 84.7 55.9 60.6 65.3 69.9 74.6 79.3 83.9 88.6 93.2

29.5 36.1 42.7 49.2 55.8 62.4 68.9 75.5 35.6 41.5 47.5 53.4 59.3 65.3 71.2 77.1 47.2 52.5 57.7 63.0 68.2 73.5 78.7 84.0 89.2 58.7 63.6 68.5 73.4 78.3 83.2 88.1 93.0 97.9

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

6–111

  6

DESIGN OF CONNECTIONS

CHAPTER 6

Design Aid 6.15.14 Concrete Tension Strength of Welded Headed-Stud Assemblies (cont.) CASE 3: Free edges on two opposite sides Applies to rectangular stud patterns with outside dimensions X and Y. See Fig. 6.5.2. If stud spacing is ≥ 3hef, single-stud capacity multiplied by number of studs may govern design. φNcb = φN'cb Ψed,N (φN'cb from Table A; Ψed,N from Table 6.5.4)

  6

Y

de1

de2

X

b = de1 + X + de2

Assumptions for Table A: φ = 0.7 (No confinement reinforcement – multiply Table A values by 0.75/0.7 when confinement reinforcement is used.) Ccrb = 1.0 (Uncracked concrete – multiply Table A values by 0.8 when concrete may be cracked.) Cbs = 3.33 (fc' / hef ) (Normalweight concrete – multiply Table A values by λ when lightweight concrete is used.) fc' = 5000 psi (Multiply Table A values by fc' / 5000 for other concrete strengths.) hef = Ls + tp – ths – 1/8 in. (for stud burnoff during welding.) tp (plate thickness) = 3/8 in. ths (stud-head thickness) = 3/8 in. Table A: φN c‘ b = φCbs(de1 + X + de2)(Y + 3hef)Ccrb

hef

b Y 0 2 4

3

6 8 10 12 14 0

2 4

4

6 8

10 12

14 0

2 4

6 6

8

10 12

14 16 0 2 4 6

8

8 10 12 14 16

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

1.7 2.1 2.5 2.9 3.2 3.6 4.0 4.4 2.0 2.3 2.6 3.0 3.3 3.6 4.0 4.3 2.4 2.7 3.0 3.2 3.5 3.8 4.0 4.3 4.6 2.8 3.0 3.3 3.5 3.7 4.0 4.2 4.4 4.7

3.4 4.2 4.9 5.7 6.5 7.2 8.0 8.8 4.0 4.6 5.3 5.9 6.6 7.3 7.9 8.6 4.8 5.4 5.9 6.5 7.0 7.5 8.1 8.6 9.2 5.6 6.1 6.5 7.0 7.5 7.9 8.4 8.9 9.3

5.1 6.3 7.4 8.6 9.7 10.8 12.0 13.1 5.9 6.9 7.9 8.9 9.9 10.9 11.9 12.9 7.3 8.1 8.9 9.7 10.5 11.3 12.1 12.9 13.7 8.4 9.1 9.8 10.5 11.2 11.9 12.6 13.3 14.0

6.9 8.4 9.9 11.4 12.9 14.5 16.0 17.5 7.9 9.2 10.5 11.9 13.2 14.5 15.8 17.1 9.7 10.8 11.8 12.9 14.0 15.1 16.1 17.2 18.3 11.2 12.1 13.1 14.0 14.9 15.9 16.8 17.7 18.6

8.6 10.5 12.4 14.3 16.2 18.1 20.0 21.9 9.9 11.5 13.2 14.8 16.5 18.1 19.8 21.4 12.1 13.5 14.8 16.1 17.5 18.8 20.2 21.5 22.9 14.0 15.2 16.3 17.5 18.6 19.8 21.0 22.1 23.3

10.3 12.6 14.8 17.1 19.4 21.7 24.0 26.3 11.9 13.8 15.8 17.8 19.8 21.8 23.7 25.7 14.5 16.1 17.8 19.4 21.0 22.6 24.2 25.8 27.5 16.8 18.2 19.6 21.0 22.4 23.8 25.2 26.6 28.0

12.0 14.7 17.3 20.0 22.6 25.3 28.0 30.6 13.8 16.2 18.5 20.8 23.1 25.4 27.7 30.0 17.0 18.8 20.7 22.6 24.5 26.4 28.3 30.1 32.0 19.6 21.2 22.8 24.5 26.1 27.7 29.4 31.0 32.6

13.7 16.7 19.8 22.8 25.9 28.9 32.0 35.0 15.8 18.5 21.1 23.7 26.4 29.0 31.6 34.3 19.4 21.5 23.7 25.8 28.0 30.1 32.3 34.5 36.6 22.4 24.2 26.1 28.0 29.8 31.7 33.6 35.4 37.3

15.4 18.8 22.3 25.7 29.1 32.5 36.0 39.4 17.8 20.8 23.7 26.7 29.7 32.6 35.6 38.6 21.8 24.2 26.6 29.1 31.5 33.9 36.3 38.8 41.2 25.2 27.3 29.4 31.5 33.6 35.7 37.8 39.9 42.0

17.1 20.9 24.7 28.5 32.4 36.2 40.0 43.8 19.8 23.1 26.4 29.7 33.0 36.3 39.6 42.9 24.2 26.9 29.6 32.3 35.0 37.7 40.4 43.1 45.8 28.0 30.3 32.6 35.0 37.3 39.6 42.0 44.3 46.6

18.8 23.0 27.2 31.4 35.6 39.8 44.0 48.2 21.8 25.4 29.0 32.6 36.3 39.9 43.5 47.1 26.6 29.6 32.6 35.5 38.5 41.5 44.4 47.4 50.3 30.8 33.3 35.9 38.5 41.0 43.6 46.2 48.7 51.3

20.6 25.1 29.7 34.3 38.8 43.4 48.0 52.5 23.7 27.7 31.6 35.6 39.6 43.5 47.5 51.4 29.1 32.3 35.5 38.8 42.0 45.2 48.4 51.7 54.9 33.6 36.4 39.2 42.0 44.8 47.6 50.3 53.1 55.9

22.3 27.2 32.2 37.1 42.1 47.0 52.0 56.9 25.7 30.0 34.3 38.6 42.9 47.1 51.4 55.7 31.5 35.0 38.5 42.0 45.5 49.0 52.5 56.0 59.5 36.4 39.4 42.4 45.5 48.5 51.5 54.5 57.6 60.6

24.0 29.3 34.6 40.0 45.3 50.6 56.0 61.3 27.7 32.3 36.9 41.5 46.2 50.8 55.4 60.0 33.9 37.7 41.5 45.2 49.0 52.8 56.5 60.3 64.1 39.2 42.4 45.7 49.0 52.2 55.5 58.7 62.0 65.3

25.7 31.4 37.1 42.8 48.5 54.2 60.0 65.7 29.7 34.6 39.6 44.5 49.4 54.4 59.3 64.3 36.3 40.4 44.4 48.4 52.5 56.5 60.6 64.6 68.6 42.0 45.5 49.0 52.4 55.9 59.4 62.9 66.4 69.9

For edge-distance modification factors, see Table 6.5.4

6–112

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS

CHAPTER 6

Design Aid 6.15.14 Concrete Tension Strength of Welded Headed-Stud Assemblies (cont.) CASE 4: Free edges on two adjacent sides Applies to rectangular stud patterns with outside dimensions X and Y. See Fig. 6.5.2. If stud spacing is ≥ 3hef, single-stud capacity multiplied by number of studs may govern design.

a = de3 + Y

φNcb = φN'cb Ψed,N (φN'cb from Table A; Ψed,N from Table 6.5.4)

Y

Assumptions for Table A: φ = 0  .7 (No confinement reinforcement – multiply Table A values by 0.75/0.7 when confinement reinforcement is used.) Ccrb = 1.0 (Uncracked concrete – multiply Table A values by 0.8 when concrete may be cracked.) Cbs = 3.33 (fc' / hef ) (Normalweight concrete – multiply Table A values by λ when lightweight concrete is used.) fc' = 5000 psi (Multiply Table A values by fc' / 5000 for other concrete strengths.) hef = Ls + tp – ths – 1/8 in. (for stud burnoff during welding.) tp (plate thickness) = 3/8 in. ths (stud-head thickness) = 3/8 in.

de3 de1

X

b = de1 + X

Table A: φN c‘ b = φCbs(de1 + X + 1.5hef)(Y + 1.5hef)Ccrb hef

3

4

6

8

b a 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

2.8 4.0 5.3 6.5 7.7 9.0 10.2 11.4 4.0 5.3 6.6 7.9 9.2 10.5 11.9 13.2 6.7 8.1 9.6 11.1 12.6 14.1 15.5 17.0 18.5 9.8 11.4 13.1 14.7 16.3 17.9 19.6 21.2 22.8

3.6 5.3 6.9 8.5 10.1 11.7 13.3 15.0 4.9 6.6 8.2 9.9 11.5 13.2 14.8 16.5 7.9 9.6 11.4 13.1 14.9 16.6 18.4 20.1 21.9 11.2 13.1 14.9 16.8 18.6 20.5 22.4 24.2 26.1

4.5 6.5 8.5 10.5 12.5 14.5 16.5 18.5 5.9 7.9 9.9 11.9 13.8 15.8 17.8 19.8 9.1 11.1 13.1 15.1 17.2 19.2 21.2 23.2 25.2 12.6 14.7 16.8 18.9 21.0 23.1 25.2 27.3 29.4

5.4 7.7 10.1 12.5 14.9 17.2 19.6 22.0 6.9 9.2 11.5 13.8 16.2 18.5 20.8 23.1 10.3 12.6 14.9 17.2 19.4 21.7 24.0 26.3 28.6 14.0 16.3 18.6 21.0 23.3 25.6 28.0 30.3 32.6

6.2 9.0 11.7 14.5 17.2 20.0 22.8 25.5 7.9 10.5 13.2 15.8 18.5 21.1 23.7 26.4 11.5 14.1 16.6 19.2 21.7 24.3 26.8 29.4 32.0 15.4 17.9 20.5 23.1 25.6 28.2 30.8 33.3 35.9

7.1 10.2 13.3 16.5 19.6 22.8 25.9 29.0 8.9 11.9 14.8 17.8 20.8 23.7 26.7 29.7 12.7 15.5 18.4 21.2 24.0 26.8 29.7 32.5 35.3 16.8 19.6 22.4 25.2 28.0 30.8 33.6 36.4 39.2

7.9 11.4 15.0 18.5 22.0 25.5 29.0 32.6 9.9 13.2 16.5 19.8 23.1 26.4 29.7 33.0 13.9 17.0 20.1 23.2 26.3 29.4 32.5 35.6 38.7 18.2 21.2 24.2 27.3 30.3 33.3 36.4 39.4 42.4

8.8 12.7 16.6 20.5 24.4 28.3 32.2 36.1 10.9 14.5 18.1 21.8 25.4 29.0 32.6 36.3 15.1 18.5 21.9 25.2 28.6 32.0 35.3 38.7 42.1 19.6 22.8 26.1 29.4 32.6 35.9 39.2 42.4 45.7

9.6 13.9 18.2 22.5 26.8 31.0 35.3 39.6 11.9 15.8 19.8 23.7 27.7 31.6 35.6 39.6 16.4 20.0 23.6 27.3 30.9 34.5 38.2 41.8 45.4 21.0 24.5 28.0 31.5 35.0 38.5 42.0 45.5 49.0

10.5 15.2 19.8 24.5 29.1 33.8 38.5 43.1 12.9 17.1 21.4 25.7 30.0 34.3 38.6 42.9 17.6 21.5 25.4 29.3 33.2 37.1 41.0 44.9 48.8 22.4 26.1 29.8 33.6 37.3 41.0 44.8 48.5 52.2

11.3 16.4 21.4 26.5 31.5 36.6 41.6 46.7 13.8 18.5 23.1 27.7 32.3 36.9 41.5 46.2 18.8 22.9 27.1 31.3 35.5 39.6 43.8 48.0 52.1 23.8 27.7 31.7 35.7 39.6 43.6 47.6 51.5 55.5

12.2 17.6 23.1 28.5 33.9 39.3 44.8 50.2 14.8 19.8 24.7 29.7 34.6 39.6 44.5 49.4 20.0 24.4 28.9 33.3 37.7 42.2 46.6 51.1 55.5 25.2 29.4 33.6 37.8 42.0 46.2 50.3 54.5 58.7

13.1 18.9 24.7 30.5 36.3 42.1 47.9 53.7 15.8 21.1 26.4 31.6 36.9 42.2 47.5 52.7 21.2 25.9 30.6 35.3 40.0 44.7 49.5 54.2 58.9 26.6 31.0 35.4 39.9 44.3 48.7 53.1 57.6 62.0

13.9 20.1 26.3 32.5 38.7 44.8 51.0 57.2 16.8 22.4 28.0 33.6 39.2 44.8 50.4 56.0 22.4 27.4 32.4 37.3 42.3 47.3 52.3 57.3 62.2 28.0 32.6 37.3 42.0 46.6 51.3 55.9 60.6 65.3

14.8 21.3 27.9 34.5 41.0 47.6 54.2 60.7 17.8 23.7 29.7 35.6 41.5 47.5 53.4 59.3 23.6 28.9 34.1 39.4 44.6 49.9 55.1 60.4 65.6 29.4 34.3 39.2 44.1 49.0 53.8 58.7 63.6 68.5

For edge-distance modification factors, see Table 6.5.4 PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

6–113

  6

DESIGN OF CONNECTIONS

CHAPTER 6

Design Aid 6.15.14 Concrete Tension Strength of Welded Headed Stud Assemblies (cont.) CASE 5: Free edges on three sides Applies to rectangular stud patterns with outside dimensions X and Y. See Fig. 6.5.2. If stud spacing is ≥ 3hef, single-stud capacity multiplied by number of studs may govern design.

a = de3 + Y

  6

φNcb = φN'cb Ψed,N (φN'cb from Table A; Ψed,N from Table 6.5.4)

Y

Assumptions for Table A: φ = 0.7 (No confinement reinforcement – multiply Table A values by 0.75/0.7 when confinement reinforcement is used.) Ccrb = 1.0 (Uncracked concrete – multiply Table A values by 0.8 when concrete may be cracked.) Cbs = 3.33 (fc' / hef ) (Normalweight concrete – multiply Table A values by λ when lightweight concrete is used.) fc' = 5000 psi (Multiply Table A values by fc' / 5000 for other concrete strengths.) hef = Ls + tp – ths – 1/8 in. (for stud burnoff during welding.) tp (plate thickness) = 3/8 in. ths (stud-head thickness) = 3/8 in.

de3 de1

X

de2

b = de1 + X + de2

Table A: φN c‘ b = φCbs(de1 + X + de2)(de3 + Y + 1.5hef)Ccrb hef

3

4

6

8

b a 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

0.9 1.2 1.6 2.0 2.4 2.8 3.1 3.5 1.0 1.3 1.6 2.0 2.3 2.6 3.0 3.3 1.2 1.5 1.7 2.0 2.3 2.6 2.8 3.1 3.4 1.4 1.6 1.9 2.1 2.3 2.6 2.8 3.0 3.3

1.7 2.5 3.2 4.0 4.8 5.5 6.3 7.0 2.0 2.6 3.3 4.0 4.6 5.3 5.9 6.6 2.4 3.0 3.5 4.0 4.6 5.1 5.7 6.2 6.7 2.8 3.3 3.7 4.2 4.7 5.1 5.6 6.1 6.5

2.6 3.7 4.9 6.0 7.1 8.3 9.4 10.6 3.0 4.0 4.9 5.9 6.9 7.9 8.9 9.9 3.6 4.4 5.2 6.1 6.9 7.7 8.5 9.3 10.1 4.2 4.9 5.6 6.3 7.0 7.7 8.4 9.1 9.8

3.4 4.9 6.5 8.0 9.5 11.0 12.6 14.1 4.0 5.3 6.6 7.9 9.2 10.5 11.9 13.2 4.8 5.9 7.0 8.1 9.2 10.2 11.3 12.4 13.5 5.6 6.5 7.5 8.4 9.3 10.3 11.2 12.1 13.1

4.3 6.2 8.1 10.0 11.9 13.8 15.7 17.6 4.9 6.6 8.2 9.9 11.5 13.2 14.8 16.5 6.1 7.4 8.7 10.1 11.4 12.8 14.1 15.5 16.8 7.0 8.2 9.3 10.5 11.7 12.8 14.0 15.2 16.3

5.1 7.4 9.7 12.0 14.3 16.6 18.8 21.1 5.9 7.9 9.9 11.9 13.8 15.8 17.8 19.8 7.3 8.9 10.5 12.1 13.7 15.3 17.0 18.6 20.2 8.4 9.8 11.2 12.6 14.0 15.4 16.8 18.2 19.6

6.0 8.7 11.3 14.0 16.7 19.3 22.0 24.6 6.9 9.2 11.5 13.8 16.2 18.5 20.8 23.1 8.5 10.4 12.2 14.1 16.0 17.9 19.8 21.7 23.6 9.8 11.4 13.1 14.7 16.3 17.9 19.6 21.2 22.8

6.9 9.9 12.9 16.0 19.0 22.1 25.1 28.2 7.9 10.5 13.2 15.8 18.5 21.1 23.7 26.4 9.7 11.8 14.0 16.1 18.3 20.5 22.6 24.8 26.9 11.2 13.1 14.9 16.8 18.6 20.5 22.4 24.2 26.1

7.7 11.1 14.6 18.0 21.4 24.8 28.3 31.7 8.9 11.9 14.8 17.8 20.8 23.7 26.7 29.7 10.9 13.3 15.7 18.2 20.6 23.0 25.4 27.9 30.3 12.6 14.7 16.8 18.9 21.0 23.1 25.2 27.3 29.4

8.6 12.4 16.2 20.0 23.8 27.6 31.4 35.2 9.9 13.2 16.5 19.8 23.1 26.4 29.7 33.0 12.1 14.8 17.5 20.2 22.9 25.6 28.3 31.0 33.6 14.0 16.3 18.6 21.0 23.3 25.6 28.0 30.3 32.6

9.4 13.6 17.8 22.0 26.2 30.4 34.5 38.7 10.9 14.5 18.1 21.8 25.4 29.0 32.6 36.3 13.3 16.3 19.2 22.2 25.2 28.1 31.1 34.0 37.0 15.4 17.9 20.5 23.1 25.6 28.2 30.8 33.3 35.9

10.3 14.8 19.4 24.0 28.5 33.1 37.7 42.3 11.9 15.8 19.8 23.7 27.7 31.6 35.6 39.6 14.5 17.8 21.0 24.2 27.5 30.7 33.9 37.1 40.4 16.8 19.6 22.4 25.2 28.0 30.8 33.6 36.4 39.2

11.1 16.1 21.0 26.0 30.9 35.9 40.8 45.8 12.9 17.1 21.4 25.7 30.0 34.3 38.6 42.9 15.7 19.2 22.7 26.2 29.7 33.2 36.7 40.2 43.7 18.2 21.2 24.2 27.3 30.3 33.3 36.4 39.4 42.4

12.0 17.3 22.6 28.0 33.3 38.6 44.0 49.3 13.8 18.5 23.1 27.7 32.3 36.9 41.5 46.2 17.0 20.7 24.5 28.3 32.0 35.8 39.6 43.3 47.1 19.6 22.8 26.1 29.4 32.6 35.9 39.2 42.4 45.7

12.8 18.6 24.3 30.0 35.7 41.4 47.1 52.8 14.8 19.8 24.7 29.7 34.6 39.6 44.5 49.4 18.2 22.2 26.2 30.3 34.3 38.4 42.4 46.4 50.5 21.0 24.5 28.0 31.5 35.0 38.5 42.0 45.5 49.0

For edge-distance modification factors, see Table 6.5.4

6–114

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

DESIGN OF CONNECTIONS

CHAPTER 6

Design Aid 6.15.14 Concrete Tension Strength of Welded Headed-Stud Assemblies (cont.) CASE 6: Free edges on four sides Applies to rectangular stud patterns with outside dimensions X and Y. See Fig. 6.5.2. If stud spacing is ≥ 3hef, single-stud capacity multiplied by number of studs may govern design.

a = de3 + Y + de4 de4

φNcb = φN'cb Ψed,N (φN'cb from Table A; Ψed,N from Table 6.5.4)

Y de3 de1

de2

X

  6

Assumptions for Table A: φ = 0.7 (No confinement reinforcement – multiply Table A values by 0.75/0.7 when confinement reinforcement is used.) Ccrb = 1.0 (Uncracked concrete – multiply Table A values by 0.8 when concrete may be cracked.) Cbs = 3.33 (fc' / hef ) (Normalweight concrete – multiply Table A values by λ when lightweight concrete is used.) fc' = 5  000 psi (multiply Table A values by fc' / 5000 for other concrete strengths.) hef = Ls + tp – ths – 1/8 in. (for stud burnoff during welding.) tp (plate thickness) = 3/8 in. ths (stud-head thickness) = 3/8 in.

b = de1 + X + de2

Table A: φN c‘ b = φCbs(de1 + X + de2)(de3 + Y + de4)Ccrb hef

3

4

6

8

b a 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

0.0 0.4 0.8 1.1 1.5 1.9 2.3 2.7 0.0 0.3 0.7 1.0 1.3 1.6 2.0 2.3 0.0 0.3 0.5 0.8 1.1 1.3 1.6 1.9 2.2 0.0 0.2 0.5 0.7 0.9 1.2 1.4 1.6 1.9

0.0 0.8 1.5 2.3 3.0 3.8 4.6 5.3 0.0 0.7 1.3 2.0 2.6 3.3 4.0 4.6 0.0 0.5 1.1 1.6 2.2 2.7 3.2 3.8 4.3 0.0 0.5 0.9 1.4 1.9 2.3 2.8 3.3 3.7

0.0 1.1 2.3 3.4 4.6 5.7 6.9 8.0 0.0 1.0 2.0 3.0 4.0 4.9 5.9 6.9 0.0 0.8 1.6 2.4 3.2 4.0 4.8 5.7 6.5 0.0 0.7 1.4 2.1 2.8 3.5 4.2 4.9 5.6

0.0 1.5 3.0 4.6 6.1 7.6 9.1 10.7 0.0 1.3 2.6 4.0 5.3 6.6 7.9 9.2 0.0 1.1 2.2 3.2 4.3 5.4 6.5 7.5 8.6 0.0 0.9 1.9 2.8 3.7 4.7 5.6 6.5 7.5

0.0 1.9 3.8 5.7 7.6 9.5 11.4 13.3 0.0 1.6 3.3 4.9 6.6 8.2 9.9 11.5 0.0 1.3 2.7 4.0 5.4 6.7 8.1 9.4 10.8 0.0 1.2 2.3 3.5 4.7 5.8 7.0 8.2 9.3

0.0 2.3 4.6 6.9 9.1 11.4 13.7 16.0 0.0 2.0 4.0 5.9 7.9 9.9 11.9 13.8 0.0 1.6 3.2 4.8 6.5 8.1 9.7 11.3 12.9 0.0 1.4 2.8 4.2 5.6 7.0 8.4 9.8 11.2

0.0 2.7 5.3 8.0 10.7 13.3 16.0 18.7 0.0 2.3 4.6 6.9 9.2 11.5 13.8 16.2 0.0 1.9 3.8 5.7 7.5 9.4 11.3 13.2 15.1 0.0 1.6 3.3 4.9 6.5 8.2 9.8 11.4 13.1

0.0 3.0 6.1 9.1 12.2 15.2 18.3 21.3 0.0 2.6 5.3 7.9 10.5 13.2 15.8 18.5 0.0 2.2 4.3 6.5 8.6 10.8 12.9 15.1 17.2 0.0 1.9 3.7 5.6 7.5 9.3 11.2 13.1 14.9

0.0 3.4 6.9 10.3 13.7 17.1 20.6 24.0 0.0 3.0 5.9 8.9 11.9 14.8 17.8 20.8 0.0 2.4 4.8 7.3 9.7 12.1 14.5 17.0 19.4 0.0 2.1 4.2 6.3 8.4 10.5 12.6 14.7 16.8

0.0 3.8 7.6 11.4 15.2 19.0 22.8 26.6 0.0 3.3 6.6 9.9 13.2 16.5 19.8 23.1 0.0 2.7 5.4 8.1 10.8 13.5 16.1 18.8 21.5 0.0 2.3 4.7 7.0 9.3 11.7 14.0 16.3 18.6

0.0 4.2 8.4 12.6 16.7 20.9 25.1 29.3 0.0 3.6 7.3 10.9 14.5 18.1 21.8 25.4 0.0 3.0 5.9 8.9 11.8 14.8 17.8 20.7 23.7 0.0 2.6 5.1 7.7 10.3 12.8 15.4 17.9 20.5

0.0 4.6 9.1 13.7 18.3 22.8 27.4 32.0 0.0 4.0 7.9 11.9 15.8 19.8 23.7 27.7 0.0 3.2 6.5 9.7 12.9 16.1 19.4 22.6 25.8 0.0 2.8 5.6 8.4 11.2 14.0 16.8 19.6 22.4

0.0 4.9 9.9 14.8 19.8 24.7 29.7 34.6 0.0 4.3 8.6 12.9 17.1 21.4 25.7 30.0 0.0 3.5 7.0 10.5 14.0 17.5 21.0 24.5 28.0 0.0 3.0 6.1 9.1 12.1 15.2 18.2 21.2 24.2

0.0 5.3 10.7 16.0 21.3 26.6 32.0 37.3 0.0 4.6 9.2 13.8 18.5 23.1 27.7 32.3 0.0 3.8 7.5 11.3 15.1 18.8 22.6 26.4 30.1 0.0 3.3 6.5 9.8 13.1 16.3 19.6 22.8 26.1

0.0 5.7 11.4 17.1 22.8 28.5 34.3 40.0 0.0 4.9 9.9 14.8 19.8 24.7 29.7 34.6 0.0 4.0 8.1 12.1 16.1 20.2 24.2 28.3 32.3 0.0 3.5 7.0 10.5 14.0 17.5 21.0 24.5 28.0

For edge-distance modification factors, see Table 6.5.4 PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

6–115

DESIGN OF CONNECTIONS

CHAPTER 6

  6

6–116

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

STRUCTURAL CONSIDERATIONS FOR ARCHITECTURAL PRECAST CONCRETE

CHAPTER 7

CHAPTER 7 STRUCTURAL CONSIDERATIONS FOR ARCHITECTURAL PRECAST CONCRETE 7.1

  7

Introduction.................................................................................................................................................................7-3

7.2 Types and Functions of Architectural Precast Concrete Components........................................................................7-3 7.2.1 Non-Load-Bearing Components...................................................................................................................7-3 7.2.1.1 Spandrels.........................................................................................................................................7-3 7.2.1.2 Column Covers and Mullions.........................................................................................................7-4 7.2.1.3 Window Panels...............................................................................................................................7-5 7.2.1.4 Wall Panels.....................................................................................................................................7-6 7.2.2 Load-Bearing Components...........................................................................................................................7-6 7.2.2.1 Spandrels.........................................................................................................................................7-6 7.2.2.2 Window Panels...............................................................................................................................7-6 7.2.2.3 Wall Panels.....................................................................................................................................7-7 7.3 Structural Design Considerations................................................................................................................................7-7 7.3.1 Design Loads.................................................................................................................................................7-7 7.3.1.1 Volume Changes.............................................................................................................................7-7 7.3.2 Support Deflections and Building Movements.............................................................................................7-7 7.3.3 Handling, Transporting, and Erecting.........................................................................................................7-11 7.3.4 Tolerances ...................................................................................................................................................7-11 7.3.5 Crack Control..............................................................................................................................................7-12 7.3.6 Reinforcement.............................................................................................................................................7-12 7.3.6.1 Welded-Wire Reinforcement........................................................................................................7-12 7.3.6.2 Reinforcing Bars...........................................................................................................................7-13 7.3.6.3 Prestressing...................................................................................................................................7-13 7.3.7 Stacking Non-Load-Bearing Panels............................................................................................................7-13 7.3.8 Shims...........................................................................................................................................................7-14 7.4

Connections...............................................................................................................................................................7-14 7.4.1 General  ......................................................................................................................................................7-14 7.4.2 Design Considerations................................................................................................................................7-14

7.5

Architectural Cladding Component Analysis . .........................................................................................................7-15 7.5.1 Wind Loads, ASCE 7-05 Method 1............................................................................................................7-15 7.5.2 Wind Loads, ASCE 7-05 Method 2............................................................................................................7-20 7.5.3 Seismic Loads.............................................................................................................................................7-20

7.6 Veneered Panels .......................................................................................................................................................7-20 7.6.1 General .......................................................................................................................................................7-20 7.6.2 Clay Product–Faced Precast Concrete........................................................................................................7-30 7.6.2.1 General Considerations.................................................................................................................7-30 7.6.2.2 Clay-Product Properties................................................................................................................7-30 7.6.2.3 Clay-Product Selection.................................................................................................................7-30 7.6.2.4 Design Considerations..................................................................................................................7-30 7.6.2.5 Other Considerations....................................................................................................................7-31 7.6.3 Stone Veneer–Faced Precast Concrete.......................................................................................................7-32 7.6.3.1 General Considerations.................................................................................................................7-32 7.6.3.2 Stone Properties............................................................................................................................7-32 7.6.3.3 Stone Sizes....................................................................................................................................7-33 PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

7–1

CHAPTER 7

STRUCTURAL CONSIDERATIONS FOR ARCHITECTURAL PRECAST CONCRETE 7.6.3.4 Design Considerations..................................................................................................................7-33 7.6.3.5 Anchorage of Stone Facing..........................................................................................................7-33 7.6.3.6 Veneer Jointing.............................................................................................................................7-35

7.7

Precast Concrete Used as Forms...............................................................................................................................7-35

7.8

References.................................................................................................................................................................7-36

7–2

First Printing/CD-ROM Edition

  7

PCI DESIGN HANDBOOK/SEVENTH EDITION

STRUCTURAL CONSIDERATIONS FOR ARCHITECTURAL PRECAST CONCRETE

7.1

Introduction

Architectural precast concrete refers to any precast concrete unit of special (or occasionally standard) shape that, through application of finish, color, and texture, contributes to the architectural form and finished effect of the structure. Components may be part of the structural building frame carrying gravity, wind, seismic, or other loads; non-structural cladding; or small, decorative accent units. They may be conventionally reinforced, prestressed, or a combination of both. The successful design of architectural precast concrete requires a thorough knowledge of the product. The designer must be aware of the types and functions of the wide variety of products used in architectural precast concrete and understand production and erection procedures. In most cases, the reinforcing and connections will be designed by either a precast plant engineer employed by the manufacturer or by a precast concrete specialty engineer (these terms are used synonymously in this chapter) retained by the precast concrete manufacturer. The building frame is usually the responsibility of the Structural Engineer of Record. The primary purpose of this chapter is to provide a brief discussion of the major aspects of architectural precast concrete structural design for the benefit of the architect and the Structural Engineer of Record. Close cooperation between them, the precast engineer, and the contractor is vital for a successful cladding system. Communication should be kept open at all times. For additional information, the user of this handbook should refer to Reference 1, which provides significantly more information on the uses and design considerations of architectural precast concrete.

CHAPTER 7

7.2

Types and Functions of Architectural Precast Concrete Components

7.2.1

Non-Load-Bearing Components

Non-load-bearing (cladding) components are those precast concrete units that transfer negligible gravity load from other parts of the structure. They are designed to resist wind, seismic forces from their self-weight, blast, and forces required to transfer the component weight to the support structure. Forces generated during manufacturing and erection will often govern the design of the architectural component. Wind may control in areas where design wind loads are high, such as hurricane regions, building corner zones, or panels adjacent to large openings. Earthquake forces usually control in areas of high seismicity. 7.2.1.1 Spandrels Non-load-bearing spandrels are precast concrete components less than one story high, and are typically an individual unit extending between columns. Support for the spandrel weight may be provided by either the floor or the columns, and stability against eccentric gravity loading is usually achieved by lateral tieback connections to the floor or to the column (Fig. 7.2.1). When spandrels are part of a window wall, consideration should be given to the effect of deflections and rotations of the spandrel on the windows. Since spandrels are generally designed to remain uncracked under service loads, stress calculations should be based on the gross uncracked concrete section. For one-piece spandrels

Wind or seismic pressure/ suction from window Window Tieback force Spandrel weight Wind or seismic pressure/ suction on spandrel

Spandrel weight

Tieback force

Spandrel weight

Tieback force Spandrel support

Tieback force

Tieback force

Spandrel support

Spandrel support Tieback force

Tieback force Wind or seismic pressure/ suction from window Floor connection

Column connection

Roof connection

Fig. 7.2.1 Forces on a spandrel panel. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

7–3

  7

STRUCTURAL CONSIDERATIONS FOR ARCHITECTURAL PRECAST CONCRETE

CHAPTER 7

Support member

  7

Kicker to prevent beam rotation

Bracing support (a)

Structural support members

(b) Fig. 7.2.2 Auxiliary strut support.

that extend between columns, it is preferable that the gravity supports be located near the ends of the panel. This will allow the gravity loads to be transferred to stiff columns and avoid potential rotation and deflection of the support structure. Column sections are generally very stiff vertically, resulting in minimal deformations, and can be readily designed to resist the eccentricity of the panel weight. While structural steel frames tend to have good dimensional control, rotation and deflection of the steel support beams can be more severe than in concrete framing, and should be considered by the Structural Engineer of Record. The flexural and torsional flexibility of the steel framing must be considered when determining the location of gravity and tieback connections. When spandrels must be supported on edge beams, it is generally not practical to extend the spandrel gravity connections to the beam centerline. The large eccentricity that is created results in high flexural stresses in the spandrel and large connections that are often difficult to conceal. It is preferable to cantilever a slab or steel bracket from the side of the beam to allow gravity support close to the back of the spandrel (Fig. 7.2.2[a]). This can cause torsion in the support beam that must be recognized from both a strength and stiffness perspective. Similarly, when tieback connections are made to the underside of a steel beam, the Structural Engineer of Record, who is typically the designer of the support system, should make provisions for torsional 7–4

loading by specifying heavier members, braces, or an intersecting beam. Tiebacks to columns may require that horizontal stiffeners be added to the columns to resist local bending. The Structural Engineer of Record needs to understand the influence of localized tieback connections so stiffeners can be detailed and supplied with the structural steel. The Structural Engineer of Record should clearly specify connection points when flexibility is a concern. Otherwise, the precast concrete engineer may assume that the structure has sufficient rigidity to allow spandrels to be erected without subsequent realignment and allow deformations to be limited to those specified for the spandrels only. Connections may be detailed to allow for final adjustment after initial erection. However, if this is not possible and they must be designed and detailed to be set and aligned without returning for later adjustment, one way to deal with this condition is to use a support scheme that does not rely on slab cantilever action, such as that shown in Fig. 7.2.2(b). The auxiliary strut supports shown in the figure, which should be designed by the Structural Engineer of Record as part of the support structure, are normally supplied and erected by the structural steel or miscellaneous metals subcontractor prior to precast concrete erection. Since the contract bid documents (contract drawings and specifications) are the first line of communication between the Structural Engineer of Record and the precast concrete engineer, it is imperative that the documents clearly indicate the connection concept. For example, if spandrel loads are to be resisted by the columns rather than the floor beams, it must be indicated on the contract documents. This intent can be shown schematically and further described in applicable notes. Also, the division of responsibilities for providing and installing miscellaneous items such as steel used to stabilize the structural members that support precast concrete components must be clearly indicated in the contract bid documents. 7.2.1.2 Column Covers and Mullions The use of precast concrete panels as covers over steel or concrete columns and beams and as mullions is a common method of achieving architectural expression, special shapes, or added fire endurance. Column covers are usually supported by the structural column or the floor, and are themselves designed to transfer no vertical load other than their own weight unless a stacked panel system is used, as described in Section 7.3.7. The vertical load of each length of column-cover section is usually supported at one elevation and tied back at the top and bottom for lateral-load transfer and stability. In order to minimize erection costs and horizontal joints, it is desirable to make the column cover as long as possible, subject to limitations imposed by weight, handling, and story drift. Mullions are vertical elements serving to separate glass areas. They generally resist only wind loads applied from the adjacent glass and must be stiff enough to maintain deflections within the limitations imposed by the window manufacturer. Since mullions are often thin, they are sometimes prestressed to prevent cracking.

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STRUCTURAL CONSIDERATIONS FOR ARCHITECTURAL PRECAST CONCRETE Column covers and mullions are usually major focal points in a structure, and aesthetic success requires careful thought be given to all facets of design and erection. The following are some items that should be considered. 1. Because column covers and mullions are often isolated elements forming a long vertical line, any variation from plumb is readily observable. This variation is usually the result of the tolerances allowed in the structural frame. To some degree, these variations can be handled by precast concrete connections that provide adjustability. The designer should plan adequate clearance between the component and the structure. For steel columns, the designer should also consider clearances around splice plates and projecting bolts. 2. Gravity support should be provided by two bearing points (or one for narrow precast concrete components such as vertical mullions) at only one elevation and connections provided at additional locations for lateral loads and stability. For long column covers or mullions, consider providing an intermediate connection for lateral support and restraint of bowing. 3. Column covers and mullions that project from the facade will be subjected to shearing wind loads. While very rarely a governing factor, the connection design must account for these loads. 4. Components that are exposed to the environment will be subjected to temperature and humidity change. Horizontal joints between abutting precast concrete column covers and mullions should be wide enough and connections ductile enough to permit length changes and rotation from temperature gradients. The behavior of thin, flexible components can be improved by prestressing. 5. Due to vertical loads and the effects of creep and shrinkage in concrete columns, structural columns will tend to shorten in tall buildings. The width of the horizontal joint between abutting precast concrete covers should be sufficient to accommodate this shortening. 6. The designer must consider the erection process. Column cover and mullion connections are often difficult to reach and, once made, difficult to adjust. This difficulty of access is compounded when column covers must be erected around all four sides of a column. Sometimes this condition can be solved by welding the lower piece to the column and anchoring the upper piece to the lower piece with dowels or through a mechanical device that does not require access.

Opening (typical)

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(a) Truss-type panel

(b) Channel-type panel

(c) Window mullion panel

Fig. 7.2.3 Horizontal and vertical window panels.

Fig. 7.2.4 Cracking due to restrained bowing.

7.2.1.3 Window Panels Window panels are usually one-bay long and one-floor high with large single or multiple openings for windows (Fig. 7.2.3). Non-load-bearing panels that contain openings may develop stress concentrations at these openings, resulting from unintended loading or restrained bowing. Hairline cracks radiating from the corners can result (Fig. 7.2.4). While these stress concentrations may be partially resisted by reinforcement, the designer should consider methods that

CHAPTER 7

Flexure of beam

Floor load imposed due to unintended restraint unless slotted connection is used to allow vertical movement

Fig. 7.2.5 Unanticipated loading on a non-load-bearing panel.

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eliminate imposed restraints. Areas of abrupt change in cross section should be reinforced and should be rounded or chamfered whenever possible. If adequate clearance is not provided between the precast concrete panels and the support structure, or if the connections do not allow for unrestrained movement, loads from adjacent floors can be imposed on non-load-bearing panels (Fig. 7.2.5). These loads can cause excessive stresses at the beam portion of an opening. A method of preventing load transfer, such as slotted holes in connection hardware, must be developed and permanently maintained. 7.2.1.4 Wall Panels Wall panels may be strictly cladding (non-load-bearing) or may be used as load-bearing panels or shear walls as part of the lateral-force-resisting system. In-place stresses are seldom a problem for cladding panels. The panel cross section is generally chosen for architectural or aesthetic reasons. A panel that is too thin may bow or deflect excessively, creat-

Window

Spandrel Weight Cast-in-place topping e

W Precast concrete floor

Window

Window

Spandrel Weight Cast-in-place topping

Precast concrete floor

Window

Fig. 7.2.6 Load-bearing spandrel.

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7.2.2

Load-Bearing Components

Load-bearing components may support roof or floor loads and may be oriented either horizontally or vertically. Horizontal units are designed as beams with proper consideration given to cracking and strength design for all loading conditions. Design of vertical panels is similar to columns. Because of the large height-to-thickness ratios and the magnitude and eccentricity of the loads, the out-of-plane stresses may be significant. 7.2.2.1 Spandrels Load-bearing spandrels are panels that span horizontally between columns and support floor or roof loads. Loadbearing spandrels support gravity loads that are often applied eccentrically with respect to the support. A typical arrangement of spandrel and supported floor is shown in Fig. 7.2.6. Rotation due to eccentricity is usually resisted by a horizontal couple developed in the floor system or by connections to suppporting columns. In order to prevent rotation, the details must provide for a compressive force transfer at the top of the floor and a tensile force transfer at the bearing of the precast concrete floor component. The load path of these floor forces must be followed through the structure and considered in the design of other members in the building. Because of stresses that may develop due to restraint of volumetric changes, tensile connections at the bottom of both ends of a floor component should not be used. Even when torsion is resisted by a couple in the floor components in the completed structure, twisting of the spandrel after erection and prior to completion of connections must be considered. If torsion cannot be accommodated by floor connections, the spandrel panel should be designed for induced stresses. See Chapter 5 for torsion design. While adding unnecessary tiebacks is not advisable due to the resulting build-up of restraint forces, many precasters will choose to provide additional tieback connections along the length of a spandrel to prevent cracking under anticipated eccentric gravity loads and lateral loads. 7.2.2.2 Window Panels

W e

ing joint-sealant difficulties at the building corners. Whether cladding, load-bearing walls, or shear walls, the design of connections is critical, and care should be taken to account for all forces that are generated by lateral loads, eccentricity of weight, thermal bowing, and volumetric changes. All non-load-bearing panels should be designed to accommodate movement freely and, with no redundant supports, to restrain bowing, except where necessary.

Most of the items addressed in the previous section must also be considered in the analysis of load-bearing window panels. Panels may be designed to span horizontally between columns or vertically between floors. When spanning horizontally, they are designed as beams, or as Vierendeel trusses if they have frequent, regularly spaced window openings (Fig. 7.2.3[a]). When designed as beams, there must be a horizontal joint between panels to ensure that they will not transfer loads to the panels below.

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STRUCTURAL CONSIDERATIONS FOR ARCHITECTURAL PRECAST CONCRETE If a large portion of a panel is an opening, as in Fig. 7.2.3(c), it may be necessary to analyze it as a rigid frame. Figures 7.2.3 (b) and (c) show architectural concrete wall panels generally designed with relatively short vertical spans, although they may sometimes span continuously over two floors if connections are located and designed properly. They are usually custom-made for each project and reinforced with non-prestressed reinforcement. Standard flat, hollowcore, and stemmed components are also used as wall panels and are frequently prestressed. When stemmed floor or roof components are used, the width of the load-bearing walls should be selected in multiples of the width of the floor or roof component being supported. As an example, if the floor componets are 10 ft wide, the walls should be 10 ft, 20 ft, or 30 ft wide. Regional precast concrete manufacturers should be contacted for their recommended modules. 7.2.2.3 Wall Panels When the panels are placed vertically, they are usually designed similar to the columns illustrated in Chapter 5, with slenderness effects considered. Because of the large heightto-thickness ratios commonly used, a second-order analysis (P-Delta) may be required for load-bearing walls. Since the deflections associated with a cracked panel are generally unacceptable, the panels are usually designed to remain uncracked. This may require prestressing of the panels. Dimensions of architectural concrete panels are usually selected based on a desired appearance. When these panels are also used to carry superimposed gravity loads or to act as shear walls, it is important to receive input from the engineering team in the preliminary stages of the project.

7.3

Structural Design Considerations

7.3.1

Design Loads

The forces that must be considered in the design of architectural precast concrete components include: 1. Those caused by the precast concrete component itself. 2. Loads during handling and erection. 3. Externally applied loads, such as wind, earthquake, blast, car impact forces, snow, roof and floor dead and live loads, soil or fluid pressure, or construction loads. These loads should be shown on the contract drawings. 4. Loads resulting from restraint of volume-change or support-system movement. These loads are generally concentrated at the connections. 5. Loads from adjacent materials such as windows, doors, signage, and the like. The designer should provide simple load paths through the connections and ductility within the connections. This will reduce the sensitivity of the connection and the necessity to precisely calculate loads and forces from, for example, restraint of volume changes and frame distortions. The num-

CHAPTER 7

ber of load transfer points should be kept to a practical minimum. A precast concrete component should have no more than two connections per panel used to resist gravity loads. 7.3.1.1 Volume Changes Volume changes of precast concrete are caused by creep, shrinkage, and variations in temperature. If precast concrete components are free to move or deform, volume changes are typically of little consequence. If bowing is restrained by attachment to the foundation or frame, stresses causing cracking may develop. Since the time between casting and final connection of precast concrete components is usually over 30 days, much of the creep due to prestressing and shrinkage will have disappated prior to erection. Temperature. The coefficient of thermal expansion of concrete varies with the aggregate. Ranges for normalweight concrete are 5 to 7 × 10-6 in./in./°F when made with siliceous aggregate and 3.5 to 5 × 10-6 in./in./°F when made with calcareous aggregate. Since the thermal coefficient for steel is approximately 6 × 10-6 in./in./°F, the addition of steel reinforcement does not significantly affect the concrete coefficient. Different temperatures on the interior and exterior of the building will cause the panel to bow. This bowing can be resisted by intermediate connections, but this creates stresses in the panel that should be considered (see Chapter 5, Section 5.8.5). Shrinkage. Precast concrete components are subject to airdrying as soon as they are cast. During exposure to the atmosphere, the concrete slowly loses some of its original water, causing shrinkage to occur. About 40% of the drying shrinkage occurs by an age of 30 days and about 60% occurs by an age of 90 days. During the first year, total unit-length change due to drying shrinkage of normalweight concrete typically ranges from about 4.0 to 6.5 × 10-6 in./in. when exposed to air at 50% relative humidity. Differential shrinkage or expansion between panels with face mixtures and/or material (brick, tile) prone to shrinkage or expansion must be carefully evaluated to avoid excessive bowing (see Section 7.6). Creep. When concrete is subjected to a sustained compressive load, the deformation may be divided into two parts: an elastic deformation that occurs immediately and a creep deformation that begins immediately and continues over time. For design, it is convenient to refer to specific creep, which is defined as the creep strain per unit of sustained stress. The specific creep of architectural precast concrete panels made with normalweight aggregates per unit stress (psi) can range from 0.5 to 1.0 × 10-6 in./in./psi. About 40% of the creep occurs within 30 days of load application and about 60% occurs within 90 days. Creep in architectural precast concrete components can be caused by prestressing or applied sustained load, as in the case of load-bearing panels. 7.3.2

 upport Deflections and Building S Movements

All components should be designed to accommodate movement with no redundant supports, except where necessary to restrain bowing or control stresses. Relatively simple analyses provide the forces required for connection design.

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Single panel

Separate panels

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Deflected position of supporting member due to weight of panels

Fig. 7.3.1 Deformation of panels on flexible beam.

Window Spandrel rotation Possible support rotation Cantilever deflection (elastic plus creep) Beam or slab Window

Fig. 7.3.2 Effect of cantilever supports.

Elevation

Elevation

(a) In-plane translation

(b) In-plane rotation

Section

Section

(c) Out-of-plane rotation

(d) Out-of-plane translation

Fig. 7.3.3 Modes of panel response to displacement.

7–8

The responsible designer can use the simplified methods discussed in Chapter 5 or computer analysis programs. When redundant supports are necessary or when movement is to be resisted, the load-deformation characteristics of the component, connections, and support system should be taken into account. The weight of a series of wall panels supported on a flexible beam will cause deflection (or rotation) of the beam (Fig. 7.3.1). To prevent imposing loads on the panel, the connections must be designed and installed to permit these deformations to freely occur. In addition, the Engineer of Record should design sufficient stiffness in the edge beam so that specified tolerances can be attained without having to reset or realign the panels. It is imperative that close coordination among the engineer responsible for the design of the support structure, the precast concrete provider, and the erector occurs throughout the shop drawing and construction planning of the precast concrete components to ensure that the anticipated behavior of the structure is understood and the desired alignment of the components is attained. The ramifications of not doing so may result in a condition as depicted in Fig. 7.3.1. Because of the difficulty in detailing these connections and the difficulty of erecting panels on a flexible support, it is generally preferable to provide spandrels that span from column to column. Consideration should also be given to spandrels that are supported at the ends of long cantilevers. The Engineer of Record must determine the effect of deflection and rotation of the support, including the effects of creep, arrange the details of all attachments, and provide adequate stiffness to accommodate this condition (Fig.7.3.2). A particularly critical condition can occur at the corners of a building, especially when there is a cantilever on both faces adjacent to the corner. Deflection of cantilever support systems may cause misalignment and out-of-tolerances jointing to occur. Refer to Chapter 13 of this handbook for more information about tolerance. Architectural precast concrete panels can be used as shear walls to provide all or a portion of the lateral stability of a structure, regardless of the type of structure. The Structural Engineer of Record should provide the required design forces on the contract drawings. If the structure includes architectural precast concrete panels that could act as shear walls, but are not intended to do so, the connections must be designed so that unintended forces do not transfer to the panels. The interdependency of panel behavior and the supporting frame must be understood, particularly in areas where seismic activity is likely. The way cladding panels behave in response to displacement of the supporting structure is illustrated in Fig. 7.3.3. In-plane translation occurs when the panel is fixed in-plane to one level. The panel translates laterally with that level, remaining vertical in elevation. Spandrel panels and wall panels are typically designed to behave this way. In-plane rotation (rocking) occurs when the panel is supported in-plane at two levels. When the structure displaces, the lateral connections drag the panel laterally, causing it to rotate in-plane. This rotation requires bearing connections that allow lift-off. Narrow components such as column covers are sometimes designed this way.

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CHAPTER 7 ∆d

Seismic joint

  7 Out-of-plane rotation

Out-of-plane rotation

∆d = Design Interstory Drift

Fig. 7.3.4 Corner joint under drift condition.

Out-of-plane rotation is the tilting of a panel perpendicular to its face. This motion is common whenever a panel is connected to the structure at different levels. The tieback connections that support the panel for wind and seismic loads will also cause the panel to tilt out-of-plane during story drift. Bearing connections should be designed to accommodate out-of-plane rotations when panels behave this way. Panel geometry and joints must be configured so that

panels do not collide with one another or with the supporting structure during a seismic event. When collisions occur, possible overloading of the connections may result. A common way to avoid collisions is to increase the joint width, positioning adjacent panels beyond the limit of movement. A common condition is shown in Fig. 7.3.4 where wall panels form a corner. At this location, one panel will rotate while the other remains vertical, resulting in the joints closing. To

Deflected position of grid

Spandrel panel in translated position

Column lines

Seismic reaction

Seismic reactions

Floor level

✖ ✖

✖

Seismic force

C.G.

✖

C.G.

✖

Seismic force

✖

Window ✖

✖

Floor level ✖

Seismic reactions

✖

Spandrel panel (a) Wall panels Note: Gravity and out-of-plane loads to connectors not shown; C.G. = center of gravity

(b) Spandrel panels Bearing connection

✖ Tie-back connection

Allowed movement direction

Fig. 7.3.5 Cladding panel connection concepts–seismic drift effect (translating panels). PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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b)

Grid

a)

Grid

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Floor

Floor

✖

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Relative lateral movement

Rotated position

✖

Initial position Seismic load

✖

Seismic reaction

✖

Gravity reaction Floor

Gravity load Gravity reaction Gravity reaction Floor

Floor

Bearing connection

Seismic reactions Gravity load ✖

✖

Tie-back connection

Seismic reactions

Section A

▼ Bearing connection ✖ Tie-back connection

Section A

Note: All connectors carry out of plane loads; gravity and out-of-plane loads to connectors not shown.

Fig. 7.3.6 Tall/narrow units subjected to drift.

avoid a collision, this joint should be increased to accommodate the expected drift. When a panel is subjected to an in-plane horizontal force, its connection system can make the panel rock up on one corner or translate without tipping or rocking (Fig. 7.3.5). It is essential that the potential movements be studied and coordinated with regard to the connection system and the joint

2. Rotation to vertical transfer to storage

1. Strip

3. Storage in yard

4. Transport to site

Fig. 7.3.7 Optimum concrete units.

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handling

sequence

5. Erected on building

of

precast

locations and widths. Such considerations may govern the connection design or the wall’s joint locations and widths. The connection system determines panel movement in a seismic event. In the case of floor-to-floor wall panels (Fig. 7.3.6[a]), the upper tiebacks become isolation connections, preventing the building movement forces from being transmitted to the panel. The panel is rigidly fixed to and translates with the floor beam at the bottom of the panel. The seismic force in the plane of the panel creates a vertical couple and shear forces at the bearing connections, where these forces and gravity loads must be resisted. Some designers prefer to provide gravity support for the panel at the top and put the tieback connections at the bottom. Similar modes of displacement must be considered for other panel configurations. (Fig. 7.3.6) Building codes set the requirements for lateral forces and story-drift accommodation. These parameters, which are too variable to detail in this handbook, depend on seismic design category, building site, occupancy, type, and configuration and should be identified in the contract documents. Required drift consideration between floors can be several inches and often present a greater challenge to the designer than resisting the forces. This drift requirement is in anticipation of frame yielding to absorb seismic energy. Connections must also accommodate the movement during a seismic event either by sliding or by bending in ductile connectors. Sliding connections must have slots long enough (after installation toler-

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ance) to account for expected travel due to story drift without binding or shearing bolts or welds. Flexible connections must have ample rod or plate length to bend and flex under drift without failing in shear. Careful installation and inspection are required to ensure that tolerances do not negate the available movement in a way to make the connection ineffective. Weather and corrosion protection of these sliding connections are also essential to ensure their long-term performance so the sliding effect can occur without binding. 7.3.3

Tolerances

Tolerances provide recommended boundaries of size and shape within which the actual precast concrete components should be manufactured and erected. The reason for specifying tolerances is to establish construction criteria to ensure that the various components fit together without having to be modified and to be certain that the structure will perform as intended. The architect establishes the tolerances required to make the building concept work and must temper the desire for close tolerances with the knowledge of what can be achieved in the field at a reasonable cost and what tolerances are practically achievable in the supporting frame. By specifying reasonable tolerances, the architect strengthens and simplifies the standards for acceptance. It is recommended that appropriate PCI publications be specified for tolerances and tolerance-acceptance criteria. The designer of architectural precast concrete must recognize that erection and manufacturing tolerances apply to architectural precast concrete as they do to other building materials. When tolerances and allowances made for them

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First step: Rigging onto truck

Handling, Transporting, and Erecting

Design consideration must be given to installation conditions for the project with respect to handling, transporting, and erection. This must be done before sizes, shapes, and other features are finalized, as erection equipment or job-site conditions may influence panel size. Excessive rehandling and rotating of units between stripping and final installation add to the cost and increase the possibility of accidental damage. Consequently, handling should be kept to a minimum. The precast concrete manufacturer is usually responsible for designing the panels for handling, transportation, and erection stresses and for the design of the handling devices. The optimum solution for economical handling is the ability to strip a component from the form and tilt it into a vertical position similar to its final erected position (Fig. 7.3.7). This procedure has the added advantage that, during prolonged storage, the panel will be subjected to conditions similar to in-service conditions. Multistory components may be stored and shipped on their long side and handled at the jobsite by rotating in the air (Fig. 7.3.8). One set of lifting devices is required for handling and erection, and another may be needed for stripping. Their location in the panel should be chosen to ensure crack-free handling. Refer to Chapter 8 for proper design of lifting inserts, rigging, and the like, and for additional information on handling and erection. 7.3.4

Rolling blocks

Second step: Rotating

Third step: Oriented correctly for installation

Fig. 7.3.8 Hoisting and rotating multistory units.

are considered in the design stage, the task of determining and specifying them becomes fairly simple. Three groups of tolerances should be established as part of the precast concrete design: 1. Product tolerances: Those related to the dimensions of the precast concrete components. 2. Erection tolerances: Those related to the matching of components after they are erected. 3. Interfacing tolerances: Those related to other materials that are in contact with precast concrete components. Tolerances should be established for the following reasons. Structural. To ensure that structural design properly accounts for factors sensitive to variations in dimensional control. Examples include eccentric loading conditions, bearing areas, hardware and hardware-anchorage locations, and locations of reinforcing or prestressing steel. Feasibility. To ensure acceptable performance of joints and interfacing materials in the finished structure, such as glazing between panels. Visual. To ensure that the variations will result in an aesthetically pleasing structure. Economic. To ensure ease and speed of production and erection with a known degree of accuracy in the dimensions of precast concrete components. Legal. To avoid encroaching on property lines and to

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establish tolerance standards against which the work can be compared in the event of a dispute. Contractual. To establish a known acceptability range and to establish responsibility for developing, achieving, and maintaining mutually agreed upon tolerances. It should be understood by all members of the design and construction team that tolerances shown in this handbook must be considered as guidelines for an acceptability range and not limits for rejection. If specified tolerances are met, the component should be accepted. If these tolerances are exceeded, the component may still be acceptable if it meets any of the following criteria. 1. Exceeding the tolerances does not affect the structural integrity or architectural performance of the component. 2. The component can be brought within tolerance by structurally and architecturally satisfactory means. 3. The total erected assembly can be modified to meet all structural and architectural requirements. The enforcement of tolerances should be based on the designer’s judgment. This design professional is able to decide whether a deviation from the allowable tolerances affects safety, appearance, or other trades. In building construction, very little out-of-tolerance work, whether it is concrete, masonry, cast-in-place concrete, steel, or precast concrete, has been rejected and removed solely because it was out of tolerance. Additional information on tolerances is given in Chapter 13 and the references cited in that chapter. 7.3.5

Crack Control

In designing architectural precast concrete components, it is generally desirable to avoid discernable cracking. Cracking may occur without having any detrimental effect on the structural capacity of the architectural precast concrete component. However, in addition to being unsightly, cracks are potential locations of concrete deterioration and crack widths should be limited. When a reinforced concrete component is subjected to flexural tension, the amount and location of reinforcing steel has a negligible effect on component performance until a crack develops. As stresses increase, hairline cracks may develop and extend into the thickness of the component. If the crack width is narrow, not more than about 0.012 in., the structural adequacy will remain unimpaired and the crack will have little influence on the potential for corrosion. When the surface is exposed to weather, cracks up to 0.005 in. wide have no influence on the corrosion of reinforcement and should be acceptable from an aesthetic viewpoint. Even when concrete stresses during in-service conditions are less than the allowable flexural tensile strength, distributed reinforcement is needed to control potential cracking. Such cracking may occur unintentionally during fabrication, handling, transportation, and erection. Reinforcement also provides ductility in the event of an unexpected overload. In components where the stresses are expected to exceed the allowable flexural tensile strength, prestressed reinforcement 7–12

may be used for performance, providing adequate safety and satisfying aesthetic requirements. Sufficient reinforcement and proper spacing must be used in each component to control the distribution of any shrinkage cracking. Where components have complex shapes, and particularly where they have unbalanced concrete volumes, unsymmetrical reinforcement, large protrusions or changes of section, the liklihood of shrinkage cracking is increased. Distortion (bowing or warping) of the panel can also occur from these causes. The presence of cracks alone should not be cause for rejection of architectural precast concrete components. Most cracks can be repaired so that performance is acceptable. 7.3.6

Reinforcement

Architectural precast concrete panels can be reinforced with all of the common reinforcing methods used in the precast concrete industry. Most cladding panels are conventionally reinforced with either welded-wire reinforcement or individual reinforcing bars. Load-bearing panels and insulated panels are often prestressed; however, conventional reinforcement may also be used. Many producers also have the ability to post-tension architectural precast concrete panels. Some precast concrete manufacturers have been successful using carbon-fiber reinforcing in architectural precast concrete products. Structural design is governed by the provisions of ACI 318-05.2 Chapter 9 discusses material requirements of reinforcing. Issues specific to architectural precast concrete are discussed in the following sections. 7.3.6.1 Welded-Wire Reinforcement Welded-wire reinforcement (WWR) is a common type of reinforcement used in architectural precast concrete. WWR in one or more layers is often used to satisfy the minimum reinforcement requirements and is then supplemented with reinforcing bars as required to meet structural requirements. WWR used in architectural precast concrete is required to comply with the requirements of ACI 318-05. WWR is available in a wide range of sizes and spacings, making it possible to furnish almost exactly the cross-sectional steel area required. Most manufacturers, however, prefer to limit inventory and will typically use only two sizes, a light and a heavy WWR. Common sizes of WWR that are used are 6×6 – W2.5×W2.5 and WWR 4×4 – W4×W4. Other sizes may be common in various geographical areas. WWR for architectural precast concrete is typically supplied in flat sheets. Reinforcement from rolls, if used in thin, precast concrete sections, must be flattened and tied to maintain required tolerances. Many precasting plants have the capability of accurately bending wire reinforcement to desired shapes, increasing its usefulness in large components. Because the wire reinforcement is closely and uniformly spaced, it is well suited to control cracking. Furthermore, the welded intersections ensure that the reinforcement will be developed close to the edge of the component, resisting cracks that may be caused by handling, and making it easier to repair damaged edges.

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7.3.6.2 Reinforcing Bars Deformed reinforcing bars are also used extensively in architectural precast concrete. As a general rule, bar sizes should be kept reasonably small (#3 through #6), even where this will increase the number of bars. Smaller, closely spaced diameter bars will control crack widths and improve the distribution of temperature stresses better than fewer, widely spaced larger bars. The use of small diameter, closely spaced bars becomes more important in thin concrete sections. Since the sum of the crack widths in concrete is essentially the same for a given set of conditions, the more cracks there are, the smaller and less visible they will be. The recommended maximum spacing of reinforcement in panels exposed to the environment is 6 in. for WWR and three times the panel thickness (18 in. maximum) for reinforcing bars. Large reinforcing bars generally are not used; they require anchorage lengths and hook sizes that may be impractical. Good bond between the reinforcing bar and concrete is essential for the bar to perform its function of resisting tension and controlling cracking. Therefore, the reinforcing bar must be free of materials injurious to bond, including loose rust. Mill scale that withstands hard-wire brushing or a coating of tight rust is not detrimental to bond. Epoxy-coated reinforcement does not control cracks as well as uncoated (black) reinforcement. If an uncracked design is used, there is usually no reason for epoxy coating. Thus, epoxy-coated reinforcement should not be specified for architectural precast concrete.

result from variations in section properties at these reveals.

7.3.6.3 Prestressing

7.3.7

Prestressing may be used to minimize component cracking by applying a precompression in the concrete that counteracts the tensile stresses generated by self-weight and applied loads. Prestressing may be either pretensioned or posttensioned. In either case, the prestressing force should generally be concentric with the effective cross section. Prestressing can be considered for strength design provided that the provisions of ACI 318-05, Chapter 18 are applied. Concrete panels may be prestressed for the following reasons:

Architectural precast concrete cladding panels are usually supported independently. That is, each panel has its own set of gravity and lateral connections to secure it to the building’s structural frame. Gravity loads are supported by the building columns and/or beams and, thus, are transferred to the foundations. In most buildings, it is preferable to support panels in this manner. However, there are some building types where it is beneficial to take advantage of concrete’s inherent compressive strength, and the architectural concrete cladding can be designed as self-supporting. Only lateral tieback connections are made to the building’s frame. One such building type is a typical suburban office building that is usually a two- to six-story, steel-frame structure. The exterior cladding may consist of horizontal spandrels and vertical column covers that are repetitive in size, shape, and layout. The vertical column covers may be able to be designed to support the weight of the spandrels, glass, and any other gravity loads being carried by the spandrels. There are several advantages to stacking precast concrete panels:

1. Structural requirements for in-service loads. 2. Units are supported near the top and it is desired to maintain the concrete in compression. 3. Units are slender and prestressing is the method chosen to facilitate handling without undue tensile stresses. 4. For general crack control. In order for prestressing to reduce or control bowing or warping, it is essential that tendons be located accurately (concentric with the effective cross section) and securely maintained at that location. Because panels tend to bow outward due to thermal and shrinkage effects and because outward bowing is generally more objectionable than inward bowing, some precasters choose to force a slight inward, initial bow by adjusting the magnitude and/or the location of the prestressing force. It may also be warranted to make slight adjustments in the strand position if significantly deep, transverse reveals exist in order to minimize bowing, which can

Spandrel

  7 Column cover

Bearing pads or dryback Foundation

Fig. 7.3.9 Stacked panels.

• • •

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Stacking Non-Load-Bearing Panels

The building frame can be lighter, thus reducing costs for the owner since it does not have to carry the weight of the precast concrete panels. Bearing brackets welded to the structure that are required to support the panels are eliminated. The eccentricity in the bearing connections is minimized and reduces the load on the lateral connections. 7–13

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There are some precautions to take when using the stacking method. In the vertical direction, all of the thermal volumechange movements accumulate at the top of the building. One must make sure that precast concrete joint sizes and building details allow this movement without causing detrimental effects. The horizontal spandrel panels should hang on the side of the column covers and not bear on top of them (Fig. 7.3.9). This allows the spandrels to move freely and accommodate axial volume change. Because it is not desirable to grout joints between architectural panels, all of the gravity loads should be transferred through shims. The joint at the bottom of the column covers should, however, be grouted if bearing pressures are high. Cladding panels should not be stacked in high seismic areas where anticipated in-plane drifts occur. Braced frames in low seismic areas typically do not have appreciable lateral drift, making the stacking of panels acceptable. 7.3.8

Shims

Shims play an important role in the construction of architectural precast concrete. They are used to transfer gravity loads from the precast concrete component to the supporting structure or foundation and must be sized to keep the bearing stress at an acceptable level. This is particularly important when using stacked, non-load-bearing, architectural concrete panels. Shims also enable the erector to adjust architectural precast concrete panels to achieve proper joint widths and alignment. It is common practice to use hard-plastic shim stacks of varying thicknesses, resulting in a joint ranging from 1/2 in. to 1 in. Plastic shim stacks higher than 1 in. should be avoided due to the inherent instability of the stack as it gets higher.

✖

✖

Column cover options (b) (c) ✖

✖

✖

✖

✖

✖

✖

✖

(a) Wall panel ✖✖

Bearing connection ✖ Tieback connection

(d) Spandrel panel

✖ ✖

✖

Optional for long panels

✖

Fig. 7.4.1 Typical cladding connection locations.

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✖ ✖

For good performance of the shims over the life of the structure, it is important that they are loaded uniformly. The effects of non-uniformly loaded plastic shim stacks have been known to gradually “walk” the shims from their intended position. This can be due to bearing supports not being level or unsymmetrical pieces where the center of gravity of the panel is not lined up with the center of the shim combined with changes in temperature over time. To avoid the potential for walking, it may be advisable to epoxy the plastic shims together or use steel shims that are tack-welded together with a single shim on top to make up the final required adjustment in the joint dimension. When using steel shims, appropriate protection should be used.

7.4

Connections

7.4.1

General

It is the intent of this section to briefly focus on connections for non-load-bearing, architectural cladding panels. Although the design of connections for architectural precast concrete panels follows the principles presented in Chapter 6 of this handbook, most of the connection types presented in that chapter apply to structural, load-bearing components. A more complete discussion of the design of connections for architectural precast concrete panels can be found in Chapter 4 of Reference 1. 7.4.2

Design Considerations

The purpose of cladding panel connections is to transfer loads that the panel must resist to the supporting structure. Generally, connections are divided into two types: those that transfer gravity loads such as panel weights and other materials that the panel may be supporting and those that transfer lateral loads such as those caused by eccentric bearing, wind, seismic or blast loads, and impact loads. It is possible to design connections to transfer all types of loads at the same time, however, the designer should consider that the simpler the connection, the less likely it is that the connection will be subjected to unintended forces. Connections for architectural precast concrete cladding panels are designed using strength design methods as presented in Chapter 6 of this handbook. Forces on a connection are calculated based on the various types of loads that the connection must resist. The resulting forces are then multiplied by the appropriate load factors and combined as prescribed by ASCE 7-053 and indicated in Chapter 4, Section 4.2.6 of this handbook. The resulting worst-case combination is compared with the connection’s design strength as calculated by the methods in Chapter 6. Connections are designed using the previously described method because it is compatible with the design method for the panels themselves. The use of the additional load factor of 1.0 to 1.33 as discussed in Chapter 6 should be left to the precast concrete specialty engineer, who is the most experienced in connection design. Connections must also meet certain design and performance considerations, which are discussed in Chapter 6. Connections for architectural precast concrete panels

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STRUCTURAL CONSIDERATIONS FOR ARCHITECTURAL PRECAST CONCRETE should be designed to be unaffected by weather conditions. In steel-framed buildings, connections should be designed and located so that they do not induce torsion into the structural steel members of the building. If torsion cannot be avoided, the steel members of the building must be adequately braced against rotation, as discussed in Section 7.2.2. This design should be done by the Structural Engineer of Record as part of the design of the support structure and be shown completely on the contract drawings. The following guidelines may be used for locating and designing connections (also refer to Fig. 7.4.1): • Provide only two bearing connections per panel. It is virtually impossible to erect a panel such that the load is distributed to more than two bearing connections in the same manner that was assumed in the design. Inaccurate prediction of load can result in a connection that is overloaded. • Never assume that a panel imparts a uniform load on a perimeter building beam. Since the panel is typically stiffer than the supporting beam, the load of the panel will be transferred to the beam at only two points. • Standardize connection types. • Design connections for worst-case loads. Designing connections for the actual load on every panel results in too many different connection details, which can lead to unintended errors. • Design connections using a limited number of different steel shapes and plate thicknesses. Minimize the number of bolt or threaded rod sizes throughout the project. • Make sure that the interior finish of the structure covers all connections. • Do not assume that inserts used for connections can also be used to hoist the panel. Use different devices for each purpose. • Provide the most direct load path possible to transfer loads. • Provide for field adjustment. • Consider accessibility. • Consider tolerances of the precast concrete and the interfacing structure. • Avoid connections that require penetrating the form. • Avoid connections that require post-pour work.

7.5

 rchitectural Cladding Component A Analysis

precast concrete buildings. It is based on Method 1 – simplified procedure of ASCE 7, which is referenced by IBC 2006. The limitations for this method are: 1. 2. 3. 4. 5.

Height ≤ 60 ft or least lateral dimension Enclosed building (includes parking structures) Regular shaped No expansion joints Fundamental frequency ≥ 1 Hz (nearly all concrete buildings under 60 ft will qualify) 6. Flat or shallow pitched roof 7. No unusual topography around the building. ASCE 7-05 should also be reviewed for more details of these provisions and for the other analysis methods that may be used for buildings that do not meet the listed limitations. The following are the procedures required for this simplified analysis: 1. Determine the basic wind speed, which may be taken from Design Aid 4.11.5. 2. Determine the topographic factor Kzt, which is determined from ASCE 7-05 Section 6.5.7 and is typically 1.0 unless all of the conditions of ASCE Section 6.5.7.1 are met. Most precast concrete structures will qualify for a topographic factor = 1.0. 3. Determine the importance factor from Design Aid 4.11.1. 4. Determine the zone that is being considered. This reflects the location of the panels in the building as shown in Fig. 6-3 of ASCE 7-05. 5. Determine exposure category that applies (ASCE 7-05 includes more detailed descriptions): a. Exposure B: Urban and suburban areas, wooded areas b. Exposure D: Flat, unobstructed areas outside hurricane-prone regions c. Exposure C: All others The pressure for cladding can be determined from

where: pnet λ Kzt I

Wind Loads, ASCE 7-05 Method 1

pnet30

4

In most areas of the United States using IBC 2006, earthquake loading will be more critical than wind, but wind loads should be checked. This section provides a method for such a check for most

pnet = λKzt Ipnet30



Architectural precast concrete components must be designed using the principles outlined in Chapters 4, 5, and 8 of this handbook. The following examples are intended to demonstrate the design process that should be used when designing a cladding panel and its connections for wind and seismic loads. 7.5.1

CHAPTER 7

(Eq. 7-1)

= net wind pressure (sum of internal and external) to be applied to cladding, but not less than 10 lb/ft2 = adjustment factor for building height and exposure from Design Aid 4.11.6(c) = topographic factor at mean roof height from ASCE 7-05 Section 6.5.7 = wind importance factor from Design Aid 4.11.1 = net design wind pressure for exposure B, at height = 30 ft and I = 1.0 from Fig. 6-3 of ASCE 7-05 and Design Aid 4.11.6(b)

See Example 7.5.1.1, which illustrates the use of Method 1 for the calculation of wind loads on a component.

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Example 7.5.1.1 Use of ASCE 7-05 Method 1 for Wind-Load Determination

  7

Given: A 114-ft-wide by 226-ft-long by 54-ft-high hospital building in Memphis, TN. This building is the same as presented in Example 4.2.3.1. A section through a typical cladding panel is shown in this example. Precast concrete wall panels are 7 ft high by 28 ft long. A 6-ft-high window is attached to the top of the panel, and an 8-ft-high window is attached to the bottom. The panel under consideration is one level down from the roof. Problem: Determine the design wind pressure to be used for cladding panels. ______________________________________________________________________________________ Solution: As this is an enclosed building under 60 ft high, Method 1 may be used. From Design Aid 4.11.5, Basic wind speed = 90 mph From Section 4.2.3.1, item 3, Exposure category is B From Design Aid 4.11.1, Occupancy category IV: I = 1.15 Kzt = 1.0 Tributary area per panel = one-half of upper window + panel + one-half of lower window times the panel length = (6/2 + 7 + 8/2)28 = 392 ft2

6'-0" tall upper window

412 "

2" 712 " z y

7'-0" z

Exterior face of panel

+y +z

+x Datum

412 " 22"

8'-0" tall lower window

2'-0" Panel cross section

Determine adjustment factor λ (mean roof height above ground is 54 ft) From Design Aid 4.11.6(c) with interpolation λ = 1.18 Determine pnet30 : Design Aid 4.11.6(b) interpolating between 100 ft2 and 500 ft2: 395 - 100 500 - 100

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= 0.73

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Example 7.5.1.1 Use of ASCE 7-05 Method 1 for Wind-Load Determination (cont.) Zone 4: Interior zone, between end zones defined below: Inward pressure

= 12.4 – 0.73(12.4 – 10.9)

pnet = λ Kzt Ipnet30

= 1.18(1.0)(1.15)(11.3)

= 15.3 lb/ft2

Outward pressure (suction) = 13.6 – 0.73(13.6 – 12.1) pnet = λ Kzt Ipnet30

= 1.18(1.0)(1.15)(12.5)

= 11.3 lb/ft2

  7

= 12.5 lb/ft2

= 17.0 lb/ft2

Zone 5: End zone: Dimension from end of building equal to the lesser of 10% of the least horizontal dimension or 0.4 times the mean roof height, but not less than 4% of the least horizontal dimension or 3 ft. Inward pressure

= 12.4 – 0.73(12.4 – 10.9)

pnet = λ Kzt Ipnet30

= 1.18(1.0)(1.15)(11.3)

= 15.3 lb/ft2

Outward pressure (suction) = 15.1 – 0.73(15.1 – 12.1) pnet = λ Kzt Ipnet30

= 1.18(1.0)(1.15)(12.9)

= 11.3 lb/ft2 = 12.9 lb/ft2

= 17.5 lb/ft2

Summary of total forces on panel: (shown for zone 5, which is slightly more critical) Force on panel: Inward: Outward:

7.0(28)(15.3) 7.0(28)(17.5)

= 2999 lb = 3.00 kip = 3430 lb = 3.43 kip

Force on panel from upper window: Inward:

⎛ 6.0 ⎞ ⎟ (28)(15.3)  = 1285 lb = 1.29 kip ⎜⎝ 2 ⎠

Outward:

⎛ 6.0 ⎞ ⎜⎝ ⎟ (28)(17.5) = 1470 lb = 1.47 kip 2 ⎠

Force on panel from lower window: Inward:

⎛ 8.0 ⎞ ⎟ (28)(15.3) = 1713 lb = 1.71 kip ⎜⎝ 2 ⎠

Outward:

⎛ 8.0 ⎞ ⎟ (28)(17.5) = 1960 lb = 1.96 kip ⎜⎝ 2 ⎠

Summary of forces on panel:

Outward



Inward

1.29 kip

1.47 kip

42" 3.00 kip

3.43 kip

42" 1.71 kip

1.96 kip

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Example 7.5.2.1 Use of ASCE 7-05 Method 2 for Wind-Load Determination

  7

Given: (Same as Example 7.5.1.1, except the building height is changed to 108 ft) A 114-ft-wide by 226-ft-long by 108-ft-high hospital building in Memphis, TN. Precast concrete wall panels are 7 ft high by 28 ft long. A 6-ft-high window is attached to the top of the panel, and an 8-ft-high window is attached to the bottom. Note: Panel being considered is one level down from roof at approximately 100 ft above the ground. Problem: Determine the design wind load on the cladding wall panels at a height of 100 ft using ASCE 7-05 Method 2. ______________________________________________________________________________________ Solution: From Design Aid 4.11.5 or ASCE 7-05 Fig. 6-1 or IBC 2006 Fig. 1609: Basic wind speed = 90 mph From ASCE 7-05 Section 6.5.6.2 or IBC 2006 Section 1609.4.2: Surface roughness is category B From Section 4.2.3.1 item 3 or ASCE 7-05 Section 6.5.6.3 or IBC 2006 Section 1609.4.3: Exposure category: B From Design Aid 4.11.1 or ASCE 7-05 Table 1-1 or IBC 2006 Table 1604.5: Occupancy category is category IV From Design Aid 4.11.1 or ASCE 7-05 Table 6-1: Importance factor, I = 1.15 Find velocity pressure qz : qz

= 0.00256 Kz Kzt KdV 2I

qz KZ Kzt Kd V I

= wind velocity pressure at height Z = velocity pressure exposure coefficient (ASCE 7-05 Section 6.5.6.6) = topographic factor (ASCE 7-05 Section 6.5.7.2) = wind directionality factor (ASCE 7-05 Section 6.5.4.4) = wind velocity (mph) = importance factor

(ASCE 7-05 Eq. 6-15)

where:

Find KZ: From ASCE 7-05 Section 6.5.6.6, Table 6-3, Note 1: At height = 100 ft, exposure B, case 1: Kz = 0.99 Find topography factor Kzt : From ASCE 7-05 Section 6.5.7.2: In order to calculate Kzt, all conditions of ASCE 7-05 Section 6.5.7.1 must be met. If not, Kzt = 1.0. Kzt = 1.0 for homogeneous topography Find directionality factor Kd : From ASCE 7-05 Section 6.5.4.4, Table 6-4: Components and cladding: Kd = 0.85

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Example 7.5.2.1 Use of ASCE 7-05 Method 2 for Wind-Load Determination (cont.) Solve velocity pressure qz : qz = 0.00256(0.99)(1.0)(0.85)(90)2 (1.15) qz = 20.1 lb/ft2

  7

Determine wind pressures for panels: p = q (GCp) – qi (GCpi)

ASCE 7-05 Eq. 6-23

q = qi = 20.1 as calculated previously Find GCp :  ind tributary area of panel = one-half of upper window + panel + one-half of lower window times the F panel length. = (6/2 + 7 +8/2)(28) = 392 ft2 From ASCE 7-05 Figure 6-17: For tributary area = 392 ft2 Zone 4 GCp = + 0.62 and – 0.75 Zone 5 GCp = + 0.62 and – 1.11 Find GCpi, positive and negative internal pressure coefficients: From ASCE 7-05 Figure 6-5: GCpi = + 0.18 (pressure) or GCpi = – 0.18 (suction)

Summarya Zone 4

Zone 5b

Suction

Pressure

Suction

Pressure

GCp

-0.75

+0.62

-1.11

+0.62

GCpi

+0.18

Design wind load

-18.7 lb/ft

-0.18 2c

+0.18

+16.1 lb/ft

2c

-0.18

25.7 lb/ft

2

+16.1 lb/ft2

a. A  SCE 7-05 refers to wind loads as being positive when toward the internal surface of a component or negative when away from the internal surface. In the table, suction is away from the external surface and pressure is toward the external surface, which is common terminology in precast concrete design. b. E  nd Zone: ASCE 7-05 defines zone 5 as dimension from end of building equal to the lesser of 10% of the least horizontal dimension or 0.4 times the mean roof height, but not less than 4% of the least horizontal dimension or 3 ft. For this building, this is 11.4 ft. Zone 4 would apply to panels between the two zone 5 edges. In most cases, it is more practical to use the zone 5 loads for all panels unless economies can be achieved by using different values. c. For example: p = q (GCp ) – qi (GCpi )

= 20.1 (-0.75) – 20.1 (+0.18) = -18.7 lb/ ft2 (suction) = 20.1 (+0.62) -20.1 (-0.18) = +16.1 lb/ ft2 (pressure)

Also note that design wind pressures can be calculated for various panels along the height of the building by varying the KZ factor for the height under consideration.

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  7

Wind Loads, ASCE 7-05 Method 2

with:

As noted above, the use of Method 1 is only applicable for buildings less than 60 ft. high. For higher buildings, Method 2 or more sophisticated methods must be used. Method 2 of ASCE 7-05 requires use of Section 6.5.12.4.1 for buildings under 60 ft high and requires use of Section 6.5.12.4.2 for buildings higher than 60 ft. Since many precast concrete cladding projects are higher than 60 ft and therefore require use of Section 6.5.12.4.2, Example 7.5.2.1 is the same as Example 7.5.1.1 with the building height changed to 108 ft. This illustrates the use of Method 2 Section 6.5.12.4.2. 7.5.3

Seismic Loads

Non-structural architectural components, except those noted in the following, must resist seismic forces locally and be attached through a continuous load path to the seismicforce-resisting system. Exceptions: 1. Seismic design category A. 2. Seismic design category B (other than parapets supported by bearing or shear walls), provided that the importance factor Ip is not equal to 1.5 (that is, the building is not a hospital or other vital structure). For precast concrete cladding, the force required for these components and connections is given in Eq. 7-2 (ASCE 7-05 Eq. 13.3-1) within the limits given by Eq. 7-3 and Eq. 7-4; (ASCE 7-05 Eq. 13.3-2 and 13.3-3, respectively).

FFpp==

( ) ( )

0.4 a p S DS Wp ⎛ z⎞ ⎜⎝ 1 + 2 ⎟⎠ h Rp I p

(Eq. 7-2)

Fp is not required to be taken greater than

Fp = 1.6SDSIPWP

(Eq. 7-3)

Fp shall not be taken less than

Fp = 0.3SDSIPWP

(Eq. 7-4)

where: Ip = component importance factor from Design Aid 4.11.1 ap = component amplification factor from Design Aid 4.11.10 Fp = seismic design force h = average roof height of structure Rp = component response modification factor from Design Aid 4.11.10 SDS = as defined in Example 4.2.4.1 Wp = component weight z = height in structure at attachment point h

CFSCp =

( )

0.4 a p S DS  z 1+ 2   h R I

(

p

p

)



(Eq. 7-5)

where ap and Rp are as defined previously.

7.6

Veneered Panels

7.6.1

General

Precast concrete panels faced with clay products (brick, tile, terra cotta) or natural stone (granite, limestone, marble) combine the rich beauty of traditional materials with the strength, versatility, and economy of precast concrete. Structural design of veneered precast concrete units is the same as for other precast concrete wall panels, except that consideration must be given to the veneer material and its attachment to the concrete. The physical properties of the facing material must be compared with the properties of the concrete back-up when facing material is bonded to the concrete back-up. When verifying strength, the concrete backup without composite action is conservatively considered the sole structural element, supporting the veneer and other loads. However, when the veneer is bonded to the backup concrete, an improved prediction of deformation (i.e. bowing) is obtained by assuming composite behavior. This is commonly the practice when the component is prestressed Because of the difference in material properties, veneered panels are somewhat more susceptible to bowing than homogeneous concrete panels. Bowing can be reduced using one or more of the following techniques: 1. Use of bond breakers and flexible anchors with thin stone veneers. 2. Use minimum thickness of 5 in. to 6 in. back-up concrete, depending on panel length. 3. Use prestressing in long, flat panels. 4. Use concrete ribs formed on the back of the panel. 5. Use intermediate tieback connections to the supporting structure. 6. Avoid veneer material that has large expansion or shrinkage characteristics. Cracking in the veneer may occur if the bonding or anchoring details force the veneer pieces to follow the panel curvature. This is particularly critical where the face materials are large pieces (cut stone) and the differential movement between concrete and veneer is significant. A good concrete design mixture with a low water–cementitious materials ratio and prolonged curing will help reduce shrinkage. The subsequent sections of this chapter provide further guidance for veneered panels.

Equation 7-2 can be rewritten to establish the seismic cladding factor CSC as Fp = CSCWp

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Example 7.5.3.1 Architectural Precast Concrete Panel with Earthquake Loading Given: The hospital in Memphis of Example 7.5.1.1. Wall panels as shown. Concrete fc' = 5000 psi, normalweight Window weight = 10 lb/ft2 From Design Aid 4.11.1: Category IV, since the structure is a hospital, Ip = 1.5 SDS = 1.0

  7

Problem: Determine the seismic forces on the panel elements (panel itself, connections, and fasteners). 336" (28'-0") 12"

156"

156"

412 "

12"

24" 7'-0" 3212 "

7'-0"

2712 "

412" y

Datum for axes at corner of panel

y x

z

z

Panel elevation (as viewed from building exterior)

x Datum

2'-0"

Panel cross section

= Bearing: resists load in y and z direction only = Lateral: resists load in x and z direction only = Tie-back: resists load in z direction only

Cross-sectional area of panel = 465.75 in.2; Panel weight = 485 lb/ft Center of gravity from datum (bottom outside corner): y = 34.5 in.; z = 4.5 in. ______________________________________________________________________________________ Solution: Determine the following design loads.

4.5"

FDU = CLC × Wp (gravity design load on any element) FPU = CLC × CSC × DF × W (seismic design load on any element) FWU = CLC × DF × FW (wind design load on any element)

Center of gravity

where: Wp = component load CLC = load combination factor CSC = seismic cladding factor (differs for each element) DF = distribution factor (differs for each connection location) FW = wind loading found in Example 7.5.1.1 or 7.5.2.1

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Example 7.5.3.1 Architectural Precast Concrete Panel with Earthquake Loading (cont.) Since the seismic cladding factor CSC is different for each design element (panel, connections, fasteners), the corresponding seismic load used to design each element is different.

  7

Ww = 1680 lb

1. Determine the unfactored forces on the panel.

Wp = 13,580 lb

1a. Determine unfactored gravity loads on the panel. Panel weight = WP = 485(28) = 13,580 lb Upper window: height = 6 ft Total window weight on wall panel = 6(28)(10) = 1680 lb Lower window (no weight on wall panel) 1b. Determine unfactored wind loads on the panel. From Example 7.5.1.1: Directly on panel: Inward: 2999 lb Outward: 3430 lb

From upper window: Inward: 1285 lb Outward: 1470 lb



From lower window: Inward: 1714 lb Outward: 1960 lb

Dead load

Wtwp = 1285 lb

Wplp = 2999 lb

Wtws = 1470 lb

Wpls = 3430 lb

Wlws = 1960 lb

Wlwp = 1714 lb

1c. Determine unfactored seismic loads on the panel.  hese loads still need to be multiplied by a seisT mic cladding factor Csc, depending on what is being designed, such as the wall panel, its connections, or the connection fasteners. This will be done after the loading is calculated in part 2.

Wind load

Upper window: height = 6 ft WTW of one-half of window = 3.0(10) = 30 lb/ft 30(28) = 840 lb, in-plane or out-of-plane

Lower window: height = 8 ft  WBW of one-half of window = 4.0(10) = 40 lb/ft 40(28) = 1120 lb, in-plane or out-of-plane Wtw = 840 lb x Csc

7–22

Wtw = 840 lb x Csc

Wpl = 13,580 lb x Csc

Wpl = 13,580 lb x Csc

Wbw = 1120 lb x Csc

Wbw = 1120 lb x Csc

Seismic load

Seismic load

(in-plane)

(out-of-plane)

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Example 7.5.3.1 Architectural Precast Concrete Panel with Earthquake Loading (cont.)

2. Determine unfactored forces on the connections. 2a. Determine unfactored gravity loads on the connections. Since the dead loads calculated previously act at an eccentricity from the connections, equivalent concentric loads on the connections must be calculated. To determine the eccentricity, find the center of dead load: Panel

W, lb

z, in.

(W)(z)

13,580

-4.5

-61,110

Upper window

1680

-2.0

-3360

Lower window

0

-22.0

0

Total

15,260

-64,470

Center of load from datum: z = 64,470/15,260 = -4.2 in. Note: As shown in the figure, the reactions from the bearing connections occur 7.5 in. from the datum. Unfactored dead loads on connections: Vertical = 15,260/2 = 7630 lb each connection Horizontal = 7630(7.5 – 4.2)/32.5 = 775 lb each connection Note: Outward on top connection, inward on bottom connection.

Distance to center of reaction 7.5" Pz = 775 lb Wp + Wtw + Wbw = 7630 lb y z

Py = 7630 lb

Pz = 775 lb x

32.5" Distance between connections

Datum 4.2" Distance to center of load End connections (y and z directions)

Unfactored loads on connections, lb Dead load Connection

Vertical, y

In, z

7630

775

Seismic for connections Out, z

Vertical, y

Horizontal, y

In., z

Wind Out, z

In, z

Out, z

■ (Center), top ▼ (End), top X (Center), bottom X (End), bottom

775

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CHAPTER 7

Example 7.5.3.1 Architectural Precast Concrete Panel with Earthquake Loading (cont.) 2b. Determine unfactored wind loads on the connections.a Note: The wind loads in the following already include the wind importance factor shown in Example 7.5.1.1.

  7

Find center of inward/outward wind force: Pw, lb

y, in.

(Pw)(y)

Panel

3430

42.0

144,060

Upper window

1470

84.0

123,480

Lower window

1960

0

0

Total

6860

267,540

Center of force from datum: y = 267,540/6860 = 39.0 in. a. For purposes of this example, wind loads used are from Example 7.5.1.1. Those calculated in Example 7.5.2.1 could also be checked. Note: This example illustrates the condition with the seismic load acting outward. It could also be acting inward.

Unfactored wind forces on connections: For outward wind loads: Pw(top) =

∑ P (y − h w

bottom  connection

4.5"

) Pz = 2427 lb

a

21.0"



Pw(top) = 6860(39.0 – 27.5)/32.5 = 2427 lb

6860 lb

39.0" 27.5"

Pw(bottom) = 6860 – 2427 = 4433 lb

e

For inward wind loads (proportional to pressure): Pw(top) = (11.3/12.9)2427 = 2126 lb Pw(bottom) = (11.3/12.9)4433 = 3883 lb

Pz = 4433 lb

Outward wind load on all connections

Wind distribution to connections : Like loads on a continuous beam, the wind forces are not evenly distributed to the connections. It is reasonable to consider that the wind forces act as evenly distributed loads across the panel, then a continuous beam distribution analysis can be done to determine the percentage of load that goes to each connection.  fter performing such an analysis, it is found that the center connection will take 58% of the load and A each end connection will take 21%.

Unfactored loads on connections, lb Dead load Connection

Vertical, y

In, z

Seismic for connections Out, z

Vertical, y

Horizontal, y

■ (Center), top

In., z

Wind Out, z

In, z

Out, z

1233

1408

▼ (End), top

446

510

X (Center), bottom

2252

2570

X (End), bottom

815

931

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Example 7.5.3.1 Architectural Precast Concrete Panel with Earthquake Loading (cont.)

2c. Determine unfactored seismic loads on the connections.  he same procedure applies to find the equivalent seismic forces acting on the connections. Notice T that the seismic loads act both in-plane and out-of-plane of the panel.

  7

2" 840 15,540 lb x Csc (center of load) 9"

y x

z

5.6"

13,580 1120

Datum 22"

Center of seismic load (out-of-plane)

To determine the eccentricity, find the center of seismic load (multiplying by CSC can be neglected for this because it will not affect the geometry): W, lb

y, in.

z, in.

13,580

34.5

-4.5

Upper window

840

84.0

-2.0

70,560

Lower window

1120

0

-22.0

0

Panel

Total

(W)(y) 468,510

15,540

539,070

(W)(z) -61,110 -1680 -24,640 -87,430

Center of force from datum: y = 539,070/15,540 = 34.7 in. z = 87,430/15,540 = -5.6 in.

840

13,580

1120

34.5"

34.7"

(center of load)

7'

15,540 lb x Csc

Center of seismic load (in plane)

Unfactored seismic (out-of-plane) loads on connections: The following figure illustrates the reaction directions resulting from various applied seismic loads:

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CHAPTER 7

Example 7.5.3.1 Architectural Precast Concrete Panel with Earthquake Loading (cont.) Gravity

Lateral in-plane restraint

Tie back

  7

ez Gravity

l ane

ey

ss

ma

Tie back

P

Tie back Tie back y z

x

ez = eccentricity for panel rotation that will increase or decrease tie-back connections ey = eccentricity for panel rotation will increase or decrease gravity connection reactions

Pp(top) =

∑ P (y − h

Pp(top)

= 15,540(34.7 – 27.5)/32. 5 = 3443 lb × CSC

w

bottom  connection

)

a

Pp(bottom) = 15,540 – 3443 = 12,097 lb × CSC Unfactored seismic (in-plane) loads on connections: (■) Parallel

= +15,540 lb × CSC

15,540 (27.5 + 32.5 − 34.7 ) (▼) Up-down = = ±1260 lb × CSC 2 (156 )

(×) In-out

15,540 (5.6 − 4.5 ) = ±55 lb × C (3443 × C above controls) = SC SC 2 (156 )

34.7" 27.5"

25.3"

Pz = (3443 lb)Csc e

15,540 lb x Csc Pz = (12,097 lb)Csc

Seismic load on all connections (out-of-plane)

= Lateral: resists load in x and z direction only = Bearing: resists load in y and z direction only = Tieback: resists load in z direction only

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Example 7.5.3.1 Architectural Precast Concrete Panel with Earthquake Loading (cont.) 6.0" 156"

156"

12"

Pz = (55 lb)Csc

32.5"

Py = (1260 lb)Csc

Px = (15,540 lb)Csc (15,540 lb)Csc

  7

Pz = (55 lb)Csc Py = (1260 lb)Csc

34.7

24.0"

12"

27.5"

Reactions from in-plane seismic load

Seismic cladding factor CSC (also refer to ASCE 7-05 Section 13.5):  he equivalent seismic loads must be multiplied by the appropriate seismic cladding factor depending T on which element is being designed (the panel itself, the connection, or the fasteners). From Design Aid 4.11.10, item 4: a. Wall component one level below top of building (z/h = 45/54):

ap

= 1.0, Rp = 2.5

From Eq. 7-5:

CSC = 

0.4 (1.0 ) (1.0 )  45   1+ 2  = 0.64 54 2.5 / 1.5

b. Body of wall panel connections:

ap = 1.0, Rp = 2.5 (same as wall element)



CSC = 0.64

From Eq. 7-5:

c. Fasteners of connection system: ap = 1.25, Rp = 1.0 CSC  =

0.4 (1.25 ) (1.0 )  45   1+2  = 2.0 54 1.0/1.5

Seismic distribution to connections :  ike the wind loads, the seismic forces are not evenly distributed to the connections and need to be L distributed. The same distribution used for the wind loads can be used. Therefore, the center connection will take 58% of the load and each end connection will take 21%. The resulting seismic loads are based on: FPU = CLC × CSC × DF × W (seismic design load on any element)  ompare load combinations with all of the forces to determine the maximum effect for design of the C connection:

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CHAPTER 7

Example 7.5.3.1 Architectural Precast Concrete Panel with Earthquake Loading (cont.) Unfactored loads on connections, lb Seismic for connections, CSC = 0.64 (Seismic for fasteners, CSC = 2.0)

Dead load Connection

  7

Vertical, y

In, z

Out, z

Vertical, y

■ (Center), top ▼ (End), top

Wind

Horizontal, x

In, z

Out, z

9946 (31,080)

1278 (3994)

1278 (3994)

463 (1446)

463 (1446)

4490 (14,033)

4490 (14,033)

1626 (5081)

1626 (5081)

806 (2520)

X (Center), bottom X (End), bottom

In, z

Out, z

Final load combinations: All of the unfactored loads are put together in the same table for comparison. These loads need to be put into load combinations to find the maximum load effect to use for design. Unfactored loads on connections, lb Seismic for connections, CSC = 0.64 (Seismic for fasteners, CSC = 2.0)

Dead load Connection

Vertical, y

In, z

7630

775

Out, z

Vertical, y

■ (Center), top ▼ (End), top

806 (2520)

X (Center), bottom X (End), bottom

775

Wind

Horizontal, x

In, z

Out, z

In, z

Out, z

9946 (31,080)

1278 (3994)

1278 (3994)

1233

1408

463 (1446)

463 (1446)

446

510

4490 (14,033)

4490 (14,033)

2252

2570

1626 (5081)

1626 (5081)

815

931

3. Check load combinations to determine controlling design loads. Possible combinations (from Section 4.2.6):

LC1: U = 1.4D

(Eq. 4-28)



LC3: U = 1.2D + 0.8W

(Eq. 4-30)



LC4: U = 1.2D + 1.6W

(Eq. 4-31)



LC5: U = (1.2 + 0.2SDS)D + 1.0E



LC6: U = 0.9D + 1.6W



LC7: U = (0.9 – 0.2SDS)D + 1.0E

(Eq. 4-33a) (Eq. 4-33) (Eq. 4-34a)

The following table will show the results for all of these combination effects on the different connections. It is an expansion of the previous summary table. The values in the summary table of unfactored loads are multiplied by the corresponding load combination factor CLC to show the combination effects for design.

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Example 7.5.3.1 Architectural Precast Concrete Panel with Earthquake Loading (cont.) Factored load combinations on connections, lb

Connection

LC

Vertical, y

Wind

Seismic for connections, CSC = 0.64 (Seismic for fasteners, CSC = 2.0)

Dead load In, z

Out, z

Vertical, y

Horizontal, x

In, z

Out, z

In, z

986

1126

1973

2253

1973

2253

  7

1 3 ■ (Center), top

4 5

9946 (31,080)

1278 (3994)

6 7

▼ (End), top

9446 (31,080)

1278 (3994)

1

10,682

1085

3

9156

930

357

408

4

9156

930

714

816

5

10.682

1085

6

6867

698

714

816

7

5341

543

1802

2057

3603

4114

3603

4114

652

745

1304

1490

1304

1490

806 (2520) 806 (2520)

463 (1446) 463 (1446)

1 3 X (Center), bottom

4 5

4490 (14,033)

6 7

X (End), bottom

4490 (14,033)

1

1085

3

930

4

930

5

1085

6

698

7

543

1626 (5081) 1626 (5081)

Using the table of loads in combinations, the connections and fasteners can be designed using the appropriate loading. The following diagram shows which type of seismic loads to use on different connection parts (reference ASCE 7-05 Section 13.5). Wind may control over–seismic loading in certain cases and should be checked.

21" Exterior face of panel Load direction Distribution reinforcement

5

4

3 6

3" 1 2

Seismic connection factors: Component Mode of failure Shear of weld 1 Flexure of angle 2 Buckling of rod 3 Shear of weld 4 Flexure of plate 5 Concrete pull out 6

Seismic load type Fastener of connection Body of connection Fastener of connection Fastener of connection Body of connection Fastener of connection

L5x5

Typical bottom tie-back connection, also see Example 6.13.1.

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CHAPTER 7 7.6.2

  7

Clay Product–Faced Precast Concrete

7.6.2.3 Clay-Product Selection

Clay product–faced precast concrete is being used increasingly as another choice to obtain an aesthetic facade. Among the types of materials that can be embedded in the precast concrete are brick, ceramic tile, porcelain, and architectural terra cotta. These clay product-facings may cover the exposed panel surface entirely or only part of the concrete face, creating accents. 7.6.2.1 General Considerations Structural design, fabrication, handling, and erection considerations for clay product–faced precast concrete units are similar to those for other precast concrete components, except that consideration must be given to the dimensional layout of the clay product material and its embedment in the concrete. The physical properties of the clay products must be compared with the properties of the concrete backup. These properties include the coefficient of thermal expansion, modulus of elasticity, and volume change due to moisture. For design purposes, clay product–faced precast concrete panels may be designed as concrete components that neglect the structural action of the face veneer. The thickness of the panel is reduced by the thickness of the veneer, and design assumptions exclude consideration of differential shrinkage or differential thermal expansion. However, if the panel is to be prestressed, the effect of composite behavior and the resulting prestress eccentricity should be considered in design. Reinforcement of the precast concrete backup should follow recommendations for precast concrete wall panels relative to design, cover, and placement. PCI has developed a standard for embedded brick in precast concrete panels to ensure size uniformity, long-term durability, and material compatibility.4 7.6.2.2 Clay-Product Properties Physical properties of clay products vary depending on the source of clay, method of forming, and extent of firing. Table 7.6.1 shows the range of physical properties of clay products. Because clay products are subject to local variation, the designer needs to obtain information on the specific brick being considered to ascertain if the variations are acceptable. As the temperature or length of the burning period is increased, the compressive strength and modulus of elasticity are increased. In general, the modulus of elasticity of brick increases with compressive strength to a compressive value of approximately 5000 psi; after that, there is little change.

Precasters should be consulted early in the design stage to determine all of the necessary properties of the clay products. The specification should identify the color, size, and manufacturer of the clay product. Usually the precast concrete producer buys the clay products and knows which products are able to conform to the PCI standard for embedded brick in precast concrete. PCI standard, thin-brick veneer units 1/2 to 1 in. thick are typically used and are available in various sizes, colors, and textures. Thin brick conforming to this standard are actually a tile and have lower water absorption than conventional brick. In addition, thin brick is less susceptible than conventional brick to freezing and thawing issues, spalling, and efflorescence. Glazed and unglazed ceramic tile units should conform to American National Standards Institute (ANSI) A137.1,5 which includes ASTM International test procedures and provides a standardized system to describe the commonly available sizes and shapes, physical properties, basis for acceptance, and methods of testing. Ceramic tiles are typically 3 /8 in. to 1/2 in. thick. Glazed units may craze from freezing and thawing cycles or the bond of the glaze may fail due to exposure to extreme environmental conditions. The body of a tile (not the glazed coating) must have a water absorption of less than 3% (measured using ASTM C3736) to be suitable for exterior applications. However, low water absorption alone is not sufficient to ensure proper selection of exterior ceramic tiles. As a result, when ceramic tile is required for exterior use, the manufacturer should be consulted for frostresistant materials for exterior exposure. Glazes are covered by ASTM C1267 and tested in accordance with ASTM C67.8 No ASTM standards exist for terra cotta, but units should meet the minimum requirements published by the Architectural Terra Cotta Institute. Architectural terra cotta is a custom-made product and, within certain limitations, is produced in sizes for specific jobs. Terra cotta is usually manufactured in 11/4-in.-thick and 21/4-in.-thick units. Sizes range from 20 in. to 30 in. for 11/4-in.-thick units and 32 in. to 48 in. for 21/4-in.-thick units. 7.6.2.4 Design Considerations The clay product surfaces are important in order to bond to the backup concrete. Textures that offer a good bonding surface include: •

scored finish, in which the surface is grooved (ribbed) or dovetailed (keybacked) as it comes from the die;

Table 7.6.1  Range of physical properties of clay products Compressive strength, psi

Modulus of elasticity, psi

3000 to 15,000

1.4 – 5.0 x 106

10,000 to 30,000

7 x 106

Glazed wall tile

8000 to 22,000

1.4 – 5.0 x 106

Terra cotta

8000 to 11,000

2.8 – 6.1 x 10

Type of unit Brick Ceramic or quarry tile

7–30

Tensile strength, psi

Coefficient of thermal expansion, in./in./˚F 4 x 10–6

Approximate 0.1 compressive strength

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0.10 Creep of 1:3 mortar by weight loaded to 1000 psi at 70 ºF

Length change, percent

0.08

  7

Free tile-setting mortar shrinkage

Free concrete shrinkage 0.06

Thermal change of 50 ºF – concrete

0.04

Tile moisture expansion at 70 ºF to 80 ºF

Creep of concrete loaded to 1000 psi at 70ºF

Brick moisture expansion

0.02

Note: Negative shrinkage (expansion) is shown in positive direction for comparison purposes

Thermal change of 50º F – tile 0

0

12

24

36

48

Time (indoors), months Fig. 7.6.1 Relative temperature, creep, and moisture movements of concrete, brick, tile, and mortar.

• • •

combed finish, in which the surface is altered by parallel scratches; roughened finish, which is produced by wire cutting or wire brushing to remove the smooth surface or die skin from the extrusion process; and brick wire cut (through extruded holes in whole bricks) to provide two (half) soaps.

With thin-brick units, no metal ties or weeps are required to attach them to the concrete because adequate bond is achieved. In general, clay products that are cast integrally with the concrete have bond strengths exceeding those obtained when laying units in the conventional manner (clay product to mortar). In pullout tests, the brick fails or shears before it pulls out of the concrete. It is necessary, however, to be careful not to entrap air or excess water-caused voids. These voids could reduce the area of contact between the units and the concrete, thereby reducing bond. The bond between the clay product–facing and the concrete depends on the absorption of the clay product and the concrete’s water–cementitious materials ratio. Either low or high absorption will result in a poor bond. Thin bricks should have a water absorption less than 6% per the PCI standard. Because of the differences in material properties between the facing and concrete, clay product–faced concrete panels may be more susceptible to bowing than homogeneous concrete units. However, panel manufacturers have devel-

oped design and production procedures to minimize bowing. When removed from the kiln after firing, clay bricks will begin to permanently increase in size as a result of absorption of atmospheric moisture. The expansion of the clay products can be absorbed by four simultaneously occurring, negative dimensional changes of the clay product and concrete: • • • •

Drying shrinkage of the concrete. Elastic deformation of the concrete under stress. Creep of the concrete under stress. Elastic deformation of the clay product under stress.

In general, strains imposed slowly and evenly will not cause problems. During the first six months to a year after panel production, tile expansion is small and the rate of strain application is slow, but concrete shrinkage is nearly complete (Fig. 7.6.1). The concrete creeps under the load to relieve the tensile stress generated in the tile when the concrete shrinks because the tiles are relatively rigid (elastic modulus of tile/ elastic modulus of concrete). After this time period, the tile has many years to accommodate the additional moisture expansion. 7.6.2.5 Other Considerations Bowing of panels in storage can be minimized by providing blocking so that panels remain dimensionally correct in storage. Storing panels so that flexure is resisted about

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the strong axis will minimize adverse stresses and bowing. Where feasible, panels should be oriented in the yard so that the sun does not overheat one side. Storing with length in north-south orientation should improve the condition. Good detailing practice will improve the probability that the finished product satisfies the owner. Use of picture-frame panels where clay products need not relate directly to those in adjacent panels will avoid alignment difficulties. All dimensions should accommodate brick coursing. 7.6.3

Stone Veneer–Faced Precast Concrete

Natural stone veneer–faced precast concrete has become widely used in building construction because of its strength, durability, aesthetic effect, availability, and inherent lowmaintenance costs. The incorporation of the stone veneer into the precast concrete panels provides an economically viable solution to cladding structures. 7.6.3.1 General Considerations The purchaser of the stone should appoint a qualified individual to be responsible for coordination, which includes delivery and scheduling responsibility and ensuring color uniformity. The responsibility for stone coordination should be written into the specifications so it can be priced. All testing to determine the physical properties of the stone veneer, with the same thickness and finish that will be used on the structure, should be conducted by the owner prior to the award of the precast concrete contract. This test data will determine the stone design and anchor placement. The responsibility for conducting various tests should be identified in the contract documents. The parties identified in this handbook are recommendations only. There is a need for close coordination between the precast concrete manufacturer and stone-veneer supplier. Shop-drawing preparation and submissions may vary from procedures established for non-veneered, precast concrete panels. Checking and approval of these details and shop drawings will be simplified and expedited if they can be combined or submitted simultaneously. Because of schedule issues, separate subcontracts and advance awards often occur in projects with stone-veneered panels. While these procedures may affect normal submission routines, it is not intended that responsibilities for accuracy should be transferred or reassigned. Typically, the precaster is responsible for precast concrete and stone layouts and details, while the stone-veneer fabricator is responsible for stone shop-fabrication drawings and drilling of anchor holes. 7.6.3.2 Stone Properties Stone is a product of geologic evolution and, therefore, does not demonstrate the consistent behavior that may apply to manufactured building materials such as concrete. The strength of natural stone depends on several factors: the size, rift, and cleavage of crystals; the degree of cohesion; the interlocking geometry of crystals; the nature of natural cementing materials present; and the type of crystal. The stone’s properties will also vary with the 7–32

locality from which it is quarried. Therefore, it is important that current testing is performed on stone quarried for each specific project. Sedimentary and metamorphic rocks, such as limestone and marble, will exhibit different strengths when measured parallel and perapendicular to their original bedding planes. Igneous rocks, such as granite, may or may not exhibit relatively uniform strength characteristics in their various planes (isotropic). In addition, the surface finish, freezing and thawing, and large temperature fluctuations will affect the stone strength and, in turn, influence the anchorage system required for the stone to the precast concrete. Information on the durability of the specified stone should be obtained through current testing in conjunction with observations of existing installations of that particular stone. This information should include such factors as tendency to warp, reaction to weathering forces, resistance to chemical pollutants, resistance to chemical reaction from adjacent materials, and reduction in strength from the effects of weathering or wetting and drying. Tests should be performed by the stone fabricator to determine the physical properties of the stone being considered prior to awarding the precast concrete contract. The testing should be done on stone with the same finish and thickness that will be used on the structure. Flexural tests (ASTM C8809) should be used to evaluate the physical properties and obtain design values. Absorption testing (ASTM C9710) helps evaluate freezing and thawing durability. These properties, along with the performance of the anchors attaching the stone veneer, should be used to ensure adequate strength of the panel to resist loads during handling, transportation, erection, and in-service conditions. The process used to obtain a thermal or flame finish on granite veneers reduces the effective stone thickness by about 1/8 in., as well as the physical strength to a measurable degree. Bushhammered and other similar surface finishes also reduce the effective thickness and strength. For 11/4-in.thick veneers, a reduction in thickness of 1/8 in. reduces the theoretical bending strength by about 19% and increases the elastic deflection under wind loads by about 27%. Laboratory tests on 11/4-in.-thick specimens of unaged, thermally finished granite revealed that the effects of the thermal finish reduced the bending strength of the specimens by as much as 25% to 30%. The loss of strength depends mainly on the physical properties of the stone-forming minerals, on the coherence of the crystalline structure of the stone, and on the presence of microfractures and macrofractures in the stone. Thermal or flame finishing and, to a certain degree, bushhammering of granite surfaces cause microfracturing, particularly of quartz and feldspars. These microcracks permit absorption of water to a depth of about 1/4 in. in the distressed surface region of the stone, which can result in degradation by cyclic freezing and thawing and a further reduction in bending strength. Weathering affects different stones in different ways. It can cause both a chemical decomposition and physical disintegration in some stones. The thinner the stone that is being sliced, the more susceptible it may be to weathering. Most natural stones lose strength as a result of aging (thermal cycling, for

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Table 7.6.2  Dimensional parameters of various stone materials Recommended thickness, in.

Length range, ft

Width range, ft

Maximum area, ft2

Marble

1.25

3 to 5

2 to 5

20

Travertinea

1.25

2 to 5

1 to 4

15

Granite

1.25

3 to 7

1 to 5

30

2

4 to 5

2 to 4

15

Stone type

Indiana limestone

example, heating to 170 °F and cooling to -10 °F, and wet/dry cycling). The modulus of rupture of building stone can also be affected by freezing and thawing of the stone. Flexural tests (ASTM C880) should be conducted on the selected stone, at the thickness and surface finish to be used, in both the new condition and the condition after 100 cycles of laboratory-accelerated aging (weathering) tests to determine the reduction in strength, if any. Suggested weathering test procedures include cycling between 170 °F and -10 °F while the face of the stone is submerged in a 4 pH sulfurous acid solution that simulates chemical weathering. For warm climates, the test procedure can be modified to cycle between 40 °F and 170 °F. Also, in areas where the pH of rainfall is above 6, the acid solution can be eliminated. Absorption testing (ASTM C97) helps evaluate the freezing and thawing durability of the stone. Stones that have a satisfactory performance record in thicknesses, sizes, and climates similar to those envisioned for a project may, at the option of the designer, be exempt from these testing requirements. For most types of stone, temperature-induced movements are theoretically reversible. However, certain stones, particularly marble, when subjected to a large number of thermal cycles, develop an irreversible expansion in the material amounting to as much as 20% of the total original thermal expansion. This residual growth is caused by the breaking of crystal bonds. Such growth, if not considered in the stone size, may result in curling or bowing of thin marble. For relatively thick marble veneers, the expansion effects are restrained or accommodated by the unaffected portion of the veneer. Tests should be performed to establish the minimum thickness required to obtain satisfactory serviceability. Stone can be exposed to differential accelerated heating and cooling cycles and measured for deformation (bowing/hyteresis). 7.6.3.3 Stone Sizes Stone veneers used for precast concrete facing are usually thinner than those used for conventionally set stone, with the maximum size generally determined by the stone strength. Table 7.6.2 summarizes typical dimensions. Veneers thinner than those listed can result in anchors being reflected on the exposed surface, excessive breakage, or permeability problems. The length and width of veneer materials should be sized to a tolerance of ±1/16 in. This tolerance becomes important when trying to line up the false joints on one panel with those on the panel above or below,

  7

particularly when there are many pieces of stone on each panel. Tolerance allowance for out-of-square is ±1/16 in. (This is the difference in length of the two diagonal measurements.) 7.6.3.4 Design Considerations Structural design, fabrication, handling, and erection considerations for veneered precast concrete units are similar to those for other precast concrete components, except that special consideration must be given to the veneer material and its attachment to the concrete. The physical properties of the stone facing material must be compared with the properties of the concrete backup. These properties include: • Tensile (axial and flexural), compressive, and shear strength • Modulus of elasticity (axial tension, flexure, and axial compression) • Coefficient of thermal expansion (Table 7.6.3) • Volume change. Because of the difference in material properties between natural stone and concrete, veneered panels are more susceptible to bowing than homogeneous concrete units. Also, the flat surfaces of cut stone reveal more prominent bowing than homogeneous concrete panels. However, there are a number of design and production procedures to help minimize bowing. For example, after the panels are erected, midpoint tieback connections can take out some bowing. 7.6.3.5 Anchorage of Stone Facing The architect, Engineer of Record, and stone fabricator should conduct tests to determine anchor type and spacing. This will allow the architect to provide anchor spacing prior to bid so that common information can be supplied to all bidders (refer to ASTM C124211). The stone fabricator should drill the anchor holes in the stone according to architectural specifications. Contract documents should clearly define type, number, and location of anchors, as well as the anchor supplier. A bondbreaker should be used between the stone veneer and concrete backup in order to minimize bowing, cracking, and staining of the veneer. Connections of natural stone to the concrete should be made with flexible mechanical anchors that can accommodate some relative in-plane movement. Two methods may be used to prevent bond between the veneer and concrete to allow for independent movement:

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Table 7.6.3 Coefficients of linear thermal expansion of aggregate and concretea Type of rock (aggregate)

  7

Average coefficient of thermal expansion × 10-6/in./°F Aggregate

Concreteb

Quartzite, cherts

6.1 to 7.0

6.6 to 7.1

Sandstones

5.6 to 6.7

5.6 to 6.5

Quartz sands and gravels

5.5 to 7.1

6.0 to 8.7

Granites and gneisses

3.2 to 5.3

3.8 to 5.3

Syenites, diorites, and andesite, gabbros, diabase, and basalt

3.0 to 4.5

4.4 to 5.3

Limestones

2.0 to 3.6

3.4 to 5.1

Marbles

2.2 to 3.9

2.3

Dolomites

3.9 to 5.5

–

Expanded shale, clay and slate

–

3.6 to 4.3

Expanded slag

–

3.9 to 6.2

Blast-furnace slag

–

5.1 to 5.9

a. S  ource - PCI Architectural Precast Manual. b. Coefficients for concretes made with aggregates from different sources vary from these values, especially those for gravels, granites, and limestones. Fine aggregates generally are the same material as coarse aggregates.

1. A 6 mil to 10 mil polyethylene sheet. 2. A closed cell 1/8 in. to 1/4 in. polyethylene foam pad. During shipment, consideration must be given to prevent cracking of the stone due to compressibility of the pad. Preformed anchors, with a 5/32 in. minimum diameter and fabricated from Type 304 stainless steel, are supplied by the stone fabricator or, in some cases, by the precaster, depending on the contract document requirements. The number and location of anchors should be predetermined by a minimum of five shear and tension tests conducted on a single anchor embedded in a stone/precast concrete test sample using ASTM E48812 or ASTM C135413 and the anticipated applied loads, both normal and transverse to the panel. Loads anticipated during handling and shipping should be included. Anchor size and spacing in veneers of questionable strengths or with natural planes of weakness may require special analysis. The number and location of anchor and size of the stone should be based on specific test values for the actual stone to be installed. Test samples for anchor tests should be a typical panel section of about 1 ft2 and should be as close as possible to actual panel-anchoring conditions. A bondbreaker should be placed between stone and concrete during sample manufacture to eliminate any bond between veneer and concrete surface. Each test sample should contain one anchor connecting stone to concrete backup, and a minimum of five tests 7–34

are needed to determine tensile (pullout) and shear strength of each type of anchor. Depending on the size of the project, it may be desirable to perform shear and tensile tests of the anchors at intervals during the fabrication period. Four anchors are usually used per stone piece, with a minimum of two recommended. The number of anchors has varied from one per 11/2 ft2 of stone to one per 6 ft2, with one per 2 ft2 to 3 ft2 the most common spacing. Anchors should be 6 in. to 12 in. from an edge with not more than 24 in. to 30 in. between anchors. The shear capacity of the spring clip (hairpin) anchors perpendicular to the anchor legs is greater than when they are parallel (Table 7.6.4) and capacity depends on the strength of the stone. A typical marble-veneer anchor detail with a toe-in spring clip anchor is shown in Fig. 7.6.2(a), while a typical granite-veneer anchor detail is shown in Fig. 7.6.2(b). The toe-out anchor in granite may have as much as 50% more tensile capacity than a toe-in anchor, depending on the stone strength. Depth of anchor holes should be approximately half the thickness of the veneer (minimum depth of 3/4 in.). Minimum stone cover over the drilled hole should be 3/8 in. to avoid spalling during drilling and spotting from absorbed moisture. The holes should be drilled at an angle of 30 deg to 45 deg to the plane of the stone. Holes, approximately 50% oversize, have been used to allow for differential movement between the stone and the concrete. However, holes 1/16 in. larger than the anchor are common, as excessive looseness reduces holding power. Anchor holes should be within ± 3/16 in. of the specified hole spacing, particularly for the spring clip anchors. Stainless steel dowels, smooth or threaded, may be installed to a depth of 2/3 of the stone thickness, with a maximum depth of 2 in. at 45 deg to 60 deg angles to the plane of the stone. The minimum embedment in the concrete backup to develop the required bond length is shown in Fig. 7.6.2(d). Dowel size varies from 3/16 in. to 5/8 in. for most stones, except that it varies from 1/4 in. to 5/8 in. for soft limestone and sandstone; it depends on the thickness and strength of the stone. Limestone has also been used traditionally with a thickness of 3 in., but it is now being used as thin as 13/4 in., although one limestone group recommends a minimum of 2 in. With limestone, use a bondbreaker along with mechanical anchors. Dowels and spring-clip anchors can be used to anchor limestone. Typical dowel details for limestone veneers are shown in Fig. 7.6.2(c); the dowels should be inserted at opposing angles to secure stone facing to backup concrete. Some flexibility should be introduced with all anchors by minimizing the anchor’s diameter to allow for the inevitable relative movements that occur with temperature variations and concrete shrinkage. Unaccommodated relative movements can result in excessive stress problems and eventual failure at an anchor location. Consideration may be given to accelerated cyclic temperature tests on the stone-concrete assembly to determine the effect of strength loss on the shear and tensile strengths of the anchors. In some climates, two-part polyester or epoxy is placed in the anchor holes in order to eliminate moisture condensation in the holes and the possible dark, damp appearance of mois-

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STRUCTURAL CONSIDERATIONS FOR ARCHITECTURAL PRECAST CONCRETE ture on the exposed-stone surface. The polyester or epoxy increases the shear capacity and rigidity of the anchors. The rigidity may be partially overcome by using 1/2-in.-long, compressible (60 durometer), rubber or elastomeric grommets or sleeves on the anchor at the back surface of the stone. Differential thermal expansion of the stone and unfilled epoxy (without sand) may cause cracking of the stone veneer. Epoxies yield under stress and, if properly formulated, will accommodate relatively large dimensional changes resulting from thermal effects. The coefficient of expansion of the stone and epoxy should closely match. However, this may be overcome by keeping the oversizing of the hole to a minimum, thereby reducing epoxy volume and using stone flour or fines or fine sand as a filler for the epoxy to reduce the coefficient of thermal expansion of the epoxy and the shrinkage. It may be desirable to fill the anchor hole with a low modulus polyurethane sealant. The overall effect of polyester, epoxy, or sealant materials on the behavior of the entire veneer should be evaluated prior to their use. At best, the long-term service life of adhesive-embedded anchors is questionable, so any increase in pullout strength of the anchors should not be used in calculating long-term anchor capacity. When using polyester or epoxy in anchor holes, the precaster needs to follow the manufacturer’s recommendations as to mixing and curing-temperature limitations. The stone trade associations and the suppliers of the various kinds of building stones recommend safety factors. Due to the variation in the physical properties of natural stones and to account for the risks of brittle failure and the effects of weathering, there are more recommended safety factors than those used for manufactured building materials such as steel and concrete. The minimum recommended safety factor, based on the average of the test results, is 4 for anchorage components in stone. If the range of test values exceeds the average by more than ±20%, then the safety factor should be applied to the lower bound value (see the appendix to ASTM C1242 for a discussion on safety factors). 7.6.3.6 Veneer Jointing Joints between veneer pieces on a precast concrete component should be a minimum of 3/8 in. The veneer pieces may be spaced with a non-staining, compressible spacing material, or a chemically neutral, resilient, non-removable gasket that will not adversely affect the sealant to be applied later. The gaskets are of a size and configuration that will provide a recess to receive the sealant and also prevent any backing concrete from entering the joint between the veneer units. Shore A hardness of the gasket should be less than 20. When stone veneer is used as an accent or feature strip on precast concrete panels, a 1/2 in. space is left between the edge of the stone and the precast concrete to allow for differential movements of the materials. This space is then caulked as if it were a conventional joint. Joint sealant should be of a type that will not stain the veneer material. In some projects, caulking may be installed more economically and satisfactorily at the same time as the caulking between precast concrete components.

CHAPTER 7

Table 7.6.4 Ultimate shear capacity of spring clip (hairpin) in granite from various sourcesa

Spring clip

Spring clip

  7 Stone

Shear parallel to anchor, lb

Shear perpendicular to anchor, lb

1

2400 to 2650

3200 to 3500

2

1800

2500

3

1500

1500

4

2500

3400

5

2800

4000

6

3400

4200

7

1000

1660

a. Need to apply a safety factor.

7.7

Precast Concrete Used as Forms

Occasionally, architectural precast concrete is used as the formwork for cast-in-place structural concrete. In most cases, the architectural precast concrete is considered solely as a form, serving only decorative purposes after the cast-in-place concrete has achieved design strength. This is accomplished by providing open or compressible joints between abutting precast concrete panels and cast-in-place concrete. Using this arrangement, the architectural precast concrete unit is non-composite with the cast-in-place concrete, and the reinforcing steel extending from the precast concrete components into the cast-in-place concrete need only be of sufficient strength to support the formwork unit. In other cases, it may be desirable to detail the structure so that the precast concrete components and cast-in-place concrete act compositely, combining the strength of both. It is then necessary to provide shear transfer as for other composite assemblies. For a more detailed discussion including design examples, refer to the fifth edition of this design handbook.14

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4" 2"

  7

Depth of concrete varies according to design t (varies) 1¼" min. preferred

2"

Depth of concrete varies according 30˚ to 45˚ to design

S.S. anchor

db = 5⁄32” min.

Face of stone veneer Bond breaker

Epoxy set 15˚ Deformed S.S. anchor db = 3⁄16" to 5⁄8"

½t ¾" min. Face of stone veneer

Depth of concrete varies according to design

S.S. anchor db = 3⁄16 to 5⁄8" 2 /3 t 2" max.

db

2½" min. 45˚ to 60˚

Bond breaker t (varies)

2"

Varies 2" to 5"

1" to 2" Stone

30˚ to 45˚

Concrete

¾" min. in 2" stone 2" max. in 5" stone

Concrete

Bond breaker

(b) Typical anchor for granite veneer

Varies

Stone

1¼"

Hole 1/16" to 1/8" > db 6" to 9" to edge of stone

(a) Typical anchor for marble veneer

Varies

db = 5⁄32" min.

t (varies) 1¼" min. preferred

½t ¾" min.

Hole 1/16" to 1/8" > db 6" to 9" to edge of stone

S.S. anchor

Hole 1⁄16" to 1⁄8" > db

1

30˚ to 45˚

Hole /16" to 1/8" > db Dowels may be epoxied

Bond breaker Close slots with tape

Use anchors at opposing angles (d) Typical cross anchor dowel for stone veneer

(c) Typical anchor for limestone veneer

Fig. 7.6.2 Typical stone-veneer anchors. Note: max. = maximum; min. = minimum; S.S. = stainless steel.

7.8

References

1. Precast/Prestressed Concrete Institute (PCI). 2007. Architectural Precast Concrete (MNL-122-07). 3rd ed. Chicago, IL: PCI. 2. American Concrete Institute (ACI). 2005. Building Code Requirements for Structural Concrete (ACI 31805) and Commentary (ACI 318R-05). Farmington Hills, MI: ACI.

7–36

3. American Society of Civil Engineers (ASCE). Minimum Design Loads for Buildings and Other Structures (ASCE 7-05). Reston, VA: ASCE. 4. International Code Council (ICC). 2006. 2006 International Building Code (IBC 2006). Washington, DC: ICC. 5. American National Standards Institute (ANSI). Standard Specifications for Ceramic Tile (ANSI A137). Washington, DC: ANSI.

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STRUCTURAL CONSIDERATIONS FOR ARCHITECTURAL PRECAST CONCRETE 6. American Society for Materials and Testing (ASTM). 2006. Standard Test Method for Water Absorption, Bulk Density, Apparent Porosity, and Apparent Specific Gravity of Fired Whiteware Products (ASTM C373). West Conshohocken, PA: ASTM. 7. ASTM. 2009. Standard Specification for Ceramic Glazed Structural Clay Facing Tile, Facing Brick, and Solid Masonry Units (ASTM C126). West Conshohocken, PA: ASTM. 8. ASTM. 2009. Sampling and Testing Brick and Structural Clay Tile (ASTM C67). West Conshohocken, PA: ASTM. 9. ASTM. 2009. Standard Test Method for Flexural Strength of Dimension Stone (ASTM C880/C880M). West Conshohocken, PA: ASTM.

CHAPTER 7

•

Marble Institute of America. 2007. Dimensional Stone: Design Manual VII. Cleveland, OH: Marble Institute of America.

•

National Building Granite Quarries Association. 2007. Standard Specifications for Architectural Granite. Washington, DC: National Building Granite Quarries Association.

•

Indiana Limestone Institute of America. 2008. Indiana Limestone Handbook. 22nd ed. Bedford, IN: Indiana Limestone Institute of America.

•

PCI. 1990. Architectural Precast Concrete Cladding — Its Contribution to Lateral Resistance of Buildings, Proceedings, SP-CP. Chicago, IL: PCI.

10. ASTM. 2009. Standard Test Methods for Absorption and Bulk Specific Gravity of Dimension Stone (ASTM C97/C97M). West Conshohocken, PA: ASTM. 11. ASTM. 2005. Standard Guide for Selection, Design, and Installation of Dimension Stone Anchoring Systems (ASTM C 1242). West Conshohocken, PA: ASTM. 12. ASTM. 2003. Standard Test Methods for Strength of Anchors in Concrete and Masonry Elements (ASTM E 488). West Conshohocken, PA: ASTM. 13. ASTM. 2009. Standard Test Method for Strength of Individual Stone Anchorages in Dimension Stone (ASTM C1354/C1354M). West Conshohocken, PA: ASTM. 14. PCI. 1999. PCI Design Handbook (MNL-120-99). 5th ed. Chicago, IL: PCI. The following references are not specifically identified in this chapter but may provide the user with additional information regarding structural design considerations of architectural precast concrete: •

Sheppard, D. A., and W. R. Phillips. 1989. Plant-Cast Precast and Prestressed Concrete — A Design Guide. 3rd ed. New York, NY: McGraw-Hill Publishing Co.

•

ACI. 2005. Formwork for Concrete, special publication SP-4. 5th ed. Farmington Hills, MI: ACI.

•

ASCE and ACI. 2008. Building Code Requirements for Masonry Structures (ACI 530-08/ASCE 5-TMS 40208,) and Specifications for Masonry Structures (ACI 530.1-08/ASCE 6-TMS 602-08).

•

Bernett, Frank E. 1976. Effects of Moisture Expansion in Installed Quarry Tile. Ceramic Bulletin, V. 5, No. 12.

•

Chin, I. R., J. P. Stecich, and B. Erlin. 1986. Design of Thin Stone Veneers on Buildings. Building Stone Magazine, May–June.

•

Merritt, Frederick S., and J. T. Rickets, eds. 1994. Building Construction Handbook. 5th ed. New York, NY: McGraw-Hill Book Co.

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CHAPTER 7

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CHAPTER 8 COMPONENT HANDLING AND ERECTION BRACING 8.1

General . ....................................................................................................................................................................8–2

8.2

Component Handling..................................................................................................................................................8–2 8.2.1 Introduction..................................................................................................................................................8–2 8.2.2 Planning and Setup.......................................................................................................................................8–2

8.3

Stripping.....................................................................................................................................................................8–2 8.3.1 Introduction..................................................................................................................................................8–2 8.3.2 Rigging Configurations................................................................................................................................8–6 8.3.3 Spreader Beams............................................................................................................................................ 8–6 8.3.4 Stripping Design..........................................................................................................................................8–8 8.3.4.1 Form Suction and Impact Factors..............................................................................................8–8 8.3.4.2 Factors of Safety........................................................................................................................8–8 8.3.4.3 Stress Limits and Crack Control................................................................................................8–9 8.3.4.4 Benefits of Prestressing.............................................................................................................8–9 8.3.5 Handling Devices...................................................................................................................................... 8–10 8.3.5.1 Aircraft-Cable Loops.............................................................................................................. 8–10 8.3.5.2 Prestressing-Strand Loops...................................................................................................... 8–10 8.3.5.3 Threaded Inserts...................................................................................................................... 8–10 8.3.5.4 Proprietary Devices................................................................................................................ 8–11

8.4

Yarding and Storage................................................................................................................................................ 8–18 8.4.1 Lateral Stability......................................................................................................................................... 8–18 8.4.2 Storage...................................................................................................................................................... 8–18

8.5

Transportation.......................................................................................................................................................... 8–19

8.6

Erection Handling.................................................................................................................................................... 8–21

8.7

Erection Bracing...................................................................................................................................................... 8–23 8.7.1 Introduction............................................................................................................................................... 8–23 8.7.2 Responsibilities......................................................................................................................................... 8–23 8.7.3 Handling Equipment................................................................................................................................. 8–25 8.7.4 Surveying and Layout............................................................................................................................... 8–26 8.7.5 Loads......................................................................................................................................................... 8–26 8.7.6 Factors of Safety....................................................................................................................................... 8–26 8.7.7 Bracing Equipment and Materials............................................................................................................. 8–26 8.7.8 Erection Analysis and Associated Bracing Requirements........................................................................ 8–28

8.8

References............................................................................................................................................................... 8–28

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COMPONENT HANDLING AND ERECTION BRACING

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8.1

General

8.2.2

This chapter provides design guidelines for precast/ prestressed components for temporary loads imposed during form removal, storage, transportation, and erection handling. Examples are included to illustrate the structural analysis for these conditions.

  8

8.2

Component Handling

8.2.1

Introduction

The loads and forces on precast and prestressed concrete components during production, transportation, or erection will frequently require a separate analysis because concrete strengths are lower as well as support points and/or orientation are usually different from their final, in-service position. Most structural components are manufactured in long-line steel forms with fixed cross-section dimensions. Standard structural product dimensions are shown in Chapter 3 and in manufacturers’ catalogs. Architectural concrete wall panels are formed in a variety of sizes and shapes. The project architect usually designs these characteristics, and the components are then manufactured in molds fabricated specifically for the project. The most economical component size for a project is usually the largest, considering the following factors: • • • • • • •

Stability and stresses on the component during handling Transportation size and weight regulations and equipment restrictions Available crane capacity at both the plant and the project site (position of the crane must also be considered since capacity is a function of reach) Storage space, truck turning radius, and other site restrictions Stiffness and deflection of haul trailers Crane rigging (use of one or two crane lines) Capacity of lifting devices

Stripping direction

Breakaway form Positive draft Fig. 8.2.1 Positive drafts and breakaway forms.

8–2

Planning and Setup

Proper planning of production methods is essential. Once a precast concrete component has been fabricated, it is necessary to remove it from the mold without causing damage. Positive drafts or breakaway forms should be used to allow a component to lift away from the casting bed without becoming wedged within the form (Fig. 8.2.1). Adequate draft also serves to reduce trapped air bubbles. Lifting points must be located to keep component stresses within allowable limits and to ensure proper alignment of the piece as it is being lifted. Common lifting configurations and analysis of these arrangements are discussed later in this chapter. Components with unsymmetrical geometry or projecting sections may require supplemental lifting points and auxiliary lifting lines during handling. Come-alongs or chain-falls are frequently used for these auxiliary lines (Fig. 8.2.2). When the component has areas of small or reduced cross section or large cantilevers, it may be necessary to add a temporary or permanent structural steel strongback to the piece to provide added strength (Fig. 8.2.3 and 8.2.4). Components that require a secondary process prior to shipment, such as sandblasting or attachment of haunches, may need to be rotated at the production facility. In these cases, it may be necessary to cast in extra lifting devices to facilitate these maneuvers. When developing component shapes, consideration should be given to the added expense associated with special rigging or forming, and with pieces requiring multiple handling.

8.3

Stripping

8.3.1

Introduction

Orientation of components during storage, shipping, and final in-service position is critical in determining stripping requirements. They can be horizontal, vertical, or some angle in between. The number and location of lifting devices are selected by the manufacturer to keep stresses within allowable limits. This will depend on whether the no-discernible-cracking or controlled-cracking criteria is to be used (Section 8.3.4.3). It is desirable to use the same lifting devices for both stripping and erection; however, additional devices may be required to rotate the component to its final position. Panels that are stripped by rotating about one edge with lifting devices at the opposite edge will develop moments as shown in Fig. 8.3.1. When panels are stripped this way, care should be taken to prevent spalling of the edge along which the rotation occurs. A compressible material or sand bed will help protect this edge. Components that are stripped flat from the mold will develop moments shown in Fig. 8.3.2. To determine stresses in flat panels for either rotation or flat stripping, the calculated moment may be assumed to be resisted by the effective widths shown in Fig. 8.3.1 and 8.3.2, respectively. In some plants, tilt tables or turning rigs are used to reduce stripping stresses, as shown in Fig. 8.3.3. When a panel is ribbed or is of a configuration or size such that stripping by rotation or tilting is not practical, vertical

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  8

Supplemental line with “come-along”

Fig. 8.2.2 Supplemental lifting points.

Steel angle bolted to slender section

Fig. 8.2.3 Strongback for slender section.

Steel angle

Fig. 8.2.4 Strongback for cantilevers. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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COMPONENT HANDLING AND ERECTION BRACING

CHAPTER 8

Re

sis

tin

gs

ge

  8 us

o inu

nt

Co

s

tio

h nt

rt o

po

up

ec

d is e

nf

or

M

y

t

b

07

0.2

(a) Two-point pick-up maximum moments

b

86

0.5 a

b

b

7 .20

w = weight per unit area

+My

0

Mx = wa (per unit of width) 8 2

M

x

-My = +My = 0.0107wab 2 My resisted by a section of width a/2

-My Re

sis

ge

us

o inu

nt

Co

rt po

d is e

o

h nt

gs

ec

tio

nf

or

M

y

t

p

su

tin

b

04

b

0.1

92

b

0.2

08

0.2

a M

x

b 92 0.2 b 04 0.1

(b) Four-point pick-up maximum moments

b

Locations shown for equal pick loads: Mx = wa (per unit of width) 8 2

+My

-My = +My = 0.0027wab 2 My resisted by a section of width a/2

-My

Fig. 8.3.1 Moments developed in panels stripped by rotating about one edge.

8–4

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COMPONENT HANDLING AND ERECTION BRACING

CHAPTER 8

Re

sis

tin

gs

ec

tio

x rM

o nf ctio /2) e b s ng or isti (15t s e

nf

or

M

y

t

R

  8

7b

0

0.2 0.2

07

a

0.5

86

a

b 86 0.5 b +My

b

07

0.2

a

(a) Four-point pick-up maximum moments w = weight per unit area Locations shown for equal pick loads

+M

x

+Mx = -Mx = 0.0107wa2 b

-M

x

+My = -My = 0.0107wab 2

-My

Mx resisted by a section of width 15t or b/2, whichever is less My resisted by a section of width a/2

Re

sis

M

or nf tio /4) c e gs rb tin 15t o s i s (

x

tin

gs

ec

tio

nf

or

M

y

t

Re

b

04

0.1 b

92

0.2

b

0.2

08

07

a

0.2

0.5 a

b 92 0.2 4b 0 0.1

+M

+M

86

a

x

b

(b) Eight-point pick-up maximum moments Locations shown for equal pick loads +Mx = -Mx = 0.0054wa2 b

y

+My = -My = 0.0027wab 2 Mx resisted by a section of width 15t or b/4, whichever is less

-M

x

-My

My resisted by a section of width a/2

Fig. 8.3.2 Moments developed in panels stripped flat. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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COMPONENT HANDLING AND ERECTION BRACING

CHAPTER 8

Crane line load = W

Side forms

T = sling load = WF 2 Sling angle = θ

(a) Hardened panel prior to stripping

θ

Hydraulic ram

Total load = W

Hinge

  8

(b) Panel tilted by table

Multiplication factor F for the total load on sling with a sling angle of θ θ 90º 75º 60º 45º 30º 1.00 1.04 1.16 1.41 2.00 F Note: θ is usually not less then 60º. Check bi-directional sling angle. A 30º sling angle is not recommended.

(c) Panel stripping

Fig. 8.3.3 Stripping from a tilt table.

Fig. 8.3.4 Force in lift lines.

pick-up points on the top surface can be used. These lifting points should be located to keep the tensile stresses on both faces within acceptable limits. Patching of inserts on critically exposed surfaces may be required. Because the section modulus with respect to the top and bottom faces may not be the same, the designer must select the controlling design limitation based on the following:

tion could occur between the ribs because of the thin cross section. The design guidelines listed previously apply to components of constant cross section. For components with varying cross sections, the lift-point locations can be calculated and adjusted. Rolling blocks and spreader beams can be used on long components of varying sections (Fig. 8.3.6), which make the forces in the lifting lines equal. The component can then be analyzed as a beam with varying loads supported by equal reactions. The force in the lift lines can be determined as shown in Fig. 8.3.5. As an alternative to rolling blocks, multiple crane lines or spreader beams can be used. Availability of such equipment and preferred methods will vary among precasters. The advantage of multiple crane lines is that lift-line forces are straight up and different forces can be applied to each crane line (Fig. 8.3.7). For components of varying cross sections, such as panels with large openings or panels with an extended narrow leg, the different lift-line forces allow for the larger or stiffer cross sections to resist the heavier lift-line forces.

• • •

Tensile stresses on both faces to be less than that which would cause discernable cracking. Tensile stress on the exposed face to be less than that which would cause discernable cracking, and controlled cracking permitted on the unexposed face. Controlled cracking permitted on both faces. If only one of the faces is exposed to view, the exposed face will generally control the stripping method.

8.3.2

Rigging Configurations

Stresses and forces that occur during handling are also influenced by the type of rigging used to hook up and lift the component. Lift-line forces for a two-point lift using inclined lines are shown in Fig. 8.3.4. When the sling angle is small, the force component parallel to the longitudinal axis of the component may generate a significant moment due to P-∆ effects. While this effect can and should be accounted for, it is not recommended that this moment control the design. Rather, consideration should be given to using spreader beams, two cranes, or other means to increase the sling angle. Any such special handling required by the design should be clearly shown on the shop drawings. In addition to longitudinal bending moments, a transverse bending moment may be caused by the orientation of the pick-up points with respect to the transverse dimension (Fig. 8.3.5). For the section shown, a critical stress condi8–6

8.3.3

Spreader Beams

Using a spreader beam, as shown in Fig. 8.3.8, can eliminate the use of rolling blocks. Determination of the appropriate steel section to use as a spreader beam is not straightforward. Design of spreader beams for use with cranes is governed by the American Society of Mechanical Engineers (ASME) B30.20 Below-the-Hook Lifting Devices.1 The only strength requirement in this standard is the spreader beam “shall be designed to withstand the stresses imposed by its rated load plus the weight of the lifter, with a minimum design factor of three, based on yield strength of the material.” This requirement, while satisfactory for bending stresses of compact

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CHAPTER 8

T

P Y θ yc

PZ Z

Center of gravity

Y

T T

P

φ

e

P tanθ Mx = PZyc PZ =

  8

(a) Four points with two cranes

P

Px Px

φ yt yc yb

Center of gravity

X

P tanφ Mz = Pxyc Px =

P = vertical component of force on lifting device T = force in sling due to two rigging angles T =P

(b) Eight points with two cranes and two spreader beams

1 + 1 tan2φ sin2 θ

Fig. 8.3.7 Hook lifting. Fig. 8.3.5 Moments caused by eccentric lifting.

Spreader Beam Center of gravity

Rolling Block

Equal

Force equal on all lines

Equal

a) Four points with spreader beam

All reactions equal R

R

R

R

b) Eight points with spreader beam Fig. 8.3.6 Arrangement for equalizing lifting loads.

Fig. 8.3.8 Use of spreader beams.

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CHAPTER 8 and non-compact sections, does not address lateral torsional buckling failure modes, which frequently govern spreaderbeam designs since the compression flange is unbraced for its entire length. Achieving this requirement within the framework of applicable design codes is the responsibility of the designer, and there are many different solutions. The following provides an allowable stress-design approach that yields conservative results:

  8

a spreader beam, the component acts as a continuous beam with multiple supports. Consideration of lifting-hook locations, hook heights, and sling angles are critical to ensure even lifting of the component. 8.3.4

Stripping Design

8.3.4.1 Form Suction and Impact Factors To account for the forces on the component caused by form suction and impact, it is common practice to apply a multiplier to the component weight and treat the resulting force as an equivalent static load. These multipliers cannot be quantitatively derived, so they are based on experience. Table 8.3.1 provides typical values. Individual precast concrete producers may have modified factors based on its local experiences and its specific formwork.

•

For compact or non-compact sections, use Fy /3 as the allowable bending stress. • For beams with the unbraced length (distance between crane pick points) greater than Lc as defined in AISC Manual of Steel Construction Ninth Edition,2 the allowable bending stress can be determined from equations F1-6, F1-7, and F1-8 as appropriate and divided by 1.8 (resulting in an effective allowable bending stress that is about 1/3 the stress that corresponds to buckling). • For allowable axial stress, modify AISC allowablestress design (ASD) Eq. E2-1 and E2-2 to have a safety factor of 3. Apply AISC ASD Eq. H1-1, H1-2, and H1-3 directly for interaction of combined bending and axial loads. Note that newer editions of AISC’s manuals may have different equations. An additional consideration for spreader-beam design includes making the spreader beam stiffer than the concrete component to limit the deflection and stresses that may cause cracking. Also, weld stress ranges should not exceed the values listed in ANSI/AWS D14.1, Specification for Welding of Industrial and Mill Cranes and Other Material Handling Equipment.3 A similar philosophy should be applied for the design of connections of spreader-beam assemblies. For analysis of a precast concrete component when using

8.3.4.2 Factors of Safety When designing for stripping and handling, the following safety factors are recommended. 1. Use embedded inserts and erection devices with a pullout strength at least equal to four times the calculated load on the device. Note that suction factors shown in Table 8.3.1 are not to be applied in addition to the weight of the component when calculating lifting-device loads. Also note that the sling angle of the rigging may affect these values. 2. For components designed without discernible cracking, the modulus of rupture (fr = 7.5 fc' ) is divided by a safety factor of 1.5 so that the computed stress is less than or equal to 7.5λ fc' = 5λ fc' 1.5



(Eq. 8-1)

Table 8.3.1  Equivalent static load multipliers to account for stripping and dynamic forcesa,b Finish Product type

Exposed aggregate with retarder

Smooth mold (form oil only)

Flat, with removable side forms, no false joints or reveals

1.2

1.3

Flat, with false joints and/or reveals

1.3

1.4

1.4

1.6

1.5

1.7

c

Fluted, with proper draft

Sculptured and other conditions d

b

Yard handling and erection All products

1.2 Transportation

d

All products

1.5

a. These factors are used in flexural design of panels and are not to be applied to required safety factors on lifting devices. At stripping, suction between product and form introduces forces, which are treated here by introducing a multiplier on product weight. It would be more accurate to establish these multipliers based on the actual contact area and a suction factor independent of product weight. b. May be higher under certain circumstances. c. For example, tees, channels, and fluted panels. d. Certain unfavorable conditions in road surface, equipment, and the like may require use of higher values.

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CHAPTER 8

8.3.4.3 Stress Limits and Crack Control

Extra layer welded-wire reinforcement at looped areas

2" clear

Stress limits for prestressed components during production are discussed in Section 5.2.2.2 of this handbook. ACI 318-054 does not restrict stresses on non-prestressed components, but does specify minimum reinforcement spacing, as discussed in Section 5.2.2.1. Components exposed to view will generally be designed for the no-discernible-cracking criteria (see Section 5.2.2.2), which limits the stress to 5λ fc' . In the case of ' stripping stresses, fci' should be substituted for fc . Whether or not the components are exposed to view, the strength-design and crack-control requirements of ACI 318-05 as discussed in Chapter 5 of this publication must be followed.

Minimum recommended radius = 24 in.

A

8'-0"

Side elevation

A

Strand is extended beyond panel to allow length for the jack

6"

Plan

3"×6" pocket for strand anchor Bottom elevation Continuous strand in plastic sheath Welded-wire reinforcement

3"

3"

Panels can be prestressed, using either pretensioning or posttensioning. Design is based on Chapter 18 of ACI 318-05, as described in Chapter 5 of this publication. Further, tensile stresses should be limited to no more than 5λ fci' to provide a factor of safety against cracking for crack-free performance. It is recommended that the average stress due to prestressing, after losses, for a non-flexural component be within a range of 125 psi to 800 psi. The prestressing force should be concentric with the effective cross section to minimize bowing of wall panels, although some manufacturers prefer to have a slight inward bow in the in-service position to counteract thermal bow (see Section 5.8.5). Concentrically prestressed components do not camber; the form adhesion, therefore, may be larger than with components that do camber. The camber that results from the prestressing force being applied below the center of gravity of the section helps release the component from the form. To minimize the possibility of splitting cracks in thin, pretensioned components, the strand diameter should not exceed that shown in Table 8.3.2. Additional transverse reinforcement may be helpful to minimize longitudinal cracking, especially at the ends. When wall panels are post-tensioned,5 care must be taken to ensure proper transfer of the anchorage force and to provide protection of anchors and tendons against corrosion. Straight strands or bars may be used, or, to reduce the number of anchors, the method shown in Fig. 8.3.9 may be used. Plastic-coated post-tensioning tendons with a low coefficient of curvature friction (µ = 0.03 to 0.05) are looped within the panel and anchors installed at only one end. The tendons remain unbonded. It should be noted that if an unbonded tendon is cut, the prestress is lost. This can happen if an unplanned opening is cut at a later date.

32'-0"

8.3.4.4 Benefits of Prestressing

Section A-A

Table 8.3.2  Suggested maximum strand diameter Concrete slab thickness, in.

Strand diameter, in.

less than 3

3

/8

3 or more

1

/2

Fig. 8.3.9 Post-tensioned wall panel.

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COMPONENT HANDLING AND ERECTION BRACING

CHAPTER 8 Table 8.3.3  Safe working load of 7 × 19a aircraft cable used as lifting loops Diameter, in.

Safe load, kipb

/8

3.6

/16

4.4

/2

5.7

3 7

1

  8

a. Seven strands with 19 wires each. b. Based on a single strand with a safety factor of 4 applied to the minimum breaking strength of galvanized cable. The user should consider embedment, loop diameter, and other factors discussed for strand loops.

8.3.5

Handling Devices

The most common lifting devices are prestressing strand or aircraft-cable loops projecting from the concrete surface, embedded threaded inserts, and proprietary devices. Since lifting devices are subject to dynamic loads, ductility of the material is a requirement. Deformed reinforcing bars should not be used because the deformations result in stress concentrations from the shackle pin. Also, reinforcing bars may be hard grade or rerolled rail steel with little ductility and low-impact strength at cold temperatures. Strain hardening from bending the bars may also cause embrittlement. Smooth bars of a known steel grade may be used if adequate embedment or mechanical anchorage is provided. The diameter must be such that localized failure will not occur by bearing on the shackle pin. 8.3.5.1 Aircraft-Cable Loops For smaller precast concrete components, aircraft cable can be used for stripping and erection purposes. Aircraft cable comes in several sizes with different capacities (Table 8.3.3). The flexible cable is easier to handle and will not leave rust stains on the concrete. For some small precast concrete components such as coping, the flexible loops can be cast in the ends and tucked back in the joints after erection. Aircraft-cable loops should not be used as multiple loops in a single location, as even pull on multiple cables in a single hook is extremely difficult to achieve. The user should ensure that the cable is clean and each leg of the loop is embedded a minimum of 48 in. Aircraft cables are usually wrapped around reinforcement in the precast concrete component. 8.3.5.2 Prestressing-Strand Loops Prestressing strand may be used for lifting loops. The capacity of a lifting loop embedded in concrete is dependent upon the strength of the strand, length of embedment, the condition of the strand, the diameter of the loop, and the type and strength of the concrete As a result of observations of lift-loop behavior over many years, it is important that certain procedures be followed to prevent both strand slippage and strand failure. Precast concrete producers’ tests and/or experiences offer the best guidelines for strand-loop capacities. A safety factor of 4 against slippage or breakage should be used. When test data are not available, the following recommendations should be consid8–10

ered when using strand as lifting loops. 1. Embedment for each leg of the loop should be a minimum of 24 in. 2. The strand surface must be free of contaminants, such as form oil, grease, mud, or loose rust, which could reduce the bond of the strand to the concrete. 3. The diameter of the hook or fitting around which the strand lifting eye will be placed should be at least four times the diameter of the strand being used. The diameter of the bend should be a minimum of 2 in. 4. Do not use heavily corroded strand or strand of unknown size and strength. 5. Vertically inserted strand lift loops used in selfconsolidating concrete have shown to have lower pullout strengths due to the attraction of air bubbles in the area of the strand. Longer embedment lengths may be required.6 In the absence of tests or experience, it is recommended that the safe load on a single 1/2-in.-diameter, 270 ksi strand loop satisfying the previously discussed recommendations not exceed 8 kip. The safe working load of multiple loops may be conservatively obtained by multiplying the safe load for one loop by 1.7 for double-strand loops and 2.2 for triplestrand loops. To avoid overstress in one strand when using multiple strands, care should be taken in the fabrication to ensure that all strands are bent the same. Thin-wall conduit over the strands in the region of the bend has been used to reduce the potential for overstress. When using double- or triple-strand loops, the embedded ends should be spread apart so that adequate concrete consolidation around the ends is achieved. Sometimes double- or triple-strand loops may not be practical due to lack of space, insufficient test data to justify capacity, or lack of experience on the part of the user. In such cases, alternative solutions may be designed by the engineer, such as the use of assemblies consisting of embedded rods and lifting plates. 8.3.5.3 Threaded Inserts Lifting heavy components with threaded inserts should be assessed carefully. Threaded inserts usually have national coarse or coil threads. Anchorage is provided by loop, strut, or reinforcing bar (Fig. 8.3.10). Inserts must be placed accurately because their safe working load decreases sharply if they are not perpendicular to the concrete surface or if they are not in alignment with the applied force. Embedment of inserts close to an edge will greatly reduce the effective area of the resisting concrete shear cone, thereby reducing the safe working capacity of the embedded insert. Refer to Chapter 6 for additional information on concrete anchorage and conditions affecting capacity. When properly designed for both insert and concrete capacities, threaded inserts have many advantages. However, correct usage is sometimes difficult to inspect during handling operations. To ensure that an embedded insert acts primarily in tension, a swivel plate as shown in Fig. 8.3.11

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Four-strut coil

Two-strut coil

  8

Coil loop

Eye bolt

Wire-rope loop

Fig. 8.3.10 Threaded inserts.

should be used. It is extremely important that sufficient threads be engaged to develop the strength of the bolt. Some manufacturers use a long threaded rod with a nut between the bolt head and the swivel plate. After the rod has bottomed out in the insert, the nut is tightened against the swivel plate. Use of only one threaded lifting device is not recommended because the bolt could unscrew itself by spinning when load is applied. For straight tension loads only, eye bolts or wire-rope loops provide a fast method for handling precast concrete components (Fig. 8.3.10). Do not use either device if shear loading conditions exist. Connection hardware designed for in-service loads should not be used for lifting or handling any component except the lightest units, unless approved by the designer. In order to prevent field error, inserts used for lifting should be of a different type or size than those used for the final connections.

with reductions for thin panels and/or close edge distances. Supplemental reinforcement, when used to achieve these values, must fully engage the embedded lifting device. Shallow units usually have a spread foot or base to increase pullout capacity. Reinforcing bars are required in two directions over the base to fully develop the lifting capacity, as shown in Fig. 8.3.12(b). They are rated up to 16 kip. Some lifting eyes do not swivel, so rotation may be a concern. The following considerations are recommended: • • •

Because many of these devices are steel castings, they may get brittle in cold weather. If the devices are to be galvanized, this should be done by the device manufacturer. In all cases, the manufacturers’ recommendations should be rigorously followed.

8.3.5.4 Proprietary Devices A variety of steel castings or proprietary steel devices, machined to accept specialized lifting assemblies, are used in the precast concrete industry (Fig. 8.3.12). These proprietary devices are usually recessed using a pocket former to provide access to the lifting device. The recess allows one panel to be placed against another in storage without cutting off the lifting device, and also helps prevent spalling around the device. Longer devices are used for edge lifting of deep precast concrete components; shallow devices are available for thin precast concrete components. The longer devices usually engage a reinforcing bar to provide greater pullout capacity, and often have holes provided for a reinforcing bar to pass through, as shown in Fig. 8.3.12(a). These units have rated capacities as high as 44 kip, PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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COMPONENT HANDLING AND ERECTION BRACING

CHAPTER 8

Vertical component V + He d Insert bolt

Angular pull Swivel plate

  8 Recess

H

Insert placed mostly in tension

e

d

V + He d

Fig. 8.3.11 Swivel plate.

Shear Bar

Tension bars

Plate (a) Edge handling for deep components

(b) For thin components

(c) Edge lifters

Fig. 8.3.12 Proprietary devices.

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EXAMPLE 8.3.1 Design of Wall Panel for Stripping This example and others in Chapter 8 illustrate the use of many of the recommendations in this chapter. They are intended to be illustrative and general only; each precast concrete manufacturer will have its own preferred method of handling. Given: A flat panel used as a load-bearing wall on a two-story structure as shown Section properties (nominal dimensions are used for design): Solid panel A = 960 in.2 Sb = St = 1280 in.3 Ix = 5120 in.4 Weight  = 35.2 kip

  8

Panel with openings A = 480 in.2 Sb = St = 640 in.3 Ix = 2560 in.4 Weight  = 29.2 kip

Concrete density at 150 lb/ft3 = 100 lb/ft2 = 0.10 kip/ft2

fc' = 5000 psi, normalweight, fci' = 3000 psi Stripping method: Inside crane height prevents panel from being turned on edge directly in mold; therefore, strip flat.

3'-6"

10'-0" wide panels /4" joint (typical)

35'-2"

6'-0"

False joints (depth = 3/4")

5'×6' openings

Building elevation

5'-6"

4'-0"

15'-6"

5'-6"

3

6'-0"

16'-2"

10'-0" 2'-6"

5'-0"

2'-6"

Nominal dimensions

4'-8"

8" Smooth form finish with false joints Typical panel section

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CHAPTER 8

EXAMPLE 8.3.1 Design of Wall Panel for Stripping (cont.) Handling multipliers: Exposed flat surface has a smooth form finish with false joints. Side rails are removable. Use multiplier of 1.4 (Table 8.3.1). Design for no discernible cracking, therefore: 5(1.0) 3000 Allowable tensile stresses at stripping from Eq. 5-7: 5λ fci' = = 0.274 ksi 1000

  8

Problem: Check critical stresses involved with stripping. Limit stresses to 0.274 ksi on both faces. __________________________________________________________________________ Solution: (a)

Solid panel From Fig. 8.3.2: a = 10 ft, b = 35.2 ft



Try four-point pick, Fig. 8.3.2(a): (Note that the full width of the resisting section is used here) My = (2)(0.0107)wab 2 = (2)(0.0107)(0.100)(1.4)(10)(35.2)2(12) = 223 kip-in. ft = fb = 223/640 = 0.348 ksi > 0.274 ksi four-point pick not adequate



Try eight-point pick, Fig. 8.3.2(b): (Note that the full width of the resisting section is used here) My = (2)(0.0054)wab 2 = (2)(0.0054)(0.100)(1.4)(10)(35.2)2(12) = 224.8 kip-in. ft = fb = 224.8/1280 = 0.176 ksi < 0.274 ksi Determine pick point loads: W = 35.2 kip W/2 = 17.6 kip W/4 = 8.8 kip

OK

W

W 2

W 2

8.8' W 4

W 4

(Note: If maximum moment occurs near a false joint, reduced section properties should be used.) 3.7'

V, kip

8.8'

10.3'

5.10

W 4

W

W 4

w = 1.0 kip/ft

3.70

3.70

5.10

6.29 M, kip-ft 6.84 Line of symmetry

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CHAPTER 8

EXAMPLE 8.3.1 Design of Wall Panel for Stripping (cont.) (b)

Panel with openings



Analyzing as a continuous beam with rigid supports (without use of rolling blocks): At solid section: ft

=

(6.8) (1.4 ) (12) 1280

7.2

6.3

8.4

= 0.089 ksi

  8

At opening: or ft

(5.3) (1.4 ) (12 ) =

640 < 0.274 ksi

= 0.139 ksi OK

 ecause there is a false joint near the B point of maximum stress, recalculate stress using reduced cross section. St at false joint: 3 (120 − 60 )  8 −  4 = 6



w = 0.5 k/ft w = 1.0 k/ft w = 0.5 k/ft w = 1.0 k/ft S = 640 in.4 S = 1280 in.4 S = 640 in.4 S = 1280 in.4

w = 1.0 k/ft S = 1280 in.4

V, kip

2



= 526 in.3

ft

=



= 0.169 ksi < 0.274 ksi OK

3.5

3.7

2.5

2.6 2.0

M, kip-ft

5.3 (1.4 )(12 ) 526

3.8

0.5

3.7

3.0 2.7

1.4

3.7

0.6

3.2 4.7 4.3

4.2

-1.8

-3.8

-5.3

-4.6

-6.8

-6.8

 lternatively, as a conservative approximation, use ±Mmax based on a solid wall panel, but determine A stresses using section properties of panel with openings: My

= 112.4 kip-in.

ft

112.4  = 526 

= 0.214 ksi < 0.274 ksi

W

OK RL

1

9.15'

2

8.35'

3

RR

4 Panel center of gravity

18.0'

17.2' If using a rolling block for handling as shown in Fig. 8.3.6, the panel cannot be analyzed as shown in Fig. 8.3.2(b). Because each leg of a continuous cable running over a rolling block must carry equal loads, the panel can be analyzed as follows. Using the diagram above: Check panel with openings using rolling block handling:

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COMPONENT HANDLING AND ERECTION BRACING

CHAPTER 8

EXAMPLE 8.3.1 Design of Wall Panel for Stripping (cont.) W = 29.2 kip RL =

(29.2) (8.35 ) 9.15 + 8.35

R1 = R2 =

  8

= 13.9 kip

13.9 = 6.95 kip 2

RR = 29.2 – 13.9 = 15.3 kip R3 = R4 =

15.3 = 7.65 kip 2

Mmax = 13.5 kip-in. ft

=

(13.5) (1.4 ) (12)

526 = 0.431 ksi > 0.274 ksi No good

Use of rolling block with standard eight-point pick locations for these panels is not acceptable under the prescribed design criteria. The designer should choose to either adjust the anchor locations in an effort to minimize stresses or introduce prestressing to lower or eliminate net tensile stresses (Example 8.3.2).

Lift loops – typical

Check transverse bending: Consider lower portion of panel with openings. Note that Fig. 8.3.2(b) is based on a solid panel with uniformly distributed weight and cross section. Without the concrete in the area of the opening, the weight is reduced and unevenly distributed. Also, the resisting section is limited to a width of 4.7 ft. Section through lifters: w2 = (4.7)(0.67)(0.15) = 0.47 kip/ft

w1

=

w1

w1

w2

7.2 − (0.47 ) (10 ) + 0.47 = 0.97 kip/ft 2 ( 2.5 )

Mmax = 2.1 kip-ft = 25.2 kip-in. Check added moment due to sling angle (Fig. 8.3.5): Using recessed proprietary lifting anchor, e = 3.5 in. Sling angle φ = 60 deg 7.2 P = = 3.6 kip 2 Px =

P

P

From previous analysis, load carried by bottom two anchors is 7.2 kip, therefore:

3.6 P = 2.08 kip = tanφ tan60

V, kip

2.5'

5.0'

2.5'

2.1'

5.8'

2.1' 2.04

1.56 1.17

1.17

2.04

1.56

M, kip-ft -2.14

-0.13

-2.14

Mx = 2.08(3.5) = 7.3 kip-in. 8–16

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CHAPTER 8

EXAMPLE 8.3.1 Design of Wall Panel for Stripping (cont.) Mtot = 25.2 + 7.3 = 32.5 kip-in. Resisting section: b

= 4.7 ft = 56 in.

t

= 8 in.

S

=

bt 2 (56 )( 8 ) = 6 6

f

=

M tot (handling multiplier ) ( 32.5 ) (1.4) = 0.076 ksi < 0.274 ksi = S 597

  8

2

= 597 in.3



OK

3

4

Add strand at centerline of 8" panel thickness

7

2'-6"

joint

Problem: Determine required number of 1/2-in.-diameter, 270 ksi strands pulled to 28.9 kip to prevent cracking in window panel. Assume 10% loss of prestress.

5'-0" opending

" False

2'-6"

Given: The panel of Example 8.3.1.

1

4

"

EXAMPLE 8.3.2 Use of Prestressing in the Wall Panel

From Example 8.3.1, tensile stress is 0.431 ksi. The desired level of tensile stress is

5 3000 = 0.274 ksi. 1000

Therefore: Compressive stress required = 0.431 – 0.274 = 0.157 ksi _________________________________________________________________________________ Solution: From Example 8.3.1, maximum moment/stress occurs at lifting points -M. This results in tensile stresses on the top face. A

= (2)(30)(7.25) = 435 in.2

St

=

P A



M S

=

=

(2 ) ( 30 ) (7.25 )2 6

= 526 in.3

(number of strands ) (28.9 ) (1.0 − 0.10) 435

(number of strands ) (28.9 )(1.0 − 0.10 ) ⎛⎜⎝ 526

= 0.06 (number of strands)

7.25 ⎞ − 4⎟ ⎠ 2

= -0.019 (number of strands)

Therefore: 0.060(number of strands) – 0.019(number of strands) = 0.157 ksi Number of strands = 3.8 Add four strands to panel (two on each side of opening). PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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CHAPTER 8

Roll axis

Center of gravity of the curved beam arc lies directly beneath the roll axis

Deflection of beam due to bending about weak axis

yt Center of gravity of cross section at lifting point

Component of weight about weak xxis = Wsinθ

  8

Lifting loops

θ

W

Center of mass of deflected shape of the beam (b) Free body diagram

(a) Perspective of a beam free to roll and deflect laterally

Fig. 8.4.1 Equilibrium of beam in tilted position.

8.4

Yarding and Storage

8.4.1

Lateral Stability

In general, prestressed concrete components are sufficiently stiff to prevent lateral buckling. However, during handling and transportation, support flexibility may result in lateral roll of a slender component, thereby producing lateral bending. This can be a particular concern with long-span bridge beams and very long spandrels in parking structures. The equilibrium conditions for a hanging beam are shown in Fig. 8.4.1. When a beam hangs from lifting points, it may have a tendency to roll about an axis through the lifting points. The safety and stability of long beams subject to roll is discussed in References 7, 8, 9, and 10. One of the best methods for minimizing stresses during shipping and handling is to move the lifting devices inward from the ends of the beam, effectively reducing the roll span. Analysis may be required to determine if end cantilevers are possible during handling, and additional reinforcement may be required to resist these cantilever moments. Temporary top prestressing strands can possibly be used and then cut after the prestressed component is in its in-service position so that the final design is as intended. Some manufacturers and haulers use temporary supplement frames that are attached to the component. These truss frames lay horizontal and provide added stability to the slender component during shipping to prevent roll over. 8.4.2

Lateral supports

 Panel tilted out of vertical for storage

Storage

Wherever possible, a component should be stored on points of support located at or near those used for stripping and handling. Thus, design for stripping and handling will usually control. Where points other than those used for stripping and handling are used for storage, the storage condition must be checked and communicated to the appropriate plant personnel. 8–18

If support is provided at more than two points and the design is based on more than two supports, precautions must be taken so that the component does not bridge over one of the supports due to differential support settlement. Particular care must be taken for prestressed components, with consideration made for the effect of prestressing. Designing for equal stresses on both faces of the component will help to minimize deformations in storage.

Fig. 8.4.2 Panel warpage in storage.

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COMPONENT HANDLING AND ERECTION BRACING Warpage in storage may be caused by a temperature or shrinkage differential between surfaces, creep, and storage conditions. Warpage cannot be totally eliminated, although it can be minimized by providing blocking so that the component remains plane. Where feasible, the component should be oriented in the yard so that the sun does not overheat one side (see Section 5.8.5). Storing components so that flexure is resisted about the strong axis will minimize stresses and deformations. For the support condition shown in Fig. 8.4.2, warping can occur in both directions. By superposition, the total instantaneous deflection ymax at the maximum point can be estimated by: 4 ⎤ 1.875 ( w ) sinθ ⎡ a 4 ymax = (Eq. 8-2) =⎢ + ⎥ Eci ⎣ Ic Ib ⎦  where: w = panel weight, lb/ft2 Eci = modulus of elasticity of concrete at age other than final, psi a = panel support height, in. l = horizontal distance between supports, in. Ic, Ib = moment of inertia of the uncracked section in the respective directions for 1 in. width of panel, in.4 This instantaneous deflection should be modified by a factor to account for the time-dependent effects of creep and shrinkage. ACI 318-05 suggests the total deformation yt at any time can be estimated as:

5 months or more

12 months 6 months

3 months

Fig. 8.4.3 Effect of compression reinforcement on creep.

Fig. 8.4.4 Area considered to compute ρ′.

CHAPTER 8

yt = ymax(1 + λ)

(Eq. 8-3)

where: yt = time-dependent displacement ymax = instantaneous displacement λ = amplification due to creep and shrinkage (Fig. 8.4.3) ρ' = reinforcement ratio for non-prestressed compression reinforcement, A's /bd (Fig. 8.4.4)

8.5

Transportation

The method used for transporting precast concrete components can affect the structural design because of size restrictions, weight limitations, and dynamic effects imposed by road conditions. Except for long, prestressed deck components, most are transported on either flatbed or low-boy trailers. These trailers deform during hauling. Thus, support at more than two points can be achieved only after considerable modification of the trailer, and even then results may be doubtful. Size and weight limitations vary from state to state, so a check of local regulations is necessary when large units are transported. Loads are further restricted on some secondary roads during spring thaws. The common payload for standard trailers without special permits is 24 tons (may vary with state law) with width and height restricted to 8 ft and length to 40 ft. Low-boy trailers permit the height to be increased to about 10 ft to 12 ft. However, low-boys cost more to operate and typically have a shorter bed length. In some states, a total height (roadbed to top of load) of 13 ft-6 in. is allowed without special permit. This height may require special routing to avoid low overpasses and overhead wires. Maximum width with a permit varies among states, and even among cities, from 10 ft to 14 ft. Some states allow lengths of over 70 ft with only a simple permit, while others require a special permit for any load over 55 ft, in addition to front and rear escorts and travel limited to certain times of the day. In some states, weights of up to 100 tons are allowed with a permit, while in other states there are very severe restrictions on loads over 25 tons. These restrictions add to the cost of precast concrete components and should be compared with savings realized by combining smaller units into one larger unit. When possible, a precast concrete component or several combined should approximate the usual payload of 24 tons. For example, a 13 ton component may not be economical because only one can be shipped per load. Erection is simplified when components are transported in the same orientation as they will be in the completed structure. For example, single-story wall panels can be transported on A-frames with the panels upright (Fig. 8.5.1). A-frames also provide good lateral support and the desired two points of vertical support. Upright shipping will also minimize erection handling time on the site because the panel is already oriented properly. Longer units can be transported on their sides to take advantage of the increased stiffness compared with flat

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EXAMPLE 8.5.1 Panel Shipping Check the 8-in.-thick panel shown for proper method of transporting to the jobsite. Assume concrete has achieved its 28-day strength of 5000 psi. Use a transportation load multiplier of 1.5.

  8

Try shipping flat with supports at four locations along the length of the panel based on Fig. 8.3.2(b) (not shown here). For this condition, it is very likely that the trailers will flex during transport and will raise or lower support points, causing bridging and unanticipated stresses. Try adjusting support points to create pairs of support points, 5 ft apart from one another, at each end of the panel. This configuration should ensure that all four supports remain in contact at all times during transportation. If wider spacing between support points is required, rocker bearings, which ensure that all four support points remain in contact with the panel at all times, are recommended. As an alternative, panels may be shipped on edge, resting against A-frames, if height restrictions are satisfied.

10' x 35' - 2" solid panel (w = 1 kip-ft)

V, kip

M, kip-ft

Mmax = 17.7 ft-kip = 212.4 in.-kip f

8–20

= 212.4 (1.5 ) = 0.249 ksi < 5 5000 = 0.354 ksi 1280 1000

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CHAPTER 8 usually supported with one or both ends cantilevered. For components not symmetrical with respect to the bending axis, the equations given in Fig. 8.5.3 can be used for determining the support locations to give equal tensile stresses for positive and negative bending moments. Note that these equations do not account for prestressing in the components.

8.6 Fig. 8.5.1 Transporting single-story panels.

shipment (Fig. 8.5.2). In all cases, the panel support locations should be consistent with the panel design. Panels with large openings sometimes require strongbacks, braces, or ties to keep stresses within acceptable limits (Fig. 8.2.3 and 8.2.4). During transportation, precast concrete components are

Erection Handling

Precast concrete components must frequently be reoriented from the position used for transportation to their final in-service position. The analysis for this tripping (rotating) operation is similar to that used during other handling stages. Figure 8.6.1 shows maximum moments and corresponding reactions for several commonly used tripping techniques. When using two operating crane lines, the center of gravity of the panel must be located between the two lines in order to prevent a sudden shifting of the load while the panel is being rotated.

Fig. 8.5.2 Transporting long panels.



 



(a) One end cantilevered

1⎡ yb y ⎤ x = ⎢1+ − 1+ b ⎥ 2⎣ yt yt ⎦ where: yb = distance from the neutral axis to the bottom surface yt = distance from the neutral axis to the top surface





(b) Both ends cantilevered

x=

1 ⎡ y ⎤ 2 ⎢1+ 1+ t ⎥ yb ⎦ ⎣

Note: These equations do not account for prestressing in the components.

Fig. 8.5.3 Equations for equal tensile stresses at top and bottom of component. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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CHAPTER 8

(a)

w 2a

Two-point rotation:

1 w 1 - 2a w

General equation b

+M

0.5wb22 w 2 1 2 1 - 2a

-M

+M

-M +M

0.022w2 0.067w2

-M

-M

+M

a

2



  8

(b) 0.70w

Two-point rotation:

0.30w w

Equal negative and positive bending moments

-M

0.29

0.044w2

+M

0.71 

(c)

Two-point pick for rotation: Lower pick point at typical two-point stripping location

(d)

0.63w

0.37w w

-M 0.21

+M

0.79



Three-point pick for rotation

0.71w

Rolling block

0.29w w 0.1 -M

+M

0.4

-MMax +MMax

-0.005w2 +0.041w2

-MMax +MMax

0.018w2 0.054w2

0.5

 (e) 0.67w

Three-point pick for rotation at top and two lower pick rotations

Rolling block 0.33w

0.1

0.3

-M

0.6

+M



Fig. 8.6.1 Typical tripping (rotating) positions for erection of precast concrete components. Note: In top diagrams, dashed lines indicate deflected shapes. (Continued on the following page)

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(f)

RT

RB Rolling block

Center of gravity

  8 Moments less critical than flat position





+

Fig. 8.6.1 (cont.) Typical tripping (rotating) positions for erection of precast concrete components. Note: RB will vary from approximately 0.7w to 0.8w and RT will vary from approximately 0.3w to 0.2w, depending on panel geometry and sling lengths. Confirm for specific conditions used.

When using a rolling block between two bottom lifting points for a three-point pick as shown in Fig. 8.6.1, the vertical alignment of the rolling-block reaction will shift toward the center of gravity of the panel as the panel is rotated. If the rolling-block reaction aligns with the center of gravity of the panel, the panel will roll uncontrollably. To avoid this condition, the two bottom lifting devices must be located below the center of gravity of the panel, as shown in Fig. 8.6.2. If stresses in the top portion of the panel become excessive, it may be necessary to use a four-point pick, shown in Example 8.6.1. The capacities of lifting devices must be checked for the forces imposed during the tripping operation because the directions and methods vary.

8.7

Erection Bracing

8.7.1

Introduction

This section addresses the temporary bracing that may be necessary to maintain stability of a precast concrete structure during construction. When possible, the final connections should be used to provide at least part of the erection bracing, but additional bracing is sometimes required to resist all of the temporary loads. These temporary loads may include wind, seismic, or eccentric dead loads, which include construction loads or unbalanced conditions due to the erection sequence and incomplete connections. Due to the low probability of full design loads occurring during erection, engineering judgment should be used to establish reasonable erection design loads (see Section 8.7.2 for suggested guidelines). 8.7.2

Responsibilities

Proper planning of the construction process is essential for efficient and safe erection. The sequence of erection must be established early, and the effects must be accounted for in the bracing analysis and the preparation of shop drawings. The responsibility for the erection of precast concrete structures may vary as follows (also see Section 14.5): Center of gravity

W

Fig. 8.6.2 Stability during erection.

1. The precast concrete manufacturer supplies the product erected, either with its own forces, or by an independent erector. 2. The manufacturer is responsible only for supplying the product, freight-on-board plant, or jobsite. Erection is done either by the general contractor or by an independent erector under a separate agreement with the general contractor.

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EXAMPLE 8.6.1 Erecting Wall Panels Given: 10 ft wide × 35 ft – 6 in. tall x 8-in.-thick wall panel. The panel has four sets of stripping devices and eight-point pick in accordance with Fig. 8.3.2 (b). fc' = 5000 psi, normalweight

  8

Solution: Try three-point rotation procedure using rollingblocks attachment to the bottom two stripping devices: The other operating line is attached to the devices in the top of the panel. w

RB

1

2

Problem: Determine appropriate procedures for erecting the wall panel. Panel will be shipped flat. 5 fc' = 0.354 ksi Limit stresses to 5λ Use an erection load multiplier = 1.2 (See Table 8.3.1) Crane has main and auxiliary lines. ________________________________________



Center of gravity of panel

 

V, kip

= 1.0 kip/ft

( 35.2 ) (1) 

35.2   2  = = 23.5 kip 0.292   35.2  0.604 +   2 

M, kip-ft (Horizontal position)

RB1 = RB2 = 23.5/2 = 11.75 kip RT   = (35.2)(1) – 23.5 = 11.7 kip In horizontal position: Mmax = 69.6 kip-ft = 835.2 kip-in. f

B

1.2 ( 835.2 ) = = 0.483 ksi > 0.354 ksi 1280

Three-point pick not adequate. Therefore, rig with rolling blocks at A and B as shown.

8–24

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EXAMPLE 8.6.1 Erecting Wall Panels (cont.) (a) Because the panel may not hang in the true vertical position after rotation, the method shown in (a) and (c) may be an alternative.

B

B

B

a) Hook both crane lines to stripping devices.

  8

(b) W  ith panel essentially vertical, disengage crane line B from bottom inserts.

c) Hook line B to lifting devices in top edge of panel from manlift, lift panel from line B.

Note: In Fig. (b) and Fig. (c), both A and B must be designed to carry the full weight of the panel. 3. The products are purchased by an independent erector who has a contract with the general contractor to furnish the complete precast concrete package. Responsibility for stability during erection must be clearly understood. Design for erection conditions must be in accordance with all local, state, and federal regulations. This design should be done with the full collaboration of the precast concrete manufacturer, erector, and the responsible engineer. Erection drawings and/or separate, approved erection plans should define the procedure on how to assemble the components into the final structure. The erection plan should also address the stability of the structure during construction and include temporary connections as required. When necessary, special drawings may be required to include shoring,

guying, bracing, and specific erection sequences. Additional guidelines are available in PCI Recommended Practice for Erection of Precast Concrete (MNL-127-99).11 For large and/or complex projects, a conference prior to the preparation of erection drawings is recommended to discuss erection methods and preferences and to identify coordination requirements with other trades. 8.7.3

Handling Equipment

The type of jobsite handling equipment selected may influence the erection sequence and affect the temporary bracing requirements. Several types of erection equipment are available, including truck-mounted and crawler mobile cranes, hydraulic cranes, tower cranes, monorail systems, derricks, and others.11

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CHAPTER 8 8.7.4

  8

Surveying and Layout

Before products are shipped to the jobsite, a field check of the jobsite conditions is recommended to ensure that prior construction is suitable to accept the precast concrete components. This check should include location, line and grade of bearing surfaces, notches, blockouts, anchor bolts, cast-in hardware, and dimensional deviations. Site conditions such as access ramps, overhead electrical lines, truck and crane access, and the like should also be checked. Any discrepancies between actual conditions and those shown on drawings should be addressed before erection is started. Surveys should be required before, during, and after erection for the following reasons: 1. Before, so that the planned starting points and starting elevations are clearly established and any potential difficulties with the support structure are determined early and rectified if required. 2. During, to maintain alignment. 3. After, to ensure that the products have been erected within acceptable tolerances. 8.7.5

Loads

The publication Design Loads on Structures During Construction (SEI/ASCE 37-02)12 provides recommended minimum design loads, including wind and seismic, as well as construction loads and load combinations for partially completed structures during construction. This publication is a standard, not a code. Subsequently, its provisions are not mandatory, and the engineer who establishes the loads to be applied during erection may use his/her judgment based on experience. In addition to analyzing the structure and components for these effects, consider the effect of temporary unbalanced loads on the stability and bracing design for components within the entire structure. Examples are shown in Fig. 8.7.1. Consider the following: •

•

 olumns with eccentric loads from other framing C components produce sidesway, which means the columns lean out-of-plumb. A similar condition can exist when cladding panels are erected only on one side of a multistory structure. (Fig. 8.7.1[a]) Unbalanced loads due to partially complete erection may result in beam rotation. The erection drawings should address these conditions. Some solutions are (Fig. 8.7.1[c]) and [d]): • • • •

•

8–26

Install wood wedges between the flange of the tee and the top of the beam. Use connections to columns that minimize rotation and prevent instability. Erect tees on both sides of the beam. Shore tees to the level below.

 otations and deflections of support components may R be caused by cladding panels. This may result in align-

ment problems and require connections that allow for alignment adjustment after all panels are erected. It is recommended that connections be designed such that adjustments in panel alignment can be made without the use of a crane. (Fig. 8.7.1[b]) and [e]) If construction equipment such as concrete buggies, lifts, and the like are to be used, information such as wheel loads and spacing should be conveyed to the designer of the precast concrete components and the designer of the erection bracing. These loads should be approved by the designer prior to application. Consideration should also be given to the storage of construction materials on precast concrete components to avoid overloading. 8.7.6

Factors of Safety

Safety factors used for temporary loading conditions are a matter of engineering judgment, and should consider failure mode (brittle or ductile), predictability of loads, quality control of products and construction, probability for human error, and economics. The total factor of safety also depends on load factors and capacity-reduction factors used in the design of the entire bracing system. These must be consistent with applicable code requirements for working stress design. Suggested safety factors are shown in Table 8.7.1. Table 8.7.1  Suggested factors of safety for construction loads Bracing inserts cast into precast concrete components

3

Lifting inserts

4

Reusable hardware

5

8.7.7

Bracing Equipment and Materials

For most one-story and two-story structures that require simple bracing, steel-pipe braces similar to those shown in Fig. 8.7.2 are used. A wide range of bracing types is available from a number of suppliers that should be consulted for dimensions and capacities. Pipe braces can resist both tension and compression. When long braces are used in compression, it may be necessary to provide supplemental lateral restraint to the brace to prevent buckling. Proper anchoring of the braces to the precast concrete components and deadmen (usually large blocks of concrete placed on the ground) must be considered. When the pipe braces are in tension, there may be significant shear and tension loads applied to the deadmen. Properly designed deadmen that resist sliding and overturning are a requirement for safe bracing. Cable guys with turnbuckles are normally used for taller structures. Because wire rope used in cable guys can resist only tension, they are usually used in combination with other cable guys in an opposite direction. A number of different types of wire rope are available. Note that the capacity of these systems may be governed by the turnbuckle capacity. Long cables will stretch due to imposed loads and temperature variations, which may necessitate a serviceability check

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Deflection of supporting slab results in rotation of panel

  8

Floor diaphram restrains or bracing loads change as loads are added

(b)

(a)

Wood wedge

Rotation

Tee (c)

(d)

Shore as required by design

Deflection position of supporting component due to weight of panels varies as each panel is erected (e)

Fig. 8.7.1 Temporary loading conditions that affect stability. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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8.8

References

1. A  merican Society of Mechanical Engineers (ASME). 2006. Below-the-Hook Lifting Device (ASME B30.20). New York, NY: ASME. 2. A  merican Institute of Steel Construction (AISC). 1989. Manual of Steel Construction. 9th ed. Chicago, IL: AISC. 3. A  merican Welding Society (AWS). 2005. Specifications for Welding of Industrial and Mill Cranes and Other Material Handling Equipment, AWS D14.1. Miami, FL: AWS.

  8

Continuous adjustment

4. A  merican Concrete Institute (ACI). 2005. Building Code Requirements for Structural Concrete (ACI 31805) and Commentary (ACI 318R-05). Farmington Hills, MI: ACI.

Incremental adjustment

5. T  anner, John. 1977. Architectural Panel Design and Production Using Post-Tensioning. PCI Journal, V. 22, No. 3 (May-June).

Fig. 8.7.2 Typical pipe braces.

if temporary deflections must be controlled. Compression struts, which may be the precast concrete components, are needed to complete truss action of the bracing system. 8.7.8

 rection Analysis and Associated E Bracing Requirements

Careful planning of the erection sequence is important to ensure structural stability and safety during various stages of construction. Actual loads, factors of safety, equipment used, and the like must be evaluated for each project. This sequence is usually dictated by the general contractor and requires coordination with the precast concrete erector, precast concrete production and shipping departments, and the design engineer. A properly planned erection sequence can reduce bracing requirements. For example, with wallpanel systems, a corner can be erected first so that immediate stability can be achieved. It is recommended that an erection sequence be established before precast concrete production begins so that multiple handling of components is minimized. Similar considerations for shear-wall structures can also reduce bracing requirements. All parties should be made aware of the necessity of closely following erection with the final diaphragm connections. This includes the diaphragm to shear-wall connections. In order for precast concrete erection to flow smoothly, site access and preparation, the products to be erected, erection equipment, and bracing equipment and deadmen must all be ready, and the precast concrete shipping must be planned.

8–28

6. P  recast/Prestressed Concrete Institute (PCI). 2003. Interim Guidelines for the Use of Self-Consolidating Concrete in Precast/Prestressed Concrete Institute Component Plants, TR-6-03. Chicago, IL: PCI. 7. M  ast, Robert F. 1989. Lateral Stability of Long Prestressed Concrete Beams  –  Part 1. PCI Journal, V. 34, No. 1 (January-February). 8. M  ast, Robert F. 1993. Lateral Stability of Long Prestressed Concrete Beams  –  Part 2. PCI Journal, V. 38, No. 1 (January-February). 9. P  CI. 1997. PCI Bridge Design Manual (MNL-133-97). Chicago, IL: PCI. 10. M  ast, Robert F. 1994. Lateral Bending Test to Destruction of a 149 ft Prestressed Concrete I-Beam. PCI Journal, V. 39, No. 4 (July-August). 11. P  CI Erectors Committee. 1999. Erectors Manual – Standards and Guideline for the Erection of Precast Concrete Products (MNL-127-99). Chicago, IL: PCI. 12. A  merican Society of Civil Engineers (ASCE), Structural Engineering Institute, cosponsor. 2002. Design Loads on Structures During Construction (SEI/ASCE 37-02). Reston, VA: ASCE.

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CHAPTER 9 PRECAST AND PRESTRESSED CONCRETE: MATERIALS 9.1

Introduction.................................................................................................................................................................9-3 9.1.1 Definitions....................................................................................................................................................9-3

9.2 Concrete.......................................................................................................................................................................9-3 9.2.1 Constituent Materials....................................................................................................................................9-3 9.2.1.1 Cement............................................................................................................................................9-3 9.2.1.2 Supplementary Cementitious Materials (SCMs)............................................................................9-4 9.2.1.3 Aggregates......................................................................................................................................9-4 9.2.1.4 Chemical Admixtures.....................................................................................................................9-5 9.2.1.5 Water...............................................................................................................................................9-9 9.2.1.6 Pigments.......................................................................................................................................9-10 9.2.2 Physical Properties......................................................................................................................................9-10 9.2.2.1 Introduction...................................................................................................................................9-10 9.2.2.2 Compressive Strength...................................................................................................................9-10 9.2.2.3 Tensile Strength............................................................................................................................9-11 9.2.2.4 Modulus of Elasticity....................................................................................................................9-11 9.2.2.5 Poisson's Ratio..............................................................................................................................9-11 9.2.2.6 Volume Changes...........................................................................................................................9-11 9.2.2.7 Durability/Reactivity....................................................................................................................9-13 9.2.3 Finishes ......................................................................................................................................................9-17 9.2.3.1 Conventional.................................................................................................................................9-17 9.2.3.2 Architectural/Decorative...............................................................................................................9-18 9.3

Grout, Mortar, and Drypack......................................................................................................................................9-19 9.3.1 Sand-Cement Mixtures...............................................................................................................................9-19 9.3.2 Non-Shrink Grouts......................................................................................................................................9-20 9.3.3 Epoxy Grouts..............................................................................................................................................9-20

9.4

Connection Materials.................................................................................................................................................9-20 9.4.1 Introduction.................................................................................................................................................9-20 9.4.2 Steel Sections..............................................................................................................................................9-20 9.4.3 Bearing Pads...............................................................................................................................................9-20 9.4.4 Structural Bolts/Anchor Bolts.....................................................................................................................9-20

9.5 Corrosion and Protection Means...............................................................................................................................9-21 9.5.1 Introduction.................................................................................................................................................9-21 9.5.2 Galvanic Series...........................................................................................................................................9-21 9.5.3 Protection of Connections...........................................................................................................................9-22 9.5.3.1 Painted Steel.................................................................................................................................9-22 9.5.3.2 Galvanized Steel...........................................................................................................................9-22 9.5.3.3 Stainless Steel...............................................................................................................................9-23

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9.6 Reinforcement...........................................................................................................................................................9-24 9.6.1 Prestressing Tendons...................................................................................................................................9-24 9.6.2 Prestressing Bars.........................................................................................................................................9-25 9.6.3 Deformed Reinforcing Bars........................................................................................................................9-25 9.6.4 Structural Welded-Wire Reinforcement.....................................................................................................9-26 9.6.5 Carbon-Fiber Mesh.....................................................................................................................................9-27 9.6.6 Protection of Reinforcement.......................................................................................................................9-27 9.6.6.1 Corrosion Mechanism/Chlorides..................................................................................................9-27 9.6.6.2 Carbonation/Cracking...................................................................................................................9-27 9.6.6.3 Concrete Cover.............................................................................................................................9-27 9.6.6.4 Galvanized Reinforcement...........................................................................................................9-27 9.6.6.5 Epoxy-Coated Reinforcement......................................................................................................9-28 9.6.6.6 Epoxy-Coated Strand....................................................................................................................9-28 9.6.6.7 Other Corrosion-Resistant Steels..................................................................................................9-28 9.7 Waterproofing............................................................................................................................................................9-29 9.7.1 Coatings for Horizontal Deck Surfaces......................................................................................................9-29 9.7.2 Clear Surface Sealers for Architectural Precast Concrete Panels...............................................................9-29 9.7.3 Surface Coatings for Architectural Precast Concrete..................................................................................9-29 9.7.4 Joint Sealants...............................................................................................................................................9-30 9.7.4.1 Introduction...................................................................................................................................9-30 9.7.4.2 Joint Profile...................................................................................................................................9-30 9.7.4.3 Sealant Types................................................................................................................................9-30 9.7.4.4 Joint Sealant Considerations.........................................................................................................9-32 9.7.5 Expansion Joints.........................................................................................................................................9-33 9.8 In-Service Considerations.........................................................................................................................................9-33 9.8.1 Cracking......................................................................................................................................................9-33 9.8.2 Repairs ......................................................................................................................................................9-34 9.8.2.1 Patching........................................................................................................................................9-34 9.8.2.2 Crack Repair.................................................................................................................................9-35 9.8.2.3 Connection Repair........................................................................................................................9-35 9.8.3 Component Strengthening...........................................................................................................................9-35 9.8.4 Maintenance................................................................................................................................................9-39 9.9

Relevant Standards and Publications.........................................................................................................................9-40

9.10

References.................................................................................................................................................................9-40

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9.1

Introduction

This chapter provides a brief review of the major materials used in precast and prestressed concrete; that is, concrete and its constituent materials, concrete physical properties, reinforcing steels, and prestressing steels. Also included is a discussion of the durability of concrete, corrosion protection of steel reinforcing and embedments, and waterproofing issues. The chapter concludes with topics on repair, should the product get damaged, and the relevant material standards that are used in specifications. Since information on material properties can be found in a number of references, specific references are only included where they are unique. A list of reference material is included in Section 9.9.

9.1.1

Definitions

Admixture — Material other than water, aggregate, or hydraulic cement, used as an ingredient in concrete and added to concrete before or during its mixing to modify its properties. Aggregate — Granular material, such as sand, gravel, and crushed stone used with a cementing medium to form a hydraulic cement concrete or mortar. Aggregate, coarse — aggregate predominantly retained on the 4.75 mm (No. 4) sieve or that portion retained on the 4.75 mm (No. 4) sieve. Aggregate, fine — Granular material filler consisting of natural sand, manufactured sand, or a combination of both. Aggregate, lightweight — aggregate of low density, such as: (a) expanded or sintered clay, shale, slate, diatomaceous shale, perlite, vermiculite, or slag; (b) natural pumice, scoria, volcanic cinders, tuff, and diatomite; or (c) sintered fly ash or industrial cinders used in lightweight concrete. Cementitious materials — Materials that have cementing value when used in concrete either by themselves, such as portland cement, blended hydraulic cements, and expansive cement, or such materials in combination with fly ash, other raw or calcined natural pozzolans, silica fume, and/or ground granulated blast-furnace slag. Concrete — Mixture of portland cement or any other hydraulic cement, fine aggregate, coarse aggregate, and water, with or without admixtures. Concrete, structural lightweight — structural concrete made with low-density aggregate; having an air-dry density of not more than 115 lb/ft3 and a 28 day compressive strength of more than 2500 psi. Concrete, sand-lightweight — concrete made with a combination of expanded clay, shale, slag, or slate or sintered fly ash and natural sand; its density is generally between 105 and 120 lb/ft3. Concrete, normalweight — concrete having a density of approximately 150 lb/ft3 made with normal-density aggregates. Grout — A mixture of cementitious material and water, with or without aggregate, proportioned to produce a pourable consistency without segregation of the constituents; also a mixture of other composition (epoxy, neat-cement, preblended) but of similar consistency.

CHAPTER 9 Modulus of elasticity — Ratio of normal stress to corresponding strain for tensile or compressive stresses below the proportional limit of material. Modulus of rupture — the calculated apparent tensile stress in the extreme tension fiber of a plain concrete beam test specimen at the load that produces rupture when tested in accordance with ASTM C78 (third-point loading) or ASTM C293 (center-point loading). Patch — Replacement of damaged or deteriorated concrete with a (cementitious) repair material placed partially against an existing concrete substrate. Partial-depth patches repair near-surface conditions constituting only a portion of the member depth. Full-depth patches replace damaged or deteriorated concrete for the full member depth. Splitting tensile strength ( fct ) — Tensile strength of concrete determined in accordance with ASTM C496 as described in ASTM C330 Standard Specification for Lightweight Aggregates for Structural Concrete. Strength, concrete compressive ( fc' ) — the measured maximum resistance of a concrete specimen to axial compressive loading; expressed as force per unit cross sectional area.

9.2

Concrete

Modern concrete is produced with a combination of cement, fine aggregate, coarse aggregate, water, mineral admixtures, and chemical admixtures. The standards covering these constituents are listed in Table 9.2.1 and described further in the following sections. 9.2.1

Constituent Materials

9.2.1.1 Cement Type I portland cement is general purpose cement suitable for all uses where the special properties of other types of cement are not required. Type II portland cement is used where precaution against moderate sulfate attack is important. This cement can also be used to reduce the heat of hydration and mitigate alkali-silica reaction (ASR) potential; a combination Type I and Type II cement is available in some areas of the country. Mill certificates should be obtained from the cement mill for record and chemistry compared with the limits shown in ASTM C150. Type III portland cement provides high strength at an early age and is particularly appropriate for obtaining high release strengths. This cement is commonly used in precast and prestressed concrete plants. Type IV portland cement is used to reduce the heat of hydration and is beneficial in mass concrete structures. Type V portland cement is used in concrete exposed to severe sulfate attack, like those found in some soils. Types IA, IIA, and IIIA correspond to their base cement-type composition, except that small quantities of dry air-entraining material are included in the cement. Refer to Table 9.2.2 for cement types.

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CHAPTER 9 9.2.1.2 S  upplementary Cementitious Materials (SCMs)

  9

Fly ash.  Fly ash is a finely divided residue resulting from the combustion of pulverized coal in fossil-fuel power plants. Class F fly ash has pozzolanic properties; Class C has some cementitious properties in addition to pozzolanic properties. Some fly ashes meet both Class F and Class C classifications. Selection of these materials will depend on their local availability and their effect on concrete properties. Fly ash is used as a partial cement substitute up to 20% by volume. It has a positive effect on the durability of the hardened concrete even though early strength gain is reduced when Type F is used. It should be noted that when fly ash is used, the color of the concrete may be altered. Ground granulated blast-furnace slag (GGBFS).  This is also called slag cement or slag. It is an industrial byproduct of the iron-making process in a blast furnace. GGBFS hydrates are more fluid than those of portland cement, which reduces pore sizes and increases the denseness of the paste. Silica fume.  Silica fume is a very fine pozzolanic material produced as a by-product in electric arc furnaces used for the production of component silicon or ferro-silicon alloys. Silica fume is also known as condensed silica fume or micro silica. The use of silica fume can improve early-age concrete strength development and is particularly beneficial in achieving high release strengths in high-strength prestressed concrete products. The use of silica fume in concrete generally results in a low permeable concrete. The use of silica fume increases the water demand in concrete. Consequently, it is generally used in combination with a water-reducing admixture or a high-range water-reducing admixture. Concrete

containing silica fume releases significantly less bleed water, increasing the potential for plastic shrinkage cracking. Therefore, early moisture loss should be prevented under conditions that promote rapid surface drying, such as low humidity and high temperatures. Silica fume concrete also presents special finishing issues, as the concrete tends to be sticky. Metakaolin, calcinated clay.  High-reactivity metakaolin and calcinated clay are formed by heating kaolinite clay or clay mixtures to elevated temperatures, so the chemically combined water is driven off, resulting in a structure of aluminosilicate. These are natural source materials, rather than by-product materials. Metakaolin reacts with calcium hydroxide to form calcium silicate and calcium aluminate hydrates. Class N pozzolans are governed by ASTM C618. 9.2.1.3 Aggregates Fine and coarse aggregates are the major constituent of concrete, occupying about three-quarters of the volume of concrete. They are very important to the performance of fresh and hardened concrete. While their primary role is economic (to serve as an inexpensive filler material), they also have roles in determining many other characteristics of concrete. Other properties of hardened concrete influenced by the properties of the aggregates include strength, durability, shrinkage, thermal and fire endurance, density, and modulus of elasticity. Properties of fresh concrete influenced by the aggregates include workability, pumpability, air content, and finishing characteristics. The primary specifications governing aggregates for concrete are ASTM C33 for normalweight and ASTM C330 for lightweight.

Table 9.2.1  Reference guide to ASTM material standards Constituent material

ASTM standard

Cement

C150

Fly ash

C618 Class C or F

Ground granulated blast-furnace slag

C989 Grade 100 or higher

Silica fume

C1240

Normalweight aggregates

C33

Lightweight aggregates

C330

Table 9.2.2  Cement types vary and are classified as follows according to ASTM C150 Cement type I

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Property Normal 1P – Same as Type 1 with a minimum 20% Class F fly ash 1S – Same as Type 1 with a minimum 35% ground granulated blast-furnace slag

IA

Normal, air-entraining

II

Moderate sulphate resistant

IIA

Moderate sulphate resistant, air-entraining

III

High early strength

IIIA

High early strength, air-entraining

IV

Low heat of hydration

V

High sulphate resistance

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PRECAST AND PRESTRESSED CONCRETE: MATERIALS Normalweight.  Normalweight aggregates have bulk densities in the range of 75 lb/ft3 to 100 lb/ft3 and create concretes with densities in the range of 135 lb/ft3 to 160 lb/ft3. Most naturally occurring aggregates are in this category. They may occur naturally in sizes desirable for concrete production or may be crushed from larger rocks to desirable particle sizes. ACI’s Manual of Concrete Practice1 provides further information. Lightweight.   According to ASTM International, lightweight coarse aggregate has a bulk density less than 55 lb/ft3. They may be used exclusively or in combination with normalweight aggregates. When used exclusively, all of the fine and coarse aggregates are lightweight; the resulting concrete density is typically in the range of 90 lb/ft3 to 110 lb/ft3 and is referred to as all-lightweight in this handbook. When used in combination with normalweight aggregates, the resulting concrete densities are in the range of 110 lb/ft3 to 135 lb/ft3 and are referred to as lightweight in this handbook. Note that other publications may refer to the former concrete as lightweight and the latter as semi-lightweight. Lightweight aggregates may be made from naturally occurring, aerated volcanic rock or may be manufactured, such as by expanding shale, clay, and slate at high temperatures. Since lightweight aggregates are more expensive than normalweight aggregates, they are primarily used only when their higher cost can be offset by reduced structural costs of columns and foundations and/or component transportation costs, or their superior fire-resistive qualities are required. Surface texture and shape.  Smooth, rounded aggregate particles are harder to bond to than rough, angular particles. Bond of the cement paste to the aggregate particles is a particularly important property where high flexural strengths are needed. The use of lightweight aggregates and some Supplemental cementitious material, such as metakaolin and silica fume, can be helpful in improving the transition zone and the bond between cement paste and certain aggregates. Improvement of the transition zone between the cement paste and aggregate can also help reduce the permeability of some concretes. Flat and elongated particles should be limited to 15% by weight of total aggregate because they require an increase in mixing water that can result in lower strength if the water– cementitious materials ratio is not adjusted by increasing the cement content. The determination of flat and elongated particles is given in ASTM D4791 and a method for providing an index of aggregate particle shape and texture is given in ASTM D3398. Grading.   An assessment of the combined grading of the coarse and fine aggregate can provide a better indication of the aggregate performance in the concrete. For example, inadequate quantities of mid-size aggregate particles (for example, 3 /8 in.) can result in concrete with poor workability (including poor pumpability), higher water demand, and, consequently, higher shrinkage characteristics. A smooth distribution of aggregate sizes represents an optimum type of gradation. Grading sizes for coarse aggregates are presented in ASTM C33 and D448, and reproduced in Table 9.2.3. Shilstone2 has suggested options for optimizing grading of aggregate and describes the benefits of a combined aggregate analysis.

CHAPTER 9 Gap grading can be used for uniform texturing of exposed aggregate finishes used in precast concrete applications. Concrete mixtures with gap-graded aggregate can show improvements in density, permeability, shrinkage, creep, strength, and consolidation. Quality / durability.  One of the techniques used to assess the durability of an aggregate is a soundness test in accordance with ASTM C88. In this test, the aggregate is cyclically soaked in a sulfate-type solution and then dried. The literature suggests this test is appropriate for stratified rocks with porous layers or weak bedding planes, but has been known to give misleading results for some other aggregate types. If the supplier can demonstrate that the aggregate has given satisfactory service when exposed to weathering similar to that to be encountered, or if the aggregate gives satisfactory performance when tested in accordance with ASTM C666 it can be accepted. As described in ASTM C33, deleterious substances in coarse aggregate supplies include clay lumps and friable particles, chert (with a relative density of less than 2.40), material finer than the 75 µm (No. 200) sieve, and coal and lignite. Maximum allowable amounts of these substances are presented in this standard. Because of some local aggregate shortages or quarry pits being exhausted of quality aggregates, ASTM C33 limits take on increasing importance for quality concrete. Aesthetic considerations.   There are many aggregate sources throughout the United States that have pleasing visual characteristics for use in exposed aggregate finishes. Examples include Wisconsin granite, Colorado granite or quartz, Missouri Meramec gravel, Vermont granite, Mt. Airy (NC) granite, Indiana limestone, Michigan or Minnesota trap rocks, various river rocks, and the like. Because of the expense of shipping these aggregates from distant points, these aggregates are usually limited to a relatively thin face mixture on the precast concrete. The specifier of these aggregates should be mindful of the long-term durability of these aggregates used in an exposed condition. The benefits of the colorful aggregate type may be outweighed by the lack of aggregate durability in an exposed, weathering condition. Aggregates should be selected with a history of good performance in concrete to avoid aggregates susceptible to adverse reactions and poor physical properties. Local aggregate suppliers may have knowledge of the durability of the local source aggregate and should be consulted. In addition, a few industry suppliers are involved with the procurement and shipping of specialty aggregates to places around the country. 9.2.1.4 Chemical Admixtures Chemical admixtures enhance the engineering properties of the fluid or hardened concrete. Table 9.2.4 presents some of the admixture effects and the standards governing their makeup. Air entrainment.   The typical dense mixtures used for precast concrete products have high resistance to freezing and thawing. Entrained air is essential to further improve this resistance in particularly severe environments. Freezing and thawing damage, which can first manifest itself by scaling of the surface, is magnified when chloride-based deicing chemi-

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CHAPTER 9

Table 9.2.3  Aggregate size and gradation limits from ASTM C33 and D448 Aggregate size No.

Nominal size (sieves with square openings)

ASTM C33 and D448

  9

Amount finer than each laboratory sieve, mass percent 4 in.

31/2 in.

3 in.

21/2 in.

2 in.

11/2 in.

1

31/2 in. to 11/2 in.

100

90 to 100

–

25 to 60

–

0 to 15

2

21/2 in. to 11/2 in.

–

–

100

90 to 100

35 to 70

0 to 15

3

2 in. to 1 in.

–

–

–

100

90 to 100

35 to 70

357

2 in. to No. 4

–

–

–

100

95 to 100

–

4

11/2 in. to ¾ in.

–

–

–

–

100

90 to 100

467

11/2 in. to No. 4

–

–

–

–

100

95 to 100

5

1 in. to 1/2 in.

–

–

–

–

–

100

56

1 in. to 3/8 in.

–

–

–

–

–

100

57

1 in. to No. 4

–

–

–

–

–

100

/4 in. to 3/8 in.

–

–

–

–

–

–

/8 in. to No. 4

–

–

–

–

–

–

/2 in. to No. 4

–

–

–

–

–

–

6

3

67

3

7

1

8

3

/8 in. to No. 6

–

–

–

–

–

–

/8 in. to No. 16

–

–

–

–

–

–

No. 4 to No. 16

–

–

–

–

–

–

89 9

3

Fig. 9.2.1 Example of a good air-void system in a concrete paste matrix, as viewed microscopically. The air-void size and void spacing are important parameters in obtaining a good freezing-and-thawing-durable concrete.

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cals are used. Deicers can be applied indirectly in various ways, such as by drippings from the underside of vehicles. This type of damage is covered further in the durability section of this chapter. In some food-processing facilities, particularly meatpacking plants, concrete surfaces may be exposed to extremely aggressive, acidic environments from brine and biological by-products and may require special surface treatments. Such facilities also frequently have flash-freeze rooms that are subject to frequent severe freezing and thawing cycles. Table 9.2.5 (Table 4.2.1, ACI 318-053) provides the required air content for both severe and moderate exposure conditions, for various maximum aggregate sizes. Severe exposure is defined as a climate where the concrete may be in almost continuous contact with moisture prior to freezing or where deicing salts come in contact with the concrete. Salt-laden air, as found in coastal areas, is also considered a severe exposure. A moderate exposure is one where deicing salts are not used or where the concrete will only occasionally be exposed to moisture prior to freezing. Admixtures are added to the concrete during the mixing

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CHAPTER 9

Amount finer than each laboratory sieve, mass percent 1 in. – – 0 to 15 35 to 70 20 to 55 – 90 to 100 90 to 100 95 to 100 100 100 – – – –

/4 in.

3

1

/2 in.

3

/8 in.

No. 4

No. 8

No. 16

No. 50

Aggregate size No.

0 to 5

–

–

–

–

–

–

1

0 to 5

–

–

–

–

–

–

2

–

0 to 5

–

–

–

–

–

3

–

10 to 30

–

0 to 5

–

–

–

357

0 to 15

–

0 to 5

–

–

–

–

4

35 to 70

–

10 to 30

0 to 5

–

–

–

467

20 to 55

0 to 10

0 to 5

–

–

–

–

5

40 to 85

10 to 40

0 to 15

0 to 5

–

–

–

56

–

25 to 60

–

0 to 10

0 to 5

–

–

57

90 to 100

20 to 55

0 to 15

0 to 5

–

–

–

6

90 to 100

–

20 to 55

0 to 10

0 to 5

–

–

67

100

90 to 100

40 to 70

0 to 15

0 to 5

–

–

7

–

100

85 to 100

10 to 30

0 to 10

0 to 5

–

8

–

100

90 to 100

20 to 55

0 to 30

0 to 10

0 to 5

89

–

–

100

85 to 100

10 to 40

0 to 10

0 to 5

9

cycle to entrain air. Figure 9.2.1 shows an example of a good air-void system created from an air entraining admixture. Tolerance on air content is usually +/-1.5%. ACI 318-05 permits an air content one percentage point (1.0%) lower than the values in Table 9.2.5 for concrete strengths higher than 5000 psi. Other studies have shown that even this amount

  9

may be too high for the very low water–cementitious materials ratio used in most precast concrete products and used in a vertical orientation.4 For some concrete mixtures, such as low-slump mixtures in extruded products or gap-graded mixtures in architectural precast concrete, it is difficult to measure air content. Thus,

Table 9.2.4  Types of admixtures for concrete Type of admixture

Effect of admixture

ASTM Standard

Air entraining

Durability improvement

Water reducing

Reduce the amount of mixture water required for a given consistancy

Retarder

Delay setting time

C494, Type B

Accelerator

Accelerate setting time and provide early strength development

C494, Type C

Water reducer and retarder

Reduce the amount of mixture water and retard set

C494, Type D

Water reducer and accelerator

Reduce the amount of mixture water and accelerate set

C494, Type E

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CHAPTER 9

  9 Fig. 9.2.2 Aggregate settlement in a double-tee flange cast with self-consolidating concrete, potentially caused by unintended vibration. Note the lack of coarse aggregate in the top layer.

it is recommended that a normal dosage of the air-entraining admixture be used instead of specifying a particular range of air-content percentage. For precast concrete components constructed above grade and oriented in a vertical position, air-entraining admixtures should be used, but air contents as low as 3% to 4% will usually provide the required durability. The precast and prestressed concrete industry does not use air-entraining portland cements because it has a negative effect on early strength. In addition to entrained air, other positive measures such as adequate concrete cover over reinforcement and embedded hardware and rapid drainage of surface water may be essential for durability in structures exposed to weather. High-range water reducers (HRWRs).   Specifications for high-range water reducers are given in ASTM C494, Types F and G, and ASTM C1017, Types 1 and 2. HRWRs consist of sulfonated melamine formaldehyde condensates, sulfonated naphthalene formaldehyde condensates, or lig-

nosulfonates. They are used for essentially the same reasons as water reducers. For a given slump, they reduce the water demand by 12% to 30%. With HRWRs, it is economically possible to achieve water–cementitious material ratios as low as 0.25 to achieve concrete with very high strength and low permeability. Viscosity modifying agents (VMAs).   VMAs are used most commonly in self-consolidating concrete (SCC) mixtures. They are added to concrete to reduce the tendency for segregation and bleeding, and to compensate for mixture characteristics that make SCC production difficult. Such characteristics are low cementitious content, use of a gapgraded aggregate, or mixture-water variations. They can improve passing ability and have also been used to reduce pumping pressures. Concrete containing VMAs is highly viscous when allowed to rest, but becomes more fluid when energy is applied through mixing or other agitation. This happens because VMAs are typically long polymers that interlock when the material is at rest, but separate when the concrete is sheared. Their use and finishing requires special attention, as overworking or vibrating the material can cause aggregate settlement, an example of which is shown in Fig. 9.2.2. Shear friction transfer can be affected on such surfaces. There is currently no ASTM specification for VMAs. It is recommended that trial batches be produced to confirm that the VMA-modified concrete is compatible with local source materials, anticipated production methods, and the plant’s placement techniques. The VMA-modified concrete should also be checked to ensure that it has no harmful influence on the hardened concrete.5 Corrosion inhibitors.   Corrosion inhibitors are used to extend the service life of concrete structures by offering protection to embedded reinforcement against chloride-induced corrosion. Corrosion inhibitors are chemical admixtures that delay the initiation of corrosion and decrease the corrosion rate of steel in concrete, without changing the concentration of the corrosive agent. Chemical compounds classified as corrosion inhibitors by ACI 212 and ACI 222 are borates, chromates, molybdates,

Table 9.2.5  Total air content for frost-resistant concrete3 Air content, percent

Nominal Maximum Aggregate Size,a in.

Severe exposure

Moderate exposure

0.375



7.5



6.0

0.5



7.0



5.5

0.75



6.0



5.0

1.0



6.0



4.5

1.5



5.5



4.5

b

2.0



5.0



4.0

3.0b



4.5



3.5

a. See ASTM C33 for tolerances on oversize for various nominal maximum size designations. b. These air contents apply to total mixture, as for the preceding aggregate sizes. When testing these concretes, however, aggregate larger than 11/2 in. is removed by handpicking or sieving and air content is determined on the minus 11/2 in. fraction of mixture. (Tolerance on air content as delivered applies to this value.) Air content of total mixture is computed from value determined on the minus 11/2 in. fraction.

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PRECAST AND PRESTRESSED CONCRETE: MATERIALS nitrites, and phosphates. Of these, calcium nitrite has been used successfully with precast and prestressed concrete since 1980. Accelerators.  These admixtures accelerate the setting and early strength gain of concrete. They should conform to a Type C chemical admixture of ASTM C494 and not contain chlorides. Retarders.  These admixtures retard the setting of concrete and sometimes retard the rate of early strength gain. They should conform to Type B chemical admixture of ASTM C494. Lithium.  Lithium is gaining acceptance and more widespread use as an admixture in concrete where aggregates susceptible to ASR are used. In states having known sources of ASR-susceptible aggregates, those state departments of transportation have been increasingly using lithium admixtures to combat the potential for ASR. ASRsusceptible aggregates are typically identified by testing through ASTM C289, ASTM C1260, and/or AASHTO T303 methods. Lithium additions to concrete, primarily in the form of lithium salts (LiOH) apparently produce an ASR-type reaction product, which is non-expansive. Testing in a Strategic Highway Research Program project6 indicated that lithium salts, when used as an admixture with fly ash, could further suppress the deleterious expansion due to ASR. ASR is discussed in more detail in Section 9.3.1.7.

CHAPTER 9 9.2.1.5 Water Water used when mixing concrete must be clean and free of oil, salt, acid, alkali, sugar, vegetable oil, or other injurious substances. Water known to be of potable quality may be used without testing. However, if there is a question, water should meet the requirements of ASTM C94 (AASHTO T26). Mixing water for concrete should not contain a chloride ion concentration in excess of 1000 ppm or sulfates as SO4 in excess of 1300 ppm. Table 9.2.6 (Table 4.2.2, ACI 318-05) provides the maximum permitted water–cementitious materials ratio (or, for lightweight concrete, minimum strength) for concrete exposed to an aggressive environment. The water– cementitious materials ratios specified in Table 9.2.6 are calculated using the weight of cement meeting ASTM C150, C595, or C845, plus the weight of fly ash and other pozzolans meeting ASTM C618, slag meeting ASTM C989, and silica fume meeting ASTM C1240, if any, except when the concrete is exposed to deicing chemicals. For concrete exposed to deicing chemicals, the maximum weight of fly ash, other pozzolans, silica fume, or slag that is included in the concrete must not exceed the percentages of the total weight of cementitious materials given in Table 9.2.7 (Table 4.2.3, ACI 318-05). In many plants, a water–cementitious materials ratio of 0.37 is frequently used for added durability of precast and prestressed concrete products.

Table 9.2.6  Requirements for special exposure conditionsa Maximum in water cementitious materials ratio, by weight, normalweight aggregate concretea

Minimum concrete strength (f 'c ) psi, normalweight and lightweight aggregate concrete

Concrete intended to have low permeability when exposed to water

0.50

4000

Concrete exposed to freezing and thawing in a moist condition or to deicing chemicals

0.45

4500

For corrosion protection of reinforcement in concrete exposed to chlorides from deicing chemicals, salt, salt water, brackish water, seawater, or spray from these sources

0.40

5000

Exposure Condition

a. Source: ACI 318-05, Table 4.2.2.

Table 9.2.7  Requirements for concrete exposed to deicing chemicals Cementitious materials Fly ash or other pozzolans conforming to ASTM C618

Maximum percent of total cementitious materials by weighta 25

Slag conforming to ASTM C989

50

Total of fly ash or other pozzolans, and slag

50b

Total of fly ash or other pozzolans

35b

a. The total cementitious material also includes ASTM C150, C595, and C845 cement. The maximum percentages also include fly ash or other pozzolans present in Type IP or I(PM) blended cement, ASTM C595; slag used in the manufacture of an IS or I(SM) blended cement, ASTM C595; present in a blended cement. b. Fly ash or other pozzolans shall constitute no more than 25% and 10%, respectively, of the total weight of the cementitious materials.

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CHAPTER 9 7000

Compressive Strength, psi

  9

V

III

6000 5000

II I

III

4000

I

is SCC, an advanced approach to the production of highly flowable, self-leveling concrete that can be placed without vibration equipment and without segregation. SCC requires a high-performance, high-range water-reducing admixture to achieve and maintain desired workability, and it can be made with standard available raw materials. However, in order to achieve the unique rheological (ablity to flow or be deformed) properties of SCC, special attention must be paid to the mixture design process.9

IV

II

3000

V IV

2000

9.2.2.2 Compressive Strength

1000 0

7

14

28

90

Days

180

1

2

3

Years

Fig. 9.2.3 Rates of strength gain for concretes made with various types of ASTM C150 portland cement.

9.2.1.6 Pigments Natural and synthetic materials are used to color concrete for aesthetic reasons. Pigments should conform to the requirements of ASTM C979 and should generally not exceed 10% by weight of the cement. Pigments used in amounts less than 6% generally do not affect the concrete properties. Several manufacturers supply pigments to the precast concrete industry. Pigments are used in either dry or liquid forms. In the liquid form, the water contribution to the mixture must be taken into consideration in the mixture design. 9.2.2

Physical Properties

9.2.2.1 Introduction Concrete properties such as stress-strain relationship, tensile strength, shear strength, and bond strength are frequently expressed in terms of the compressive strength of concrete. Generally, these expressions have been empirically established based on experimental data of concretes with compressive strengths less than 6000 psi. These expressions are given in this section and are applicable to most precast and prestressed concrete structures because it is usually specified in the 5000 psi to 6000 psi compressive-strength range. Use of the equations given in this section are reasonable for compressive strengths up to 10,000 psi. For strengths in excess of 10,000 psi, the recommendations given by ACI Committee 363 in References 7 and 8 should be followed. Concrete with compressive strengths higher than 8000 psi has been used in framing components of multistory construction and in prestressed concrete piling and bridge girders. Often, higher strength is a result of using high-performance concrete to enhance durability. Interest in a more widespread use of such concrete is growing. The strict use of ACI standard mixture design concepts will not always result in the achievement of high-strength concrete. Another type of concrete with widespread acceptability 9–10

The compressive strength of concrete, made with aggregates of adequate strength, is governed by either the strength of the cement paste or the bond between the paste and the aggregate particles. At early ages, the bond strength is lower than the paste strength; at later ages, the reverse may be the case. For given cementitious materials and acceptable aggregates, the strength that may be developed by a workable, properly placed mixture of cementitious materials, aggregates, and water (under the same mixing, curing, and testing conditions) is influenced by the water–cementitious materials ratio; the ratio of cementitious materials to aggregate; grading, surface texture, shape, and strength of aggregate particles; and maximum size of the aggregate. Mixture factors, partially or totally independent of water–cementitious materials ratio, that also affect the strength are type and brand of cement, amount and type of admixture or pozzolan, and mineral composition. Compressive strength is measured by testing 6 in. × 12 in. cylinders in accordance with ASTM C39. The precast concrete industry also uses 4 in. × 8 in. cylinders and 4 in. cube specimens. Adjustment factors may need to be applied to these non-standard specimens to correlate with the standard 6 in. × 12 in. cylinders. Because of the need for early strength gain, Type III cement is often used by precasters so forms may be cycled more frequently. Structural precast concrete, and often architectural precast concrete, is made with gray cement that meets ASTM C150. Type III and Type I white and buff portland cements are frequently used in architectural concrete products. These are usually assumed to have the same characteristics (other than color) as gray cement. Pigments are also available to achieve colored concrete, and have little effect on strength at the recommended dosages. Cement types, use of other cementitious materials, and experience with color should be coordinated with the regional producers. Higher-strength concrete mixtures well over 6000 psi are available in many areas. Regional suppliers should be contacted to furnish mixture and design information. It is important to recognize that coarse aggregate strength usually limits the compressive strength of the very high-strength concretes (greater than 10,000 psi). Initial curing of precast concrete takes place in the form, usually by covering to prevent loss of moisture and sometimes, especially in structural prestressed products, by the application of radiant heat or live steam. Curing, in addition to the initial curing cycle of approximately 12 hours, has been

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PRECAST AND PRESTRESSED CONCRETE: MATERIALS shown to rarely be necessary to attain the specified strength. Control techniques for the most effective and economical accelerated curing are reported in PCI Technical Report TR 1-82.10 When concrete is subjected to freezing and thawing and other aggressive environments, air entrainment is often specified. In some concrete mixtures, a slight reduction of strength may occur with air entrainment. Figure 9.2.3 shows the relationship of strength gain with time for various cement types. 9.2.2.3 Tensile Strength Magnitude.   A critical performance measure for architectural precast concrete is its resistance to cracking, which is dependent on the tensile strength of concrete. Nonprestressed reinforcement does not prevent cracking, but controls crack widths after cracking occurs. Tensile stresses in prestressed concrete, which could result in cracking, are permitted in ACI 318-05. Flexural tensile strength is measured by the modulus of rupture. It can be determined by test, but testing is not required or necessary in the codes. ACI 318-05 prescribes the tensile strength (modulus of rupture):

fr = 7.5λ fc'

(Eq. 9 -1)

For lightweight concrete, if the splitting tensile strength fct is specified, the value of fct /6.7 may be substituted for λ fc' Otherwise: Normalweight concrete: λ = 1.0 Sand-lightweight concrete: λ = 0.85 All-lightweight concrete: λ = 0.75 For higher strength concrete, modulus if rupture values have been shown to be greater than 7.5λ fc' Flexural strength.   Flexural strength is measured by two methods. The most common method is ASTM C78 (AASHTO T97). In this method, a concrete beam with dimensions of 6 in. × 6 in. × 21 in. is supported at the ends and loaded at the third points until failure. The modulus of rupture (MOR) is calculated as the stress at the extreme fiber at the time of failure. The second method is ASTM C293 (AASHTO T177), which loads the beam at its center point. This method is rarely used because its results can be more variable.11 Because the test specimens are large and heavy for both tests, neither of these test methods is convenient. The test results may be influenced by the concrete moisture content at the time of testing. Also, the MOR calculations are based on elastic beam theory, which is not completely accurate for these conditions and overestimates the concrete tensile strength. Neville11 cites a reference that states the correct tensile strength is 0.75 of the calculated modulus of rupture. Split cylinder test.  Tensile strength can be measured indirectly using the splitting tensile test, ASTM C496 (AASHTO T198). This test is also referred to as the Brazilian tensile test. In this test, a concrete cylinder or core is compressed perpendicular to its axis, resulting in a splitting failure. The tensile strength

CHAPTER 9 is calculated from the peak compressive load. Neville reports that the results are believed to be closer to the actual tensile strength of concrete than those measured in flexural strength testing. Also, the tensile splitting test is less variable and easier to conduct. If the splitting tensile strength results will be used to show compliance with flexural strength specifications, a correlation should be established for the mixture in question. 9.2.2.4 Modulus of Elasticity Modulus of elasticity Ec is the ratio of normal stress to corresponding strain in tension or compression. It is the material property that determines the deformability of a concrete component under load. Thus, it is used to calculate deflections, axial shortening and elongation, buckling, and relative distribution of applied forces in composite and non-homogeneous structural components. The modulus of elasticity of concrete and other masonry materials is not as well defined as it is for materials, such as steel. It is, therefore, defined by some approximation, such as the secant modulus. Thus, calculations involving its use have inherent imprecision, but this is seldom critical enough to affect performance. While it may be desirable in some instances to determine modulus of elasticity by test, especially with some lightweight concretes, the equation given in ACI 318-05 is usually adequate for design:

Ec = w1.5 33 fc'

(Eq. 9-2)

where: Ec = modulus of elasticity of concrete, psi w = density of concrete, lb/ft3 fc' = compressive strength, psi For concrete compressive strengths greater than 6000 psi, Eq. 9-2 may predict a higher modulus of elasticity than is actually achieved. Alternative equations are given by ACI Committee 363 and Ahmad and Shah.8 The concrete modulus of elasticity can also be affected by local aggregate types and size used in the mixture. Some aggregate sources in the United States are known to produce concretes with significantly lower values of Ec than predicted by Eq. 9-2. If deflections are a sensitive consideration, the designer should check the value of Ec with the material suppliers. 9.2.2.5 Poisson's Ratio Poisson’s ratio is the ratio of transverse strain to axial strain resulting from uniformly distributed axial load. It generally ranges between 0.11 and 0.27, and, for design, is usually assumed to be 0.20 for both normalweight and lightweight concrete. 9.2.2.6 Volume Changes Volume changes of precast and prestressed concrete are caused by variations in temperature, shrinkage due to airdrying, and by creep caused by sustained stress. If precast concrete is unrestrained and free to deform, volume changes are of little consequence. If these components are restrained by foundations, connections, steel reinforcement, or connect-

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Table 9.2.8  Coefficients of linear thermal expansion of rock (aggregate) and concretea Average coefficient of thermal expansion x 10-6 in./in./°Fb

Type of rock (aggregate)

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Aggregate

Concrete

Quartzite and cherts

6.1 – 7.0

6.6 – 7.1

Sandstones

5.6 – 6.7

5.6 – 6.5

Quartz sands and gravels

5.5 – 7.1

6.0 – 8.7

Granites and gneisses

3.2 – 5.3

3.8 – 5.3

Syenites, diorites, andesite, gabbros, diabas, and basalt

3.0 – 4.5

4.4 – 5.3

Limestones

2.0 – 3.6

3.4 – 5.1

Marbles

2.2 – 3.9

2.3

Dolomites

3.9 – 5.5

Expanded shale, clay, and slate

3.6 – 4.3

Expanded slag

3.9 – 6.2

Blast-furnace slag

5.1 – 5.9

Pumice

5.2 – 6.0

Perlite

4.2 – 6.5

Vermiculite

4.6 – 7.9

Barite

10.0

Limonite, magnetite

4.6 – 6.0

None (neat cement)

10.3

Cellular concrete

5.0 – 7.0

1:1 (cement:sand)c

7.5

1:3 (cement:sand)

6.2

c

5.6

1:6 (cement:sand)c

a. Source is Bureau of Reclamation, 1981. b. Coefficients for concretes made with aggregates from different sources vary from these values, especially those for gravels, granites, and limestones. Fine aggregates generally are the same material as coarse aggregates. c. Tests made on 2-year-old samples. 12

ing components, significant forces may develop over time. The volume changes due to temperature variations can be positive (expansion) or negative (contraction), while volume changes from creep and shrinkage are only negative. Precast concrete components are generally kept in yard storage for a period of time. Thus, much of the shrinkage and creep will have taken place by the time of erection and completion of connections. However, connection details and joints must be designed to accommodate the changes occuring after the precast concrete component is erected and connected to the structure. In most cases, the shortening that takes place prior to making the final connections will reduce the total shrinkage and creep strains to manageable levels. Temperature effects.  The coefficient of thermal expansion of concrete varies with the aggregate used, as shown in Table 9.2.8 from the Bureau of Reclamation’s Concrete Manual.12 Range for normalweight concrete is 5 to 7 × 10-6 in./in./°F when made with siliceous aggregates and 3.5 to 5 × 10-6 in./in./°F when made with calcareous aggregates. The range for structural lightweight concretes is 3.6 to 6 × 10-6 in./in./°F depending on the type of aggregate and amount of natural sand. For design, coefficients of 6 × 10-6 in./in./°F for normalweight concrete and 5 × 10-6 in./in./°F for sand9–12

lightweight concrete are frequently used. If greater accuracy is needed, tests should be made on the specific concrete. Since the thermal coefficient for steel is also about 6 × 10-6 in./in./°F, the thermal effects on precast and prestressed concrete may be evaluated by treating it as plain concrete. Shrinkage and creep.   Precast concrete components are subject to air-drying as soon as they are removed from the forms. During exposure to the atmosphere, the concrete slowly loses some of its original water, causing a shrinkage volume change to occur. When concrete is subjected to a sustained load, the deformation may be divided into two parts: an elastic deformation that occurs immediately and a time-dependent deformation that begins immediately and continues at a decreasing rate over time. This time-dependent deformation is called creep (Fig. 9.2.4). Creep and shrinkage strains vary with relative humidity, volume-surface ratio (or ratio of area to perimeter), level of sustained load including prestress, concrete strength at time of load application, amount and location of steel reinforcement, and other characteristics of the material and design. When high-strength concretes are used, different values of shrinkage and creep may be needed. The joints between precast concrete components are typically detailed to relieve such strains.

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1200 Recoverable Creep Irreversible Creep Total Creep

Creep (microstain)

1000

800

  9

600

400

200

0

0

50

100

150

200

250

Time after Loading (days)

Fig. 9.2.4 Relationship of creep with time.

9.2.2.7 Durability / Reactivity Good quality aggregates are becoming more difficult to find in some areas of the country, and local shortages may become more commonplace. In the global economy, aggregate sources in Canada, Mexico, and other locales may become more common, and their geological origins and composition may be harder to trace. As such, precasters and concrete suppliers may be using aggregates that once were considered undesirable. In addition, local aggregate sources may be known to have long-term durability issues that must be addressed from the material’s standpoint to extend the service life of the precast concrete product. Freezing and thawing.   This mechanism in concrete is the progressive deterioration of the cement paste through cyclic freezing and thawing. Deterioration of saturated concrete may occur when concrete freezes. Concrete distress occurs when the water increases its volume as it freezes (about 10%) and the capillary water pressure in the concrete increases. Increased internal concrete pressure from these actions can exceed the concrete's tensile strength and cause internal cracking of the concrete, usually at the exposed surface (called scaling). Once the concrete is cracked, additional water is able to penetrate and, upon freezing, causes additional damage. Deterioration of the concrete is progressive with time as it experiences a number of freezing and thawing cycles. This type of damaged concrete is marked by parallel, planar cracking starting at the surface, as shown in Fig. 9.2.5.

Fig. 9.2.5 Planar cracking marking freezing and thawing damage on a horizontal surface due to an inadequate airentrainment system.

The addition of an air-entraining admixture, by introducing properly entrained air in the concrete, is the most effective method of increasing the resistance of concrete to damage due to freezing and thawing. Air-entrained concrete contains many tiny, closely spaced air bubbles acting as relief valves

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for excess water. Excess internal water is forced into the air voids, which relieves pressure during the freezing of the water and prevents concrete damage. The entrained air-void size and spacing in the concrete is also important. The type and quantity of air-entraining admixture should be selected and batched to be compatible with other admixtures and additives in the concrete mixture. Air-entraining admixtures are introduced in Section 9.2.1.4. D-Cracking.  The D-cracking mechanism is analogous to freezing and thawing damage in the cement paste, except the deterioration stems from porous, non-durable aggregates. Certain aggregates from the midwestern United States have a high rate of water absorption (porosity) coupled with low permeability, which is a measure of ease of moisture flow through a material. When the aggregate becomes saturated, internal hydraulic pressures in the particle will develop due to freezing. The aggregate particle attempts to relieve this pressure by water migration to the outside surface. If the saturated aggregate particle is relatively large and exceeds its critical size, the water cannot diffuse quickly enough and freezing occurs. This process results in micro-fractures of the aggregate particle that can continue unimpeded with time, if the moisture conditions persist. Another consideration is the rapid expelling of moisture from the aggregate particle. If the surrounding cement paste is unable to accommodate this water, the paste could also suffer freezing and thawing damage. A common example of this deterioration mechanism is concrete surface pop-outs of chert or shale particles. The surface damage occurs at this location because these surface aggregates are more susceptible to saturation, they have little cover, and freezing and thawing cycles happen more frequently. D-cracking is common at the joint edges of concrete pavements, but has been observed at other locations. At the pavement joints, water usually accumulates in the base material directly under the concrete slab. D-cracking on the concrete surface is characterized by fine cracks generally parallel to the control joint. The cracks will often have a wet appearance. To avoid the occurrence of D-cracking, the non-durable aggregates susceptible to this damage should be screened out. If this is not practical, concrete containing these aggregates should not be used where saturation could occur in freezing conditions. Chemical resistance.  Some chemicals are so aggressive to concrete that the only way to provide protection for the concrete is to provide a corrosion-protection system, such as a coating or covering. The system should provide not only corrosion protection but also, to the maximum extent possible, the flexibility to span cracks and accommodate the expansion and contraction the concrete will experience due to moisture and temperature changes. To reduce permeability, the minimum cementitious materials content should be 700 lb/yd3 for primary containment and 600 lb/yd3 for secondary containment. ACI 350.2 defines a primary containment system as the first containment system in contact with the hazardous material. A secondary containment system is a backup system for containment of hazardous materials in case the primary system leaks or fails for 9–14

any reason. When fly ash or other pozzolans exceed 25% of total cementitious materials content, the designer should consider their effects on durability and chemical resistance. Silica fume may be used to increase chemical resistance, density, durability, and strength, and to decrease permeability. Plastic / drying shrinkage cracking.  Plastic shrinkage is initiated by surface drying, which begins whenever the evaporation rate is greater than the rate at which water rises to the surface of recently placed concrete through bleeding. It occurs in exposed concrete, primarily in flatwork and double-tee flanges (cast outdoors), but also in beams and footings, and may develop in other climates when the surface of freshly cast concrete dries and subsequently shrinks. The introduction of external moisture through proper curing to combat the drying will avoid this cracking type. The probability of plastic-shrinkage cracking increases when the evaporation rate exceeds the bleeding rate. Drying shrinkage initiates after final set of the concrete. The concrete begins to lose free water, which results in a volumetric change in the concrete. During early drying, cracks develop around the aggregate due to the weak paste relative to the aggregate strength. Over a long period of time, the changes in volume cause cracking of weak aggregates. Drying shrinkage is non-structural, as there is aggregate interlock present to maintain continuity and reinforcement to keep the cracks tight. However, this can raise issues with durability. It is important to recognize that drying shrinkage is a longterm condition, depending on the drying characteristics of the particular concrete component. Hansen and Mattock13 studied drying shrinkage under laboratory conditions (drying in air, 50% relative humidity), and correlated drying with the volume/surface ratio of the concrete component. Figures 9.2.6 and 9.2.7 show this effect. If the concrete component can only dry from one side, like a floor slab or footing, it will take some time for the concrete to dry out and realize its ultimate shrinkage potential. Figure 9.2.6 shows an example for 2-in.- to 8-in.-thick components; for example, a 6-in.-thick slab-on-grade will experience about 80% of its ultimate shrinkage after 30 months. Thus, cracking may continue or existing cracks may widen, depending on the percentage of reinforcement provided. When the concrete component can dry from two sides, thereby doubling the surface area for drying, the drying shrinkage occurs at a faster rate (Fig. 9.2.7). Given the same 6-in.-thick component, about 92% of its ultimate shrinkage would be expected to occur after about 30 months. Finally, restraint of the shrinkage plays a key factor in the cracking distress that could be realized in the particular concrete component. As shown in Fig. 9.2.8, restrained shrinkage can cause cracking in the concrete. ASR.   An ASR in concrete occurs when the alkalis in the cement chemically react with reactive silica in specific aggregate types when moisture is present. The alkalis in cement are sodium and potassium, and the silica is generally present as opaline material, cristobalite and tridymite minerals, and natural and/or artificial glass. Some of these materials are present in the sand and gravel typically used to make

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100

2 in. thick

80

Percent of Ultimate Shrinkage

4 in. thick 6 in. thick

60

  9

8 in. thick 40

Drying shrinkage in a concrete slab or wall, one-sided drying

20

0

0

6

12

18

24

30

Concrete Age (Months) Fig. 9.2.6 Ultimate shrinkage for concrete elements dried from one-side. Source: Hansen and Mattock, 1966.13

concrete in Alabama, Kansas, Georgia, Idaho, and Nebraska, as well as Canada. During the alkali-silica reaction, the alkalis and silica are consumed and a white alkali-silica gel is formed as a reaction product. The gel reaction product is expansive, creating a need for the gel to increase in volume internal to the concrete. Persistent volume expansion from the gel will eventually exceed the concrete tensile strength. Continued gel production eventually causes local failure of the concrete in the form of random or pattern cracking, with the white gel by-product evident. Figure 9.2.9 illustrates ASR damage to concrete. Generally, two of the three requirements for ASR, cement alkali and reactive silica, are fixed components of the concrete and, therefore, present the potential for expansion, regardless of exposure condition. However, alkali levels can be increased from those in the initial mixture by external sources such as deicing salts or saltwater and mist in coastal areas. The alkalis can also be concentrated in areas of the concrete, causing localized reaction. The third requirement, moisture availability, is a major variable in concrete and has a significant impact on the severity of distress and volume change due to ASR.

ASR can be controlled to some degree in the mixing stage. Some fly ash pozzolans have proven effective in controlling the expansion due to ASR. In addition, lithium admixtures are being introduced to chemically address the expansion issues. The ASR susceptibility of an aggregate source can be tested by AASHTO T303, ASTM C289, C1260, or C1293. Note that these tests are long duration tests. Expansions greater than a certain percentage determined according to one of these test methods will be considered potentially reactive. The precaster or concrete supplier is encouraged to obtain this test information from the aggregate source supplier if reactive aggregates are contemplated. Alkali-carbonate reactions (ACR).   Alkali-carbonate reaction is a deterioration mechanism resulting in deleterious expansion of concrete made with a certain type of aggregate. Reactions observed with certain dolomitic limestones containing some clay are associated with ACR. Typical indicators of the presence of ACR are map (random pattern) cracking and, in advanced cases, closed joints, spalled concrete surfaces, or relative displacements of different portions of a structure. Because ACR deterioration is slow, the risk of significant failure is low.

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100 2 in. thick 6 in. thick 4 in. thick

80

Percent of Ultimate Shrinkage

8 in. thick

  9

60

40

Drying shrinkage in a concrete slab or wall, two-sided drying

20

0

0

6

12

18

24

30

Concrete Age (Months) Fig. 9.2.7 Ultimate shrinkage for a concrete element dried from two sides. Source: Hansen and Mattock, 1966.13

Delayed ettringite formation (DEF).   The chemistry of the cement also has implications for the long-term durability of the concrete. DEF is a deterioration of concrete due to internal sulfate attack. Ettringite is one form of calcium sulfoaluminate and is found in all portland cement paste. Calcium sulfate sources include gypsum and supplementary cementitious materials. Ettringite forms shortly after water is added, consuming the sulfate. At this stage, the ettringite is uniformly distributed throughout the cement paste as small diameter deposits. When fresh concrete is exposed to temperatures exceeding 150 °F, it prevents normal ettringite formation and holds the sulfate and alumina in the calcium silicate hydrate (CSH) gel of the cement paste. Over time, when exposed to moisture, the sulfate is released and forms ettringite in the hardened concrete. It is believed that the expansive ettringite subsequently causes cracking. As a result of paste volume expansion, separation of the paste from the aggregate is observed from DEF. It is characterized by the development of white ettringite rims around the aggregate particles, and is sometimes mistaken for ASR. This issue plagued the precast concrete industry in the 9–16

early 1990s, as DEF was deteriorating some very new precast concrete structures. PCI’s policy on this is contained in the current editions of PCI’s quality control manuals MNL116-9914 and MNL-117-96.15 These manuals indicate that the maximum concrete temperature during initial curing for products exposed to damp or continuously wet environmental conditions shall be limited to 150 °F. This temperature shall be measured inside the unit, in the portion of the unit that is likely to experience the highest concrete temperature during curing. A temporary spike in maximum initial curing concrete temperature, not to exceed the maximum allowable by more than 5 °F for a period not to exceed 2 hours, is allowed. If this is not practically possible, mitigating concrete mixture design measures can be specified to enhance long-term durability and shall be employed. Examples of mitigation measures include the use of cement Type 1P (where P is minimum 20% Class F fly ash), or 1S (where S is minimum 35% GGBFS). There is some evidence in the literature that using fly ash for cement replacement at percentages less than 20% has little protective effect against DEF.

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Scaling.   Scaling is a near-surface deterioration resulting from freezing and thawing cycles and deicing-salt applications. Overworking the concrete surface causes the surface to become paste-rich, have a high water–cementitious materials ratio, and lower air content. Figure 9.2.10 shows an example of the resultant damage of scaling on a horizontal surface. Sulfate attack.  Chemical attack of concrete materials may occur from sulfates found in ground water, soils, processing liquids, or sewage. The proper choice of cement is particularly effective in resisting sulfate attack. Section 4.3.1 of ACI 318-05 and the references contained therein provide detailed guidance. 9.2.3

Original Length

Unrestrained Shrinkage

Finishes

  9

9.2.3.1 Conventional As discussed in PCI’s Quality Control Personnel Certification Level III Training Manual,16 there are three general steps in the finishing of the exposed concrete surface. 1. Strike off or screeding to achieve the desired surface contour and level of concrete in the form. 2. Bull floating or darbying soon after strike off, to finalize the surface and eliminate screeding marks. The bull float is a long-handled tool used for larger surfaces and the darby is a smaller tool used for smaller confined areas. These wood or magnesium tools do not close the surface. Steel trowels should not be used until much later, usually following a cure period while the bleed water rises and starts evaporating. 3. Final finish. This depends on the surface textures desired, and some of the more common finishes are discussed in the following sections. The level and type of finish should be clearly stated on the design drawings or agreed to with the client prior to work. Approved samples of architectural finishes should be prepared before work starts and should be kept nearby during finishing operations for comparison throughout the job. SCC brings about some special finishing issues. Normal concrete finishing practices can be employed with SCC; however, bull floating and finishing should be delayed slightly longer than for conventional HRWR admixture concrete. The nature of SCC is such that with a similar amount of bleed water, the surface may dry faster than normal HRWR concrete. Float finish.   A wood, aluminum, or magnesium float is used to even the surface. If only floating is required, the result is a rougher surface, compared with a trowel finish. No bleed water should be on the surface and the concrete should be stiff enough so that a finisher walking on the surface leaves footprints no more than 1/4 in. deep. Floating embeds the large particles at the surface, removes slight imperfections, and compacts the concrete. If floating is done carefully, a fully usable surface can result. However, this operation is often used as a preliminary step to other finishes; it must be recognized that the quality of final finish is directly related to the quality of the float finish. Broom finish.  A broom finish is often used for non-slip surfaces on deck components, especially in parking decks or on pedestrian ramps. Brooming is normally done immediately

Unrestrained Shrinkage Develops Tensile Stress

If Tensile Stress is Greater than Tensile Strength, Concrete Cracks Fig. 9.2.8 Mechanism of shrinkage cracking in a concrete component. Source: ACI 224.

Fig. 9.2.9 Example of alkali-silica damage to concrete. Expansion around the perimeter of reactive aggregates eventually results in cracking in the concrete matrix.

after floating with the lines running transverse to the component. The stiffness and length of the broom bristle is chosen to give the desired result. Surfaces to receive composite concrete.   Many precast concrete products are designed to receive cast-in-place concrete toppings or achieve a certain surface roughness to ensure horizontal shear transfer and a composite section. Chapter 11 of ACI 318-05 contains the shear transfer requirements,

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The finish of untreated formed surfaces is subject to variation in form joints, pin holes due to entrapped air, sand pockets, rock pockets, pour marks, vibrator marks, and many other possible appearance altering items. All finishes must be clearly defined, specified and understood or problems can result when an architect or owner thinks the final finish is not acceptable. Recent advances in SCC admixture technology have mitigated a number of these issues with formed surface finishes. A form finish should have fins exceeding 1/4 in. in height chipped or rubbed off and otherwise left with the texture imparted by the forms. Small surface holes caused by air bubbles, normal color variation, normal joint form marks, and minor chips and spalls are usually permitted. No major or unsightly imperfections, honeycomb, or other defects are permitted. Any special finishes, such as rubbed or sandblasted, must be clearly defined and specified.

  9

9.2.3.2 Architectural / Decorative

Fig. 9.2.10 Example of concrete surface scaling on a horizontal surface.

while Chapter 17 provides design provisions for composite concrete flexural components. ACI 318-05 requires that surfaces between two layers of concrete in a composite component be clean and free of laitance. For the usual design condition of lower design stresses, ACI 318-05 allows heavy brooming or similar finishing to be used to provide a roughened surface. If the surface is "intentionally roughened to an amplitude of approximately 1/4 in.," a higher design stress is allowed. Experience and tests indicate that normal finishing methods used for precast concrete components will qualify as intentionally roughened. The use of SCC admixtures in a concrete may require careful monitoring of set time in the plant to adequately capture the time window as to when a composite finish can be applied. Steel-trowel finish.  A trowel finish is accomplished with a one-hand, smooth, steel trowel or a steel-bladed finishing machine. Troweling is performed after the surface has been floated and the concrete has hardened enough to walk on, leaving minor imprints. The more passes, the harder and smoother the surface becomes; troweling is intended to produce a hard, smooth, closed surface, and experienced finishers help achieve good results. It should be noted that concrete surfaces will typically darken with increased troweling. Formed surface finishes.   The final finish required on formed surfaces must be considered in concrete work. If sandblasting or waterblasting to expose aggregate or achieve a special surface is required, the form can be treated with a retarder or other special chemicals to more easily achieve the desired result. The different types of finishes are discussed in the next section. 9–18

Chapter 3 of the PCI Architectural Precast Concrete17 contains detailed discussion of the specific points of surface aesthetics. Chapter 1 of this handbook also shows a variety of different finishes. The following information is intended to be an introduction to the different methods of achieving architectural finishes. The user is directed to the previously mentioned PCI manual for further information on architectural precast concrete. Sandblast.   Sand or abrasive blasting of surfaces can provide three degrees of exposure. This process is suitable for exposure of either large or small aggregates. The degree of uniformity obtained in a sandblasted finish is directly proportional to the depth of material removed, that is, greater depth of sandblast results in greater unifomity of the finish. Exposed-aggregate finishes are popular because they are economical and provide an infinite variety of colors and textures. This is achieved by varying the type, color, and size of aggregate, color of matrix, method of exposure, and depth of exposure. There are different degrees of exposure: • Light exposure, where the surface skin of cement and some sand is removed, just sufficiently to expose the edges of the closest coarse aggregate. This imparts a fine, sandy texture. Matrix color will greatly influence the overall surface color. • Medium exposure, where further removal of cement and sand has caused the coarse aggregate to visually appear approximately equal in area to the matrix. • Deep exposure, where cement and sand have been removed from the surface so that the coarse aggregate becomes the major surface feature. To the extent that aggregates are exposed or revealed is largely determined by their size. The time when sandblasting should take place is determined by plant scheduling, economics, desired visual appearance, and hardness of the aggregate. All surfaces should be blasted at approximately the same age or compressive strength for uniformity of appearance. The mixture used and the matrix strength at time of blasting will affect the final exposure, as

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PRECAST AND PRESTRESSED CONCRETE: MATERIALS will the gradation and hardness of the abrasive. Retarded / exposed aggregate.  The application of a chemical retarder to the form surface prior to concrete placement delays hardening of the surface cement paste within a certain time period, and to a depth dependent on the type or concentration of retarder. The action of any chemical is always subject to change as temperatures change, and is judged and monitored carefully by the plant. After some concrete hardening (normally overnight), the retarded outer layer of cement paste is removed by high-pressure water washing, exposing the aggregate to the desired depth. This process should take place at a predetermined time after casting. The aggregate exposure obtained is controlled by the retarder; therefore, any exposure variations are not as correctable as they are in sandblasting. Acid etching.   Acid etching is commonly used for light or light-to-medium exposures. Acid etching dissolves the surface cement paste to reveal the sand; only a very small percent of coarse aggregate is visible. The acid-etched finish is typically used to produce a fine sand texture closely resembling natural stones, such as limestone or sandstone, with retention of detail. This technique is often substituted for a light sandblast texturing. Where aggregates are to be exposed to a considerable depth, only acid-resistant, siliceous aggregates (quartz, granite) should be used. Carbonate aggregates (limestone, dolomite, marble) may discolor or dissolve due to their high calcium content. The aggregates on an acid-etched surface present a clean or bright look. After normal weathering, the aggregates will lose this brightness and will closely resemble their original condition. All surfaces should be acid-etched at approximately the same age or compressive strength for uniformity of appearance. Bush-hammering.  Concrete can be mechanically spalled or chipped with a variety of hand and power tools to produce an abraded, exposed-aggregate texture. Each type of tool produces a distinctive surface effect and a unique shade of concrete color. Tooling removes a layer of hardened concrete while fracturing larger aggregates at the surface. It produces an appearance somewhat different from other types of aggregate exposure. The color of the aggregate, but not necessarily the aggregate shape, is revealed. This finishing technique is most suitable for flat or convex surfaces, and is more labor intensive than most other finishing processes. All surfaces should be tooled at approximately the same age or compressive strength for uniformity of appearance.

9.3

Grout, Mortar, and Drypack

When water, sand, and a cementitious material are mixed together without coarse aggregate, the result is called grout, mortar, or drypack, depending on consistency. These materials have numerous applications. Sometimes they are used only for fire or corrosion protection or for cosmetic treatment; other times they are used to transfer loads through horizontal and vertical joints.

CHAPTER 9 Different cementitious materials are used: • Portland cement • Shrinkage-compensating portland cement • Expansive portland cement made with special additives • Gypsum or gypsum/portland cements • Epoxy-cement resins In masonry mortar, about one-half of the portland cement is replaced with lime. This improves its bonding characteristics, but reduces its strength. Such mortar should not be used indiscriminately as a substitute for grout. Care should be taken to be sure that chlorides are not present in grout material. Quality control of grout is as important as that of concrete. Grout should be made and tested at regular intervals according to ASTM C109, which parallels ASTM C39 for concrete. For more general information on grout, see PCA’s bulletin on the subject.18 9.3.1

Sand-Cement Mixtures

Most grout is a simple mixture of portland cement, sand, and water. Proportions are usually one part portland cement to two to three parts sand. The amount of water depends on the method of placement of the grout. Flowable grouts are used to fill voids that are either formed in the field or cast into the precast concrete component. They are used at joints that are heavily congested but not confined, thus requiring some formwork. These grouts usually have a high water–cementitious materials ratio (typically about 0.5), resulting in low strength and high shrinkage. There is also a tendency for the solids to settle, leaving a layer of water on the top. Special ingredients or treatments can improve these characteristics. For very small spaces in confined areas, grout may be pumped or pressure injected. The confinement must be of sufficient strength to resist the pressure. Less water may be used than for flowable grouts, resulting in less shrinkage and higher strength. A stiffer grout, or mortar, is used when the joint is not totally confined, such as in horizontal joints between wall panels. This material will usually develop strengths of 3000 psi to 6000 psi, and have much less shrinkage than flowable grouts. Drypack is the common name used for very stiff sand-cement mixtures. They are used if a relatively high strength is desired, such as under column base plates. Compaction is attained by hand tamping. When freezing-and-thawing durability is a factor, the grout should be air-entrained. Air content of plastic grout or mortar of 9% to 10% is required for adequate protection. Typical portland cement mortars have very slow early strength gain when placed in cold weather. Heating the material is usually not effective, because the heat is rapidly dissipated to surrounding concrete. Thus, unless a heated enclosure can be provided, special proprietary mixtures are often used with specific procedures for cold-weather application. As some of these mixtures may contain gypsum, it should be noted by the specifier that mixtures containing a high degree of gypsum are known to deteriorate under prolonged exposure to water, due to its tendency to expand with moisture.

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Non-Shrink Grouts

Shrinkage can be reduced, or more appropriately, compensated for by the use of commercially available non-shrink, high-strength pre-mixed grouts. These mixes expand during the initial hardening to offset the subsequent shrinkage of the grout. Because the non-shrink grouts are primarily proprietary, their chemical composition is usually not available to study their potential effects on the interfacing materials, such as reinforcement and inserts in a connection. Thus, it is advisable that manufacturers’ recommendations should be carefully followed. For general information on the characteristics and methods of testing of non-shrink grouts, the Corps of Engineers’ Specification 19 is a good reference. 9.3.3

Epoxy Grouts

Epoxy grouts are mixtures of epoxy resins and a filler material, usually oven-dried sand. These are used when high strength is desired or when improved bonding to concrete is necessary. ACI Committee 50320 has issued a comprehensive report on the subject. The physical properties of epoxy compounds vary widely. Also, the epoxy grouts behave very differently from the sand-cement grouts. For example, the thermal expansion of an epoxy grout can be as much as seven times the thermal expansion of sand-cement grout. Epoxy grouts may not be applicable where fire rating is required. Therefore, it is important that the use of these grouts be based on experience and/or appropriate tests. Recommended tests and methods are provided in the ACI Committee 503 report.

9.4

Connection Materials

9.4.1

Introduction

Connection design is discussed in Chapter 6 of this handbook. In this section, a brief review of connection materials is discussed. Connections are generally composed of steel embedments, standard steel sections, bearings, proprietary connections, and attachment hardware, such as bolts. Proprietary connections are not covered in this handbook; the engineer is directed to the catalogs or internet sites of one of the many industry accessory suppliers of this hardware. A note of caution is offered. Many of the proprietary anchors, embedments, or connections are used in handling and erection. Even though some specialty anchors or embedments are intended to carry temporary loads and are used only a few times, these embedments should still be required to meet minimum material standards. Some embedments may have very low notch toughness (Charpy V-notch) and have exhibited brittle fracture behavior in cold weather. Therefore, if cold-weather use of a proprietary embedment is a possibility, the precaster should request notch toughness testing as part of the mill certificate documentation for the embed hardware. The Charpy V-notch test involves taking samples with a prefabricated notch and splitting them with an impact force of a known energy; results are called CVNs. The toughness or ability of a material to absorb energy is related to tempera9–20

ture and tests are usually performed at temperatures in the 10 °F to 40 °F range. As a minimum, it is recommended that the steel have Charpy V-notch fracture toughness of 25 ft-lb at 40 °F, which is equivalent to an A36 material in a Zone 2 temperature range (below 0 °F to -30 °F), per AASHTO LRFD Bridge Design Specifications.21 9.4.2

Steel Sections

Steel sections commonly used in precast concrete connections include plates, angles, channels, structural tubes (HSS sections), and, occasionally, wide-flange sections. The dimensions and engineering properties of most steel sections are found in American Institute of Steel Construction’s Steel Construction Manual.22 Relevant specifications for structural steel include ASTM A6, ASTM A36, ASTM A500, and ASTM A992. Stainless steel plate is governed by ASTM A666. 9.4.3

Bearing Pads

A comprehensive discussion of bearing pads is presented in Chapter 6, Section 6.10. Much of the initial research work on bearing pads was contained in PCI's Technical Report No. 4.23 Additional research has been conducted on bearing pads in the industry, and is usually contained in the manufacturer’s catalog for the specific bearing pad. Some bearings require greater movement capabilities than a pad can achieve alone. In these joints, polytetrafluoroethylene (commonly known as Teflon [TFE]) is used on the sliding surface in combination with stainless steel. The TFE material should be 100% virgin material, premium grade, and should meet the requirements of ASTM D489. The TFE sheet (premium grade) should consist of pure TFE resin, compression molded, and skived into sheets of the required thickness on the drawings. 9.4.4

Structural Bolts / Anchor Bolts

Bolts to connect precast concrete components are usually installed in standard, oversized, or slotted holes. The bolts usually conform to ASTM A307, 60 ksi tensile strength; ASTM A325, 120/105 ksi minimum tensile strength; or ASTM A490, 150 ksi minimum tensile strength. The latter two types are classed as high-strength structural bolts that can be pretightened, if necessary. ASTM A193 Grade B5, 100 ksi minimum tensile strength, and Grade B7, 125 ksi minimum tensile strength, are also used. Both the hot-dip galvanizing and the mechanical galvanizing process are recognized in ASTM A307 and A325. As addressed in the following corrosion protection section, ASTM A490 bolts cannot be galvanized. High strength bolts, ASTM A325 and A490, and the associated nuts are typically alloyed and heat treated. As a result, any welding to them is likely to result in micro cracking at a minimum with larger cracking more likely. The extent of cracking is dependent on the preheat and welding procedure used. Anchor bolts embedded in foundations and other components are to conform to ASTM F1554, 36 ksi, 55 ksi, and 105 ksi yield strength.

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Table 9.5.1  Anodic index of selected common metals that may be used in precast concrete construction Metals / metallurgy

Anodic index, V

Gold, solid and plated; gold-platinum alloy

0.00

Silver, solid or plated; monel metal, high nickel-copper alloys

0.15

Nickel, solid or plated; titanium alloys; Monel

0.30

Copper, solid or plated; low brasses or bronzes; silver solder; German, silvery, high copper-nickel alloys; nickel-chromium alloys

0.35

Brass and bronzes

0.40

High brasses and bronzes

0.45

18% chromium-type corrosion-resistant steels (stainless)

0.50

Chromium plated; tin plated; 12% chromium-type corrosion-resistant steels (stainless)

0.60

Aluminum, wrought alloys of the 2000 Series

0.75

Plain carbon and low-alloy steels

0.85

Aluminum, wrought alloys other than 2000 Series aluminum, cast alloys of the silicon type

0.90

Aluminum; cast alloys other than silicon type; cadmium, plated and chromate

0.95

Hot-dip-zinc plated, galvanized steel

1.20

Zinc, wrought; zinc-base die-casting alloys; zinc plated

1.25

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Source: http://corrosion-doctors.org/Definitions/galvanic-series/htm.

9.5

Corrosion and Protection Means

9.5.1

Introduction

Corrosion is an issue of which all engineers must be aware, as it affects the durability and service life of the structures that are built. Avoiding corrosion of reinforcing steel and connections is one of the foremost challenges designers have with concrete products. Engineers combat this with high-quality concrete materials, maintaining clear cover, and applying sealers or coatings to the finished product. Precast concrete products have long been recognized as having enhanced corrosion durability due to their actual in-service performance in harsh climates. This is the result of production being done under plant-controlled conditions and being done by plants that are part of the PCI Certification Program. Precast concrete structures are often assembled structurally with steel connections that may be exposed to the environment. Other miscellaneous metallic items can influence the performance of the product, such as metal flashings, miscellaneous pipe or lighting hardware attachments, or bumper guards. Unprotected steel connections or other dissimilar metal contact in a humid environment can cause corrosion of the steel or other metallic element. Corrosion occurs naturally in a moist environment when a metal oxidizes. 9.5.2

Galvanic Series

When designing for exterior metal exposure in a moist or humid environment, it is necessary to consider corrosion induced by the use of dissimilar metals. In coastal regions, the climate can be very aggressive; as such, salt is present at relatively high levels in the humid air. Consequently, the salt is readily deposited on exterior, exposed surfaces and forms corrosive electrolyte concentrates to promote galvanic corrosion.

All metals have an electro-motive potential (tendency to be oxidized or to give up electrons), and, given the proper conditions, one metal will tend to corrode in the presence of another metal. Under such conditions, one metal becomes the anode (corrosion occurs) and the other becomes the cathode (more resistant to corrosion or at least partially protected by the anode). When a design requires dissimilar metal contact, the galvanic compatibility is managed by finishes, such as painting or galvanizing, or through isolation means, such as barrier coatings or inert (plastic, neoprene) washers or spacers. The finishing or isolation material that is selected prevents the dissimilar materials from being in contact and protects the base materials from corrosion. One tool available to aid in galvanic corrosion control is to consider the anodic index of the metals in contact, presented in Table 9.5.1. For design, the following guidelines have been suggested in the literature24 to address corrosion: • Harsh environments. A coastal locale or northern environment would fit into this category, that is, outdoors, high humidity, and potentially a high-chloride (salt) environment. Typically, there should be not more than 0.15 V difference in the anodic index. • Normal environments. This is consistent with storage in warehouses or non-temperature and humiditycontrolled environments. The difference in the anodic index should typically not be more than 0.25 V. • Controlled environments. These would likely be interior environments that are temperature and humidity controlled; a 0.50 V difference in the anodic index should be used as a guide. For example, an unprotected (unpainted) aluminum flashing placed in contact with a galvanized steel connection may not be desirable in a harsh environment. Table 9.5.1 indicates that the hot-dip galvanized connection will likely corrode in the presence (and electrical contact) of the flashing, if the flashing is

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CHAPTER 9 exposed to the environment (for example 1.20 - 0.90 = 0.30V, which is greater than 0.15V, the maximum recommended difference to control corrosion in harsh environments). The hotdip galvanized connection becomes the sacrificial anode in this couple and will corrode, exhibiting “white” rust. 9.5.3

Protection of Connections

9.5.3.1 Painted Steel

  9

In most building environments, painting of exposed steel in connections is sufficient to prevent corrosion. There is a broad spectrum of paint system choices, from one coat of primer to multicoat systems using zinc-rich paint or epoxy systems. Long oil alkyds have the advantage of low-cost surface preparation and the ease of application and touch up. The disadvantage is their relatively short life span in corrosive conditions. Epoxy polyamidoamines have an extended life span and are good in corrosive environments. However, they have higher material and surface-preparation costs. Epoxy polyamidoamines are more difficult to touch up in the field, because they are a twopart mixture requiring controlled temperatures to apply. Any epoxy-based topcoat has the disadvantage of chalking due to weathering and environmental effects, especially direct or indirect ultraviolet radiation (UV) exposure. For both long oil alkyd and epoxy polyamidoamine systems, the protection is lost once the surface is broken (scratch, incomplete coverage) because corrosion can start undercutting adjacent areas. Zinc-rich urethanes minimize this problem by providing galvanic protection, and they have the best corrosion resistance and life expectancy. Zinc-rich paints contain metallic zinc dust in suspension and should be continuously agitated during application to prevent settling of the zinc dust. Zinc-rich primers come in organic and inorganic formulations. An organic, zinc-rich primer is more forgiving to the surface conditions of the substrate and is easier to use in the field. Typical surface preparation would be SSPC SP-6 (commercial blast cleaning). An inorganic, zinc-rich primer provides a better corrosion protection system than an organic zinc, but typically demands a good, clean surface approaching SSPC SP-10 (near-white blast cleaning). Better success with this system is achieved with shop application. These paints are applied with dry film thicknesses (DFT) of 2.5 mils to 3.5 mils per layer, depending on the carrier vehicle. Excessive film build-up per coat can cause mud-cracking of the coating upon drying. Organic-zinc, primer, polyamide epoxy intermediate coat, and an aliphatic polyurethane finish coat would be one possible generic coating system for steel. Potentially, this is a 15-year system. Surface preparation should include complete removal of all contaminants from the surface and preparation in accordance with SSPC SP-6 or 10.25 Consult the regional precasters in the area for paint systems that are commonly used. 9.5.3.2 Galvanized Steel There are typically three methods for applying zinc to steel for corrosion protection that are applicable to precast concrete construction:26 9–22

• Hot-dip galvanized • Mechanical galvanized • Zinc plating Batch hot-dip galvanizing is a common form of corrosion protection that produces a varied coating thickness. In this process, the steel is cleaned, fluxed, and then lowered in a bath of molten zinc. Tank sizes and material handling issues are the only restrictions to the size of the steel piece to be coated. Coating thickness ranges from 1.4 mils to 3.9 mils and usually depends on the immersion time. Because of the immersion in the molten zinc, the zinc tends to flow in all difficult-to-access areas of the steel part. Prior to erection, residual zinc whiskers may require removal for fit-up and connection purposes. Mechanical galvanizing involves the plating of a zinc coating onto bare steel. The prepared steel is placed in a tumbling drum with a mixture of promoting chemicals, zinc powder, and glass beads. The tumbling process causes the glass beads to peen the zinc powder on the steel. Coating thickness is controlled through the zinc quantity and tumbling time, and ranges from 0.2 mils to 4.3 mils. The steel pieces are then separated and dried. Mechanical galvanizing produces a more uniform zinc appearance, such as with bolts, and is distinguished by the overall peened appearance. The zinc-plating process is an electro-deposition process used on small parts, such as fasteners. It starts with degreasing and cleaning the metal. The steel is then lowered into a plating solution, where it becomes the cathode of the electrochemical reaction. The zinc coating forms on the surface as zinc ions in the solution become electrically reduced to zinc metal and deposit on the cathode. The coating thickness of this process tends to be the least of the three, ranging from 0.2 mils to 1.0 mils; this process provides only minimal corrosion protection, and should be considered only for interior applications. Bolts.   Both the hot-dip galvanizing process and the mechanical galvanizing process are recognized in ASTM A307 and A325. The effects of the two processes upon the performance characteristics and requirements for proper installation are distinctly different. Steels in the 200 ksi and higher tensile-strength range are subject to embrittlement if hydrogen is permitted to remain in the steel and the steel is subject to high tensile strength. Black, ASTM A490 bolts are close to this range; therefore, because of the introduction of hydrogen during the pickling operations of hot-dip galvanizing and sealing in of the zinc coating, coated A490 are not allowed. Because of the over-tapping required in nuts due to the galvanizing, thread engagement becomes an issue. Only stronger, hardened nuts will have adequate strength, and only ASTM A563 Grade DH nuts are to be used. This requirement should not be overlooked if non-galvanized nuts are purchased and sent to a galvanizer for hot-dip galvanizing. Galvanizing increases the friction between the bolt and nut, and a lubricant is required to achieve proper pretension if pretensioning of the bolt is required. The presence of lubricant on the nut needs to be readily observable in the field.

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PRECAST AND PRESTRESSED CONCRETE: MATERIALS Welding.   Connections should be designed to minimize field welding if galvanized connections are used. The fumes from welded galvanized material are very toxic and present a serious threat to the welder, even with the use of protective equipment. The process of welding destroys the protective coating, requiring touch up with a cold-applied, zinc-rich paint. Care must be used in preparing the surface of the areas affected by the heat, which then must be coated with a suitable, cold, galvanizing compound. Embrittlement.   In order to ensure that the strength of the various components of a connection are not reduced by embrittlement during the hot-dip galvanizing process, several precautions are recommended. When items of a connection assembly require welding, such as anchor bars to plates, the following recommendations have been found to produce satisfactory results and are recommended by the American Hot Dip Galvanizers Association:27 1. An uncoated electrode should be used whenever possible to prevent flux deposits. 2. If a coated electrode is used, all welding flux residues must be removed by wire brushing, flame cleaning, chipping, grinding, needle gun, or abrasive blast cleaning. This is necessary because welding flux residues are chemically inert in the normal pickling solutions used by galvanizers; their existence will produce rough and incomplete zinc coverage. 3. A welding process such as metal-inert gas (MIG), tungsten-inert gas (TIG), or CO2 shielded arc is recommended when possible because they produce essentially no slag. 4. If special process welding is not available, select a coated rod specifically designed for self-slagging, as recommended by welding equipment supplier (refer also to item 2). It should also be recognized that many parts of connection components are fabricated using cold-rolled steel or cold-working techniques, such as bending of anchor bars. In some instances, cold working may cause the steel to become strain-age embrittled. The embrittlement may not be evident until after the work has been galvanized. This occurs because aging is relatively slow at ambient temperatures, but is more rapid at the elevated temperature of the galvanizing bath. It is recognized that any form of cold working reduces the ductility of steel. Operations such as punching holes, notching, producing fillets of small radii, shearing, and sharp bending may lead to strain-age embrittlement of susceptible steels. The following precautions are recommended by the American Hot Dip Galvanizers Association 28 if cold-worked steel is to be galvanized: 1. Select steel with a carbon content below 0.25%. 2. Choose steel with low transition temperatures, because cold working raises the ductile-brittle transition temperature and galvanizing (heating) may raise it even more. 3. For steels having a carbon content between 0.10% and 0.25%, a bending radius of at least three times the section thickness (3t) should be maintained. In

CHAPTER 9 some cases, 6t yields even better results. If less than 3t bending is unavoidable, the material should be stressrelieved at 1100 °F for 1 hour per inch of section thickness after bending. 4. Drill, rather than punch, holes in material thicker than 3 /4 in. If holes are punched, they should be punched undersize, then reamed an additional 1/8 in. overall or drilled to size. 5. Edges of steel sections greater than 5/8 in. thick subject to tensile loads should be machined or machine cut. 6. In critical applications, the steel should be hot worked above 1200 °F in accordance with steelmaker’s recommendation. Where cold working cannot be avoided, stress-relieve as recommended in item 3. ASTM A143 and CSA Specification G164 provide guidance on cold-working and stress-relieving procedures. However, severe cold working of susceptible steels is better avoided, if possible. Another area of concern is hydrogen embrittlement. Hydrogen embrittlement is a ductile-to-brittle change that occurs in certain high-strength steels. Hydrogen released during the pickling operation, prior to hot dipping, can cause this embrittlement. This hydrogen can be absorbed into the steel during the acid pickling, but at galvanizing temperatures it is generally expelled from the steel. Hydrogen embrittlement is not common, but precautions should be taken if the steel involved has an ultimate tensile strength exceeding about 150 ksi, or if the pickling process is poorly controlled, resulting in long exposure to hydrochloric acid. In those cases, grit blasting is recommended instead of acid pickling. These precautions are also outlined in PCI’s Recommended Practice for Parking Structures.29 An alternative to hot-dip galvanizing is cold galvanizing using zinc-rich paint, although this alternative is generally believed to provide less protection. 9.5.3.3 Stainless Steel In highly corrosive environments, stainless steel may be used for connections and embedments. The American Iron and Steel Institute (AISI) 200 and 300 Series stainless steels contain nickel and chromium and are essentially nonmagnetic; these are referred to as austenitic stainless steels. The AISI 200 Series contains manganese in addition to the nickel and chromium. The AISI 400 Series contain straight chromium and is referred to as ferritic stainless steel. They are magnetic and are less ductile than the austenitic grades. Austenitic grades are weldable, and, therefore, are more applicable for connections. AISI Types 304 (or 18-8) and 316 are most commonly used in structural applications. These types are a low-carbon modification of Type 302 for limiting carbide precipitation during welding. Type 316 has a higher corrosion resistance than Type 304, and is usually used for chemical handling equipment or in aggressive corrosion environments. There are Types 304L and 316L, which are extra-low-carbon modifications of Types 304 and 316, respectively, and can be used where carbide precipitation is a problem. There are a limited

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  9 Fig. 9.6.1 Wire prestressing strand of various sizes.

Fig. 9.6.2 Strand pack in position for distributing strand to a prestressing bed.

number of structural shapes and sizes available in stainless steel. Consult with the local steel suppliers for availability of different shapes and sizes. Austenitic stainless steel can be welded by all common methods, and the equipment that is used is basically the same as that used for carbon steel. The choice of electrodes should be made for compatibility with the base metal. E308 electrode is used with 304, E308L with 304L, E316 with 316, and E316L with 316L. When stainless steel and carbon materials are to be joined, an E309 electrode should be used. All stainless-steel submerged metal arc welding (SMAW) electrode coverings are of the low-hydrogen type and must be protected from moisture. Electrodes should be purchased in hermetically sealed containers, which can be stored for several months without deterioration. After opening, the electrodes should be reconditioned after 4 hours of exposure. Fillet welds should be designed using the same guidelines as for carbon steel. Joints must be clean and dry. Moisture should be removed by heating or by blowing with dry air. Slag needs to be thoroughly removed and the weld completely cleaned before starting a new pass. Only stainlesssteel wire brushes should be used for cleaning. Inspection of welds should include verification of the proper electrode, proper storage of the electrode, and operator certification, in addition to the non-destructive testing required. The method and frequency of inspection should be as directed by the design engineer. Typically, the inspection will only be visual. The welding of stainless steel produces more heat than conventional welding. This, and the fact that stainless steel has a coefficient of thermal expansion greater than structural steel, can create adverse expansion of embedments during welding; thus, special detailing is required to avoid cracking the adjacent concrete. Stainless-steel embedment edges should be kept free from adjacent concrete to allow expansion during welding to avoid spalling the concrete.

9.6

Reinforcement

Reinforcement used in structural and architectural precast concrete includes prestressing tendons, deformed steel bars, and welded-wire reinforcement. Fibers, which are sometimes used to control shrinkage cracks, do not have well-defined structural properties and, therefore, cannot be used to replace structural reinforcement such as welded-wire reinforcement. This is particularly important for structural toppings over precast concrete decks. The reinforcement in these toppings cannot be replaced with fibers. 9.6.1

Prestressing Tendons

Tendons for prestressing concrete may be wires, strands, or high-strength bars. In precast, prestressed structural concrete, nearly all tendons are seven-wire strands conforming to ASTM A416. There is limited use of two-wire and threewire strands conforming to ASTM A910. The strands are pretensioned; that is, they are tensioned prior to placement of

Fig. 9.6.3 Prestressing bars ranging in size from 1 in. diameter to 2 1/2 in. diameter

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Fig. 9.6.4 Reinforcing bars of various sizes, from #18 to #3. (See Design Aid 15.2.6.)

the concrete. After the concrete has reached a predetermined strength, the strands are cut and the prestress force is transferred to the concrete through bond. Two types of strand are covered in ASTM A416 and A910: low-relaxation strand and stress-relieved strand. Lowrelaxation strand is the standard in North America and is used in the load tables in Chapter 3 and in the various examples throughout this handbook. Figure 9.6.1 shows several sizes of typical seven-wire strand used in the precast concrete industry. Figure 9.6.2 shows a strand pack that can hold from 12,500 ft to 15,500 ft of 1/2-in.-diameter strand and from 6500 ft to 9000 ft of 0.6-in.-diameter strand. Sometimes architectural precast concrete contains tendons. Depending on the facilities available at the plant, these tendons may be either pretensioned or post-tensioned. In posttensioning, the tendons are either placed in a conduit or are coated so they will not bond to the concrete. The tendons are then tensioned after the concrete has reached the predetermined strength. The compressive forces are transferred to the concrete from the strand by end fittings on the strand, which bear directly against the end surfaces of the concrete component. When the tendons are placed in a conduit, they are usually grouted after tensioning (bonded post-tensioning). When they are greased and wrapped, or coated, they are not grouted (unbonded post-tensioning). For more information on post-tensioning, see the Post-Tensioning Institute’s PostTensioning Manual.30 Prestressing bars meeting ASTM A722 have been used in connections between components, and may be applicable for prestressing short components where the seating losses associated with strand anchors are not acceptable. The properties of prestressing strand, wire, and bars are given in Chapter 15. The ability of strands to properly bond should be certified by the strand supplier. Recent research31 suggests that the strand bond characteristics are affected by the amount of concrete above the strands at the time of casting, as well as the concrete fluidity. This latter effect could be brought about by the use of SCC. Consequently, the equations for transfer and development length may not be conservative in certain cases. 9.6.2

Prestressing Bars

Prestressing bars (Fig. 9.6.3) are used in the industry primarily to tie precast concrete components together after they are erected. Proprietary system components are usually designed to be fully integrated for field assembly, and then later grouted in ducts. They can also be used in precast con-

CHAPTER 9 crete construction as external tendons with various types of corrosion protection. Prestressing bars are covered by ASTM A722 and are available with minimum strengths of 150 ksi. These bars are typically furnished in mill lengths and can be cut to application-specific length. Diameters of these bars range from 1 in. to 21/2 in. They are usually marked by coarse threads, which are oriented opposite to normal threads; thus, they usually require longer lockoff nut lengths in order to provide greater thread engagement. These bars are also conveniently joined together with the use of coupling nuts. Special attention should be taken to avoid tack welding nuts to prestressing bars. 9.6.3

Deformed Reinforcing Bars

Reinforcing bars (Fig. 9.6.4) are hot-rolled from steel with varying carbon content. They are usually required to meet ASTM A615, or A996. These specifications are of the performance type and do not closely control the chemistry or manufacture of the bars. Bars are usually specified to have a minimum yield of 40,000 psi (Grade 40) or 60,000 psi (Grade 60). Grade 40 bars will usually have lower carbon content than Grade 60. It is sometimes possible to weld these grades of reinforcing bars after appropriate preheating, depending on the carbon equivalent.32 ASTM A706 specifies a bar with controlled chemistry that is weldable. In accordance with ASTM A706 the mechanical characteristics of the reinforcement is more closely controlled than ASTM A615. For example a maximum yield strength of 60 ksi to 78 ksi and a minimum tensile strength of 80 ksi is prescribed. See Chapter 6 for discussion of welding without preheating. In order for the reinforcing bar to develop its full strength in the concrete, a minimum length of embedment is required or the bars may be hooked. Information on bar sizes, bend, and hook dimensions and development length is given in Chapter 6 of Concrete Reinforcing Steel Institute’s Manual of Standard Practice.33 and Chapter 15 of this handbook Closely spaced bars of small diameter will control crack width and improve the distribution of temperature stresses better than fewer, larger bars at a wider spacing. The use of small diameter, closely spaced bars becomes more important in thin concrete sections. Since the sum of the widths of cracks in concrete is essentially the same for a given set of conditions, the more cracks there are, the smaller and less visible they will be. The recommended maximum spacing of reinforcement in panels exposed to the environment is 6 in. for welded-wire reinforcement and three times the panel thickness (18 in. maximum) for reinforcing bars. Good bond between the reinforcing bar and the concrete is essential if the bar is to perform its functions of resisting tension and keeping crack widths small. Therefore, the reinforcing bar must be free of materials injurious to bond, including loose rust. Mill scale that withstands hard-wire brushing or a coating of tight rust is not detrimental to bond. Epoxy-coated reinforcement does not control cracks as well as uncoated reinforcement. If uncracked design is used, then there is no reason for epoxy coating. Thus, epoxy-coated reinforcement is not usually specified for architectural precast concrete.

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9.6.5

  9 Fig. 9.6.5 Example of deformed welded-wire reinforcement.

9.6.4

Structural Welded-Wire Reinforcement

Structural welded-wire reinforcement (WWR) (Fig. 9.6.5) is a prefabricated reinforcement consisting of parallel, colddrawn wires welded together in square or rectangular grids. Each wire intersection is electrically resistance-welded by a continuous automatic welder. Pressure and heat fuse the intersecting wires into a homogeneous section and fix all wires in their proper position. Plain wires (ASTM A185), deformed wires (ASTM A497), or a combination of both may be used in WWR. Plain wire sizes are specified by the letter W followed by a number indicating the cross-sectional area of the wire in hundredths of a square inch. For example, W16 denotes a plain wire with a cross-sectional area of 0.16 in.2 Similarly, deformed wire sizes are specified by the letter D and followed by a number that indicates area in hundredths of a square inch. Plain WWR bonds to concrete by the mechanical anchorage at each welded-wire intersection. Deformed WWR utilizes wire deformations as well as welded intersections for bond and anchorage. WWR for architectural precast concrete is normally supplied in flat sheets. Use of WWR from rolls, particularly in the thin precast concrete sections and topping pours, is not recommended because the rolled WWR cannot be easily and reliably flattened to the required placement tolerance. In addition to using WWR in flat sheets, many plants have equipment for bending sheets into various shapes, such as U-shaped stirrups, four-sided cages, and the like. Available wire sizes, common stock sizes, and other information on WWR are given in Chapter 15 of this handbook and through the Wire Reinforcement Institute.34 Some suppliers to the precast concrete industry also manufacture specialty mesh sizes and patterns for specific products such as double-tees.

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Carbon-Fiber Mesh

Carbon-fiber reinforced polymer (CFRP) grids used in precast concrete resemble WWR in appearance, but differ in other aspects. CFRP grids are being used in precast concrete components to reinforce double-tee flanges for cantilever, transverse bending moments. They are also used for composite shear connectors in wall panels; they are cut at a 45 deg angle to create truss-like connectors used to transfer shear between the outer concrete wythes of insulated sandwich wall panels, thus providing composite action. Besides being non-corrosive, CFRP grids require little concrete cover to develop their strength, which can lead to lighter structures. Thinner and lighter precast concrete components usually reduce the transportation and erection costs of a project. Their use will increase as strength demands necessitate their use, coupled with the benefit of corrosion resistance. However, economics and deflection-related serviceability should be considered when using this type of reinforcement. CFRP mesh should only be used with the consultation of precast concrete manufacturers that have experience and testing data to substantiate its application. Figures 9.6.6 and 9.6.7 show two types of CFRP mesh used in the industry. 9.6.6

Protection of Reinforcement

9.6.6.1 Corrosion Mechanism / Chlorides Reinforcing steel is protected from corrosion by embedment in concrete. A protective iron-oxide film forms on the surface of the bar, wire, or strand as a result of the high alkalinity of the cement paste. As long as the high alkalinity is maintained, the film is effective in preventing corrosion. The protective high alkalinity of the cement paste may be lost in the presence of oxygen, moisture, and chlorides. Chlorides may be found in concrete aggregates, water, cementitious materials, or admixtures, and, therefore, may be present in small quantities in the concrete when cast. Concrete of low permeability and sufficient cover over the steel will usually provide the necessary protection against chloride penetration in the presence of deicing salts. Moisture and oxygen alone can cause corrosion. Cracking can allow oxygen and moisture to reach the embedded steel, resulting in conditions where rusting of the steel and staining of the surface may rapidly occur. Prestressing can control cracking. Non-prestressed components should be designed for low flexural stress to minimize the potential for cracking. Design for crack control is governed by ACI 318-05, Section 10.6. Chloride compounds as an admixture should not be used in prestressed or reinforced concrete. Consideration should be given to the chloride ion content in hardened concrete, contributed by the ingredients of the mixture. Table 9.6.1 (Table 4.4.1, ACI 318-05) presents the maximum chloride ion content to maintain corrosion protection of the reinforcement. These limits are intended for use with uncoated reinforcement. Chloride ion content values can be determined in accordance with ASTM C1218.

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9.6.6.2 Carbonation / Cracking Carbonation is a natural process whereby carbon dioxide in the air reacts with calcium hydroxide in the concrete to form calcium carbonate and water. The occurrence of carbonation at the embedded reinforcement level disrupts the normally protective concrete environment by lowering the pH, similar to the results of chloride ion ingress. If moisture and oxygen are available in the concrete, corrosion activity can occur. The depth of the carbonated zone at an exposed concrete surface is a function of the concrete quality, the aggregate type, and the length of exposure to the atmosphere. Cracking can allow the carbonation front to penetrate into the concrete surface in localized areas. High-quality, normalweight concretes exposed for a short time period will exhibit minimal carbonation levels. Low-quality concretes or those exposed over long time periods may exhibit extensive levels of carbonation. A concrete clear cover greater than the carbonation depth ensures that the reinforcing bars remain in the high pH environment. 9.6.6.3 Concrete Cover In order to provide corrosion protection to reinforcement, concrete cover should conform to ACI 318-05 Section 7.7.3. Concrete cover is the minimum clear distance from the reinforcement to the face of the concrete. For exposed-aggregate surfaces, the concrete cover is not measured from the original surface; instead, the depth of the mortar removed between the pieces of coarse aggregate (depth of reveal) should be subtracted. Attention must also be given to scoring, reveals, false joints, and drips, as these reduce the cover. High-quality concrete provides adequate corrosion protection for reinforcement for most conditions. Even in moderate to severe aggressive environments, concrete will provide adequate protection with proper attention to mixture design, steel stress level, the extent of cracking under service loads, and the depth of concrete cover. It may be necessary to consider other ways of protecting reinforcement, such as galvanizing, corrosion inhibitors, or epoxy coating when these protection measures are not feasible. They are described in the following sections. 9.6.6.4 Galvanized Reinforcement Except for exposed connections, there is rarely any technical need for galvanized reinforcement. With proper detailing and specifications, galvanizing may be superfluous. Galvanizing is not recommended for components subjected to chlorides, because a deleterious chemical reaction can take

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Fig. 9.6.6 Carbon-fiber-reinforced polymer used as shear reinforcement in a sandwich wall panel.

Fig. 9.6.7 Carbon-fiber-reinforced polymer mesh used in flat deck components and architectural concrete panels.

place between the chloride and the galvanizing when the concrete is damp and chlorides are present. Therefore, the benefit obtained by galvanizing is questionable for components subjected to deicing salts and similar exposures. Galvanized welded-wire reinforcement is usually available as a stock item in selected sizes. Individual wires are galvanized before they are welded together to form the fabric; zinc at each wire intersection is burned off during welding, but

Table 9.6.1 Maximum chloride ion content for corrosion protection of reinforcement. Type of member

Maximum water soluble cholride ion CI¯ in concrete, percent by weight of cement

Prestressed concrete

0.06

Reinforced concrete exposed to chloride in service

0.15

Reinforced concrete that will be dry or protected from moisture in service

1.00

Other reinforced concrete construction

0.30

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the resulting ungalvanized spots have not caused noticeable problems. After welding, the fabric is shipped without further treatment. There is no current ASTM specification for galvanized welded-wire reinforcement. When galvanized reinforcement is used in concrete, it should not be coupled directly to ungalvanized steel reinforcement, copper, or other dissimilar materials. Care should be taken to provide insulating material between galvanized reinforcing and other dissimilar metals at points of contact. The use of galvanized reinforcement close to steel forms or non-galvanized reinforcement in fresh concrete may cause shadowing or reflection of the reinforcement onto the final concrete surface. When galvanized and non-galvanized reinforcement or steel forms are in close proximity in fresh concrete, galvanic cell problems may occur during the initial processes of hydration. The reactions of zinc in concentrated alkaline material such as concrete (pH of 12.5 to 13.5) liberate hydrogen gas. This release of gas bubbles results in the shadowing or reflection of reinforcement. Ways to avoid this occurrence, by passivating either the galvanized steel or the concrete mixture, are discussed in PCI’s Architectural Precast Concrete. 9.6.6.5 Epoxy-Coated Reinforcement Epoxy-coated reinforcing bars and welded-wire reinforcement are also available for use in components that require special corrosion protection. Epoxy-coated reinforcing bars should conform to ASTM A775 or A934, and epoxy-coated, welded-wire reinforcement should conform to ASTM A884. The epoxy provides enhanced protection from corrosion if the bar is uniformly coated. Bars generally are coated when they are straight; subsequent bending should have no adverse effect on the integrity of the coating. If the coating is removed or damaged, the reinforcement should be touched up with commercially available epoxy-patching compounds. Epoxy coating reduces bond strength; reference should be made to Section 12.2.4 of ACI 318-05 and Chapter 15 of this handbook for the required increase in development length. Similarly, the requirements for crack control may need to be modified. Supplemental items must also be protected to retain the full advantage of protecting the main reinforcement. For example, bar supports should be solid plastic and bar ties should be nylon-, epoxy-, or plastic-coated wire, rather than black wire. Epoxy-coated reinforcing bars should be handled with nylon slings. 9.6.6.6 Epoxy-Coated Strand Epoxy-coated strand, which is covered by ASTM A882, is sometimes proposed for use in unusually aggressive environments. In order for it to be used as bonded strand, the epoxy coating is impregnated with a grit to ensure development of bond. Without grit, the epoxy-coated strand has virtually no bond strength. With adequate density and a proper distribution of the grit, the bond strength of the epoxy-coated strand is comparable to that of uncoated strand. Tests by LeClaire and Shaikh35 have shown the transfer and the development lengths of the epoxy-coated (with grit) strand to be some9–28

what shorter than the corresponding lengths for the uncoated strand. Also, there are differences in some other properties of the two types of strand. For example, the relaxation loss of epoxy-coated strand is greater (about double) than uncoated, low-relaxation strand. The behavior of epoxy-coated strand at elevated temperatures is of concern due to softening of the epoxy. Pull-out tests35 show that there is a progressive reduction in bond strength initiating at about 125 °F with a virtually complete loss of bond occurring at about 200 °F. These temperatures often occur during curing of prestressed products. This behavior necessitates a careful monitoring of concrete temperature at transfer of prestress. Because of the uncertainties of the properties noted in previous paragraphs, particularly the behavior under elevated temperatures, it is recommended that epoxy-coated strand not be used for pretensioned, prestressed concrete products. 9.6.6.7 Other Corrosion-Resistant Steels Stainless-steel-clad reinforcing bar, developed as an economical alternative to solid stainless-steel reinforcing bar, is a composite material consisting of a carbon steel core and a metallurgical-bonded cladding of stainless steel. The stainless steels used as cladding materials are typically Type 304 or 316L. Mechanical and cladding property requirements for SCR are outlined in AASHTO MP13M/MP 13-04. A number of investigations have reported that defect-free SCR demonstrated corrosion resistance comparable to solid stainless-steel reinforcing bar in test programs up to seven years. SCR, however, is susceptible to corrosion at cladding discontinuities, which may result from inferior production quality control, unexpected mechanical damage, or unprotected cut-ends. Nevertheless, the stainless-steel cladding is more resistant to damage than organic coatings, and it has been reported that SCR, with isolated sub-millimeter defects in high-quality concrete, can provide service life as long as 75 years or more. Availability of SCR should be verified prior to specifying. Another alternative reinforcing material is ASTM A1035 reinforcing bar. Produced from a proprietary process, these steels typically contain about 10% chromium and have a unique alternating martensite/austenite microstructure. ASTM A1035 reinforcing bar has been reported to have corrosion resistance slightly higher than traditional carbon-steel reinforcing bar. In addition, the tensile strengths of these steels are about 50% higher than other common reinforcing bars. Therefore, use of ASTM A1035 reinforcing bar can potentially introduce both improvements in corrosion resistance and saving in reinforcing bar usage. However, a number of investigations have reported that the corrosion resistance of this material is inferior to austenitic stainless steels and it can experience significant corrosion in very aggressive environments.

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9.7

Waterproofing

9.7.1

Coatings for Horizontal Deck Surfaces

Concrete surface sealers reduce moisture and salt (chloride) penetration, which is particularly important in parking structures. While these sealers can enhance the durability of any concrete surface, they do not substitute for basic, durable concrete design, nor do they provide protection against penetration of moisture and chlorides through cracks wider than about 0.01 in. Research has shown that the performance of concrete sealers will vary, depending on the product and application. Products should be evaluated against the criteria established in the NCHRP 244 study.36 Sealers may be classified into two groups: penetrants and surface sealers.37,38 Silanes or siloxanes penetrate the surface, reacting with cementitious materials and making the concrete hydrophobic. They do not have crack-bridging capabilities, and do not appreciably affect the appearance or characteristics of the surface to which they are applied. While generally more expensive than other types of sealers, they are typically longer lasting and less subject to wear under traffic or deterioration from exposure to ultraviolet radiation. Surface sealers are generally polymer resins such as urethanes, epoxies, acrylics, or other proprietary blends. They provide protection by penetrating the surface slightly, and/ or by providing a tough film over the surface; these materials also do not bridge cracks. Surface sealers are generally less expensive than penetrants, and performance characteristics of many of these products compare favorably with the penetrating sealers, as demonstrated by the NCHRP 244 criteria. These sealers are more likely to be subject to wear under traffic. They may be more slippery than the bare concrete surface and, thus, require a grit surface. Urethane membranes are often employed on parking decks to provide enhanced protection to the wearing surface. Urethane membranes typically consist of a two- or three-coat urethane coating with a rounded sand broadcast into the top layer, which enhances traction and slip resistance. Membrane thicknesses range from 40 mils to 60 mils, with the heavier thicknesses required for high-traffic applications. Depending on exposure conditions and intensity and nature of traffic, membranes can be expected to have a service life of 7 years to 15 years. Longer service lives can be achieved when the product is maintained, and wear areas and holes are patched before growing in size. Membranes provide an almost impenetrable barrier to moisture ingress into the concrete substrate. It is important that membranes be placed on a dry substrate and that the concrete has properly cured. Membranes applied over a concrete surface that is still curing and losing internal free water can blister due to moisture entrapment under the barrier coat of the membrane.

CHAPTER 9 9.7.2

 lear Surface Sealers for Architectural C Precast Concrete Panels

Clear surface coatings or sealers39 are sometimes used on precast concrete wall panels to improve weathering qualities or to reduce attack of the concrete surface by airborne pollutants. Because of the quality of concrete normally achieved under plant-cast, precasting conditions, even with very thin sections, sealers are not required for waterproofing. Because the results are uncertain, use of sealers in locations having little or no air pollution is not recommended. A careful evaluation should be made before deciding on the type of sealer, including consultations with regional precasters. In the absence of nearly identical experience, it is desirable to test sealers on reasonably sized samples of varying age to verify performance over a suitable period of exposure or usage, based on prior experience under similar exposure conditions. Clear, penetrating sealers are typically applied to reduce water penetration into the precast concrete substrate. These sealers are commonly known as silanes or siloxanes, with silanes penetrating the deepest into concrete pores. Various silane- or siloxane-based proprietary products are available on the market. These products react chemically with pore surfaces and fine cracks in the concrete to make them water repellant or hydrophobic, while allowing moisture that does enter the concrete to escape (breathable). These sealers do not fill or bridge cracks. Any coating that is used should be guaranteed by the supplier or applicator not to stain, soil, or discolor the precast concrete finish. Also, some clear coatings may cause joint sealants to stain concrete. Consult manufacturers of both sealants and coatings or pre-test before applying the coating. Sealers are usually applied to wall panels after joints are caulked to avoid problems with adhesion of joint sealants. Sealers should be applied in accordance with manufacturers’ recommendations. Good, airless spray equipment is generally used for uniformity and to prevent surface rundown. Two coats are usually required to provide a uniform coating, because the first coat is absorbed into the concrete. The second coat does not penetrate as much and provides a more uniform surface color. Care must be taken to keep sealers off glass and other adjacent surfaces. 9.7.3

 urface Coatings for Architectural S Precast Concrete

Pigmented coatings are applied to reduce water penetration into the concrete substrate, while improving or changing aesthetics. Pigmented coatings are used in architectural applications to create a more homogenous appearance and to hide color and texture differences, yet they cannot mask any changes in surface profile. These coatings can be breathable or completely film-forming to prevent any vapor or moisture transmission. Products typically include high build, 100%-acrylic sealers or acrylic copolymer coatings applied at a 15 mils to 20 mils wet-film thickness; some are extended with aggregate (perlite, quartz) to aid in texturing. Film-forming products may alter the vapor permeability

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CHAPTER 9 of the substrate and also affect the surface texture, ability to reflect light, and overall appearance. The breathability of film-forming coatings is usually dependent on the type and amount of binder on the thickness of the coating. Anti-graffiti coatings are either permanent or sacrificial and may change the color of the concrete by altering the refractive qualities. This may create difficulty in matching adjacent panels. 9.7.4

Joint Sealants

9.7.4.1 Introduction

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Successful performance of wall, roof, and parking-deck systems depends on the proper sealant selection and the attention given to the details. Generally, a joint sealant is any material used as a means of first defense to prevent the passage of moisture, air, heat, or dirt into or through a joint. Sealants have four inherent characteristics: adhesion, cohesion, elasticity, and weathering ability. ASTM C1193 provides further information on this subject. For specific information and recommendations for joints in precast concrete parking garages, refer to PCI Parking Structures Committee report on joints.40 Joint sealants include viscous liquids, mastics, or pastes, and tapes, gaskets, and foams. Viscous liquid sealants are typically poured in horizontal joint applications. Mastics are applied with a gun and are compounded to prevent sagging or flowing when used in vertical joints. Tapes are most often used around glass. Elastomeric gaskets are used in joints that experience considerable movement. Foams are used as air seals or backup for more durable surface seals. Most of the raw materials are manufactured by a few major chemical companies and then compounded with other ingredients by numerous sealant manufacturers. The quality of the finished products varies widely; proven performance should be viewed as a key indicator of future success. The design and selection of joint sealants can be found in References 41, 42, and 43, as well as ACI Committee 504 Guide to Sealing Joints in Concrete Structures,44 and ASTM's Standard Guide for Use of Joint Sealants.45 Parking structures in particular require special attention to joint detailing and material selection. A high-quality, trafficbearing polyurethane or silicone sealant is necessary to prevent intrusion of water-borne salts into the joints and, therefore, prevent the subsequent deterioration of embedded metals. For conditions of severe UV exposure, silicone should be considered from the standpoint of longevity; however, two-part polyurethane sealants manufactured specifically for vehicular traffic are typically recommended for parkingstructure applications. 9.7.4.2 Joint Profile Joint sealant profiles must be designed to accommodate the actual as-built joint width, which is affected by product and erection tolerances and may not be as detailed on drawings. The sealant joint is then sized to have a profile or aspect ratio (width-to-depth) of 2:1; that is, the sealant depth is set to be 1/2 of the sealant joint width. Wide joints (greater than 1 in.) may 9–30

have limits on the sealant depth, as recommended by the manufacturer. The proper aspect ratio allows the sealant to accommodate the joint movement and adhere to the concrete surfaces at the joint. The backer rod does not bond to the sealant, so the sealant stretch or strain is accommodated in the joint width. If the sealant depth or thickness at its thinnest point (the crown of the backer rod) is too thin, the sealant will stretch too much and tear. Conversely, if the sealant is too thick, it cannot elongate to accommodate the movement and will tear. For horizontal, field-topped, precast concrete systems, joints should be hand-tooled and not saw-cut at a later time, so as to reflect the joints between all of the precast concrete components under the topping. The typical tooled joint is 3/4 in. deep and 1/2 in. wide and is filled with sealant to provide water tightness. For pretopped systems, the joints must be prepared with an edging tool in the plant during final finish to provide a rounded edge, and then finished by grinding or sandblasting to remove any potentially sharp or rough edges. Some precasters form an indented edge along the continuous edge of the flange to facilitate the installation of the sealant. After a backer rod is installed, the joint is then primed to enhance the bond between the sealant and the concrete and to provide additional moisture protection at the bond line. The sealant should be installed in a concave configuration, slightly recessed below the deck surface, to protect it from wheel impact and wear. 9.7.4.3 Sealant Types Sealants come as single-component or multi-component sealants. Single-component sealants are ready-mixed and furnished in tubes, cartridges, or sausages. These singlecomponent sealants have a longer cure time, relying on atmospheric moisture, and usually have a limited color selection based on manufacturers' standard color spectrums. Multicomponent sealants are mixed at the project site prior to use and packaged in bulk containers requiring proper site mixing. Multi-component sealants have the advantage of rapid cure time and multiple color selections through the use of manufacturers' color-packs. Improper mixing is an issue with these products and can introduce many variables into the quality of the installed joint. Non-sag sealant is a gun-grade material for building joint application, furnished as either a single- or multi-component compound. Although classed as non-sag, the sealant may exhibit sag characteristics under certain conditions of high temperature or large joint width. Under certain circumstances, the non-sag sealant will require some tooling to achieve the proper profile and surface finish. A self-leveling sealant can also be a single- or multi-component compound. It is used for horizontal joints and formulated to self-level at normal installation temperatures (greater than or equal to 40 °F). A non-sag sealant can be used for deck joints in horizontal applications, but the self-leveling sealant is more viscous and, hence, easier to install because it is poured into the joint opening, seeking its own fluid level. Therefore, it normally requires no tooling. Should the slope of the horizontal surface be too great, such as the camber in a double-tee or normal drainage slope, a non-sag sealant may be required;

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PRECAST AND PRESTRESSED CONCRETE: MATERIALS a self-leveling sealant will have a tendency to flow downhill. The manufacturer’s literature should be consulted to ascertain the maximum slope to prevent flow (usually 5%). Elastomeric sealants are the most common types of sealants used today to seal joints between building components.46 These consist of polyurethane, polysulfide, silicone, acrylic, latex, and butyl-based products. Polyurethane.   Polyurethane sealants are polyurethane synthetic-rubber materials with various fillers, adhesionpromoting additives, and solvents. They are well-suited for porous surfaces such as concrete and stone in highmovement joints. These high-performance sealants wear well and are suited for joints exposed to abrasive action, such as traffic areas. They are frequently used for precast concrete wall panel joints. Urethane sealants typically have a movement capability of +/-25%, which can reach as high as +/-50% movement capability in some products. Silicone.  Silicone-based sealants are most frequently used for non-porous surfaces in high movement joints, yet their use in precast concrete construction has been increasing. They are commonly found in metal and glass cladding joints. Staining of porous substrates and dirt accumulation has been an ongoing problem for some silicone sealants. Silicone sealants generally have a movement capability of +/-50%, and some are approaching +100%/-50%, depending on the type. Silicone sealants are considered to have better resistance to ultraviolet radiation and heat aging, and better moisture stability than other types of sealants. Polysulfide.   Polysulfide sealant is a high-performance, elastomeric sealant that is based on a synthetic polysulfide polymer or rubber (Thiokol was a popular trade name.) Polysulfide sealants were common several years ago, but performance issues and competition from better urethanes and silicones saw their use diminish. Polysulfide sealants are still used for submerged joint applications because of superior resistance to water and chemical degradation. Polysulfide sealants generally have a movement capability of +/- 25%. Other sealant types.  Other types of sealants used in the construction industry include acrylic, latex, and butyl rubber sealants. In general, these types of sealants are not classed as high-performance sealants, as their movement capability is typically +/-12.5% or less. Because of their low movement capability, these sealants are limited at light building and residential construction. Latex sealants are popular with contractors because they can be painted with latex paint, are generally less expensive, and are easier to clean up than highperformance sealants. Joint backing.   The sealant depth in joints is controlled with foam backer-rod fillers made of polyethylene or polyurethane, or polyethylene bond-breaker tape. Closed-cell backer rod does not absorb or transmit water that potentially can leak into the joint. Open-cell backer rod has the advantage of being more easily installed because of its compressibility; however, it holds water if the joint seal leaks. Some sealants may potentially form bubbles while curing because of air or gases (outgassing) released from certain closed-cell back-up materials cut during installation. To help eliminate this problem, consult the manufacturer for sealant backer-rod compatibility.

CHAPTER 9 9.7.4.4 Joint Sealant Considerations Adhesion / cohesion.   Joint sealant failures are classed as adhesive or cohesive failures. Adhesion failures occur when the sealant does not bond well to the substrate. Adhesive failures can be attributed to poor surface preparation of the joint sides, which inhibits bond. Form-oil residue, dirt, grease, and the like on the concrete can contribute to poor surface bonding.47 Cohesive failures occur within the sealant material. This can be attributed to a poor aspect ratio on the sealant joint, improper mixing of the sealant components, and/or lack of proper cure. Improper mixing is marked by joint sealant feeling tacky or gummy to the touch, even after several months of service. Joint-cleaner chemicals can impede curing. If isopropyl alcohol is used to clean the joint sides, the alcohol residue could impact the curing if it did not flash off. Figure 9.7.1 shows both of these failure types in a joint sealant. Plasticizer migration.   A commonly observed sealant problem is dark band staining of substrate materials adjacent to a joint, particularly with silicone sealants. Some silicone and polyurethane sealants contain certain types and amounts of plasticizers, binders, or oily components that increase the staining probability. Staining is evidenced by dirt accumulation or discoloration on the adjacent substrate due to plasticizer migration or incompletely polymerized polymers migrating into the adjacent substrate. An example of this type of staining is shown in Fig. 9.7.2 for joints between granite blocks in a wall; note the dark stain bands adjacent to the vertical joints. Light-colored stone and masonry substrates are particularly vulnerable to migration and staining from certain silicone sealants. This tendency to attract dirt darkens the vertical sealant line and makes it much more noticeable against the lighter precast concrete panel color. Faced precast concrete wall panels are also susceptible to this problem. ASTM C1248 should be specified when using such susceptible sealants.48 Geometry.  Precast concrete wall-panel corner joints are a difficult sealant detail because of the movements that can occur at the corner joint. Precast concrete wall-panel corner joints generally take two configurations: a butt joint or a quirk miter. Two panels meeting at a butt-joint corner want to deform in two different directions, which causes fish mouthing or pillowing at the joints. This condition can be further exacerbated by the panels being restrained by floor supports, which restrains the horizontal movement due to panel thermal bowing. For more in-depth discussion of bowing in precast concrete wall panels, see Section 2.6, “Bowing Considerations,” in PCI’s State-of-the-Art Report on Precast/Prestressed Sandwich Wall Panels.49 Different lateral support conditions and different sun exposures on two panels meeting at a corner are the main contributors to the panel bowing and the daily, resultant lateral (horizontal) deflections. These conditions create an actively moving joint requiring a very flexible joint sealant. For more information on joint configurations, refer to PCI’s Architectural Precast Concrete.

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Fig. 9.7.2 Examples of plasticizer migration adjacent to a sealant joint, as marked by a dark staining band that tends to attract dirt. Fig. 9.7.1 Examples of sealant adhesion failure (top) and sealant cohesion failure (bottom) in a stadium riser joint.

9.7.5

Expansion Joints

For expansion joints to be effective, they are required to be watertight, provide a full range of movement, complement the durability of the deck, and be low maintenance. For user comfort on a parking deck, joints also need to be smooth, providing good ride quality. Unfortunately, the perfect joint has yet to be developed. Joint selection is usually dependent on anticipated movement, joint depth restrictions, economics, and desired service life. Wide, premolded, urethane, expansion-joint seals have been used in parking decks with moderate success. The joint consists of a wide, premolded piece of urethane, about 1/2 in. thick, placed in formed blockout. The urethane strip is affixed in the joint with field-applied (poly)urethane nosings along each longitudinal edge. To provide support for traffic loads across the open joint, an aluminum plate is placed below the premolded urethane strip; stainless steel plates have also been employed for greater stiffness characteristics (recall that Esteel 9–32

= 29 × 106, Ealuminum = 10 × 106 psi). The wide, premolded, urethane, expansion-joint seal is subject to UV degradation where it is exposed. Field-applied nosing sealants have been observed to fail consistent with other sealant-type failures, specifically, adhesion and cohesion failures. Shoving and tearing of a wide seal has been observed when the seal heats up and becomes more pliable. Tearing of the premolded, urethane joint seal from below can also occur when the traffic support plate deforms and the edges uplift into the seal underside. Compression seals use a square or rectangular, preformed, extruded, elastic joint seal manufactured from neoprene and installed with a lubricating adhesive (Fig. 9.7.3). The seal is usually installed in a preformed blockout in the concrete, which has a narrow shelf or lip to support the seal bottom. In some instances, an armoring angle is embedded into the sides of the joint with welded, square bar lips set below the surface to support the seal, as shown in Fig. 9.7.4. The angle corner provides protection to the joint edge from traffic and snowplow blades, which prevents concrete raveling at the joint edge. Other types of expansion joint systems are available on

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PRECAST AND PRESTRESSED CONCRETE: MATERIALS the market, and usually employ an accordion type gland with knuckled ends or flat, perforated wings. In the case of the knuckled ends, these serve as the male ends and are inserted into a special steel nosing extrusion. This joint is commonly known as the strip-seal. Expansion joint seals using flat, perforated wings on the gland are usually laid into blockouts that are cast in the concrete, adjacent to the joint opening. The gland is affixed using a field-poured, epoxy-modified concrete in the blockout, or the gland is mechanically attached using polymer anchoring blocks fixed with cast-in or post-installed anchors (cushion seals). These joint systems usually have a shallow profile and are suitable for use in parking garages. They come in a wide-range of sizes, depending on the anticipated movement. Figure 9.7.5 shows this type of seal system. The owner should be made aware of the maintenance required with these joint types. The accordion shape to the gland holds dirt, debris, and moisture. Occasional cleaning of the gland will help prolong the service life and preclude potential tearing. Snowplow blades and traffic can wear down the edges of the nosing material and cause spalling that progresses inward over time. The constant pounding of traffic can loosen the mechanical anchors through fatigue, and they should be inspected and tightened periodically.

9.8

In-Service Considerations

9.8.1

Cracking

Minor cracking may occur in precast concrete without being detrimental, and it is impractical to impose specifications that prohibit all cracking.50,51 However, in addition to being unsightly, cracks are potential locations of moisture intrusion and possible concrete deterioration over time. Prestressing and proper handling procedures are two of the best methods of keeping cracks to a minimum. To evaluate the acceptability of a crack, the cause and service conditions of the precast concrete unit should be determined. (Note: In other sections, the term crack-free design is used. This refers to a design in which concrete tension stress is kept within limits, and should not be construed as being a guarantee that there will be no cracking.) Crazing (that is, fine, random, hairline cracks) may occur in the cement film on the surface of concrete. The primary cause is the shrinkage of the surface with respect to the mass of the unit. Crazing has no structural significance and does not significantly affect durability, but it may be visually accentuated if dirt settles in these minute cracks. Crazing should not be cause for rejection. Tension cracks are sometimes caused by temporary loads during production, transportation, or erection of these products (see Chapter 8). These cracks may extend through to the reinforcement. If the crack width is narrow, the structural adequacy of the component will remain unimpaired as long as corrosion of the embedded reinforcement crossing the crack is prevented. The acceptability of cracks wider than recommended maximums should be governed by the function of the unit. Most cracks can be effectively repaired and sealed. Long-term volume changes can also cause cracking after

CHAPTER 9

Fig. 9.7.3 Typical expansion-joint compression seal profiles.

  9

Fig. 9.7.4 Typical expansion-joint armoring angles to protect spalling and edge raveling. This compression seal is supported on bearing bars welded to vertical legs.

Elastomeric seal

Epoxy-type concrete

Fig. 9.7.5 Example of a proprietary-system expansion joint, where a elastomeric gland profile is bedded in an epoxy-type nosing concrete.

the component is in place in the structure, if the connections provide enough restraint to the component. Internal causes, such as corrosion of reinforcement or cement-aggregate reactivity, can also lead to long-term cracking and should be considered when materials are selected. ACI Committee 201 and 224 reports provide general information on cracking in concrete.52,53,54 PCI provides information on cracking in certain precast/prestressed concrete components.50,51

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Repair

Precast concrete components may occasionally require repairing on the jobsite. A number of different time-tested repair methods are used, as discussed in the following sections. With proper design and installation, repairs can be made to satisfy the original requirements of the component. To ensure that the repair is permanent, analysis to determine the cause of the defect or distress should be made. If the defect has structural significance, it may be possible to transfer loads to other components or connections. Considerations relating to the type of repair include evaluation of the following: • Environmental conditions during installation and service • Fire-protection requirements • Aesthetic requirements • Access to the repair and impact on adjacent construction • Requirements and limitations for supplementary supports • Load testing, if required, to evaluate the repair • Requirements for design approval and inspection 9.8.2.1 Patching Patches are the replacement of damaged or deteriorated concrete with a cementitious material. They may be either structural or cosmetic. Structural patches may be required to satisfy some load-transfer requirements, while cosmetic patches are related to appearance only. Large spalls require repair by structural patching. Concrete honeycombing may require no patching or only cosmetic patching. Procedures for the preparation of the materials and application of the patch are important. Surface preparation is about the same for all types of material chosen for the patch. All loose concrete must be removed from the patch area. If possible, the edges of the repair should be sawcut or chiseled with a slight undercut to allow keying action for the repair material; feathered edges should be avoided. The surface must be clean, sound, and rough to accept the patch, with any laitance removed from any exposed reinforcement. Cosmetic patching should match the surrounding concrete in form, color, and texture. The materials used in the repair should weather in a manner similar to the base concrete. Substrate preparation and bonding of the patch to the substrate are essentially the same as for structural patching. The patching mixture consists of the basic ingredients of cement, fine aggregate, and water. Coarse aggregate, color additives, and various admixtures may also be required. The proportions are usually best determined by an experienced finisher at the plant or the site. It is recommended that records be kept on patching mixtures and techniques to establish proper patching procedures on future projects. Occasionally, mechanical anchorage may be advisable in addition to a bonding agent to anchor the patch. Ideally, the concrete substrate should be saturated surface dry (unless using an epoxy bonding agent or patching mortar, in which 9–34

case the presence of moisture may not be allowed). The bonding agent, if used, should be applied thoroughly over the entire area to be patched, following the manufacturer’s instructions. Information on the commonly used patching materials is presented in the following paragraphs. Cementitious mortars.   They are composed of cement, sand (usually about two to three parts sand per part cement), and water. Various admixtures may be incorporated. Water quantity can vary from minimal, creating a dry-pack mortar, to a moderate amount for a more workable mixture. The advantage of dry-pack mortars is that they develop high strengths with very little shrinkage. Wetter mortars have better bond characteristics and are easier to place. Proper curing is essential. Pre-packaged cementitious mortars.  Pre-packaged grouts or repair mortars are a mixture of cement, aggregate (usually sand), and often one or more admixtures. They are mixed with water according to the manufacturer’s instructions to create the patching mortar. The more commonly used admixtures reduce shrinkage, increase strength and/ or strength gain, and enhance durability. Patching materials containing calcium chloride should be avoided. The manufacturer’s recommendations should always be followed. Some patch mortars can be extended with pea gravel (3/8 in. size) for deep patches. Additionally, some proprietary patch materials may have restrictions on the aggregate type that can be used, as these aggregate types (chemistry) are detrimental to the concrete set or long-term durability of the patch. Concrete.  As a patching material, this is especially desirable in larger repairs. Concrete should be properly proportioned mixtures of cement, aggregate, and water to produce a workable mixture with minimum water–cementitious materials ratio to minimize shrinkage. Ideally, the concrete repair material should be the same as the concrete in the component. Proper curing is essential. Epoxy mortars.  This is a mixture of epoxy resin and aggregate (usually sand). The mortar is prepared by thoroughly mixing as much aggregate as possible into the mixed epoxy, consistent with workability needs. The sand must be oven dry. Maximizing sand content minimizes heat buildup from the chemical reaction and the associated tendency toward shrinkage and cracking. Epoxy mortars are strong and cure rapidly. Dimensional compatibility due to differing modulus of elasticity with the base concrete should be considered. Bonding agents.   These are used to increase the bond between a hardened concrete and fresh mortar. Bonding agents may be an unsanded cement paste, a commercially available latex-based material, or an epoxy. Epoxy bonding agents must have a long pot life to prevent hardening prior to curing of the patching mortar. It is important to follow the manufacturer’s recommendations for the use of commercially prepared bonding agents to ensure their effectiveness. Bonding agents are not required for all patches. They are most advisable when using a stiff mortar or when the patch surface is large and the thickness is relatively thin. Scrubbing-in a mortar paste from the parent patch material into a saturated surface dry surface can be as or more effective in achieving good bond.

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PRECAST AND PRESTRESSED CONCRETE: MATERIALS 9.8.2.2 Crack Repair Cracks do not always require repair, or they may only need cosmetic treatment. Several PCI manuals50,51 discuss cracking in precast concrete components, and they should be reviewed before a repair program is initiated. If repair of a crack is necessary, low-viscosity epoxy is usually the best material. There are many available epoxy materials that can fill and repair cracks. As with patching, surface preparation is important. The crack should be clean and clear of loose material and free of oil, grease, and dust. If moisture is present, a moisture-resistant epoxy should be selected. It is important to follow the manufacturer’s directions in mixing and applying epoxies to concrete. Epoxy may be introduced by either gravity flow or pressure injection. Gravity flow involves forming a small ridge of sand or other material along each side of the crack, or a V-groove may be chipped out along the top of the crack. This serves to direct the epoxy into the crack. If the crack extends to the underside of the component, it is recommended to patch the bottom of the crack with plaster of paris or other suitable material. Low-viscosity epoxy is poured into the crack until no more is accepted. Cracks should be wider than 0.005 in. and less than about 4 in. deep to allow epoxy entry. Injection involves forcing epoxy (normally low viscosity) into the crack under pressure. Injection applications generally start with setting injection ports into the crack, spaced 6 in. to 10 in., but no further apart than the crack depth. The surface of the crack is sealed between the ports, usually with a high-viscosity epoxy. Injection progresses from one end of the crack to the other, pumping material into each port until epoxy begins exiting the next port. After sealing that port, the pumping operation is shifted to the next one. After the epoxy is cured, the injection ports are removed and the sealing material is ground flush to the surface.55 9.8.2.3 Connection Repair Connections may require repair or modification for various reasons, such as placement errors, tolerance issues, damage, or omission of an embedment. Prior to choosing a repair, the magnitude of the design load should be verified. Eccentricities, load paths, and effect of edge distances on connection strength should be considered. Connection repair methods include, but are not limited to, the following: • Up-sizing welds on connection materials to increase connection strength when embedded plates are misaligned • Increasing the size of connection material • Adding reinforcement in a topping slab to replace a deficient connection • Adding thru bolts or post-installed anchors with appropriate connection materials • Installing a new connection in the vicinity of the repair • Adding stiffeners to a connection When choosing a repair method, the fire-rating requirements should be considered. When selecting proprietary expansion anchors and epoxy anchors, it should be noted that some have load limitations that require special inspection.

CHAPTER 9 Note that epoxy anchors should be used with caution when adjacent to welding, which could heat the epoxy. Epoxy anchors should not be used in connections where fire rating is a consideration. If using epoxy anchors in conditions where sustained loads exist, the designer should consult with the epoxy manufacturer prior to using. 9.8.3

Component Strengthening

Capacity of existing precast/prestressed concrete components can be increased by different methods. The following paragraphs discuss a few of the common methods. Drilling and installing reinforcement.  Reinforcing bars can be installed by drilling holes and anchoring the bars in the holes by use of epoxy and grout. This is most commonly used to install missing dowels or shear ties. Incorporating reinforcement in hollow-core voids.  Hollow-core can be strengthened by grouting or concreting reinforcing bars into the voids. If shear strengthening alone is required, then filling the voids with grout or concrete may be sufficient to increase the effective width. The procedure consists of cutting into the desired void(s), cleaning out and verifying that the surfaces are sound enough to bond new concrete, placing reinforcement for the length required, and filling the void around the reinforcement with concrete of a similar strength to that of the slab. External post-tensioning.   By adding external posttensioning to existing components, the flexural and shear strengths can be increased. This usually consists of installing anchorages on the sides or bottom of each end of the component, installing deflection devices (if required) at points along the component, installing the post-tensioning strand attached to these points, and stressing. Corrosion protection and fireresistance protection must be considered. Refer to Section 18.22 of ACI 318-05 for applicable regulations for external post-tensioning. Fiber-reinforced polymers (FRP).  FRP systems offer a simple solution to restore or supplement the strength of concrete components. These polymers are a composite system comprising fibers embedded in an epoxy-resin matrix. Fibers of carbon, glass, or aramid are formed into a unidirectional or bidirectional fabric. The fabric is then saturated in an epoxy resin during manufacture or during application. The resin transfers load from the structural component to and between the fibers. FRP can be bonded to a concrete component in strips or sheets to increase flexural and/or shear strength, and possibly confinement. By wrapping a column, the axial strength, shear strength, and ductility can be upgraded. It is recommended that design proceed in close consultation with the manufacturer’s technical staff, which may involve the manufacture/repair installer providing professional engineer–sealed drawings for the proprietary product design. Inspection should be provided for all aspects of application.56 Additional fire protection may be required. Structural plate bonding and steel jacketing.  Structural plate bonding and jacketing are methods for attaching steel plates or other steel components to concrete components, to increase strength. Steel plates are attached to the concrete by adhesives and mechanical fasteners. The process requires

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American Association of State Highway and Transportation Officials (AASHTO) MP13M/MP 13-04

Stainless Clad Deformed and Plain Steel Bar for Concrete Reinforcement

T 303

Standard Method of Test for Accelerated Detection of Potentially Deleterious Expansion of Mortar Bars Due to Alkali-Silica Reaction

201.2

Guide to Durable Concrete

207.1

Mass Concrete

209R

Predictions of Creep, Shrinkage, and Temperature Effects in Concrete Structures

211.1

Standard Practice for Selecting Proportions for Normal, Heavyweight, and Mass Concrete

211.2

Standard Practice for Selecting Proportions for Structural Lightweight Concrete

212.3R

Chemical Admixtures for Concrete

213R

Guide for Structural Lightweight-Aggregate Concrete

221R

Guide for the Use of Normalweight and Heavyweight Aggregates in Concrete

223

Standard Practice for the Use of Shrinkage-Compensating Concrete

224

Control of Cracking in Concrete Structures

226.1R

Ground Granulated Blast-Furnace Slag as a Cementitious Constituent in Concrete

226.3R

Use of Fly Ash in Concrete

308

Standard Practice for Curing Concrete

315

Details and Detailing of Concrete Reinforcement

318

Building Code Requirements for Structural Concrete

343R

Analysis and Design of Reinforced Concrete Bridge Structures

363R

State-of-the-Art Report on High-Strength Concrete

423.3R

Recommendations for Concrete Components Prestressed with Unbonded Tendons

439.3R

Mechanical Connections of Reinforcing Bars

440

State-of-the-Art Report on Fiber Reinforced Plastic Reinforcement for Concrete Structures

506

Guide to Shotcrete

325

Steel Construction Manual

American Concrete Institute (ACI)

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American Institute of Steel Construction (AISC) ASTM International – Specifications Concrete A82

Specification for Steel Wire, Plain, for Concrete Reinforcement

A184

Specification for Fabricated Deformed Steel Bar Mats for Concrete Reinforcement

A185

Specification for Steel Welded Wire Fabric, Plain, for Concrete Reinforcement

A416

Specification for Steel Strand, Uncoated Seven-Wire for Prestressed Concrete

A421

Specification for Uncoated Stress-Relieved Wire for Prestressed Concrete

A496

Specification for Steel Wire, Deformed, for Concrete Reinforcement

A497

Specification for Steel Welded Wire Fabric, Deformed, for Concrete Reinforcement

A617

Specification for Axle-Steel Deformed and Plain Bars for Concrete Reinforcement

A706

Specification for Low-Alloy Deformed Bars for Concrete Reinforcement

A722

Specification for Uncoated High Strength Steel Bar for Prestressing Concrete

A767

Specification for Zinc-Coated (Galvanized) Steel Bars for Concrete Reinforcement

A775

Specification for Epoxy-Coated Reinforcing Steel Bars

A882

Specification for Epoxy-Coated Seven- Wire Prestressing Steel Strand

A884

Specification for Epoxy-Coated Steel Wire and Welded Wire Fabric for Reinforcement

A934

Standard Specification for Epoxy-Coated Prefabricated Steel Reinforcing Bars

A996

Specification for Rail-Steel and Axle-Steel Deformed Bars for Concrete Reinforcement

A1035

Standard Specification for Deformed and Plain, Low-Carbon, Chromium, Steel Bars for Concrete Reinforcement

C33

Specification for Concrete Aggregates

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C94

Specification for Ready-Mixed Concrete

C150

Specification for Portland Cement

C260

Specification for Air-Entraining Admixtures for Concrete

C330

Specification for Lightweight Aggregates for Structural Concrete

C470

Specification for Molds for Forming Concrete Test Cylinders Vertically

C494

Specification for Chemical Admixtures for Concrete

C595

Specification for Blended Hydraulic Cements

C618

Specification for Coal Fly Ash and Raw or Calcined Natural Pozzolan for Use as a Mineral Admixture in Portland Cement Concrete

C845

Specification for Expansive Hydraulic Cement Concrete and Mortar

C989

Specification for Ground Granulated Blast-Furnace Slag for Use in Concrete and Mortars

C1107

Specification for Package Dry, Hydraulic-Cement Grout (Nonshrink)

C1240

Specification for Silica Fume for Use in Hydraulic Cement, Concrete, and Mortar

D98

Specification for Calcium Chloride

D448

Specification for Standard Sizes of Coarse Aggregate for Highway Construction

D3963

Specification for Fabrication and Jobsite Handling of Epoxy-Coated Reinforcing Steel Bars

D4894

Standard Specifications for Polytetrafluoroethylene (PTFE) Granular Molding and Ram Extrusion Materials

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ASTM International – Specifications Other Relevant Materials A6

Standard Specification for General Requirements for Rolled Structural Steel Bars, Plates, Shapes, and Sheet Piling

A36

Standard Specification for Carbon Structural Steel

A108

Standard Specification for Steel Bar, Carbon, and Alloy, Cold-Finished

A123

Standard Specification for Zinc (Hot-Dip Galvanized) Coatings on Iron and Steel Products

A143

Standard Practice for Safeguarding Against Embrittlement of Hot-Dip Galvanized Structural Steel Products and Procedure for Detecting Embrittlement

A153

Standard Specification for Zinc Coating (Hot-Dip) on Iron and Steel Hardware

A193

Standard Specification for Alloy-Steel and Stainless Steel Bolting Material Temperature or High Pressure Service and Other Special Purpose Applications

A307

Standard Specification for Carbon Steel Bolts and Studs, 60,000 psi Tensile Strength

A325

Standard Specification for Structural Bolts, Steel, Heat Treated, 120/105 ksi Minimum Tensile Strength

A384

Standard Practice for Safeguarding Against Warpage and Distortion During Hot-Dip Galvanizing of Steel Assemblies

A385

Standard Practice for Providing High-Quality Zinc Coatings (Hot-Dip)

A489

Standard Specification for Carbon Steel Lifting Eyes

A490

Standard Specification for Structural Bolts, Alloy Steel, Heat Treated, 150 ksi Minimum Tensile Strength

A500

Standard Specification for Cold-Formed Welded and Seamless Carbon Steel Structural Tubing in Rounds and Shapes

A563

Standard Specification for Carbons and Alloy Steel Nuts

A666

Standard Specification for Annealed or Cold-Worked Austenitic Stainless Steel Sheet, Strip, Plate, and Flat Bar

A772

Standard Specification for Uncoated High-Strength Steel Bars for Prestressing Concrete

A780

Standard Practice for Repair of Damaged and Uncoated Areas of Hot-Dip Galvanized Coatings

A910

Specification for Uncoated, Weldless, 2- and 3-Wire Steel Strand for Prestressed Concrete

A979

Standard Specification for Pigments for Integrally Colored Concrete

A992

Standard Specification for Structural Steel Shapes

B695

Standard Specification for Coatings of Zinc Mechanically Deposited on Iron and Steel

C330

Standard Specification for Lightweight Aggregates for Structural Concrete

C1017

Standard Specification for Chemical Admixtures for Use in Producing Flowing Concrete

C1193

Standard Guide for Use of Joint Sealants

C1218

Standard Test Method for Water-Soluble Chloride in Mortar and Concrete

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Standard Specification for Anchor Bolts, Steel, 36, 55, and 105 ksi Yield Strength.

A370

Standard Test Methods and Definitions for Mechanical Testing of Steel Products

C42

Test Method for Obtaining and Existing Drilled Cores and Sawed Beams of Concrete

C78

Test Method for Flexural Strength of Concrete (Using Simple Beam with Third-Point Loading)

C88

Standard Test Method for Soundness of Aggregates by Use of Sodium Sulfate or Magnesium Sulfate

C109

Test Method for Compressive Strength of Hydraulic Cement Mortars (Using 2 in. or [50 mm] Cube Specimens)

C138

Test Method for Unit Weight, Field, and Air Content (Gravimetric) of Concrete

C157

Test Method for Length Change of Hardened Hydraulic-Cement Mortar and Concrete

C173

Test Method for Air Content of Freshly Mixed Concrete by the Volumetric Method

C185

Test Method for Air Content of Hydraulic Cement Mortar

C186

Test Method for Heat of Hydration of Hydraulic Cement

C191

Test Method for Time of Setting of Hydraulic Cement by Vicat Needle

C227

Test Method for Potential Alkali Reactivity of Cement-Aggregate Combinations (Mortar-Bar Method)

C231

Test Method for Air Content of Freshly Mixed Concrete by the Pressure Method

C289

Test Method for Potential Alkali-Silica Reactivity of Aggregates (Chemical Method)

C293

Test Method for Flexural Strength of Concrete (Using Simple Beam with Center-Point Loading)

C342

Test Method for Potential Volume Change of Cement-Aggregate Combinations

C418

Test Method for Abrasion Resistance of Concrete by Sandblasting

C441

Test Method for Effectiveness of Mineral Admixtures of Ground Blast-Furnace Slag in Preventing Excessive Expansion of Concrete Due to the Alkali-Silica Reaction

C452

Test Method for Potential Expansion of Portland Cement Mortars Exposed to Sulfate

C469

Test Method for Static Modulus and Poisson’s Ratio of Concrete in Compression

C496

Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens

C512

Test Method for Creep of Concrete in Compression

C586

Test Method for Potential Alkali Reactivity of Carbonate Rocks for Concrete Aggregates (Rock Cylinder Method)

C597

Test Method for Pulse Velocity through Concrete

C618

Standard Specification for Coal Fly Ash and Raw or Calcined Natural Pozzolan for Use in Concrete

C666

Test Method for Resistance of Concrete to Rapid Freezing and Thawing

C671

Test Method for Critical Dilation of Concrete Specimens Subjected to Freezing

C672

Test Method for Scaling Resistance of Concrete Surfaces Exposed to Deicing Chemicals

C682

Practice for Evaluation of Frost Resistance of Coarse Aggregates in Air-Entrained Concrete by Critical Dilation Procedures

C779

Test Method for Abrasion Resistance of Horizontal Concrete Surfaces

C803

Test Method for Penetration Resistance of Hardened Concrete

C805

Test Method for Rebound Number of Hardened Concrete

C827

Test Method for Change in Height at Early Ages of Cylindrical Specimens from Cementitious Mixtures

C900

Test Method of Pullout Strength of Hardened Concrete

C944

Test Method for Abrasion Resistance of Concrete or Mortar Surfaces by the Rotating-Cutter Method

C1012

Test Method for Length Change of Hydraulic-Cement Mortars Exposed to a Sulfate Solution

C1090

Test Method for Measuring Changes in Height of Cylindrical Specimens from Hydraulic-Cement Grout

C1202

Test Method for Electrical Indication of Concrete’s Ability to Resist Chloride Ion Penetration

C1248

Standard Test Method for Staining of Porous Substrate by Joint Sealants

C1260

Standard Test Method for Potential Alkali Reactivity of Aggregates (Mortar-Bar Method)

C1293

Standard Test Method for Determination of Length Change of Concrete Due to Alkali-Silica Reaction

D3398

Standard Test Method for Index of Aggregate Particle Shape and Texture

D4791

Standard Test Method for Flat Particles, Elongated Particles, or Flat and Elongated Particles in Coarse Aggregate

E376

Practice for Measuring Coating Thickness by Magnetic-Field or Eddy-Current (Electromagnetic) Test Methods

F1554

Standard Specification for Anchor Bolts, Steel

ASTM International - Test Methods

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American Welding Society (AWS) D1.1

Structural Welding Code - Steel

D1.4

Structural Welding Code - Reinforcing Steel

D1.6

Structural Welding Code - Stainless Steel

MSP-2

Manual of Standard Practice

Concrete Reinforcing Steel Institute (CRSI) Placing Reinforcing Bars Reinforcement Anchorages and Splices

Canadian Standards Association (CSA) G164

Hot Dip Galvanizing of Irregularly Shaped Articles

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International Concrete Repair Institute (ICRI) 03730

Guideline for Surface Preparation for the Repair of Deteriorated Concrete Resulting from Reinforcing Steel Corrosion

03732

Guideline for Selecting and Specifying Concrete Surface Preparation for Sealers, Coatings, and Polymer Overlays

Precast/Prestressed Concrete Institute (PCI) MNL-116

Manual for Quality Control for Plants and Production of Structural Precast Concrete Products

MNL-117

Manual for Quality Control for Plants and Production of Architectural Precast Concrete Products

MNL-122

Architectural Precast Concrete

TM-103

Quality Control Personnel Certification – Level III Training Manual

Research Council on Structural Connections (RCSC) Specification for Structural Joints Using ASTM A325 or A490 Bolts

Society for Protective Coatings (SSPC) Good Painting Practice, SSPC Painting Manual, Volume 1 Systems and Specifications, SSPC Painting Manual, Volume 2

removing damaged concrete from the surface, repairing the substrate, roughening the concrete surface, installing drilled mechanical anchors (used for positioning the steel and for load transfer), and epoxying the steel to the concrete surface. Cosmetic treatment and corrosion-resistant and fire-resistant coatings may be applied as necessary. Design is as it is for reinforced concrete. The interface should be analyzed for horizontal shear using the shear capacity of the epoxy and of the mechanical anchors. ACI SP-16557 provides additional information on the subject. Shotcrete. Shotcrete is mortar or concrete conveyed through a hose and pneumatically projected at high velocity onto a surface. This process can be used to add concrete to existing components for various purposes, including to increase the size of a concrete component, to add reinforcement cover for increasing fire or corrosion resistance, or to encase added reinforcement. Shotcrete can be an advantageous solution for either tight-access or high-volume repairs. Before shotcreting, all loose and damaged concrete is removed. A bonding agent is usually not required if the surface is roughened by sandblasting or needle scaling. Microcracking of the substrate, which is detrimental to bond, can be caused by removing loose concrete with bush hammers or jackhammers in an overly aggressive manner. The substrate should be at saturated surface-dry condition just prior to shotcrete application.

Shotcrete can be applied by either the dry or wet method. In the dry method, water is added to the mixed dry ingredients at the nozzle. In the wet method, water is added to the mixer prior to entering the hose. Advantages of the dry method include thinner placement layers, suitable for intermittent application and better for remote locations (longer pumping distances). Advantages of the wet method include ability to use air entrainment and other admixtures, a higher placement rate, less rebound, and fewer cleanups. Shotcrete should be installed by certified nozzlemen and should be monitored by a qualified inspector. Prior to shotcreting, test panels mimicking the actual application should be prepared at the site by the same personnel, using the same mixture and equipment to be used in the actual installation. See ACI 50658 committee report on shotcrete. 9.8.4

Maintenance

Concrete surfaces normally require little maintenance except for those that are subject to harsh environments, such as parking structures in northern climates. These should receive regular inspections and washings to help in identifying and preventing long-term maintenance problems. Surfaces that have had sealers applied to them should have a program for reapplying the sealer at specified intervals. It is important that drains be kept open to keep water from ponding and potentially freezing on the concrete. Routine inspec-

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CHAPTER 9 tion and maintenance can do much to extend the life of precast concrete structures. PCI’s Precast, Prestressed Concrete Parking Structures: Recommended Practice for Design and Construction29 provides guidance for parking-structure maintenance, and PCI’s Architectural Precast Concrete provides maintenance information for architectural precast concrete.

9.9

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 elevant Standards and R Publications

The following list of codes, specifications, standards, and manuals are provided for the convenience of the precast concrete design engineer, as not all documents are referenced in the text of this chapter. The complete designation of each document typically includes a year of adoption. Because these documents are updated on a frequent basis, the year has been omitted for clarity. The engineer is referred to the respective organizations for the latest revisions and year of adoption.

9.10

References

1. American Concrete Institute (ACI). 2008. Manual of Concrete Practice, Farmington Hills, MI: ACI. 2. Shilstone, J. M. Sr. 1990. Concrete Mixture Optimization. Concrete International, Vol. 12, No. 6 (June): pp. 33–39. 3. ACI Committee 318. 2005. Building Code Requirements for Structural Concrete and Commentary (ACI 318-05 / 318R-05, Farmington Hills, MI: ACI. 4. Suprenant, B. A. and W. R. Malisch. 2000. Get the Air Out?. The Concrete Producer Online/Concrete Journal Magazine, October 19. 5. Precast/Prestressed Concrete Institute (PCI). 2003. Interim Guidelines for the Use of Self-Consolidating Concrete in Precast/Prestressed Concrete Institute Component Plants, TR-6-03. Chicago, IL: PCI. 6. Stark, D., B. Morgan, P. Okamoto, and S. Diamond. 1993. Eliminating or Minimizing Alkali-Silica Reactivity, SHRP Report C-343, Washington, DC: Strategic Highway Research Program, National Research Council, 266 pp. 7. ACI Committee 363. 1997. State-of-the-Art Report on High Strength Concrete (ACI 363R-92, Re-approved 1997). Farmington Hills, MI: ACI. 8. Ahmad, S. H., and S. P. Shah. 1985. Structural Properties of High Strength Concrete and Its Implications for Precast Prestressed Concrete. PCI Journal, V. 30, No. 6 (Nov-Dec). 9.  Naito, C. J., Parent, G., and Brunn, G. 2006. Performance of Bulb-Tee Girders Made with Self-Consolidating Concrete. PCI Journal, V. 51, No. 6, (Nov-Dec) pp 77-85.

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10. Pfeifer, D. W., S. Marusin, and J. R. Landgren. 1982. Energy-Efficient Accelerated Curing of Concrete, Technical Report TR 1-82. Chicago, IL: PCI. 11. Neville, A. M. 1996. Properties of Concrete. 4th ed. New York, NY: John Wiley & Sons, Inc. 12. Bureau of Reclamation. 1981. Concrete Manual — A Manual for the Control of Concrete Construction. 8th ed. Revised. Denver, CO: U.S. Department of Interior, Bureau of Reclamation. 13. Hansen, T. C. and A. H. Mattock. 1966. Influence of Size and Shape of Component on the Shrinkage and Creep of Concrete, Development Department Bulletin D103. Skokie, IL: Portland Cement Association (PCA). 14. PCI. 1999. Manual for Quality Control for Plants and Production of Structural Precast Concrete Products, MNL-116-99. 4th ed. Chicago, IL: PCI. 15. PCI. 1996. Manual for Quality Control for Plants and Production of Architectural Precast Concrete Products, MNL- 117-96. 3rd ed. Chicago, IL: PCI. 16. PCI. 1996. Quality Control Personnel Certification— Level III Training Manual, TM-103. Chicago, IL: PCI. 17. PCI. 2007. Architectural Precast Concrete, MNL-12207. 3rd ed. Chicago, IL: PCI. 18. PCA. 1990. Cementitious Grouts and Grouting, EB 111T. Skokie, IL: PCA. 19. U.S. Army Corps of Engineers. 1984. Engineering and Design - Grouting Technology, EM 1110-2-3506. Vicksburg, MS: U.S. Army Corps of Engineers. 20. ACI Committee 503. 1998. Use of Epoxy Compounds with Concrete (ACI 503R-93, Reapproved 1998), ACI Manual of Concrete Practice, Part 5. Farmington Hills, MI: ACI. 21. American Association of State Highway and Transportation Officials (AASHTO). 2007. AASHTO LRFD Bridge Design Specifications. 4th ed. Washington, DC: AASHTO. 22. American Institute of Steel Construction (AISC). 2005. Steel Construction Manual. 13th ed. Chicago, IL: AISC. 23. Iverson, J. K. and D. W. Pfeifer. 1985. Criteria for Design of Bearing Pads, Technical Report No. 4. Chicago, IL: PCI. 24. Corrosion source, 2007: http://corrosion-doctors.org/ Definitions/galvanic-series.htm. 25. Society for Protective Coatings (SSPC). 2005. SSPC Painting Manual, Volume 2. Pittsburgh, PA: SSPC. 26. American Galvanizers Association (AGA). 2006. Zinc Coatings. Centennial, CO: AGA. 27. AGA. 2002. Welding and Hot-Dip Galvanizing. Centennial, CO: AGA. 28. AGA. 2007. Designing with Hot-Dip Galvanized Steel Fabricator Version. Centennial, CO: AGA.

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PRECAST AND PRESTRESSED CONCRETE: MATERIALS 29. PCI. 1998. Precast, Prestressed Concrete Parking Structures: Recommended Practice for Design and Construction, MNL-129-98. Chicago, IL: PCI.

CHAPTER 9 ACI Manual of Concrete Practice, Part 5. Farmington Hills, MI: ACI.

30. Post-Tensioning Institute (PTI). 2006. Post-Tensioning Manual. 6th ed. Phoenix, AZ: PTI.

45. American Society for Testing and Materials (ASTM). 2000. Standard Guide for Use of Joint Sealants, ASTM C1193-90. West Conshohocken, PA: ASTM.

31. Peterman, R. J. 2007. The Effects of As-Cast Depth and Concrete Fluidity of Strand Bond. PCI Journal, V. 52, No. 3 (May-June).

46. Scheffler, M. J., D. Slaton, and J. D. Connolly. 1993. Building Sealant. Building Renovation, SeptemberOctober.

32. American Welding Society (AWS). 2005. Structural Welding Code - Reinforcing Steel, AWS D1.4/D1.4M. Miami, FL: AWS.

47. Slaton, D. and M. J. Scheffler. 2003. New Technique for Avoiding Sealant Failures. The Construction Specifier, V. 56, No. 8 (August): p. 114.

33. Concrete Reinforcing Steel Institute (CRSI). 2003. Manual of Standard Practice (MSP-2-01). 27th ed. Schaumburg, IL: CRSI.

48. Slaton, D. and M. J. Scheffler. 2004. Plasticizer Migration & Sealant Staining. The Construction Specifier, V. 57, No. 2 (February): p. 82.

34. Wire Reinforcement Institute (WRI). 2006. Manual of Standard Practice - Structural Welded Wire Reinforcement, WWR-500. 7th ed. Hartford, CT: WRI.

49. PCI Committee on Sandwich Wall Panels. 1997. Stateof-the-Art of Precast/Prestressed Sandwich Wall Panels. PCI Journal, V. 42, No. 2 (March-April): pp. 92–134.

35. LeClaire, P. J., and A. F. Shaikh. 1996. Effect of Elevated Temperature on the Bond Strength of EpoxyCoated Prestressing Strand. PCI Journal, V. 41, No. 4 (July-August).

50. PCI Committee on Quality Control Performance Criteria. 1983. Fabrication and Shipment Cracks in Prestressed Hollow-Core Slabs and Double Tees. PCI Journal, V. 28, No. 1 (January-February).

36. Pfeifer, D. W. and M. J. Scali. 1981. Concrete Sealers for Protection of Bridge Structures, NCHRP Report 244. Washington, DC: Transportation Research Board.

51. PCI Committee on Quality Control Performance Criteria. 1985. Fabrication and Shipment Cracks in Precast or Prestressed Beams and Columns. PCI Journal, V. 30, No. 3 (May-June).

37. ACI Committee 515. 1985. A Guide to the Use of Waterproofing, Dampproofing, Protective, and Decorative Barrier Systems for Concrete (ACI 515.1R-85), ACI Manual of Concrete Practice, Part 5. Farmington Hills, MI: ACI. 38. Pfeifer, D. W., and W. F. Perenchio. 1982. Coatings, Penetrants and Specialty Concrete Overlays for Concrete Surfaces. Preprint No. 12. Paper presented at Solving Rebar Corrosion Problems in Concrete, National Association of Corrosion Engineers seminar, September, Chicago, IL. 39. Litvin, A. 1968. Clear Coatings for Exposed Architectural Concrete, Development Department Bulletin D137. Skokie, IL: PCA. 40. PCI Parking Structures Committee. 2007. Joints in Precast Parking Structures. Reprinted in PCI Journal, V. 52, No. 5 (September-October). 41. Sealant, Waterproofing and Restoration Institute (SWR). 1995. Sealants: The Professionals’ Guide. Kansas City, MO: SWR. 42. Panek, J. R. and J. P. Cook. 1991. Construction Sealants and Adhesives. 3rd ed. New York, NY: WileyInterscience. 43. Kubal, M. T. 1992. Waterproofing the Building Envelope. New York, NY: McGraw-Hill Companies, Inc. 44. ACI Committee 504. 1997. Guide to Sealing Joints in Concrete Structures (ACI 504R-90, Reapproved 1997),

52. ACI Committee 201. 2001. Guide to Durable Concrete (ACI 201.2R-01), ACI Manual of Concrete Practice, Part 1. Farmington Hills, MI: ACI. 53. ACI Committee 224. 2001. Control of Cracking in Concrete Structures, (ACI 224R-01), ACI Manual of Concrete Practice, Part 3. Farmington Hills, MI: ACI. 54. ACI Committee 503. 1998. Use of Epoxy Compounds with Concrete (ACI 503R-93, Reapproved 1998), ACI Manual of Concrete Practice, Part 5. Farmington Hills, MI: ACI. 55. Trout, J. 2006. Epoxy Injection in Construction. 2nd ed. Florence, KY: Thomson Delmar Learning. 56. ACI Committee 440. 2002. State-of-the-Art Report on Fiber Reinforced Plastic (FRP) Reinforcement for Concrete Structures (ACI 440R-96, Reapproved 2002), ACI Manual of Concrete Practice, Part 5. Farmington Hills, MI: ACI. 57. Swami, R. N. and R. Gaul, eds. 1996. Repair and Strengthening of Concrete Components with Adhesive Bonded Plates, SP-165. Presented at ACI Technical Session, Washington, DC, March 15–16, 1992. Farmington Hills, MI: ACI. 58. ACI Committee 506. 2005. Guide to Shotcrete (ACI 506R-05), ACI Manual of Concrete Practice, Part 5. Farmington Hills, MI: ACI.

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CHAPTER 10

CHAPTER 10 DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE 10.1

Definitions.................................................................................................................................................................10-2

10.2

Introduction...............................................................................................................................................................10-2

10.3

Standard Fire Tests....................................................................................................................................................10-2 10.3.1 Fire Endurance, End-Point Criteria, and Fire Rating..................................................................................10-3 10.3.2 Restrained Fire Ratings...............................................................................................................................10-5

10.4

Fire Tests of Prestressed Concrete Assemblies.........................................................................................................10-5 10.4.1 Fire Tests of Flexural Components.............................................................................................................10-5 10.4.2 Fire Tests of Walls and Columns................................................................................................................10-5

10.5

Designing for Heat Transmission..............................................................................................................................10-5 10.5.1 Single Course Slabs or Wall Panels............................................................................................................10-5 10.5.2 Floors, Roofs, or Walls Faced with Gypsum Wallboard............................................................................10-7 10.5.3 Ribbed Panels..............................................................................................................................................10-7 10.5.4 Multi-Course Assemblies............................................................................................................................10-9 10.5.5 Sandwich Panels.......................................................................................................................................10-10 10.5.6 Treatment of Joints between Wall Panels.................................................................................................10-10

10.6

Fire Endurance by Rational Design.........................................................................................................................10-11 10.6.1 Simply Supported Components................................................................................................................10-11 10.6.2 Continuous Components...........................................................................................................................10-12 10.6.3 Components Restrained against Thermal Expansion................................................................................10-14

10.7

Shear Resistance......................................................................................................................................................10-19

10.8

Requirements for Parking Structures.......................................................................................................................10-19

10.9

Protection of Connections.......................................................................................................................................10-21

10.10

Precast Concrete Column Covers............................................................................................................................10-22

10.11

Code and Economic Considerations........................................................................................................................10-24

10.12

References...............................................................................................................................................................10-24

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CHAPTER 10

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Definitions

Carbonate aggregate concrete.  Concrete made with aggregates consisting mainly of calcium or magnesium carbonate, for example, limestone or dolo­mite. Fire endurance.  A measure of the elapsed time during which a material or assembly continues to exhibit fire resistance under specified conditions of test and performance. As applied to components of buildings, it shall be measured by the methods and to the criteria defined in ASTM E1191 (defined in ASTM E1762). Fire resistance.  The property of a material or assembly to withstand fire or to give protection from it. As applied to components of buildings, it is character­ized by the ability to confine a fire or to continue to perform a given structural function, or both (defined in ASTM E176). Fire-resistance rating (sometimes called fire rating, fireresistance classification, or hourly rating).  A legal term defined in building codes, usually based on fire endurances. Fire resistance ratings are assigned by building codes or building officials for various types of construction and occupancies and are usually given in half-hour increments. Normalweight concrete.  Concrete having a density of approximately 150 lb/ft3 made with normal-density aggregates. Lightweight aggregate concrete.  Concrete made with lightweight, coarse, and fine aggregate (expanded clay, shale, slag, or slate, or sintered fly ash) and having a 28-day air-dry density of 95 to 105 lb/ft3. Sand-lightweight concrete.  Concrete made with a combination of expanded clay, shale, slag, slate, or sintered fly ash and natural sand; its density is generally between 105 and 120 lb/ft3. Siliceous aggregate concrete.  Concrete made with normalweight aggregates consisting mainly of silica or compounds other than calcium or magnesium carbonate.

10.2

Introduction

Precast and prestressed concrete components can be designed to meet any degree of fire resistance that may generally be required by building codes, insurance companies, and other authorities. Fire resistance ratings of building assemblies can be determined from ASTM E119 standard fire tests, code-approved empirical data, or by calculation procedures detailed in Section 10.6. The calculation method is based on engineering principles, taking into account the time-temperature condition of the standard fire test. This method, hereafter referred to as the rational design method of determining fire resistance, was formulated as a result of extensive research sponsored in part by the Precast/Prestressed Concrete Institute (PCI) and conducted by the Portland Cement Associ­ation (PCA) and other laboratories. Examples using the rational design method are provided in Section 10.6, along with a brief explanation of the method’s underlying principles. For additional examples, design charts, and an in-depth explanation of the method, refer to the PCI manual MNL 124-89, Design for Fire Resistance of Precast, Prestressed Concrete3 as well as the Concrete Rein10–2

2500 Furnace atmosphere temperature, °F

10.1

DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE

2000

1500 1000

500 0

0

2

4

6

8

Fire test time, hour Fig. 10.3.1 Standard time-temperature curve.

forcing Steel Institute (CRSI) manual Reinforced Concrete Fire Resistance.4 High-strength concrete (compressive strengths up to 10,000 psi) will perform under fire conditions as described herein provided that minimum cover and other dimensional requirements are being adhered.5 Underwriters Laboratories (UL) provides certifi­cation of fire-resistance ratings of some building assemblies for precast concrete manufacturers that subscribe to the service. These certifications are based on standard fire tests. UL certification is not required by PCI or any model building code.

10.3

Standard Fire Tests

The fire resistance of building components can be measured using standard fire tests defined by ASTM E119, Standard Test Methods for Fire Tests of Building Construction and Materials. During these tests, the building assembly, such as a portion of floors, walls, roofs or columns, is subjected to increasing temperatures that vary with time (Fig. 10.3.1). This time-temperature relationship is used as a standard to represent the combustion of about 10 lb of wood (with a heat potential of 8000 Btu/lb) per square foot of exposed area per hour of test. Actually, the fuel consumption to maintain the standard time-temperature relationship during a fire test depends on the design of the furnace and on the test specimen. When fire tested, assemblies with exposed concrete components, such as double-tees and hollow-core slabs, likely require considerably more fuel than other assemblies due to their favorable heat-absorption capacity. This fact is not recognized when evaluating fire resistance by current standard test methods. In addition to defining a standard time-temperature relationship, standard fire tests involve regulations concerning the size of the assemblies, the amount of externally applied

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DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE load, the region of the assembly to be exposed to fire, the extent of restraint, and the end-point criteria on which fire resistance (duration) is based. ASTM E119 specifies the minimum sizes of specimens to be exposed in fire tests, although much valuable data have been developed from tests on specimens smaller than the ASTM minimum sizes. For floors and roofs, at least 180 ft2 must be exposed to fire from beneath and neither dimension can be less than 12 ft. For tests of walls, either load-bearing or non-load-bearing, the minimum specified area is 100 ft2 with neither dimension less than 9 ft. The minimum length for columns is specified to be 9 ft, while for beams it is 12 ft. During fire tests of floors, roofs, beams, load-bearing walls, and columns, loads are applied that, along with the dead weight of the specimen, closely approximate the maximum loads required by the model codes. Tests that have been conducted on precast, prestressed components were generally done with full design loads, whereas other materials and elements have been tested using less than the maximum loads. This, in effect, limits those test results to the specific loading conditions. Floor and roof specimens are exposed to fire from beneath, beams from the bottom and sides, walls from one side, and columns from all sides. ASTM E119 distinguishes between restrained and unrestrained assemblies and defines them as follows: Floor and roof assemblies and individual beams in buildings shall be considered restrained when the surrounding or supporting structure is capable of resisting substantial thermal expansion throughout the range of anticipated elevated temperatures. Constructions not complying with this definition are assumed to be free to rotate and expand and shall therefore be considered as unrestrained. While the focus of this definition is mainly on the axial resistance of the supporting or surrounding structure to thermal expansion, the intent of restraint actually can be expanded for concrete components to include rotational restraint and continuity as well (see Section 10.6.2 on continuous components). During early standard ASTM E119 fire tests performed on precast concrete floors, the gaps between the ends of the components and the furnace frame were grouted, which prevented the components from expanding or rotating as the furnace temperature increased. Some observers concluded that this degree of restraint could not happen in real buildings. However, field experience and observation of real fires have shown that precast concrete buildings have consistently performed as well as would be expected if the precast concrete components were assumed to be restrained. This is further supported by the statement in the International Conference of Building Officials’ Fire Resistive Workbook6 indicated in Section 10.3.2. It should also be noted that ASTM E119 testing requires the specimens to be representative of actual building construction. However, because of the test furnace size, the results derived from components tested in laboratory furnaces cannot accurately reflect their behavior in a real building. In ICBO’s Fire Resistive Workbook, the following is stated:

CHAPTER 10

Although UBC Standard 7-1 [ASTM E119] is frequently described as a large-scale test, it clearly is not a full-scale test. Most floor slabs and roof decks are continuous over supports. Beams, girders, and trusses are framed into columns and other structural members in a variety of ways. As a result, testing laboratories are faced with the difficult problem of providing both end support or restraint for test assemblies representative of actual field conditions. ASTM E119 includes a guide for classifying types of construction as restrained or unrestrained and is reproduced in Table 10.3.1. The guide indicates that, typically, cast-in-place and precast con­crete assemblies are considered restrained. Sec­tion 10.3.2 provides additional information on restraint. 10.3.1

 ire Endurance, End-Point Criteria, F and Fire Rating

The fire resistance of an assembly is mea­sured by its fire endurance, defined as the period of time elapsed before a prescribed condition of failure or end point is reached during a standard fire test. A fire rating or classification is a legal term for a fire endurance required by a building code authority. End-point criteria defined by ASTM E119 include: 1. Load-bearing specimens must sustain the applied loading. Collapse is an obvious end point (structural end point). 2. Holes, cracks, or fissures through which flames or gases hot enough to ignite cotton waste must not form (flame passage end point). 3. The temperature increase above the initial temperature of the unexposed surface of floors, roofs, or walls must not exceed an average of 250 °F or a maximum of 325 °F at any one point (heat transmission end point). After a dual rating system of fire-rating classification of restrained and unrestrained was introduced around 1970 by ASTM Committee E-5, the decision was made to apply structural end-point criteria to concrete that had been tested in a restrained test procedure so as to avoid the expense of retesting a large number of assemblies. The original ratings determined by the restrained test procedure were kept intact and unrestrained ratings were added based on temperature criteria. Thus, unrestrained assembly classifications can be derived from tests of re­strained floor, roof, or beam specimens provided that the average temperature of the tension steel at any section does not exceed 800 °F for cold-drawn prestressing steel or 1100 °F for reinforcing bars, the structural end point assumed for an unrestrained condition. These temperatures may be exceeded when rational design is used as discussed in Section 10.6. Additional end-point criteria for restrained specimens are: 1. Beams more than 4 ft on centers: the above steel temperatures must not be exceeded for classifications of 1 hour or less; for classifications longer than 1 hour, the above temperatures must not be exceeded for the first half of the classification period or 1 hour, whichever is longer. 2. Beams 4 ft or less on centers or slabs are not subjected to steel temperature limitations. Walls and partitions must meet the same structural,

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DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE

flame passage, and heat transmission end points described previously. In addition, they must withstand a hose stream test (simulating, in a specified manner, a fire fighter’s hose stream). An additional aspect of fire ratings that should be considered is, since precast concrete is a non-combustible material, it will not serve as additional fuel for a fire even if the heat transmission or structural performance end points are reached. That is not the case for many other building materials. Table 10.3.1  Considerations of restraint for common constructiona I. Wall bearing: Single span and simply supported end spans of multiple bays:b

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1. Open-web steel joists or steel beams supporting concrete slabs, precast concrete units, or metal decking.................. Unrestrained 2. Concrete slabs, precast concrete units, or metal decking................................................................................................ Unrestrained

Interior spans or multiple bays: 1. Open-web steel joists, steel beams, or metal decking supporting continuous concrete slabs........................................... Restrained 2. Open-web steel joists or steel beams supporting precast concrete units or metal decking............................................ Unrestrained 3. Cast-in-place concrete slab systems................................................................................................................................... Restrained 4. Precast concrete where the potential thermal expansion is resisted by adjacent constructionc. ....................................... Restrained

II. Steel framing: 1. Steel beams welded, riveted, or bolted to the framing components................................................................................... Restrained 2. A  ll types of cast-in-place floor and roof systems (such as beam-and-slabs, flat slabs, pan joists, and waffle slabs) where the floor or roof system is secured to the framing components............................................................................... Restrained 3. A  ll types of prefabricated floor or roof systems where the structural components are secured to the framing components and the potential thermal expansion of the floor or roof system is resisted by the framing system or the adjoining floor or roof constructionc. ............................................................................................................................. Restrained

III. Concrete framing: 1. Beams securely fastened to the framing components........................................................................................................ Restrained 2. A  ll types of cast-in-place floor or roof systems (such as beam-and-slabs, flat slabs, pan joists, and waffle slabs) where the floorsystem is cast with the framing components...............................................................................................Restrained 3. Interior and exterior spans of precast concrete systems with cast-in-place joints resulting in restraint equivalent to that which would exist in condition III-1............................................................................................................................... Restrained 4. A  ll types of prefabricated floor or roof systems where the structural components are secured to such systems and the potential thermal expansion of the floor or roof systems is resisted by the framing system or the adjoining floor or roof constructionc............................................................................................................................................................ Restrained IV. Wood construction: All types Unrestrained

a. Source: ASTM E119, “Standard Test Methods for Fire Tests of Building Construction and Materials,” Table X3.1. b. Floor and roof systems can be considered restrained when they are tied into walls with or without tie beams, the walls being designed and detailed to resist thermal thrust from the floor or roof system. c. For example, resistance to potential thermal expansion is considered to be achieved when: 1.  Continuous structural concrete topping is used; 2. The space between the ends of precast units or between the ends of units and the vertical face of supports is filled with concrete or mortar; or 3. The space between the ends of precast units and the vertical faces of supports, or between the ends of solid or hollow-core slab units does not exceed 0.25% of the length for normalweight concrete components or 0.1% of the length for structural lightweight concrete components.

10–4

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DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE 10.3.2

Restrained Fire Ratings

The dual rating system mentioned previously has caused much confusion over the years to designers and building officials alike. In response to this, ASTM Committee E-5 developed a table that greatly simplified the decision making process. This table is reproduced as Table 10.3.1. The footnotes at the bottom of Table 10.3.1 list the requirements that must be satisfied for a structure to be considered restrained. ICBO’s Fire Resistive Workbook paraphrases the table as follows: Concrete framing may be classified as restrained. Examples of restrained conditions for concrete framing are (1) beams securely fastened to the structural framing members, (2) all types of cast-in-place floor or roof systems where the system is cast with the structural framing members, and (3) all types of prefabricated floor or roof systems where the structural members are secured to such systems and the potential thermal expansion of the floor or roof system is resisted by the framing system or the adjoining floor or roof construction. Restraint is often defined as the ability of the adjacent structure to resist thermal expansion of structural components. In continuous components, restraint is provided by the adjacent bays so continuous components have an obvious advantage over simply supported ones. Almost all precast/prestressed buildings are designed with the floor and roof systems acting as diaphragms that transfer lateral loads to the resisting systems. This is accomplished by tying the deck components together and to the framing components with welded connections or with reinforcement when cast-in-place topping is used. Note that this is also done to meet the ACI 318-057 requirements for structural integrity. The total structural system will, in most buildings, provide the necessary resistance to thermal expansion during a fire. The second edition of Design for Fire Resistance of Precast Prestressed Concrete (MNL-124-89) discusses this subject in more detail. Restraint is also the subject of ongoing PCI-sponsored research.

10.4

 ire Tests of Prestressed Concrete F Assemblies

The first fire test of a prestressed concrete assembly in the United States was conducted in 1953, and since then, more than 150 prestressed concrete assemblies have been subjected to standard fire tests. Although many of the tests were conducted for the purpose of deriving specific fire ratings, most of the tests were performed in conjunction with broad research studies whose objectives have been to understand the behavior of prestressed concrete subjected to fire. The knowledge gained from these tests has resulted in the development of lists of fire-resistant, prestressed concrete building components and procedures for determining the fire endurance of prestressed concrete components by calculation. 10.4.1

Fire Tests of Flexural Components

Reports of a number of tests sponsored by PCI have been issued by UL. Most of the reports have been reprinted by

CHAPTER 10

PCI, and the results of the tests are the basis for UL’s listings and specifications for non-proprietary products such as double-tee and single-tee floors and roofs, wet-cast hollowcore and solid slabs, and prestressed concrete beams. The Portland Cement Association (PCA) also conducted fire tests of prestressed concrete assemblies. PCA’s unique furnaces have made it possible to study in depth the effects of support con­ditions. Four series of tests dealt with simply supported slabs and beams, two series dealt with continuous slabs and beams, and one major series dealt with the effects of restrained thermal expansion on the behavior during a fire of prestressed concrete floors and roofs. PCA has also conducted a number of miscellaneous fire tests of prestressed and reinforced concrete assemblies. Test results that have been published as research and development bulletins are available from PCA.8,9 10.4.2

Fire Tests of Walls and Columns

A test was conducted by UL on a double-tee wall assembly in which fire was applied to the flat surface of the 11/2 in. thick flange. A gravity load of about 10 kip/ft was applied at the top of the wall. The wall withstood a 2-hour fire and a subsequent hose-stream test followed by a load test with a doubled design load. No distress was observed. Because the flange was only 11/2 in. thick, the heat transmission requirement was exceeded for most of the test. By providing adequate flange thickness or insulation, the heat transmission requirement would have been met in addition to the structural requirement. Fire tests of reinforced concrete columns have been conducted by PCA and the National Research Council of Canada. While no tests have been conducted for prestressed concrete columns, results from these tests are considered to be equally applicable to prestressed concrete columns with adjustment made for the difference in thermal properties between mild reinforcing steel and prestressing strand, as may be appropriate.

10.5

Designing for Heat Transmission

As noted in Section 10.3.2, ASTM E119 imposes heat transmission criteria for floor, roof, and wall assemblies. Thus, floors, roofs, or walls re­quiring a fire-resistance rating must satisfy the heat-transmission requirements as well as the various structural criteria. The heat transmission fire endurance of a concrete assembly is essentially the same whether the assembly is tested as a floor (oriented horizontally) or as a wall (tested vertically). Because of this, and unless otherwise noted, the information that follows is applicable to floors, roofs, or walls. 10.5.1

Single Course Slabs or Wall Panels

For concrete slabs or wall panels, the temperature rise of the unexposed surface depends mainly on the thickness and aggregate type of the concrete. Other less important factors include density, moisture condition, air content, and maximum aggre­ gate size. Within the usual ranges, water-cementitious-materials ratio, strength, and age have only insignificant effects. Figure 10.5.1 shows the fire endurance (heat transmission)

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DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE

CHAPTER 10

5.0 Sand-lightweight - 115 lb/ft

3

4.5 Lightweight - 100 lb/ft 3 4.0

Fire endurance, hour

3.5

  10

3.0 2.5

2.0 1.5 1.0 Carbonate aggregate 0.5 Siliceous aggregate 0 1.0

1.5

2.0

3.0

2.5

3.5

4.0

5.0

4.5

5.5

6.0

6.5

7.0

Slab or panel thickness, in. *Interpolation for different concrete unit weights is reasonably accurate

Fig. 10.5.1 Fire endurance (heat transmission) of concrete slabs or panels.

of concrete slabs as influenced by aggregate types and thickness. For a hollow-core slab, this thickness may be obtained by dividing the net cross-sectional area by its width. The curves represent air-entrained concrete made with air-dry Table 10.5.1  Thickness of concrete slabs or wall panels faced with 5/8 in. Type X gypsum wallboard to provide fire endurances of 2 and 3 hours10

aggregates having a nominal maximum size of 3/4 in. and fire tested when the concrete was at the stan­dard moisture condition (75% relative humidy [RH] at mid-depth). On the graph, concrete aggregates are designated as lightweight, sandlightweight, carbonate, or siliceous. Lightweight aggregates include expanded clay, shale, and slate, which produce concretes hav­ing densities of about 95 lb/ft3 to 105 lb/ft3 without normalweight sand replacement. Lightweight concretes, in which normalweight sand is used as part or all of the fine

Thickness of concrete panel for noted fire endurance, in. With no air space Fire endurance, hour

2

3

With 6 in. air space

2

t

t

te

3

Aggregate: Sand-lightweight

2.5

3.6

2.0

2.5

Carbonate

2.8

4.0

2.0

2.7

Siliceous

2.9

4.2

2.0

2.8

10–6

2t

(Neglect hatched area in calculation of equivalent thickness) (a)

s

(b)

Fig. 10.5.2 Cross sections of ribbed wall panels.

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DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE aggregate and weigh no more than about 120 lb/ft3, are designated as sand-lightweight. Carbonate aggregates include limestone and dolomite, that is, those consisting mainly of calcium and/or magnesium carbonate. Siliceous aggregates include quartzite, granite, basalt, and most hard rocks other than limestone and dolomite.

Example 10.5.3.1 Fire Endurance of a Ribbed Panel

5"

10.5.2 Floors, Roofs, or Walls Faced with Gypsum Wallboard Table 10.5.1 shows the fire endurance of con­crete slabs with 5/8 in. gypsum wallboard (Type X) for two cases: (1) a 6 in. air space between the wall­board and slab, and (2) no air space between the wall­board and slab. Materials and techniques of attaching the wallboard should be similar to those used in the UL test on which the data are based. 10.5.3

Ribbed Panels

Heat transmission through a ribbed or corrugated panel is influenced by the thinnest portion of the panel and by the panel’s equivalent thickness te. Here, equivalent thickness is defined as the net cross-sectional area of the panel divided by the width of the cross section. In calculating the net cross-sectional area of the panel, portions of ribs that project beyond twice the minimum thickness should be neglected, as shown in Fig. 10.5.2(a). The heat transmission fire endurance can be governed by either the thinnest section, or by the average thickness, or by a combination of the two. The following rule-of-thumb expressions appear to give a reasonable guide for selecting R: s If t ≤ , fire endurance R is governed by t and is equal to Rt 4 s If t ≥ , fire endurance R is governed by te and is equal to Rte 2 s s If > t > : 4 2

R = Rt +

4t 1 ( Rte s

Rt )

(Eq. 10-1)

where: s = rib spacing t = minimum thickness te = equivalent thickness of panel and where R is the fire endurance of a concrete panel, and subscripts t and te relate the corresponding R-values to concrete slab thicknesses t and te, respectively. These expressions apply to ribbed and corrugated panels, but, for panels with widely spaced grooves or rustications, they give excessively low results. Consequently, engineering judgment must be used when applying the above expressions.

CHAPTER 10

1.5"

12"

4" 1.5" t = 4.8"

t = 4"

H = 5.5"

Given: The section of a wall panel shown. The panel is made of sand-lightweight concrete (115 lb/ft3). Problem: Estimate the fire endurance. Solution: H = 5.5 in. < 2t, therefore, full section can be considered: te = [5.5(12) – 1.5(4 + 1.5)]/12 = 4.8 in. s s t = 4 in., = 6 in., = 3 in. 2 4 Therefore, s/2 > 4 > s/4 From Eq. 10-1:

⎛ 4t ⎞ R = Rt + ⎜ − 1⎟ (Rte − Rt ) ⎠ ⎝s From Fig. 10.5.1: Rt = fire endurance of 4 in. sand-lightweight panel = 135 min Rte = fire endurance of 4.8 in. sand-lightweight panel = 193 min ⎡⎛ 4 ( 4 ) ⎞ ⎤ − 1⎟ (193 − 135 ) ⎥ R = 135 + ⎢⎜ ⎠ ⎣⎝ 12 ⎦



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= 154 min = 2 hr 34 min

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DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE

CHAPTER 10

20

Ca

Material

tc

on

cr et

e

ete

cr

on

3

5

0

1

2

4

3

R

Cellular plastic (1 in. or thicker)

eg

gr

g sa

c

c ate

te

re

c on

0.59

11.20 16.85 21.41 25.37

60 120 180 240

u eo

ilic

S

gr

ag

n

o rb

te

a eg

gh ei

w ht

e at

lig nd

Sa

Li gh

tw

ei gh

tc on

cr e

te

(35 lb/ ft 3) 10

Ins ula tin gc on cre te

R0.59 for use in Eq. 10-2

  10

15

R

R, minutes

0.59

2.57

4 in. glassfiber board

4.03

112 in. glassfiber board

8.57

Continuous air space

3.33

Two continuous air spaces

6.67

2 in. foam glass

10.61

5

Thickness of one course, in. Fig. 10.5.3 Design aid for use is solving Eq. 10-2. Table 10.5.2  Values of R of various insulating materials for use in Eq. 10-2 Roof insulation material

Thickness, in.

R, minute

Cellular plastic

>1

5

Glass-fiber board

3

/4

11

11/2

35

Foam glass

2

55

Mineral board

1

19

Mineral board

2

62

Mineral board

3

123

Glass-fiber board

Table 10.5.3  Thickness of two-course roof assemblies consisting of concretea slabs with insulating concrete overlaysb

Insulating concrete overlay Concrete base slab

Note: Some of these materials may be used only where combustible construction is permitted.

Thickness of overlay for fire resistance rating of, in.

Base slab thickness, in. 1 hr

1½ hr

2 hr

3 hr

4 hr

11/2

11/8

11/2

17/8

2 5/8

31/8

2

1

13/8

13/4

21/2

3

/4

11/4

2

2 5/8

/8

13/8

2

3 4

/8

3

0

3

0

5

a. V  alues shown are for siliceous aggregate concrete and are conservative for other concretes. b. Insulating concrete having a dry density less than 35 lb/ft3.

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DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE Table 10.5.4  Thickness of spray-applied insulation on fireexposed surface of concretea slabs or panels to resist transfer of heat through the assemblies

CHAPTER 10

Table 10.5.5  Thickness of roof assemblies consisting of concretea slabs with insulation and built-up roofing

Standard 3-ply built-up roofing

Thickness for fireresistance rating of, in.

Base slab equivalent thickness, in.

Type of insulation

11/2

SMF

1

/2

3

/4

2

SMF

3

/8

5

/8

1

2 /2

SMF

1

/4

1

3

SMF

1

/8

1

4

SMF

1½

VCM

2

VCM

1 hr 1 /2 hr 2 hr 3 hr 4 hr 1

0 1 3

/2 /8

MB

3 1

NA

7

/8

13/8

NA

/2

5

/8

1

1 /8

1 /8

2

MB

/4

1

/2

7

/8

1 /8

3

MB

0

0

1

/4

5

/8

1

4

MB

13/4

NA

11 /2

GFB

13/4

2

GFB

11/4

11/8

3

13/8

4

3 5

/4

11/8

/8

7

/8

13/8

1

/4

1

/2

3

/4

3

VCM

1

/8

3

/8

5

/8

7

/8

4

VCM

0

1

/4

5

/8

5

3

7

/8

a. Values shown are for siliceous aggregate concrete and are conservative for other concretes. Note: NA = not applicable; SMF = sprayed mineral fiber consists of refined mineral fibers with inorganic binders and water added during the spraying operation. The density of the oven-dry material should be at least 13 lb/ft3; VCM = vermiculite cementitious material consists of expanded vermiculite with inorganic binders and water. The density of the oven-dry material should be at least 14 lb/ft3.

Multi-Course Assemblies

Floors and roofs often consist of concrete base slabs with overlays or undercoatings of other types of concrete or insulating materials. In addition, roofs generally have built-up roofing. If the fire endurance of the individual courses is known, the fire endurance of the composite assem­bly can be estimated from the following formula (reference IBC11 Section 721.2.1.2.1):

R0.59 = R10.59 + R20.59 + ... + Rn0.59



11 /2

Thickness of insulation for fire-resistance rating of, in.

NA

VCM

10.5.4

Insulation

11/8

21/2

0

Base slab thickness, in.

(Eq. 10-2)

where: R

= f ire endurance of composite assembly in minutes R1, R2, Rn = fire endurances of individual courses in minutes

1 hr

11/2 hr

2 hr

3 hr

4 hr

/4

11/4

17/8

2 3/4

NA

/2

1

3

1 /8

1

2 /4

2 7/8

13/8

17/8

/4

11/4

/4

3

/4

0

0

1

/4

5

/8

13/8

2

NA

NA

1

/4

7

/8

1

1 /2

7

2  /8

NA

GFB

0

3

/4

1

1 /2

21/8

GFB

0

/4

11/4

3

/8

3

0

1

/4

3

3

a. Values shown are for siliceous aggregate concrete and are conservative for other concretes. Note: GFB = glass-fiber-board fibrous glass roof insulation consisting of inorganic glass fibers formed into rigid boards using a binder. The board has a top surface faced with glass-fiber reinforced with asphalt and kraft; MB = mineral board insulation composed of spherical cellular beads of expanded aggregate and fibers formed into rigid, flat, rectangular units with an integral waterproofing treatment; NA = not applicable.

insulating materials (in the table) and for concrete of various types and thicknesses (in the graph). Table 10.5.2 gives R-values that can be used in this equation for certain insulating materials. For heat transmission, three-ply built-up roofing contributes 10 minutes to the fire endurance. Either set of data can be used in solving Eq. 10-1, as shown in Example 10.5.4.1. Equation 10-2 has certain shortcomings in that it does not account for the location of the individual courses relative to the fired surface. Also, it is not possible to directly obtain the fire endurances of many insulating materials. Nevertheless, in a series of tests, the formula estimated the fire endurances within about 10% for most assemblies. A report12 on two-course floors and roofs gives results of many fire tests, and also shows the fire endurances of assemblies con­sisting of various thicknesses of two materials. Tables 10.5.3 through 10.5.5, which are based on test results, can be used to estimate the required thicknesses of two-course materials for various fire endurances.

Figure 10.5.3 gives R-values raised to the 0.59 power for PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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  10

CHAPTER 10

DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE Table 10.5.6  Fire endurance of precast concrete sandwich walls (calculated, based on Eq. 10-2)

Example 10.5.4.1 Fire Endurance of an Assembly Problem: Determine the fire endurance of a slab consisting of a 2 in. base slab of siliceous aggregate concrete with a 21/2 in. topping of sand-lightweight concrete (115 lb/ft3). Solution:

  10

From Fig. 10.5.1, the fire endurances of a 2-in.thick slab of siliceous aggregate concrete and 21/2 in. of sand-lightweight aggregate concrete are 25 minutes and 62 minutes, respectively. R 0.59 = (25)0.59 + (62)0.59 R 0.59 = 6.68 + 11.42 = 18.10 R = (18.10)1/0.59 = 135 min = 2 hr 15 min Alternatively, from Fig. 10.5.3: R 0.59 = 6.7 + 10.5 = 17.2

Outside and inside wythes

1 in. CP

1:23

11/2 in. Carb

1 in. CP

1:23

11/2 in. SLW

1 in. CP

1:45

2 in. Sil

1 in. CP

1:50

2 in. Carb

1 in. CP

2:00

2 in. SLW

1 in. CP

2:32

3 in. Sil

1 in. CP

3:07

11/2 in. Sil

3

/4 in. GFB

1:39

2 in. Sil

3

/4 in. GFB

2:07

2 in. SLW

3

/4 in. GFB

2:52

1

1 /2 in. Sil

1 /2 in. GFB

2:35

2 in. Sil

11/2 in. GFB

3:08

2 in. SLW

11/2 in. GFB

4:00

1 /2 in. Sil

1 in. IC

2:12

1 /2 in. SLW

1 in. IC

2:39

2 in. Carb

1 in. IC

2:56

2 in. SLW

1 in. IC

3:33

11/2 in. Sil

1½ in. IC

2:54

1 /2 in. SLW

1½ in. IC

3:24

2 in. Sil

2 in. IC

4:25

1 /2 in. SLW

2 in. IC

4:19

1

1

10.5.5

1

Sandwich Panels

Some wall panels are made by sandwiching an insulating material between two face slabs (wythes) of con­crete (see Section 5.11.1 of this handbook). The IBC requires that where noncombustible construction is specified, combustible elements in walls are limited to thermal and sound insulation having a flame-spread index of 25 or less. When the insulation is sandwiched between two layers of noncombustible materials such as concrete, the maximum flame-spread index allowed is 100, except that it shall not exceed 75 for foam plastic insulation. When insulation is not installed in this manner, it is required to have a flame spread of not more than 25. Data on flame spread classification are available from insulation manufacturers. A fire test was conducted of one such panel that consisted of a 2 in. wythe of carbonate aggregate concrete, a 1 in. layer of cellular poly­styrene insulation, and a 2 in. wythe of carbonate aggregate concrete. The resulting fire endurance was 2 hr 00 min. From Eq. 10-2, the contribution of the 1 in. layer of polystyrene was calculated to be 5 minutes. For raw data on various insulation types, consult with insulation manufacturers. It is likely that the comparable R-value for a 1 in. layer of cellular polyurethane would be somewhat greater than that for a 1 in. layer of cellular polysty­rene, but test values are not available. Until more definitive data are obtained, it is suggested that 5 minutes be used as the value for R for any layer 10–10

Fire endurance, hour:minute

11/2 in. Sil

1

By linear interpolation from Fig. 10.5.3: 17.2 − 16.85 (60 ) = 125 min R = 120 + 21.41− 16.85 R = 123 min = 2 hr 5 min

Insulation

1

Note: Carb = carbonate aggregate concrete; CP = cellular plastic (polystyrene or polyurethane); GFB = glass-fiber board; IC = lightweight insulating concrete (35 lb/ft3 maximum); Sil = siliceous aggregate concrete; SLW = sand-lightweight concrete (115 lb/ft3 maximum).

of cellular plastic 1 in. or greater. It should be noted that the cellular plastics melt and are consumed at about 400 °F to 600 °F. Thus, additional thickness or changes in composition probably have only a minor effect on the fire endur­ance of sandwich panels. The danger of toxic fumes caused by burning cellular plastics is practically eliminated when the plastics are completely encased within concrete sandwich panels.13 Table 10.5.6 lists fire endurances of sandwich panels with either cellular plastic, glass-fiber board, or insulating concrete used as the insulating material. The fire resistance values were obtained from Eq. 10-2. 10.5.6

 reatment of Joints between Wall T Panels

When required by code, joints between wall panels should be detailed so that the passage of flame or hot gases is prevented and that the transmission of heat does not exceed the limits specified in ASTM E119. Concrete wall panels expand when heated, so the joints tend to close during fire exposure. Non-combustible materials that are flexible, such as ceramic

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DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE fiber blankets, provide thermal, flame, and smoke barriers, and, when used in conjunction with caulking materials, can provide the necessary weather-tightness while permitting normal volume-change movements. Joints that do not move can be filled with mortar. For a more detailed discussion and additional information, refer to PCI MNL-124-89. The IBC addresses joints in exterior walls in various sections of the code: 1. In Section 713 of IBC, joints are specified to have the same fire-resistance rating as the wall. Walls that are permitted to have unprotected openings are noted as an exception to this requirement. 2. Table 704.8 of IBC is used to determine if unprotected openings are allowed as well as designating the percentage of unprotected openings allowed. 3. Section 704.13 of IBC also addresses joints and has the same exception as Section 713. 4. Section 721.2.1.3 of IBC addresses joints in precast concrete walls. This section requires that unprotected joints be included as openings in the calculation of opening percentages for comparison to the allowed opening percentage of Table 704.8. Where no openings are permitted, the fire resistance required for the wall should be provided at the joints. Table 10.5.7 is based on results of fire tests of panels with butt joints.14 The tabulated values apply to one-stage butt joints and are conservative for two-stage and ship-lap joints. Joints between adjacent precast concrete floor or roof components may be ignored in calculating the slab thickness, provided that a concrete topping at least 11/2 in. thick is used. Where no concrete topping is used, joints should be grouted to a depth of at least one-third the slab thickness at the joint, or the joints made fire resistant in a manner acceptable to the authority having jurisdiction. No joint treatment is required in pretopped, double-tee parking structures when classified by code as open parking structures.

10.6

Fire Endurance by Rational Design

It was noted previously that many fire tests and related research studies have been directed toward an understanding

CHAPTER 10

of the structural behavior of prestressed concrete subjected to fire. The information gained from that work has led to the development of calculation procedures that can be used in lieu of fire tests. The purpose of this section is to introduce these calculation procedures. Because the method of support is the most important factor affecting structural behavior of flexural components during a fire, the discussion that follows deals with three conditions of support: simply supported components, continuous slabs and beams, and components that are restrained from thermal expansion. For additional examples and more detailed information, refer to PCI MNL-124-89. The fire endurance of concrete walls as determined by fire tests is normally governed by the ASTM criteria for temperature rise of the unexposed surface, rather than by structural behavior during fire tests. This is probably due to the low level of stresses, even in concrete bearing walls, and the fact that reinforcement generally does not perform a primary structural function. In most cases, the amount of cover protection required by code exceeds that required for fire protection, so there is, in effect, reserve structural fire endurance within the concrete wall. 10.6.1

Simply Supported Components

To understand the effects of fire, let us assume that a simply supported prestressed concrete slab is exposed to fire from below, that the ends of the slab are free to rotate, and that expansion can occur without restriction. Also, assume that the reinforcement consists of straight, uncoated strands located near the bottom of the slab. With the underside of the slab exposed to fire, the bottom will expand more than the top, causing the slab to deflect downward; also, the strength of the steel and concrete near the bottom will decrease as the temperature rises. When the strength of the steel diminishes to less than that required to support the slab, flexural collapse will occur. In essence, the applied moment remains practically constant during the fire exposure but the resisting moment capacity is reduced as the steel strength reduces. Figure 10.6.1 illustrates the behavior of a simply supported slab exposed to fire from beneath, as described previously. Because strands are parallel to the axis of the slab, the design

Table 10.5.7  Protection of joints between wall panels using ceramic fiber felt Panel equivalent thickness,a in.

Thickness of ceramic fiber felt required for fire resistance ratings and joint widthsb shown, in. Joint width = 3/8 in.

4

Joint width = 1 in.

1 hr

2 hr

3 hr

4 hr

/2

NA

NA

NA

3

/4

NA

NA

1

1

1

1 hr

2 hr

3 hr

4 hr

/4

NA

NA

NA

/2

1

2 /8

NA

NA

/4

5

0

6

0

0

1 /8

NA

1

7

0

0

0

1

1

3

/4

1 /4

1

3 /2

NA

/8

2

33/4

1

7

a. Panel equivalent thicknesses are for carbonate concrete. For siliceous aggregate concrete change 4, 5, 6, and 7 to 4.3, 5.3, 6.5, and 7.5. For sand-lightweight concrete change 4, 5, 6, and 7 to 3.3, 4.1, 4.9, and 5.7. b. Interpolation may be used for joint width between 3/8 in. and 1 in. The tabulated values apply to one-stage butt joints and are conservative for two-stage and ship-lap joints. Note: NA = not applicable.

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CHAPTER 10

moment strength is constant throughout the length:

  10

a⎞ ⎛ Mn = Aps f ps ⎜ d − ⎟ ⎝ 2⎠

(Eq. 10-3)

where: fps = stress in uncoated prestressing steel at nominal strength. It can be determined from Design Aid 5.14.3 or Eq. 18-3 of ACI 318-05. Aps = area of uncoated prestressing steel d = distance from the centroid of prestressing steel to the extreme compression fiber a = depth of equivalent rectangular compression stress block If the slab is uniformly loaded, the moment diagram will be parabolic with a maximum value at midspan of:

M=

w 2 8

(Eq. 10-4)

where: w = dead plus live load per unit of length l = span length As the material strengths decrease with elevated temperatures, the remaining nominal strength becomes:

aθ ⎞ ⎛ Mnθ = Aps f psθ ⎜ d − ⎟ ⎝ 2⎠

(Eq. 10-5)

in which θ signifies the effects of high temperatures. Note that Aps and d are not affected but fps is reduced (fpsθ). Similarly, a is reduced (aθ), but the concrete strength at the top of the slab, fc' , is generally not reduced significantly because of its lower temperature.

Fire At 0 hour M

Mn

At 2 hours M

Mnθ M = applied gravity load moment Mn = moment capacity before fire Mnθ = reduced moment capacity due to fire

Fig. 10.6.1 Moment diagrams for simply supported beam or slab.

10–12

Flexural failure can be assumed to occur when Mnθ is reduced to M. ACI load factors and strength reduction factors φ are not applied because a safety factor is included in the required ratings.3 From this expression, it can be seen that the fire endurance depends on the applied loading and on the strength-temperature characteristics of the steel. In turn, the duration of the fire before the critical steel temperature is reached depends on the protection provided to the reinforcement. To solve problems involving the previous equations, it is necessary to utilize data on the strength-temperature relationships for steel and concrete, and information on temperature distributions within concrete components during fire exposures. Figure 10.6.2 shows strengths of certain steels at elevated temperatures, and Fig. 10.6.3 shows similar data for concrete. Data on temperature distribution in concrete slabs during fire tests are shown in Fig. 10.6.4 and 10.6.5. These figures can also be used for beams wider than about 10 in. An effective u, u¯  , is used, which is the average of the distances between the centers of the individual strands or bars and the nearest fire-exposed surface. The values for corner strands or bars are reduced one-half to account for the exposure from two sides. The procedure does not apply to bundled bars or strands. Data on temperature distribution for stemmed components during fire tests are shown in Fig. 10.6.6 through 10.6.9. 10.6.2

Continuous Components

Continuous components undergo changes in stresses when subjected to fire. These stresses result from temperature gradients within the struc­tural components, or changes in strength of the materi­als at high temperatures, or both. Figure 10.6.10 shows a two-span continuous beam whose underside is exposed to fire. The bot­tom of the beam becomes hotter than the top and tends to expand more than the top. This differential temperature effect causes rotation that increases the reaction at the interior support. This action results in a redistribution of moments, that is, the negative moment at the interior support increases while the positive moments decrease. During a fire, the negative moment reinforcement (Fig. 10.6.10) at the top remains cooler than the positive moment reinforcement at the bottom because it is better protected from the fire and has a lower strength loss from high temperatures. In addition, the redistribution that occurs is sufficient to cause yielding of the negative moment reinforcement. Thus, a relatively large increase in negative moment can be accommodated. The resulting decrease in positive moment means that the positive moment reinforcement can be heated to a higher temperature before failure will occur. Therefore, the fire endurance of a continuous concrete beam is generally significantly longer than that of a simply supported beam having the same cover and the same applied loads. It is possible to design the reinforcement in a continuous beam or slab for a particular fire-endur­ance period. From Fig. 10.6.10, the beam can be expected to experience significant deflections when the positive moment capacity M n+θ is reduced to the value of the maxi­mum redistributed positive moment at a distance x1 from the outer support.

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CHAPTER 10

100 High strength alloy steel bars (tensile strength) Percent of strength at 70 °F

80 Hot-rolled steel (yield strength) 60

40

20

0

  10

Prestressing steel 250 or 270 ksi (tensile strength) conforming to ASTM A416

200

70

400

600

800

1200

1000

1400

Temperature, °F Fig. 10.6.2 Strength-temperature relationships for various steels.

120

Percent of original compressive strength

Carbonate aggregate 100 Sand-lightweight aggregate

80

Siliceous aggregate

60

40

20

0

Original strength = f 'c Average f 'c = 3900 psi Stressed to 0.4f 'c during heating 70

200

400

600 800 Temperature, °F

1000

1200

1400

Fig. 10.6.3 Compressive strength of concrete at high temperatures. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE

CHAPTER 10

Carbonate aggregate concrete

1600

1500

1300

in.

in.

12

1200

in.

3

. 4 in

1100

1

in.

1000

1

12

900

in.

n.

600 3

2

in.

1100 1 2

1

1000

in.

n.

2i

n.

3i

600

n.

4i

112

1

1200

700

n. 3i

1

n.

3 4i

800

700

1 2

1300

900

2i

800

500

1 4

1400

1 2

1 4

Temperature, °F

Temperature, °F

1400

in .

1500

  10

Siliceous aggregate concrete

1600

4

500

n.

4i 1 2

Fire test time, hour

1

112

2

3

4

Fire test time, hour

Fig. 10.6.4 Temperature within concrete slabs or panels during fire tests — normalweight concrete. Note: Dimensions shown are from the exposed surface. This is also the effective u dimension used when averaging the distance from the nearest fire-exposed surface to the center of mulitple bars or strands.

Sand-lightweight aggregate concrete

1600

10.6.3 1 4

in.

1500 1400 Temperature, °F

For more detailed information related to fire endurance considerations for continuous construction, refer to PCI MNL-124-89.

1 2

1300

.

in

.

3 4 in

1200 1

1100 1000

in.

1 2

1

900

in.

n.

2i

800 700

n.

3i

600 500

1 2

1

112 2 3 Fire test time, hour

4

Fig. 10.6.5 Temperatures within concrete slabs or panels during fire tests — sand-lightweight concrete. Note: Dimensions shown are from the exposed surface. This is also the effective u dimension used when averaging the distance from the nearest fire-exposed surface to the center of mulitple bars or strands.

10–14

 omponents Restrained against C Thermal Expansion

If a fire occurs beneath a portion of a large concrete floor (or roof), the heated portion will tend to expand and push against the surrounding portion and creates restraint. In turn, the unheated portion exerts compressive forces on the heated portion and creates restraint. Using the rational design method for determining the fire endurance of a restrained precast concrete flexural component is to determine the endurance of the component as if it is unrestrained (Section 10.6.1). That value is then doubled to obtain the restrained fire en­durance. This method of determining fire endurance is not valid for assemblies with an unrestrained fire rating of less than one hour. Conversely stated, for a given required fire rating, the restrained component would be checked for one-half of the required rating (but not less than one hour) as an unrestrained component (Example 10.6.3.1). Full value of the heat-transmission requirement must also be checked. The rationale for this method is the ASTM E119 criteria for deriving unrestrained component ratings from restrained fire tests (see Section 10.3.1). This method is further supported by Tables 10.8.1 through 10.8.5 since, for all cases, the cover required for any parti­cular restrained rating is equal to or less than the cover required for the unrestrained rating at half the time period.

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Temperature, °F

DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE

1100

1100

900

900

700

CHAPTER 10

700

u = 112 in.

u = 1 1 2 in.

500

  10

500

u = 2 in.

u = 2 in. u = 3 in. u = 4 in.

300

100

300

u = 5 in. u = 6 in. u = 10 in.

4

5

6

7

u

u = 10 in.

Sand-lightweight 9

8

b

u = 5 in.

Normalweight (carbonate or siliceous aggregate) 3

•

u = 3 in.

10

100

3

5

4

6

7

8

9

10

b, in.

b, in. Stemmed units, 1 hour

Fig. 10.6.6 Temperatures on vertical centerline of stemmed units at 1 hour of exposure.

1300

1300

1100

1100

1

Temperature, °F

u = 1 2 in. u = 11 2 in.

900

900

u = 2 in.

u = 3 in.

700

u = 2 in.

u = 3 in.

700

u = 4 in.

u = 4 in.

u = 5 in.

u = 5 in.

u = 6 in.

500

u = 10 in.

u = 10 in.

Normalweight (carbonate or siliceous aggregate)

300 3

4

5

6 7 b, in.

8

9

•

500

b

u

Sand-lightweight 10

300

3

4

5

6 b, in.

7

8

9

10

Stemmed units, 2 hours

Fig. 10.6.7 Temperatures on vertical centerline of stemmed units at 2 hours of exposure. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE

CHAPTER 10

1400

1400

1200

1200 u = 1 12 in.

u = 2 in.

1000

1000

u = 2 in.

u = 3 in. u = 4 in.

800

800

u = 5 in.

u = 3 in.

u = 6 in. u = 4 in.

600

600

u = 10 in.

3

4

5

6

7

8

u = 5 in.

b

•

u = 10 in.

Normalweight (carbonate or siliceous aggregate)

400

u

Sand-lightweight

9

10

400

3

4

5

b, in.

6

7

8

9

10

b, in. Stemmed units, 3 hours

Fig. 10.6.8 Temperatures on vertical centerline of stemmed units at 3 hours of exposure.

1500

1500

1300 Temperature, °F

  10

Temperature, °F

u = 11 2 in.

u = 1 1 2 in.

1300

u = 11 2 in.

u = 2 in. u = 2 in.

1100

1100 u = 3 in.

u = 3 in.

u = 4 in. u = 5 in.

900

u = 4 in.

900

u = 5 in.

u = 6 in. u = 10 in.

u = 10 in.

700

500

700 Normalweight (carbonate or siliceous aggregate) 3

4

5

6

7

8

•

b

u

Sand-lightweight 9

10

500 3

4

5

6

7

8

9

10

b, in.

b, in. Stemmed units, 4 hours

Fig. 10.6.9 Temperatures on vertical centerline of stemmed units at 4 hours of exposure.

10–16

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CHAPTER 10

EXAMPLE 10.6.3.1 Fire Endurance by Rational Design Given: The 12RB24 shown. Span = 30 ft Dead load (including beam weight) = 1.20 kip/ft Live load = 1.30 kip/ft

24"

Part of a precast concrete frame well-connected to meet lateral load and structural integrity requirements; therefore, consider the component restrained for fire endurance determination. Siliceous aggregate concrete, fc' = 5000 psi, normalweight Stress-relieved, 1/2-in.-diameter strand, fpu = 270 ksi Eight strands as shown provide a satisfactory design without fire considerations.

4"

2"

2"

8"

  10

2"

12"

Problem: Determine the necessary reinforcement for a 4-hour fire-endurance rating. The beam is subjected to fire from below. Solution: Since the component is considered restrained, use rational design procedures for unrestrained component at one-half the rating, that is, 2 hours. Try eight strands as shown: Aps = 8(0.153) = 1.224 in.2 ys =

5 (2 ) + 3 ( 4 ) = 2.75 in. 8

d = 24 – 2.75 = 21.25 in. u¯ =

5 (2 ) + 1( 4 ) + 2 ( 2 ) (0.5) = 2.00 in. 8

From Fig. 10.6.4, siliceous aggregate: at 2 hours, strand temperature = 750 °F From Fig. 10.6.2: fpuθ = 0.54(270) = 145.8 ksi From Fig. 5.2.2 with γp = 0.4, 1 = 0.8, ρp =

Aps , fpu = fpuθ, d = 21.25 in. bd

⎡ 0.4 (1.224 ) (145.8) ⎤ ⎡ γ A f ⎤ fpsθ = fpuθ ⎢1− p ps pu' θ ⎥ = 145.8 ⎢1− ⎥ = 135.6 ksi β1bdfc ⎦ ⎣ ⎣ 0.8 (12 ) (21.25 ) (5 ) ⎦

aθ =

Apsfpsθ 1.224 (135.6) = 3.25 in. = ' 0.85fc b 0.85 ( 5 ) (12 )

a ⎞ 3.25 ⎞ ⎛ ⎛ Mnθ = Apsfpsθ ⎜ d − θ ⎟ = 1.224 (135.6) ⎜ 21.25 − ⎟ = 3257 kip-in. = 271 kip-ft ⎝ ⎝ 2⎠ 2 ⎠

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CHAPTER 10

EXAMPLE 10.6.3.1 Fire Endurance by Rational Design (cont.) Service load moment (conservatively check condition as a simple span): w = 1.20 + 1.30 = 2.50 kip/ft 2 w  2 2.50 ( 30 ) M = = 281 kip-ft > 271 kip-ft = 8 8

  10

2"

Therefore, the beam will not satisfy criteria for a four-hour fire endurance. Try adding (2) #4 bars, fy = 60 ksi, at 6 in. from bottom as shown: As = 0.40 in.2; fy = 60 ksi d (bars) = 24 – 6 = 18 in. u (bars) = 2 in.

(2) #4 Grade 60

6"

From Fig. 10.6.4: Bar temperature at 2 hour = 750 °F From Fig. 10.6.2: fyθ = 0.77, fy = 46.2 ksi Reevaluate fpsθ considering the effect of bars: ⎧ ⎤⎫ ⎡ ⎛ 18 ⎞ ⎟⎠ ( 0.40 ) ( 46.2 ) ⎥ ⎪ ⎜⎝ ⎪⎪ ⎢ 145.8 1.224 ( ) ( ) 0.4 ⎪ 21.25 ⎞ fpsθ = 145.8 ⎨1− ⎛⎜ ⎥ ⎬ = 134.5 ksi + ⎟⎠ ⎢ ⎝ 12 21.25 5 12 18 5 0.8 ( ) ( ) ( ) ( ) ( ) ⎥ ⎢ ⎪ ⎪ ⎥⎦ ⎪ ⎢⎣ ⎪⎩ ⎭

aθ =

1.224 (134.5 ) + 0.40 ( 46.2 ) = 3.59 in. 0.85 ( 5 ) (12 )

3.59 ⎞ ⎛ Mnθ (strand) = 1.224 (134.5) ⎜ 21.25 − ⎟ = 3203 kip-in. = 267 kip-ft ⎝ 2 ⎠ 3.59 ⎞ ⎛ Mnθ (bars) = 0.40 ( 46.2 ) ⎜ 18 − ⎟ = 299 kip-in. = 25 kip-ft ⎝ 2 ⎠

Mnθ (total)

10–18

= 267 + 25 = 292 kip-ft > 281 kip-ft

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

Fire

Fire MnM +

M Mn+

At 0 hour Mnθ

X2

M +

+

Mnθ

X0

X1

At 2 hours

Fig. 10.6.10 Moment diagram for a two-span continuous beam.

10.7 Shear Resistance Many fire tests have been conducted on simply supported reinforced or prestressed concrete components, as well as on components in which restraint to thermal expansion has occurred. Shear failures did not occur in any of those tests. It should be noted that when beams that are continuous over one support are exposed to fire, both the moment and the shear at the interior support increase. Such a redistribution of moment and shear results in a severe stress condition. However, of the several fire tests of reinforced concrete beams in which this condition was simulated, shear failure occurred only in one beam.7 In that test, the design of the shear reinforcement was not adequate based on the requirements of ACI 318-05. Thus, it appears from available test data that components that are designed for shear strength in accordance with ACI 318-05 will perform satisfactorily in fire situations; that is, failure will not occur prematurely due to a shear failure.

10.8

Requirements for Parking Structures

The IBC specifies the requirements for the components within a parking structure as determined by the type of construction, a function of the area of the footprint, and the number of supported levels. Whether or not the structure is to have an automated sprinkler system influences the allowable number of supported levels. Parking decks are classified as either open or enclosed, the amount of open space within the perimeter vertical surfaces being the determinant, and the

CHAPTER 10

amount of openness impacting the parameters of area and height restrictions. Once the deck has been classified as either open or enclosed and it is known whether it will have a sprinkler system, the type of construction is identified based on the area and height restrictions shown in tabular form within the code (amended by allowance easements based on the number of open sides and the degree of openness). In the situation where the structure contains both parking and other uses, such as office, retail, or commercial, Chapter 5 of IBC outlines the specific requirements for the required separation between the occupancies, thereby allowing each portion of the building to be constructed to the classification requirements of its specific utilization. Chapter 6 of IBC contains in tabular form (Table 601) the component requirements for the various building classification types. In common precast concrete parking deck construction, beams, columns, and walls will typically be found to meet at least a 3-hour fire endurance rating. Floor components, which typically require a more thorough review, may be required to be designed to provide zero, one-, or two-hour fire-resistance. The structural integrity of a floor component during a fire can be determined by one of two methods: rational design methodology (see Section 10.6) or by the amount of cover on the primary tensile reinforcing, determined by the type of aggregate within the concrete and whether the element is restrained or unrestrained (Table 10.8.1 through 10.8.5). For the prescriptive approach, the cover for a prestressed stemmed component is determined as the distance from the bottom of the stem to the centroid of the strands, with the stipulation that the actual cover on any single strand be not less than the smaller of one-half of the value shown in the table or 1 in. It can be shown that the typical double- tee used for parking decks (reference Chapter 3 for cross sections) provides the required resistance for up to two hours based on cover alone (Example 10.8.1). In general building construction, other considerations for fire resistance are heat transmission and flame passage through the horizontal floor system. Both end point criteria are defined in ASTM E119. Due to the physical characteristics of a parking structure, however, these criteria are generally deemed not applicable to this type of construction. The vast open space on and between floor levels makes compartmentilization of a fire virtually a non-issue, since heat and smoke transmission throughout the building is uninhibited. Further, in the interior of many parking decks, ramp or lite walls provide support for the floor system. These are wall components with large openings to allow for greatly enhanced lighting and, therefore, security for the user. In effect, between the ends of adjoining bays, vertical air shafts are created in the gap between the ends of the double-tees, roughly equal to the thickness of the supporting wall times the distance between stems, less the width of the supporting wall column section. If floor openings such as these are not required to be enclosed, it is illogical to require either of the end point criteria discussed previously in the determination of fire resistance; that is generally the basis of their being waived. The code specifically recognizes this in allowing

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an exception for fire-resistant joint systems in open parking structures (Section 713.1 of IBC 2006). Research was performed to evaluate realistic vehicle fire loads (time-temperature or time-heat flux relationships) for precast concrete parking structures, and to investigate the influence of structure geometry and fire characteristics on the resulting fire loading.15,16 A typical precast concrete parking structure was analyzed for a series of vehicle fires, and the resulting fire loads at various points in the structure were determined. Fire analyses were run on nine simplified parking garage models. Seven analyses were single-vehicle fires, and two analyses were sequential, multiple-vehicle fires. Analyses were performed using the Fire Dynamics Simulator

  10

(FDS), a computational fluid dynamics computer program. Heat flux time-histories from the FDS analyses were used as input to subsequent heat-transfer finite element analyses to determine the temperature rise in the prestressing strand of the double-tee floor components. Results show that the highest steel temperature reached in any of the analyses occurred in analysis 9, which involved a multiple-vehicle fire confined to one floor of the parking structure. In this analysis, the peak gas temperature and peak heat flux at a given double-tee location were similar to a single-vehicle fire, but because more than one vehicle was burned, the duration of the thermal input to any location was longer than for a singlevehicle fire. Using the equations for reduction in strength in

Table 10.8.1  Cover thickness for reinforced concrete floor or roof slabs, in.a Concrete aggregate type

Fire-resistance rating, hour Restrained 1

Siliceous

3

Carbonate

3

Sandlightweight or lightweight

3

1 /2

Unrestrained

1

2

3

4

1

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

1

1 /2

2

3

4

/4

1

11/4

15/8

/4

11/4

11/4

/4

11/4

11/4

/4

3

/4

3

/4

3

/4

3

/4

3

Table 10.8.2  Cover thickness for prestressed concrete floor or roof slabs, in.a Concrete aggregate type

Fire-resistance rating, hour Restrained 1

Siliceous

3

Carbonate

3

Sandlightweight or lightweight

3

1 /2

Unrestrained

1

2

3

4

/4

3

/4

3

/4

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

/4

3

1

1

1 /2

2

3

4

11/8

11/2

13/4

23/4

23/4

/4

1

13/8

15/8

21/8

21/4

/4

1

13/8

11/2

2

21/4

Table 10.8.3  Minimum cover for main reinforcing bars of reinforced concrete beamsb (applicable to all types of structural concrete), in.a Restrained or unrestrainedc

Beam width,d in.

Restrained

5 7 ≥10

Unrestrained

5 7 ≥10

Fire-resistance rating, hour 1

1 /2

2

3

4

/4 /4 3 /4

1c 3 /4 3 /4

11/4c 3 /4 3 /4

11/4 3 /4 3 /4

 —   13/4  1

 —  3 13/4

1

/4 /4 3 /4

3

3

3

3

3

/4 /4 3 /4

1 /4 3 /4

3

3

3

/4 /4 3 /4 3

a. Cover is measured to the main flexural reinforcement. b. The cover for an individual reinforcing bar is the minimum thickness of concrete between the surface of the bar and the fire-exposed surface of the beam. For beams in which several bars are used, the cover for corner bars used in the calculation shall be reduced to one-half of the actual value. The cover for an individual bar must be not less than one-half of the value given in Table 10.6.1(3) nor less than 3/4 in. c. Tabulated values for restrained assemblies apply to beams spaced more than 4 ft on centers. For restrained beams spaced 4 ft or less on centers, minimum cover of 3/4 in. is adequate for ratings of 4 hours or less. d. For beam widths between the tabulated values, the minimum cover thickness can be determined by direct interpolation.

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Table 10.8.4  Minimum cover for prestressed concrete beams 8 in. or greater in width, in.a Restrained or unrestrainedb

Restrained

Unrestrained

Fire-resistance rating, hour

Concrete aggregate type

Beam width,c in.

1

11/2

2

3

4

Carbonate or siliceous

8

11/2

11/2

11/2

13/4b

21/2b

Carbonate or siliceous

≥12

11/2

11/2

11/2

11 /2

17/8b

Sand-lightweight

8

11/2

11/2

11/2

11 /2

2b

Sand-lightweight

≥12

11/2

11/2

11/2

11 /2

15/8b

Carbonate or siliceous

8

11/2

13/4

21/2

5d

 — 

Carbonate or siliceous

≥12

1

1 /2

1

1 /2

7

1 /8

1

2 /2

3

Sand-lightweight

8

1

1 /2

1

1 /2

2

1

3 /4

 — 

Sand-lightweight

≥12

11/2

11/2

15/8

2

21/2

a. Cover is measured to the main flexural reinforcement. b. Tabulated values for restrained assemblies apply to beams spaced more than 4 ft on centers. For restrained beams spaced 4 ft or less on centers, minimum cover of 3/4 in. is adequate for ratings of 4 hours or less. c. For beam widths between 8 in. and 12 in., minimum cover thickness can be determined by direct interpolation. d. Not practical for 8 in. wide beam but shown for purposes of interpolation.

Table 10.8.5  Minimum cover for prestressed concrete beams of all widths, in.a Restrained or unrestrainedb

Restrained

Unrestrained

Concrete aggregate type

Beam area A, in.c

All

Fire-resistance rating, hour 1

1½

2

3

4

40 ≤ A ≤ 150

1

1 /2

1

1 /2

2

1

2 /2

 — 

Carbonate or siliceous

150 < A ≤ 300

1

1 /2

1

1 /2

1

1 /2

3

1 /4

21/2

300 < A

11/2

11/2

11/2

11 /2

2

Sand-lightweight

150 < A

11/2

11/2

11/2

11 /2

2

All

40 ≤ A ≤ 150

2

21/2

 — 

 — 

 — 

Carbonate or siliceous

150 < A ≤ 300

1

1 /2

3

1 /4

1

2 /2

 — 

 — 

300 < A

1

1 /2

1

1 /2

2

3d

4d

Sand-lightweight

150 < A

11/2

11/2

2

3d

4d

a. Cover is measured to the main flexural reinforcement. b. Tabulated values for restrained assemblies apply to beams spaced more than 4 ft on centers. For restrained beams spaced 4 ft or less on centers, minimum cover of 3/4 in. is adequate for ratings of 4 hours or less. c. The cross-sectional area of a stem is permitted to include a portion of the area in the flange, provided the width of flange used in the calculation does not exceed three times the average width of the stem. d. U-shaped or hooped stirrups spaced not to exceed the depth of the components and having a minimum cover of 1 in. shall be provided.

prestressing steel as a function of temperature, the impact of the fire loading was evaluated. The maximum temperature reached in the concrete at the level of the prestressing steel corresponded to a strength reduction in the prestressing steel of about 20%. For all of the single-vehicle fire analyses, the concrete temperature at the level of the strand is much lower, with a maximum temperature corresponding to about an 8% reduction in prestressing steel strength.

10.9

Protection of Connections

Many types of connections in precast concrete construction are not vulnerable to the effects of fire, and consequently require no special treatment. For example, connections such as the bearing between precast concrete panels and concrete

footings or beams that support them do not generally require special fire protection. If the panels rest on elastomeric bearing pads or other combustible materials, protection of the pads is not generally needed because deterioration of the pads will not cause collapse. Connections that can be weakened by fire and jeopardize the structure’s load-carrying capacity should be protected to the same degree as that required for the supported component. For example, an exposed steel bracket supporting a panel or spandrel beam will be weakened by fire and might fail causing the panel or beam to collapse. Such a bracket should be protected. The amount of protection depends on the stress-strength ratio in the steel at the time of the fire and the intensity and duration of the fire. The thickness of protection materials

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CHAPTER 10

DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE

EXAMPLE 10.8.1 Fire Endurance by Code Tables Problem: Determine if the 10DT24+3 (stem as shown) meets a 2-hour restrained fire rating. Strands are 1/2 in. diameter. Both double-tee and topping are of siliceous aggregate. Solution:

  10

Reinforcement cover: Refer to Table 10.8.5. See footnote c for flange width allowed to be included in beam area. Average stem width = (3.75 + 5.75)/2 = 4.75 in. Flange width to be considered = 3(4.75) = 14.25 in. A = 22(4.75) + 14.25(5) = 175.75 in.2 Therefore, 150 < A < 300 From the table, required strand cover = 11/2 in. from bottom of stem to centroid of the strand.

b (effective) = 14.25" 53 4 " 3" 2"

22"

Center of gravity of strand 312 "

2" 33 4 "

Cover provided = 3.5 in., which is greater than 1.5 in.; therefore, Minimum cover provided on any individual strand = [3.75 + (2/22)(5.75 – 3.75) – 0.5]/2 = 1.71 in. 1.71 in. is greater than 1 in. (minimum required by IBC) or 1.5/2 = 0.75 in., therefore,

OK OK

Heat transfer: Per Fig. 10.5.1, slab thickness required = 5.0 in. Slab thickness provided = 2 + 3 = 5 in.

required is greater as the stress level and fire severity increase. Figure 10.9.1 shows the thickness of various commonly used fire-protection materials required for fire endurances up to 4 hours. The values shown are based on a critical steel temperature of 1000 °F, that is, a stress-strength ratio (fs /fy) of about 65%. Values in Fig. 10.9.1(b) are applicable to concrete or dry-pack mortar encasement of structural steel shapes used as brackets or lintels.

10.10

Precast Concrete Column Covers

Steel columns are often clad with precast concrete panels or covers for architectural reasons. Such covers also provide fire protection for the columns. Figure 10.10.1 shows the relationship between the thickness of concrete column covers and fire endurance for various steel column sections. The fire endurances shown are based on an empirical relationship developed by Lie and Harmathy.17 These authors also found that the air space between the steel core and the column covers has only a minor effect on the fire endurance. An air space will probably increase the fire endurance but only by an insignificant amount. Most precast concrete column covers are 3 in. or more in 10–22

OK

thickness, but some are as thin as 21/2 in. From Fig. 10.10.1, it can be seen that they can qualify the column for fire endurances of at least 21/2 hours, and usually more than 3 hours. For steel column sections other than those shown, including shapes other than wide flange sections, interpolation between the curves on the basis of weight per foot will generally give reasonable results. For example, the fire endurance afforded by a 3-in.-thick column cover of normalweight concrete for an 8 × 8 × 1/2 in. steel-tube column, section weight 47.35 lb/ft, can be determined by using the data for a W10×49. By Fig. 10.10.1, the fire endurance is about 3 hours 20 minutes. Precast concrete column covers (Fig. 10.10.2) are made in various shapes, such as (a) four flat panels with butt or mitered joints that fit together to enclose the steel column, (b) four L-shaped units, (c) two L-shaped units, (d) two U-shaped units, and (e and f) U-shaped units and flat closure panels. The flat panels with butt or mitered joints would probably be the most vulnerable to bowing during fire exposure while the flat closure panels would probably be the least vulnerable. There are, of course, many combinations to accommodate isolated columns, corner columns, and column walls. To be fully effective, the column covers must remain in place without severe distortion. Many types of connections

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t = 5 16 in.

3

SMF or VCM

2

SMF

IM

t = minimum thickness of steel subjected to fire from both sides

t = 5 16 in. 1

4

VCM

t = 1116 in.

0

3 b

2

1

4

1 2 3 Thickness, protection material, in.

b = 8 in.

b > 12 in.

Fire endurance, hour

Fire endurance, hour

4

CHAPTER 10

(a)

0

Concrete or dry-pack mortar b = minimum width of concrete protection 1 2 3 Thickness, protection material, in. (actual cover to steel) (b)

  10

4

Fig. 10.9.1 Thickness of protection materials applied to connections of structural steel shapes. Note: IM = intumescent mastic; SMF = sprayed mineral fiber; VCM = vermiculite cementitious material.

are used to hold the column covers in place. Some connections consist of bolted or welded clip angles attached to the tops and bottoms of the covers. Others consist of steel plates embedded in the covers that are welded to angles, plates, or other shapes, which are, in turn, welded or bolted to the steel column. In any case, the connections are used primarily to position the column covers and are not highly stressed. As a result, temperature limits need not be applied to the steel in 5

5 W14 x 320

4 Fire endurance, hour

most column cover connections. If restrained, either partially or fully, concrete panels tend to deflect or bow when exposed to fire. For example, for a steel column that is clad with four flat panels attached top and bottom, the column covers will tend to bulge at midheight, thus tending to open gaps along the sides. The gap size decreases as the panel thickness increases. With L-, C-, or U-shaped panels, the gap size is further

W14 x 320

4

W10 x 112

W10 x 112

3

3 W8 x 31

W8 x 31

W10 x 49

2

W10 x 49

2

t ESTCODE

1

0

1 Normalweight concrete (carbonate or siliceous aggregate) 0

1

2

(a)

3

Sand-lightweight concrete 4

0

0

1

t, thickness of column cover, in. (actual cover to steel)

2

3

4

(b)

Fig. 10.10.1 Fire endurance of steel columns afforded protection by concrete column covers. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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CHAPTER 10

DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE ment, a life-cycle cost analysis using fire resistive construction should be prepared. Beyond the theoretical considerations is the history of excellent performance of precast/prestressed concrete in fires. Structural integrity has been maintained, fires are contained in the area of origin, and, in many instances, repairs consist of cosmetic treatment only, leading to early re-occupancy of the structure.

10.12

References

1. A  merican Society for Testing and Materials (ASTM). 2000. Standard Test Methods for Fire Tests of Building Construction and Materials, ASTM E119-00. West Conshohocken, PA: ASTM.

  10

2. A  STM. 2008. Standard Terminology for Fire Standards (ASTM E176-08). West Conshohocken, PA: ASTM.

Fig. 10.10.2 Types of precast concrete column covers.

reduced. The gap size can be further minimized by connections at mid-height. In some cases, ship-lap joints can be used to minimize the effects of joint openings. Joints should be sealed in such a way to prevent passage of flame to the steel column. A non-combustible material such as sand-cement mortar or ceramic fiber blanket can be used to seal the joint. Precast concrete column covers should be installed in such a manner that, if they are exposed to fire, they will not be restrained vertically. As the covers are heated, they tend to expand. Connections should accommodate such expansion without subjecting the cover to additional loads. Fire-resistive compressible materials, such as mineral fiber safing, can be used to seal the tops or bases of the column covers, thus permitting the column covers to expand.

10.11

Code and Economic Considerations

An important aspect of dealing with fire resistance is to understand what the benefits are to the owner of a building in the proper selection of materials incorporated in a structure. These benefits fall into two areas: codes and economics. Building codes are laws that must be satisfied regardless of any other considerations. The designer or representative of the owner has no option in the code regulations, but he or she does have a number of options in the materials and assemblies that meet these regulations, such as those included in this handbook. Economic benefits associated with increased fire resistance should be considered by the designer/owner team at the time the decisions are made on the structural system. Proper consideration of fire-resistive construction through a life-cycle cost analysis will provide the owner with economic benefits over other types of construction in many areas, such as lower insurance costs, larger allowable gross area under certain types of construction, fewer stairwells and exits, increased value for loan purposes, longer mortgage terms, and better resale value. To assure an owner of the best return on his/her invest10–24

3. P  recast/Prestressed Concrete Institute (PCI). 1989. Design for Fire Resistance of Precast Prestressed Concrete, second edition (MNL-124-89). Chicago, IL: PCI. 4. C  oncrete Reinforcing Steel Institute (CRSI). 1980. Reinforced Concrete Fire Resistance. Schaumburg, IL: CRSI. 5. S  hirley, Scott T., Ronald G. Burg, and Anthony E. Fiorato. 1988. Fire Endurance of High Strength Concrete Slabs. ACI Materials Journal, V. 85, No. 2, MarchApril. 6. I nternational Conference of Building Officials (ICBO). 1999. Fire-Resistive Workbook: A Design Guide to the Fire-Resistive Provisions of the Uniform Building Code. Washington, DC: ICBO. 7. A  CI Committee 318. 2005. Building Code Requirements for Reinforced Concrete (ACI 318-05) and Commentary (ACI 318R-05). Farmington Hills, MI: American Concrete Institute. 8. A  brams, M. S., A. H. Gustaferro, and E. A. B. Salse. 1971. Fire Tests of Concrete Joist Floors and Roofs, RD Bulletin 006B. Skokie, IL: Portland Cement Association (PCA). 9. A  brams, M. S., A. H. Gustaferro, and T. D. Lin. Fire Endurance of Continuous Reinforced Concrete Beams, RD Bulletin 072B. Skokie, IL: Portland Cement Association. 10. U  nderwriters Laboratories Inc. 1973. Report on Floor and Ceiling Assembly Consisting of Prestressed, Precast Concrete Double Tee Units with a Wallboard Ceiling, File R1319-131. Northbrook, IL: Underwriters Laboratories Inc. 11. I nternational Code Council. 2006. International Building Code (IBC 2006). Falls Church, VA: ICC. 11.

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CHAPTER 10

12. A  brams, M. S., and A. H. Gustaferro. 1969. Fire Endurance of Two-Course Floors and Roof. Journal of the American Concrete Institute, V. 66, No. 2: February. 13. L  ie, T. T. Contribution of Insulation in Cavity Walls to Propagation of Fire, Fire Study No. 29. Ottawa, Ontario, Canada: National Research Council of Canada. 14. G  ustaferro, A. H., and M. S. Abrams. 1975. Fire Tests of Joints between Precast Concrete Wall Panels: Effect of Various Joint Treatments. PCI Journal, V. 20, No. 5 (September–October). 15. B  ayreuther, J. L., and S. Pessiki. 2006. Analytical Investigation of Fire Loads for Precast Concrete Parking Structures, ATLSS Report No. 06-19. Bethlehem, PA: Center for Advanced Technology for Large Structural Systems (ATLSS).

  10

16. S  trenchock, K., and S. Pessiki, S. 2008. Multiple-Vehicle Fire Loads for Precast Concrete Parking Structures, ATLSS Report No. 08-03. Bethlehem, PA: ATLSS. 17. L  ie, T. T., and T. Z. Harmathy. 1974. Fire Endurance of Concrete-Protected Steel Columns. Journal of the American Concrete Institute, V. 71, No. 1: January 1974.

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DESIGN FOR FIRE RESISTANCE OF PRECAST AND PRESTRESSED CONCRETE

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CHAPTER 11

CHAPTER 11 THERMAL AND ACOUSTICAL PROPERTIES OF PRECAST CONCRETE 11.1

Thermal Properties of Precast Concrete....................................................................................................................11-2 11.1.1 Definitions...................................................................................................................................................11-2 11.1.2 General........................................................................................................................................................11-3 11.1.3 Thermal Properties of Materials, Surfaces, and Air Spaces.......................................................................11-3 11.1.4 Computation of Thermal Transmittance Values.........................................................................................11-3 11.1.5 Thermal Storage (Mass) Effects...............................................................................................................11-11 11.1.6 Thermal Bridges........................................................................................................................................11-15 11.1.7 Condensation Control...............................................................................................................................11-18 11.1.7.1 Air Barriers..............................................................................................................................11-19 11.1.7.2 Vapor Retarders.......................................................................................................................11-20 11.1.7.3 Prevention of Condensation on Wall Surfaces........................................................................11-22 11.1.7.4 Condensation Prevention within Wall Construction...............................................................11-22

11.2 Acoustical Properties of Precast Concrete....................................................................................................................11-23 11.2.1 Definitions.................................................................................................................................................11-23 11.2.2 General......................................................................................................................................................11-23 11.2.3 Dealing with Sound Levels.......................................................................................................................11-23 11.2.4 Sound Transmission Loss.........................................................................................................................11-23 11.2.5 Impact Noise Reduction............................................................................................................................11-23 11.2.6 Establishment of Noise Insulation Objectives..........................................................................................11-24 11.2.7 Composite Wall Considerations................................................................................................................11-24 11.2.8 Leaks and Flanking...................................................................................................................................11-24 11.2.9 Acoustical Test Results.............................................................................................................................11-24 11.3 References.................................................................................................................................................................... 11-26

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CHAPTER 11

  11

11.1

 hermal Properties of Precast T Concrete

11.1.1

Definitions

THERMAL AND ACOUSTICAL PROPERTIES OF PRECAST CONCRETE

Affected zone.  Area around a concrete thermal bridge in an insulated panel, which is larger than the bridge, that affects the R-value of the panel. British thermal unit (Btu).  The amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit. Building envelope.  The exterior plus semi-exterior portions of a building that separate conditioned space from unconditioned space. Degree day.  The difference in temperature between the outdoor mean temperature over a 24-hour period and a given base temperature. For the purposes of determining building envelope requirements, the classifications are defined as follows: (a) Cooling degree-day base 50 °F (CDD50): for any one day, when the mean temperature is more than 50 °F, there are as many degree days as degrees Fahrenheit temperature difference between the mean temperature for the day and 50 °F. Annual cooling degree days (CDDs) are the sum of the degree days over a calendar year. (b) H  eating degree-day base 65 °F (HDD65): for any one day, when the mean temperature is less than 65 °F, there are as many degree days as degrees Fahrenheit temperature difference between the mean temperature for the day and 65 °F. Annual heating degree days (HDDs) are the sum of the degree days over a calendar year. Dew-point temperature (ts).  The temperature at which condensation of water vapor begins for a given humidity and pressure as the vapor temperature is reduced. The temperature corresponding to saturation (100% RH) for a given absolute humidity at constant pressure. Film or surface conductance (f).  The time rate of heat exchange by radiation, conduction, and convection of a unit area of a surface with its surroundings. Its value is usually expressed in Btu/[(hr)(ft2 of surface area)(°F temperature difference)]. Subscripts i and o are usually used to denote inside and outside surface conductances, respectively. Free heat.  Heat generated inside a building as a byproduct of other systems such as lights, equipment, appliances, and people. Heat capacity (Hc).  The amount of heat required to raise the temperature of a given mass one degree Fahrenheit. Numerically, Hc is the mass multiplied by the specific heat. For a wall assembly, Hc is the sum of the products of the mass per unit area of each individual material in the assembly multiplied by its individual specific heat. Heat transmittance (U).  U-factor (thermal transmittance) is the heat transmission in unit time through unit area of a material or construction and the boundary air films, induced by unit temperature difference between the environments on each side. Units of U are (BTU per hr)(ft2 of surface 11–2

area)(°F temperature difference). Perm.  A unit of permeance. A perm is 1 grain per ft2 of area(hr)(in. of Hg vapor pressure difference). Permeability, water vapor (µ).  The rate of water vapor transmission by diffusion per unit area of flat material of unit thickness induced by unit vapor pressure difference between two surfaces, under specified temperature and humidity conditions. Permeance (M).  The rate of water vapor transmission by diffusion per unit area of a body between two specified parallel surfaces, induced by unit vapor pressure difference between the two surfaces, (grain/H × ft2 )(in. Hg) or perm. Relative humidity (RH).  The ratio of the water vapor present in air to the water vapor present in saturated air at the same temperature and pressure. Thermal conductance (C).  The time rate of heat flow expressed in Btu/[(hr)(ft2 of area)(°F average temperature difference between two surfaces)]. The term is applied to specific materials as used, either homogeneous or heterogeneous for the thickness of construction stated, not per inch of thickness. Thermal conductance of an air space (a).  The time rate of heat flow through a unit area of an air space per unit temperature difference between the boundary surfaces. Its value is usually expressed in Btu/[(hr)(ft2 of area)(°F)]. Thermal conductivity (k).  The time rate of heat flow by conduction only through a unit thickness of a homogeneous material under steady-state conditions per unit area per unit temperature gradient in the direction perpendicular to the isothermal surface. Its unit is (Btu-in.)/[(hr)(ft2 of area)(°F)]. Thermal inertia.  The resistance to raising or lowering the temperature of a body. Thermal mass.  Characteristic of materials with mass heat capacity and surface area capable of affecting building heating and cooling loads by storing and releasing heat as the interior and/or exterior temperature and radiant conditions fluctuate. Thermal resistance (R).  The reciprocal of a heat transmission coefficient, as expressed by U, C, f, or a. Its unit is (°F)(hr)(ft2 of area) per Btu. For example, a wall with a U-value of 0.25 would have a resistance value of R = 1/U = 1/0.25 = 4.0.

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General

Energy conservation codes and standards specify the heat transmission requirements for buildings in many different ways. Prescriptive standards specify U- or R-values for each building component, whereas with performance standards, an energy budget for a given building is defined. The designer then has latitude to design a building that meets the prescribed budget, regardless of the U- or R-values of the components. This allows the designer to choose conservation strategies that provide the required performance at the least cost. In ANSI/ASHRAE/IESNA Standard 90.1-2004, Energy Standard for Buildings Except Low-Rise Residential Buildings (ASHRAE 90.1)1, Section 5 specifies requirements for the building envelope as a whole. Section 5.4 states that “where insulation is required in [Sections] 5.5 or 5.6, it shall comply with requirements found in 5.8.1.1 through 5.8.1.9.” Section 5.5 provides for a “Prescriptive Building Envelope Option” while Section 5.6 provides for a “Building Envelope Trade-Off Option” to establish insulation properties of materials used to make up the building envelope. See Reference 1 for more detail. Thermally efficient building envelope systems are a combination of many things. To take advantage of thermal mass effects offered by precast concrete construction, the design team (architect, structural and mechanical engineers, contractor, precast concrete manufacturer, door and glazing contractor, roofing contractor, and others) must first provide a quality design that includes both specifications and details to achieve both a thermal envelope and vapor envelope specific to the site’s climatic conditions. All special conditions must have details to maintain the thermal integrity of the building envelope. Procedures should be in place to monitor the construction to ensure that the design is properly implemented. As energy costs continue to escalate, energy-efficient design becomes more economically attractive by reducing a structure’s long-term energy consumption and, therefore, annual operational costs. Higher energy costs will ultimately translate into greater energy and cost savings when using the mass effects of precast concrete. Even greater savings can be potentially realized by using insulated precast concrete walls and cladding. Precast and prestressed concrete, with its high thermal mass, has an advantage over lighter weight materials. Information related to the benefits of heavier materials is presented in ASHRAE 90.1. ASHRAE 90.1 establishes minimum standards for energy efficiency in buildings. Achieving truly energy-efficient building design requires consideration of not only greater levels of insulation, but all aspects of building design, including material selection and equipment efficiencies. Thermal mass, glass area, air infiltration, ventilation, building orientation, exterior color, shading or reflections from adjacent structures, surrounding surfaces or vegetation, building aspect ratio, number of stories, wind direction, and wind speed all have an effect on a building’s energy efficiency. This section is condensed from a more complete treatment given in Reference 1. Except where noted, the information and design criteria are taken or derived from the ASHRAE Handbook­—Fundamentals2 and from ASHRAE 90.1. All

CHAPTER 11

design criteria are not given in this section, and may change as ASHRAE 90.1 and the ASHRAE Handbook—Fundamentals are revised. Local codes and latest references must be used for specified values and procedures. 11.1.3

 hermal Properties of Materials, T Surfaces, and Air Spaces

The thermal properties of materials and air spaces are based on steady-state tests, which measure the heat that passes from the warm side to the cool side of the test specimen. The tests, usually ASTM C1773 and ASTM C1363,4 determine the conductivity k, or for non-homogeneous sections, compound sections, and air spaces, the conductance C, for the total thickness. The values of k and C do not include surface conductances fi and fo. The overall thermal resistance of wall, floor, and roof sections is the sum of the resistances R (reciprocal of k, C, fi, and fo). The R-values of construction materials are not influenced by the direction of heat flow, but the R-values of surfaces and air spaces differ depending on whether they are vertical, sloping, or horizontal. The R-values of surfaces are also affected by air velocity at the surfaces and by their reflective properties. Tables 11.1.1 and 11.1.2 give the thermal resistances of surfaces and surfaces with a 31/2-in.-thick air space, respectively. Table 11.1.3 gives the thermal properties of most commonly used building materials. Only U-values are given for glass because the surface resistances and air space between panes account for nearly all of the U-value. Table 11.1.4 gives the thermal properties of various density concretes and some standard precast/prestressed concrete products in the normally dry condition. The normally dry condition occurs when concrete contains an equal amount of free water after extended exposure to warm air at 35 to 50% relative humidity (RH). Thermal conductances and resistances of other building materials are usually reported for oven-dry conditions. Normally dry concrete in combination with insulation generally provides about the same R-value as equally insulated, oven-dry concrete, but because of the moisture content, it has the ability to store a greater amount of heat than oven-dry concrete. However, higher moisture content in concrete causes higher thermal conductance. 11.1.4

 omputation of Thermal Transmittance C Values

The heat transmittance (U-values) of a building wall, floor, or roof is computed by adding together the R-values of the materials in the section, the surfaces (Rfi and Rfo), and air spaces (Ra) within the section. The reciprocal of the sum of the R values is the U values defined by the following relationship: U=

1 R fi + Rmaterials + Ra + R fo

(Eq. 11-1) where: Rmaterials = sum of all opaque materials in the wall. A number of typical wall and roof U-values are given in Tables 11.1.5, 11.1.6, and 11.1.7. Examples 11.1.4.1 and 11.1.4.2 show the use of Tables 11.1.1 through 11.1.4 in calculating R- and U-values for wall and roof assemblies.

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  11

THERMAL AND ACOUSTICAL PROPERTIES OF PRECAST CONCRETE

CHAPTER 11

EXAMPLE 11.1.4.1 Thermal Resistance of Wall

EXAMPLE 11.1.4.2 Thermal Resistance of Roof

  11 Given: The roof section shown. There are no thermal bridges.

Given: The insulated wall section shown.

Problem: Determine U-values and R-values.

There are no thermal bridges. Problem: Determine R-values and U-values.

Solution:

Solution: R

R

Reference

winter

summer

A. Surface, outside

0.17

0.25

11.1.1

B. Concrete, 2 in. (110 lb/ft3)

0.38

0.38

11.1.4

C. E  xtruded polystyrene, 1.5 in.

7.50

D. Concrete, 2.5 in. (110 lb/ft3)

0.48

0.48

11.1.4

E. Surface, inside

0.68

0.68

11.1.1

Total R =

9.21

9.29

U = 1/R =

0.109

0.108

11–4

7.50

Table

11.1.3

R

R

Reference

winter

summer

A. S  urface, outside

Table

0.17

0.25

11.1.1

B. Roofing built-up

0.33

0.33

11.1.3

C. E  xpanded polystyrene, 2 in.

7.3a

7.3a

11.1.3

D. Concrete, 2 in. (145 lb/ft3)

0.15

0.15

11.1.4

E. Surface, inside

0.61

0.92

11.1.1

Total R =

8.56

8.95

U = 1/R =

0.117

0.112

a. Average.

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Table 11.1.1  Thermal resistances Rf of surfaces Still air, Rfi Position of surface

Direction of heat flow

Vertical

Horizontal

Moving air, Rfo

Reflective surface

Non-reflective surface

Non-reflective surface

Aluminumpainted paper

Bright aluminum foil

15 mph winter design

71/2 mph summer design

Horizontal

0.68

1.35

1.70

0.17

0.25

Up (winter)

0.61

1.10

1.32

0.17

0.25

Down (summer)

0.92

2.70

4.55

0.17

0.25

  11

Table 11.1.2  Thermal resistances Ra of air spacesa

Position of air space

Direction of heat flow

Air space Mean temperature, °F

Reflective surface

Temperature difference, °F

Nonreflective surfaces

One sideb

One sidec

Both sidesc

Winter Horizontal (walls)

50 50

10 30

1.01 0.91

2.32 1.89

3.40 2.55

3.69 2.67

10

0.85

2.15

3.40

3.69

Vertical Summer Horizontal (walls)

90

Winter

Horizontal

Up (roofs)

50 50

10 30

0.93 0.84

1.95 1.58

2.66 2.01

2.80 2.09

Down (floors)

50

30

1.22

3.86

8.17

9.60

10

1.00

3.41

8.19

10.07

Summer Down (roofs)

90

a. For 31/2-in.-thick air space. The values, with the exception of those for reflective surfaces, heat flow down, will differ about 10% for air-space thickness of 3/4 in. Refer to ASHRAE Handbook—Fundamentals2 for values of other thicknesses, reflective surfaces, heat flow down. b. Aluminum-painted paper. c. Bright aluminum foil.

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CHAPTER 11

Table 11.1.3  Thermal properties of various building materialsa,b

Material

Insulation, rigid Cellular glass

Resistance, R Per inch of thickness, 1/k

For thickness shown, 1/C

Transmittance, U

Specific heat, Btu/(lb)(°F)

8.5

2.86

0.18

4 – 9

4.00

0.23

15

3.45

0.17

Mineral fiberboard, wet felted, roof   insulation

16 – 17

2.94

 — 

Cement fiber slabs (shredded wood with magnesia oxysulfide binder)

22

1.75

0.31

Extruded polystyrene smooth-skin   surface

1.3 – 3.5

5.00

0.29

Expanded polystyrene molded bead

0.7 – 1.8

3.1 – 4.2

 — 

1.5

5.5 – 6.3

0.38

18

2.86

0.19

Glass fiber, organic-bonded Mineral fiber, resin binder

  11

Density, lb/ft3

Polyisocyanurate Miscellaneous Acoustical tile (mineral fiberboard,   wet felted) Carpet, fiberous pad

2.08

0.34

Carpet, rubber pad

1.23

0.33

0.05

0.30

Floor tile, asphalt, rubber, vinyl c

Gypsum board

50

0.88

0.26

Particle board

50

1.06

0.31

Plaster   cement, sand aggregate   gypsum, lightweight aggregate   gypsum, sand aggregate

116 45 105

0.20 0.63c 0.18

0.20  —  0.20

Roofing, 3/8 in. built-up

70

0.33

0.35

Wood, hard

38 – 47

0.94 – 0.80

0.39

Wood, soft

24 – 41

1.00 – 0.89

0.33

34

1.25

0.29

Plywood Glass doors and windowsd Single, winter Single, summer Double, wintere Double, summere

1.11 1.04 0.50 0.61

Doors, metalf Insulated

0.40

a. See Table 11.1.4 for all concretes, including insulating concrete for roof fill. b. See manufacturer’s data for specific values. c. Average value. d. Does not include correction for sash resistance. Refer to ASHRAE Handbook—Fundamentals2 for sash correction. e. 1/4-in.-thick air space; coating on either glass surface facing air space. f. Urethane foam core without thermal break.

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THERMAL AND ACOUSTICAL PROPERTIES OF PRECAST CONCRETE

CHAPTER 11

11.1.4  Thermal properties of concretea Table

Description

Concretec

Concrete density, lb/ft3

Resistance, R Thickness, in.

Per inch of thickness, 1/k

For thickness shown, 1/C

0.10 – 0.05 0.18 – 0.09 0.27 – 0.17 0.40 – 0.29 0.63 – 0.56 1.08 – 0.90 1.33 – 1.10 1.59 – 1.20

140 120 100 80 60 40 30 20

Specific heat,b Btu/(lb)(°F) 0.22 0.21

0.21

Normalweight teesd and solid slabs

145

2 3 4 5 6 8

0.15 0.23 0.30 0.38 0.45 0.60

0.21

Normalweight hollow-coree

145

6 8 10 12

1.07 1.34 1.73 1.91

0.21

Structural lightweight teesd and solid slabs

110

2 3 4 5 6 8

0.38 0.57 0.76 0.95 1.14 1.52

0.21

Structural lightweight hollow-core

110

8 12

2.00 2.59

0.21

  11

a. Based on normally dry concrete (see Chapter 4 of Reference 5). b. The specific heats shown are from Table 4.1 of ACI 122R-02.6 c. Includes normalweight, lightweight, and lightweight insulation concretes. d. Thickness for tees is thickness of slab portion including topping, if used. The effect of the stems generally is not significant; therefore, their thickness and surface area may be disregarded. e. The thickness of hollow-core is the total thickness.

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THERMAL AND ACOUSTICAL PROPERTIES OF PRECAST CONCRETE

CHAPTER 11

Table 11.1.5 Wall U-values: prestressed tees, hollow-core, and solid and sandwich panels; winter and summer conditionsa Thickness t and resistance R of concrete Concrete density, lb/ft3 145

Type of wall panel Solid walls, tees,b and sandwich panels

  11 145

110

110

Hollowcorec

Solid walls, tees,b and sandwich panels

Hollowcorec

Winter Rfo = 0.17, Rfi = 0.68

Summer Rfo = 0.25, Rfi = 0.68

Insulation resistance R t

R

2

0.15

1.00

0.20

0.14

0.11

0.09

0.93

0.20

0.14

0.11

0.09

3

0.23

0.93

0.20

0.14

0.11

0.09

0.86

0.19

0.14

0.11

0.09

4

0.30

0.87

0.19

0.14

0.11

0.09

0.81

0.19

0.14

0.11

0.09

5

0.38

0.81

0.19

0.14

0.11

0.09

0.76

0.19

0.14

0.11

0.09

6

0.45

0.77

0.19

0.14

0.11

0.09

0.72

0.19

0.14

0.11

0.09

8

0.60

0.69

0.18

0.13

0.11

0.09

0.65

0.18

0.13

0.10

0.09

6(o)

1.07

0.52

0.17

0.13

0.10

0.08

0.50

0.17

0.13

0.10

0.08

6(f)

1.86

0.37

0.15

0.11

0.09

0.08

0.36

0.15

0.11

0.09

0.08

8(o)

1.34

0.46

0.16

0.12

0.10

0.08

0.44

0.16

0.12

0.10

0.08

8(f)

3.14

0.25

0.13

0.10

0.08

0.07

0.25

0.12

0.10

0.08

0.07

10(o)

1.73

0.39

0.15

0.12

0.09

0.08

0.38

0.15

0.12

0.09

0.08

10(f)

4.05

0.20

0.11

0.09

0.08

0.07

0.20

0.11

0.09

0.08

0.07

12(o)

1.91

0.36

0.15

0.11

0.09

0.08

0.35

0.15

0.11

0.09

0.08

12(f)

5.01

0.17

0.10

0.08

0.07

0.06

0.17

0.10

0.08

0.07

0.06

2

0.38

0.81

0.19

0.14

0.11

0.09

0.76

0.19

0.14

0.11

0.09

3

0.57

0.70

0.18

0.13

0.11

0.09

0.67

0.18

0.13

0.11

0.09

4

0.76

0.62

0.18

0.13

0.10

0.09

0.59

0.18

0.13

0.10

0.09

5

0.95

0.56

0.17

0.13

0.10

0.09

0.53

0.17

0.13

0.10

0.08

6

1.14

0.50

0.17

0.13

0.10

0.08

0.48

0.16

0.12

0.10

0.08

8

1.52

0.42

0.16

0.12

0.10

0.08

0.41

0.16

0.12

0.10

0.08

8(o)

2.00

0.35

0.15

0.11

0.09

0.08

0.34

0.14

0.11

0.09

0.08

8(f)

4.41

0.19

0.11

0.09

0.08

0.07

0.19

0.11

0.09

0.07

0.07

12(o)

2.59

0.29

0.13

0.11

0.09

0.07

0.28

0.13

0.11

0.09

0.07

12(f)

6.85

0.13

0.09

0.07

0.06

0.06

0.13

0.08

0.07

0.06

0.06

None

4

6

8

10

None

4

6

8

10

a. When insulations having other R-values are used, U-values can be interpolated with adequate accuracy, or U can be calculated as shown in section 11.1.4. When a finish, air space, or any other material layer is added, the new U-value is: 1 1 + R  of add ed finish, ai rspace, or material U  from table

b. Thickness for tees is thickness of slab portion. For sandwich panels, t is the sum of the thicknesses of the wythes. c. For hollow-core, (o) and (f) after thickness designate cores open or cores filled with insulation, respectively.

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THERMAL AND ACOUSTICAL PROPERTIES OF PRECAST CONCRETE

CHAPTER 11

Table 11.1.6  Roof U-values: concrete units with built-up roofing, heat flow upward,a,b winter conditions

Rfo Rbr

Outside surface Built-up roofing

R of insulation, varies, see table R of concrete, varies, see table Accoustical ceiling, 3/4 in.

Ra Rc

Inside surface

Rfi

Air space

With or without acoustical ceiling

Suspended ceiling

With ceiling Thickness Without ceiling Pret and resisApplied direct Suspended Concrete stressed tance R of density, Top insulation resistance R concrete concrete lb/ft3 component t R None 4 10 16 None 4 10 16 None 4 10 145

145

110

110

Solid slabs and teesc

Hollow-cored

Solid slabs and teesc

Hollow-cored

  11 16

2

0.15

0.79

0.19

0.09

0.06

0.29

0.13

0.07

0.05

0.24

0.12

0.07

0.05

3

0.23

0.75

0.19

0.09

0.06

0.29

0.13

0.07

0.05

0.23

0.12

0.07

0.05

4

0.30

0.71

0.18

0.09

0.06

0.28

0.13

0.07

0.05

0.23

0.12

0.07

0.05

5

0.38

0.67

0.18

0.09

0.06

0.27

0.13

0.07

0.05

0.22

0.12

0.07

0.05

6

0.45

0.64

0.18

0.09

0.06

0.27

0.13

0.07

0.05

0.22

0.12

0.07

0.05

8

0.60

0.58

0.18

0.09

0.06

0.26

0.13

0.07

0.05

0.21

0.11

0.07

0.05

6(o)

1.07

0.46

0.16

0.08

0.06

0.23

0.12

0.07

0.05

0.19

0.11

0.07

0.05

6(f)

1.86

0.34

0.14

0.08

0.05

0.20

0.11

0.07

0.05

0.17

0.10

0.06

0.05

8(o)

1.34

0.41

0.16

0.08

0.05

0.22

0.12

0.07

0.05

0.18

0.11

0.06

0.05

8(f)

3.14

0.24

0.12

0.07

0.05

0.16

0.10

0.06

0.04

0.14

0.09

0.06

0.04

10(o)

1.73

0.35

0.15

0.08

0.05

0.20

0.11

0.07

0.05

0.17

0.10

0.06

0.05

10(f)

4.05

0.19

0.11

0.07

0.05

0.14

0.09

0.06

0.04

0.12

0.08

0.06

0.04

12(o)

1.91

0.33

0.14

0.08

0.05

0.19

0.11

0.07

0.05

0.17

0.10

0.06

0.05

12(f)

5.01

0.16

0.10

0.06

0.05

0.12

0.08

0.05

0.04

0.11

0.08

0.05

0.04

2

0.38

0.67

0.18

0.09

0.06

0.27

0.13

0.07

0.05

0.22

0.12

0.07

0.05

3

0.57

0.60

0.18

0.09

0.06

0.26

0.13

0.07

0.05

0.21

0.12

0.07

0.05

4

0.76

0.53

0.17

0.08

0.06

0.25

0.12

0.07

0.05

0.21

0.11

0.07

0.05

5

0.95

0.49

0.17

0.08

0.06

0.24

0.12

0.07

0.05

0.20

0.11

0.07

0.05

6

1.14

0.44

0.16

0.08

0.05

0.23

0.12

0.07

0.05

0.19

0.11

0.07

0.05

8

1.52

0.38

0.15

0.08

0.05

0.21

0.11

0.07

0.05

0.18

0.10

0.06

0.05

8(o)

2.00

0.32

0.14

0.08

0.05

0.19

0.11

0.07

0.05

0.16

0.10

0.06

0.05

8(f)

4.41

0.18

0.11

0.06

0.05

0.13

0.09

0.06

0.04

0.12

0.08

0.05

0.04

12(o)

2.59

0.27

0.13

0.07

0.05

0.17

0.10

0.06

0.05

0.15

0.09

0.06

0.04

12(f)

6.85

0.13

0.08

0.06

0.04

0.10

0.07

0.05

0.04

0.09

0.07

0.05

0.04

a. When insulations having other R-values are used, U-values can be interpolated with adequate accuracy, or U can be calculated as shown in section 11.1.4. When a finish, air space, or any other material layer is added, the new U-value is: 1 1 + R  of add ed finish, ai rspace, or material U  from table

b. ASHRAE does not require solar surface heat to be considered because the color of a roof determines or affects the requirements. c. Thickness for tees is thickness of slab portion. d. For hollow-core, (o) and (f) after thickness designate cores open or cores filled with insulation, respectively.

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THERMAL AND ACOUSTICAL PROPERTIES OF PRECAST CONCRETE

CHAPTER 11

Table 11.1.7  Roof U-values: concrete units with built-up roofing, heat flow downward,a,b summer conditions

Rfo Rbr

Outside surface Built-up roofing

0.25 0.33

R of insulation, varies, see table R of concrete, varies, see table Accoustical ceiling, 3/4 in.

Ra Rc

1.00 1.88

Inside surface

Rfi

0.92

Air space

With or without acoustical ceiling

  11

Suspended ceiling

With ceiling Thickness Without ceiling t and resisApplied direct Suspended Concrete Prestressed tance R of density, concrete Top insulation resistance R concrete lb/ft3 component t R None 4 10 16 None 4 10 16 None 4 10 145

145

110

110

Solid slabs and teesc

d

Hollow-core

Solid slabs and teesc

d

Hollow-core

16

2

0.15

0.61

0.18

0.09

0.06

0.26

0.13

0.07

0.05

0.21

0.11

0.07

0.05

3

0.23

0.58

0.17

0.09

0.06

0.26

0.13

0.07

0.05

0.20

0.11

0.07

0.05

4

0.30

0.56

0.17

0.08

0.06

0.25

0.13

0.07

0.05

0.20

0.11

0.07

0.05

5

0.38

0.53

0.17

0.08

0.06

0.25

0.12

0.07

0.05

0.20

0.11

0.07

0.05

6

0.45

0.51

0.17

0.08

0.06

0.24

0.12

0.07

0.05

0.20

0.11

0.07

0.05

8

0.60

0.48

0.16

0.08

0.06

0.24

0.12

0.07

0.05

0.19

0.11

0.07

0.05

6(o)

1.07

0.39

0.15

0.08

0.05

0.21

0.11

0.07

0.05

0.17

0.10

0.06

0.05

6(f)

1.86

0.30

0.14

0.07

0.05

0.18

0.11

0.06

0.05

0.15

0.10

0.06

0.04

8(o)

1.34

0.35

0.15

0.08

0.05

0.20

0.11

0.07

0.05

0.17

0.10

0.06

0.05

8(f)

3.14

0.22

0.12

0.07

0.05

0.15

0.09

0.06

0.04

0.13

0.08

0.06

0.04

10(o)

1.73

0.31

0.14

0.08

0.05

0.19

0.11

0.07

0.05

0.16

0.10

0.06

0.04

10(f)

4.05

0.18

0.10

0.06

0.05

0.13

0.09

0.06

0.04

0.11

0.08

0.06

0.04

12(o)

1.91

0.29

0.13

0.07

0.05

0.18

0.10

0.06

0.05

0.15

0.09

0.06

0.04

12(f)

5.01

0.15

0.10

0.06

0.04

0.12

0.08

0.05

0.04

0.10

0.07

0.05

0.04

2

0.38

0.53

0.17

0.08

0.06

0.25

0.12

0.07

0.05

0.20

0.11

0.07

0.05

3

0.57

0.48

0.16

0.08

0.06

0.24

0.12

0.07

0.05

0.19

0.11

0.07

0.05

4

0.76

0.44

0.16

0.08

0.05

0.23

0.12

0.07

0.05

0.18

0.11

0.06

0.05

5

0.95

0.41

0.16

0.08

0.05

0.22

0.12

0.07

0.05

0.18

0.10

0.06

0.05

6

1.14

0.38

0.15

0.08

0.05

0.21

0.11

0.07

0.05

0.17

0.10

0.06

0.05

8

1.52

0.33

0.14

0.08

0.05

0.19

0.11

0.07

0.05

0.16

0.10

0.06

0.05

8(o)

2.00

0.29

0.13

0.07

0.05

0.18

0.10

0.06

0.05

0.15

0.09

0.06

0.04

8(f)

4.41

0.17

0.10

0.06

0.05

0.12

0.08

0.06

0.04

0.11

0.08

0.05

0.04

12(o)

2.59

0.24

0.12

0.07

0.05

0.16

0.10

0.06

0.04

0.14

0.09

0.06

0.04

12(f)

6.85

0.13

0.08

0.06

0.04

0.10

0.07

0.05

0.04

0.09

0.07

0.05

0.04

a. When insulations having other R-values are used, U-values can be interpolated with adequate accuracy, or U can be calculated as shown in section 11.1.4. When a finish, air space, or any other material layer is added, the new U-value is: 1 1 + R  of add ed finish, ai rspace, or material U  from table

b. ASHRAE does not require solar surface heat to be considered because the color of a roof determines or affects the requirements. c. Thickness for tees is thickness of slab portion. d. For hollow-core, (o) and (f) after thickness designate cores open or cores filled with insulation, respectively.

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THERMAL AND ACOUSTICAL PROPERTIES OF PRECAST CONCRETE 11.1.5

Thermal Storage (Mass) Effects

The U-factor of a building assembly is a significant variable in determining overall heat transmission (loss/gain). Laboratory tests demonstrate that thermal transmission is directly proportional to the U-factor during steady-state heat flow. However, the steady-state condition is rarely realized in actual practice. External conditions, such as temperature, position of the sun, and presence of shadows, vary throughout a 24-hour day. Due to their ability to absorb and store heat, massive building materials, such as concrete, delay the transmission of heat energy. Therefore, heat gain is not instantaneous through solid materials, resulting in the phenomenon often referred to as time lag or thermal inertia. As temperatures rise on one side of a wall, heat begins to flow toward the cooler side. Before heat transfer can be achieved, the wall must undergo a temperature increase. The amount of thermal energy necessary to achieve this increase is directly proportional to the specific heat and density of the wall. This property is known as heat capacity. Due to its density, concrete has the capacity to absorb and store large quantities of heat. Because of its heat capacity, concrete is slow to warm or cool, therefore it is slow to equalize its temperature with the surrounding temperature. This behavior delays the transfer of energy. In this way, thermal mass reduces peak heating and cooling loads by delaying the time at which these peak loads occur by several hours. This delay reduces demands on heating and cooling equipment, since the peak heating or cooling loads are delayed, allowing time for the external conditions to cycle from peak to moderate. In environments where external temperature cycling is frequent, peak loads are reduced by thermal storage (mass) effect. Energy use differences between light and heavy materials are illustrated in the computer analyses shown in Fig. 11.1.1. Figure 11.1.1(a) compares the heat flow through three walls having the same U-value, but made of different materials. The concrete wall consists of a layer of insulation sandwiched between inner and outer wythes of 2-in.-thick concrete with a weight of 48.3 lb/ft2. The metal wall, with a density of 3.3 lb/ft2, has insulation sandwiched between an exterior metal panel and 1/2-in.-thick drywall. The wood frame wall has a weight of 7.0 lb/ft2 and has wood siding on the outside, insulation between 2 × 4 studs, and 1/2-in.-thick drywall on the inside. The walls are exposed to simulated outside temperatures that represent a typical spring day in a moderate climate. The massive concrete wall has lower peak loads by about 13% for heating and 30% for cooling than the less massive walls. Normalweight concrete walls of various thicknesses exposed to the same simulated outside temperatures are compared in Fig. 11.1.1(b). The walls have a layer of insulation sandwiched between concrete on the outside and 1 /2-in.-thick drywall on the inside; U-values are the same. The figure shows that the more massive the wall, the lower the peak loads and the more the peaks are delayed.

CHAPTER 11

Figure 11.1.1(c) compares concrete sandwich panels having an outer wythe of 2 in., a constant thickness of insulation, and various thicknesses of inner wythes. All walls have U-values of 0.091 and are exposed to the same simulated outside temperatures. The figure shows that by increasing the thickness of the inner concrete wythes, peak loads are reduced and delayed. A metal roof is compared to a concrete roof in Fig. 11.1.1(d). Both roof systems have built-up roofing on rigid board insulation on the outside and acoustical tile on the inside. The concrete roof weighs 48.3 lb/ft2 and the metal roof 1.5 lb/ft2. The roofs have identical U-values of 0.10 and are exposed to the same simulated outside temperatures. The figure shows that the concrete roof has lower peak loads by about 70% for heating and by 95% for cooling, and peaks are delayed by about 1.8 hours for heating and about 4 hours for cooling. Another factor affecting the behavior of thermal mass is the availability of free heat, which is heat generated inside the building as a by-product of other systems such as lights, equipment, appliances, and people. It also includes heat from the sun entering through windows. Generally during the heating season, the benefit of thermal mass increases due to its ability to store the available free heat. Tables 11.1.8 and 11.1.9 show the relative importance of free heat design considerations. Thus, office buildings that have high internal heat gains from lights, people, and large glass areas represent an ideal application for thermal mass designs. This is especially true if the glass has been located to take maximum advantage of the sun. During cooling seasons, or in cooling dominated climates, the storage of internal heat is not desirable, but walls with external mass may help limit additional internal heat gain by storing and slowing the rate of entry of external heat energy.  The benefits of thermal mass are different for each climate, location, and building orientation, and it should be examined exclusively for each building design. Building codes and standards now provide for the benefits of thermal mass. In increasing numbers, they are beginning to acknowledge the effect of the greater heat storage capacity in buildings having high thermal mass. The rates of many utilities are structured so that the use of energy at lower and/or delayed peak times can result in significant cost savings. Other studies have shown that concrete buildings have lower average heating and cooling loads than lightweight buildings for a given insulation level. Thus, life-cycle costs will be lower, or less insulation can be used for equivalent performance.

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Heating load, Btu / (hr)(ft2)

Heating load, Btu / (hr)(ft2)

All walls have U-values = 0.091

All walls have U-values = 0.091

Concrete sandwich wall (2" inner and outer wythes)

,

,

  11 Metal wall

Wood frame wall

Normalweight concrete Cooling load, Btu / (hr)(ft2)

Cooling load, Btu / (hr)(ft2)

(b) Concrete walls

(a) Walls Heating load, Btu / (hr)(ft2)

Heating load, Btu / (hr)(ft2)

All walls have U-values = 0.091

Both roofs have U-values = 0.10

2" concrete inner wythe Metal roof 4" normalweight concrete ,

,

Normalweight concrete Cooling load, Btu / (hr)(ft2)

Cooling load, Btu / (hr)(ft2)

(d) Roofs

(c) Concrete sandwich walls

Fig. 11.1.1 Heating and cooling load comparisons.

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Table 11.1.8  Design considerations for building with high free heata Relative importance of design considerationsb Climate classification

Thermal Increase External mass insulation finsc

Surface color

Daylighting

Reduce infiltration

2

1

3

1

3

Light Dark

Winter Long heating season (6000 degree days or more)

Moderate heating season (3000 to 6000 degree days)

Short heating season (3000 degree days or less)

With sund and winde With sun, without wind Without sun and wind Without sun, with wind With sun and wind With sun, without wind Without sun and wind Without sun, with wind With sun and wind

With sun, without wind Without sun and wind Without sun, with wind Summer

1

2

2

1

2

2

2

1

3 3

1

2

2

1

2

2

1

1

2

2

2

2

1

2

2

1

2

1

2

3

1

2

1

3

1

2

1

2

1

1

2

1

1

2 1

2

Long cooling season (more than 1500 hr at 80 °F)

Dryf or humidg

3

3

3

3

3

Moderate cooling season (600 to 1500 hr at 80 °F)

Dryf or humidg

3

2

2

2

3

Short cooling season (less than 600 hr at 80 °F)

Dryf or humidg

2

1

1

1

2

a. Includes office buildings, factories, and commercial buildings. b. Higher numbers indicate greater importance. c. Provide shading and protection from direct wind. d. With sun: Sunshine during at least 60% of daylight time. e. With wind: Average wind velocity over 9 mph. f. Dry: Daily average relative humidity less than 60% during summer. g. Humid: Daily average relative humidity greater than 60% during summer.

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Table 11.1.9  Design considerations for building with low free heata Relative importance of design considerationsb Climate classification

Thermal mass

Increase insulation

External finsc

3

2

Surface color Light

Dark

Daylighting

Winter With sund and winde With sun, without wind Without sun and wind Without sun, with wind With sun and wind Moderate heating season (3000 to 6000 degree With sun, without days) wind Without sun and wind Without sun with wind With sun and wind Short heating season (3000 degree days With sun, without wind or less) Without sun and wind Without sun, with wind Summer

Long heating season (6000 degree days or more)

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3

3

3

3

3

3

2

3

3

2

2

3

1

2

1

2

3

1

2

2

3

2

1

3

1

3

1

2

1

2

1

1

2

2

1

1

2

1

1

2

1

1

2

Long cooling season (More than 1500 hr at 80 °F)

Dryf or humidg

3

2

2

3

Moderate cooling season (600 to 1500 hr at 80 °F)

Dryf

2

1

1

2

Humidg

2

1

1

3

Short cooling season (Less than 600 hr at 80 °F)

Dryf or humidg

1

1

a. Includes low-rise residential buildings and some warehouses. b. Higher numbers indicate greater importance. c. Provide shading and protection from direct wind. d. With sun: Sunshine during at least 60% of daylight time. e. With wind: Average wind velocity over 9 mph. f. Dry: Daily average relative humidity less than 60% during summer. g. Humid: Daily average relative humidity greater than 60% during summer.

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THERMAL AND ACOUSTICAL PROPERTIES OF PRECAST CONCRETE 11.1.6

Thermal Bridges

Metal ties connecting the outer wythes of sandwich wall panels and solid concrete paths through sandwich panels as described in Section 5.11.4 may cause localized cold spots. The most significant effect of these cold spots is condensation, which may cause annoying or damaging wet streaks, and wasted heating and cooling energy. Low thermal–conductivity ties are available that minimize thermal bridging. The effect of metal-tie thermal bridges on the heat transmittance can be calculated with reasonable accuracy by the zone method described in Chapter 22 of Reference 2. With the zone method, the panel is divided into Zone A, which contains the thermal bridge, and Zone B, where thermal bridges do not occur, as shown in Fig. 11.1.2. The width of Zone A is calculated as W = m + 2d, where m is the width or diameter of the metal or other conductive bridge material and d is the distance from the panel’s outside surface to the metal. After the width W and area of Zone A are calculated, the heat transmissions of the zonal sections are determined and converted to area resistances. These are then added to obtain the total resistance Rt of that portion of the panel. The resistance of Zone A is combined with that of Zone B to obtain the overall resistance and the gross transmission value Uo, where Uo is the overall weighted average heat transmission coefficient of the panel. The net effect of metal ties is to increase the U-value by approximately 5 to 10%, depending on their type, size, and spacing. For example, a wall as shown in Fig. 11.1.2 would have a U-value of 0.091 if the effect of the ties were neglected. If the effect of 1/4 in. diameter ties at 16 in. on center is included, U = 0.101; at 24 in. spacing, U = 0.093. The effect of solid concrete path thermal bridges can be calculated by the characteristic section method described in Reference 7. In this method, the panel is divided into two

W

Welded-wire reinforcement

Outside

Inside

CHAPTER 11

regions. The first is treated as a perfectly insulated panel without any thermal bridges. The second is treated as a solid concrete panel without insulation. The total thermal resistance of the panel is calculated as the resistances of these two regions added in parallel. The portion of the panel that is treated as a solid concrete panel without any insulation is larger than the actual solid concrete region that exists in the panel. There is an affected zone around each solid concrete region that is added to the actual area of the solid concrete region to obtain the modified concrete area used in the calculation. The size of the affected zone Ez is computed as: Ez = 1.4 − 0.1tinα + ⎡⎣ 0.4tcf + 0.1( tcb − tcf )⎤⎦ β (Eq. 11-2) In this equation, tin, tcf, and tcb are the thicknesses of the insulation layer, concrete face wythe, and concrete back wythe, respectively. This is an empirical equation with all dimensions expressed in inches. The parameters α and  account for the insulation and concrete conductivity values (kin and kcon) that are used to construct the panel. Their values are computed as:

and



k − 0.26 ⎞ α = 1 + 2.25 ⎛⎜ in ⎝ 0.26 ⎟⎠

(Eq. 11-3)

k − 12.05 ⎞ β = 1+ 1.458 ⎛⎜ con ⎝ 12.05 ⎟⎠

(Eq. 11-4)

In these equations, kin and kcon have units of (Btu-in.)/[(hr)(ft2)(°F)]. To calculate an R-value, a panel is divided into two regions: a solid concrete region and a perfectly insulated region, as explained previously. Equation 11-2 is used to calculate Ez, and the area of each region is then calculated. The thermal resistance of the solid concrete region Rs is then added in parallel with the thermal resistance of the perfectly insulated region Rp to obtain the thermal resistance of the panel R:



1 As' A'p = + R Rs Rp

(Eq. 11-5)

where A's and A'p represent the areas of the solid concrete region As and perfect panel region Ap divided by the total panel area At (that is, A's = As /At, A'p = Ap /At). The procedure is illustrated in Example 11.1.6.1.

Zone B

Ties

Zone A

Rigid insulation

d = 1 clear (typical) Fig. 11.1.2 Metal tie thermal bridges. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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CHAPTER 11

EXAMPLE 11.1.6.1 Determination of R-Value for Sandwich Panel Problem: Determine the R-value for the sandwich panel shown below for conductivities of 10.0 (Btu-in.)/[(hr)(ft2)(°F)] and 0.15 (Btu-in.)/[(hr)(ft2)(°F)] for the concrete and insulation, respectively. Face and back wythe thicknesses are 3 in. and the insulation layer thickness is 2 in.

12'-0"

12" + 2.3" = 14.3"

1'-0"

  11

Solid zone

12" + 2 x (2.3") = 16.6"

1'-0"

12" + 2 x (2.3") = 16.6"

1'-0"

40'-0"

Solid concrete bridges (typical)

1'-0"

Transverse section

Vertical section

Affected zones

Solution: Calculate the parameters α and  from Eq. 11-3 and 11-4 respectively:

⎛ k − 0.26 ⎞ ⎛ 0.15 − 0.26 ⎞ = 1+ 2.25 ⎜ α = 1+ 2.25 ⎜ in ⎟⎠ = 0.05 ⎝ 0.26 ⎟⎠ ⎝ 0.26



⎛ k − 12.05 ⎞ ⎛ 10.00 − 12.05 ⎞ = 1+ 1.458 ⎜ β = 1+ 1.458 ⎜ con ⎟⎠ = 0.75 ⎝ 12.05 ⎟⎠ ⎝ 12.05

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EXAMPLE 11.1.6.1 Determination of R-Value for Sandwich Panel (cont.) From the panel thicknesses, the affected zone dimension Ez is computed from Eq. 11-2 as: Ez = 1.4 – 0.1(tin)(α) + [0.4tcf + 0.1(tcb – tcf)]β

= 1.4 – 0.1(2)(0.05) + [0.4(3) + 0.1(0)](0.75)



= 2.3 in.

Add Ez to the actual solid concrete areas to obtain the areas of the panel to treat as solid concrete (shown as dashed lines on previous page). Calculate the areas of the panel At, solid concrete region As, and perfectly insulated region Ap: At = panel area = (40)(12) = 480 ft2 = 69,120 in.2

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As = concrete area = 2(14.3)(144) + 8(16.6)(16.6) = 6323 in.2 Ap = insulated area = 69,120 – 6323 = 62,797 in.2 The resistance of that portion of the panel that is treated as perfectly insulated is calculated from the resistances of the concrete, insulation, and surfaces in series. Insulated path

A

Outside surface

B

Concrete

C D E

Inside surface

k

Thickness

U = k/t

R = 1/U Winter

R = 1/U Summer

 — 

 — 

 — 

0.17

0.25

10.00

3

3.33

0.30

0.30

Insulation

0.15

2

0.075

13.33

13.33

Concrete

10.00

3

3.33

0.30

0.30

 — 

 — 

 — 

0.68

0.68

Total

13.95

14.03

The resistance of that portion of the panel that is treated as solid concrete is calculated from the resistances of the concrete and surfaces in series. Concrete path

A

Outside surface

B

Concrete

C

Inside surface

k

Thickness

U = k/t

R = 1/U Winter

R = 1/U Summer

 — 

 — 

 — 

0.17

0.25

10.00

8

1.25

0.80

0.80

 — 

 — 

 — 

0.68

0.68

Total

1.65

1.73

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EXAMPLE 11.1.6.1 Determination of R-Value for Sandwich Panel (cont.) Calculate the fractional areas of the panel that are treated as solid concrete and as insulated: A's = As /At

= 6323/69,120 = 0.091

A'p = Ap /At

= 62,797/69,120 = 0.909

Compute the R-value of the panel treating the solid concrete and perfectly insulated regions in parallel.

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11.1.7

Winter:

Summer:

1 0.909 0.091 = + R 13.95 1.65

1 0.909 0.091 = + R 14.03 1.73

R = 8.31 hr · ft2(°F)/Btu

R = 8.52 hr · ft2(°F)/Btu

Condensation Control

Moisture that condenses on the interior of a building is unsightly and can cause damage to the building or its contents. Even more undesirable is moisture condensation within a building wall or ceiling assembly where it is not readily noticed until damage has occurred. All air in buildings contains some amount of water vapor. The amount of water vapor may be high or low depending on the air temperature and the amount of available moisture. Warm air has the potential to hold more moisture than cold air. The ratio of moisture vapor actually present in air compared with the total amount that could be present based on the temperature of the air is called relative humidity (RH). Fifty percent RH means that the air is holding one-half of the total amount of moisture vapor that it is capable of holding at a given temperature and pressure. When air is at 100% RH, it is saturated, unable to hold more moisture. At a given temperature, a 100% RH means that the air is at its dew-point temperature. When the air is at 100% RH, any more added moisture or air cooling will cause a portion of the vapor present to condense. In many buildings, moisture is added to the air by industrial processes, cooking, laundering, or humidifiers. If the inside surface temperature of a wall, floor, or ceiling is too cold (below the dew-point temperature), the air contacting this surface will be cooled and condense its excess water on that surface. Condensation occurs on any surface whose temperature is below the dew-point temperature of the surrounding air. Windows in winter are an example of this behavior. A prime design objective is to ensure that condensation does not occur on interior room surfaces or inside building walls. Surface condensation can be controlled by design conditions such as reducing the interior dew-point temperature by removing moisture from the interior air mass or raising the temperature of interior surfaces above the dew point through the use of insulation and/or warm-air distribution. Condensation inside building walls is controlled primarily by using 11–18

vapor barriers properly located inside the wall assembly to limit the migration or permeation of vapor through the wall. Moisture vapor that migrates through a wall assembly will, at times, encounter increasingly lower temperatures as it makes its way to the outside. If allowed to unabatedly migrate, the vapor will at some point reach the dew-point temperature for the amount of moisture present. The interior air dew-point temperature can be lowered by removing moisture from the air, either through ventilation or dehumidification. Adequate surface temperatures can be maintained during the winter by incorporating sufficient thermal insulation, using double or triple glazing, circulating warm air over the surfaces, directly heating the surfaces, paying proper attention during the design phase to the prevention of thermal bridging, or some combination of these (see Section 11.1.6). Moisture vapor can move into or across a wall assembly by means of vapor diffusion and/or air movement. Air infiltration and exfiltration are air leakage into and out of a building, respectively. Air moves through cracks or joints between infill components and structural elements, interstices around windows and doors, through floors and walls, and openings for building services. Sources of air infiltration/exfiltration are often a major contributor to energy loss in buildings. Warm, moisture-laden air, especially exfiltrating, that leaks into an enclosure can be a major source of moisture into construction assemblies. Air migration occurs from air pressure differentials that are independent of moisture pressure differentials. However, the consequence of unabated moving air is often unabated moving moisture. Atmospheric air pressure differences between the inside and outside of a building envelope exist because of the action of wind; the density difference between outside, cold, heavy air and inside, warm, light air (creating a “stack effect”); and the operation of equipment such as fans. The pressure differences will tend to equalize, and the air will flow through holes or cracks in the building envelope carrying with it the

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THERMAL AND ACOUSTICAL PROPERTIES OF PRECAST CONCRETE water vapor it contains. A thorough analysis of air leakage is complex and involves many parameters, including wall construction, building height, and orientation. Many condensation-related problems in building enclosures are caused by exfiltration and subsequent condensation within the enclosure assembly. Condensation due to air movement is usually much greater than that due to vapor diffusion for most buildings. However, when air leakage is controlled or avoided, the contribution from vapor diffusion can still be significant. In a well-designed wall, attention must be given to the control of airflow using air barriers and vapor diffusion using vapor retarders. An air barrier and a vapor retarder are both needed, and in many instances a single material can be used to provide both of these as well as serving other functions. The principal function of the air barrier is to limit air movement through the building walls, windows, or roof. This includes limiting inside air from exfiltrating and outside air from infiltrating through the building envelope. It is important to limit air movement whether the air is humid or dry, because air leakage can result in problems other than the deposition of moisture in cavities. Exfiltrating air carries away heating and cooling energy, while incoming air may bring in pollution and reduce the effectiveness of a rain-screen wall system. 11.1.7.1 Air Barriers Materials and the method of assembly chosen to build an air barrier must meet several requirements if they are to successfully perform the air-leakage control function. These requirements are: 1. There must be continuity throughout the building envelope. The low air-permeability materials of the wall must be continuous with the low air-barrier materials of the roof (for example, roofing membrane) and must be connected to other air-barrier materials such as that of the window frame. 2. Each membrane or assembly of materials intended to support a differential air-pressure load must be designed and constructed to carry that load inward or outward, or it must receive the necessary support from other elements of the wall to accomplish this function. If the air-barrier system is made of flexible materials, then it must be supported on both sides by materials capable of resisting the peak air-pressure loads; or it must be made of self-supporting materials, such as board products adequately fastened to the structure. If an air pressure difference cannot move air, it will act to displace the materials that prevent the air from flowing. 3. The air-barrier system must be virtually air-impermeable. A value for maximum allowable air permeability has not yet been widely agreed upon in consensus standards. Some states and segments of industry have established standards. One example is the metal and glass-curtain wall industry in the United States that has adopted a value of 0.06 ft3/min/ft2 at 1.57 lb/ft2 as the maximum allowable air-leakage rate for its wall

CHAPTER 11

constructions. Individual materials that qualify as low air-permeable materials when joints are properly sealed include polyethylene sheet, gypsum board, precast concrete panels, metal sheeting, or glass. Materials that do not qualify include concrete block, fiberous batt insulation, molded polystyrene insulation board, and fiberboard. 4. The air-barrier assembly must be durable in the same sense that the building is durable and be made of materials that are known to have a long service life or be located so that it may be serviced from time to time. In climates where the heating season dominates, it is strongly recommended that the visible interior surface of a building envelope be installed and treated as the primary air barrier and vapor retarder. Where floors and cross walls are made of solid concrete, it is necessary to seal only the joints, as floors and walls themselves are monolithic air-barrier surfaces and do not pass air. Where hollow partitions such as steel stud or hollow masonry units are used, the interior finish of the envelope should be made continuous. Where this is impractical, polyethylene film should be installed across these junctions and later sealed to the interior finish material. An interior finish of gypsum wallboard or plaster painted with two coats of enamel paint will provide a satisfactory air barrier/vapor retarder in many instances if the floor/wall and ceiling/wall joints are tightly fitted and sealed with caulking. A development in concrete panel construction techniques over the last several years is an air barrier and vapor-retarder system cast into the panel featuring a thermal fusible membrane seal around the panel joints, sealed from the inside with a foam backer rod and sealant. When the membrane is sealed from panel to structure, surfaces should be clean, as dry as possible, smooth, and free of foreign matter that may impede adhesion. The bond between the concrete and membrane may be improved by priming the concrete before bonding the membrane to this substrate. While it is preferable that the air-barrier system be placed on the warm side of an insulated assembly, where thermal stresses will be at a minimum, it is not an essential requirement. (This does not necessarily mean on the inside surface of the wall.) The position of the air barrier in a wall is more a matter of suitable construction practice and the type of materials to be used. However, if the barrier is positioned on the outside of the insulation, consideration must be given to its water-vapor permeability in case it also acts as a barrier to vapor that is migrating out from inside the wall assembly. A vapor-retarding layer on the cold side of insulation encourages moisture accumulation and condensation prior to exiting the wall assembly. Choosing an air barrier material that is 10 to 20 times more permeable to water vapor than the vaporbarrier material minimizes this detrimental situation. In the case of construction assemblies that do not lend themselves to the sealing of interior surfaces, or where it is desirable to limit condensation to very small amounts, the use of alternative vapor-retarding techniques must be considered.

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An example is concrete sandwich wall panel construction, which often has no air leaks through the panels themselves, but also has no internal air space for drainage, venting, and drying out in summer. In such cases, the insulation material itself, if it is a rigid, closed-cell type such as extruded polystyrene, can be installed on a complete bed of adhesive applied to the interior face of the inner wythe of the wall with joints fully sealed with adhesive to provide a barrier to both air and vapor movement. The previous commentary has focused on the flat areas of walls; however, the joints between them may well present the most important design and construction details. The most critical joint locations are the roof/wall connection, the wall/­ foundation connection, soffit connections, cor­ner details, and connections between different types of exterior wall systems, such as brick and precast concrete or curtain wall and precast concrete. The designer should give special attention to detailing these critical transitions between different systems and materials. 11.1.7.2 Vapor Retarders Water-vapor diffusion, which is another way in which indoor water can move through a building envelope to condense in the colder zones, occurs when water vapor molecules diffuse through solid interior materials at a rate dependent on the permeability of the materials, the vapor pressure, and temperature differentials. High vapor pressure inside versus low pressure outside creates a vapor pressure difference that drives the water vapor in the warm inside air toward the cooler, drier outside air. The principal function of a vapor retarder made of low permeability materials is to slow or retard the passage of moisture as it diffuses through the assembly of wall materials. Vapor diffusion control is simple to achieve and is primarily a function of the water-vapor diffusion resistance of the chosen materials and their position within the building envelope assembly. Installation detailing is critical, therefore the vapor retarder should be clearly identified by the designer as well as clearly identifiable by the general contractor. In cold and temperate climates, vapor retarders should be applied on or near the warm side (inner surface) of assemblies. Vapor retarders may be structural, or in the form of thin sheets or coatings. Vapor retarders may also be positioned part way into the insulation but, to avoid condensation, they should be no farther than the point at which the dew-point temperature is reached when assessed at the outside winter design temperature. In climates with high exterior humidity, coupled with high temperature, especially where cooling systems run continuously, inward moisture diffusion is minimized by placing a vapor-retarder system in the building envelope near the outer surface. For cooled buildings in hot/humid climates without extended cold periods, it may be more economical to use only adequate air-infiltration retarding systems rather than vapor retarders because the interior temperature is rarely below the dew point of the outside air. The designer of record should assess all conditions to verify the expected performance. Where warm and cold sides may reverse, resulting in 11–20

reversal of vapor flow, careful analysis of the condition is recommended. If the climate is heating-dominated such as in the northern tier of the United States, the vapor retarder is generally placed on the “warm in winter” side. When vapor flow reversal occurs, such as in the summer months, the interior vapor retarder will slow the dissipation of exterior moisture vapor driven toward the cooled interior. During the summer months, a wall may reservoir moisture until conditions reverse again as the season changes and then dries during the winter months. This is a common cycle for successful designs. Many wall assemblies have reservoir capability, meaning they can store moisture vapor for a time and not become wet. It is generally not the best practice to omit a vapor retarder under such circumstances because it may allow excess amounts of moisture to accumulate that may result in wetting. In general, a vapor retarder should not be placed at both the inside and outside surfaces of wall assemblies because this can trap moisture within the assembly. For a complete discussion, the designer should refer to the ASHRAE Handbook—Fundamentals or ASTM C755, Selection of Vapor Barriers for Thermal Insulation.8 High thermal conductance paths, or thermal bridging, reaching inward from or near the colder surfaces, may cause condensation within the construction. Thermal bridging may occur at steel framing members (studs, joists, rafters) that penetrate the insulation layer and extend from inside to out. It may also occur at junctions of floors and walls, walls and ceilings, walls and roofs, around wall or roof openings, at perimeters of slabs on the ground, and at connections. Fittings installed in outer walls, such as electrical boxes without holes and conduits, should be completely sealed against moisture and air passage, and they should be installed on the warm side of unbroken vapor retarders or air barriers that are completely sealed.

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CHAPTER 11

Table 11.1.10  Dew-point temperaturesa ts, °F Dry bulb or room temperature, °F

Relative humidity, % 10

20

30

40

50

60

70

80

90

100

40

–7

6

14

19

24

28

31

34

37

40

45

–3

9

18

23

28

32

36

39

42

45

50

–1

13

21

27

32

37

41

44

47

50

55

5

17

26

32

37

41

45

49

52

55

60

7

21

30

36

42

46

50

54

57

60

65

11

24

33

40

46

51

55

59

62

65

70

14

27

38

45

51

56

60

63

67

70

75

17

32

42

49

55

60

64

69

72

75

80

21

36

46

54

60

65

69

73

77

80

85

23

40

50

58

64

70

74

78

82

85

90

27

44

55

63

69

74

79

83

85

90

a. Temperatures are based on barometric pressure of 29.92 in. Hg.

Table 11.1.11  Typical permeance M and permeability µ valuesa

Heat transmittance U

Single glass

Material

M, perms

µ, perm-in.

Concrete (1:2:4 mixture)b

—

3.2

Wood (sugar pine)

—

0.4 – 5.4

Extruded polystyrene (XPS)

—

1.2

Molded polystyrene (bead, EPS)

—

2.0 – 5.8

Paint–two coats Asphalt paint on plywood

0.4

Double glass

Enamels on smooth plaster

0.5 – 1.5

Airspace

Various primers plus one coat flat oil paint on plaster

1.6 – 3.0

RH =

Outside temperature, ˚F Fig. 11.1.3 Relative humidity (RH) at which visible condensation occurs on inside surface; inside temperature -70 °F.

Plaster on gypsum lath (with studs)

20.00

Gypsum wallboard, 0.375 in.

50.00

Polyethylene, 2 mil

0.16

Polyethylene, 10 mil

0.03

Aluminum foil, 0.35 mil

0.05

Aluminum foil, 1 mil

0.00

Built-up roofing (hot mopped)

0.00

Duplex sheet, asphalt laminated aluminum foil one side

0.002

a. ASHRAE Handbook—Fundamentals.2 b. Permeability for concrete varies depending on the concrete’s water– cementious materials ratio and other factors.

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11.1.7.3 Prevention of Condensation on Wall Surfaces

11.1.7.4 Condensation Prevention within Wall Construction

The U-value of a wall must be such that the surface temperature will not fall below the dew-point temperature of the room air, thus preventing condensation on the interior surface of a wall (Example 11.1.7.1). Figure 11.1.3 gives U-values for any combination of outside temperatures and inside RH above which condensation will occur on the interior surfaces. For example, if a building were located in an area with an outdoor design temperature of 0 °F and it was desired to maintain an RH within the building of 25%, the wall must be designed so that all components have a U-value less than 0.78; otherwise, there will be a potential problem with condensation. In many designs, the desire to conserve energy will dictate the use of lower U-values than those required to avoid the condensation problem. The degree of wall heat transmission resistance that must be provided to avoid condensation may be determined from the following relationship:

Water vapor in air behaves as a gas and will diffuse through building materials at rates that are dependent on vapor permeability of materials and vapor-pressure differentials. The colder the outside temperature, the greater water-vapor pressure in the warm inside air must be to reach the cooler, drier outside air. Also, leakage of moisture-laden air into an assembly through small cracks may be a greater problem than vapor diffusion. The passage of water vapor through material is in itself generally not harmful. Water-vapor passage becomes harmful when the vapor flow path encounters a temperature below the dew point. Condensation then results within the material. Building materials have water-vapor permeances from very low to very high (Table 11.1.11). When properly used, low permeance materials keep moisture from entering a wall or roof assembly. Materials with higher permeance allow construction moisture and moisture that enters inadvertently or by design to escape. When a material such as plaster or gypsum board has a permeance that is too high for the intended use, one or two coats of paint is frequently sufficient to lower the permeance to an acceptable level; a vapor barrier can be used directly behind such products. Polyethylene sheet, aluminum foil, and roofing materials are commonly used. Proprietary vapor barriers, usually combinations of foil and polyethylene or asphalt, are frequently used in freezer and cold-storage construction. Where climatic conditions require insulation, a vapor retarder is generally necessary to prevent condensation. Closed-cell insulation, if properly applied, will serve as its own vapor retarder. For other insulation materials, a vapor retarder should be applied to the warm side of the insulation. For a more complete treatment of the subject of condensation within wall or roof assemblies, see References 2 and 9.

⎛t −t ⎞ Rt = R fi ⎜ i o ⎟ ⎝ ti − t s ⎠



(Eq. 11-6)

Dew-point temperatures in degrees Farenheit for various values of ti and RH are shown in Table 11.1.10.

EXAMPLE 11.1.7.1 Condensation Prevention Given: A room in which the temperature and relative humidity are to be maintained at 70 °F and 40%, respectively. During heating season, to = –10 °F. Problem: Determine the heat transmission resistance Rt required to prevent condensation. Solution: From Table 11.1.10, the dew-point temperature ts is 45 °F, and from Table 11.1.5, Rfi = 0.68. From Eq. 11-7:  t − t  0.68 70 − ( −10 )  Rt = Rfi  i o  = = 2.18  ti − ts  [70 − 45 ] U = 1/Rt = 0.46

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11.2.1

 coustical Properties of Precast A Concrete

Sound transmission class (STC)

11.2

CHAPTER 11

Definitions

Hertz (Hz).   A measure of sound wave frequency. The number of complete vibration cycles per second. IIC.  Impact insulation class. STC.  Sound transmission class. 11.2.2

General

The basic purpose of architectural acoustics is to provide a satisfactory environment in which desired sounds are clearly heard by the intended listeners and unwanted sounds (noise) are isolated or absorbed. The sound-reduction needs of a building are determined by location, environmental ambiance, and the degree of sound reduction necessary for occupants to function effectively. Under most conditions, the architect/engineer can determine the acoustical needs of the space and then design the building to satisfy those needs. Good acoustical design utilizes absorptive and reflective surfaces, sound barriers, and vibration iso­ lators. Some surfaces must reflect sound so that the loudness will be adequate in all areas where listeners are located. Other surfaces absorb sound to avoid echoes, sound distortion, and long reverberation times. Sound is isolated from rooms where it is not wanted by selected wall and floor-ceiling construc­ tions. Vibration generated by mechanical equipment must be isolated from the structural frame of the building by means of mechanical isolators or compressible materials. Information is provided on the commonly used acoustical properties of some of the more common precast concrete products used in building construc­tion. This information can be incorporated into the acoustical design of a building and/ or can show com­pliance with local ordinances or other minimum acoustical requirements (see Section 11.2.7). For buildings or occupancies that require more sophisticated acoustical analysis, such as churches, concert halls, auditoriums, recording studios, and the like, it may be desirable to use the services of a competent acoustical-design consultant or specialist. 11.2.3

Dealing with Sound Levels

The problems of sound insulation are usually considerably more complicated than those of sound absorption. Sound insulation involves greater reductions than can be achieved by absorption. These large reductions of sound level from space to space can be achieved only by continuous, impervious barriers. If the problem also involves structure-borne sound, it may be necessary to introduce resilient layers or discontinuities into the barrier. Sound-absorbing and sound-insulating materials are used for different purposes. There is not much sound absorption from an 8-in.-thick concrete wall; similarly, low sound transmission is not available from a porous, lightweight material that may be applied to room surfaces for sound absorption. It is important to recognize that the basic mechanisms of sound absorption and sound insulation are quite different.

65 60

Flat or ribbed panels, tees with topping, hollow-core slabs

55 50

STC = 0.1304 W + 43.48 45

Statistical tolerance ± 2.5 STC

40 40

50

60

70

80

90

Weight per unit area (W), lb/ft

100 2

Fig. 11.2.1 Sound transmission class as a function of weight of floor or wall.

11.2.4

Sound Transmission Loss

The ability of a barrier to reduce the intensity of airborne sound is commonly designated by its sound transmission class (STC). The influence of the concrete density on STC is shown in Fig. 11.2.1. Precast concrete walls, floors, and roofs usually do not need additional treatments to provide adequate sound insulation. If desired, greater sound insulation can be obtained by using a resiliently attached layer or layers of gypsum board or other building material. The increased transmission loss occurs because the energy flow path is now increased to include a dissipative air space and additional mass. 11.2.5

Impact Noise Reduction

Footsteps, dragged chairs, dropped objects, slammed doors, and plumbing generate impact noise. Even when airborne sounds are adequately controlled there can be severe impact-noise prob­lems. The test method used to evaluate systems for impact-sound insulation is described in ASTM E492, Standard Test Method for Laboratory Measurement of Impact Sound Transmission through Floor-Ceiling Assemblies Using the Tapping Machine.10 The impact-sound-pressure levels are measured in the 16 contiguous one-third-octave bands with center frequencies in the range from 100 to 3150 Hz. For performance specification purposes, the single number impact insulation class (IIC) is used (Table 11.2.1). Table 11.2.1  Impact insulation class (IIC) for concrete slabs Thickness, in.

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5

10

Density of concrete, lb/ft3

IIC

79

23

114

24

144

24

79

28

114

30

144

31

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In general, thickness or density of concrete does not greatly affect the transmission of impact sounds as shown in the table. Structural concrete floors in combination with resilient materials effectively control impact sound. One simple solution consists of good carpeting on resilient padding. Resilient flooring materi­als, such as linoleum, rubber, asphalt, vinyl, or parquet or strip wood floors are not entirely satisfac­tory when applied directly on concrete. Impact sound also may be controlled by provid­ing a discontinuity in the structure such as would be obtained by adding a resilient-mounted plaster or drywall suspended ceiling or a floating floor consist­ing of a second layer of concrete cast over resilient pads, insulation boards, or mastic. The thickness of floating slabs is usually controlled by structural requirements; however, a thickness providing as little as 8 lb/ft2 would be acoustically adequate in most instances. 11.2.6

Often, acoustical control is specified as to the minimum insulation values of the dividing partition system. Local building codes, lending institutions, and the Department of Housing and Urban Develop­ment (HUD) list both airborne STC and impact IIC values for different living environments. For exam­ple, the HUD recommendations11 are given in Table 11.2.2. Table 11.2.2  HUD recommendations for sound transmission class (STC) and impact insulation class (IIC) STC

IIC

Between living units

45

45

Between living units and public space

50

50

Grade I suburban

Grade II residential, urban, and suburban

Grade III urban

Walls

STC 55

STC 52

STC 48

Floor-ceiling assemblies

STC 55 IIC 55

STC 52 IIC 55

STC 48 IIC 48

Leaks and Flanking

The performance of a building section with an otherwise adequate STC can be seriously reduced by a relatively small hole or any other path that allows sound to bypass the acoustical barrier. All noise that reaches a space by paths other than through the primary barrier is called flanking. Com­mon flanking paths are gaps between floor perime­ters and curtain walls, openings around doors or windows, at electrical outlets, telephone and televi­sion connections, and pipe and duct penetrations. Sealants, safing, and/or closure plates are useful in reducing flanking. Suspended ceilings in rooms where walls do not extend from the ceiling to the roof or floor above allow sound to travel to adjacent rooms. Use of full-height walls will alleviate this source of leakage. In general, the probability of flanking paths in a concrete structure is much lower than in a structure of steel or wood. 11.2.9

Table 11.2.3  Sound insulation criteria for reference 3

Composite Wall Considerations

An acoustically composite wall is made of elements of varying acoustical properties. Doors and windows are often the weak link in an otherwise effective sound barrier. Minimal effects on sound transmission loss will be achieved in most cases by a proper selection of glass (plate versus insulating).13 Mounting of the glass in its frame should be done with care to eliminate noise leaks and to reduce the glass-plate vibrations. Sound transmission loss of a door depends on its material and construction and the sealing between the door and the frame. Acoustical design must consider the acoustical properties of doors, windows or other elements, the ratio of openings in the wall system, and the dis­tances between openings. Installation procedures and materials must be specified to ensure desired acoustical seals. 11.2.8

 stablishment of Noise Insulation E Objectives

Location

11.2.7

Acoustical Test Results

Table 11.2.4 presents the ratings for various precast concrete walls and floor-ceiling assemblies.

Note: ICC = impact insulation class; STC = sound transmission class.

Other community ordinances are more specific, listing the sound insulation criteria with relation to particular ambient environments (Table 11.2.3).12 Once the objectives are established, the designer should refer to available data, for example, Figure 11.2.1 or Table 11.2.4, and select the system that best meets these requirements. In this respect, concrete systems have superior properties and can, with minimal effort, comply with these criteria.

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Table 11.2.4 Airborne sound transmission class (STC) and impact insulation class (IIC) ratings from tests of precast concrete assemblies Assembly

STC

Description

IIC

Wall systems 49a

–

55

–

Assembly 2 with “Z” furring channels, 1 in. insulation, and /2 in. gypsum board, 75.5 lb/ft2

62

–

4

Assembly 2 with wood furring, 11/2 in. insulation, and 1/2 in. gypsum board, 73 lb/ft2

63

–

5

Assembly 2 with 1/2 in. space, 15/8 in. metal stud row, 11/2 in. insulation, and 1/2 in. gypsum board

63b

–

6

8-in.-thick flat panel, 95 lb/ft2

58

–

7

14 in. prestressed double-tees with 4-in.-wide flange, 75 lb/ft

54

–

1

4-in.-thick flat panel, 54 lb/ft2

2

6-in.-thick flat panel, 75 lb/ft

3

2 1

2

Floor-ceiling systems 8

8 in. hollow-core prestressed units, 57 lb/ft2

50

28

9

Assembly 8 with carpet and pad, 58 lb/ft

50

73

10

1

8 in. hollow-core prestressed units with /2 in. wood block flooring adhered directly, 58 lb/ft2

51

47

11

Assembly 10 except 1/2 in. woodblock flooring adhered to 1/2 in. sound-deadening board underlayment adhered to concrete, 60 lb/ft2

52

55

12

Assembly 11 with acoustical ceiling, 62 lb/ft2

59

61

13

Assembly 8 with quarry tile, 11/4 in. reinforced mortar bed with 0.4 in. nylon and carbon black spinerette matting, 76 lb/ft2

60

54

14

Assembly 13 with suspended 5/8 in. gypsum board ceiling with 31/2 in. insulation, 78.8 lb/ft2

61

62

15

14 in. prestressed double-tees with 2-in.-thick concrete topping, 75 lb/ft2

54

24

16

Assembly 15 with carpet and pad, 76 lb/ft

54

72

17

Assembly 15 with resiliently suspended acoustical ceiling with 1 /2 in. mineral fiber blanket above, 77 lb/ft2

59

51

18

Assembly 17 with carpet and pad, 78 lb/ft2

59

82

19

4-in.-thick flat slabs, 54 lb/ft

49

25

20

5-in.-thick flat slabs, 60 lb/ft

21

2

2 1

2

52

a

24

5-in.-thick flat slab concrete with carpet and pad, 61 lb/ft

52a

68

22

6-in.-thick flat slabs, 75 lb/ft2

55

34

23

8-in.-thick flat slabs, 95 lb/ft

58

34a

24

10-in.-thick flat slabs, 120 lb/ft2

59a

31

25

10-in.-thick flat slab concrete with carpet and pad, 121 lb/ft

59a

74

2 2

2

2

a. The STC of sandwich panels is approximately the same as the STC of the thickness of the two concrete wythes (ignoring the insulation thickness). b. Estimated values.

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CHAPTER 11 11.3

THERMAL AND ACOUSTICAL PROPERTIES OF PRECAST CONCRETE

References

1. A  NSI/ASHRAE/IESNA. 2004. Energy Standard for Buildings Except Low-Rise Residential Buildings. Standard 90.1. Atlanta, GA. 2. A  merican Society of Heating, Refrigerating, and AirConditioning Engineers (ASHRAE). 2003. ASHRAE Handbook­—Fundamentals. New York, NY: ASHRAE. 3. A  merican Society of Testing and Materials (ASTM). 2004. Standard Test Method for Steady-State Heat Flux Measurements and Thermal Transmission Properties by Means of the Guarded-Hot-Plate Apparatus (ASTM C177). West Cohonshockon, PA: ASTM.

  11

The following are additional useful references that are not cited in the text: •

 arris, C. M. 1997. Handbook of Acoustical Measure­ H ments and Noise Control. Melville, NY: Acoustical Society of America.

•

Litvin, A., and H. W. Belliston. December 1978. Sound Trans­mission Loss through Concrete and Concrete Masonry Walls. Journal of the American Con­crete Institute, V. 75, No. 12.

•

 recast Prestressed Concrete Institute. 1978. Acoustical P Properties of Precast Concrete. PCI Journal, V. 23, No. 2.

4. A  STM. 2005. Standard Test Method for Thermal Performance of Building Materials and Envelope Assemblies by Means of a Hot Box Apparatus (ASTM C1363). West Cohonshockon, PA: ASTM. 5. P  ortland Cement Association (PCA). 1981. Simplified Thermal Design of Building Envelopes. Bulletin EB089. Skokie, IL: PCA. 6. A  merican Concrete Institute (ACI). 2002. Guide to Thermal Properties of Concrete and Masonry Systems (ACI 122-02). Farmington Hills, MI: ACI. 7. L  ee, Y. J., and S. Pessiki. 2003. Development of the Characteristic Section Method to Estimate Thermal R-Values for Precast Concrete Sandwich Wall Panels, ATLSS Report No. 03-06. Center for Advanced Technology for Large Structural Systems, Lehigh University, 73 pp. 8. A  STM. 2003. Recommended Practice for Selection of Vapor Barriers for Thermal Insulation (ASTM C755). West Conhoshocken, PA: ASTM. 9. B  alik, J. S., and G. B. Barney. 1984. Thermal Design of Precast Concrete Buildings. PCI Journal, V. 29, No. 6. 10. A  merican Society for Testing and Materials (ASTM). 2009. Standard Test Method for Laboratory Measurement of Impact Sound Transmission through Floor-Ceiling Assemblies Using the Tapping Machine (ASTM E492). West Cohonshocken, PA: ASTM. 11. B  erendt, R. D., G. E. Winzer, and C. B. Burroughs. 1975. A Guide to Airborne, Impact and Structure-Borne Noise Control in Multi-Family Dwellings, prepared for Federal Housing Administration. Washington, DC: U.S. Government Printing Office. 12. S  abine, H. J., M. B. Lacher, D. R. Flynn, and T. L. Quindry. 1975. Acoustical and Thermal Perfor­mance of Exterior Residential Walls, Doors and Windows. National Bureau of Standards. Washington, DC: U.S. Government Printing Office. 13. H  edeen, Robert A. 1980. Compendium of Materials for Noise Control, U.S. Department of Heath, Education and Welfare. Washington, DC: U.S. Government Printing Office. 11–26

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CHAPTER 12

CHAPTER 12 VIBRATION DESIGN OF PRECAST / PRESTRESSED CONCRETE FLOOR SYSTEMS 12.1

Introduction...............................................................................................................................................................12-2

12.2

Human Response to Floor Vibrations.......................................................................................................................12-2

12.3

Types of Floor Vibration...........................................................................................................................................12-2 12.3.1 Walking.......................................................................................................................................................12-2 12.3.2 Rhythmic Activities....................................................................................................................................12-2 12.3.3 Mechanical Equipment...............................................................................................................................12-2

12.4

Natural Frequency of Vibration.................................................................................................................................12-2 12.4.1 Computing the Natural Frequency..............................................................................................................12-2 12.4.2 Computing Deflection.................................................................................................................................12-2 12.4.3 Effect of Supporting Girders.......................................................................................................................12-3 12.4.4 Minimum Natural Frequency......................................................................................................................12-4 12.4.5 Graphs of Natural Frequency......................................................................................................................12-4

12.5

Damping....................................................................................................................................................................12-4 12.5.1 Types of Damping.......................................................................................................................................12-4 12.5.2 Estimation of Damping...............................................................................................................................12-4

12.6

Vibrations Caused by Walking..................................................................................................................................12-5 12.6.1 Minimum Natural Frequency......................................................................................................................12-5 12.6.2 Effective Weight.........................................................................................................................................12-5 12.6.3 Recommended Values for Kw and ßm..........................................................................................................12-5

12.7

Design for Rhythmic Excitation................................................................................................................................12-5 12.7.1 Harmonics...................................................................................................................................................12-5 12.7.2 Recommended Minimum Natural Frequency.............................................................................................12-5 12.7.3 Higher Harmonics.......................................................................................................................................12-5 12.7.4 Adjacent Activities......................................................................................................................................12-6

12.8

Stadium Seating.........................................................................................................................................................12-6

12.9

Vibrations in Mixed-Use Structures with Parking....................................................................................................12-8

12.10

Vibration Isolation for Mechanical Equipment.........................................................................................................12-8

12.11

References.................................................................................................................................................................12-9

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CHAPTER 12

12.1

VIBRATION DESIGN OF PRECAST / PRESTRESSED CONCRETE FLOOR SYSTEMS

Introduction

When the natural frequency of a floor sytem is close to a forcing frequency (the frequency resulting from applied forces or activity), and the deflection of the system is significant, motion will be perceptible and possibly even annoying. Perception is related to the activity of the occupant: a person at rest or engaged in quiet work will tolerate less vibration than a person performing an active function, such as dancing or aerobics. If a floor system dissipates the imparted energy in a very short period of time, the motion is less likely to be perceived as disruptive. Thus, the damping characteristics of the system affect acceptability. This chapter discusses the vibration characteristics of precast, prestressed concrete systems and is a condensation of the material contained in Reference 1, which is based on information in References 2 through 6.

  12

12.2

Human Response to Floor Vibrations



Building vibrations are generally controlled by specifying a minimum natural frequency for a structural system. These, in turn, depend on the permissible peak accelerations (as a fraction of gravitational acceleration), the mass engaged during an activity, the degree of continuity of the floor system, the environment in which the vibration occurs, the effectiveness of interaction between connected structural components, and the degree of damping. Vibration theory is mostly derived from experience with steel and wood floors. In gen­eral, floor vibrations are much less likely to be a problem with stiffer, more massive concrete floors. Because of a lack of source information, some building types common in precast concrete con­struction are not dealt with in this handbook. Limits described for the structure types listed in this chapter may be extended to other structure types using sound engineering judgement. It must be emphasized that vibration calculations are very approximate. The natural fre­quency of a floor can be estimated to a reasonable degree of accuracy, but the calculation of the required frequency is based on damping and on human response, both of which are subject to much variation. When the acceptability of a proposed floor system is in doubt, the same method of analysis can be used to compare it with similar existing systems that are known to be acceptable or unacceptable.

12.3

Types of Floor Vibration

Walking

As a walking person’s foot touches the floor, a vibration of the floor system is created. This vibration may be annoying to other persons sitting or lying in the same area, such as an office, a church, or a residence. Although more than one person may be walking in the same area at the same time, 12–2

12.3.2

Rhythmic Activities

In some cases, several or many people may engage in a coordinated activity that is at least par­tially synchronized. Spectators at sports events, rock concerts, and other entertainment events often move in unison in response to music, a cheer, or other stimuli. The people engaged in the rhythmic activity have a higher level of tolerance for the induced vibrations, while those at rest nearby will have a lower level of tolerance. 12.3.3

Mechanical Equipment

Mechanical equipment may produce a constant impulse at a fixed frequency, causing the structure to vibrate.

12.4

Natural Frequency of Vibration

Each of the three input types described in Section 12.3 requires a somewhat different solution; however, all require knowledge of an important response parameter of the floor system, its natural frequency of vibration. The natural frequency of a floor system is important in determining how human occupants will perceive vibrations. It has been found that certain frequencies seem to set up resonance with internal organs of the human body, making these frequencies more annoying to people. The human body is most sensitive to frequencies in the range of 4 Hz to 8 Hz (cycles/second). This range of natural frequencies is commonly found in typical floor systems. Human perception of vibration varies, depending on what the person is doing. A person sitting or lying down is more sensitive to vibration than a person who is walking or active. This is accounted for in design by the various Kw values and acceleration limits in Tables 12.6.1 and 12.7.1. 12.4.1

Computing the Natural Frequency

The natural frequency of a vibrating beam is determined by the ratio of its mass (or weight) to its stiffness. The deflection of a simple span beam is also dependent on its weight and stiffness. A simple relationship exists between deflection ∆j and natural frequency fn of a uniformly loaded, simple-span beam on rigid supports:2,3

Analysis methods for three types of vibration are described. These analyses differ because the characteristics causing the vibration differ. 12.3.1

their footsteps are normally not synchronized. Therefore, the analysis is based on the effect of the impact of an individual person walking.

fn = 0.18

g Δj

(Eq. 12-1)

NOTE: All the equations in this chapter are dimensionally correct. Provided the reader is careful to be sure that the units used cancel out to produce the desired units for the answer, correct results will be obtained using either U.S. customary or SI units.

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CHAPTER 12

12 11

2

With 10 lb/ft superimposed load f c’ = 5000 psi, normalweight Ed = 1.2 × 33 × 1501.5 × f c’

10

10

DT

8D

T2

4H

+2

12

4+

2

DT

2

2 8+

2

2+

C1

C 4H

7

32

6+ FS

Natural frequency fn, Hz

9

28

+2

15

DT

34

12

DT

5

30

  12

Use of values below 3 Hz is not recommended

1

Span, ft Fig. 12.4.1 Natural frequency of selected floor units. Note: See Chapter 3 for component descriptions.

12.4.2

Computing Deflection

The deflection Δj for a uniformly loaded, simple-span floor unit is:

Δj =

5w 4 384EdI



(Eq. 12-2)

Many vibration problems are more critical when the mass (or weight) is small. When computing ∆j, use a minimum realistic live load when computing w, not the maximum live load. For prestressed components, I can be taken as the gross moment of inertia, even though the component may theoretically be cracked at full service load. The dynamic modulus of elasticity Ed, as measured by the natural frequency, is higher than the static modulus given in ACI 318‑05. It is recommended that ACI 318-05 code modulus be multiplied by 1.2 when computing ∆j for use in determining fn, the natural frequency.2 For continuous spans of equal length, the natural frequency is the same as for simple spans. During vibration, one span deflects down while the adjacent spans deflect upward. An inflection point exists at the supports, and the deflection and natural frequency are the same as for a simple span. For unequal continuous spans, the theoretical simple-span deflection ∆j using Eq. 12-2 may be multiplied by the following coefficients.

Beam continuous at one end:

0.4 + 0.6 ls/l



Beam continuous at both ends:

0.2 + 0.8 ls/l

PCI DESIGN HANDBOOK/SEVENTH EDITION

where: l = span length of beam or one-way slab; clear projection of cantilever



ls = span length of side span

The modified ∆j may then be used in Eq. 12-1 to find the natural frequency of the continuous beam. These multipliers are based on a conservative straight-line relationship between a simple-span beam and one with fixed end(s). See Reference 2, Fig. 4.3 for a more precise multiplier. References 2 and 3 provide additional information concerning the natural frequency of indeterminate beams. Of course, the natural frequency of indeterminate structures may be found directly by modeling with appropriate software. 12.4.3

Effect of Supporting Girders

The deflection of beams or girders supporting the floor system also affects the natural frequency of the floor system. The simple-span deflection ∆g of the floor girder may be calculated in the same manner as ∆j. The natural frequency of the floor system may then be estimated by the following formula:2,3

fn = 0.18

g Δ j + Δg

(Eq. 12-3)

For concrete floor systems supported on walls, ∆g may be assumed to be zero. For concrete floor systems supported by

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concrete girders, ∆g is normally small and is often neglected, unless the girders are unusually long or flexible. For concrete floor units supported on steel beams, the beam deflection can have a significant effect, and should be included in computing fn. 12.4.4

Minimum Natural Frequency

Floors and floor systems with natural frequencies lower than 3 Hz are not recommended because people may be able to synchronize their actions at lower frequencies.3 12.4.5

12.5.2

Estimation of Damping

Damping of a floor system is highly dependent on the nonstructural items (partitions, ceilings, furniture, etc.) present. The modal damping ratio of a bare structure undergoing lowamplitude vibrations can be very low, on the order of 0.01. Non-structural elements may increase this up to 0.05. The results of a vibration analysis are highly influenced by the choice of the assumed damping, which can vary widely. Yet, this choice is based more on judgment than science.

Graphs of Natural Frequency

For a floor unit on rigid supports, Eq. 12-1 and 12-2 may be combined to produce Eq. 12-4:

  12

1.58 EdI g fn = ⎛⎜ 2 ⎞⎟ ⎝  ⎠ w

(Eq. 12-4)

Figure 12.4.1 shows the relation between span and expected natural frequency for selected floor units given in Chapter 3.

12.5

Damping

Damping determines how quickly a vibration will decay and die out. This is important because human perception and tolerance of vibration or motion are dependent on how long it lasts. Seasickness is an example of this, in which the duration of motion is much more important than the amplitude or frequency. Damping is usually expressed as a fraction or percent of critical damping. A critically damped system is so dampened that motion slowly returns to zero without ever having completed a cycle of motion in the opposite direction. Real building structures have damping from 1% to a few percentage points of the critical value. 12.5.1

Types of Damping

Given: 10DT32 + 2 (see Chapter 3) Open office area: 60 ft span Problem: Check for vibration caused by walking. Solution: Use Eq. 12-5 to find minimum required fn:

⎡ ⎛ K ⎞⎤ fn ≥ 2.86 ⎢In ⎜ w ⎟ ⎥ (Eq. 12-5) ⎢⎣ ⎝ βdWf ⎠ ⎥⎦

m = 0.02 Kw = 13 kip

(Table 12.6.1) (Table 12.6.1)

Estimate effective weight Wf :

There are two types of damping used in the literature on building vibrations. Unfortunately, many earlier papers are not clear on which type is used. The two types are: Modal damping – This is the type of damping used in (nearly) steady-state vibration analysis. The damping is caused by energy dissipation from friction and viscous (hysteretic) processes within the system. Textbooks on vibration commonly refer to this type of damping. Log-decrement damping – This type of damping is observed after a single (nonrepetitive) impulse on the system. The term “log-decrement” refers to the logarithmic decay rate. The decay of motion caused by a single impulse occurs at a faster rate because the energy of the impulse is transferred to other parts of the structure, as well as being absorbed by the loaded element itself. Log-decrement damping was commonly used in earlier writings about vibration due to walking, because it seemed more closely related to the motion caused by individual footfall impact. The modal damping is approximately half of the log-decrement damping.3 Care should be taken not to confuse the two types of damping. References 2 through 6 are based on modal damping. Larger values of damping (that might be based on log-decrement) should not be mixed with damping values used in those references. 12–4

EXAMPLE 12.6.1 Vibrations Caused by Walking



wt = 89 lb/ft2 + 10 lb/ft2 (assumed superimposed) = 99 lb/ft2 = 0.099 kip/ft2 Estimate effective width B = 0.6 = 36 ft:

Wf = wt(B)() = (0.099) (36) (60) = 214 kip

Note that in this case, it was not necessary to convert feet to inches, because the feet units cancel out. Minimum requirement from Eq. 12-5:

⎡ ⎛ ⎞⎤ 13 fn = 2.86 ⎢ln ⎜ ⎟ ⎥ = 3.18 Hz ⎢⎣ ⎝ 0.02 214 ⎠ ⎥⎦

(

)

From Fig. 12.4.1 for a 10DT32+2 with a 60 ft span, the expected fundamental frequency is approximately 4.1 Hz, which is greater than the required minimum value of 3.18 Hz. Therefore, the floor system satisfies vibration recommendations.

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12.6

Vibrations Caused by Walking

12.7

CHAPTER 12

Design for Rhythmic Excitation

Vibrations caused by walking are seldom a problem in a concrete floor system because of the system’s mass and stiffness. When using concrete floor systems of ordinary proportions, it is usually not necessary to check for vibrations caused by walking. When designing concrete floor systems of long-span or slender proportions, this section may be used to evaluate their serviceability with respect to vibrations.

Rhythmic excitation occurs when a group of people move in unison to a cadence that is defined as a rhythmical series of movements. A resonance can occur when the input frequency is at or near the fundamental frequency of the floor system. Therefore, the fundamental frequency of the floor system must be sufficiently higher than the input frequency to prevent resonance. (See Section 12.7.1.)

12.6.1

12.7.1

Minimum Natural Frequency

An empirical formula, based on resonant effects of walking, has been developed to determine the minimum natural frequency of a floor system needed to prevent disturbing vibrations caused by walking:4

⎡ ⎛ K ⎞⎤ fn ≥ 2.86 ⎢ ln ⎜ w ⎟ ⎥ ⎢⎣ ⎝ βmW f ⎠ ⎥⎦

(Eq. 12-5)



ln = natural logarithm and the constant 2.86 has the unit Hertz (cycles/second).

12.6.2

Effective Weight

The effect of an impact such as a footfall is strongly influenced by the mass (or weight) of the structure affected by the impact. This weight Wf is normally taken as the unfactored unit dead load (per square foot) of the floor units plus some (not full code) live load, multiplied by the span and by a width B. For solid or hollow-core slabs, which are stiff in torsion, it is recommended that B equal the span.2 For double-tees, it is recommended that B vary from 0.8l for 18 in. double-tees with 2 in. to 3 in. topping to 0.6l for 32 in. double-tees with 2 in. to 3 in. topping.5 For continuous spans, Wf may be increased 50%.2,3 At an unstiffened edge of a floor, the width B used for estimating floor-system weight should be multiplied by 0.5.2 12.6.3

Recommended Values for Kw and ßm

The recommended values of Kw and ßm for use in Eq. 12-5 are given in Table 12.6.1. Table 12.6.1  Values of Kw and βm for use in Eq. 12-5 (based on Table 3 of Reference 4) Occupancies affected by the vibrations Offices, residences, churches

A harmonic of a frequency is any higher fre­quency that is equal to the first or fundamental frequency multiplied by an integer. Resonance occurs when the forcing frequency and the natural frequency are nearly equal, causing greater amplitudes of vibrations. If the fundamental frequency of a floor system is equal to a harmonic of the exciting frequency, resonance may occur. 12.7.2

where

Kw, kip 13

ßm

0.02a 0.03b 0.05c

Shopping malls

4.5



0.02

Footbridges

1.8



0.01

a. For floors with few non-structural components (ceilings, ducts, partitions, and the like) and furnishings, open work area, and churches. b. For floors with non-structural components and furnishings, but with only small, demountable partitions, typical of many modular office spaces. c. For floors with full-height partitions.

PCI DESIGN HANDBOOK/SEVENTH EDITION

Harmonics

Recommended Minimum Natural Frequency

The following design criterion for minimum natural frequency for a floor system subjected to rhythmic excitation is based on dynamic response of the floor system to dynamic loading:2,3

⎛ k ⎞ αi wp Minimum fn = f f 1 + ⎜ r ⎟ (Eq. 12-6) ⎝ ao / g ⎠ wt

Recommended values for all of the parameters on the right side of Eq. 12-6 are given in Tables 12.7.1 and 12.7.2, except for kr, which is shown above, and wt, which includes the actual distributed dead weight of the floor system. Note that Eq. 12-6 uses the distributed weight wt (unit weight per area), not the total weight of a panel Wf that was used in Eq. 12-5. See Table 12.7.1 for limiting values of ao/g and Table 12.7.2 for αi and ff. Suggested values for kr are 1.3 for dancing, 1.7 for lively concert or sport events, and 2.0 for aerobics. The computation of the natural frequency of the floor system fn is discussed in Section 12.4. If rhythmic activities take place on the upper floors of a tall building, it is sometimes necessary to take the elastic shortening of the columns into effect, in a manner similar to Eq. 12-3 for girder flexibility. This is discussed in Reference 7. Table 12.7.1  Recommended acceleration limits for rhythmic activities (based on Table 2-3, Reference 2) Occupancies affected by the vibrations

Acceleration limit, fraction of gravity, ao/g

Office or residential

0.004 – 0.007

Dining

0.015 – 0.025

Weightlifting

0.015 – 0.025

Rhythmic activity only

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0.04 – 0.07

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CHAPTER 12

Table 12.7.2  Estimated loading during rhythmic events (based on Table 5.2, Reference 3) Forcing frequency ff Hz

Activity Dancing: first harmonic Lively concert or sports event: first harmonic second harmonic

Weight of Dynamic coefficient αi participants wp (lb/ft2)a

Dynamic load αiwp (lb/ft2)b

1.5 – 3

12

0.5

6

1.5 – 3 3 – 5

30 30

0.25 0.05

8 1.5

4 4 4

1.5 0.6 0.1

6 2.4 0.4

Jumping exercises: first harmonic second harmonic third harmonic

2 – 2.75 4 – 5.5 6 – 8.25

a. Based on maximum density of participants on the occupied area of the floor for commonly encountered conditons. For special events, the density of participants can be greater.

  12

b. αi represents a particular harmonic being considered.

12.7.3

Higher Harmonics

Equation 12-6 will always require a higher natural frequency fn than the forcing frequency ff. Thus, it is crucial to determine whether the forcing frequencies for higher harmonics need be considered. Equation 12-7 gives the peak acceleration apk/g for a condition of resonance:3

⎛ 1.3 ⎞ ⎛ α i w p ⎞ =⎜ g ⎝ 2βm ⎟⎠ ⎜⎝ wt ⎟⎠

a pk



(Eq. 12-7)

North American standards show the same requirements for lively concerts and sports events, as shown in Table 12.7.2. However, a British publication treats these two activities quite differently.8 The British recommendations for sports events are similar to those used in North America; however, the British publication warns that rock concerts may result in a much more synchronized loading, and it recommends a minimum natural frequency of 6 Hz for facilities used for rock concerts. In applying Eq. 12-7, Reference 3 recommends a value for the damping ratio ßm as follows: “Because participants contribute to the damping, a value of approximately 0.06 may be used, which is higher than … for walking vibration.” If the damping ratio ßm or the total distributed weight wt is high enough, the dynamic load αiwp from Table 12.7.2 for higher harmonics may result in a peak acceleration apk /g within the acceleration limits ao /g given in Table 12.7.1. If this occurs, higher harmonics need not be considered. Most topped or pretopped concrete floors weigh 75 lb/ft2 or more. For these floors, the weight wt is such that the resonant acceleration at the third harmonic frequency will usually be within limits. Usually, only the first and second harmonics need be considered for topped concrete floors. 12.7.4

Adjacent Activities

A space with a quiet activity may be located next to a space with rhythmic activity. In such cases, it is desirable to have a rigid wall between the two spaces, supporting the floor system in each space. If this is not practical, the acceleration lim12–6

its for the quiet activity should be used in combination with the rhythmic loading for the rhythmic activity. This combination can often be critical for concrete floor systems, requiring a stiffer floor than needed for supporting gravity loads.

12.8

Stadium Seating

Precast, prestressed concrete seating units, as shown in Example 12.8.1, are often used in stadiums and arenas. They are usually manufactured in units that are two or three rows wide. Connections are usually provided between the upper and lower units, to prevent differential deflection of the adjacent units. These seating units are subjected to rhythmic excitation, as a crowd responds in unison to a cheer or song. The response of the seating units is different from that of an ordinary flat floor. The seating units have a three-dimensional nature and vibrate and deflect about their weakest principal axis, as shown in the example. Furthermore, the bays in stadiums are often of non-uniform span. Each seating unit has a different span, and thus a different natural frequency, which helps to prevent resonance. Fifty-six different seating units made by PCI Producer Members have been examined. All are known to have satisfactory performance in service. This exam­ination produced the following items to consider: 1. The units should be sufficiently interconnected, with a minimum of three connections per bay, to prevent differential deflection between adjacent units. If people sit on one unit with their feet resting on another unit below, they are much more sensitive to differential deflections of the two units. 2. For bays of uniform width or with an angle in plan θ less than 5 degrees (Fig. 12.8.1), the minimum natural frequency requirement for the first harmonic should be satisfied. For bays of non-uniform width with an angle in plan θ of 5  degrees or more, the minimum frequency requirement may be reduced 25%. 3. For interconnected units, the minimum natu­ral fre-

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CHAPTER 12

EXAMPLE 12.8.1 Stadium Seat Given: Stadium seat section shown fc' = 5000 psi, normalweight Ed = 4287 ksi × 1.2 = 5144 ksi w = 474 lb/ft I = 12,422 in.4 on inclined weak principal axis

Next unit Principal axes

Problem: Find maximum span governed by vibration. Solution: Use Eq. 12-6 to find minimum natural frequency:

Minimum, fn

⎛ k r ⎞ ⎛ α iw p ⎞ = fr 1+ ⎜ ⎝ ao / g ⎟⎠ ⎜⎝ w t ⎟⎠

  12

Note: " = inch; º = degree.

where: kr = 1.7 for sports events (see Section 12.7.2). Refer to Tables 12.7.1 and 12.7.2. For first harmonic, use the following assumptions: Forcing frequency ff = 2.5 Hz

(engineer’s judgement within range of Table 12.7.2)

Acceleration limit ao /g = 0.06

(engineer’s judgement within range of Table 12.7.1)

Weight of participants wp = 30 lb/ft

(Table 12.7.2)

Dynamic load αiwp = 8 lb/ft2

(Table 12.7.2)

2

⎛ 64 ⎞ Dynamic load component in weak direction = 8 ⎜ ⎟ (cos 31.8) = 36.3 lb/ft ⎝ 12 ⎠

Total weight (a measure of mass) = 474 + 30 ×

64 = 634 lb/ft 12

Note that the mass is not reduced by cos 31.8 deg, because mass is the same in all directions. For bays of uniform width (Fig. 12.8.1)

⎛ 1.7 ⎞ ⎛ 36.3 ⎞ fn fn == 2.5 1+ ⎜ = 4.0 Hz ⎝ 0.06 ⎟⎠ ⎜⎝ 634 ⎟⎠

Find maximum span from Eq. 12-4:

fn

= 1. 58 2

l max

EIg 1. 58 = 2 w l max

(

)(

5144 12, 422 386 0.634 / 12

) = 1,079,550 l 2max

1,079,550 1,079,550 = fn 4.0



22max = max =



2 = max 269, 888 = 519.5 in. = 43.3 ft max =

For bays of non-uniform width (Fig. 12.8.1), the minimum frequency may be reduced by 25% fn = 0.75(4) = 3 Hz

2 max == max

1,079,550 = 600 in. = 50 ft 3.0

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CHAPTER 12

90 °

rm unifo Non- bay width

Uniform width bay

90

°

deg Plan of stadium seating Fig. 12.8.1 Uniform- and non-uniform-width bays in a stadium.

  12

quency requirement for the second harmonic need not be applied. Apparently, vibration in a diagonal plane caused by the second harmonic of the input motion is not occurring in these seating units.

12.9

Vibrations in Mixed-Use Structures with Parking

Mixed-use structures combining retail, residential, or commercial tenant space with ancillary parking areas have become a widely accepted use of precast concrete construction. Such structures commonly incorporate the required parking levels above or below the occupied space, thus allowing the structure to serve multiple functions. With the simultaneous presence of moving vehicles and building occupants, there may be concern that vibrations from the vehicles will prove uncomfortable to the tenants. While there is no authoritative collection of research data on this topic, the widespread successful use of such systems endorses their suitability. Regional precasters can be contacted for component and connection configurations that have proven effective on previous projects. Special considerations may be necessary for structures housing vibration-sensitive equipment or processes.

12.10

ment. The required weight of an inertia block depends on the total weight of the machine and the unbalanced force. For a long-stroke compressor, five to seven times the compressor weight might be needed. For high-pressure fans, one to five times the fan weight is usually sufficient. A floor that supports resiliently mounted equipment must be stiffer than the isolation system. If the static deflection of the floor approaches the static deflection of the mounts, the floor becomes a part of the vibrating system, and little vibration isolation is achieved. In general, the floor deflection should be limited to about 15% of the deflection of the mounts. Simplified theory shows that for 90% vibration isolation, a single resilient supported mass (isolator) should have a natural frequency of about one-third the driving frequency of the equipment. The natural frequency of this mass can be calculated by:9

fn = 0.16

g Δi

(Eq. 12-8)

From the above, the required static deflection of an isolator can be determined as follows:

fn =

fdr g = 0.16 3 Δi

or: g fdr2



Δi = 0.23

and:

∆f ≤ 0.15 ∆i

(Eq. 12-9)

(Eq. 12-10)

Vibration Isolation for Mechanical Equipment

Vibration produced by equipment with unbal­anced operating or starting forces can usually be isolated from the structure by being mounted on a heavy concrete slab placed on resilient supports. This type of slab, called an inertia block, provides a low center of gravity to compensate for thrusts, such as those generated by large fans. For equipment with less unbalanced weight, a “housekeeping” slab is sometimes used below the resilient mounts to provide a rigid support and to keep them above the floor so they are easier to clean and inspect. This slab may also be mounted on pads of precompressed glass fiber or neoprene. The natural frequency of the total load on resilient mounts must be well below the frequency generated by the equip12–8

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12.11 EXAMPLE 12.10 Vibration Isolation

Problem: Determine the approximate minimum deflection of the isolator and the maximum deflection of the floor system that should be allowed.



fdr = 800 (cycles/min)/60 (sec/min) = 13.33 Hz



⎛ g ⎞ ( 0.23) ( 386 ) = 0.50 in. Δi = 0.23 ⎜ 2 ⎟ = ⎝ fdr ⎠ (13.3)2



∆i = 0.50 in.

∆f = 0.15∆i ≤ 0.15(0.5) = 0.075 in.

2. A  pplied Technology Council (ATC). 1999. ATC Design Guide 1, Minimizing Floor Vibration. Redwood City, CA: ATC, 49 pp. 3. A  merican Institute of Steel Construction (AISC). 1997. AISC Design Guide 11. Floor Vibrations Due to Human Activity. Chi­cago, IL: AISC. 4. A  llen, D. E., and T. M. Murray. 1993. Design Criterion for Vibrations Due to Walking. Engineering Journal, Fourth Quarter, AISC: pp. 117–129. 5. C  hen, Y., and A. Aswad. 1994. Vibration Character­ istics of Double Tee Building Floors. PCI Journal, V. 39, No. 1: pp. 84–95.

Solution: Use Eq. 12-9



References

1. M  ast, R. F. 2001. Vibration of Precast Prestressed Concrete Floors. PCI Journal, V. 46, No. 6: pp. 76–86.

Given: A piece of mechanical equipment has a driving frequency of 800 cycles per minute.

From Eq. 12-10:

CHAPTER 12

6. M  urray, T. M. 2000. Floor Vibrations: Tips for Design­ ers of Office Buildings. Structure, Fall, National Council of Structural Engineers: pp. 26–30. 7. A  llen, D. E. 1990. Building Vibration from Human Activities. Concrete International, V. 12, No. 6: pp. 66–73. 8. I nstitution of Structural Engineers. 2001. Dynamic Performance Requirements for Permanent Grandstands Subject to Crowd Action. London, England: Institution of Structural Engineers. 9. H  arris, C. M., and C. E. Crede. 1976, updated 2002. Shock and Vibration Handbook. 5th ed. New York, NY: McGraw-Hill Book Co.

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TOLERANCES FOR PRECAST AND PRESTRESSED CONCRETE

CHAPTER 13

CHAPTER 13 TOLERANCES FOR PRECAST AND PRESTRESSED CONCRETE 13.1

General..................................................................................................................................................................... 13–2 13.1.1 Definitions.................................................................................................................................................. 13–2 13.1.2 Purpose....................................................................................................................................................... 13–3 13.1.3 Responsibility............................................................................................................................................. 13–3 13.1.4 Tolerance Acceptability Range.................................................................................................................. 13–3 13.1.5 Relationships between Different Tolerances............................................................................................. 13–4

13.2

Product Tolerances................................................................................................................................................... 13–4 13.2.1 General....................................................................................................................................................... 13–4 13.2.2 Overall Dimensions................................................................................................................................... 13–4 13.2.3 Sweep or Horizontal Misalignment.......................................................................................................... 13–4 13.2.4 Position of Strands.................................................................................................................................... 13–4 13.2.5 Camber and Differential Camber.............................................................................................................. 13–4 13.2.6 Weld Plates............................................................................................................................................... 13–5 13.2.7 Haunches of Columns and Wall Panels.................................................................................................... 13–5 13.2.8 Warping and Bowing................................................................................................................................ 13–7 13.2.9 Smoothness............................................................................................................................................... 13–7 13.2.10 Architectural Panels versus Structural Products....................................................................................... 13–7

13.3

Erection Tolerances................................................................................................................................................. 13–7 13.3.1 General....................................................................................................................................................... 13–7 13.3.2 Recommended Erection Tolerances.......................................................................................................... 13–8 13.3.3 Mixed Building Systems........................................................................................................................... 13–8 13.3.4 Connections and Bearing.......................................................................................................................... 13–9

13.4

Clearances............................................................................................................................................................... 13–26 13.4.1 General..................................................................................................................................................... 13–26 13.4.2 Joint Clearance......................................................................................................................................... 13–26 13.4.3 Procedure for Determining Clearance...................................................................................................... 13–26 13.4.4 Clearance Examples................................................................................................................................. 13–26

13.5

Interfacing Tolerances............................................................................................................................................ 13–32 13.5.1 General..................................................................................................................................................... 13–32 13.5.2 Interface Design Approach...................................................................................................................... 13–32 13.5.3 Characteristics of the Interface................................................................................................................13–33

13.6

References.............................................................................................................................................................. 13–34

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TOLERANCES FOR PRECAST AND PRESTRESSED CONCRETE

CHAPTER 13

13.1

General

This chapter introduces the subject of tolerances as related to buildings and provides the designer with some of the basic tolerances that should be considered during the layout and design of precast concrete struc­tures. This chapter is a cursory presentation of infor­mation that has been previously published by PCI and reviewed by the precast concrete industry. Because of this, PCI documents (see References 1 through 4) that discuss the subject of tolerances more fully should be specified in contract docu­ments and referred to when resolving questions about tolerances. 13.1.1

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Definitions

Bowing. An overall out-of-plane condition in which two opposite edges of a component, such as a panel, fall in the same plane and the portion of the panel between the edges is out of plane. Camber. (1) The out-of-plane translation of a point within the span of a prestressed component that occurs due to the net bending resulting from an eccentric prestressing force (not including dimen­sional inaccuracies); (2) a built-in curvature. Camber is typically measured at midspan. Connection. A device for the attachment of pre­cast concrete components to each other or to the structure to which it is attached. Connection design must account for the cumulative effects of all allowed tolerance variations. Contract documents. General conditions, project specifications, and drawings issued on behalf of the owner by the design professionals of record (architect/engineer) and from which the project erection drawings and production drawings are developed. Clearance. Interface space (distance) be­tween two components. Clearance is normally speci­fied to allow for the effects of product and erection tolerances and for anticipated movement such as deflection, volume change movement, and the like. Clear distance. The least distance between the surface of the reinforcement and the referenced surface. The referenced surface may be the form, adjacent reinforcement, embedments, concrete sur­face, or other surfaces. Concealed surface. Surface not visible during normal use of the component. Deviation. The departure from an established reference point, line, plane, or surface measured in a direction that is perpendicular to the reference line, plane, or surface. Dimensions. The following are several differ­ent categories of dimensions relevant to precast concrete fabrication. • Actual dimension. The measured dimension of the precast concrete component after casting. The actual or as-built dimension may differ from the working dimension due to construction and material-induced variations. • Basic dimension. The dimensions shown on the contract drawings or called for in the specifica­tions. The basic dimension applies to size, location, and relative location. It may also be called the nominal dimension. 13–2

• Working dimension. The planned dimension of the precast concrete component obtained from its basic dimension, the necessary joint or clearance dimen­ sions, and other adjustments. Draft. The taper given to features of a mold or form to allow the precast concrete piece to be removed from the mold or form without damage. Draft can result in different feature dimensions between the front and back of a piece. Drawings. The following are typical terms used by the precast/prestressed concrete industry: • Shop drawings. (1) Collective term used for erection drawings, production drawings, and hardware details. (2) Diagrams of individual precast concrete components and their connecting hardware, developed from information in the contract documents. Shop drawings show information needed for both field assembly (erection) and manufacture (production) of the precast concrete components. • Erection drawings. Drawings that show the relationship of the precast components and their connections in the erected structure and that provide necessary information to properly erect and connect the various components. • Production drawings. A set of instructions in the form of diagrams and text that contain all of the information necessary for the manufacturer to produce the precast concrete component. These documents are usually produced by or under the direction of the precast plant engineering department or by an entity hired by the precast concrete manufacturer. Flatness. The degree to which a surface approximates a plane (see smoothness). This toler­ance is most important in wall and slab components. Flushness. The offset relationship of an embedded plate to the surrounding concrete. Plumb. In a vertical line. Pretopped systems. A construction ap­proach, typically used in the floor system of parking structures, in which the double-tee flange for the floor component is constructed to its final thickness in the plant, resulting in cast-in-place concrete topping not being required in the field. Quality. The appearance, strength, durability, and dimensional conformance that is appropriate for the specific product, its particular application, and its expected performance requirements. Quality also refers to the totality of features and characteristics of a product and on its ability to satisfy stated needs. Quality assurance (QA). All those planned or systematic actions necessary to ensure that the final product or service will satisfy given requirements for quality and performance of intended function. Typically, the quality assurance effort will focus on the requirements of the overall project, thereby identify­ing the tolerance quality control requirements for component fabrication. Quality control (QC). Those planned actions that provide a means to measure and control the characteristics of components and materials to pre­determined, quantitative criteria. Relative alignment. The distance between two or more

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components in any plane, or the distance between adjacent components, or the distance between a component and a defined point or plane. Setup. The process of preparing molds or forms for casting, including installation of materials (reinforcement and hardware) prior to the actual placing of concrete. The setup process is second only to the mold or form construction in its import­ ance in the achievement of specified component tolerances. Shrinkage. The volume change in concrete caused by drying that normally occurs during its curing and initial life. The expected shrinkage must be sub­tracted from the form setup dimensions to deter­mine the as-cast dimensions of a component. Smoothness. The absence of local irregularity or roughness. It does not refer to the overall shape of the component. Specially finished structural precast concrete. A component fabricated using forms and techniques common to the production of structural components and having specified surface finishes that require uniformity and detailing more demanding than the typical requirements for structural components. See Chapter 14, Section 14.2.3 of this handbook for PCI plant certification categories. Sweep. An overall variation in a component’s horizon­tal alignment. This can sometimes be caused by horizontally eccentric prestress in narrow components. Tipping. The offset relationship of an embedded plate from one edge to another. Tolerance. The specified permissible deviation from specified requirements such as dimensions, location, and alignment. Examples are: • the permitted deviation from a basic dimension or quantity, as in the length, width, and depth of a component; • the range of variation permitted in maintaining a basic dimension, as in an alignment tolerance; and • a permitted variation from location or alignment. Tolerances, erection. Those allowable deviations in dimensions of a component’s placement in the completed structure required for acceptable layout and placement of precast concrete components after they are erected. Tolerances, interfacing. Those allowable deviations in dimensions associated with other materials or systems in contact with or in close proximity to the precast concrete. Tolerances, product. Those allowable deviations in dimensions relating to individual precast concrete components. Warping. Twisting of a component, resulting in overall out-of-plane curvature of surfaces character­ized by all edges being non-parallel. Warping is most often a concern in panel components, although it can be a concern in other types of components, such as pretopped double-tees.

be developed with the practical limitations of dimensional control in mind, as the tolerances will affect the dimensions of the completed structure. Tolerances are required for the following reasons: • Structural — To ensure that the structural design accounts for factors that are sensitive to variations in dimen­sion and plumbness. Examples include eccentric loadings, bearing areas, and locations of reinforcement and embedded items. • Feasible — To ensure acceptable performance of joints and interfacing materials in the finished structure. • Visual — To ensure that the variations will be controllable and will result in an acceptable-looking structure. • Economical — To ensure ease and speed of production and erection. • Legal — To avoid encroaching on property lines and to establish a standard against which the work can be compared. • Contractual — To establish an acceptability range and also to establish responsibility for developing and maintaining specified tolerances.

13.1.2

Purpose

Tolerances are normally established by economical and practical production, erection, and interfacing considerations, and are based on References 1 through 4. Once established, they should be shown in the contract documents, and used in design and detailing of components and connections. Architectural and structural concepts should

13.1.3

Responsibility

While the responsibility for specifying and main­taining tolerances of the various elements of construction may vary among projects, it is important that these responsibil­ities be clearly assigned. The conceptual design phase of a precast concrete project is the time to begin considering dimensional control. The established tolerances or required performance should fall within generally accepted industry ranges and should not be made more restrictive than necessary. Once the tolerances have been specified, and connections that consider those tolerances have been designed, the production and erection of the components must be organized to ensure tolerance compliance. A quality control program that emphasizes dimensional control is necessary. Likewise, an erection quality assurance program that includes a clear definition of responsibilities will aid in ensuring that the products are assembled in accordance with the specified erection tolerances. Responsibility should include dimension verification and adjustment, if necessary, of both precast concrete components and any interfacing structural elements. 13.1.4

Tolerance Acceptability Range

Tolerances must be used as guidelines for acceptability and not as limits for rejection. If specified toler­ances are met, the product should be accepted. If not, the product may be accepted if it meets any of the following criteria: • Exceeding the tolerance does not affect the structural integrity or architectural performance of the component. • The component can be brought within tolerance by structurally and architecturally satisfactory means. • The total erected assembly can be modified to meet all structural and architectural require­ments.

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 elationships between Different R Tolerances

restrictive tolerances may significantly increase costs; they should not be specified unless absolutely necessary.

A precast concrete component is erected so that its primary control surface is in conformance with the established erection and interfacing tolerances. The secondary control surfaces are generally not directly positioned during erection but are controlled by the product tolerances. Thus, if the primary control surfaces are within erection and interfacing tolerances, and the secondary surfaces are within product tolerances, the component is erected within tolerance. The resulting tolerance limit for the secondary surface may be the sum of the product and erection tolerances. Because tolerances for some features of a precast concrete component may be additive, it must be clear to the erector which are the primary control surfaces. If both primary and secondary control surfaces must be controlled, provisions for adjustment should be included. The accumulated tolerance limits may have to be accommodated in the interface clearance. Surface and feature control requirements should be clearly outlined in the plans and specifications. On occasion, the structure may not perform properly if the tolerances are allowed to accumulate. Which tolerance takes precedence is a question of economics. The costs associated with each of the three tolerances must be evaluated, recognizing unusual situations. This may include difficult erection requirements, connections that are tolerance-sensitive, or production requirements that are set by the available equipment. Any special tolerance requirements should be clearly noted in the contract documents. It is important for the designer of record to be aware of and take into consideration the tolerances of other building materials and systems used in the project.5, 6, 7

13.2

Product Tolerances

13.2.1

General

Product tolerances are listed in the primary report of the PCI Committee on Tolerances, Tolerance Manual for Precast and Prestressed Concrete Construction, MNL-135-00.1 This report contains a more complete discussion of tolerances and should be referred to for more specific details, such as location tolerances for inserts, voids, haunches, and corbels, and for warping tolerances and local smoothness requirements. Tolerances are also presented more completely in three PCI publications, Manual for Quality Control for Plants and Production of Structural Precast Concrete Products, MNL-116-99; Manual for Quality Control for Plants and Production of Architectural Precast Concrete Products, MNL-117-96; and Erectors’ Manual: Standards and Guidelines for the Erection of Precast Concrete Products, MNL-127-99.2,3,4 The products included are listed in Table 13.2.1 in this handbook. Discussion of the more critical tolerances are given in following sections. The values shown have become the consensus standards of the precast concrete industry, and these values are occasionally different from tolerances published by other organizations.6 More

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13.2.2

Overall Dimensions

Typical tolerances for most precast/prestressed concrete products are given in Table 13.2.1. Architectural precast concrete panels have plan dimension tolerances that vary with panel size from ± 1/8 in. for a dimension under 10 ft to ± 1/4 in. for a dimension of 20 ft to 40 ft. The thickness tolerance for top and bottom slabs (flanges) of box beams and hollow-core units are dependent on the position of cores. Flange thickness tolerances are not given for hollow-core units. Instead, measured flange areas cannot be less than 85% of the nominal calculated area. MNL-135-00 emphasizes that the recommended tolerances are only guidelines. Different values may be applicable in some cases, and each project should be considered individually. The designer should also make reference to applicable building codes to establish possibly different tolerances for certain products. For example, Section 1009.3.2 of International Building Code 20068 requires that “the tolerance between the largest and smallest riser height or between the largest and smallest tread depth shall not exceed 0.375 in. in any flight of stairs.” Other similar situations may exist. 13.2.3

Sweep or Horizontal Misalignment

Horizontal misalignment, or sweep, usually occurs as a result of form and component width tolerances. It can also result from prestressing with lateral eccentricity, which should be considered in the design. Joints should be dimensioned to accommodate such variations. Sweep tolerances generally vary with the length of a unit, for example, ± 1/8 in. per 10 ft. The upper limit of sweep varies from ± 3/8 in. for wall panels and hollow-core units to ± 3/4 in. for joists usually used in composite construction. 13.2.4

Position of Strands

It is a common practice to use 5/8 in.-diameter holes in end dividers (bulkheads or headers) for 3/8, 7/16, 1/2, and 0.6-in.diameter strands, because it is costly to switch end dividers for different strand diameters. Therefore, better accuracy in strand placement is achieved when using larger diameter strands. Generally, individual strands must be positioned within ± 1 /4 in. of design position and bundled strands within ± 1/2 in. Hollow-core units have greater individual strand tolerances as long as the center of gravity of the strand group is within ± 1 /4 in. and a minimum cover of 3/4 in. is maintained. 13.2.5

Camber and Differential Camber

Predicted camber is generally based on camber at release of prestress; therefore, camber measurements on products should be made as soon after stripping from the forms as possible. Differential camber refers to the final in-place condition of adjacent components.

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TOLERANCES FOR PRECAST AND PRESTRESSED CONCRETE It is important that cambers are measured at the same time of day, preferably in the early hours before the sun has warmed the components. Cambers for all units used in the same assembly should be checked at the same age. If a significant deviation in camber from calculated values is observed, the cause should be determined and the effect of the deviation on the performance of the component should be evaluated. It should be understood that calculations predicting camber are approximate and that the normal variations of the parameters used can cause deviations of ± 20% over predicted camber. The final installed differential displacement between two adjacent cambered components erected in the field may be the combined result of component differential cambers, variations in support elevations, variation in component depth, and any adjustments made to the components during erection. If differential cambers exceed recommended tolerances, additional effort is often required to erect the components in a manner that is satisfactory for the intended use. For most flexural components, the tolerance for maximum camber variation from predicted camber is ± 3/4 in., and maximum differential camber between adjacent units of the same design is 3/4 in. This may be increased for joists that are used in composite construction. Pretopped precast concrete double-tees in parking structures should have a more stringent tolerance for differential camber between adjacent doubletees so that a smooth riding surface is achieved. A 1/4 in. differential is recommended in Reference 9. Recommendations for camber and differential camber of hollow-core units are not listed because production variations between hollow-core systems result in different tolerances for each type. Regional precast concrete manufactureres should be consulted for appropriate tolerances if differential hollow-core unit camber tolerances are important for a particular project application. 13.2.6

Weld Plates

In general, it is easier to hold plates to closer tolerances at the bottom of a component (as cast or against the side form) than with plates cast in the top of the component. Bottom and side plates can be fastened to the form and, hence, are less susceptible to movement caused by vibration. This applies to position of weld plates as well as tipping and flushness. The tolerance on weld plates is less restrictive than for bearing plates. The position tolerance is ± 1 in. for all products. Tipping and flushness tolerance is ± 1/4 in. 13.2.7

Haunches of Columns and Wall Panels

The importance of corbel- or haunch-location tolerances depends on the connection at the base of the component. Because base connections usually allow some adjustability, it is more important to control dimensions from haunch to haunch in multilevel columns or walls than from haunch to the base of the component. The haunch-to-haunch tolerance is ± 1/8 in. to ± 1/4 in. Bearing surface squareness tolerance is ± 1/8 in. per 18 in. with a maximum of ± 1/4 in., except for architectural precast concrete panels, which have a tolerance of ± 1/8 in., and columns, which have a maximum tolerance of ± 1/8 in. in the short direction and ± 3/8 in. in the long direction.

CHAPTER 13 Table 13.2.1  Typical tolerances for precast/prestressed concrete components Product tolerances Length ± 1/4 in. ± 3/8 in. ± 1/2 in. ± 3/4 in. ± 1 in. Width ± 1/4 in.



Depth



+ /8 in. + 3/8 in., – 1/4 in. ± 3/8 in. ± 1/2 in. 3

+ 1/4 in., – 1/8 in. ± 1/4 in.

+ 1/2 in., – 1/4 in. ± 3/8 in. Flange thickness + 1/4 in., –1/8 in. ± 1/4 in. Web thickness  ± 1/8 in. ± 1/4 in. + 3/8 in., –1/4 in. ± 3/8 in. Position of tendons



± 1/4 in.

± 1/4 in. thickness, ± 1 in. width Camber, variation from design  ± 1/4 in. per 10 ft, ± 3/4 in. maximum ± 1/8 in. per 10 ft, ± 1 in. maximum ± 3/4 in. maximum 1 ± /2 in. maximum Camber, differential 1 /4 in. per 10 ft, 3 /4 in. maximum ± 1/4 in. per 10 ft, ± 1/2 in. maximum Bearing plates, position ± 1/2 in. ± 5/8 in. Bearing plates, tipping and flushness ± 1/8 in. Key: 1 = double-tee 2 = single-tee 3 = building beam (rectangular and ledger) 4 = I-beam 5 = box beam 6 = column 7 = hollow-core unit 8 = ribbed wall panel 9 = insulated wall panel

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Products

18 16, 17 6, 7, 8, 9, 13, 15 3, 5 1, 2, 4, 11, 12, 14  , 2, 3, 5, 6, 7, 8, 9, 12, 15, 1 16, 18 14 4 11, 13 17 10,18  , 2, 3, 5, 6, 7, 8, 9, 12, 13, 1 14, 15 4 11 1, 2, 8, 10, 12, 15 3, 4 1, 8, 10, 12, 15 2,3 4 5  , 2, 3, 4, 5, 6, 8, 9, 11, 12, 1 14, 15, 18 10 1, 2, 12, 15 4 3 5, 15 1, 2, 5 15 1, 2, 3, 12, 15 4

1, 2, 3, 4, 12, 13, 15

10 = architectural wall panel 11 = pile 12 = joist 13 = step unit (see section 13.2.2) 14 = sheet piling 15 = stadium riser unit 16 = prison cell module – single 17 = prison cell module – double 18 = prestressed concrete panels for storage tanks

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Precast concrete panel

Warped plane

True plane

Distance to farthest adjacent corner

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Corner warping Distance to nearest adjacent corner (controls the magnitude of warping)

Fig. 13.2.1 Definition of panel warping.

Exposed face

Maximum bowing

Maximum bowing

Length of bow

Length of bow

Plan (convex bowing)

Plan (concave bowing)

Bowing (plan)

Exposed face (convex) Exposed face (concave)

Length of bow

Bowing elevation

Length of bow (elevation)

Maximum bowing Precast concrete panel

Elevation

Length of bow (plan) Panel bowed in both plan and elevation

Fig. 13.2.2 Definition of panel bowing.

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Warping and Bowing

Warping and bowing tolerances affect panel-edge matchup during erection and the appearance of the erected components. These tolerances are especially critical with architectural precast concrete panels. Warping is a deviation from plane in which the corners of the panel do not fall within the same plane. Warping tolerances are given in terms of corner deviations (Fig. 13.2.1). The allowable deviation from the nearest adjacent corner is 1/16 in. per ft. Bowing differs from warping in that two opposite edges of a panel may fall in the same plane, but the portion of the panel between the edges is out of plane (Fig. 13.2.2). Bowing tolerance is L /360, where L is the length of panel. Maximum tolerance on differential bowing between panels of the same design is 1/2 in. The effects of differential temperature and moisture absorption between the inside and outside of a panel and the prestress eccentricity should be considered in design of the panel and its connections. Pre-erection storage conditions may also affect warping and bowing (see Sections 5.8.5 and 8.4.2). Thin panels are more likely to bow than thick panels, and the tolerances for thinner panels should be more liberal. Similarly, panels made from concrete with a maximum aggregate size greater than 3/4 in., panels using two significantly different concretes, and veneered and insulated panels may require special consideration. In all cases, the regional precaster should be consulted regarding overall economic and construction feasibility. 13.2.9

CHAPTER 13

Smoothness

Local smoothness describes the condition where small areas of the surface may be out-of-plane (Fig. 13.2.3). The tolerance for this type of variation is 1/4 in. per 10 ft for all products. The tolerance is usually checked with a 10 ft straight edge or the equivalent, as explained in Fig. 13.2.3. 13.2.10 A  rchitectural Panels versus Structural Products When discussing tolerances, an architectural panel refers to a class of specified tolerances, not necessarily to the use of the component in the final structure. Architectural panels usually require more restrictive tolerances than structural components for aesthetic reasons. These types of panels are produced in PCI-Certified plants that have an A1 certification. Structural products such as load-bearing spandrel panels, insulated sandwich panels, double-tees, hollow-core units, and solid slabs are often used for exterior facades but are not considered architectural panels. Because of the production method used, structural products with an applied architectural finish have the same tolerance requirements that they would have if they were made without an aesthetic finish. Many structural products are larger than typical architectural panels and require the larger tolerances given in MNL-116-99. Also, structural panels with architectural finishes often carry substantial loads, as in the case of a spandrel panel of a parking garage. These type of panels need to have the larger tolerances specified for structural panels because

Exposed surface of precast concrete unit Variation in local smoothness 10 ft straight edge

3

8 in.

shim

1 2

in. roller (should not fit between surface and straight edge at any point)

1

in. roller 3 8 in. shim (must fit between panel surface and straight edge over entire surface 4

Fig. 13.2.3 Local smoothness variation.

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they are produced by the same people, using the same type of formwork as plain, gray structural panels. Structural panels with an architectural finish are made in PCI-Certified plants that have a C-A certification. If more restrictive tolerances are required, they must be clearly indicated in the contract documents, and the subsequent increased costs should be considered.

13.3

Erection Tolerances

13.3.1

General

Erection tolerances are those to which the primary control surfaces of the component should be set. The final location of other features and surfaces will be the result of the combination of the the erection tolerances given in this section and the product tolerances given in Section 13.2. Table 13.3.1 lists erection tolerances for interface design of precast and cast-in-place concrete components. Table 13.3.2 lists recommended clearances. Because erection depends on the equipment used and site, there may be good reasons to vary some of the recommended tolerances to account for unique project conditions. In general, the more restrictive the erection tolerances are, the higher the cost of erection will be. To minimize erection problems, the dimensions of the in-place structure should be checked prior to starting erection. After erection, and before other trades interface with the precast concrete components, it should be verified that the precast concrete components are erected within tolerances.6

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CHAPTER 13 Table 13.3.1  Erection tolerances for interface design of precast and cast-in-place concrete components Recommended tolerances

Item

Variation in plan location (any column or beam, any location)....................... ± 1/2 in. for columns, ± 1 in. for beams Variation in plan parallel to specified building lines....................... + 1/40 in. per ft for any beam less than 20 ft long or adjacent to columns spaced less than 20 ft apart

/2 in. maximum for adja-

Table 13.3.2  Recommended clearances Recommended minimum clearance

Item Precast concrete component to precast concrete component

/2 in. (1 in. preferred)

1

Precast concrete component to cast-in-place concrete

1 in. (2 in. preferred)

Precast concrete component to steel

1 in. (2 in. preferred)

Precast concrete column covers

11/2 in. (3 in. preferred for tall buildings)

13.3.2

Recommended Erection Tolerances

1

cent columns spaced 20 ft or more apart

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Difference in relative position of adjacent columns from specified relative position (at any check level).................................................. + 1/2 in. Variation from plumb.......................... + 1/4 in. for any 10 ft of height 1 in. maximum for the entire height Variation in elevation of bearing surfaces from specified elevation (any column or beam, any location).. Maximum low = 1/2 in. Maximum high = 1/4 in. Variation of top of spandrel from specified elevation (any location)..................................... + 1/2 in.

Figures 13.3.2 through 13.3.9 show erection tolerances for the following four mixed building systems: • precast concrete component to precast concrete component • precast concrete component to cast-in-place concrete • precast concrete component to masonry • precast concrete component to structural steel construction See Reference 4 for recommended erection tolerances for additional precast concrete components. The tolerances outlined in this section should be the specified tolerances for erection of precast concrete components. If tolerances are desired that are different from those published in PCI documents, this should be made very clear to bidders in the bid documents. 13.3.3

Variation in elevation of bearing surfaces from lines parallel to specified grade lines.......................... + 1/40 in. per ft for any beam less than 20 ft long or for adjacent columns spaced less than 20 ft apart

/2 in. maximum for any beam 20 ft or more in length or for adjacent columns spaced 20 ft or more apart

Mixed Building Systems

Mixed building systems combine precast and prestressed concrete with other materials, usually cast-in-place concrete, masonry, or steel. Typically each industry has its own recommended erection tolerances that apply when its products are used exclusively. The compatibility of those tolerances

1

Precast concrete component

Bearing pad

Variation from specified bearing length on support............................... ± 3/4 in.

Set back distance

Variation from specified bearing width on support................................ ± 1/2 in.

Bearing length Length over support

Jog in alignment of matching edges................................................. 1/2 in. maximum

Support Fig. 13.3.1 Relationship between bearing length and length over support.

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with the precast concrete tolerances should be checked and adjusted when necessary. Example 13.4.2 presents a problem that can occur when erection tolerances are chosen for each system without considering the project as a whole. 13.3.4

Connections and Bearing

The details of connections must be considered when specifying erection tolerances. Space must be provided to perform the tasks necessary to complete the connection under the most adverse combination of tolerances. Bearing length is measured in the direction of the span, and bearing width is measured perpendicular to the span. Bearing length is often not the same as the length of the component’s end projecting over the support (Fig. 13.3.1). When they differ, it should be noted on the erection drawings. The engineer may wish to specify a minimum bearing (size, length, and width) for various precast concrete products. For additional information, see Reference 6.

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CHAPTER 13 Fig 13.3.2  Beam erection tolerances

Building grid datum a d e

f g

Vertical primary control surface (N/A at inverted tee beam)

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Plan

c c • d

b b Ledge both sides at inverted tee beam

Horizontal primary control surface (at support)

Precast concrete beam a1

Support component Centerline of steel support

Elevation

Precast concrete component to precast concrete component, cast-in-place concrete, masonry, or structural steel

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Fig. 13.3.2  Beam erection tolerances (cont.)

The primary control surfaces for beam erection tolerances are usually as shown, although this needs to be confirmed on a job-by-job basis. a = Plan location from building grid datum................................................................................. ± 1 in. a1 = Plan location from centerline of steela................................................................................. ± 1 in. b = Bearing elevationb from nominal elevation at support: Maximum low...................................................................................................................... 1/2 in. Maximum high..................................................................................................................... 1/4 in. c = Maximum plumb variation over height of component: Per 12 in. height.................................................................................................................. 1/8 in. Maximum at rectangular or L-beam.................................................................................... 1/2 in. Maximum at inverted-tee beam.......................................................................................... 3/4 in.

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d = Maximum jog in alignment of matching edges: Architectural exposed edges............................................................................................... 1/4 in. Visually non-critical edges.................................................................................................. 1/2 in. e = Joint width: Architectural exposed joints............................................................................................. ± 1/4 in. Hidden joints.................................................................................................................... ± 3/4 in. Exposed structural joint not visually critical..................................................................... ± 1/2 in. f

= Bearing lengthc (span direction).......................................................................................... ± 3/4 in.

g = Bearing widthc..................................................................................................................... ± 1/2 in. Note: When bearing pads are used at unarmored edges, they should be set back a minimum of 1/2 in. from the face of the support or at least the chamfered dimension at chamfered edges.

a. For precast concrete components on a steel frame, this tolerance takes precedence over tolerance on dimension a. b. Or component top elevation where component is part of a frame without bearing ledges. c. This is a setting tolerance and should not be confused with structural performance requirements set by the architect/engineer. The nominal bearing dimensions and the allowable variations in the bearing length and width should be specified by the engineer and shown on the erection drawings.

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Fig. 13.3.3  Floor and roof component erection tolerances

Building grid datum

Building grid datum a

a

a

a

g g

d

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d

c

c

Double-tee plan

Hollow-core plan

Centerline of steel support

Centerline of steel support

Primary control surface for carpet direct

a1

e

e

Double-tee

Hollow-core h Primary control surface for topped deck with exposed underside

Support component b To allow for -3 4 in. tolerance 3 in. 4

a1

Support component b

Bearing pad by design f

Hollow-core elevation

Holdback as required Building elevation datum

To allow for -3 4 in. tolerance 3 in. 4

Primary control surface for pretopped tee Bearing pad by design f

Holdback as required

Double-tee elevation

Precast concrete component to precast, cast-in-place concrete, masonry or structural steel support

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Fig. 13.3.3  Floor and roof component erection tolerances (cont.) The primary control surfaces for floor and roof component erection tolerances are usually as shown. Tyipcally, there is no designated vertical, primary control surface, and in some scenarios, there are no primary control surfaces at all. This needs to be determined on a job-by-job basis. a = Plan location from building grid datum................................................................................. ± 1 in. a1 = Plan location from centerline of steel supporta.................................................................... ± 1 in. b = Top elevation from building elevation datum at component ends: Covered with topping....................................................................................................... ± 3/4 in. Pretopped tee/carpet direct hollow-core unit................................................................... ± 1/4 in. Untopped roof.................................................................................................................. ± 3/4 in. c = Maximum jog in alignment of matching edges (both topped and untopped construction)................................................................................1 in. d = Joint width: 0 ft to 40 ft component..................................................................................................... ± 1/2 in. 41 ft to 60 ft component................................................................................................... ± 3/4 in. 61 ft + component............................................................................................................. ± 1 in. e = Differential top elevation as erected (for units of same design and length): Field topped........................................................................................................................ 3/4 Pretopped tees at driving lanes.......................................................................................... 1/4 Carpet direct hollow-core slabs.......................................................................................... 1/4 Untopped roof b................................................................................................................... 3/4 f

  13

in. in. in. in.

= Bearing lengthc (span direction).......................................................................................... ± 3/4 in.

g = Bearing widthc (not applicable for hollow-core slabs)......................................................... ± 1/2 in. h = Differential bottom elevation of exposed hollow-core slabsd................................................. 1/4 in. Note: When bearing pads are used at unarmored edges they should be set back a minimum of 1/2 in. from the face of the support or from at least the chamfered dimension at chamfered edges.

a.

 or precast concrete erected on a steel frame building, this tolerance takes precedence over tolerF ance on dimension a.

b. It may be necessary to feather the edges to ± 1/4 in. to properly apply some roof membranes. c.

 his is a setting tolerance and should not be confused with structural performance requirements T set by the architect/engineer. The nominal bearing dimensions and the allowable variations in the bearing length and width should be specified by the engineer and shown on the erection drawings.

d. Untopped installations will require a larger tolerance.

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CHAPTER 13 Fig. 13.3.4  Column erection tolerances

a

•

a

d d •

Building grid datum

a a

Plan

  13 Vertical primary control surface Splice Horizontal primary control surface (at first corbel)

f

•

e

10'-0"

100'-0"

e

b c Building elevation datum

a

Building elevation datum Elevation

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Building grid datum Elevation

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Fig 13.3.4  Column erection tolerances (cont.)

The primary control surfaces are usually as shown, although this needs to be confirmed on a job-byjob basis. a = Plan location from building grid datum: Structural applications...................................................................................................... ± 1/2 in. Architectural applications................................................................................................. ± 3/8 in. b = Top elevation from nominal top elevation: Maximum low..................................................................................................................... 1/2 in. Maximum high.................................................................................................................... 1/4 in. c = Bearing haunch elevation from nominal elevation: Maximum low..................................................................................................................... 1/2 in. Maximum high.................................................................................................................... 1/4 in. d = Maximum plumb variation over height of component (component in structure of maximum height of 100 ft):......................................................... 1 in.

  13

e = Plumb in any 10 ft of element height.................................................................................... 1/4 in. f = Maximum jog in alignment of matching edges: Architectural exposed edges.............................................................................................. 1/4 in. Visually non-critical edges................................................................................................. 1/2 in.

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CHAPTER 13 Fig. 13.3.5  Structural wall panel erection tolerances

A d

d Building grid datum Precast concrete panel

Vertical primary control surface

e e

i

a

h 10

Building elevation datum

Cast-in-place or precast concrete Plan

  13

h

b c

10'-0"

Cast-in-place foundation of precast concrete support

f

10'-0"

a

g

Horizontal primary control surface

Nominal joint width Elevation

Section A

Precast concrete component to precast concrete or cast-in-place concrete or masonry

d

d

Building grid Vertical primary datum control surface Support component e

i

Horizontal primary control surface

e h10

10'-0"

c

Steel structure

Plan

h

b

a

a1

f g

10'-0"

a

g

Building grid datum

Centerline of steel structure

Nominal joint width Elevation

Section

j

Precast concrete components to structural steel

Bowing section – panels

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Fig. 13.3.5  Structural wall panel erection tolerances (cont.)

The primary control surfaces are usually as shown, although this needs to be confirmed on a job-byjob basis. a = Plan location from building grid datuma.............................................................................. ± 1/2 in. a1 = Plan location from centerline of steel support..................................................................... ± 1/2 in. b = Top elevation from nominal top elevation: Exposed individual panel................................................................................................. ± Non-exposed individual panel.......................................................................................... ± Exposed relative to adjacent panel.................................................................................. ± Non-exposed relative to adjacent panel.......................................................................... ±

/2 /4 1 /2 3 /4

1

3

in. in. in. in.

c = Support elevation from nominal elevation: Maximum low...................................................................................................................... 1/2 in. Maximum high..................................................................................................................... 1/4 in.

  13

d = Maximum plumb variation over height of structure or over 100 ft, which ever is lessa........................................................................... 1 in. e = Plumb in any 10 ft of element height.................................................................................... 1/4 in. = Maximum jog in alignment of matching edges...................................................................... 1/2 in.

f

g = Joint width (governs over joint taper).................................................................................. ± 3/8 in. h = Joint taper over height of panel............................................................................................. 1/2 in. h10 = Joint taper over 10 ft height.................................................................................................. 3/8 in. i = Maximum jog in alignment of matching faces: Exposed to view................................................................................................................. 3/8 in. Not exposed to view.......................................................................................................... 3/4 in. j = Differential bowing as erected between adjacent components of the same designb............................................................ 1/2 in. a. For precast concrete buildings in excess of 100 ft tall, tolerances a and d can increase at the rate of 1 /8 in. per story to a maximum of 2 in. b. Refer to Section 13.2.8 for description of bowing tolerance.

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CHAPTER 13

Fig. 13.3.6  Architectural walls/spandrel erection tolerances

Building grid datum

dd •

a

h

Horizontal primary control surface

f

Vertical primary control surface

i

e a

e

•

c

a1

Support component

Building grid datum

Building elevation datum

Section Walls

Plan Walls

Elevation Walls

dd •

a

g

10'-0"

10'-0"

Centerline of steel support

  13

h10 b

Horizontal primary control surface

h or h 10

Vertical primary control surface

i

e

•

e k

b 10'-0"

a Centerline of steel support

g c

Support component

a1 Plan Spandrels

f

Building elevation datum

Side Spandrels

Elevation Spandrels

j Bowing plan Spandrels

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Fig. 13.3.6  Architectural walls/spandrel erection tolerances (cont.)

The primary control surfaces are usually as shown, although this needs to be confirmed on a job-byjob basis. a = Plan location from building grid datuma.............................................................................. ± 1/2 in. a1 = Plan location from centerline of steel supportb................................................................... ± 1/2 in. b = Top elevation from nominal top elevation: Exposed individual panel.................................................................................................. ± 1/4 in. Non-exposed individual panel........................................................................................... ± 1/2 in. c = Support elevation from nominal elevation: Maximum low....................................................................................................................... 1/2 in. Maximum high...................................................................................................................... 1/4 in. d = Maximum plumb variation over height of structure or 100 ft, whichever is lessa................................................................................................... 1 in.

  13

e = Plumb in any 10 ft of element height.................................................................................... 1/4 in. f = Maximum jog in alignment of matching edges: Exposed relative to adjacent panel..................................................................................... 1/4 in. Non-exposed relative to adjacent panel............................................................................. 1/2 in. g = Joint width (governs over joint taper).................................................................................. ± 1/4 in. h = Joint taper maximum............................................................................................................. 3/8 in. h10 = Joint taper over 10 ft length.................................................................................................. 1/4 in. i

= Maximum jog in alignment of matching faces....................................................................... 1/4 in.

j

= Differential bowing as erected between adjacent components of the same design: Exposed relative to adjacent panel..................................................................................... 1/4 in. Non-exposed relative to adjacent panel............................................................................. 1/2 in.

k = Opening height between spandrels..................................................................................... ± 1/4 in.

a. For precast concrete buildings in excess of 100 ft tall, tolerances a and d can increase at the rate of 1/8 in. per story to a maximum of 2 in. b. For precast concrete components erected on a steel frame, this tolerance takes precedence over tolerance on dimension a.

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CHAPTER 13

Fig. 13.3.7  Single, double, and triple riser erection tolerances

Theoretical centerline of support b

a

Building grid or datum (typical)

e

f

h

Vertical primary control surface

e

k

Plan

  13 To allow for -1 in. tolerance Holdback as required 1 in. Shims per design f

Horizontal primary control surface

d

c Building grid or datum (typical)

Elevation Horizontal primary control surface

e g or j

Vertical primary control surface

Cross section

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Fig. 13.3.7  Single, double, and triple riser erection tolerances (cont.)

The primary control surfaces for single, double, and triple riser erection tolerances are usually as shown, although this is something that needs to be confirmed with the contractor on a job-by-job basis. Local building codes may require more restrictive riser-height tolerances, which could also affect product tolerance. a = Plan location from building grid line datum.......................................................................... ± 1 in. b = Plan location from theoretical centerline of support structure.............................................. ± 1 in. c = Top elevation from building elevation datum at member’s end (datum may be adjusted to accommodate existing field conditions.)............................................................................. ± 1/2 in. d = Maximum jog in alignment of matching edges at the horizontal primary control surface................................................................................ 1/4 in. e = Maximum jog in alignment of matching edges at the vertical primary control surface.................................................................................... 1/2 in. f

  13

= Bearing in span direction........................................................................................................–1 in.

g = Joint width (horizontal) at end of piece (joint width needs to be 1/4 in. minimum)...................................................................................... ± 1/2 in. h = Joint width (joint width needs to be 1/4 in. minimum in either case) 90 deg angle.................................................................................................................... ± 1/2 in. Joint width at skewed ends . ........................................................................................... ± 5/8 in. j

= Differential camber (at midspan as erected) between adjacent components of the same design................................................................................ ± 3/16 in. per 10 ft of component length

k = Differential sweep (at midspan as erected) between adjacent components of the same design................................................................................ ± 3/16 in. per 10 ft of component length

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CHAPTER 13 Fig. 13.3.8  Room module erection tolerances

Building grid or datum (typical) f

a

e

  13 a Plan

Vertical primary control surface (front)

d

d

•

c e

b

Horizontal primary control surface (door head)

c Elevation

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Fig. 13.3.8  Room module erection tolerances (cont.)

The tolerances listed below (a–g) are used at the primary control surfaces only, and only those tolerances that are applicable to that surface are used. Normally, the primary control surfaces are the front face of the room module as the vertical primary control surface, and either the head of the door, top of room module, or the bottom of balcony as the horizontal primary control surface. Note: On jobs where pretopped balconies are cast as part of the room module, the horizontal primary control surface may be the top surface of the balcony. a = Plan location from building grid line datum......................................................................... ± 1/2 in. b = Vertical control (at primary control surface) from a horizontal datum...................................................................................................... ± 3/8 in. c = Actual grout joint.................................................................................................... 1/2 in. minimum d = Plumb at element height........................................................................................................ 1/4 in.

  13

e = Maximum jog in alignment of matching edges....................................................................... 1/4 in. f

= Vertical joint width............................................................................................................... ± 3/8 in.

g = Joint taper.................................................................................................................Not applicable

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CHAPTER 13 Fig. 13.3.9  Stair unit erection tolerance

a

d c e

a

  13

Building grid or datum (typical)

Plan

Primary control surface

f

Line of topping pan (if applicable)

Intermediate landing

b

g

Elevation

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Fig. 13.3.9  Stair unit erection tolerance (cont.)

The primary control surface for stair units is the top of landing at floor levels. The tolerances listed here (a–g) are the same whether landings are monolithic or separate pieces. Local building codes may require more restrictive riser-height tolerance, which could also affect the product tolerance. a = Plan location from building grid line datum......................................................................... ± 1/2 in. b = Differential elevation as erecteda........................................................................................ ± 3/8 in. c = Joint width........................................................................................................................... ± 3/4 in. d = Maximum jog in alignment of matching edges.........................................................................1 in. e = Maximum jog in alignment of stair tread nosings (tolerance overrides d if needed)........................................................................................... 1/2 in. f

= Maximum jog in alignment of matching edges at the primary control surfacea............................................................................................... 3/8 in.

  13

g = Bearing (in span direction).................................................................................................. ± 3/4 in.

a. At stair units that have pretopped precast concrete landings, the maximum jog between stair units, as well as from stair unit to finish floor, cannot exceed 1/4 in. However, units that have landings that are topped have more leeway. This needs to be discussed and agreed on with the general contractor. See Section 13.2.2.

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CHAPTER 13

13.4

Clearances

13.4.1

General

ponents in the structure and how connections will be made. Adjust the clearance as required.

Clearance is the space between adjacent construction elements and provides a buffer area where erection and production tolerance deviations can be absorbed. The following items should be addressed when determining the appropriate clearance to provide in the design: • • • • • • • • • •

  13

product tolerance type of component size of component type of abutting construction location of component component movement function of component erection tolerance space required for fireproofing of steel thickness of plates, bolt heads, and other projecting elements

Of these factors, product tolerances and component movement are the most significant. As shown in the following examples, it may not always be practical to account for all possible factors in the clearance provided. Table 13.3.2 provides recommended minimum clearances for various mixed building systems. 13.4.2

Step 5: Review the clearance to see whether increasing its dimensions will allow easier, more economical erection without adversely affecting aesthetics. Adjust the clearance as required. Step 6: Review structural considerations such as types of connections involved, sizes required, bearing area requirements, and other structural issues. Step 7: Check design to ensure adequacy in the event that minimum component size should occur. Adjust clearance as required for minimum bearing and other structural considerations. Step 8: Select final clearance that will satisfy all of the conditions considered. 13.4.4

Clearance Examples

The following examples are given to show the thought process, and may not be the only solutions for the situations that are described (Fig. 13.4.1 and 13.4.2).

Joint Clearance

Joints between architectural panels must accommodate variations in the panel dimensions and erection tolerances for the panels. They must also provide a good visual line and be sufficiently wide to allow for proper joint-sealant installation. Generally, the larger the panels are, the wider the joints should be. For most situations, architectural panel joints should be designed as being not less than 3/4 in. wide. Tolerances in overall building width and length are normally accommodated in panel joints. 13.4.3

Procedure for Determining Clearance

The following is a systematic approach for making a trial selection of a clearance value and then verifying that selection to ensure that it will allow practical erection to occur: Step 1: Determine the maximum size of the components involved (basic or nominal dimension and additive tolerances). This should include not only the precast/prestressed concrete components, but also other materials. Step 2: To the maximum component size, add the minimum space required for component movement resulting from deflection and thermal variations. Step 3: Check if the resulting clearance allows the component to be erected within the erection and interfacing tolerances, such as plumbness, face alignment, and the like. Adjust the clearance as required to meet all the needs. Step 4: Check if the component can physically be erected with this clearance. Consider the size and location of com13–26

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60'-0" (+ –1 in.) Double-tee roof component (long term shortening, – 14 in.) Detail

25'-0"

Wall thickness tolerance (+14 in., –18 in.)

Plumb tolerance (14 in. per 10 ft)

Ribbed wall panels

  13

1 + – 2 in. plan variance

1 + – 2 in. plan variance

Elevation

3

4 in.

clearance

Precast concrete ribbed wall panel

Precast, prestressed concrete double-tee roof component 6 in.

Detail

Fig. 13.4.1 Clearance example. PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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CHAPTER 13

EXAMPLE 13.4.1 Clearance Determination – Single-Story Industrial Building Given: A 60-ft-long double-tee roof component is bearing on ribbed wall panels that are 25 ft high with a haunch depth of 6 in. beyond the face of the panel. Long-term roof movement is expected to be 1/4 in. Tolerance items to consider (refer to Fig. 13.4.1):

• Double-tee length tolerance ±1 in.



• Maximum plan variance



• Variation from plumb 1/2 in. per 10 ft

± 1/2 in.

Problem: Find the minimum acceptable clearance. _________________________________________________________________________________________

  13

Solution: Step 1: Determine maximum component sizes.

(Refer to Table 13.2.1) Maximum double-tee length Wall thickness Initial clearance chosen

= +1 in. = +1/4 in. = 3/4 in. per end

Step 2: Component movement.  Long-term shrinkage and creep will increase the clearance, so this movement can be neglected in the initial clearance determination, although it must be considered structurally. Required clearance adjustment as a result of component movement 0 3 Clearance chosen (from step 1) /4 in. Step 3: Other erection tolerances. If the ribbed wall panel is set inward toward the building interior 1/2 in. and erected plumb, this would suggest the clearance should be increased by 1/2 in. However, if the panel is erected out of plumb outward 1/2 in., no clearance adjustment is needed. Clearance adjustment required for erection tolerances =0 Clearance chosen (from step 1) = 3/4 in. Step 4: Erection considerations.



13–28

If all components are fabricated perfectly, then the joint clearance is 3/4 in. at either end (13/4 in. total). This is ample space for erection. If all components are at maximum size variance, maximum inward plan variance, and maximum inward variance from plumb, then the total clearance is zero. This is undesirable, as it would require some rework during erection. A judgment should be made as to the likelihood of maximum product and erection tolerances all occurring in one location. If the likelihood is low, the 3/4 in. clearance does not need adjustment, but, if the likelihood is high, the engineer might increase the clearance. In this instance, the likelihood has been judged low; therefore, no adjustment has been made. Clearance chosen (from step 1) = 3/4 in.

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EXAMPLE 13.4.1 Clearance Determination – Single-Story Industrial Building (cont.) Step 5: Economy. In single-story construction, increasing the clearance beyond 3/4 in. is not likely to speed up erection as long as product tolerances remain within allowables. Adjustment is not required for economic considerations. Step 6: Review structural considerations. Allowing a setback from the edge of the corbel, assumed in this instance to have been set by the engineer at 1/2 in. plus the clearance, the bearing is 4 in. There should be space to allow component movement. The engineer judges this to be acceptable from a structural and architectural point of view and no adjustment is required for structural considerations.

Step 7: Check for minimum component sizes.

  13

(Refer to Table 13.2.1) Tee length –1 in. (1/2 in. each end) Wall thickness –1/8 in. Bearing haunch No change 3 Clearance chosen /4 in. Minimum bearing with setback +4 in. (OK in this instance) Wall plumbness would also be considered in an actual application.

Step 8: Solution.

Minimum clearance used



(Satisfies all conditions considered.)

3

/4 in. per end

Note: For simplicity in this example, end rotation, flange skew, and global skew tolerances have not been considered. In an actual situation, these issues should also be considered.

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CHAPTER 13

Theoretical centerline of column

Maximum displacement from theoretical column centerline: toward building line

2 in.

Away from building line

3 in. 36 stories

Possible position of precast concrete facade

1

4

in.

Actual position of column 1 in.

  13

20 stories

2 in.

Theoretical plane of precast concrete facade building line

Steel framing constructed as per AISC Code of Standard Practice

Detail

2 3 4 in. (clearance)

Detail

Precast concrete facade

Steel framing

Fig. 13.4.2 Clearance example – high-rise steel-frame structure.

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CHAPTER 13

EXAMPLE 13.4.2 Clearance Determination – High-Rise Steel-Frame Structure Given: A 36-story, steel-frame structure, with precast concrete cladding, steel tolerances per AISC 303-05 and negligible component movement. In this example, precast concrete tolerance for variation in plan is ± 1/4 in. Refer to Fig. 13.4.2. Problem: Determine whether the panels can be erected plumb and determine the minimum acceptable clearance at the 36th story. _________________________________________________________________________________________ Solution: Step 1: Product tolerances.

(refer to Table 13.2.1) Precast concrete cladding thickness Steel width Steel sweep (varies) Initial clearance chosen

= = = =

  13

+ 1/4 in., – 1/8 in. + 1/4 in., – 3/16 in. ± 1/4 in. (assumption) 3 /4 in.

Step 2: Component movement.

For simplification, assume this can be neglected in this example. Step 3: Other erection tolerances.



Steel variance in plan, maximum Initial clearance Clearance chosen

= 2 in. = 3/4 in. = 23/4 in.

Step 4: Erection considerations.

No adjustment required for erection considerations. Step 5: Economy.



Clearance chosen = 23/4 in. Increasing clearance will not increase economy. No adjustment for economic considerations. Step 6: Structural considerations.



Clearance chosen = 23/4 in. Expensive connection, but possible. No adjustment. Step 7: Check minimum component sizes at 36th story (refer to Table 13.2.1).



Initial clearance Precast concrete thickness Steel width Steel sweep Steel variance in plan minimum Clearance calculated

= 23/4 in. = 1/8 in. = 3/16 in. = 1/4 in. = 3 in. = 65/16 in.

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CHAPTER 13

EXAMPLE 13.4.2 Clearance Determination – High-Rise Steel-Frame Structure (cont.) Step 8: Solution. A clearance of over 6 in. would require an extremely expensive connection for the precast concrete panel, and would produce high torsional stresses in the steel supporting beams. The 6 in. clearance is not practical, although the 23/4 in. minimum initial clearance is still needed. Either the precast concrete panels should be allowed to follow the steel frame or the tolerances for the exterior columns need to be made more stringent, such as the AISC requirements for elevator columns. The most economical choice will likely be for the precast concrete panels to follow the steel frame.

  13

Minimum clearance used: Allow panels to follow the steel frame.

13.5

Interfacing Tolerances

13.5.1

General

= 23/4 in.

as conflict with prestressing strands.

In interfacing with other materials, the tolerances may be very system-dependent. For example, different brands of windows may have different tolerance requirements. If product substitutions are made after the initial design is complete, the interface details must be reviewed for the new system. Following is a partial checklist for consideration in determining interfacing requirements: • • • • • • • • • • • •

structural requirements volume change exposure and corrosion protection waterproofing drainage requirements architectural requirements dimensional considerations vibration considerations fire-rating requirements acoustical considerations economics manufacturing/erection considerations

13.5.2

Step 3: Review the tolerances of each interfacing system. For example, determine the external tolerances on the door jamb from the manufacturer’s specifications. Determine the tolerance on a large-panel door blockout from the precast concrete product tolerances. For the door installation, determine the floor surface tolerance in the area of the door swing path. Step 4: Review the operational clearances required. For example, determine the magnitude of operational clearances that are needed to align the door so it functions properly, and then choose dimensions that include necessary clearances. Step 5: Review the compatibility of the interface tolerances. Starting with the least precise system, check the tolerance requirements and compare them with the minimum and maximum dimensions of the interfacing system. If interferences result, alter the nominal dimension of the appropriate system. For example, it is usually more economical to make a somewhat larger or smaller opening than to specify a non-standard window size.

Interface Design Approach

The following approach is one method of organizing the task of designing the interface between two systems. Step 1: Review the interface between the two systems, show shape and location, and determine contractual responsibilities. For example, the precast concrete panel is furnished by the precast concrete manufacturer, the window is furnished and installed by the window manufacturer, and the sealant between the window and the precast concrete is furnished and installed by the general contractor. Step 2: Review the functional requirements of each interfacing system. For example, the building drain line must have a flow line slope that allows for adequate drainage. This will place limits on where the line must penetrate precast concrete units. Note whether this creates problems such 13–32

Use 3 in.

Step 6: Review assembly and installation procedures for the interfacing systems to ensure compatibility. Show the preferred adjustments to accommodate the tolerances of the systems. Consider such things as minimum bearing areas, minimum and maximum joint gaps, and other dimensions that will vary as a result of interface tolerances. Consider economic trade-offs such as in-plant work versus field work, and minor fit-up rework versus more restrictive tolerances. Step 7: Review the final project specifications as they relate to interfacing. Be aware of the interface consequences of subsystem substitutions that might be made during the final bidding and procurement.

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CHAPTER 13

Characteristics of the Interface

The following list of questions will help to define the nature of the interface: 1. What specifically is to be interfaced? 2. How does the interface function? 3. Is there provision for adjustment upon installation? 4. How much adjustment can occur without rework? 5. What are the consequences of an interface tolerance mismatch? • Rework requirements (labor and material) • Rejection limits 6. What are the high material-cost considerations of the interface? 7. What are the high labor-cost considerations of the interface? 8. What are the normal tolerances associated with the systems to be interfaced? 9. Are the system interface tolerances simple planar tolerances or are they more complex and threedimensional? 10. Do all of the different products of this type have the same interface tolerance requirements? 11. Does the designer of the precast concrete system have control over all of the aspects of the interfaces involved? If not, what actions need to be taken to accommodate this? Listed below are common characteristics to be considered for most systems of the type listed: 1. Windows and doors • No gravity load transfer through window element • Compatible with air and moisture sealant system • Open/close characteristics (swing or slide) • Compatibility with door locking mechanisms 2. Mechanical equipment • Duct clearances for complex prefabricated ductwork • Large-diameter prefabricated-pipe clearance requirements • Deflections from forces associated with largediameter piping and valves • Expansion/contraction allowances for hot and cold piping • Vibration isolation/transfer considerations • Acoustical shielding considerations • Hazardous gas/fluid containment requirements 3. Electrical equipment • Multiple mating conduit runs • Prefabricated cable trays • Embedded conduits and outlet boxes • Corrosion related to DC (direct current) power • Special insert placement requirements for isolation • Location requirements for embedded grounding cables

•

Shielding clearance requirements for special clean electrical lines

4. Elevators and escalators • Elevator guide location requirements • Electrical conduit location requirements • Elevator door mechanism clearances • Special insert placement requirements • Door opening size 5. Architectural cladding • Joint tolerance for sealant system • Flashing and reglet fit-up (Lining up cast-in reglets from panel to panel is very difficult and often costly. Surface-mounted flashing should be considered.) • Expansion and contraction provisions for dissimilar materials • Effects of rotation, deflection, and differential thermal gradients 6. Structural steel and miscellaneous steel • Details to prevent rust staining of concrete • Details to minimize potential for corrosion at field connections between steel and precast concrete • Coordination of structural steel expansion/contraction provisions with those of the precast concrete system • Special provisions for weld plates or other attachment features for steel structures • Consideration of thermal insulation and fireproofing requirements 7. Masonry • Coordination of masonry expansion/contraction provisions with those of the precast concrete system • Detailing to ensure desired contact bearing between masonry and precast concrete units • Detailing to ensure desired transfer of load between masonry shear wall and precast concrete frame • Requirements for dovetail anchors—field installation always preferred 8. Roofing • Roof camber, both upon erection and over the long-term, as it relates to roof drain placement • Fit-up of prefabricated flashing • Dimensional effects of added material during reroofing • Coordination of structural control joint locations with roofing system expansion/contraction provisions • Location of embedded heating, ventilating, and air-conditioning unit supports • Deflections due to live load and added equipment dead loads

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CHAPTER 13 9. Waterproofing • Location and dimensions of flashing reglets grooves • Coordination of waterproofing system requirements with structural system expansion/provisions • Special details around special penetrations 10. Interior finishes • Floors, walls, and ceilings • Joints between precast concrete members for direct-carpet overlay • Visual appearance of joints for exposed ceilings • Fit-up details to ensure good appearance of interior corners • Appearance of cast-in-place to precast con­ crete interfaces

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11. Interior walls and partitions • Clearance for prefabricated cabinetry • Interfacing of mating embedded conduit runs

13.6

References

1. P  CI Committee on Tolerances. 2000. Tolerance Manual for Precast and Prestressed Concrete Construction, MNL-135-00. Chicago, IL: Precast, Prestressed Concrete Institute (PCI). 2. P  CI Plant Certification Committee. 1999. Manual for Quality Control for Plants and Production of Structural Precast Concrete Prod­ucts, MNL-116-99. 4th edition. Chicago, IL: PCI. 3. A  rchitectural Precast Concrete Services Committee and Plant Certification Committee. 1996. Manual for Quality Control for Plants and Production of Architectural Precast Concrete Products, MNL-117-96. 3rd edition. Chicago, IL: PCI. 4. P  CI Erectors Committee. 1999. Erectors Manual  —  Standards and Guidelines, for the Erection of Precast Concrete Products, MNL-127-99. Chicago, IL: PCI. 5. A  merican Institute of Steel Construction (AISC). 2005. Code of Standard Practice for Steel Buildings and Bridges, AISC 303-05. Chicago, IL: AISC. 6. A  merican Concrete Institute (ACI) Committee 117. 1990. Standard Specifications for Tolerances for Concrete Construction and Materials, ACI 117-90. Farmington Hills, MI: ACI. 7. N  ational Concrete Masonry Association (NCMA). 1995. Specification for Masonry Structures, NCMATEK 1-2A. Herndon, VA: NCMA. 8. I nternational Code Council Inc. (ICC). 2006. International Building Code. Washington, DC: ICC. 9. P  CI Committee on Parking Structures. 1998. Precast, Prestressed Parking Structures: Recommended Practice for Design and Construction, MNL-129-98. Chicago, IL: PCI. 13–34

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CHAPTER 14 SPECIFICATIONS AND STANDARD PRACTICES 14.1

PCI Standard Design Practice...................................................................................................................................14-3

14.2 Guide Specification for Structural Precast Concrete and Structural Precast Concrete with Commercial Architectural Finish.................................................................14-23 14.3

Guide Specification for Architectural Precast Concrete.........................................................................................14-23

14.4

Standard Operations Practice Recommendations for Precast Concrete..................................................................14-24 14.4.1 Definitions of Precast Concrete................................................................................................................14-24 14.4.1.1 Structural Precast Concrete.....................................................................................................14-24 14.4.1.2 Architectural Precast Concrete...............................................................................................14-24 14.4.1.3 Prestressed Concrete...............................................................................................................14-24 14.4.2 Samples, Mockups, and Qualifications of Manufacturers and Erectors...................................................14-24 14.4.2.1 Samples and Mockups............................................................................................................14-24 14.4.2.2 Qualification of Manufacturer................................................................................................14-24 14.4.2.3 Certification Categories..........................................................................................................14-24 14.4.2.4 Qualification of Erector..........................................................................................................14-25 14.4.3 Contract Documents and Design Responsibility......................................................................................14-25 14.4.3.1 Contract Documents...............................................................................................................14-25 14.4.3.2 Design Responsibility.............................................................................................................14-25 14.4.4 Shop Drawings..........................................................................................................................................14-26 14.4.4.1 Erection Drawings..................................................................................................................14-26 14.4.4.2 Production Drawings..............................................................................................................14-26 14.4.4.3 Discrepancies..........................................................................................................................14-26 14.4.4.4 Approvals................................................................................................................................14-26 14.4.5 Materials .................................................................................................................................................14-27 14.4.6 Tests and Inspections................................................................................................................................14-27 14.4.6.1 Tests of Materials...................................................................................................................14-27 14.4.6.2 Inspections..............................................................................................................................14-27 14.4.6.3 Fire-Rated Products................................................................................................................14-27 14.4.7 Finishes .................................................................................................................................................14-27 14.4.8 Delivery of Materials................................................................................................................................14-27 14.4.8.1 Manner of Delivery.................................................................................................................14-27 14.4.8.2 Marking and Shipping of Materials........................................................................................14-28 14.4.8.3 Precautions during Delivery...................................................................................................14-28 14.4.8.4 Access to Jobsite.....................................................................................................................14-28 14.4.8.5 Unloading Time Allowance....................................................................................................14-28 14.4.9 Erection .................................................................................................................................................14-28 14.4.9.1 Special Erection Requirements...............................................................................................14-28 14.4.9.2 Tolerances...............................................................................................................................14-28 14.4.9.3 Foundations, Piers, Abutments, and Other Bearing Surfaces.................................................14-28 14.4.9.4 Building Lines and Benchmarks.............................................................................................14-28 14.4.9.5 Anchor Bolts and Bearing Devices.........................................................................................14-28 14.4.9.6 Grout at Bearing Areas...........................................................................................................14-29 14.4.9.7 Utilities...................................................................................................................................14-29 14.4.9.8 Working Space and Crane Access..........................................................................................14-29 14.4.9.9 Materials of Other Trades.......................................................................................................14-29 14.4.9.10 Correction of Errors................................................................................................................14-29 14.4.9.11 Field Assembly.......................................................................................................................14-29 14.4.9.12 Blockouts, Cuts, and Alterations............................................................................................14-29 14.4.9.13 Temporary Floors and Access................................................................................................14-29 14.4.9.14 Painting, Caulking, and Closure Panels..................................................................................14-29

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14.4.9.15 Patching..................................................................................................................................14-29 14.4.9.16 Safety......................................................................................................................................14-29 14.4.9.17 Security Measures...................................................................................................................14-30 14.4.10 Interface with Other Trades......................................................................................................................14-30 14.4.11 Warranty and Acceptance.........................................................................................................................14-30 14.4.11.1 Warranties...............................................................................................................................14-30 14.4.11.2 Acceptance..............................................................................................................................14-30 14.4.12 Contract Administration............................................................................................................................14-30 14.4.12.1 General Statement...................................................................................................................14-30 14.4.12.2 Retentions...............................................................................................................................14-30 14.4.12.3 Contract Agreements..............................................................................................................14-31 14.4.12.4 Terms and Conditions.............................................................................................................14-31

14.5 Recommendations on Responsibility for Design and Construction of Precast Concrete Structures......................14-34 14.5.1 Introduction...............................................................................................................................................14-34 14.5.2 Terminology..............................................................................................................................................14-34 14.5.3 Design Practices........................................................................................................................................14-35 14.5.4 Recommendations.....................................................................................................................................14-36 14.5.4.1 To the Owner..........................................................................................................................14-36 14.5.4.2 To the Licensed Design Professional (LDP)..........................................................................14-36 14.5.4.3 To the Structural Engineer of Record (SER)..........................................................................14-36 14.5.4.4 To the General Contractor......................................................................................................14-37 14.5.4.5 To the Manufacturer (Precaster).............................................................................................14-37 14.5.4.6 To the Specialty Structural Engineer (SSE)...........................................................................14-37 14.6

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PCI Standard Design Practice

Precast and prestressed concrete structures have provided decades of satisfactory performance. This performance is the result of the practices reported herein, conformance with ACI 318-05, Building Code Requirements for Structural Concrete,1 incorporation of industry-specific research programs, and a plant certification program that provides an industry-wide quality control system beyond those found in onsite construction. Precast and prestressed concrete design is based on the provisions of ACI 318-05. In most cases, these provisions are followed explicitly. Occasionally, the interpretation of some sections of ACI 318-05 are required to ensure maintenance of quality in conjunction with the unique characteristics of precast and prestressed concrete fabrication, shipping, and erection. Members of the PCI Building Code Committee, along with other experienced precast concrete design engineers, have identified code provisions that are detailed in this chapter, which require clarification or interpretation. These design practices are followed by a majority of precast concrete design engineers and have produced safe, economical precast/prestressed concrete structures and provided a consistent approach for the members of the design and construction team. Occasionally, strict compliance with the ACI provisions as applied to precast concrete products can cause design, performance, and production problems that may unnecessarily increase the cost of a structure and/or may actually result in an inferior product. In such cases, PCI-sponsored and nationally sponsored research projects have been used to support alternative design and construction practices. Section 1.4 of ACI 318-05 specifically allows variances when analysis, research, or testing demonstrates adequate structural performance. Suggested changes to code provisions resulting from experience, analysis, or testing can provide a point for discussion with building officials for acceptance of revised provisions within the guidance and scope of Section 1.4 of ACI 318-05. This list of provisions is based on ACI 318-05, and the numbers refer to sections in that document and are presented in numerical order. For notation used within this document, refer to the notation in Chapter 2 of ACI 318-05. References to the PCI Design Handbook: Precast and Prestressed Concrete are to the seventh edition, unless otherwise noted. Excerpts from ACI 318-05 are reprinted here with permission of the American Concrete Institute.

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CHAPTER 1 - GENERAL REQUIREMENTS 1.2 Drawings and Specifications

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1.2.1(e) Size and location of all structural elements, reinforcement, and anchors.

1.2.1(e) Reinforcement in this case does not refer to prestressing steel. In precast concrete members, reinforcement may be shown only on the piece drawings. (Reference PCI Design Handbook, Section 14.4.4.1)

1.2.1(g) Magnitude and location of prestressing forces.

1.2.1(g) For pretensioned concrete products, the prestressing design and detailing may be left to an engineer employed or retained by the manufacturer and may be shown only on the piece drawings and design calculations. (Reference PCI Design Handbook, Sections 14.4 and 14.5)

1.2.2 Calculations pertinent to design shall be filed with the drawings when required by the building official. Analyses and designs using computer programs shall be permitted provided design assumptions, user input, and computergenerated output are submitted. Model analysis shall be permitted to supplement calculations.

1.2.2 Product calculations and frequently other items such as connections are usually performed by an engineer designated by the precast concrete manufacturer. They are then submitted to the Engineer or Architect of Record, who is responsible for filing these documents with the building official. (Reference PCI Design Handbook, Sections 14.4 and 14.5)

1.3.1 Concrete construction shall be inspected as required by the legally adopted general building code. In the absence of such inspection requirements, concrete construction shall be inspected throughout the various work stages by or under the supervision of a registered design professional or by a qualified inspector.

1.3.1 Precast concrete products produced by PCI member producers are inspected by internal quality control inspectors under the guidance of PCI's Manual for Quality Control for Plants and Production of Structural Precast Concrete Products (MNL-116-99)2 or Manual for Quality Control for Plants and Production of Architectural Precast Concrete Products (MNL-117-96).3 These PCI member producers are required to follow these procedures and are periodically monitored by independent quality certification inspectors. PCI-Certified plants are "Approved Fabricators," as defined in the model codes and satisfy the special inspection requirements.

CHAPTER 2 - DEFINITIONS 2.1 Code Notation bw = web width, or diameter of circular section, in., Chapters 10–12, 21, 22, Appendix B

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2.1 The quantity bw is the sum of the average stem width of an individual stem in tapered stem members such as doubletees. This is critical in Eq. 11-14. In hollow-core units, bw is the minimum web width.

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Moment frame. Frame in which members and joints resist forces through flexure, shear, and axial force. Moment frames shall be categorized as follows:

2.2 Design of precast concrete moment frames is discussed in Chapter 4 of the PCI Design Handbook. Designs consistent with ACI T1.1-014 (which has been replaced by ACI 374-1.055) are in full compliance with ACI 318-05 (see Section 3.8.8).

Intermediate moment frame. A cast-in-place frame complying with the requirements of 21.2.2.3 and 21.12 in addition to the requirements for ordinary moment frames.

Definitions of these terms are also located in Chapter 21 of ACI 318-05. Definition of special moment frame in Chapter 21 is more specific in its references to sections that require compliance.

2.2 Definitions

 rdinary moment frame. A cast-in-place or precast O concrete frame complying with the requirements of Chapters 1 through 18. Special moment frame. A cast-in-place frame complying with the requirements of 21.2 through 21.5, or a precast frame complying with the requirements of 21.2 through 21.6. In addition, the requirements for ordinary moment frames shall be satisfied. Structural walls. Walls proportioned to resist combinations of shears, moments, and axial forces induced by earthquake motions. A shear wall is a structural wall. Structural walls shall be categorized as follows:

Design of precast concrete shear wall buildings is discussed in Chapter 4 of the PCI Design Handbook. Designs consistent with ACI ITG 5.16 are in full compliance with ACI 318-05.

Intermediate precast structural wall. A wall complying with all applicable requirements of Chapters 1 through 18 in addition to 21.13.

Precast concrete walls that are designed to conform to ACI 318-05 Section 21.8, and by reference to 21.7 and 21.13, are special reinforced concrete shear walls, with the design factors as defined in ASCE 7-05,7 Table 12.2-1.

 pecial precast structural wall. A precast wall S complying with the requirements of 21.8. In addition, the requirements of ordinary reinforced concrete structural walls and the requirements of 21.2 shall be satisfied.  pecial reinforced concrete structural wall. A S cast-in-place wall complying with the requirements of 21.2 and 21.7 in addition to the requirements for ordinary reinforced concrete structural walls.

Tendon. In pretensioned applications, the tendon is the prestressing steel. In post-tensioned applications, the tendon is a complete assembly consisting of anchorages, prestressing steel, and sheathing with coating for unbonded applications or ducts with grout for bonded applications.

PCI DESIGN HANDBOOK/SEVENTH EDITION

Definitions of these terms are also located in Chapter 21 of ACI 318-05. Definitions of special precast concrete structural wall and special reinforced concrete structural wall in Chapter 21 are more specific in their references to sections that require compliance.

Precast, prestressed concrete products are nearly always pretensioned with seven-wire strand. Thus, the terms tendon, prestressing steel, and strand are used interchangeably.

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CHAPTER 3 – MATERIALS 3.5.2 Welding of reinforcing bars shall conform to Structural Welding Code — Reinforcing Steel (ANSI/AWS D1.4)8 from the American Welding Society (AWS). Type and location of welded splices and other required welding of reinforcing bars shall be indicated on the design drawings or in the project specifications. ASTM reinforcing bar specifications, except for ASTM A 706,9 shall be supplemented to require a report of material properties necessary to conform to the requirements in ANSI/AWS D1.4.

3.5.2 A significant amount of connection field welding is common in precast concrete construction. AWS and the American Institute of Steel Construction (AISC) recommendations are generally followed, as modified in the PCI Design Handbook and the PCI manual Design and Typical Details of Connections for Precast and Prestressed Concrete.10 Other connection devices, such as welded headed studs and deformed bar anchors, are also shown in these publications. AWS specifications should be followed when welded stainless- or galvanized steel reinforcing bars or plates are used. (Reference PCI Design Handbook, Section 6.5.1)

3.5.5 Prestressing steel

3.5.5 Nearly all strand used in precast, prestressed concrete products is seven-wire strand conforming with ASTM A416, manufactured with low-relaxation wire conforming with the supplement to ASTM A421. Other prestressing steel that is occasionally used includes three-wire strand, deformed prestressing wire, and higher-strength strand. These prestressing steels are acceptable provided the requirements of 3.5.5.2 are met.

3.5.5.1 Steel for prestressing shall conform to one of the following specifications:

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(a) Wire conforming to Standard Specification for Uncoated Stress-Relieved Steel Wire for Prestressed Concrete (ASTM A 421);11 (b) Low-relaxation wire conforming to Standard Specification for Uncoated Stress-Relieved Steel Wire for Prestressed Concrete, including ASTM A 421; (c) Strand conforming to Standard Specification for Steel Strand, Uncoated Seven-Wire for Prestressed Concrete (ASTM A 416);12 (d) Bar conforming to Standard Specification for Uncoated High-Strength Steel Bars for Prestressing Concrete (ASTM A 722).13 3.5.5.2 Wire, strands, and bars not specifically listed in ASTM A 421, A 416, or A 722 are allowed provided they conform to minimum requirements of these specifications and do not have properties that make them less satisfactory than those listed in ASTM A 421, A 416, or A 722. 3.8.8 Acceptance Criteria for Moment Frames Based on Structural Testing (ACI T1.1-01) is declared to be part of this code as if fully set forth herein.

CHAPTER 4 – DURABILITY REQUIREMENTS

3.8.8 ACI T1.1-01 (which has been replaced by ACI 374.1-05) is primarily intended to address precast concrete moment frames using unbonded post-tensioning and is in compliance with ACI 318-05.

4.2 Freezing and Thawing Exposures 4.2.1 Normalweight and lightweight concrete exposed to freezing and thawing or deicing chemicals shall be airentrained with air content indicated in Table 4.2.1. Tolerance on air content as delivered shall be ±1.5%. For specified compressive strength fc' greater than 5000 psi, reduction of air content indicated in Table 4.2.1 by 1.0 % shall be permitted. 14–6

4.2.1 Some studies have shown that the very low water– cementitious materials ratios used in most precast concrete products require less air entrainment than cast-in-place concrete. (Reference Some Physical Properties of High Strength Concrete14 and Frost and Scaling Resistance of High Strength Concrete.15)

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4.2.2 Concrete that will be subject to the exposures given in Table 4.2.2 shall conform to the corresponding maximum water-cementitious materials ratios and minimum specified concrete compressive strength requirements of that table. In addition, concrete that will be exposed to deicing chemicals shall conform to the limitations of 4.2.3.

4.2.2 (Note: See ACI 318-05 for the table referenced in this section.) The exposures discussed in this section affect the cover requirements given in Chapter 7 of ACI 318-05. While the high-quality concrete produced in precasting plants is generally resistant to severe exposure, the use of deicing chemicals directly on all concrete surfaces is strongly discouraged.

4.4.1 For corrosion protection of reinforcement in concrete, maximum water soluble chloride ion concentrations in hardened concrete at ages from 28 to 42 days contributed from the ingredients including water, aggregates, cementitious materials, and admixtures shall not exceed the limits of Table 4.4.1. When testing is performed to determine water-soluble chloride ion content, test procedures shall conform to ASTM C 1218.16

4.4.1 Calcium chloride or other admixtures containing chlorides are rarely used in precast concrete, and never in prestressed concrete, as required in ACI 318-05 Section 3.6.3. The requirements of this section regarding prestressed concrete are assumed to be met when all materials used in the concrete meet the appropriate ASTM specifications. See PCI Journal article, “Concrete, Chlorides, Cover and Corrosion.”17 (Reference PCI Design Handbook, Section 9.6.6)

CHAPTER 5 – C  ONCRETE QUALITY, MIXING, AND PLACING 5.2.3 Concrete proportions shall be established in accordance with 5.3 or, alternatively, 5.4, and shall meet applicable requirements of Chapter 4.

5.2.3 Producers of precast concrete products use standard mixtures that have been designed and substantiated in accordance with this section unless specifically stated for unusual conditions.

5.11.3.2 Accelerated curing shall provide a compressive strength of the concrete at the load stage considered at least equal to required design strength at that load stage.

5.11.3.2 The Commentary states “...the modulus of elasticity Ec of steam-cured specimens may vary from that of specimens moist-cured at normal temperatures.” It is, however, most common for the ACI equation to be used to calculate Ec even when accelerated curing is used. Some producers may recommend other values based on testing. (Reference PCI Design Handbook, Section 9.2.2.4.) Also note that curing by direct exposure to steam is seldom used in precasting plants.

CHAPTER 7 – D  ETAILS OF REINFORCEMENT 7.5.2 Unless otherwise specified by the registered design professional, reinforcement, including tendons, and posttensioning ducts shall be placed within the tolerances in 7.5.2.1 and 7.5.2.2.

7.7.5 Corrosive environments

7.5.2 Precast concrete products conform to PCI tolerance standards specified in PCI’s Tolerance Manual for Precast and Prestressed Concrete Construction (MNL-135-00)18 and Chapter13 of the PCI Design Handbook, unless specifically stated. There are some situations in which production practices warrant wider tolerances, which are explained further in the PCI Tolerance Manual (Reference PCI Design Handbook, Section 13.2.4)

In corrosive environments or other severe exposure conditions, amount of concrete protection shall be suitably increased, and denseness and nonporosity of protecting concrete shall be considered, or other protection shall be provided.

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7.7.5.1 For prestressed concrete members exposed to corrosive environments or other severe exposure conditions, and which are classified as Class T or C in 18.3.3, minimum cover to the prestressed reinforcement shall be increased 50%. This requirement shall be permitted to be waived if the pre-compressed tensile zone is not in tension under sustained loads.

7.7.5.1 Nearly all precast, prestressed concrete members will be in compression in the precompressed tensile zone under sustained loads. Because of the compression and the high-quality concrete achieved in precasting plants, members that meet the requirements of this section have met the requirement of Section 7.7.5.

7.10.3 It shall be permitted to waive the lateral reinforcement requirements of 7.10, 10.16, and 18.11 where tests and structural analysis show adequate strength and feasibility of construction.

7.10.3 Section 7.10.3 waives minimum lateral ties with “tests and structural analysis...” Section 18.11.2.3 specifically excludes prestressed walls with a minimum average prestress of 225 psi from lateral (transverse) reinforcement requirements where structural analysis shows adequate strength and stability . (Reference PCI Design Handbook, Example 5.7.1)

7.10.4 Spirals

7.10.4 and 7.10.5 Precast, prestressed concrete columns frequently use continuously wound wire in a rectangular configuration for lateral reinforcement. PCI Prestressed Columns Committee recommendations state that for such members, spiral ties may be substituted for individual lateral ties if the spiral has an area equivalent to that of ties spaced in accordance with Section 18.11.2.2. For further information on this topic, see report by PCI Prestressed Concrete Columns Committee, Recommended Practice for the Design of Prestressed Concrete Columns and Walls.19 Section 7.10.4.2 specifically applies to only cast-in-place construction and Section 7.10.5.1 refers to non-prestressed bars, so the committee’s recommendations are in full compliance with ACI 318-05.

Spiral reinforcement for compression members shall conform to 10.9.3 and to the following: 7.10.4.1 Spirals shall consist of evenly spaced continuous bar or wire of such size and so assembled to permit handling and placing without distortion from designed dimensions. 7.10.4.2 For cast-in-place construction, size of spirals shall not be less than 3/8 in. diameter.

7.10.5 Ties Tie reinforcement for compression members shall conform to the following: 7.10.5.1 All non-prestressed bars shall be enclosed by lateral ties, at least #3 in size for longitudinal bars #10 or smaller, and at least #4 in size for #11, #14, #18, and bundled longitudinal bars. Deformed wire or welded-wire reinforcement of equivalent area shall be permitted. 7.12 Shrinkage and Temperature Reinforcement 7.12.3.3 When spacing of tendons exceeds 54 in., additional bonded shrinkage and temperature reinforcement conforming to 7.12.2 shall be provided between the tendons at slab edges extending from the slab edge for a distance equal to the tendon spacing.

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7.12 The nature of fabrication and storage of precast, prestressed concrete stemmed members is such that the flanges of stemmed members are not subjected to restraint forces caused by initial shrinkage. Section 16.4.1 waives the requirement for shrinkage and temperature reinforcement in one-way precast concrete slabs and wall panels that are not wider than 12 ft where mechanical connections do not cause restraint. The flexural reinforcement in the flange of a stemmed member is transverse to the stems, and is usually welded-wire reinforcement. Practice varies, but the Wire Reinforcement Institute requires that the longitudinal wires have an area at least 0.4 times that of the transverse wires. Section 7.12.3 is intended for post-tensioned slabs as illustrated in the commentary and Fig. R7.12.3.

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CHAPTER 8 – A  NALYSIS AND DESIGN – GENERAL CONSIDERATIONS 8.1.3 Anchors within the scope of Appendix D, “Anchoring to Concrete”, installed in concrete to transfer loads between connected elements shall be designed using Appendix D.

8.1.3 Appendix D has specific provisions allowing modifications based on research. PCI has sponsored research on connections using welded headed studs that are in full compliance with the requirements of Appendix D. The design methods provided in Chapter 6 of the PCI Design Handbook reflect the results of this testing.

8.3.2 Except for prestressed concrete, approximate methods of frame analysis shall be permitted for buildings of usual types of construction, spans, and story heights.

8.3.2 The intent of this section is to prohibit Section 8.3.3 to be used for post-tensioned concrete framing. Approximate (that is, portal) methods are sometimes used to design precast concrete litewalls in parking structures.

8.10.2 Width of slab effective as a T-beam flange shall not exceed one-quarter of the span length of the beam, and the effective overhanging flange width on each side of the web shall not exceed:

8.10.2 Section 18.1.3 states that this section does not apply to prestressed concrete. Commentary R18.1.3 states that the effective flange width is left to the experience and judgment of the engineer. Eight times the slab thickness is often used as a guide for determining the topping width to be used in designing composite beams. Thin flange members are commonly designed including the entire flange width in the compression block. (Reference PCI Design Handbook, Examples 5.2.1.5 and 5.3.5.1)

(a) Eight times the slab thickness; (b) One-half the clear distance to the next web.

CHAPTER 9 – S  TRENGTH AND SERVICEABILITY REQUIREMENTS 9.2 Required Strength 9.2.1 Required strength U shall be at least equal to the effects of factored loads in Eq. (9-1) through (9-7). The effect of one or more loads not acting simultaneously shall be investigated. U = 1.4(D + F) 

(9-1)

U = 1.2(D + F + T) + 1.6(L + H) + 0.5(Lr or S or R)  (9-2) U = 1.2D + 1.6(Lr or S or R) + (1.0L or 0.8W) 

(9-3)

U = 1.2D + 1.6W + 1.0L + 0.5(Lr or S or R) 

(9-4)

U = 1.2D + 1.0E + 1.0L + 0.2S 

(9-5)

U = 0.9D + 1.6W + 1.6H 

(9-6)

U = 0.9D + 1.0E + 1.6H 

(9-7)

except as follows: (a) The load factor on L in Eq. (9-3) to (9-5) shall be permitted to be reduced to 0.5 except for garages, areas occupied as places of public assembly, and all areas where the live load L is greater than 100 lb/ft2. 9.2.3 Estimations of differential settlement, creep, shrinkage, expansion of shrinkage-compensating concrete, or temperature change shall be based on a realistic assessment of such effects occurring in service.

PCI DESIGN HANDBOOK/SEVENTH EDITION

9.2.1 It should be emphasized that volume changes, settlement, and other movements T are not to be considered simultaneously with wind or earthquake forces. Structural effects of T need only be considered when the structural element is restrained and can produce internal forces as a result of T. See PCI Design Handbook Examples 5.8.5.2 and 5.9.2.1 for computation of restraint forces.

The load factor modification of 9.2.1(a) must be distinguished from live-load reductions allowed in the applicable building code. Where allowed, the reduced live loads establish a value for L to be used in the load combinations of 9.2.1 and 9.2.1(a).

9.2.3 Chapter 4 of the PCI Design Handbook provides guidelines for estimating creep, shrinkage, and temperature changes in precast concrete structures that are in compliance with ACI 318-05.

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R9.2.3 The designer should consider the effects of differential settlement, creep, shrinkage, temperature, and shrinkagecompensating concrete. The term realistic assessment is used to indicate that the most probable values rather than the upper bound values of the variables should be used.

9.3.2.7 Flexural sections in pretensioned members where strand embedment is less than the development length as provided in 12.9.1.1:

9.3.2.7 Section 5.2.3 of the PCI Design Handbook shows examples of designing for partially developed strands.

(a) From the end of the member to the end of the transfer length = 0.75 (b) From the end of the transfer length to the end of the development length, shall be permitted to be linearly increased from 0.75 to 0.9.

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Where bonding of a strand does not extend to the end of the member, strand embedment shall be assumed to begin at the end of the debonded length. See also 12.9.3.

9.5 Control of Deflections 9.5.4 Prestressed concrete construction 9.5.4.1 For flexural members designed in accordance with provisions of Chapter 18, immediate deflection shall be computed by usual methods or formulas for elastic deflections, and the moment of inertia of the gross concrete section Ig shall be permitted to be used for Class U flexural members, as defined in 18.3.3. 9.5.4.2 For Class C and Class T flexural members, as defined in 18.3.3, deflection calculations shall be based on a cracked transformed section analysis. It shall be permitted to base computations on a bilinear moment-deflection relationship, or an effective moment of inertia Ie, as defined by Eq. (9-8).

9.5.4 Deflections are always calculated for precast, prestressed concrete members in building structures. Calculations will usually include both instantaneous and long-term camber and dead and live load deflection. The engineer or architect of record will determine if this meets requirements, for example, Table 9.5(b). Satisfactory performance may depend on many non-structural considerations. (Reference PCI Design Handbook, Section 5.8) The PCI Design Handbook provides guidance for deflection computations that exceed the requirements of ACI 318-05.

9.5.4.3 Additional long-term deflection of prestressed concrete members shall be computed taking into account stresses in concrete and steel under sustained load and including effects of creep and shrinkage of concrete and relaxation of steel. 9.5.4.4 Deflection computed in accordance with 9.5.4.1 or 9.5.4.2, and 9.5.4.3 shall not exceed limits stipulated in Table 9.5(b).

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CHAPTER 10 – F  LEXURE AND AXIAL LOADS 10.4.1 Spacings of lateral supports for a beam shall not exceed 50 times b, the least width of compression flange or face.

10.4.1 The spans of non-load-bearing and loadbearing spandrels on parking structures have frequently exceeded 50 times the width of the top of the member and no problems have been observed. Lateral supports are provided to these spandrel beams by connection to the floor diaphragm near mid-depth of the section to address the effects of lateral stability, lateral impact loads, and the orientation of the spandrel beam principal axis for non-rectangular sections. The practical spacing of these connections is usually much less than the limit imposed by this section.

10.6.4 The spacing of reinforcement closest to the tension face s shall not exceed that given by

10.6.4 Note that Section 10.6 is specifically excluded for prestressed concrete (Section 18.1.3), except as specified in 18.4.4. (Reference PCI Design Handbook, Section 5.2.2.1)



⎛ 40,000 ⎞ s = 15 ⎜ − 2.5cc ⎝ fs ⎟⎠

(10-5)

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but not greater than 12(40,000/fs), where cc is the least distance from surface of reinforcement of prestressing steel to the tension face. If there is only one bar or wire nearest the extreme tension face, s used in Eq. (10-4) is the width of the extreme tension face. Calculated stress fs in reinforcement closest to the tension face at service load shall be computed based on the unfactored moment. It shall be permitted to take fs as 2/3 fy. 10.9.3 Volumetric spiral reinforcement ratio ρs shall be not less than the value given by

⎛ A ⎞ f' ρs = 0.45 ⎜ g − 1⎟ c ⎝ Ach ⎠ f yt



10.9.3 See discussion of Sections 7.10.4 and 18.11.2.2.

(10-5)

where the value of fyt used in Eq. (10-5) shall not exceed 100,000 psi. For fyt greater than 60,000 psi, lap splices according to 7.10.4.5(a) shall not be used.

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10.10 S  lenderness Effects in Compression Members 10.10.1 Except as allowed in 10.10.2, the design of compression members, restraining beams, and other supporting members shall be based on the factored forces and moments from a second-order analysis considering material nonlinearity and cracking, as well as the effects of member curvature and lateral drift, duration of the loads, shrinkage and creep, and interaction with the supporting foundation. The dimensions of each member cross section used in the analysis shall be within 10% of the dimensions of the members shown on the design drawings or the analysis shall be repeated. The analysis procedure shall have been shown to result in prediction of strength in substantial agreement with the results of comprehensive tests of columns in statically indeterminate reinforced concrete structures.

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10.10.2 As an alternate to 10.10.1, it shall be permitted pression members, restraining members on axial forces and described in 10.11.

the procedure prescribed in to base the design of combeams, and other supporting moments from the analyses

10.10 The PCI Design Handbook, Chapter 5, addresses the application of this section to precast and prestressed concrete columns. (Reference PCI Design Handbook, Section 5.9)

10.10.2 The moment magnifier method is not recommended for prestressed concrete compression members.

CHAPTER 11 SHEAR AND TORSION 11.1.3.2 For prestressed members, sections located less than a distance h/2 from face of support shall be permitted to be designed for the same shear Vu as that computed at a distance h/2.

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11.1.3.2 In beams with loads applied near the bottom, such as L-beams or inverted tees, h is taken as the depth of the ledge for shear calculations, but not necessarily for torsion. (Reference PCI Design Handbook, Section 5.3)

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11.5.6 Minimum shear reinforcement 11.5.6.1 A minimum area of shear reinforcement, Av,min, shall be provided in all reinforced concrete flexural members (prestressed and non-prestressed) where factored shear force Vu exceeds 0.5φVc, except: (a) slabs and footings; (b) concrete joist construction defined by 8.11; and (c) beams with h not greater than the largest of 10 in., 2.5 times thickness of flange, or 0.5 the width of web.

11.5.6 If Vu is less than φVc at the end region of prestressed double-tees not subjected to point loads, shear reinforcement may be omitted with a nominal minimum provided for 5 ft to 10 ft from the ends. This is based on research by Alex Aswad and George Burnley, “Omission of Web Reinforcement in Prestressed Double Tees.”20 The approach is permitted by Section 11.5.6.2. A reduction in the φ-factor in flexure may be warranted when Po /A levels are low. See recommendations by Aswad, et al, “Load Testing of Prestressed Concrete Double Tees without Web Reinforcement.”21 Since the effective shear performance of the tee stems at the ends is dependent on the prestressing, this exception should only be used when the strand bond has been qualified as meeting ACI transfer and development-length provisions. (Reference PCI Design Handbook, Sections 5.3 and 5.3.4) Prestressed hollow-core and flat slab units fall under (a) slabs and footings, and require no shear reinforcement, provided Vu ≤ φVc. R11.5.6.1 indicates that deeper hollow-core sections may have reduced web shear strength. ACI 318-05 does not require minimum area of shear reinforcement Av,min in hollow-core units where the untopped depth is not greater than 12.5 in. or where Vu is not greater than 0.5φVcw.

11.6 Design for Torsion Design for torsion shall be in accordance with 11.6.1 through 11.6.6, or 11.6.7.

PCI DESIGN HANDBOOK/SEVENTH EDITION

11.6 Torsion design has typically been done using the Zia-McGee method (PCI Design Handbook second edition22) or Zia-Hsu method (fourth edition23). See also ZiaHsu article, “Design for Torsion and Shear in Prestressed Concrete Flexural Members.”24 The thin-walled tube model, which has been in ACI 318 since 1995, typically requires significantly greater reinforcement than the previous methods in, for example, spandrel beams in parking structures. Based on performance of beams designed by the previous methods, this additional reinforcement is unnecessary and uneconomical, and most precast concrete engineers are using the methods indicated previously in this section, which is in full compliance with Section 11.6.7. The ZiaHsu method usually is more economical for spandrel beams with large aspect ratios, but still may result in conservative designs. (Reference PCI Design Handbook, Section 5.4), and see paper by Lucier, et al, “Precast Concrete, L-Shaped Spandrels Revisited: Full-Scale Tests.”25 Research is available and underway to address the design of beams with large aspect ratios for eccentric loading in a more comprehensive and more cost-effective manner.

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11.7 Shear-friction

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11.7.3 A crack shall be assumed to occur along the shear plane considered. The required area of shear-friction reinforcement Avf across the shear plane shall be designed using either 11.7.4 or any other shear-transfer design methods that result in prediction of strength in substantial agreement with results of comprehensive tests.

11.7.3 The effective shear-friction method described in the PCI Design Handbook is most often used. Use is permitted under Section 11.7.3. (Reference PCI Design Handbook, Section 5.3.6)

11.7.7 Net tension across shear plane shall be resisted by additional reinforcement. Permanent net compression across shear plane shall be permitted to be taken as additive to the force in the shear-friction reinforcement Avf fy when calculating required Avf.

11.7.7 At shear-wall bases, for example, the sustained dead load on the wall (including the weight of the wall) is added to the force developed in the bars across the shear plane. The minimum positive anchorage requirements of Chapter 16 still apply.

11.9.1 Brackets and corbels with a shear span-to-depth ratio av /d less than 2 shall be permitted to be designed using appendix A. Design shall be permitted using 11.9.3 and 11.9.4 for brackets and corbels with:

11.9.1 Section 5.9.4 of the PCI Design Handbook describes a method of corbel design that has been used successfully. It is consistent with the strut-and-tie method of Appendix A permitted by this section.

(a) av /d not greater than 1; and ( b) subject to horizontal tensile force for Nuc not larger than Vu. The requirements of 11.9.2, 11.9.3.2.1, 11.9.3.2.2, 11.9.5, 11.9.6, and 11.9.7 shall apply to design of brackets and corbels. Effective depth d shall be determined at the face of the support. 11.9.3.2 Design of shear-friction reinforcement Avf to resist shear Vu shall be in accordance with 11.7. 11.9.3.2.1 For normalweight concrete, Vn shall not be taken greater than the smaller of 0.2 fc' bwd and 800bwd.

11.9.3.2.1 The PCI Design Handbook allows Vn up to 1000bwd. This is consistent with the effective shear-friction approach when concrete strengths of 5000 psi and greater are used. (Reference PCI Design Handbook, Table 5.3.6.1)

11.9.3.2.2 For all-lightweight or sand-lightweight concrete, Vn shall not be taken greater than the smaller of (0.2 – 0.07av /d) fc' bwd and (800 – 280av /d) bwd.

11.9.3.2.2 It is worth noting that equations given here for lightweight concrete are more conservative in relation to normalweight concrete than the use of the λ factor in the effective shear-friction coefficient applied to the expressions of Section 11.9.3.2.1.

11.9.3.4 Reinforcement An to resist tensile force Nuc shall be determined from φAn fy ≥ Nuc. Factored tensile force Nuc shall not be taken less than 0.2Vu unless special provisions are made to avoid tensile forces. Nuc shall be regarded as a live load even if tension results from restraint of creep, shrinkage, or temperature change.

11.9.3.4 Bearing pads are used to avoid tensile forces. The PCI Design Handbook suggests that a value of Nuc that will cause the pad to slip is the maximum that can occur, or, alternatively, a value of 0.2 times the shear attributable to the factored dead load is used as a guide. (Reference PCI Design Handbook, Chapter 6)

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11.9.6 At front face of bracket or corbel, primary tension reinforcement shall be anchored by one of the following:

11.9.6 Frequently, front-face anchorage is ensured by welding to an angle or a plate with vertical anchors. This is permitted by Section 11.9.6(c).

(a) By a structural weld to a transverse bar of at least equal size; weld to be designed to develop fy of primary tension reinforcement; (b) By bending primary tension reinforcement back to form a horizontal loop; or (c) By some other means of positive anchorage.

11.9.7 Bearing area on bracket or corbel shall not project beyond straight portion of primary tension reinforcement, nor project beyond interior face of transverse anchor bar (if one is provided).

11.9.7 If primary tension bars are anchored by welding (Section 11.9.6), the bearing area can be considered to extend to the exterior face of the anchoring bar or plate. This section is not typically applied to beam ledges where ledge reinforcement is typically anchored by bending bars near the front face. Research sponsored by PCI and Development Project No. 5, “Design of Spandrel Beams,”26 addressed this issue and found that placement of bars is critical.

11.10.8 Where Vu is less than 0.5φVc, reinforcement shall be provided in accordance with 11.10.9 or in accordance with Chapter 14. Where Vu exceeds 0.5φVc, wall reinforcement for resisting shear shall be provided in accordance with 11.10.9.

11.10.8 For precast concrete walls, the reference should be to Section 16.4.2 rather than to Chapter 14.

11.10.9 Design of shear reinforcement for walls

11.10.9 Section 11.10.9 applies only when the in-plane shear Vu > 0.5φVc as described in Section 11.10.8. Otherwise, minimum reinforcement required by Section 16.4 for precast concrete walls applies (0.001 times the gross cross-sectional area in the case of Section 16.4.2). Where Vu > 0.5φVc and Vu < φVc, the reinforcement ratios and spacing limitations set forth in Section 11.10.9.2 through 11.10.9.5 must be satisfied. In situations where Vu > φVc, Section 11.10.9.1 must be satisfied as well.

11.10.9.1 Where Vu exceeds φVc, horizontal shear reinforcement shall be provided to satisfy Eq. (11-1) and (11-2), where Vs shall be computed by

Vs =

Av f y d s

(11-31)

where Av is area of horizontal shear reinforcement within spacing s, and d is determined in accordance with 11.10.4. Vertical shear reinforcement shall be provided in accordance with 11.10.9.4.

CHAPTER 12 – D  EVELOPMENT AND SPLICES OF REINFORCEMENT 12.5 Development of Standard Hooks in Tension 12.5.1 Development length for deformed bars in tension terminating in a standard hook (see 7.1) ldh shall be determined from 12.5.2 and the applicable modification factors of 12.5.3, but ldh shall not be less than the larger of 8db, nor less than 6 in.

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12.5.1 Reinforcing ties in beam ledges are assumed to be developed with a hook, even when the straight portion measured from the end of the hook to the face of the beam web is less than 6 in., measured to the stem face. See the research project listed as Reference 11-53 in ACI 318-05.

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12.11.1 At least one-third the positive moment reinforcement in simple members and one-fourth the positive moment reinforcement in continuous members shall extend along the same face of member into the support. In beams, such reinforcement shall extend into the support at least 6 in.

12.11.1 Does not apply to precast concrete construction. Excluded by Section 16.6.2.3.

12.13.2.4 For each end of a single leg stirrup of weldedwire reinforcement, two longitudinal wires at a minimum spacing of 2 in. and with the inner wire at least the greater of d/4 or 2 in. from d/2. Outer longitudinal wire at tension face shall not be farther from the face than the portion of primary flexural reinforcement closest to the face.

12.13.2.4 Figure R12.13.2.4 shows how welded-wire reinforcement is used as shear reinforcement in double-tee stems. For further information, see the Joint PCI/WRI Ad Hoc Committee on Welded Wire Fabric for Shear Reinforcement report, “Welded Wire Fabric for Shear Reinforcement.”27

CHAPTER 13 – TWO-WAY SLAB SYSTEMS

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13.2.4 For monolithic or fully composite construction, a beam includes that portion of slab on each side of the beam extending a distance equal to the projection of the beam above or below the slab, whichever is greater, but not greater than four times the slab thickness.

13.2.4 Section 18.1.3 states that Chapter 13 does not apply to prestressed concrete. Commentary R18.1.3 states that the effective flange width is left to the experience and judgment of the engineer. See Section 8.10.2 for more information.

CHAPTER 14 – WALLS 14.3 Minimum Reinforcement

14.3 Minimum reinforcement for precast concrete walls is specified in Sections 16.4.1 and 16.4.2. Section 18.11.2.3 states that Section 14.3 does not apply for walls with effective prestress force equal to or greater than 225 psi where structural analysis shows adequate strength and stability.

14.6.1 Thickness of nonbearing walls shall not be less than 4 in., nor less than 1/30 the least distance between members that provide lateral support.

14.6.1 Minimum thickness is not applicable to prestressed walls. See Section 18.1.3.

CHAPTER 15 – FOOTINGS 15.8.3.1 Connection between precast concrete columns or pedestals and supporting members shall meet the requirements of 16.5.1.3(a).

15.8.3.1 Note reference to Chapter 16.

CHAPTER 16 – PRECAST CONCRETE 16.2.4 In addition to the requirements for drawings and specifications in 1.2, (a) and (b) shall be included in either the contract documents or shop drawings: (a) Details of reinforcement, inserts, and lifting devices required to resist temporary loads from handling, storage, transportation, and erection; and (b) Required concrete strength at stated ages or stages of construction.

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16.2.4 Connection design is typically a part of the precast concrete contract, and connection forces are typically developed by the precast concrete engineer, or sometimes listed by the Engineer of Record on the contract drawings. It is common practice for stripping, handling, and design criteria to be documented in the design calculations prepared by the precast engineer. (Reference PCI Design Handbook, Sections 14.4 and 14.5)

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16.5.1.3 Vertical tension tie requirements of 7.13.3 shall apply to all vertical structural members, except cladding, and shall be achieved by providing connections at horizontal joints in accordance with (a) through (c):

16.5.1.3(b) Some panels may be too narrow to accommodate two connections. The engineer may determine that the behavior of such members justifies classifying the panel as cladding (cladding is exempt from the requirements of this section).

(a) Precast concrete columns shall have a nominal strength in tension not less than 200Ag, in pounds. For columns with a larger cross section than required by consideration of loading, a reduced effective area Ag, based on cross section required but not less than one-half the total area, shall be permitted.

This section applies to structures composed of many elements that must be tied together. Structures that use modules, or boxes, will require different details to ensure integrity. (Reference PCI Design Handbook, Section 4.3.2, note 5).

(b) Precast concrete wall panels shall have a minimum of two ties per panel, with a nominal tensile strength not less than 10,000 lb per tie. (c) When design forces result in no tension at the base, the ties required by 16.5.1.3(b) shall be permitted to be anchored into an appropriately reinforced concrete floor slab on grade.

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16.5.1.4 Connections designed in accordance with the shear-friction provisions of Section 11.7 are in compliance with this section. See Section 11.7.7 for more information.

16.6.2.2 Unless shown by test or analysis that performance will not be impaired, (a) and (b) shall be met:

16.6.2.2 When shorter bearing lengths occur in the field, analysis by the precast engineer for the approval by the Engineer of Record is usually the basis for acceptability. When designing bearing lengths, the effects of member shortening and movement at expansion joints should be considered.

(a) Each member and its supporting system shall have design dimensions selected so that, after consideration of tolerances, the distance from the edge of the support to the end of the precast concrete member in the direction of the span is at least ln/180, but not less than: For solid or hollow-core slabs.....................2 in. For beams or stemmed members...............3 in. (b) Bearing pads at unarmored edges shall be set back a minimum of 1/2 in. from the face of the support, or at least the chamfer dimension at chamfered edges. 16.6.2.3 The requirements of 12.11.1 shall not apply to the positive bending-moment reinforcement for statically determinate precast concrete members, but at least one-third of such reinforcement shall extend to the center of the bearing length, taking into account permitted tolerances in 7.5.2.2 and 16.2.3.

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CHAPTER 17 – C  OMPOSITE CONCRETE FLEXURAL MEMBERS

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17.5.3.1 Where contact surfaces are clean, free of laitance, and intentionally roughened, Vnh shall not be taken greater than 80bvd.

17.5.3.1 The 80bvd horizontal shear-strength level can be obtained by many finishes that appear smooth when compared with the roughness required in 17.5.3.3. Examples include floated, light-broomed, or machine extruded surfaces. (Reference PCI Design Handbook, Section 5.3.5) Because the strength of the interface in this case is developed by cementitious bond, proper preparation of the surface is of utmost importance.

17.5.3.3 When ties are provided in accordance with 17.6, and contact surfaces are clean, free of laitance, and intentionally roughened to a full amplitude of approximately 1/4 in., Vnh shall be taken equal to (260 + 0.6v fy)λbvd, but not greater than 500bvd. Values for λ in 11.7.4.3 shall apply and ρv is Av /(bvs).

17.5.3.3 The surface should not be so rough as to allow bridging of the cast-in-place coarse aggregate and the formation of voids at the interface. The most important element is the statement “clean, free of laitance.”

17.6.3 All ties shall be fully anchored into interconnected elements in accordance with 12.13.

17.6.3 Ties for horizontal shear in precast concrete members are typically U-shaped reinforcing bars that are embedded after the member has been cast and the top surface has been intentionally roughened and finished. The anchorage of the tie in the precast concrete member is achieved by embedding the bar for the required development length without hooks. See also R16.7.1. Anchorage of hooked or bent ties in cast-in-place topping is considered adequate if a minimum distance of 2 1/4, 2 3/4, and 3 1/4 in. is provided between the shear transfer interface and the outside ends of standard hooks or U-bends of #3, #4, and #5 ties, respectively, based on research cited in PCI Design Handbook, Section 5.3.5.

CHAPTER 18 – PRESTRESSED CONCRETE

18.3.3 Prestressed flexural members shall be classified as Class U, Class T, or Class C based on ft, the computed extreme fiber stress in tension in the precompressed tensile zone calculated at service loads, as follows: (a) Class U:

ft ≤ 7.5 fc' ;

(b) Class T: 7.5 fc' < ft ≤ 12 fc' (c) Class C:

ft > 12 fc'

18.3.3 Table R18.3.3 clearly defines the differences between Class U (uncracked), Class T (transition), and Class C (cracked) prestressed concrete members. Most members are designed as Class U or T, and, thus, the design procedures are essentially unchanged from previous editions of the code. For special cases, a member may be designed as Class C, but more attention must be paid to performance using the provisions of 18.3.4 and 9.5.4. Chapter 5 of the PCI Design Handbook provides examples of detailed transformed cracked section analysis.

Prestressed, two-way slab systems shall be designed as Class U with ft ≤ 6 fc' .

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R18.4.1(b) and (c) Where tensile stresses exceed the permissible values, the total force in the tensile stress zone may be calculated, and reinforcement proportioned on the basis of this force at a stress of 0.6fy but not more than 30,000 psi.

R18.4.1(b) and (c) Where beam tops are in tension at transfer of prestress forces, but are in compression under service load, and are not exposed to weather, the large amounts of steel indicated by this commentary item is excessive. Experience has shown that nominal top reinforcing bars or prestressing strand will adequately control temporary top cracking. Use of fy (up to 60,000 psi) for the steel stress has been shown to be adequate. Bars must be detailed (for example, hooks, C-bars, U-bars) to ensure development in the top tensile region.

18.4.1 Stresses in concrete immediately after prestress transfer (before time-dependent prestress losses) shall not exceed the following:

18.4.1 Recent research28 has shown that the compression limitations at transfer are more conservative than necessary and have an effect on economy and safety due to the potential need for debonding or depressing prestressing strands.. It has been common practice to allow compression up to 0.70fci' . Utilizing a compression limit of 0.70fci' at the ends of simply supported members is in full compliance with ACI 318-08. For beams, it has been common practice to allow tension limit 6 fc' throughout their length since service load compression in the top is higher at midspan. Even when tension limits are not exceeded, it is recommended that nominal reinforcement (at least two #4 or nominally tensioned strands) be provided in tops of beams.

(a) Extreme fiber stress in compression. 0.60 fci' (b) Extreme fiber stress in tension except as permitted in (c) 3 fci'

(c) Extreme fiber stress in tension at ends of simply supported members 6 fci'

Where computed tensile stresses ft exceed the limits in (b) or (c), additional bonded reinforcement (nonprestressed or prestressed) shall be provided in the tensile zone to resist the total tensile force in concrete computed with the assumption of an uncracked section. 18.4.4 For Class C prestressed flexural members not subject to fatigue or to aggressive exposure, the spacing of bonded reinforcement nearest the extreme tension face shall not exceed that given by 10.6.4. For structures subject to fatigue or exposed to corrosive environments, special investigations and precautions are required. 18.4.4.1 The spacing requirements shall be met by nonprestressed reinforcement and bonded tendons. The spacing of bonded tendons shall not exceed 2/3 of the maximum spacing permitted for nonprestressed reinforcement. Where both reinforcement and bonded tendons are used to meet the spacing requirement, the spacing between a bar and a tendon shall not exceed 5/6 of that permitted by 10.6.4. See also Section 18.4.4.3.

18.4.4 This section refers to maximum spacing requirements by applying Eq. (10-4) to prestressed concrete: ⎛ 40,000 ⎞ s = 15 ⎜ − 2.5c c ⎝ fs ⎟⎠

where s is the maximum spacing and cc is the clear cover to the reinforcement nearest the tension face. Note that these requirements are for Class C members only (that is, those in which the concrete tension under service loads exceeds 12 fc' ). In checking this requirement, first check Section 18.4.4.3. If the spacing requirements can be met by substituting 36,000 psi for fs in Eq. (10-4), no further check is necessary. If not, check to verify that ∆fps is less than 20,000 psi (which will often be the case). If so, no further check is necessary.

18.4.4.3 In applying Eq. (10-4) to prestressing tendons, the magnitude of ∆fps shall not exceed 36,000 psi. When ∆fps is less than or equal to 20,000 psi, the spacing requirements of 18.4.4.1 and 18.4.4.2 shall not apply.

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18.6 Loss of Prestress 18.6.1 To determine effective stress in the prestressing steel fse, allowance for the following sources of loss of prestress shall be considered:

18.6 Most structural engineers who specialize in the design of prestressed concrete follow the recommendations of ACIASCE Committee 423 task force given in Reference 18.6, which is in compliance with the code. (Reference PCI Design Handbook, Section 5.7)

(a) Prestressing steel seating at transfer; (b) Elastic shortening of concrete; (c) Creep of concrete; (d) Shrinkage of concrete; (e) Relaxation of prestressing steel stress; and (f) Friction loss due to intended or unintended curvature in post-tensioning tendons.

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18.7.2 As an alternative to a more accurate determination of fps based on strain compatibility, the following approximate values of fps shall be permitted to be used if fse is not less than 0.5fpu. (a) For members with bonded tendons: ⎤ ⎪⎫ d ⎪⎧ γ ⎡ f f ps = f pu ⎨1 − p ⎢ ρ p pu' + (ω − ω ' )⎥ ⎬ fc d p ⎪⎩ β1 ⎣ ⎦ ⎪⎭



18.7.2 Many engineers and most computer programs use strain compatibility analysis for determining fps, which is a more accurate determination as indicated in R18.7.2. Others use Eq. (18-3). With lowrelaxation strand, the results are not substantially different. (Reference PCI Design Handbook, Section 5.2.1)

(18-3)

Where ω is ρfy /fc', ω' is ρ' fy /fc', and γp is 0.55 for fpy /fpu not less than 0.80; 0.40 for fpy /fpu not less than 0.85; and 0.28 for fpy /fpu not less than 0.90. If any compression reinforcement is taken into account when calculating fps by Eq. (18-3), the term ⎡ f pu d ⎤ ⎢ ρ p ' + (ω − ω ' ) ⎥ fc d p ⎣ ⎦



shall be taken not less than 0.17 and d' shall be no greater than 0.15dp. 18.8.2 Total amount of prestressed and nonprestressed reinforcement shall be adequate to develop a factored load at least 1.2 times the cracking load computed on the basis of the modulus of rupture fr, specified in 9.5.2.3. This provision shall be permitted to be waived for: (a) Two-way, unbonded post-tensioned slabs; and

18.8.2 This provision only applies at critical flexural sections where cracking will first occur. (Reference PCI Design Handbook, Section 5.2.1.) This provision is intended as a precaution against abrupt flexural failure immediately after cracking. Cracking and the subsequent considerable deflection prior to the fracture of the prestressed reinforcement are the desired distress indicators that will be apparent.

(b) Flexural members with shear and flexural strength at least twice that required by 9.2.

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18.11.2 Limits for reinforcement of prestressed compression members 18.11.2.1 Members with average compressive stress in concrete due to effective prestress force only less than 225 psi shall have minimum reinforcement in accordance with 7.10, 10.9.1, and 10.9.2 for columns, or 14.3 for walls.

18.11.2.1 Columns which, for architectural or other reasons, are larger than necessary to carry the applied loads will use the level of prestress for the size of column needed. For example, if a 16 in. × 16 in. column will carry the load, but a 24 in. × 24 in. column is used, the total prestress force necessary is 225(16 × 16) = 57,600 lb. This practice is supported by Sections 10.8.4 and 16.5.1.3(a).

18.11.2.2 Except for walls, members with average compressive stress in concrete due to effective prestress force only equal to or greater than 225 psi shall have all tendons enclosed by spirals or lateral ties in accordance with (a) through (d):

18.11.2.2 Columns that are prestressed to the effective average prestress of 225 psi are not subject to longitudinal reinforcement buckling and have been shown not to require ties or spirals by research and practice. Where prestressed columns gain additional strength by the addition of longitudinal, nonprestressed reinforcement, where high moments may occur at joints or connections, and where the column may be subject to high shear forces, ties or spirals should be provided.

(a) Spirals shall conform to 7.10.4; (b) Lateral ties shall be at least #3 in size or weldedwire reinforcement of equivalent area, and shall be spaced vertically not to exceed 48 tie bar or wire diameters, or the least dimension of the compression member;

Note that walls are excluded from the lateral tie requirements.

(c) Ties shall be located vertically not more than half of a tie spacing above top of footing or slab in any story, and not more than half a tie spacing below the lowest horizontal reinforcement in members supported above; (d) Where beams or brackets frame into all sides of a column, ties shall be terminated not more than 3 in. below lowest reinforcement in such beams or brackets.

CHAPTER 21 – S  PECIAL PROVISIONS FOR SEISMIC DESIGN

Chapter 4 of the PCI Design Handbook, PCI’s Seismic Design of Precast/Prestressed Concrete Structures (MNL-140-07),29 and other publications and research reports are available to assist the designer in the design of precast concrete structures in seismic areas.

1 APPENDIX A – STRUT-AND-TIE MODELS

Strut-and-tie modeling may have many applications in precast concrete construction, including corbels and dapped ends of beams. The design procedures for these elements given in the PCI Design Handbook have certain limits of applicability, and strut-and-tie methods may be used for cases that fall outside these limits.

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PCI PRACTICE

2 APPENDIX D – A  NCHORING TO CONCRETE

The PCI Design Handbook and the PCI Connections Manual30 have given design recommendations for connections that use welded headed studs and other anchorage devices for many years. Connections designed by these recommendations have performed satisfactorily.

D4.2 The nominal strength for any anchor or group of anchors shall be based on design models that result in predictions of strength in substantial agreement with results of comprehensive tests. The materials used in the tests shall be compatible with the materials used in the structure. The nominal strength shall be based on the 5% fractile of the basic individual anchor strength. For nominal strengths related to concrete strength, modifications for size effects, the number of anchors, the effects of close spacing of anchors, proximity to edges, depth of the concrete member, eccentric loadings of anchor groups, and presence or absence of cracking shall be taken into account. Limits on edge distances and anchor spacing in the design models shall be consistent with the tests that verified the model.

D4.2 PCI has sponsored tests of stud assemblies that meet these requirements and result in design criteria that are in full compliance with the requirements of this appendix. For further information on this topic, see PCI Design Handbook, Section 6.5, and “Design Criteria for Headed Stud Groups in Shear: Part 1 – Steel Capacity and Back Edge Effects.”31

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14.2

CHAPTER 14

 uide Specification for Structural Precast Concrete and Structural Precast G Concrete with Commercial Architectural Finish

This guide specification is intended to be used as a basis for the development of an office master specification or in the preparation of specifications for a particular project. In either case, this guide specification must be edited to fit the conditions of use. Particular attention should be given to the deletion of inapplicable provisions. Also, necessary items related to a particular project should be included and appropriate requirements should be added where blank spaces have been provided. The actual specification section is included on the CD that accompanies this handbook.

14.3

Guide Specification for Architectural Precast Concrete

This guide specification is intended to be used as a basis for the development of an office master specification or in the preparation of specifications for a particular project. In either case, this guide specification must be edited to fit the conditions of use. Particular attention should be given to the deletion of inapplicable provisions. Also, necessary items related to a particular project should be included and appropriate requirements should be added where blank spaces have been provided. The actual specification section is included on the CD that accompanies this handbook.

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CHAPTER 14

14.4

Standard Operations Practice Recommendations for Precast Concrete

The precast and prestressed concrete industry has grown rapidly, and certain practices related to the design, manufacture, and erection of precast concrete have become standard in many areas of North America. This section comprises a compilation of these practices presented in the form of guide recommendations for people involved with the use of structural and architectural precast concrete. The goal of this standard operations practice is to build a better understanding by suggesting standards that more clearly define procedures and responsibilities, thus resulting in fewer misunderstandings for everyone involved in the planning and execution of projects. As the precast and prestressed concrete industry continues to evolve, additional practices will become standard in the industry and current standards will require modification. The Precast/Prestressed Concrete Institute will continue updating its standard operations practice. 14.4.1 

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Definitions of Precast Concrete

14.4.1.1 Structural Precast Concrete Structural precast concrete usually includes beams, tees, hollow-core, joists, purlins, girders, lintels, columns, spandrels, poles, posts, piers, piles, slab or deck components, and wall panels. In order to avoid misunderstandings, contract documents for each project should specifically list all of the components that are considered to be structural precast concrete. Some structural components may be left exposed in the structure for desired aesthetic appearance. High-quality, attractive architectural treatments may be provided on the surfaces of these structural components, and these should be specifically listed in the contract documents. Quality assurance for structural precast concrete and structural precast concrete with an architectural finish is defined in PCI's Manual for Quality Control for Plants and Production of Structural Precast Concrete Products (MNL-116-99). 14.4.1.2 Architectural Precast Concrete Architectural precast concrete is characterized by a higher standard of appearance uniformity with respect to surface details, color, and texture. Typical architectural precast concrete components fall into two groups: major primary components (including wall panels, window wall panels, and column covers) and other components considered decorative pieces and trim units (including copings, mullions, sills, and appurtenances such as benches and bollards). In order to avoid misunderstandings, contract documents for each project should specifically list all of the components that are considered to be architectural precast concrete. Quality assurance for architectural precast concrete is defined in PCI's Manual for Quality Control for Plants and Production of Architectural Precast Concrete Products (MNL-117-96). 14.4.1.3 Prestressed Concrete Both structural and architectural precast concrete may be prestressed or nonprestressed. All structural precast concrete 14–24

products referred to herein that are prestressed are specifically referred to as prestressed concrete. 14.4.2

 amples, Mockups, and Qualifications S of Manufacturers and Erectors

14.4.2.1 Samples and Mockups Samples, mockups, and the like are rarely required for structural precast concrete. If samples are required, they should be described in the contract documents. Samples should be manufactured in accordance with Section 3.2, “Uniformity and Development of Samples”, in Architectural Precast Concrete, third edition (MNL-122-07).32 14.4.2.2 Qualification of Manufacturer Manufacture, transportation, erection, and testing should be provided by a company, firm, corporation, or similar organization specializing in providing precast concrete products and services normally associated with structural or architectural precast concrete construction. The manufacturer should be certified by the PCI Plant Certification Program. Because plant certification identifies the types of products for which the manufacturer has demonstrated capability and experience, project specifications should require the appropriate group and category as defined in the following section. In addition, for special and unique projects, the manufacturer may be required to list similar and comparable work that has been completed successfully. Standards of performance are given in the latest editions of the PCI manuals for quality control, MNL-116-99 and MNL-117-96, and Manual for Quality Control for Plants and Production of Glass Fiber-Reinforced Concrete Products (MNL-130-91).33 14.4.2.3 Certification Categories PCI plant certification is divided into four groups of products: A – Architectural Products; B – Bridges; C – Commercial (Structural); and G – Glass-Fiber-Reinforced Concrete (GFRC). A description of groups and categories may be found in PCI’s PCI Certification for Plants, Personnel, and Product Erection.34 Product Group A has two categories: A1 for Architectural Cladding and Load-Bearing Units (primarily architectural panels and products), and AT for Architectural Trim Units. Groups B and C each have four separate categories that identify the experience and type of product available at the certified plant. Groups B and C categories are as follows (a designation with a higher number qualifies all those with lower designations): B1 - Precast Bridge Products (No Prestressed Reinforcement) B2 - Prestressed Miscellaneous Bridge Products (NonSuperstructure) B3 - Prestressed Straight-Strand Bridge Beams (Superstructure)

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SPECIFICATIONS AND STANDARD PRACTICES B4 - Prestressed Deflected-Strand Bridge Beams (Superstructure) C1 - Precast Concrete Products (No Prestressed Reinforcement) C2 - Prestressed Hollow-Core and Repetitively Produced Products C3 - Prestressed Straight-Strand Structural Components C4 - Prestressed Deflected-Strand Structural Components Many producers have experience with applying architectural finishes to typical structural products. This certified architectural capability is identified with an “A” following the group and category designations (for example, C3A for a spandrel panel for a parking structure made with straight strands and having a special architectural pattern and/or finish on the face). Therefore, group and category designations B1 through B4 and C1 through C4 may be modified with an “A” suffix. Structural products with simple architecturalfinish requirements, such as warehouse panels and parking structure spandrels, should not be required to meet the more restrictive requirements of PCI's MNL-117-96, which is intended for purely architectural components. The requirements of MNL-116-99 meet the requirement of CA certification, ensuring an acceptable, simple architectural finish without requiring unduly stringent and more costly tolerances. A current list of PCI-Certified plants is published in the PCI publication Ascent or may be obtained by calling PCI or by visiting www.pci.org. 14.4.2.4 Qualification of Erector The Field Certification Program extends PCI quality assurance from fabrication (plant certification) to field installation. It has been found that participation in the program is highly beneficial in improving the quality of the installation and the safety and efficiency of the installation crews. The PCI Field Certification Program evaluates producererectors and independent erectors of precast concrete products against nationally adopted standards. Specifying a PCIQualified or Certified Erector assures the project specifier and owner that the installation meets the industry standards as prescribed in PCI's Erectors’ Manual — Standards and Guidelines for the Erection of Precast Concrete Products (MNL-127-99).35 An erector may be qualified/certified in up to three categories (see Reference 34 for more detailed descriptions): S1 Simple Structural Systems (horizontal decking components, bridge beams, singlelift walls) S2 Complex Structural Systems (category S1, plus all other structural products) A Architectural Systems (non-load-bearing cladding and GFRC products) The auditing criteria for a PCI qualified erector are based on the industry’s quality, procedural, and safety standards as presented in References 35 and 36. Audits are conducted by certified field auditors accredited by PCI. An erection company can choose to participate in the PCI Field CertificaPCI DESIGN HANDBOOK/SEVENTH EDITION

CHAPTER 14 tion Program at a higher level by becoming a PCI-Certified Erector. In addition to meeting the requirements set forth for qualified status, a certified erector must annually demonstrate that the company performs on all projects in accordance with industry erection standards as presented in References 37 and 38. Confirmation of conformance to these standards is accomplished via an audit of the company by a PCI-trainedand-accredited certified company auditor (CCA). The audit is performed at the erector’s offices and all jobs performed during the previous twelve months are subject to review by the CCA. The company audit is scored and a failing grade, without acceptable remediation, results in loss of certified status. A current list of PCI-Certified plants and PCI-Qualified and Certified erectors is published in the PCI publication Ascent or may be obtained by calling PCI or by visiting www.pci.org. 14.4.3

 ontract Documents and Design C Responsibility

14.4.3.1 Contract Documents Prior to beginning engineering and drafting, the manufacturer should have the following contract documents at his disposal: 1. Architectural drawings; 2. Structural drawings; and 3. Specifications (complete with addenda). Other pertinent drawings may also be desirable, such as approved shop drawings from other trades, roofing requirements, and alternates that have been accepted by the owner. 14.4.3.2 Design Responsibility It is the responsibility of the owner (the owner of the proposed structure or his designated representative who may be the architect, engineer, general contactor, public authority, or others contracting directly with the precast concrete manufacturer) to keep the manufacturer supplied with up-to-date contract documents and written information. The manufacturer should not be held responsible for problems arising from the use of outdated or obsolete contract documents. If revised documents are furnished, it may also be necessary to modify the contract. The contract documents should clearly define the following: 1. Structural design criteria and assigned design responsibilities (see additional information in Section 14.5 regarding design responsibility relationships) 2. Items to be furnished by the manufacturer 3. Size, location, and function of all openings, blockouts, and cast-in items 4. Detailing requirements for other trades, including connections and reinforcement 5. Allowable tolerances (normal field tolerances should be recommended by the manufacturer) 6. Dimensions and material requirements

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CHAPTER 14 7. General and supplemental general conditions 8. Any other special requirements and conditions 9. Interface requirements with other trades 10. Governing codes 11. Fire-resistance rating requirements (if there are any) Other design responsibility relationships are described in section 14.5 of this handbook. 14.4.4

Shop Drawings

Shop drawings consist of erection and production drawings. Different areas of the country may use different terminology; for example, production drawings that are used by a plant to manufacture specific components may be referred to as shop tickets, shop cards, or piece details. Normal practices for the preparation of drawings for precast concrete are described in the second edition of PCI Drafting Handbook — Precast and Prestressed Concrete (MNL-119-90).39 14.4.4.1 Erection Drawings

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The information provided in the contract documents is used by the manufacturer to prepare erection drawings for approval and field use. The erection drawings should contain: 1. Plans and/or elevations locating and dimensioning all components furnished by the manufacturer; 2. Sections and details showing connections, finishes, openings, blockouts, and cast-in items and their relationship to the structure; 3. Description of all loose and cast-in hardware including information on who furnishes the hardware and its finish requirement; 4. Drawings showing location of anchors installed in the field, especially if they are designated as “by others” or “not by – name of manufacturer”; and 5. Component handling and certain bracing/stability information (unless otherwise contained in a fully developed erection plan, refer to Section 14.5). 14.4.4.2 Production Drawings The contract documents and erection drawings are used to prepare production drawings for manufacturing, showing all dimensions together with locations and quantities for all castin materials (reinforcement, inserts, handling device, and the like) and completely defining all finish requirements. These drawings typically include a specific bill-of-material list for the piece. 14.4.4.3 Discrepancies When discrepancies or omissions are discovered on the contract documents, the manufacturer has the responsibility to check with the design and construction team to resolve the descrepancy. Barring other specific order of document governance stated specifically within the contract, the following procedures are normally followed: 1. Anything handwritten and initialed by authorized parties governs over anything printed. 14–26

2. Contract terms govern over specifications and drawings. 3. Answers to requests for information and change orders govern over original specifications and drawings. 4. Specifications govern over drawings. 5. Structural drawings govern over architectural drawings in structural matters only. This is especially relevant in ensuring coordination between the precast concrete layout and the foundations, as well as other structural components. Written or graphic verification should be requested for any unclear condition. If the contract documents specify procedures for requesting information, they should be followed. It is typically the responsibility of the general contractor to ensure that the information is obtained in a timely manner. Whenever possible, any additional information or clarification needed for the complete description of the work should be requested and obtained prior to the bid. 14.4.4.4 Approvals Completed erection drawings and supporting calculations, when required, should be submitted to the owner or his or her representative for approval. The exact sequence of drawing submittals is usually dictated by construction schedules and erection sequences, and is determined when the contract is awarded. Construction documents should specify a reasonable amount of time for approval (for example, two weeks). Preferably, production drawings should not be started prior to receipt of approved or approved-as-noted erection drawings. Production drawings are normally not submitted for approval.a Corrections should be noted on the reproducible erection drawings and copies made and distributed to all parties. The following approval interpretations are normal practice.b 1. Approved — The approversc have completely checked and verified the drawings and calculations for conformance with contract documents and all expected loading conditions. Such approval should not relieve the manufacturer from responsibility for the design when that responsibility is placed on him or her in the contract. The manufacturer may then proceed with production drawings and production without resubmitting. Erection drawings may then be released for plant and field use. 2. Approved as noted — This is the same as approved, except that noted changes should be made and corrected erection drawings issued. Production drawings and production may be started after noted changes have been made. a. When production drawings showing reinforcement are requested for approval or review by the Structrual Engineer of Record, representative drawings or design summaries should be submitted. b. When production drawings are submitted, the same applies. c. The contract should state who has approval authority.

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SPECIFICATIONS AND STANDARD PRACTICES 3. Not approved — Drawings must be corrected and resubmitted. Production drawings cannot be completed correctly until approved or approved-as-noted erection drawings are returned. 4. Reviewed – The approvers have reviewed the drawings for general conformance with design intent and coordination with other parts of the design, and they acknowledge that the fabrication and erection may proceed on the basis of that review. 14.4.5

Materials

The relevant national standards that apply to materials for a project should be listed in the contract documents with any special requirements that are not included in the ASTM standards. Additional information regarding material specifications can be found in this manual in Section 14.2, “Guide Specification for Structural Precast Concrete and Structural Precast Concrete with Commercial Architectural Finish,” and Section 14.3, “Guide Specification for Architectural Precast Concrete.” 14.4.6

CHAPTER 14 14.4.7

Finishes

Finishes of precast concrete products, both structural and architectural, are the cause of more misunderstandings between the various members of the building team than any other question concerning product quality. It is extremely important that the contract documents, as well as the erection drawings, clearly and completely describe the required finishes for all of the components’ surfaces. When the finish is not specified, the standard grade finish described in Section 14.2 should be furnished. The architect’s approval of a reasonably sized sample of the specified finish is recommended. For descriptions of the usual finishes for structural precast concrete, see Section 14.2, and for architectural precast concrete, see Section 14.3. Where special or critical requirements exist or where large expanses of exposed precast concrete will occur on a project, samples are essential and, if required, should be so stated and described in the contract documents. 14.4.8

Delivery of Materials

14.4.8.1 Manner of Delivery

Tests and Inspections

14.4.6.1 Tests of Materials Manufacturers are required to keep test records in accordance with PCI manuals MNL-116-99, MNL-117-96, and MNL-130-91. The contract documents may require the precast concrete manufacturer to make these records available for inspection by the owner’s representative upon his or her request. When the manufacturer is required to submit copies of test records to the owner and/or required to perform or have performed tests not required by the PCI manuals for quality control, these special testing requirements should be clearly described in the contract, documents along with who is responsible for payment.

The manufacturer should deliver the precast concrete to the erector on a schedule to facilitate the planned erection schedule for the structure. Special requirements of the owner for the delivery of materials or the method of transport, should be stated in the contract documents. Note that the erector may be the manufacturer, a subcontractor engaged by the manufacturer, or a subcontractor engaged directly by the general contractor.

14.4.6.2 Inspections The 2006 International Building Code (IBC)40 recognizes PCI plant certification as satisfying the requirements for special inspection for precast concrete manufacturers. Some state agencies also recognize plant participation in the PCI Plant Certification Program as meeting their minimum requirements for inspection. On certain projects, the owner may require inspection of precast concrete products in the manufacturer’s yard by persons other than the manufacturer’s own quality control personnel. Such inspections are normally made at the owner’s expense. The contract documents should describe how, how often, and by whom the inspections are to be made; the responsibility of the inspection agency; and who is responsible for payment. 14.4.6.3 Fire-Rated Products The contract documents must specify the required fireendurance ratings for the product(s) used in the project.

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CHAPTER 14 14.4.8.2 Marking and Shipping of Materials The precast concrete components should be separately marked in accordance with approved drawings in such a manner as to distinguish varying components and to facilitate erection of the structure. The owner should provide the manufacturer with sufficient time in the schedule to fabricate and ship any special plates, bolts, anchorage devices, and the like, and are contractually agreed to be furnished by the manufacturer. 14.4.8.3 Precautions during Delivery Special precautions beyond those required by MNL-116-99, MNL-117-96, and MNL-130-91 should not be expected unless stated in the bid invitation or specifications. The manufacturer is not responsible for the product, including loose material, after delivery to the site unless required by the contract documents. 14.4.8.4 Access to Jobsite

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Free and easy access to the site should be provided to the manufacturer, including backfilling and compacting, drainage, and snow removal, so that delivery trucks and cranes can operate under their own power. The responsibility for which party ensures adequate access should be clearly defined in the contract, but it is typically the responsibility of the general contractor. 14.4.8.5 Unloading Time Allowance Delivery of components should include a reasonable allowance for unloading time. Any delay beyond a reasonable time is normally paid for by the party who is responsible for the delay. 14.4.9 Erection

14.4.9.3 F  oundations, Piers, Abutments, and Other Bearing Surfaces The invitation to bid should state the anticipated time when all foundations, piers, abutments, and other bearing surfaces required for precast concrete erection will be ready and accessible to the erector. Before authorizing the commencement of precast concrete erection, the owner/general contractor should ensure that the precast concrete manufacturer and erector are provided with the following written notifications: 1. The concrete in the footings, piers, and walls and/or mortar in the masonry piers has attained sufficient strength to support the loads imposed during precast concrete erection. 2. Any repairs, replacements, and modifications to the anchor bolts or other embedded hardware have been completed as directed by the Structural Engineer of Record. 3. The structural elements to receive the precast concrete have been accepted by the designated approval authority. 4. An as-built survey of the supporting structure showing that it is within specified tolerances has been completed and has been provided to the erector. 14.4.9.4 Building Lines and Benchmarks

14.4.9.1 Special Erection Requirements When the owner requires a particular erection method or sequence of erection for his own needs, this information should be stated in the contract documents. In the absence of such stated restrictions, the erector may proceed using the most efficient and economically safe method and sequence available to him, consistent with the contract documents, and as directed by the manufacturer. 14.4.9.2 Tolerances Some variation is to be expected in the overall dimensions of any building or other structure. It is common practice for the manufacturer and erector to work within the tolerances shown in PCI’s Tolerance Manual for Precast and Prestressed Concrete Construction (MNL-135-00). The owner, by whatever agencies he or she may elect, should determine if the work is plumb, level, aligned, and properly fastened immediately upon completion of any portion of the erection. Discrepancies should be brought to the attention of the precast engineer immediately so that proper corrective action can be taken. The work is considered complete once the precast con14–28

crete components have been properly plumbed, leveled, aligned within the established tolerances, and all connections have been completed. In addition, all punchlist work required to bring the structure into conformance with the contract requirements should have been addressed. Acceptance for the completed work should be secured from the authorized representative of the owner (see Section 14.2).

The precast concrete erector should be furnished with all building lines and bench marks at each floor level of the structure, as appropriate. The entity responsible for providing this information should be identified in the contract documents along with who is responsible for payment for these services. 14.4.9.5 Anchor Bolts and Bearing Devices If required by contract, the precast concrete manufacturer normally furnishes, but does not install, anchor bolts, plates, and the like that are to be installed in the cast-in-place concrete or masonry for connections with precast concrete components. However, if this is to be the responsibility of the precast concrete manufacturer, it should be so defined in the specifications. It is important that such items be installed true to line and grade, and that installation be completed in time to avoid delays or interference with the precast concrete erection. Anchor bolts and foundation bolts are typically set by the general contractor in accordance with an approved drawing. A template designed and placed to achieve the required tolerance should always be used for setting anchor bolts. Division 5 of PCI's Erector’s Manual — Standards and Guidelines for

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SPECIFICATIONS AND STANDARD PRACTICES the Erection of Precast Concrete Products (MNL-127-99) provides tolerance information for anchor bolts. Special embedded items or hardware, such as grout sleeves for reinforcing bars or proprietary corbel hangers, may require more stringent tolerances as specified by the specialty hardware manufacturer. Where ties at anchor bolts are required by code, the contractor installing the bolts is responsible for furnishing and placing the ties. Erectors should check both line and grade of the interfacing structure in sufficient time before scheduled erection to permit any necessary corrections. Proposed corrections by the general contractor should be submitted to the owner for approval. Responsibility for corrections is that of the general contractor.

CHAPTER 14 connections between precast concrete components that will satisfy structural requirements without altering the function or appearance of the structure. The manufacturer furnishes those items embedded in the precast concrete components, and if required by contract, generally furnishes all loose materials for temporary and permanent connections of precast concrete components. Temporary guys, braces, falsework, and cribbing are the property of the erector and are removed only by the erector, or with the erector’s approval, upon completion of the erection of the structure, unless otherwise agreed. 14.4.9.12 Blockouts, Cuts, and Alterations

Water and electricity should be furnished by the owner for erection and grouting operations.

Neither the manufacturer nor the erector is responsible for the blockouts, cuts, or alterations by or for other trades unless so specified in the contract documents. Whenever such additional work is required, all information regarding size, location, and number of alterations should be furnished by the owner prior to preparation of the precast concrete erection and production drawings. The general contractor is responsible for ensuring that other trades do not cut or alter the precast concrete components without prior approval of the Engineer of Record and the precast concrete engineer, as applicable.

14.4.9.8 Working Space and Crane Access

14.4.9.13 Temporary Floors and Access

The owner should furnish adequate, properly drained, graded, and convenient working space for the erector and access for his or her equipment as necessary to erect the structure. The owner should provide adequate storage space for the precast concrete products to enable the erector to safely operate at the erection rate required to meet the established schedule. Unusual hazards such as high-voltage lines, buried utilities, or areas of restricted access should be stated in the invitation to bid. Hazards should be marked on the site by the general contractor.

The manufacturer or erector is not required to furnish temporary flooring for access unless it is specified in the contract documents.

14.4.9.9 Materials of Other Trades

14.4.9.15 Patching

Other building materials or work of other trades should not be built above the bearing elevation of the precast concrete until after erection of the precast concrete components.

A certain amount of patching due to incidental damage of precast concrete components during handling and erection is to be expected. Patching should be durable and meet the finish requirements of the project, and color and texture should be reasonably matched. Responsibility for accomplishing this work should be resolved between the manufacturer and erector.

14.4.9.6 Grout at Bearing Areas At critical bearing locations shown on the drawings, grout should be placed as soon as possible after erection, not later than the end of the day when the precast concrete component is set, unless otherwise directed by the precast concrete engineer. 14.4.9.7 Utilities

14.4.9.10 Correction of Errors Corrections of minor misfits are considered a part of erection even if the precast concrete is not erected by the manufacturer. Any error that prevents proper connection or fitting of precast concrete components should be immediately reported to the precast concrete engineer or Engineer of Record so that corrective action can be taken. The manufacturer should approve any alterations or corrections to the precast concrete product. 14.4.9.11 Field Assembly The size of precast concrete components may be limited by transportation restrictions for weight and clearance dimensions. Unless special transportation provisions for large pieces without joints are agreed upon between the manufacturer and owner, the manufacturer should provide for field PCI DESIGN HANDBOOK/SEVENTH EDITION

14.4.9.14 Painting, Caulking, and Closure Panels Painting, caulking, and placing of closure panels between stems of flanged concrete components, such as double-tees, are services not ordinarily supplied by the manufacturer or erector. If any of these services are required of the manufacturer, it should be stated in the contract documents.

14.4.9.16 Safety Safety procedures for the erection of the precast concrete components is the responsibility of the erector and must be in accordance with all local, state, or federal rules and regulations having jurisdiction in the area where the work is to be performed. In addition, safety requirements should not be less than required in ANSI Standard A10.9, Safety Requirements for Concrete Construction and Masonry Work.37 PCI’s MNL132-95 provides additional information on this subject.

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CHAPTER 14 14.4.9.17 Security Measures Security protection at the jobsite should be the responsibility of the general contractor. 14.4.10

Interface with Other Trades

14.4.11.2 Acceptance

Coordination of any requirements for other trades to be included in the precast concrete components should be the responsibility of the owner unless clearly defined otherwise in the contract documents. The PCI manuals for quality control (MNL-116-99, MNL-117-96, and MNL-130-91) and MNL-135-00 specify manufacturing tolerances for precast concrete components. Interfaces designed and specified for other materials and trades must take these tolerances into account. Unusual requirements or allowances for interfacing should be stated in the contract documents. 14.4.11

Warranty and Acceptance

Warranties of product and workmanship have become a widely accepted practice in the precast concrete industry, similar to other construction materials and/or trades. Warranties given by the precast concrete manufacturer and erector should indicate that their product and work meet the project specifications. In no case should the warranty required of the manufacturer and erector be in excess of the warranty required by the specifications. In all instances, warranties should include a time limit and it is recommended that this should not exceed one year. In order to protect the interests of all parties concerned, warranties should also state that any deviations in the designed use of the product, modifications of the product by the owner and/or contractor or changes in other products used in conjunction with the precast concrete will invalidate said warranty. A warranty may be included as a part of the conditions of the contract agreement, or it may be presented in letter form as requested by the owner. A sample warranty follows: Manufacturer warrants that all materials furnished have been manufactured in accordance with the specifications for this project. Manufacturer further warrants that if erection of said material is to be performed by those subject to his control and direction, work will be completed in accordance with the same specifications. In no event shall manufacturer be held responsible for any damages, liability or costs of any kind or nature occasioned by or arising out of the actions or omissions of others, or for work, including design, done by others; or for material manufactured, supplied or installed by others; or for inadequate construction of foundations, bearing walls, or other units to which materials furnished by the precast manufacturer are attached or affixed. This warranty is valid for one year starting on ______________. Should any defect develop during the contract warranty period, which can be directly attributed to defect in quality of product or workmanship, precast manufacturer shall, upon written notice, 14–30

The manufacturer should request approval and acceptance for all materials furnished and all work completed by him periodically and in a timely manner, as deemed necessary, in order to adequately protect the interests of everyone involved in the project. The size and nature of the project will dictate the appropriate intervals for securing approval and acceptance. Periodic approval, in writing, should be requested as soon as it appears that such action will minimize possible problems which would seriously affect the progress of the project. Final inspection and acceptance of erected precast and prestressed concrete should be made by the owner’s representative within a reasonable time after the work is completed. 14.4.12

14.4.11.1 Warranties

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correct defects or replace products without expense to owner and/or contractor. COMPANY NAME Signature Title Date

Contract Administration

14.4.12.1 General Statement Contract agreements may vary widely from area to area, but the objective should be the same in all instances. The contract agreement should be written to equitably and fairly protect the interests of all parties concerned and, at the same time, be specific enough in content to avoid misunderstandings during the course of the entire project. Information relative to invoicing, payment, bonding and other data pertinent to a project or material sale should be specifically provided for in the major provisions of the contract documents or in the special terms and conditions applicable to all contractual agreements between manufacturer and owner. The intent of this section is to recommend those matters which ought to be considered, but not necessarily the form in which they should be expressed. The final contract document should be the result of careful consideration of all pertinent factors as well as of the normal practices in the area. 14.4.12.2 Retentions Although retentions have been used for many years as a means of ensuring satisfactory job performance, it is apparent that they directly add to the cost of construction, frequently lead to disputes, and often result in job delays. In view of the unfavorable consequences of retentions and possible abuse, it is recommended that the following procedure be followed: 1. Wherever possible, retentions should be eliminated and bonding should be used as the best source of protection. This should apply to prime contractors and subcontractors equally. 2. Where there are no bonding requirements, the retention percentage should be as low as possible. It is recommended that this not be more than 5% of the work invoiced. 3. The percentage level of any retention should be the same for subcontractors as for prime contractors on a

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SPECIFICATIONS AND STANDARD PRACTICES project. 4. Release of retained funds and final payment, as well as computing the point of reduction of the retention, should be performed on a line-item basis, that is: each contractor's or subcontractor’s work is considered as a separate item and the retention reduced by 50% upon substantial completion and the balance released within 30 days after final completion of that work. 5. Retained funds should be held in an escrow account with interest accruing to the benefit of the party to whom the funds are due. 6. When materials are furnished freight-on-board plant or jobsite, it is recommended that there not be retentions. 7. Retention should be paid in full within 90 days after the last precast concrete item has been delivered. 14.4.12.3 Contract Agreements 1. Contract agreements should fully describe the project involved, including job location, project name, name of owner/developer, architect or other design professionals, and all reference numbers identifying job-relation information such as plans, specifications, addenda, bid number, and the like. 2. Contract agreements should fully describe the materials to be furnished and/or all work to be completed by the manufacturer. This can be done in a scope-ofwork document attached to and referenced in the contract agreement. 3. All inclusions and exclusions should be stated to avoid the possibility of any misunderstanding. 4. The quoted price should be stated to eliminate the possibility of any misunderstanding. 5. Reference should be made to the terms and conditions governing the proposed contract agreement. Special terms or conditions should be stated in sufficient detail to avoid the possibility of any misunderstanding. 6. The terms of payment should be specifically detailed so there is no doubt as to the intent. Special care should be exercised where the terms of payment will differ from those normally in effect or where they deviate from the general terms and conditions appearing in the contract. 7. A statement of policy should be made with reference to the inclusion or exclusion of taxes in the stated price. 8. The proposal form stating the full conditions under which the project will be performed may contain an acceptance clause to be signed by the purchaser. At such time as said acceptance clause is signed, the proposal form then becomes the contract agreement. 9. The manufacturer should clearly state the limits of time within which an accepted proposal will be recognized as a binding contract. 10. A statement indicating the classification of labor to perform the work in the field is advisable to eliminate later dispute over jurisdiction of the work performed.

PCI DESIGN HANDBOOK/SEVENTH EDITION

CHAPTER 14 14.4.12.4 Terms and Conditions The terms and conditions stated on the proposal contract agreement should include, but are not necessarily limited to, the following: 1. Lien laws — Where the lien laws of a state specifically require advance notice of intent, it is advisable to include the required statement in the general terms and conditions. 2. Specifications — The manufacturer should make a specific declaration of material and/or work specifications, but normally this should not be in excess of the specifications required by the contract agreement. 3. Contract control — A statement should be made indicating that the agreement, when duly signed by both parties, supersedes and invalidates any verbal agreement and can only be modified in writing with the approval of those signing the original agreement. 4. Terms of payment — Terms of payment should be specifically stated either on the face of the contract or in the general terms and conditions. The method and frequency of invoicing should be so stated, indicating time within which payment is expected. 5. Late payment charges — The contract may provide for legal interest charges for late payments not made in accordance with contract terms and, if this is desired, it should be stated in the general terms and conditions. A statement indicating that the seller is entitled to reasonable attorney’s fees and related costs should collection proceedings be necessary may also be included. 6. Overtime work — Prices quoted in the proposal should be based on an eight-hour day and a five-day week, excluding holidays, under prevailing labor regulations. Provisions should be included in the contract agreement to provide for recovery of overtime costs plus a reasonable markup when the seller is requested to provide such service. 7. Financial responsibility — General terms and conditions may indicate the right of the manufacturer to suspend or terminate material delivery and/or work on a project if there is a reasonable doubt in the ability of the purchaser to fulfill his financial responsibility. 8. Payment for inventory — a. It has become common practice to include in the contract terms and conditions provisions for the invoicing and payment of all materials purchased for the project and stored at the plant. When deliveries or placement of said materials at the jobsite are delayed for more than a stipulated time beyond the originally scheduled date because of the purchaser’s inability to either accept delivery of materials or to provide proper job access, terms for costs of extended storage should be stated in the contract. b. Under certain conditions, it may be necessary to purchase special materials or to produce components well in advance of job requirements to ensure timely deliveries. When job requirements are of

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such a nature, it is advisable to include provisions for payment of such raw materials and finished products stored in the manufacturer’s plant or on jobsites on a current basis. 9. Payment for suspended or discontinued projects — The terms and conditions should provide that in the event of a discontinued or suspended project, the manufacturer shall be entitled to payment for all material purchased and/or manufactured including costs, overhead, and profit. This should also include the cost of engineering work performed to date and other costs incurred, including reasonable overhead caused by the plant being idle from late notification of suspension of work. 10. Change orders— Requests for additional compensation resulting from extra work should be confirmed in writing as change orders. Invoicing should be presented immediately following completion of the extra work, with payment subject to the terms and conditions of the contract agreement or as otherwise stated in the change order. 11. Claims for shortages, damages, or delays — The seller should, upon immediate notification in writing on the face of the delivery ticket of rejected material or shortage, acknowledge and furnish replacement material, when appropriate, at no cost to the purchaser. It is normal practice that the seller should not be responsible for any loss, damage, detention, or delay caused by fire, accident, labor dispute, civil or military authority, insurrection, riot, flood, or by occurrences beyond his or her control. 12. Back charges — Back charges should not be binding on the seller, unless the condition is part of the contract and promptly reported in writing, and opportunity is given to the seller to inspect and correct the reason for the back charge. 13. Permits, fees, and licenses — Costs of permits, fees, and licenses required for the project and other similar expenses are normally paid for by the purchaser. 14. Bonds — The cost of bonds required by the owner is normally paid for by the purchaser. 15. Taxes — Federal, state, county, or municipal occupation or similar taxes that may be imposed are normally paid for by the purchaser and, in the case of sales taxes, through the seller (varies by locale). For tax-exempt projects, the purchaser should issue to the seller a taxexempt certificate when the purchase agreement is finalized. 16. Insurance — The seller shall carry worker’s compensation, public liability, property damage, and auto insurance, and a certificate of insurance should be given to the purchaser upon request. Additional coverage required over and above that typically provided by the manufacturer is normally paid for by the purchaser. A statement specifically excluding both additional insured status for the owner and a waiver of subrogation should be included. 17. Services — Heat, water, light, electricity, toilet, tele14–32

phone, security watchmen, and general services of a similar nature are normally the responsibility of the purchaser unless specifically stated otherwise in the contract agreement. 18. Safety equipment — The purchaser is normally responsible for necessary barricades, guard rails, and warning lights for the protection of vehicular and pedestrian traffic. The owner is responsible for furnishing, installing, and maintaining all safety appliances and devices required on the project under U.S. Department of Labor's Safety and Health Requirements for Construction (OSHA 2207).38 The purchaser must also satisfy all other safety regulations imposed by other agencies having jurisdiction over the project, not specifically within the scope of the erection of the precast concrete. 19. Warranty — The seller should provide specific information relative to warranties given, including limitations, exclusions, and methods of settlement. Warranties should not be in excess of the warranty required by the specific project. 20. Title — The contract should provide for proper identification of title to material furnished. It is normal practice for title and risk of loss or damage to the product furnished to pass to the purchaser at the point of delivery, except in cases of freight-on-board plant, in which case, title to and risk of loss or damage to the product normally should pass to purchaser at plant pickup. 21. Shop-drawing approval — The seller should prepare and submit to the purchaser for approval all shop drawings necessary to describe the work to be completed (See Section 14.4.4, "Standard Operations Practice Recommendations for Precast Concrete," for the definition of shop drawings). Shop-drawing approval should constitute final agreement related to quantity and general description of material to be supplied. No work should be done by the seller to material to be furnished by seller until approved shop drawings are in the seller’s possession. 22. Delivery — Delivery times or schedules set forth in the contract agreements should be computed from the date of delivery to the seller of approved shop drawings. Where materials are specified to be delivered freighton-board to jobsite, the purchaser should provide labor, cranes, or other equipment to remove the materials from the trucks and should pay seller for truck expense for time at the jobsite in excess of a specified unloading time for each truck. On shipments to be delivered by trucks, delivery should be made as near to the construction site as the truck can travel under its own power. In the event that delivery is required beyond the curb line, the purchaser should assume full liability for damages to sidewalks, driveways, or other properties and should secure in advance all necessary permits or licenses that affect such deliveries. 23. Builder’s risk insurance — The purchaser should provide builder’s risk insurance without cost to the seller, protecting seller’s work, materials, and equip-

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SPECIFICATIONS AND STANDARD PRACTICES ment at the site from loss or damage caused by fire or the standard perils of extended coverage, including vandalism and malicious acts. 24. Erection — The purchaser should ensure that the proposed project will be accessible to all necessary equipment including manlifts, cranes, and trucks, and that the operation of this equipment will not be impeded by construction materials, water, presence of wires, pipes, poles, fences, or framings. The purchaser should further indemnify and hold harmless the seller and his or her respective representatives, including subcontractors, vendors, assigns, and successors from any and all liability, fines penalty or other charge, cost, or expense and defend any action or claim brought against seller for any failures by the purchaser to provide suitable access for work to be performed. The seller also reserves the right to discontinue the work for failure of the purchaser to provide suitable access and the purchaser should be responsible for all expenses and costs incurred. 25. Exclusions of work to be performed — Unless otherwise stated in the contract, all shoring, forming, framing, cutting holes, openings for mechanical trades, and other modifications to the seller’s products should not be performed by the seller nor are they included in the contract price. The seller should not be held responsible for modifications made by others to his or her product unless said modifications are previously approved. 26. Sequence of erection — The sequence of erection, when required to satisfy the stability of the structure, should be as agreed upon between the seller and purchaser and expressly stated in the contract agreement. The purchaser should have ready all foundations, bearing walls, or other units to which seller’s material is to be affixed, connected, or placed, prior to the start of erection. The purchaser should be responsible for the accuracy of all as-built job dimensions, bench marks, and true and level-bearing surfaces. Claims or expenses arising from the purchaser’s neglect to fulfill this responsibility should be paid for by the purchaser. 27. Mediation/arbitration — In view of the difficulties and misunderstandings that may occur due to misinterpretation of contractual documents, it is recommended that the seller stipulate that all claims, disputes, and other matters in question, arising out of or related to the contract, be decided by mediation or arbitration in accordance with the construction industry rules of the American Arbitration Association then in effect, or some other rules acceptable to both parties. The location for such alternate dispute resolution should be stipulated. 28. Contract form — The contract documents should stipulate the policy governing acceptance of proposals on other than the manufacturer’s form. All identifying information such as proposal number, dates, and the like should be included so there is no question as to which PCI DESIGN HANDBOOK/SEVENTH EDITION

CHAPTER 14 document is referred to. Standard subcontract forms are available from the American Institutue of Architects, the Council of American Structural Engineers, the Associated General Contractors of America, Association of Subcontractors, and other organizations. 29. Indemnification — Any indemnification or holdharmless obligation of the seller should extend only to claims relating to bodily injury and property damage and then only to that part or proportion of any claim, damage, loss, or defect that results from the negligence or intentional act of the seller or someone for whom it is responsible. The seller should have no duty to defend.

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CHAPTER 14

14.5

 ecommendations on Responsibility for Design and Construction of Precast R Concrete Structures

14.5.1 Introduction Design and construction of structures is a complex process. Defining the scope of work and the responsibilities of the parties involved in this process by contract is necessary to achieve a safe, high quality structure. Besides the owner, the parties involved in the design and construction of precast concrete structures or other structures containing precast concrete components may include the Structural Engineer of Record, architect, construction manager, general contractor, manufacturer, precast concrete engineer, specialty engineer, erector and inspector. Terms related to precast concrete construction are defined in Section 14.5.2. This section is taken primarily from Reference 1. Excerpts from Reference 41 have been added where appropriate. Other organizations have published documents on the same subject as noted in References 42, 43, and 44.

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14.5.2 Terminology Terms used in engineering practice and the construction industry may have meanings that differ somewhat from ordinary dictionary definitions. The following definitions are commonly understood in the precast concrete industry. Approval (of shop drawings or submittals). The action with respect to shop drawings, samples, and other data that the general contractor are required to submit, but only for conformance with the design requirements and compliance with the information given in the contract documents. Such action does not extend to means, methods, techniques, sequences, or procedures of construction, or to safety precautions and programs incident thereto, unless specifically required in the contract documents. Authority. The power, conferred or implied by contract, to exercise effective direction and control over an activity for which a party has responsibility. Connection. A structural assembly or component that transfers forces from one precast concrete component to another, or from one precast concrete component to another type of structural member. Contract documents. The design drawings and specifications, as well as general and supplementary conditions and addenda, that define the construction and the terms and conditions for performing the work. These documents are incorporated by reference into the contract. Contractor. A person or firm that enters into an agreement to construct all or part of a project. Construction manager. A person or firm engaged by the owner to manage and administer the construction. Design (as a transitive verb). The process of applying the principles of structural engineering, structural mechanics, and materials science, and interpreting code regulations to determine the geometry, composition, and arrangement of components and their connections in order to establish the composition and configuration of a structure. 14–34

Design (as a noun). The product of the design process, as usually represented by design drawings and specifications. Design drawings. Graphic diagrams with dimensions and accompanying notes that describe the structure. Detail (as a transitive verb). The process of utilizing the principles of geometry and the art of graphics to develop the dimensions of structural components. Detail (as a noun). The product of the detailing process, shown on either design or shop drawings, such as the graphic depiction of a connection or other detailed assembly. Engineer of Record (EOR). See “Structural Engineer of Record” and “licensed design professional in responsible charge." Erector. Usually the subcontractor that erects the precast concrete components at the site. The manufacturer will typically self-perform or subcontract the erection, but, on occasion, this is undertaken directly by the general contractor. General contractor. A person or firm engaged by the owner to construct all or part of the project. The general contractor supervises the work of its subcontractors and coordinates the work with other contractors. Inspector. The person or firm retained by the owner or the owner’s representative to observe and report on compliance of the construction with the contract documents or local governing codes. Licensed design professional (LDP); also licensed design professional in responsible charge (LDPIRC). A person or firm engaged by the owner or the owner’s representative to design the project and/or to provide services during the construction process. This person is typically required to be an engineer or architect whose specialty is that particular field for each discipline of the work and is recognized accordingly by the local building official. This is the LDPIRC for that specific discipline. In some cases, the engineer may be a subcontractor to the architect, or vice versa. In this document, LDPIRC and LDP will be used interchangeably. Manufacturer (producer, precaster, fabricator). The firm that manufactures the precast concrete components. Member. In this document, a precast concrete piece or component. Owner. The public body or authority, corporation, association, firm, or person for whom the structure is designed and constructed. Precast concrete. Concrete cast at a location other than in its final position, usually under plant-controlled conditions. This includes prestressed and non-prestressed components used in structural or non-structural applications. Precast concrete engineer. The engineer or firm who designs precast concrete components for specified loads and who may also direct the preparation of the shop drawings. The precast concrete engineer may be employed by the manufacturer or be an independent consultant or firm to whom

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SPECIFICATIONS AND STANDARD PRACTICES the manufacturer subcontracts the work. This person is usually required to be a licensed professional by contract documents and/or applicable law. Responsibility. Accountability for providing the services and/or for performing the work required by contract. Shop drawings. Graphic diagrams of precast concrete components and their connecting hardware, developed from information in the contract documents. The contract documents show information needed for both field assembly (erection) and manufacture (production) of the precast concrete. Shop drawings for precast concrete may be separated into erection and production drawings. Erection drawings typically describe the location and assembly details of each precast concrete component at the construction site. Connection hardware is detailed on the erection drawings and may be shown on production drawings. Production drawings contain all of the information necessary for the manufacturer to cast the component, including all necessary dimensions and bills of material. Specialty structural engineer (SSE). This is the same as “precast concrete engineer” in this document. Used by References 42 and 44 to indicate any engineer designated by the Structural Engineer of Record (SER) to perform specific tasks. Structural Engineer of Record (SER). The registered professional engineer (or structural engineer in some states of the United States) who is responsible for developing the project design, design drawings, and specifications in such a manner as to meet the applicable requirements of governing state laws and local building authorities. The SER is commonly identified by the professional engineer’s seal on the design drawings and specifications. This role is also often referred to as the Engineer of Record (EOR). Specifications. Written requirements for materials and workmanship that complement the design drawings. Subcontractor. A person or firm contracted to perform all or part of another person's or firm’s contract. 14.5.3

Design Practices

Practices vary throughout North America with respect to design of structures using precast concrete components. However, it is of fundamental importance that every aspect of the design is performed in accordance with the requirements of all state laws governing the practice of engineering and/or architecture, and also meets all requirements of local regulatory authorities. This generally requires that a registered professional engineer or architect accepts responsibility as the (LDPIRC) for ensuring that these requirements are met. The LDP seals the contract documents. These documents constitute the structural design and are customarily submitted to regulatory authorities for a building permit. In addition, the LDP ordinarily approves shop drawings. The LDP may also have other ongoing responsibilities during construction to satisfy local authorities. Structures are usually designed by an engineering firm retained by or on behalf of the owner. A person within the firm is selected to prepare and/or to supervise the preparation of the contract documents. This person normally is registered PCI DESIGN HANDBOOK/SEVENTH EDITION

CHAPTER 14 to practice engineering in the state where the structure will be built and becomes the SER when the design drawings and specifications are approved by the local regulatory authority. An individual in private practice may also be retained by an owner to prepare the design and become the SER. The design drawings and the specifications become a part of the contract documents used by contractors to construct the structure. A critical function of the contract documents is to clearly define responsibility among involved design professionals. The contract drawings, at a minimum, should include all of the items listed in Section 14.3.1. Owners may also directly seek proposals from general contractors who are willing to prepare the design (designbuild). The general contractor may use an employed registered professional engineer or architect, who is the LDP, or subcontract the design to a firm or individual who becomes the LDP. In some instances, a manufacturer may perform the role of the general contractor. Since the owner may already have a contract with the selected general contractor, any additional contracts will be between the general contractor and selected designers. Under this arrangement, the owner often retains an engineering consultant to review the proposals and the design-related work of the selected general contractor. Normally the precast concrete manufacturer is a subcontractor to the general contractor. Most manufacturers are willing to accept responsibility for component design of the components that they produce, provided sufficient information is contained in the contract documents. This design work is commonly done by a precast concrete engineer. The manufacturer may also accept responsibility for design of the connections when the forces acting on the connections are defined by the SER, or in certain instances, design for the entire precast concrete system when the SER has assigned that role and provided the design parameters. At the time of bidding, if there is insufficient information or lack of direction in the contract documents, the manufacturer customarily assumes that industry minimum standards are acceptable. Local regulatory authorities may approve design documents for starting construction without final design of the precast concrete components. These initial design documents are typically referred to as building permit drawings or drawings for permit. In most cases, the design of the precast concrete can be performed and submitted at a later time, often in conjunction with preparation of shop drawings. When part of the layout drawings prepared by the precaster are to be included with the permit set, it is important to keep in mind that they may require the seal of the SER. The SER typically requires a registered engineer seal to the documents depicting the designs assigned to the precast concrete scope of the work. This does not relieve the SER of the responsibility of reviewing the designs, ensuring that the designated loading requirements have been properly interpreted and interactive forces with other construction are fully coordinated.

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CHAPTER 14 14.5.4

Recommendations

PCI is aware of the competitiveness in the marketplace for building systems, and believes the use of precast concrete products provides for a high-quality finished structure. Along with quality, it is essential that a structure be both safe and serviceable, that is, have structural integrity and perform as intended. Because the construction process involves many parties, it is essential that work assignments and responsibilities be clearly defined in the contractual arrangements. The following comments and recommendations towards achieving quality and integrity in precast concrete structures are intended to provide clarity to this process. 14.5.4.1 To the Owner

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At the outset, the owner must decide whether to enter into a contract with an engineer or architect to design and prepare contract documents for the structure that subsequently can be used to obtain bids by a general contractor. This is traditionally known as design-bid-build. Alternatively, the owner may contract with a general contractor (or manufacturer willing to assume that responsibility) to both design and build the structure. This is know as design-build. These two arrangements may be summarized as follows: 1. Owner retains an engineer or architect who will be the LDPIRC:

a. To design and prepare contract documents sufficient for construction without further design by the general contractor or subcontractors. b. To prepare contract documents sufficient for construction with further design by the general contractor or subcontractor. An example of this may include component design, post-tensioning, cladding panels, and the like.

2. Owner contracts with a general contractor for design and construction (design-build). Under the second arrangement, where the LDP will be engaged or employed by the contractor, it may be desirable for the owner to retain another engineer or architect for consultation on design criteria and verification that the design intent is achieved. The owner should consider the experience and qualifications of both the engineer or architect and the general contractor with precast concrete construction similar to that for the intended project. If the owner plans to have an active role in the project, it is essential that both this role and the lines of communication with the other parties be clearly defined in written documents pertaining to the project. The owner must allow sufficient time in the various phases of the construction process to achieve the necessary review, coordination, and implementation of the project requirements. Changes initiated after the start of construction invariably add cost to the structure. A thorough review by the owner after the design is completed and before construction is started is essential. PCI producer members are required to adhere to the formal and rigorous requirements of the PCI Plant Certification 14–36

Program. This program is recognized in the master specifications of the American Institute of Architects. It is also recommended and recognized in standard specifications by numerous federal, state, and local government agencies. PCI Plant Certification is recognized by the International Code Council, the organization responsible for the International Building Code. The owner or LDP should require that PCI Plant Certification be written into the project specifications. 14.5.4.2 T  o the Licensed Design Professional (LDP) As discussed in Section 14.5.3, the role of the LDP (engineer/ architect) varies significantly depending on whether this party is retained by the owner or by other parties. If retained by the owner, the LDP’s lines of communication among the parties involved in the project should be established by written documents. Pre-bid and pre-construction conferences should be held, during which, lines of communication and responsibilities are reviewed and the design requirements are discussed. If retained or employed by the general contractor or manufacturer, the LDP must remain cognizant of his professional responsibility to satisfy state laws and local regulatory authorities. Procedures should be established to allow the LDP to discharge these responsibilities without restriction by other parties involved in the construction. Review and approval of shop drawings by the LDP is essential to ensure that the design intent is achieved. Timeliness of review may be crucial to the manufacturer. The LDP must be responsive to the shop drawing submittal and review schedules for the various parties. These parties should accept that the approval of the LDP does not relieve them of their responsibilities. The LDP should make clear whether the contract documents, specifications, or drawings prevail in the event of conflicts. This subject is addressed in Section 14.4.4.3. 14.5.4.3 T  o the Structural Engineer of Record (SER) The licensed design professional responsible for the structural aspects of the design is typically referred to as the Structural Engineer of Record (SER). Under either arrangement for contracting the work mentioned in Section 14.5.4.1, overall structural integrity will be best ensured if the SER assumes responsibility for the lateral stability of the structure, including relevant connection details. Under arrangement 1b in Section 14.5.4.1, the contract documents must establish the loadings and identify the criteria for design to be used by the contractor. If the design of the lateralload-resisting system is assigned to the specialty structural engineer (SSE), the SER should assure himself as to the adequacy of the system. Design work by any contractor should be submitted to and approved by the SER. The SER may require the design and shop drawings to be sealed by a registered professional engineer as a demonstration of qualifications and acceptance of design responsibility. Coordination and communication between the SER and the SSE are of paramount importance. This aspect and its importance are recognized on the national level by CASE: “The primary failure in projects involving SSE is the lack of coordination and delineation of responsibility. When interfacing with the

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SPECIFICATIONS AND STANDARD PRACTICES SSE, the SER should always be the one who delineates responsibility for the various structural requirements.”42 Where the design involves a non-self-supporting precast concrete frame, the contract documents should indicate which party is responsible for the design of the construction bracing and how long it needs to remain in place. Interfaces between precast concrete components and other construction types and materials require special attention. The SER is responsible for considering these interface conditions during structural design and shop drawings review, including temporary loading conditions during erection. Regarding stability of the structure during erection, the SER’s review of erection/bracing plans should be limited to its effect on the integrity of the completed structure and the impact of the temporary loading on other structural elements that are not part of the precast concrete system. In cases where the SER has performed the complete design of the lateral-load-resisting system, his or her involvement in the erection/bracing plans needs to be to a greater level of detail in order to provide adequate guidance to the erector of the precast. 14.5.4.4 To the General Contractor When undertaking construction of a building independently designed for the owner on a design-bid-build basis, the general contractor’s responsibility is to build the structure in accordance with the contract documents. When design responsibility is accepted by the general contractor, the specialized nature of this function must be recognized and allowed to be achieved in a manner that does not compromise the integrity of the facility or impair its quality. The responsibilities of the manufacturer must be clearly defined. It must be understood that all design is submitted through the LDPIRC for approval or acceptance. The manufacturer’s responsibility is often limited to component design and preparation of shop drawings. However, it may include the design of the entire precast structural system if agreed to by the manufacturer in the contract. When the manufacturer is responsible only for component design, all loads applied to the precast concrete components, including forces developed by restraint, must be provided by the SER. The manufacturer should be given responsibility and authority for properly implementing the intent and requirements of the design drawings, properly furnishing materials and workmanship, maintaining the specified fabrication and erection tolerances, and for fit and erectibility of the structure. When responsible only for component design, the manufacturer must be provided with all of the drawings and specifications that convey the full requirements for the precast concrete components. Drawings are commonly divided into civil, architectural, structural, electrical, mechanical, fire protection, and other groupings, depending on the size and scope of the project. Other pertinent drawings may also be desirable, such as approved shop drawings from other trades, roofing requirements, alternates, and the like. Timely review and approval by the LDPIRC of shop drawings and other pertinent information submitted by the manufacturer are essential.

PCI DESIGN HANDBOOK/SEVENTH EDITION

CHAPTER 14 14.5.4.5 To the Manufacturer (Precaster) After the contract is awarded, the manufacturer, erector, and precast concrete engineer should meet with the overall construction team to review project design and construction requirements. Detailed discussion of the requirements for special inspections should be another important agenda item for this meeting. Experience has shown that active participation on the part of the precast concrete team during the inspection process significantly adds to the positive conclusion of the building construction sign-off by the appropriate parties. The precast concrete engineer should prepare shop drawings in accordance with the design information supplied in the contract documents and subsequent written instructions from the LDPIRC. In cases where the manufacturer requests permission to revise connections that are already part of the design or approval documents, in order to facilitate manufacture and/or erection or for remedial purposes, information supporting the revision should be submitted to the LDP for review and approval. The manufacturer and/or the precast concrete engineer should have a direct channel of communication for technical issues with the LDP as the project goes forward and is also required to keep the general contractor informed. The manufacturer should request clarification in writing from the LDP on special or unusual conditions not clearly defined by the design drawings or specifications furnished to the manufacturer. In those cases where the manufacturer is responsible for the design, fabrication, and erection of the precast concrete structure, the manufacturer should convene a meeting between the precast concrete engineer and the erector prior to the start of erection. This meeting is used to discuss the necessary sequence and details of erecting the precast and to plan for the safe erection of the structure at the various stages until fully completed. The erector should be responsible for handling and bracing all standard individual components that comprise the structure. 14.5.4.6 T  o the Specialty Structural Engineer (SSE) The SSE is responsible for the design of the components, connections, and structural systems as designated by the SER within the contract documents. The SSE is responsible to review the contract documents to fully understand the responsibilities assigned and the design criteria set forth by the SER. The SSE is cautioned to understand clearly who is responsible for the complete design of each structure on which they work. The SSE is not to be considered as the SER unless contract documents or subcontracts clearly assign the SSE with the responsibility, authority, and liability normally assumed by the SER. Acceptance by the SSE of the responsibilities delineated within the contract documents is provided by virtue of his professional seal and signature on the structural submittals. In additon to erection drawings, the structural submittals should include applicable design calculations with sufficient fabrication drawings and component details to substantiate

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SPECIFICATIONS AND STANDARD PRACTICES

CHAPTER 14 the design intent. If the design of a complete structural system is included within the SSE’s scope of work, the calculations should include all relevant information regarding behavior of the system under load, as well as the magnitude of the reactions under all design conditions on other portions of the structure (for example, foundations).

13. A  STM. 2006. Standard Specification for Uncoated High-Strength Steel Bars for Prestressing Concrete (ASTM A722/A722M-06). Reston, VA: ASTM.

14.6

15. H  over, K. C. and R. A. C. Pinto. 2001. Frost and Scaling Resistance of High-Strength Concrete. Skokie, IL: Portland Cement Association.

1.

References

 merican Concrete Institute (ACI) Committee 318. A 2005. Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R05). Farmington Hills, MI: ACI.

2.

PCI Plant Certification Committee (PCI). 1999. Manual for Quality Control for Plants and Production of Structural Precast Concrete Products (MNL-116-99). Chicago, IL: Precast, Prestressed Concrete Institute.

3.

PCI Architectural Precast Concrete Services Committee and Plant Certification Committee. 1996. Manual for Quality Control for Plants and Production of Architectural Precast Concrete Products (MNL-117-96). Chicago, IL: PCI.

  14 4.

5.

 CI. 2005. Acceptance Criteria for Moment Frames A Based on Structural Testing (ACI T1.1-01). Farmington Hills, MI: ACI. ACI. 2005. Acceptance Criteria for Moment Frames Based on Structural Testing and Commentary (3741.05). Farmington Hills, MI: ACI.

6.

ACI. 2008. Acceptance Criteria for Special Unbonded Post-Tensioned Precast Walls Based on Validation Testing (ITG 5.1-07). Farmington Hills, MI: ACI.

7.

 merican Society of Civil Engineers (ASCE). 2005. A Minimum Design Loads for Buildings and Other Structures (ASCE/SEI 7-05). Reston, VA: ASCE.

8.

 merican Welding Society (AWS). 2005. Structural A Welding Code - Reinforcing Steel (AWS D1.4/D1.4M). Miami, FL: AWS.

9.

 merican Society for Testing and Materials (ASTM). A 2008. Standard Specification for Low-Alloy Steel Deformed and Plain Bars for Concrete Reinforcement (ASTM A706/A706M). West Conshohocken, PA: ASTM.

10. PCI Connections Committee. 1980. Design and Typical Details of Connections for Precast and Prestressed Concrete. Chicago, IL: PCI. 11. A  STM. 2005. Standard Specification for Uncoated Stress-Relieved Steel Wire for Prestressed Concrete (ASTM A421/A421M-05). West Conshohocken, PA: ASTM. 12. A  STM. 2006. Standard Specification for Steel Strand, Uncoated Seven-Wire for Prestressed Concrete (ASTM A416/A416M-06). West Conshohocken, PA: ASTM.

14–38

14. P  erenchio, W. F., and P. Klieger. 1978. Some Physical Properties of High-Strength Concrete. PCA Research Development Bulletin RD056. Skokie, IL: Portland Cement Association.

16. A  STM. 1999. Standard Test Method for Water-Soluble Chloride in Mortar and Concrete (ASTM C1218/ C1218M-99). West Conshohocken, PA: 1999. 17. P  feifer, Donald W., J. R. Landgren, and William Perenchio. 1986. Concrete, Chlorides, Cover and Corrosion. PCI Journal, V. 31, No. 4 (July-August). 18. PCI Committee on Tolerances. 2000. Tolerance Manual for Precast and Prestressed Concrete Construction (MNL-135-00). Chicago, IL: PCI. 19. P  CI Committee on Prestressed Concrete Columns. 1988. Recommended Practice for the Design of Prestressed Concrete Columns and Walls. PCI Journal, V. 33, No. 4 (July-August): pp. 56–95. 20. A  swad, Alex and George Burnley. 1989. Omission of Web Reinforcement in Prestressed Double Tees. PCI Journal, V. 34, No. 2 (March-April): pp. 48–65. 21. A  swad, A., G. Burnley, N. Cleland, D. Orndorff, and C. Wynings. 2004. Load Testing of Prestressed Concrete Double Tees without Web Reinforcement. PCI Journal, V. 49, No. 2 (March-April), pp. 66–77. 22. P  CI Design Handbook Committee. 1978. PCI Design Handbook: Precast and Prestressed Concrete. 2nd ed. Chicago, IL: PCI. 23. P  CI Industry Handbook Committee. 1992. PCI Design Handbook: Precast and Prestressed Concrete. 4th ed. Chicago, IL: PCI. 24. Z  ia-Hsu, Paul. 2004. Design for Torsion and Shear in Prestressed Concrete Flexural Members. PCI Journal, V. 49, No. 3 (May-June). 25. L  ucier, G., Rizkalla, P. Zia, and G. Klein. 2007. Precast Concrete, L-Shaped Spandrels Revisited: Full-Scale Tests. PCI Journal, V. 52, No. 2 (March-April). 26. K  lein, G. J. 1986. Design of Spandrel Beams. PCI Specially Funded Research Project No. 5. Chicago, IL: PCI. 27. J oint PCI/WRI Ad Hoc Committee on Welded Wire Fabric for Shear Reinforcement. 1980. Welded Wire Fabric for Shear Reinforcement. PCI Journal, V. 25, No. 4 (July-August): pp. 32–36. 28. D  olan, C, and Krohn, J. 2007. A Case for Increasing the Allowable Compressive Release Stress for Prestressed Concrete. PCI Journal, V. 52, No. 1 (January-February).

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SPECIFICATIONS AND STANDARD PRACTICES 29. G  hosh, S. K. and Ned Cleland. 2007. Seismic Design of Precast/Prestressed Concrete Structures (MNL-140-07). Chicago, IL: PCI.

CHAPTER 14 44. C  ASE. 1997. National Practice Guidelines for the Structural Engineer of Record. Washington, DC: CASE.

30. P  CI Connections Details Committee. 2008. PCI Connections Manual for Precast and Prestressed Concrete Construction (MNL-138-08). 1st ed. Chicago, IL: PCI. 31. A  nderson, Neal S., and Donald F. Meinheit, Donald F. 2000. Design Criteria for Headed Stud Groups in Shear: Part 1 – Steel Capacity and Back Edge Effects. PCI Journal, V. 45, No. 5 (September-October). 32. P  CI Architectural Precast Concrete Committee. 2007. Architectural Precast Concrete (MNL-122-07). 3rd edition. Chicago, IL: PCI. 33. P  CI Committee on Glass Fiber Reinforced Concrete Panels. 2009. Manual for Quality Control for Plants and Production of Glass Fiber-Reinforced Concrete Products (MNL-130-09). Chicago, IL: PCI. 34. P  CI. 2007. PCI Certification for Plants, Personnel, and Product Erection (MKT-43204-07). Chicago, IL: PCI.

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35. P  CI Erectors Committee. 1999. Erectors’ Manual — Standards and Guidelines for the Erection of Precast Concrete Products (MNL-127-99). 2nd edition. Chicago, IL: PCI. 36. P  CI Erectors Committee. 1995. Erection Safety for Precast and Prestressed Concrete (MNL-132-95). Chicago, IL: PCI. 37. American National Standards Institute (ANSI). 1997. Standard A10.9, Safety Requirements for Concrete Construction and Masonry Work (R2004). Washington, DC: ANSI. 38. U.S. Department of Labor, Occupational Safety and Health Administration (OSHA). 1998. Part 1926, Safety and Health Requirements for Construction, Subpart Q (Concrete and Masonry). Washington, DC: OSHA. 39. PCI Committee on Detailing of Precast Concrete. 1990. PCI Drafting Handbook — Precast and Prestressed Concrete (MNL-119-90). 2nd edition. Chicago, IL: PCI. 40. I nternational Code Council (ICC). 2006. International Building Code. Falls Church, VA: ICC. 41. CASE Task Group on Specialty Engineering. 1996. National Practice Guidelines for Specialty Structural Engineers. Washington, DC: Coalition of American Structural Engineers (CASE).  42. ACI Committee on Responsibility in Concrete Construction. 1995. Guidelines for Authorities and Responsibilities in Concrete Design and Construction. Concrete International, V. 17, No. 9, September. 43. A  SCE. 2001. Construction Contract Submittals, Manuals and Reports on Engineering Practice No. 73. In Quality in the Constructed Project. Reston, VA: ASCE. PCI DESIGN HANDBOOK/SEVENTH EDITION

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GENERAL DESIGN INFORMATION

CHAPTER 15

CHAPTER 15 GENERAL DESIGN INFORMATION 15.1

Design Information....................................................................................................................................................15-2 Design Aid 15.1.1 Dead Weights of Floors, Ceilings, Roofs, and Walls..............................................................15-2 Design Aid 15.1.2 Recommended Minimum Uniformly Distributed and Concentrated Live Loads...................15-3 Design Aid 15.1.3 Beam Design Equations and Diagrams....................................................................................15-5 Design Aid 15.1.4 Camber (Deflection) and Rotation Coefficients for Prestress Force and Loads....................15-23 Design Aid 15.1.5 Moments in Beams with Fixed Ends.....................................................................................15-25 Design Aid 15.1.6 Torsion Diagrams, Reactions, and Rotations.........................................................................15-26 Design Aid 15.1.7 Moving Load Placement for Maximum Moment and Shear.................................................15-27 Design Aid 15.1.8 Moments, Shears, and Deflections in Beams with Overhangs..............................................15-28

15.2

Material Properties – Concrete................................................................................................................................15-29 Design Aid 15.2.1 Concrete Modulus of Elasticity as Affected by Concrete Density and Strength...................15-29

15.3

Material Properties – Prestressing Steel..................................................................................................................15-30 Design Aid 15.3.1 Properties and Design Strengths of Prestressing Strand and Wire........................................15-30 Design Aid 15.3.2 Properties and Design Strengths of Prestressing Bars...........................................................15-31 Design Aid 15.3.3 Typical Design Stress-Strain Curve, 7-Wire Low-Relaxation Prestressing Strand...............15-32 Design Aid 15.3.4 Transfer and Development Lengths for 7-Wire Uncoated Strand.........................................15-33

15.4

Material Properties – Reinforcing Bars...................................................................................................................15-34 Design Aid 15.4.1 Reinforcing Bar Data.............................................................................................................15-34 Design Aid 15.4.2 Typical Bar Bends……………………………………………….………………………… 15-35 Design Aid 15.4.3 Location of Reinforcement Confined by Stirrups or Ties.....................................................15-38 Design Aid 15.4.4 Required Development Lengths for Reinforcing Bars (Grade 60)........................................15-39 Design Aid 15.4.5 Bar Area Equivalents in a 1-Foot-Wide Section....................................................................15-41

15.5

Material Properties – Structural Welded-Wire Reinforcement (WWR).................................................................15-42 Design Aid 15.5.1 Nomenclature for Structural Welded-Wire Reinforcement...................................................15-42 Design Aid 15.5.2 Minimum Requirements of Steel Wires in Welded-Wire Reinforcement.............................15-42 Design Aid 15.5.3 Wires Used in Structural Welded-Wire Reinforcement........................................................15-43 Design Aid 15.5.4 Common Styles of Welded-Wire Shear Reinforcement Used in Double-Tee Stems............15-45

15.6

Standard Bolts, Nuts, and Washers.........................................................................................................................15-45 Design Aid 15.6.1 Dimensions of Nuts and Bolts...............................................................................................15-46 Design Aid 15.6.2 Dimensions of Standard Washers..........................................................................................15-47

15.7

Welding Information...............................................................................................................................................15-48 Design Aid 15.7.1 Weld Symbols Commonly Used in Precast Concrete Construction......................................15-48 Design Aid 15.7.2 Typical Welded Joints in Precast Concrete Construction......................................................15-49 Design Aid 15.7.3 Properties of Weld Groups Treated as Lines.........................................................................15-51

15.8

Section Properties ...............................................................................................................................................15-52 Design Aid 15.8.1 Properties of Geometric Sections...........................................................................................15-52 Design Aid 15.8.2 Plastic Section Moduli and Shape Factors.............................................................................15-57

15.9

Metric Conversion Design Aid 15.9.1 Design Aid 15.9.2 Design Aid 15.9.3 Design Aid 15.9.4

...............................................................................................................................................15-58 Metric Calculations and Example..........................................................................................15-58 Conversion from U.S. Customary Units to International System (SI)..................................15-59 Preferred SI Units and U.S. Customary Equivalents.............................................................15-61 Concrete Stress Coefficients .................................................................................................15-61

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15.1 DESIGN INFORMATION Design Aid 15.1.1 Dead Weights of Floors, Ceilings, Roofs, and Wallsa

Component

Load, lb/ft2

Ceilings Acoustical fiberboard 1 Gypsum board (per 1⁄8 in. thickness) 0.55 Mechanical duct allowance 4 Plaster on tile or concrete 5 Plaster on wood lath 8 Suspended steel channel system 2 Suspended metal lath and cement plaster 15 Suspended metal lath and gypsum plaster 10 Wood furring suspension system 2.5 Coverings, roof and wall Asbestos − cement shingles Asphalt shingles Cement tiles

  15

Clay tile (for mortar add 10 lb) Book tile, 2 in. Book tile, 3 in. Ludowici Roman Spanish Composition: Three-ply ready roofing Four-ply felt and gravel Five-ply felt and gravel Copper on tin Corrugated asbestos-cement roofing Deck, metal 20 gage Deck, metal 18 gage Decking, 2 in. wood (Douglas fir) Decking, 3 in. wood (Douglas fir) Fiberboard, 1⁄2 in. Gypsum sheathing, 1⁄2 in.

4 2 16 12 20 10 12 19 1 5.5 6 1 4 2.5 3 5 8 0.75 2

Insulation, roof boards (per in. thickness) Cellular glass 0.7 Fibrous glass 1.1 Fiberboard 1.5 Perlite 0.8 Polystyrene foam 0.2 Urethane foam with skin 0.5 Plywood (per 1⁄8 in. thickness) 0.4 Rigid insulation, 1⁄2 in. 0.75 Skylight, metal frame, 3/8 in. wire glass 8 Slate, 3⁄16 in. 7 Slate, 1⁄4 in. 10 Waterproofing membranes Bituminous, gravel-coated 5.5 Bituminous, smooth surface 1.5 Liquid applied 1 Single-ply, sheet 0.7 Wood sheathing (per inch thickness) 3 Wood shingles 3

Load, lb/ft2

Component Floor fill Cinder concrete, per inch Lightweight concrete, per inch Sand, per inch Stone concrete, per inch

9 8 8 12

Floors and floor finishes Asphalt block (2 in.), 1⁄2 in. mortar Cement finish (1 in.), on stone concrete fill Ceramic or quarry tile (3⁄4 in.) on 1⁄2 in. bed Ceramic or quarry tile (3⁄4 in.) on 1 in. bed Concrete fill finish (per inch thickness) Hardwood flooring, 7⁄8 in. Linoleum or asphalt tile, 1⁄4 in. Marble and mortar on stone-concrete fill Slate (per inch thickness) Solid flat tile on 1 in. mortar base Subflooring, 3⁄4 in. Terazzo (11⁄2 in.) directly on slab Terazzo (1 in.) on stone-concrete fill Terazzo (1 in.) 2 in. stone concrete Wood block (3 in.) on mastic, no fill Wood block (3 in.) on 1⁄2 in. mortar base

30 32 16 23 12 4 1 33 15 23 3 19 32 32 10 16

Floors, wood joist (no plaster) Double wood floor Joist size, in.

12 in. spacing, lb/ft2

16 in. spacing, lb/ft2

24 in. spacing, lb/ft2

2×6

6

5

5

2×8

6

6

5

2 × 10

7

6

6

2 × 12

8

7

6

Load, lb/ft2

Component Masonry wallsb Clay brick wythes: 4 in. 8 in. 12 in. 16 in.

39 79 115 155

Hollow concrete masonry unit wythe: Wythe thickness, in. 4

6

8

10

12

24 29 30

31 38 40

37 47 49

43 55 57

32 34 40 55

42 46 53 75

52 57 66 95

61 67 79 115

28 33 34

36 44 45

44 54 56

50 62 65

36 39 44 59

47 51 59 81

58 63 73 102

68 75 87 123

30 36 37

39 47 48

47 57 59

54 66 69

38 41 46 62

50 54 61 83

62 67 76 105

72 78 90 127

Density of unit, 105 lb/ft

3

No grout (grout spacing) 48 in. o.c. 40 in. o.c. 32 in. o.c. 24 in. o.c. 16 in. o.c. Full grout

22

Density of unit, 125 lb/ft3 No grout (grout spacing) 48 in. o.c. 40 in. o.c. 32 in. o.c. 24 in. o.c. 16 in. o.c. Full grout

26

Density of unit, 135 lb/ft3

Frame partitions Movable steel partitions 4 Wood or steel studs, 1⁄2 gypsum board each side 8 Wood studs, 2 × 4, unplastered 4 Wood studs, 2 × 4, plastered one side 12 Wood studs, 2 × 4, plastered two sides 20

No grout (grout spacing) 48 in. o.c. 40 in. o.c. 32 in. o.c. 24 in. o.c. 16 in. o.c. Full grout

29

Solid concrete masonry unit wythe: Wythe thickness, in. 4

6

8

10

12

Frame walls Exterior stud walls: 2 × 4 @ 16 in., 5⁄8 in. gypsum, insulated, 3⁄8 in. siding 11 2 × 6 @ 16 in., 5⁄8 in. gypsum, insulated, 3⁄8 in. siding 12

Density of unit, 105 lb/ft3

32

51

69

87

105

Density of unit, 125 lb/ft3

38

60

81

102

124

Exterior stud walls with brick veneer Windows, glass, frame, and sash

Density of unit, 135 lb/ft3

41

64

87

110

133

48 8

a. Source: American Society of Civil Engineers (ASCE): Minimum Design Loads for Buildings and Other Structures (ASCE 7-05) (Reston, VA: ASCE, 2005), Table C3-1. b. Weights of masonry include mortar but not plaster. For plaster, add 5 lb/ft2 for each face plastered. Values given represent averages. In some cases, there is a considerable range of weight for the same construction. Note: o.c. = on center.

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Design Aid 15.1.2 Recommended Minimum Uniformly Distributed and Concentrated Live Loadsa Occupancy or use Apartments (see residential) Access floor systems Computer use Office use Armories and drill rooms Assembly areas and theaters Fixed seats (fastened to floor) Lobbies Movable seats Platforms (assembly) Stage floors Balconies (exterior) On one- and two-family residences only, and not exceeding 100 ft2 Bowling alleys, poolrooms, and similar recreational areas Corridors First floor Other floors, same as occupancy served except as indicated Dance halls and ballrooms Decks (patio and roof) Same as area served, or for the type of occupancy accommodated Dining rooms and restaurants Dwellings (see residential) Elevator machine room grating (on area of 4 in.2) Finish light-floor-plate construction (on area of 1 in.2) Fire escapes On single-family dwellings only Garages (passenger vehicles only) Truck and buses Grandstands (see stadium and arena bleachers) Gymnasiums, main floors, and balconies (see note e) Handrails, guardrails, and grab bars Hospitals Corridors above first floor Operating room, laboratories Patient rooms Wards Hotels (see residential) Libraries Corridors above first floor Reading rooms Stack rooms (see note d) Manufacturing Heavy Light Marquees and canopies Office buildings Corridors above first floor File and computer rooms shall be designed for heavier loads based on anticipated occupancy Lobbies and first-floor corridors Offices

Uniform load, lb/ft2

Concentrated load, lb

100 50 150

2000 2000

60 100 100 100 150 100 60 75 100 100 100

  15

300 200 100 40 40 note c

note b

100 note i 80 60 40 40

1000 1000 1000 1000

80 60 150

1000 1000 1000

250 125 75

3000 2000

80

2000

100 50

2000 2000

See following page for all notes.

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Design Aid 15.1.2 R  ecommended Minimum Uniformly Distributed and Concentrated Live Loadsa (cont.) Occupancy or use

Uniform load, lb/ft2

Penal institutions Cell blocks Corridors Residential Dwellings (one- and two-family) Habitable attics and sleeping areas Uninhabitable attics with storage Uninhabitable attics without storage All other areas except stairs and balconies Hotels and multifamily houses Private rooms and corridors serving them Public rooms and corridors serving them

  15

Concentrated load, lb

40 100 30 20 10 40 40 100

Reviewing stands, grandstands, and bleachers (see note e) Roofs Schools Classrooms Corridors above first floor First-floor corridors Scuttles, skylight ribs, and accessible ceilings Sidewalks, vehicular driveways, and yards, subject to trucking (see notes f, g) Stadiums and arenas Bleachers (see note e) Fixed seats, fastened to floor (see note e) Stairs and exitways One- and two-family residences only Storage areas above ceilings Storage warehouses (shall be designed for heavier loads if required for anticipated storage) Heavy Light Stores Retail First floor Upper floors Wholesale, all floors Vehicle barriers Walkways and elevated platforms (other than exitways) Yards and terraces, pedestrian

100 note j 40 80 100 250 100 60 100 40

1000 1000 1000 200 8000

note h

20 250 125 100 75 125 note i 60 100

1000 1000 1000

a. Source: American Society of Civil Engineers (ASCE): Minimum Design Loads for Buildings and Other Structures (ASCE 7-05) (Reston, VA: ASCE, 2005). b. Floors in garages or portions of a building used for the storage of motor vehicles shall be designed for the uniformly distributed live loads of Design Aid 15.1.2 or the following concentrated load: (1) for garages restricted to passenger vehicles accommodating not more than nine passengers, 3000 lb acting on an area of 4.5 in. by 4.5 in. (footprint of a jack); and (2) for mechanical parking structures without slab or deck that are used for storing passenger cars only, 2250 lb per wheel. c. Garages accommodating trucks and buses shall be designed in accordance with an approved method that contains provisions for truck and bus loadings. d. The loading applies to stack room floors that support nonmobile, double-faced library book stacks subject to the following limitations: (1) The nominal book stack unit height shall not exceed 90 in.; (2) the nominal shelf depth shall not exceed 12 in. for each face; and (3) parallel rows of double-faced book stacks shall be separated by aisles not less than 36 in. wide. e. In addition to the vertical live loads, the design shall include horizontal swaying forces applied to each row of the seats as follows: 24 lb per linear ft of seat applied in a direction parallel to each row of seats and 10 lb per linear ft of seat applied in a direction perpendicular to each row of seats. The parallel and perpendicular horizontal swaying forces need not be applied simultaneously. f. Other uniform loads in accordance with an approved method that contains provisions for truck loadings shall also be considered where appropriate. g. The concentrated wheel load shall be applied on an area of 4.5 in. by 4.5 in. (footprint of a jack). h. Minimum concentrated load on stair treads on area of 4 in.2 is 300 lb. i. See ASCE 7-05, Section 4.4. j. See ASCE 7-05, Sections 4.3 and 4.9.

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CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams

Simply supported

Single span with overhang

Support

Cantilever

fixed

Free

Continuous two span

Fixed

Fixed

Concentrated load P

w Uniform load entire span w

  15

Uniform load partial span

w Varying load

M 0 Couple

Settlements of supports Rotation of supports

This visual index assists in quickly locating the desired beam equations. The top row shows the support type and the left column shows the load. For example, to find the equations for a beam fixed on both ends with a uniform load, go down from column 4 and right on row B. Locate 4B.1 on upper left corner and then see page 15-17 for correct equation.

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CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.)

1A

1A.1 SIMPLE BEAM – CONCENTRATED LOAD AT CENTER R = V........................................................=

P 2

 P

x

P Mmax (at point of load)...............................= 4

Mx (when x <

 2

).....................................=

∆max (at point of load)...............................= ∆x (when x <

 2

)......................................=

R

Px 2

R





V

P 3 48EI Px ( 3 2 − 4x 2 ) 48EI

V

Mmax

1A.2 SIMPLE BEAM – CONCENTRATED LOAD AT ANY POINT

  15

R1 = V1 (max when a < b)........................=

Pb 

R2 = V2 (max when a > b)........................=

Pa 

Mmax (at point of load)...............................=

Pab 

Mx (when x < a)........................................=

Pbx 

 P

x

R1

R2 a

b

V1

∆max

⎛ ⎞ Pab (a + 2b ) 3a (a + 2b ) a (a + 2b )  when a > b ⎟ . ....= ⎜ at x = 27EI  3 ⎝ ⎠

Pa 2b 2 ∆a (at point of load)..................................= 3EI 

∆x (when x < a)........................................=

V2

Mmax

Pbx 2 ( − b 2 − x 2 ) 6EI 

1A.3 SIMPLE BEAM – TWO EQUAL CONCENTRATED LOADS SYMMETRICALLY PLACED R = V........................................................= P

 P

x

Mmax (between loads)...............................= Pa Mx (when x < a)........................................= Px

R

R a

Pa ∆max (at midspan).....................................= ( 3 2 − 4a2 ) 24EI

∆x (when x < a)........................................=

P

a

V V

Px ( 3a − 3a 2 − x 2 ) 6EI Mmax

Pa ∆x [when x > a and < ( − a)]....................= ( 3 x − 3x 2 − a 2 ) 6EI

15–6

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.)

1A, 1B

1A.4 SIMPLE BEAM – TWO UNEQUAL CONCENTRATED LOADS ASYMMETRICALLY PLACED R1 = V1..................................................=

P1 (l − a ) + P2b l

R2 = V2..................................................=

P1a + P2 (  − b ) 

 x P1

P2

R1

Vx [when x > a and < ( − b)].................= R1 − P1

R2 a

M1 (max when R1 < P1).........................= R1a

b

V1

M2 (max when R2 < P2).........................= R2b

V2

Mx (when x < a).....................................= R1x

M2

M1

Mx [when x > a and < ( − b)]................= R1x − P1(x − a) 1B.1 SIMPLE BEAM – UNIFORMLY DISTRIBUTED LOAD R = V.....................................................=



w 2

x

⎛ ⎞ Vx..........................................................= w ⎜ − x ⎟ ⎝2 ⎠ R

Mmax (at center).....................................=

w 2 8

Mx.........................................................=

wx ( − x ) 2

  15

w





V

5w  4 384EI wx ∆x. ........................................................= (  3 − 2 x 2 + x 3 ) 24EI

R

V

∆max (at center)......................................=

Mmax

1B.2 SIMPLE BEAM – UNIFORMLY DISTRIBUTED LOAD AND VARIABLE END MOMENTS R1 = V1..................................................=

w  M1 − M 2 + 2 

R2 = V2..................................................=

w  M1 − M 2 − 2 

 x M1

M + M 2 (M1 − M 2 ) w ⎛  (M − M 2 ) ⎞ − 1 + M ....................= M33 ⎜ at x = + 1 ⎟ 8 2 2w  2 2 w ⎝ ⎠ 2

R2

V1 V2

⎛ (M − M ) ⎞ wx (  − x ) + ⎜ 1 2 ⎟ x − M1 2  ⎝ ⎠

b (to locate inflection points) . ..............=

 2 ⎛ M1 + M 2 ⎞ ⎛ M1 − M 2 ⎞ −⎜ ⎟⎠ + ⎜⎝ ⎟ 4 ⎝ w w ⎠ wx 24EI

M2

2

Mx.........................................................=

∆x. ........................................................=

M1

R1

⎛ ⎞ M − M2 Vx..........................................................= w ⎜ − x ⎟ + 1 ⎝2 ⎠ 

M2

w

2

M3 M1

b

b

M2

⎡ 3 ⎛ 4M1 4M 2 ⎞ 2 12M1 8M1 4M 2 ⎤ 3 ⎢ x − ⎜⎝ 2 + w  − w  ⎟⎠ x + w x +  − w − w ⎥ ⎣ ⎦

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

15–7

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.)

1C, 1D

1C.1 SIMPLE BEAM – UNIFORM LOAD PARTIALLY DISTRIBUTED R1 = V1 (max when a < c).........................= R2 = V2 (max when a > c).........................=

wb (2c + b ) 2

 x

wb (2a + b ) 2

w

Vx [when x > a and < (a + b)]...................= R1 − w(x − a)

R1

R1 ⎞ ⎛ R1 ⎞ ⎛ Mmax M max ⎜ at x = a + ⎟ ................................= R1 ⎜ a + ⎟ ⎝ w⎠ ⎝ 2w ⎠

a

w ( x − a )2 2

b

c

R2

V1

Mx (when x < a)........................................= R1x Mx [when x > a and < (a + b)]...................= R1x −

a

R1 w

V2

Mmax

Mx [when x > (a + b)]................................= R2( − x) 1D.1 SIMPLE BEAM – LOAD INCREASING UNIFORMLY TO ONE END (W IS TOTAL LOAD)

  15

W.............................................................=

w 2

R1 = V1.....................................................=

W 3

R2 = V2 (max)...........................................=

2W 3

Vx.............................................................=

W Wx 2 − 2  3

 x

w

R1

R2



⎛  ⎞ 2W  = 0.5774 ⎟ ....................= Mmax ⎜ at  x = = 0.1283W  ⎝ ⎠ 3 9 3

Mx............................................................=

W

Wx 2 ( − x 2 ) 3 2

V1 V2 Mmax

⎞ ⎛ W 3 8 ∆max ⎜ at x =  1− = 0.5193 ⎟ .........= 0.01304 EI ⎟⎠ ⎜⎝ 15 Wx ∆x. ...........................................................= ( 3x 4 − 10 2x 2 + 7 4 ) 180EI  2

1D.2 SIMPLE BEAM – LOAD INCREASING UNIFORMLY TO CENTER (W IS TOTAL LOAD) w W.............................................................= 2 W x R = V........................................................= 2 W ⎞ ⎛ Vx ⎜ when x < ⎟ .....................................= (  2 − 4x 2 ) ⎝ 2 2 2⎠ R  Wl Mmax (at center)........................................= 6

W3 60EI

W



w R

V

⎞ ⎛ ⎛ 1 2x 2 ⎞ Mx ⎜ when x < ⎟ . ...................................= Wx ⎜ − 2 ⎟ ⎝ ⎝ 2 3 ⎠ 2⎠ ∆max (at center).........................................=



V Mmax

⎞ ⎛ ∆x ⎜ when x < ⎟ .....................................= Wx ( 52 − 4x 2 )2 ⎝ 2⎠ 480EI2

15–8

First Printing/CD-ROM Edition

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GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.)

1E

1E.1 BEAM SIMPLY SUPPORTED AT BOTH ENDS – MOMENT APPLIED AT ONE END −R1 = R2 = V............................................... =

Mo  Mo

Mmax (at R1)................................................ = Mo ⎛ x⎞ Mx = Mo − R1x............................................. = M o = ⎜ 1− ⎟ ⎝ ⎠

∆max (when x = 0.423)............................... = 0.0642

x

R1

R2



M o 2 EI

V

∆x. ............................................................. =

Mo ⎛ 2 x 3 ⎞ − 2 x ⎟ ⎜ 3x − ⎠ 6EI ⎝ 

θ1 (at R1).................................................... =

Mo 3EI

θ2 (at R2).................................................... =

Mo 6EI

Mmax

1E.2 BEAM SIMPLY SUPPORTED AT BOTH ENDS – MOMENT APPLIED AT ANY POINT Mo  Ma Mmax(−) (at x = a).......................................... = o  ⎛ a⎞ Mmax(+) (at x = a).......................................... = M o ⎜ 1− ⎟ ⎝ ⎠

  15

R1 = R2 = V (when a > b)............................ =

Mx (when x < a).......................................... =

 x Mo R1

Mo x 

⎛ x⎞ Mx (when x > a).......................................... = M o ⎜ 1− ⎟ ⎝ ⎠

a

b

R2

V

Mo x 2 ( − 3b 2 − x 2 ) 6EI  Mo ( − x ) ∆x (when x > a).......................................... = ( 3a 2 − 2 x + x 2 ) 6EI 

∆x (when x < a).......................................... =

⎞ ⎛ M o ⎛  − 3b ⎞  − 3b  if a > 0.4226 ⎟ . .... = ∆max ⎜ at x = ⎜ ⎟⎠ 3EI  ⎝ 3 3 ⎠ ⎝

3/ 2

M o ⎛  2 − 3a 2 ⎞ ⎞ ⎛  2 − 3a 2  if a > 0.5774 ⎟ .= ∆max ⎜ at x =  − ⎜ ⎟⎠ 3EI  ⎝ 3 3 ⎠ ⎝ M MCL (at center)............................................ = – o 2

3/ 2

2

∆CL (at center)............................................. = ∆max (when a = b = at x =

2

2

2

Mmax Mmax

Mo (  2 − 4b 2 ) 16EI

 ), 2

3 Mo 2  = 0.28867l...................... = 6 124.71EI

θCL (at center)............................................. =

Mo 12EI

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

15–9

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.)

1E, 2A

1E.3 BEAM SIMPLY SUPPORTED AT BOTH ENDS – MOMENTS APPLIED AT EACH END R1 = −R2 = V ................................ =

M 2 − M1 

∆ θ

x1

x Mx ................................................ = (M 2 − M1 ) + M1 

x

M1

M2

R1

R2



x ( − x ) ⎡M1 ( 2 − x ) + M 2 (  + x ) ⎤⎦ ∆x ................................................ = 6EI  ⎣ V

at x1 =

6M1 ± 36M12 2 − 12 (M1 − M 2 )  2 (2M1 + M 2 ) 6 (M1 − M 2 )

,

∆ = max and θ = 0 θ1 (at end) ................................... = −

M2

M1

 ( 2M1 + M 2 ) 6EI ∆ θ

x1

 θ2 (at end) ................................... = (M 1 + 2M 2 ) 6EI

x M2

M1

  15

If M1 and M2 are of opposite signs, the above formulas hold; just use actual sign of moment. ⎛ M 1 ⎞ Mx (at point of contraflexure), ⎜ where x = =0 ⎝ M 2 − M 1 ⎟⎠

R1

R2



V M1  M2 M1

M2

M1

2A.1 BEAM OVERHANGING ONE SUPPORT – CONCENTRATED LOAD AT ANY POINT BETWEEN SUPPORTS Pb  Pa R2 = V2 (max when a > b) ....................... =  Pab Mmax (at point of load) ............................. =  Pbx Mx (when x < a) ...................................... = 

R1 = V1 (max when a < b) ....................... =

 x

x1

R1

R2 a

⎛ ⎞ Pab (a + 2b ) 3a (a + 2b ) a (a + 2b )  when a > b ⎟ .....= ∆max ⎜ at x = 3 27EI  ⎝ ⎠ 2 2 Pa b ∆a (at point of load)..................................= 3EI  Pbx 2 ∆x (when x < a)........................................= ( − b 2 − x 2 ) 6EI 

∆x (when x > a)........................................=

Pa (  − x ) ( 2x − x 2 − a 2 ) 6EI 

∆x1. ..........................................................=

Pabx 1 ( + a ) 6EI 

15–10

P

First Printing/CD-ROM Edition

b

V1 V2

Mmax

PCI DESIGN HANDBOOK/SEVENTH EDITION

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.)

2A, 2B

2A.2 BEAM OVERHANGING ONE SUPPORT – CONCENTRATED LOAD AT END OF OVERHANG R1 = V1.....................................................=

Pa 

R2 = V1 + V2. ............................................=

P ( + a ) 



V2.............................................................= P

a

Mmax (at R2)..............................................= Pa

P

x1

x

R2

R1

Pax Mx (between supports).............................= 

Mx1 (for overhang)....................................= P(a − x1) ∆max (between supports x =

V2 V1

 Pa 2 Pa 2 )............= = 0.06415 EI 3 9 3EI

∆max (for overhang at x1 = a)....................=

Pa 2 ( + a ) 3EI

∆x (between supports).............................=

Pax 2 ( − x 2 ) 6EI 

Mmax

  15

Px 1 ∆x1 (for overhang)....................................= (2a + 3ax1 − x12 ) 6EI

2B.1 BEAM OVERHANGING ONE SUPPORT – UNIFORMLY DISTRIBUTED LOAD R1 = V1.....................................................=

w 2 ( − a 2 ) 2

R2 = V2 + V3. ............................................=

w (  + a )2 2

a



V2........................................................................................................ = wa

x1

x w

V3.............................................................= w ( 2 + a 2 ) 2 Vx (between supports).............................= R1 − wx Vx1 (for overhang)....................................= w(a − x1)

R1 

a2 2

V2

V1

⎡  ⎛ a2 ⎞ ⎤ w M1 ⎢at  x = ⎜ 1− 2 ⎟ ⎥ . ...........................= ( + a )2 (  − a )2 2 ⎝ ⎠ 2   8 ⎣ ⎦

V3

M2 (at R2).................................................=

wa 2 2

Mx (between supports).............................=

wx 2 ( − a 2 − x  ) 2

Mx1 (for overhang)....................................=

w (a − x 1 )2 2

∆x (between supports).............................=

wx ( 4 − 2 2x 2 +  x 3 − 2a 2 2 + 2a 2 x 2 ) 24EI 

∆x1 (for overhang)....................................=

wx 1 ( 4a 2 −  3 + 6a 2 x 1 − 4ax 12 + x 13 ) 24EI

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

R2

M1



a2 2

M2

15–11

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.)

2C

2C.1 BEAM OVERHANGING ONE SUPPORT – UNIFORMLY DISTRIBUTED LOAD BETWEEN SUPPORTS R = V........................................................=

w 2

⎛ ⎞ Vx.............................................................= w ⎜ − x ⎟ ⎝2 ⎠

  15

x1 w

Mmax (at center)........................................=

w 2 8

Mx............................................................=

wx ( − x ) 2

∆max (at center).........................................=

5w  4 384EI

∆x. ...........................................................=

wx (  3 − 2 x 2 + x 3 ) 24EI

∆x1 . .........................................................=

a

 x

R



R



V V Mmax

3

w  x1 24EI

2C.2 BEAM OVERHANGING ONE SUPPORT – UNIFORMLY DISTRIBUTED LOAD ON OVERHANG R1 = V1.....................................................=

wa 2 2

R2 = V1 + V2. ............................................=

wa ( 2 + a ) 2

a

 x

V2.............................................................= wa

x1 w

Vx1 (for overhang)....................................= w(a − x1) R1

R2

wa 2 Mmax (at R2)..............................................= 2 V2

Mx (between supports).............................=

wa 2 x 2

Mx1 (for overhang)....................................=

w (a − x 1 )2 2

∆max (between supports at x =

V1

 wa 2 2 wa 2 2 = 0.03208 ).........= 3 EI 18 3EI

∆max (for overhang at x1 = a)....................=

Mmax

wa 3 ( 4 + 3a ) 24EI

2 ∆x (between supports).............................= wa x ( 2 − x 2 ) 12EI

∆x1 (for overhang)....................................=

15–12

wx 1 ( 4a 2 + 6a 2x 1 − 4ax 12 + x 13 ) 24EI

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.)

3A

3A.1 BEAM FIXED AT ONE END, SIMPLY SUPPORTED AT THE OTHER END – CONCENTRATED LOAD AT CENTER R1 = V1.....................................................=

5P 16

R2 = V2 (max)...........................................=

11P 16

Mmax (at fixed end)....................................=



3P  16

R

Mx (when x >

 2  2

)......................................=





5P  M1 (at point of load).................................= 32

Mx (when x <

P

x

V

5Px 16

⎛  11x ⎞ )......................................= P ⎜ − ⎝ 2 16 ⎟⎠

R

V

Mmax

1 P 3 P 3 = 0.4472 )....................= = 0.009317 5 EI 48EI 5

∆max (at x = 

∆x (at point of load)..................................=

7P  3 768EI

  15



Px ∆x (when x < )......................................= ( 3 2 − 5x 2 ) 96EI 2

∆x (when x >

 2

)......................................=

P ( x −  )2 (11x − 2 ) 96EI

3A.2 BEAM FIXED AT ONE END, SIMPLY SUPPORTED AT THE OTHER END – CONCENTRATED LOAD AT ANY POINT R1 = V1.....................................................=

Pb 2 ( a + 2 ) 2 3

R2 = V2.....................................................=

Pa ( 3 2 − a 2 ) 2 3

 x

P

M1 (at point of load).................................= R1a M2 (at fixed end)......................................=

R2 R1

Pab (a +  ) 2 2

Mx (when x < a)........................................= R1x

a

b

V1 V2

Mx (when x > a)........................................= R1x − P(x − a)

(

)

(

)

3

Pa (  2 − a 2 )  2 + a2 ⎞ ⎛  , at x ∆max when a< >0.414 0.414, at x =  = ⎜ when a 6EI 2 + a ⎟⎠ ⎝

M1

a 2 + a

∆a (at point of load)..................................=

Pa 2b 3 ( 3 + a ) 12EI  3

∆x (when x < a)........................................=

Pb 2 x ( 3a 2 − 2 x 2 − ax 2 ) 12EI  3

∆x (when x > a)........................................=

Pa ( − x )2 ( 3 2x − a 2 x − 2a2 ) 12EI  2

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

Pa R2

M2

15–13

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.)

3B, 3C

3B.1 BEAM FIXED AT ONE END, SIMPLY SUPPORTED AT THE OTHER END – UNIFORMLY DISTRIBUTED LOAD R1 = V1.................................................=

3w  8

R2 = V2 (max).......................................=

5w  8

 x w R2

Vx.........................................................= R1 − wx Mmax.....................................................=

R1

w 2 8

V1

9 3 ⎞ ⎛ M1 ⎜(at x ==  ⎟)......................................= w 2 at x ⎝ 128 8 ⎠

Mx........................................................= R1x − at x ∆max [at x ==

V2



wx 2 2

M1 Mmax

 w 1+ 33 ==0.4215 0.4215].....= 16 185EI

(

4

)

∆x. .......................................................=

  15



wx ( 3 − 3 x 2 + 2x 3 ) 48EI

3C.1 B  EAM FIXED AT ONE END, SIMPLY SUPPORTED AT THE OTHER END – UNIFORM LOAD PARTIALLY DISTRIBUTED OVER SPAN  d x

R1 = V1.................................................= wb (12e 2  − 4e 3 + b 2d ) 8 3

w

R2 = V2.................................................= wb − R1 Mmax(−)...................................................=

R1

a

b

c

R2

wb (12e 2 − 4e 3 + b 2d − 8e 2 ) 8 2 V1

R1 ⎞ ⎛ M1........................................................= R1 ⎜⎝ a + ⎟ 2w ⎠

a

Mx (when x < a)....................................= R1x Mx [when x > a and x < (a + b)]............= R1x −

w ( x − a )2 2

R1 w

V2

M1

Mx (when x > [a + b] and x < )............= R1x − wb(x − d)

Mmax

Note:

= centerline.

∆x (when x < a)

=

x ⎡ 4R1 ( x 2 − 3 2 ) + wb (b 2 + 12e 2 ) ⎤⎦ 24EI ⎣

∆x [when x > a and x < (a + b)]

=

1 ⎡ 4 4R1x ( x 2 − 3 2 ) + wbx (b 2 + 12e 2 ) − w ( x − a ) ⎤⎦ 24EI ⎣

∆x [when x > (a + b) and x < c]

=

1  2 3 3M max (  − x ) + R2 (  − x )  6EI 

15–14

e

l

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.) 3E.1 B  EAM FIXED AT ONE END, SIMPLY SUPPORTED AT THE OTHER END – MOMENT APPLIED AT THE FLEXIBLE END 3M o R1 = −R2 = V.............................................= 2 Mo

M1............................................................= Mo

∆max (at x =

 3

)........................................=

 x R2

M2............................................................= 1⁄2Mo Mx............................................................=

3E, 3F

R1

Mo (2 − 3x ) 2

V

Mo 2 27EI

Mox ( − x )2 4EI  M  θ (at supported end)................................= o 4EI

M1

∆x. ...........................................................=

M2

3F.1 BEAM FIXED AT ONE END – DIFFERENTIAL SETTLEMENT OF SUPPORTS 3EI V = R1 = R2. .............................................= 3 ( Δ2 − Δ1 )  x Mmax.........................................................=

3EI ( Δ2 − Δ1 ) 2

R2

∆1

R1

⎛ x⎞ Mx............................................................= M max ⎜ 1− ⎟ ⎝ ⎠

∆x. ...........................................................= Δ1 +

  15



∆2

V

2 3 Δ2 − Δ1 ⎡ ⎛ x ⎞ ⎛ x ⎞ ⎤ ⎢3 ⎜ ⎟ − ⎜ ⎟ ⎥ 2 ⎢⎣ ⎝  ⎠ ⎝  ⎠ ⎥⎦

Mmax ∆1

∆2

3F.2 BEAM FIXED AT ONE END – ROTATION OF SUPPORT V = −R1 = R2. ...........................................=

φ1

3EI φ1 2

⎡  ⎤ ∆max..........................................................= φ1 ⎢ ⎣ 5.196 ⎥⎦ 3x 2 x 3 ⎤ ⎡ − ∆x. ...........................................................= φ1 ⎢ −x + 2 2 2 ⎥⎦ ⎣

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

R2

R1

3EI Mmax.........................................................= φ1  ⎛ x⎞ Mx............................................................= M max ⎜ 1− ⎟ ⎝ ⎠



x

V

Mmax

φ1 ∆max

15–15

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.)

4A

4A.1 BEAM FIXED AT BOTH ENDS – CONCENTRATED LOAD AT CENTER Total equivalent uniform load..................= P

R = V........................................................=

 P

x

P 2

R

R



Mmax (at center and ends)........................=

(

Mx when x <

 2

)

. ...................................=

∆max (at center).........................................=

(

∆x when x <

  15

 2

)

.....................................=



P 8 V

P ( 4x −  ) 8

V



P 3 192EI

Mmax

Px 2 ( 3 − 4x ) 48EI

Mmax

Mmax

4A.2 BEAM FIXED AT BOTH ENDS – CONCENTRATED LOAD AT ANY POINT R1 = V1 (max when a < b)........................=

Pb 2 ( 3a + b ) 3 

Pa 2 R2 = V2 (max when a > b)........................= (a + 3b ) 3

x

P

R1

R2 a

Pab 2 M1 (max when a < b)................................= 2

M2 (max when a > b)................................=

Pa 2b 2

Ma (at point of load).................................=

2Pa 2b 2 3

b

V1 V2

Ma M1

M2

Pab 2 Mx (when x < a)........................................= R1x − 2 

(

)

2Pa 3b 2 2a ⎞ ⎛ ∆max ⎜ when a> > b, at x b, at x == .............= when a 2 ⎟ ⎝ 3a + b ⎠ 3EI ( 3a + b )

∆a (at point of load)..................................=

Pa 3b 3 3EI  3

∆x (when x < a)........................................=

Pb 2x 2 ( 3a − 3ax − bx ) 6EI  3

15–16

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Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.)

4B, 4C

4B.1 BEAM FIXED AT BOTH ENDS – UNIFORMLY DISTRIBUTED LOADS R = V........................................................=

w 2

 x

⎛ ⎞ Vx.............................................................= w ⎜ − x ⎟ ⎝2 ⎠

Mmax (at ends)..........................................=

w 2 12

M1 (at center)...........................................=

w 2 24

Mx............................................................=

w (6 x −  2 − 6x 2 ) 12

∆max (at center).........................................=

w 4 384EI

∆x. ...........................................................=

wx 2 ( − x )2 24EI

w R

R





V V

 M1 Mmax

Mmax

  15

4C.1 BEAM FIXED AT BOTH ENDS – UNIFORM LOAD PARTIALLY DISTRIBUTED OVER SPAN R1 = V1........................................ =

wb ⎡ 4e 2 (  + 2d ) − b 2 (c − a ) ⎤⎦ 4 3 ⎣ 

R2 = V2........................................ = wb − R1 M1............................................... =

wb b 2 ⎡⎣ + 3 (c − a ) ⎤⎦ − 24e 2d 24 2

{

x w

}

R1

R2 a

M2............................................... = R1 − wbe + M1

b

c

d

e

l V1

R ⎞ R ⎞ ⎛ ⎛ Mmax(+) ⎜ at x = a + 1 ⎟ . ............... = M1 + R1 ⎜ a + 1 ⎟ ⎝ ⎝ w⎠ 2w ⎠

a

Mx (when x < a)........................... = M1 + R1x

R1 w

V2

Mmax

w 2 Mx [when x > a and x < (a + b)]... = M1 + R1x − ( x − a ) 2

∆x (when x < a)........................... =

1 ( 3M 1x 2 + R1x 3 ) 6EI

∆x [when x > a and x < (a + b)]... =

1 ⎡ 4 12M1x 2 + 4R1x 3 −w (w − a ) ⎤⎦ 24EI ⎣

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

M1

M2

Note:

= centerline.

15–17

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.)

4E, 4F

4E.1 BEAM FIXED AT BOTH ENDS – MOMENT APPLIED AT ANY POINT R1 = V............................................... = − R2. .................................................... =

a

6M oab 3

b Mo

R1

6M oab 3

R2 x



Mb M1..................................................... = − o2 (  − 3a ) 

M2..................................................... = −

M oa (2 − 3a ) 2

Mx (when x < a)................................. = −

M o ⎡ 6abx ⎤ + b (  − 3a ) ⎥  2 ⎢⎣  ⎦

Mx (when x > a)................................. =

V

6bx Moa   6b − − 2 + 3a   2  

Mmax

M1

  15

M2

Mmax

Mmax(−) (at x = a on left side).............. = Mmax(+) − Mo ⎡ 6a 2b b ⎤ Mmax(+) (at x = a on right side)............ = M o ⎢ − 3 − 2 (  − 3a ) + 1⎥  ⎣  ⎦

∆x (when x < a)................................. = −

2ax  M o bx 2    − 3a +    2EI2  2

∆x (when x > a)................................. =

M oa (  − x ) ⎛ 2bx ⎞ ⎜⎝ 3a − 2 + 2b − 2EI  2  ⎟⎠

MCL (at center)................................... = −

Mo ⎡ 3ab + b (  − 3a ) ⎤⎦ 2 ⎣

∆CL (at center).................................... = −

M ob (  − 2a ) 8EI

∆max (when a = 0.232)..................... = −

0.01615M o  2 EI

4F.1 BEAM FIXED AT BOTH ENDS – DIFFERENTIAL SETTLEMENT OF SUPPORTS V = −R1 = R2. .................................... =

12EI ( Δ2 − Δ1 ) 3

M1 = −M2........................................... =

6EI ( Δ2 − Δ1 ) 2

Mx..................................................... =

 x ∆1

2x 6EI ( Δ2 − Δ1) ⎛⎜⎝ 1− ⎞⎟⎠ 2 

3 ⎡ ⎛ x ⎞2 ⎛x⎞ ⎤ ∆x. .................................................... = Δ1 + ( Δ2 − Δ1 ) ⎢ 3 ⎜ ⎟ − 2 ⎜ ⎟ ⎥ ⎝  ⎠ ⎥⎦ ⎢⎣ ⎝  ⎠

∆2 R1 V M2 M1

∆1

15–18

R2

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∆2

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GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.)

4F, 5A

4F.2 BEAM FIXED AT BOTH ENDS – ROTATION OF SUPPORT V = −R1 = R2. ...........................................=

6EI φ2 2



R1

M2............................................................=

4EI φ2 

Mx............................................................=

2EI ⎛ 3x ⎞ φ2 ⎜ 1− ⎝   ⎟⎠

∆max (at x =

φ2

x

2EI M1............................................................= φ2 

R2

V

M1

2 4  )......................................= − φ2 3 27

M2

⎡⎛ x ⎞ 2 ⎛ x ⎞ 3 ⎤ ∆x. ...........................................................= − φ2 ⎢⎜ ⎟ − ⎜ ⎟ ⎥ ⎢⎣⎝  ⎠ ⎝  ⎠ ⎥⎦

∆max

5A.1 CANTILEVER BEAM – CONCENTRATED LOAD AT FREE END R = V........................................................= P

  15

 x

P

Mmax (at fixed end)....................................= P

R

Mx............................................................= Px ∆max (at free end).....................................=

P 3 3EI

∆x. ...........................................................=

P ( 2 3 − 3  2 x + x 3 ) 6EI

V

Mmax

5A.2 CANTILEVER BEAM – CONCENTRATED LOAD AT ANY POINT R = V........................................................= P

 x

Mmax (at fixed end)....................................= Pb

P R

Mx (when x > a)........................................= P(x − a)

a

∆max (at free end).....................................=

Pb 2 ( 3 − b ) 6EI

∆a (at point of load)..................................=

Pb 3 3EI

∆x (when x < a)........................................=

Pb 2 ( 3 − 3x − b ) 6EI

∆x (when x > a)........................................=

P ( − x ) 6EI

b

V

Mmax

2

( 3b −  + x )

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GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.)

5B, 5C, 5D

5B.1 CANTILEVER BEAM – UNIFORMLY DISTRIBUTED LOAD 

R = V......................................= w

x

Vx...........................................= wx

w

Mmax (at fixed end)..................=

w 2 2

Mx..........................................=

wx 2 2

R

V

w 4 ∆max (at free end)...................= 8EI

∆x. .........................................=

Mmax

w ( x 4 − 4 3 x + 3 4 ) 24EI

5C.1 CANTILEVER BEAM – UNIFORM LOAD PARTIALLY DISTRIBUTED AT FREE END R = V......................................= wb

  15

e

l

b

Mmax (at support)....................= wbe

c

w

wx 2 Mx (when x < b)......................= 2

R

x

wb Mx (when x > b)......................= (b − 2x ) 2



∆max (at free end)...................=

wb ( 8e 3 − 24e 2 − b 3 ) 48EI

∆x (when x < b)......................=

w ⎡8be 3 − 24be 2 (  − x ) + 2b 3x − b 4 − 2x 4 ⎤⎦ 48EI ⎣

∆x (when x > b)......................=

wb ⎡ 3 3 8e − 24e 2 (  − x ) − ( 2x − b ) ⎤⎦ 48EI ⎣

θ (at free end)........................=

wb (b 2 + 12e 2 ) 24EI

V

Mmax

Moment Note:

= centerline.

5D.1 CANTILEVER BEAM – LOAD INCREASING UNIFORMLY TO FIXED END (W IS TOTAL LOAD) W...........................................=

w 2



R = V......................................= W Vx...........................................= W

x W

x2 2

Mmax (at fixed end)..................=

W 3

Mx..........................................=

Wx 3 3 2

∆max (at free end)...................=

W3 15EI

∆x. .........................................=

W ( x 5 − 5 4x + 4 5 ) 60EI  2

15–20

w R

V

Mmax

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GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.)

5D, 5E

5D.2 CANTILEVER BEAM – VARYING LOAD INCREASING UNIFORMLY FROM SUPPORT TO FREE END (W IS TOTAL LOAD) W ............................................ =

w 2

R = V........................................ = W Vx.............................................=

x⎞ 2Wx ⎛ − ⎟ 2 ⎜ ⎝  2⎠

Mmax (at support)...................... =

2W  3

Mx............................................=

Wx 2 ( x − 3 ) 3 2

∆max (at free end)..................... =

11W  3 60EI

∆x. ...........................................=

W ⎡  4 (15x − 11 ) − x 4 ( 5 − x ) ⎤⎦ 60EI  2 ⎣

θ (at free end).......................... =

W2 4EI

W

w x

R



V

M

  15

5E.1 CANTILEVER BEAM – MOMENT APPLIED AT FREE END R = V........................................ = 0

Mo

Mx............................................= Mo x

∆max (at free end)..................... =

Mo 2 2EI

∆x. ...........................................=

Mo (  − x )2 2EI

θ (at free end).......................... =

Mo EI

R



V

Mmax

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GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.3 Beam Design Equations and Diagrams (Cont.)

6A, 6B

6A.1 TWO SPANS, CONTINUOUS BEAM – CONCENTRATED LOAD AT CENTER OF ONE SPAN ONLY R1 = V1.....................................................=

13 P 32

R2 = V2 + V3. ............................................=

11 P 16

R3 = V3.....................................................= −





19 P 32

Mmax (at point of load)...............................=

13 P 64

M2 (at R2).................................................=

3 P 32



R1

3 P 32

V2.............................................................=



R2

R3

V1

V3 V2

Mmax M2

6A.2 TWO SPANS, CONTINUOUS BEAM – CONCENTRATED LOAD AT ANY POINT OF ONE SPAN ONLY

  15

R1 = V1.....................................................=

Pb ⎡ 4 2 − a (  + a ) ⎤⎦ 4 3 ⎣

R2 = V2 + V3. ............................................=

Pa ⎡2 2 + b (  + a ) ⎤⎦ 2 3 ⎣

R3 = V3.....................................................= −

Pab ( + a ) 43

a

P

b





R1

R2

V1

V3

Pa  42 + b (  + a ) V2.............................................................= 43 

Mmax (at point of load)...............................=−

Pab  42 − a (  + a ) 43 

M2 (at R2).................................................=

Pab ( + a ) 4 2

R3

V2

Mmax M2

6B.1 TWO SPAN, CONTINUOUS BEAM – UNIFORM LOAD OVER ONE SPAN ONLY 7 R1 = V1.....................................................= w 16 R2 = V2 + V3. ............................................=

5 w 8





1 R3 = V3.....................................................= − w  16

V2.............................................................=

9 w 16

49 7 ⎞ ⎛ Mmax ⎜ at x = w 2  ⎟ ...................................= ⎝ 16 ⎠ 512



M1 (at R2).................................................=

w 2 16

Mx (when x < )........................................=

wx (7 − 8x ) 16

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CHAPTER 15

Design Aid 15.1.4 Camber (Deflection) and Rotation Coefficients for Prestress Force and Loads CAMBER EQUIV. MOMENT OR LOAD

PRESTRESS PATTERN

END ROTATION

EQUIVALENT LOADING

 P e



M = Pe M

+

M 2 16EI

+

M 3EI

−

M 6EI

+

M 2 16EI

+

M 6EI

−

M 3EI

P

(1)  M



P

M = Pe

e P

(2)

  15

 

M

e

M

M = Pe

e

P

M 2 8EI

M 2EI

−

N 3 48EI

N 2 16EI

−

+

P

M 2EI

(3)  P



P

e'

N= 

4Pe' 



+



N 2 16EI



(4)  P



P

Pe' N= b

e' b

b

b

N

N

b

b ( 3 − 4b 2 ) N  3 b (1− b ) N  2 b (1− b ) N  2 − 2EI 2EI 24EI

(5)  P



P

e'



(6)



8Pe' w= 2 

5w  4 384EI

w 3 24EI

−

w 3 24EI

W

Note: c.g. = center of gravity

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15–23

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.4 Camber (Deflection) and Rotation Coefficients for Prestress Force and Loads (Cont.) CAMBER EQUIVALENT MOMENT OR LOAD

PRESTRESS PATTERN

P

END ROTATION

EQUIVALENT LOADING





w=

e'





8Pe' 2

w





5w  4 768EI

9w  3 384EI

−

7w  3 384EI

5w  4 768EI

7w  3 384EI

−

9w  3 384EI

(7) 

 P

e'



w=



8Pe' 2

w





(8)

  15

 P

P e' b

w= 4Pe' (0.5 − b )  2

(9)

P e' b

w1 = w (0.5 − b ) b



w= 4Pe' (0.5 − b )  2

(10)

P

(11)

⎡5 b 2 ⎤ ⎢⎣ 8 − 2 ( 3 − 2b ) ⎥⎦

w1 w

b

w= 4Pe' (0.5 − b )  2



b

w1

w1 = w (0.5 − b ) b

b

e'



b



w b





w (0.5 − b ) b

×

w 3 48EI

w b

×

w 3 48EI

Determination of camber along length of member based on camber at midspan: Camber at midspan = yc

15–24

y x = yc − yc

⎛ ⎞ ⎜⎝ − x ⎟⎠ 2 ⎛⎞ ⎜⎝ ⎟⎠ 2

2

2⎤ ⎡ 7 ⎢⎣ − 8 + b ( 2 − b ) ⎥⎦

w 3 48EI

×

2⎤ ⎡7 ⎢⎣ 8 − b (2 − b ) ⎥⎦

×

Yx

24EI

2⎤ ⎡9 ⎢⎣ 8 − b (2 − b ) ⎥⎦

×

⎡5 b 2 ⎤ ⎢⎣ 16 − 4 ( 3 − 2b ) ⎥⎦

w1



24EI

w 3 48EI

⎡5 b 2 ⎤ ⎢⎣ 16 − 4 ( 3 − 2b ) ⎥⎦

w1

w1 =

×

(1− b ) (1− 2b )w  3 − (1− b ) (1− 2b )w  3

w 3 48EI

2⎤ ⎡ 9 ⎢⎣ − 8 + b ( 2 − b ) ⎥⎦

w 3 48EI

×

w 3 48EI

Yc

2

X



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

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GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.5 Moments in Beams with Fixed Ends LOADING 

MOMENT AT A

MOMENT AT CENTER

MOMENT AT B

−P  8

P 8

−P  8



P

A

B

(1) a

P

A

B

−P  a (1− a )

2

−P  a 2 (1− a )

(2) 

P





P

A

B

−2P  9

P 9

−2P  9

B

−5P  16

3P  16

−5P  16

(3) 

P



P



P



A

(4)

  15

W

A

B

−W  12

W 24

−W  12

B

−W  (1+ 2a − 2a 2 ) 12

W  (1+ 2a − 2a 2 ) 24

−W  (1+ 2a − 2a 2 ) 12

−W  ( 3a − 2a 2 ) 12

W a2 6

−W  ( 3a − 2a 2 ) 12

(5) W a

a A

(6) a

a W

W

A

B

(7) a W A

B

−W  a (6 − 8a + 3a 2 ) 12

−W  a 2 ( 4 − 3a ) 12

(8) 



−5W  48

W A

3W  48

−5W  48

B

(9) W

A

B

−W  10

−W  15

(10) Note: W = total load on the beam.

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GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.6 Torsion Diagrams, Reactions, and Rotations Torsional diagram

Rotations

Reactions T

Component 

(1)

θ = T GJT

At support: T = T

T

t (uniform torque)



At support: T = t

θ=

T2 2GJT

θ1 =

T1ab GJT

T

(2)

a:

T1 a

Ta

(3)

T2

T1 a

b

c

Tb =

T1a 

a:

Ta =

T1 (b + c ) +T2c 

b:

Tb =

T2c −T1a 

c:

Tc =

T1a +T2 (a + b ) 

a:

Ta =

T1 (b + c + d ) +T2 (c + d ) +T3d 

b:

Tb =

−T1a +T2 (c + d ) +T3d 

θ1 =

Taa GJT

c:

Tc =

−T1a −T2 (a + b ) +T 3d 

θ3 =

Td d GJT

a Ta

T1

T3

T3

b

c

d



Td Tb

d:

Td =

−T1a −T2 (a − b ) +T3 (a + b + c ) 

Tc



Tsupport =

T

t 2

T 4GJT

θ1 =

Taa GJT

θ2 = Tc c GJT When a = b = c = T/8 T1 = T2 = T/2

Tc

Tb

(5)

θ1 =

Ta

(4)

 2

b:



Ta



When a = b =

Ta

Ta

T1b 

b



  15

Ta =

and θ1 = θ2 =

θ2 =

T 6GJT

Tbb +Taa GJT

θCL =

t 2 8GJT

T

(6) Note: G = shear modulus, JT = torsion constant; see Section 6.6.

15–26

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GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.7 Moving Load Placement for Maximum Moment and Sheara (1) SIMPLE BEAM – ONE CONCENTRATED MOVING LOAD x

R1 max = V1 max (at x = 0) ................................................................... = P Mmax (at point of load, when x =

 P )................................................. = 2 4

P

R1

R2



(2) SIMPLE BEAM – TWO EQUAL CONCENTRATED MOVING LOADS a⎞ ⎛ R1 max = V1 max (at x = 0)..................................................................... = P ⎜ 2 − ⎟ ⎝ ⎠

(

)

when a < 2 − 2  .. = 0.586

Mmax

under load 1, at x =

(

............ = P   − a  2  2

a⎞ 1⎛ ⎜  − ⎟⎠ 2 2⎝

x

2

a P

P

R1

)

when a > 2 − 2  .= 0.586 ........ = with one load at center of span

R2



P 4

  15

(3) SIMPLE BEAM – TWO UNEQUAL CONCENTRATED MOVING LOADS R1 max = V1 max (at x = 0) .................................................................... = P1 + P2

under P1, at X =

Mmax

1⎛ Pa ⎞ − 2 ⎟ ⎜ 2⎝ P1 + P2 ⎠

 −a 

.............. = (P1 + P2 )

Mmax may occur with larger load at center of span and other load off span

....  =

P1 4

P1

x2 

x

P2 a

P1 R1

P2



R2

a. Source: American Institute of Steel Construction (AISC): Steel Construction Manual, thirteenth edition (Chicago, IL: AISC, 2005).

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15–27

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.1.8 Moments, Shears, and Deflections in Beams with Overhangs REACTIONS AND VERTICAL SHEAR

LOADING AND SUPPORT

EQUAL OVERHANGS, UNIFORM LOAD

Y

W

w

RB = RC =

BENDING MOMENT M AND MAXIMUM BENDING MOMENT

W 2

( A to B ) M = −

( A to B ) y = −

Wx 6c 2 (d + x ) − x 2 ( 4c − x ) − d 3  24EI  

(B  to C ) y

Wx (d − x )  x (d − x ) + d 2 − 6c 2  24E l 

(B  to C ) M = −

( A to B )V = W (c − x ) −

w

W (c − x )2 2

DEFLECTION y, MAXIMUM DEFLECTION, AND END SLOPE θ

W 2 ⎡c − x (d − x ) ⎤⎦ 2 ⎣

=−



A

C c

B

c

d 

x D

Wc 2 at B  and C 2 d2 ⎞ W ⎛ M = − ⎜c 2 − ⎟ 4⎠ 2 ⎝

Wc ⎡ 3c 2 (c + 2d ) − d 3 ⎤⎦  at A and D 24EI  ⎣ d Wd 2 y =− ( 5d 2 − 24c 2 ) at x = 384EI  2

d  if d > 2c, M = 0 2 d2 d −c2 at x = ± 4 2 if c = 0.207,

if 2c < d < 2.449c, the maximum deflec­tion between supports is:

M =−

(B  to C )V = ⎛ 1 x +c ⎞ W⎜ − ⎝2  ⎠⎟

y =−

at x =

(C  to D )V = W (c + d − x ) 

y=

  15

M = − W at x = 0 = d 46.62 and M = W 46.62 at x =

W d d2 (6c 2 − d 2 )2  at x = ± 3  − c 2  96EI  2 4

W ( 6c 2d + 4c 3 − d 3 ) at A 24EI  W φ=− (6c 2d + 4c 3 − d 3 ) at D 24EI

φ=

d 2

x is considered posi­tive on both sides of the origin.

UNEQUAL OVERHANGS, UNIFORM LOAD

Y

A

c

W

B d 

w

( A to B ) M =

RB = W (c + d − e ) 2d

w

C c

x D

W 2 − (c − x ) 2 (B  to C )M = W 2 − (c + x ) + RB x 2 (C  to D ) M =

RC = W (d + e − c ) 2d ( A to B )V = W − (c − x ) 

−

W (e + d − x )2 2

−

Wc 2  at B 2 2 We  at C M =− 2 M max  between supports W = (c 2 − x 12 ) at x = x 2 c2 + d 2 − e2  if x 1 > c, = 2d M =0

=

=

W (d + e − x ) 

At x = x 1 ± x 12 − c 2

x is considered posi­tive on both sides of the origin.

15–28

=−

Wx (d − x ) 24EI 

2    x (d − x ) + d 2 − 2 (c 2 + e 2 ) − e 2 x + c 2 (d − x )  d   W (x − d ) 2 2 2 [2d (c + 2e ) + 6e ( x − d ) (C  to D ) y = − 24EI 2

W RB − (c + x ) 

(C  to D )V

(B  to C ) y

                    − ( x − d ) ( 4e + d − x ) − d 3 ]

M =−

(B  to C )V

Wx 24EI   2d (e 2 + 2c 2 ) + 6c 2 x − x 2 ( 4c − x ) − d 3 

( A to B ) y = −

First Printing/CD-ROM Edition

Wc  2d (e 2 + 2c 2 ) + 3c 3 − d 3   at A 24El   We  2d (c 2 + 2e 2 ) + 3e 3 − d 3   at D y =− 24El  

y =−

This case is too complicated to obtain a general expression for critical deflections between the supports. W ( 4c 3 + 4c 2d − d 3 + 2de 2 ) at A 24El  W φ=− ( 2c 2d + 4de 2 − d 3 + 4e 3 ) at D 24El 

φ=

PCI DESIGN HANDBOOK/SEVENTH EDITION

GENERAL DESIGN INFORMATION

CHAPTER 15

15.2 MATERIAL PROPERTIES — CONCRETE Design Aid 15.2.1 Concrete Modulus of Elasticity as Affected by Concrete Density and Strength

6.1

6 Ec = w

1.5

33 fc'

5.8

a

Ec = (40,000 f c' + 1.0 x 106)(wc /145)1.5

b

5.4

a

fc' = 10,000

5

9000 f c' = 10,000 psi

a

5.1

a

4.7

8000

a

Ec modulus of elasticity, million psi

7000

4.3

6000

4

3.8

5000

3

3.6

4000

3.3

3500

3.0

3000 2500 fc' = 9000 psi

2

fc' = 8000 psi fc' = 7000 psi

1

90

100

110

120

130

140

145

150

w, density of concrete, lb/ft 3 a. Solid curves use Ec = w1.5 33 fc' where fc' in psi. These values comply with ACI 318-05 for all values of fc' . b. Dashed curves comply with ACI 363R-92, State-of-the-Art Report on High Strength Concrete, which states that ACI 318-05 expression overestimates the modulus of elasticity for concretes with compressive strengths over 6000 psi. The report recommends using Ec = (40,000 fc' + 1.0 x 106)(wo /145)1.5 psi. Alternatively, ACI 318-05 allows use of Ec = 57,000 fc' for normalweight concrete, which is not shown above.

a. These curves for Ec comply with ACI 363R-92, State-of-the-Art Report on High Strength Concrete states that the ACI 318 expression over estimates the modulus of elasticity for concretes with compressive strengths over 6000 psi. The report recommends using Ec = (40,000 f ' + 1.0 x 106)(wc /145)1.5 psi.

c

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  15

GENERAL DESIGN INFORMATION

CHAPTER 15

15.3 MATERIAL PROPERTIES — PRESTRESSING STEEL Design Aid 15.3.1 Properties and Design Strengths of Prestressing Strand and Wire Seven-wire strand, fpu = 270 ksi Nominal diameter, in. Area, in.

⁄8

3

7

0.085

2

⁄16

1

0.115

⁄2

0.153

1

⁄2 Speciala 0.167

⁄16

0.6

0.192

0.217

9

Weight, lb/ft

0.29

0.40

0.52

0.53

0.65

0.74

0.7fpuAps, kip

16.1

21.7

28.9

31.6

36.3

41.0

0.75fpuAps, kip

17.2

23.3

31.0

33.8

38.9

43.9

0.8fpuAps, kip

18.4

24.8

33.0

36.1

41.5

46.9

fpuAps, kip

23.0

31.1

41.3

45.1

51.8

58.6

⁄2

0.6

Seven-wire strand, fpu = 250 ksi Nominal diameter, in. Area, in.

  15

⁄4

1

5

⁄16

⁄8

3

7

⁄16

1

0.036

0.058

0.080

0.108

0.144

0.216

Weight, lb/ft

0.12

0.20

0.27

0.37

0.49

0.74

0.7fpuAps, kip

6.3

10.2

14.0

18.9

25.2

37.8

0.8fpuAps, kip

7.2

11.6

16.0

21.6

28.8

43.2

fpuAps, kip

9.0

14.5

20.0

27.0

36.0

54.0

2

Three- and four-wire strand, fpu = 250 ksi Nominal diameter, in.

⁄4

1

⁄16

3

⁄8

5

7

⁄16

Number of wires

3

3

3

4

Area, in.

0.036

0.058

0.075

0.106

Weight, lb/ft

0.12

0.20

0.26

0.36

0.7fpuAps, kip

6.3

10.2

13.1

18.6

0.8fpuAps, kip

7.2

11.6

15.0

21.2

fpuAps, kip

9.0

14.5

18.8

26.5

2

Prestressing Wire Diameter, in.

0.105

0.120

0.135

0.148

0.162

0.177

0.192

0.196

0.250

0.276

Area, in.

0.0087

0.0114

0.0143

0.0173

0.0206

0.0246

0.0289

0.0302

0.0491

0.0598

Weight, lb/ft

0.030

0.039

0.049

0.059

0.070

0.083

0.098

0.10

0.17

0.20

Ultimate strength fpu, ksi

279

273

268

263

259

255

250

250

240

235

0.7fpuAps, kip

1.70

2.18

2.68

3.18

3.73

4.39

5.06

5.29

8.25

9.84

0.8fpuAps, kip

1.94

2.49

3.07

3.64

4.27

5.02

5.78

6.04

9.43

11.24

fpuAps, kip

2.43

3.11

3.83

4.55

5.34

6.27

7.23

7.55

11.78

14.05

2

a. The 1⁄2 in. special strand has a larger actual diameter than the 1⁄2 in. regular strand. The table values take this difference into account.

15–30

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PCI DESIGN HANDBOOK/SEVENTH EDITION

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.3.2 Properties and Design Strengths of Prestressing Bars Plain prestressing bars, fpu = 150 ksia Nominal diameter, in.

⁄4

3

7

⁄8

1

11⁄8

11⁄4

13⁄8

Area, in.2

0.44

0.60

0.78

0.99

1.23

1.48

Weight, lb/ft

1.50

2.04

2.67

3.38

4.17

5.05

0.7fpuAps, kip

46.2

63.0

81.9

104.0

129.2

155.4

0.8fpuAps, kip

52.8

72.0

93.6

118.8

147.7

177.6

fpuAps, kip

66.0

90.0

117.0

148.5

184.5

222.0

Deformed prestressing bars,b fpu 150 ksia Nominal diameter, in.

1

11⁄4

13⁄8

13⁄4

21⁄2

Area, in.2

0.85

1.25

1.58

2.62

5.20

Weight, lb/ft

3.01

4.39

5.56

9.23

17.71

0.7fpuAps, kip

89.3

131.3

165.9

270.9

541.8

0.8fpuAps, kip

102.0

150.0

189.6

309.6

619.2

fpuAps, kip

127.5

187.5

237.0

387.0

774.0

a. Verify availability before specifying. b. Also available in 3 in. nominal diameter, not covered by ASTM A722. Also available in 5/8 in. and 3/4 in., not covered by ASTM A722.

  15

Bars conform to ASTM A722, Standard Specifications for Uncoated High Strength Steel Bars for Prestressing Concrete. Stress-strain characteristics (all prestressing bars): For design purposes, the following assumptions are satisfactory: Es = 29,000 ksi fy = 0.85fpu for plain bars and 0.80 fpu for deformed bars.

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GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.3.3 Typical Design Stress-Strain Curve, 7-Wire Low-Relaxation Prestressing Strand

Stress, fps ksi

yield strength elongation

yield strength

e

  15

Minimum yield strength at 1% elongation

Strain, εps in./in. Note: Approximate strain at rupture is 0.05 to 0.07 in./in. Minimum elongation at the ultimate strength = 3.5%.

These curves can be approximated by the following equations: 250 ksi strand: ε ps ≤ 0.0076 : f ps = 28,800ε ps ( ksi ε ps > 0.0076 : f ps = 250 −

270 ksi strand:

0.04 ( ksi ε ps − 0.0064

ε ps ≤ 0.0085: f ps = 28,800ε ps ( ksi ε ps > 0.0085: f ps = 270 −

15–32

) )

)

0.04 (ksi ε ps − 0.007

)

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GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.3.4 Transfer and Development Lengths for 7-Wire Uncoated Strand The ACI 318-05 (Section 12.9.1) equation for required development length may be rewritten as: d = ( fse/3)db + ( fps − fse)db where: d = required development length, in. fse = effective prestress, ksi fps = stress in prestressing steel at nominal strength, ksi db = nominal diameter of strand, in. The first term in the equation is the transfer length and the second term is the additional length required for the stress increase (fps − fse) corresponding to the nominal strength. Transfer and development length,a in. fse = 170 ksi

Development length

Development length

240

240

Transfer length

fse = 160 ksi

Development length

Transfer length

fse = 150 ksi Transfer length

Nominal diameter, in.

240

3

⁄8

18.8

52.5

56.3

60.0

63.8

20.0

50.0

53.8

57.5

61.3

21.3

47.5

51.3

55.0

58.8

⁄16

21.9

61.3

65.6

70.0

74.4

23.3

58.3

62.7

67.0

71.4

24.8

55.4

59.8

64.2

68.5

⁄2

25.0

70.0

75.0

80.0

85.0

26.7

66.7

71.7

76.7

81.7

28.3

66.3

68.3

73.3

78.3

⁄2 S

26.1

73.1

78.4

83.6

88.8

27.9

69.7

74.9

80.1

85.4

29.6

66.1

71.3

76.6

81.8

⁄16

28.1

78.8

84.4

90.0

95.6

30.0

75.0

80.6

86.3

91.9

31.9

71.3

76.9

82.5

88.1

⁄5

30.0

84.0

90.0

96.0

102.0

32.0

80.0

86.0

92.0

98.0

34.0

76.0

82.0

88.0

94.0

7

1

b

1

9

3

fps, ksi 250

260

270

fps, ksi 250

260

270

fps, ksi 250

260

270

a. The development length values given in the table must be doubled where bonding of the strand does not extend to the member end and the member is designed such that tension in the precompressed tensile zone is produced under service loads (see ACI 318-05, Section 12.9.3). b. The 1⁄ 2 in. special (1⁄ 2 S) strand has a larger nominal diameter than the 1⁄ 2 in. regular (1⁄ 2) strand. The table values for transfer and development length reflect this difference in diam­eters.

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  15

GENERAL DESIGN INFORMATION

CHAPTER 15

15.4 MATERIAL PROPERTIES — REINFORCING BARS Design Aid 15.4.1 Reinforcing Bar Data ASTM standard reinforcing bars Nominal dimensions

Bar size designationa

Diameter

U.S. customary, #

SI, #

in.

3

10

4 5 6 7 8 9 10 11 14 18

13 16 19 22 25 29 32 36 43 57

Area mm

in.2

0.375

9.5

0.500 0.625 0.750 0.875 1.000 1.128 1.270 1.410 1.693 2.257

12.7 15.9 19.1 22.2 25.4 28.7 32.3 35.8 43.0 57.3

Weight or mass mm2

lb/ft

kg/m

0.11

71

0.376

0.560

0.20 0.31 0.44 0.60 0.79 1.00 1.27 1.56 2.25 4.00

129 199 284 387 510 645 819 1006 1452 2581

0.668 1.043 1.502 2.044 2.670 3.400 4.303 5.313 7.650 13.600

0.994 1.552 2.235 3.042 3.973 5.060 6.404 7.907 11.380 20.240

a. Many mills will mark and supply bars only with metric (SI) designation, which is a soft conversion. Soft conversion means that the metric (SI) bars have exactly the same dimensions and properties as the equivalent U.S. customary designation.

Standard hooks

Stirrup and tie-hooks

Detailing dimension

db

Hook A or G

A or G

J D

12db for #6, 7, 8 6db for #3, 4, 5

Hook A or G

  15

Detailing dimension

db

J db

6db

D

D

D

A or G

H

Detailing dimension

Detailing dimension

4d or 21/2 in. minimum

D 12db

Bar size, # 3 4 5 6 7 8 9 10 11 14 18

D 2 ⁄4 3 33⁄4 41⁄2 1

51⁄4a 6a 9 10 11 1–51⁄2 1–101⁄2

180°

90°

A or G

J

A or G

5 6 7 8 10 11 1–3 1–5 1–7 2–3 3–0

3 4 5 6 7 8 111⁄4 1–01⁄2 1–13⁄4 1–9 2–3

6 8 10 1–0 1–2 1–4 1–7 1–10 2–0 2–7 3–5

D 1 ⁄2 2 21⁄2 41⁄2 51⁄4 6 1

90°

135°

A or G

A or G

H

4 41⁄2 6 1–0 1–2 1–4

4 /4 41⁄2 51⁄2 8 9 101⁄2

21⁄2 3 33⁄4 41⁄2 51⁄4 6

1

U.S. customary units: in. or ft-in.

a. ASTM A767 requires that bars bent cold prior to hot-dip galvanizing must be fabricated to a minimum bend diameter equal to 7 in. for #7 bar and 8 in. for #8 bar.

15–34

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GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.4.2 Typical Bar Bends G

A B

A

D

B

A

H

G D

G

H

B

D

A

G

B

D

A

G

B

D

C

C

C

C

C

S1

S2

S3

S4

S5

B

B

A

Lap - G

D

G

G B

D

C

H

C

B

S6

S11

A

B A C

E

= total ( Blength )

K

A

A

E

C

C (circumference)

E

D

D

O

T1

T2

T3

K

A E

G

E

G

U

H

G D

B

D

B

H

A

H

G B

D

C

C

T6

T7

T8

G

A

A

J

J

A

B

B

1

1A

2

O

O F

C

A

E

F C

J

H G

D

A

E

4A

F C

A

J

H

C

A

H

G

4

O

B

H

E D

O F

D

H

D

O C

E

B

3A

B J

O

B

3

A

G

B

B J

  15

T9

B

G J D

5

A

H

C

G D

6

Notes: 1. All dimensions are out-to-out of bar except A and G on standard 180 and 135 deg hooks. 2. J dimensions on 180 deg hooks to be shown only where necessary to restrict hook size, otherwise ACI standard hooks are to be used. 3. Where J is not shown, J will be kept equal or less than H on Types 3, 5, and 22. Where J can exceed H, it should be shown. 4. H dimension stirrups to be shown where necessary to fit within concrete. 5. Where bars are to be bent more accurately than standard fabricating tolerances, bending dimensions that require closer fabrication should have limits indicated. 6. Figures in circles show types. 7. For recommended diameter D of bends and hooks, and for dimensions of hooks, see Design Aid 15.4.1. 8. Type S1 through T3, T6 through T9; apply to bar sizes #3 through #8. 9. Source: American Concrete Institute (ACI): Details and Detailing of Concrete Reinforcement (ACI 315-99) (Farmington Hills, MI: ACI, 1999).

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15–35

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.4.2 Typical Bar Bends (Cont.) O C

A

E

H

A

G

J

D

H

G

B

O

K

7

8

B

R

B

R

9 K

O

C J

A B

A

C

J

C

O

B H

R

D

D

O

11

10

H

A

12

K

K C

J

J

B

H

B

H

D

A

  15

B

C

A C

O

O

G

R

H D O

12A

12B

13

O

O

O

A H

E B

A H

D

A B

H

D C

K 14

B C

K

14A K

14B K

C

C D

B

H

D

B

H

A O 16

O 16A

B

D

C 17

Notes: 1. All dimensions are out-to-out of bar except A and G on standard 180 and 135 deg hooks. 2. J dimensions on 180 deg hooks to be shown only where necessary to restrict hook size, otherwise ACI standard hooks are to be used. 3. Where J is not shown, J will be kept equal or less than H on Types 3, 5, and 22. Where J can exceed H, it should be shown. 4. H dimension stirrups to be shown where necessary to fit within concrete. 5. Where bars are to be bent more accurately than standard fabricating tolerances, bending dimensions that require closer fabrication should have limits indicated. 6. Figures in circles show types. 7. For recommended diameter D of bends and hooks, and for dimensions of hooks, see Design Aid 15.4.1. 8. Type S1 through T3, T6 through T9; apply to bar sizes #3 through #8. 9. Source: American Concrete Institute (ACI): Details and Detailing of Concrete Reinforcement (ACI 315-99) (Farmington Hills, MI: ACI, 1999).

15–36

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PCI DESIGN HANDBOOK/SEVENTH EDITION

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.4.2 Typical Bar Bends (Cont.) O K

A

B

H

J C

C

C

B

17A

B

D

18

19 O

B

H

C

19A

J A

D

B H

E

C

H

G

K

K

D

Standee (isometric view)

J

D C

E

B

D

G

23

K

Standee (isometric view)

Standee (isometric view)

C E

B

F

26

D

Standee (isometric view)

C 26C

B

F

D

  15

25

C E

B

F

26A

Standee (isometric view)

H

B

24

D

G

22

A

F

E

C

20

O

A

F

B

B

C

D

B

J

D

C

D

H

C

D B

26B

K

D

Enlarged view showing bar bending details Notes: 1. All dimensions are out-to-out of bar except A and G on standard 180 and 135 deg hooks. 2. J dimensions on 180 deg hooks to be shown only where necessary to restrict hook size, otherwise ACI standard hooks are to be used. 3. Where J is not shown, J will be kept equal or less than H on Types 3, 5, and 22. Where J can exceed H, it should be shown. 4. H dimension stirrups to be shown where necessary to fit within concrete. 5. Where bars are to be bent more accurately than standard fabricating tolerances, bending dimensions that require closer fabrication should have limits indicated. 6. Figures in circles show types. 7. For recommended diameter D of bends and hooks, and for dimensions of hooks, see Design Aid 15.4.1. 8. Type S1 through T3, T6 through T9; apply to bar sizes #3 through #8. 9. Source: American Concrete Institute (ACI): Details and Detailing of Concrete Reinforcement (ACI 315-99) (Farmington Hills, MI: ACI, 1999).

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GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.4.3 Location of Reinforcement Confined by Stirrups or Ties z

Cover

Stirrup or tie

Main reinforcement

Main reinforcement size, #

z dimension, in. Stirrup or tie size #3

#4

#5

⁄8

1

1 ⁄16

11⁄4

⁄8

1

1 ⁄8

15⁄16

⁄16

13⁄16

13⁄8

7

4

7

5

7

6

15

1

13⁄16

17⁄16

8

1

1 ⁄16

1

1 ⁄4

17⁄16

9

11⁄16

15⁄16

11⁄2

10

1

1 ⁄8

5

1 ⁄16

11⁄2

11

13⁄16

13⁄8

19⁄16

  15

To determine location of main reinforcement, add specified cover to the z dimension from the table.

15–38

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GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.4.4 Required Development Lengths,a in., for Reinforcing Bars (Grade 60) Tension development length: d d = 2400 b ' ; min. 12 in. (#6 and smaller) fc db ; min. 12 in. (#7 and larger) fc' Note: For Grade 40 bars, replace 2400 and 3000 with 1600 and 2000, respectively.

d = 3000

Multiply d values by : (a) 1.3 for lightweight concrete (b) 1.3 for “top bars”b (c) 1.5 for epoxy-coated bars with cover < 3db or clear spacing < 6db, otherwise multiply by 1.2 Note: Product of factors (b) and (c) need not exceed 1.7. (d) 1.5 for bars with less than minimum stirrups or ties, clear spacing less than 2db, or clear cover less than db (e) As (required)/As (provided) for excess reinforce-ment unless development of fy is specifically required. This multiplier is not to be applied to lap splices per ACI 318-05, Section R12.15.1.

fc' = 3000 psi

Bar size, # 3 4 5 6 7 8 9 10 11

Tension d 16 22 27 33 48 55 62 70 77

1.3d 21 28 36 43 62 71 80 90 100

1.5d 25 33 41 49 72 82 93 104 116

3 4 5 6 7 8 9 10 11

Tension d 12 14 18 22 31 36 40 46 51

1.3d 14 19 23 28 41 47 53 59 66

1.5d 16 22 27 32 47 54 61 68 76

The values of fc' used in these equations shall not exceed 100 psi (see ACI 318-05, Section 12.1.2).

  15

fc' = 4000 psi

Compression d 8 11 14 16 19 22 25 28 31

Tension d 14 19 24 28 42 47 54 60 67

fc' = 7000 psi

Bar size, #

(f) F  or tension lap splices, item (e) does not apply. Lap splice lengths must conform to ACI 318-05, Section 12.15. Compression development length: 1200d b dc = larger of or 18db but no less than 8 in. fc' Note: For Grade 40 bars, replace 1200 with 800 and 18 with 12. Multiply d values by: (a) A  s (required)/As (provided) for excess reinforcement (b) 0.75 for adequate spiral or tie enclosure (see ACI 318-05, Section 12.3.3b) Compression splice lap length: Lap length = 30db; min. 12 in. for fy = 60,000 psi Lap length = (0.0009fy – 24) db for fy > 60,000 psi

1.3d 18 25 31 37 54 62 70 78 87

1.5d 21 28 36 43 62 71 80 90 100

fc' = 5000 psi

Compression d 8 9 12 14 17 19 21 24 27

Tension d 13 17 21 25 37 42 48 54 60

fc' = 8000 psi

Compression d 8 9 11 14 16 18 20 23 25

Tension d 12 13 17 20 29 34 38 43 47

1.3d 13 17 22 26 38 44 49 55 61

1.5d 15 20 25 30 44 50 57 64 71

1.3d 17 22 28 33 48 55 62 70 78

1.5d 19 25 32 38 56 64 72 81 90

fc' = 6000 psi

Compression d 8 9 11 14 16 18 20 23 25

Tension d 12 15 19 23 34 39 44 49 55

fc' = 9000 psi

Compression d 8 9 11 14 16 18 20 23 25

Tension d 12 13 16 19 28 32 36 40 45

1.3d 12 16 21 25 36 41 46 52 58

1.5d 14 19 24 28 42 47 54 60 67

1.3d 15 20 25 30 44 50 57 64 71

Compression

Min. comp. splice

d 8 9 11 14 16 18 20 23 25

12 15 19 23 26 30 34 38 42

Compression

Min. comp. splice

d 8 8 8 9 11 12 14 15 17

12 15 19 23 26 30 34 38 42

1.5d 17 23 29 35 51 58 66 74 82

fc' ≥ 10,000 psi

Compression d 8 8 8 9 11 13 14 16 17

Tension d 9 12 15 18 26 30 34 38 41

1.3d 12 16 20 23 34 39 44 49 54

1.5d 14 18 23 27 39 45 51 56 62

a. For limitations and items related to hooked bars, stirrups or ties in excess of minimum, and spacing of non-contact lap splices, etc., see ACI 318-05, Chapter 12. b. A top bar is any horizontal reinforcement placed such that more than 12 in. of fresh concrete is cast below the development length. Note: comp. = compression; min. = minimum.

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GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.4.4 Required Development Lengthsa, in., for Reinforcing Bars (Grade 60) (Cont.) Minimum tension embedment lengths dh for standard hooks, in. General use (non-seismic) [see ACI 318-05, Sections 12.5.2 and 12.5.3(a)] Bar size, #

3000 6

3

4000 6

5000 6

Normalweight concrete, fc′, psi 6000 7000 6 6

8000 6

9000 6

≥ 10,000 6

4

8

7

6

6

6

6

6

6

5

10

9

8

7

7

6

6

6

6

12

10

9

8

8

7

7

6

7

14

12

11

10

9

9

8

7

8

16

14

12

11

10

10

9

8

9

18

15

14

13

12

11

10

9

10

20

17

15

14

13

12

11

11

11

22

19

17

16

14

14

13

12

Notes: 1. Side cover ≥ 21⁄ 2 in. 2. End cover (90 deg hooks) ≥ 2 in. 3. When the full dh cannot be provided, do not prorate As provided for interpolation or other means. Use a smaller diameter bar for which dh can be provided.

  15

Minimum tension embedment lengths dh for standard hooks, in. Special confinement (non-seismic) [see ACI 318-05, Section 12.5.3(b)] Bar size, #

3000 6

3

4000 6

5000 6

Normalweight concrete, fc′, psi 6000 7000 6 6

8000 6

9000 6

≥ 10,000 6

4

6

6

6

6

6

6

6

6

5

8

7

6

6

6

6

6

6

6

10

8

7

7

6

6

6

6

7

11

10

9

8

7

7

6

6

8

13

11

10

9

8

8

7

6

9

14

12

11

10

9

9

8

7

10

16

14

12

11

11

10

9

9

11

18

15

14

13

12

12

10

10

Notes: 1. Side cover ≥ 21⁄ 2 in. 2. End cover (90 deg hooks) ≥ 2 in. 3. When the full dh cannot be provided, do not prorate As provided for interpolation or other means. Use a smaller diameter bar for which dh can be provided.

Bars with standard hooks dh

dh

db

a

a

AsFy

AsFy db

s

12db 4db or 21/2 in. minimum

s

Standard 180 deg hook Dimension a = 4db for #3 through #8,h= 5db for #9, #10, and #11 Modification factors: Grade 40 bars = 0.67 Lightweight concrete = 1.3 Epoxy-coated reinforcement = 1.2 15–40

First Printing/CD-ROM Edition

Standard 90 deg hook h

PCI DESIGN HANDBOOK/SEVENTH EDITION

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.4.5 Bar Area Equivalents in a 1-Foot-Wide Section Bar spacing c/c, in. 2 21⁄2 3 31⁄2 4 41⁄2 5 51⁄2 6 61⁄2

Reinforcing bar size (nominal diameter [in.]) #3 (0.375)

#4 (0.500)

#5 (0.625)

#6 (0.750)

#7 (0.875)

#8 (1.000)

0.66 0.53

1.20

1.86

3.60

0.96 0.80

1.49 1.24 1.06

2.64 2.11

4.74 3.79 3.16

0.44 0.38 0.33 0.29 0.26 0.24 0.22

0.69 0.60 0.53 0.48 0.44 0.40

0.74 0.68 0.62

0.37 0.34 0.32 0.30 0.28 0.27

0.57 0.53

7 71⁄2 8 81⁄2 9 91⁄2 10 101⁄2 11 111⁄2 12

0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.13 0.12 0.11 0.11

0.25 0.24 0.23 0.22 0.21 0.20

13 14 15 16 17 18 19 20 21 22 23 24

0.10 0.09 0.09 0.08 0.08 0.07 0.07 0.07 0.06 0.06 0.06 0.06

0.18 0.17 0.16 0.15 0.14 0.13 0.13 0.12 0.11 0.11 0.10 0.10

Area range

0.93 0.83

0.50 0.47 0.44 0.41 0.39 0.37 0.35 0.34 0.32 0.31 0.29 0.27 0.25 0.23 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.16

1.76 1.51 1.32 1.17 1.06 0.96 0.88 0.81 0.75 0.70 0.66 0.62 0.59 0.56 0.53 0.50 0.48 0.46 0.44 0.41 0.38 0.35 0.33 0.31 0.29 0.28 0.26 0.25 0.24 0.23 0.22

2.88 2.40 2.06 1.80 1.60

2.71 2.37 2.11

1.44 1.31 1.20

1.90 1.72 1.58

1.11 1.03

1.46 1.35 1.26 1.19 1.12 1.05

0.96 0.90 0.85 0.80 0.76

1.00 0.95 0.90 0.86 0.82 0.79

0.72 0.69 0.65 0.63 0.60 0.55 0.51

0.73 0.68 0.63 0.59 0.56 0.53

0.48 0.45 0.42 0.40 0.38 0.36 0.34 0.33 0.31 0.30

≤ 0.25 in.2

0.50 0.47 0.45 0.43 0.41 0.40

#9 (1.128)

#10 (1.270)

#11 (1.410)

Area range

Exceeds min. bar clear spacing of db 4.80 4.00 3.43 3.00 2.67 2.40 2.18 2.00 1.85 1.71 1.60

5.08 4.35 3.81 3.39 3.05 2.77 2.54 2.34 2.18 2.03

1.50 1.41 1.33 1.26 1.20 1.14 1.09 1.04

1.45 1.39 1.33

1.00 0.92 0.86 0.80

1.27 1.17 1.09 1.02

0.75 0.71 0.67 0.63 0.60 0.57 0.55 0.52

0.95 0.90 0.85 0.80 0.76

0.50

0.25 to 0.50 in.2

1.91 1.79 1.69 1.60 1.52

0.73 0.69 0.66 0.64

6.24 5.35 4.68 4.16 3.74 3.40 3.12

> 3.0 in.2

2.88 2.67 2.50 2.34 2.20 2.08

2.0 to 3.0 in.2

  15

1.97 1.87 1.78 1.70 1.63 1.56

1.5 to 2.0 in.2

1.44 1.34 1.25 1.17 1.10 1.04

1.0 to 1.5 in.2

0.99 0.94 0.89 0.85 0.81 0.78

0.75 to 1.0 in.2

0.50 to 0.75 in.2

Note: Check minimum requirements for temperature and shrinkage steel. c/c = center to center.

How to use this design aid.  Given a design (or minimum temperature/shrinkage) reinforcement required per foot, enter the design aid along right col­umn or bottom row. Select one of the bar area ranges from that given in.2/ft, and follow the range band upward and/or to the left. Select the combina­tion of bar size and spacing satisfying the design and spacing requirements for the section.

Example.  A design that requires reinforcement at 0.62 in.2/ ft, with bar size restricted to #7 or smaller. Enter the design aid in the 0.50 to 0.75 in.2 range located along the bottom row. Follow the shaded band up to the top of the table. Select one of the following combinations: one layer of #4 at about 3.5 in. on center, #5 at 6 in. on center, #6 at 8.5 in. on center, or #7 at 11.5 in. on center. Similar spacing(s) could be determined for two reinforcement layers, if desired.

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GENERAL DESIGN INFORMATION

CHAPTER 15

15.5 MATERIAL PROPERTIES — STRUCTURAL WELDED-WIRE REINFORCEMENT (WWR) Design Aid 15.5.1 Nomenclature for Structural Welded-Wire Reinforcementa m

d

w

s

w

s

w

s

w

s

p d

w w

l d

s

s

w

  15 w w 5 5.

5 s

W

R

I

a. Source: Wire Reinforcement Institute (WRI): Manual of Standard Practice – Structural Welded Wire Reinforcement (Hartford, CT: WRI, 2008).

Design Aid 15.5.2 Minimum Requirements of Steel Wires in Welded-Wire Reinforcementa Welded plain-wire reinforcement ASTM A185 Wire size

Tensile strength, psi

Yield strength, psi

Weld shear strength

W1.2 and over

75,000

65,000

35,000

Under W1.2

70,000

56,000

–

Welded deformed-wire reinforcement ASTM A497 Wire size

Tensile strength, psi

Yield strength, psi

Weld shear strength

D 45–D 4

80,000

70,000

35,000

Under D 4

80,000

70,000

–

a. Source: Wire Reinforcement Institute (WRI): Manual of Standard Practice – Structural Welded Wire Reinforcement (Hartford, CT: WRI, 2008).

15–42

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GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.5.3 Wires Used in Structural Welded-Wire Reinforcementa Wire size numberb c

d

Area, in.2/ft of width

Nominal diameter, in.

Nominal weight, lb/ft

3

4

6

12

0.757

1.530

1.800

1.350

0.900

0.450

Center to center spacing, in.

Plain W45

Deformed D45

W34

D34

0.658

1.160

1.360

1.020

0.680

0.340

W31

D31

0.628

1.054

1.240

0.930

0.620

0.310

W25

D25

0.564

0.850

1.000

0.750

0.500

0.250

W24

D24

0.553

0.816

0.960

0.720

0.480

0.240

W23

D23

0.541

0.782

0.920

0.690

0.460

0.230

W22

D22

0.529

0.748

0.880

0.660

0.440

0.220

W20

D20

0.504

0.680

0.800

0.600

0.400

0.200

W18

D18

0.478

0.612

0.720

0.540

0.360

0.180

W16

D16

0.451

0.544

0.640

0.480

0.320

0.160

W14

D14

0.422

0.476

0.560

0.420

0.280

0.140

W12

D12

0.390

0.408

0.480

0.360

0.240

0.120

W11

D11

0.374

0.374

0.440

0.330

0.220

0.110

W10.5

D10.5

0.366

0.357

0.420

0.315

0.210

0.105

W10

D10

0.356

0.340

0.400

0.300

0.200

0.100

W9.5

D9.5

0.348

0.323

0.380

0.285

0.190

0.095

W9

D9

0.338

0.306

0.360

0.270

0.180

0.090

W8.5

D8.5

0.329

0.289

0.340

0.255

0.170

0.085

W8

D8

0.319

0.272

0.320

0.240

0.160

0.080

W7.5

D7.5

0.309

0.255

0.300

0.225

0.150

0.075

W7

D7

0.298

0.238

0.280

0.210

0.140

0.070

W6.5

D6.5

0.288

0.221

0.260

0.195

0.130

0.065

W6

D6

0.276

0.204

0.240

0.180

0.120

0.060

W5.5

D5.5

0.264

0.187

0.220

0.165

0.110

0.055

W5

D5

0.252

0.170

0.200

0.150

0.100

0.050

W4.5

D4.5

0.240

0.153

0.180

0.135

0.090

0.045

W4

D4

0.225

0.136

0.160

0.120

0.080

0.040

W3.5

0.211

0.119

0.140

0.105

0.070

0.035

W3

0.195

0.102

0.120

0.090

0.060

0.030

W2.9

0.192

0.098

0.116

0.087

0.058

0.029

W2.5

0.178

0.085

0.100

0.075

0.050

0.025

W2.1

0.162

0.070

0.084

0.063

0.042

0.021

W2

0.159

0.068

0.080

0.060

0.040

0.020

W1.5

0.138

0.051

0.060

0.045

0.030

0.015

W1.4

0.135

0.049

0.056

0.042

0.028

0.014

a. Source: Wire Reinforcement Institute (WRI): Manual of Standard Practice – Structural Welded Wire Reinforcement (Hartford, CT: WRI, 2008). b. The number following W or D identifies the cross-sectional area of the wire in hundreths of a square inch. c. ASTM A82, available fy = 65,000 psi to 80,000 psi in 2500 psi increments. d. ASTM A496, available fy = 70,000 psi to 80,000 psi in 2500 psi increments.

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  15

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.5.4 C  ommon Styles of Welded-Wire Shear Reinforcement (ASTM A185 Plain WWR)a,b,c,d Used in Double-Tee Stems

Wire size

Wire gage

W-7.4

0

0.306

0.074

0.251

6

0.444

0.296

0.222

0.148

0.111

0.089

0.074

W-6.3

1

0.283

0.063

0.214

7

0.378

0.252

0.189

0.128

0.095

0.076

0.063

W-5.4

2

0.263

0.054

0.184

8

0.324

0.216

0.162

0.108

0.081

0.065

0.054

/4 in.

0.250

0.049

0.167

9

0.294

0.196

0.147

0.098

0.074

0.059

0.049

W-4.7

3

0.244

0.047

0.158

9

0.282

0.188

0.141

0.094

0.071

0.056

0.047

W-4.0

4

0.225

0.040

0.135

10

0.240

0.160

0.120

0.080

0.060

0.048

0.040

W-3.4

5

0.207

0.034

0.114

10

0.202

0.136

0.102

0.068

0.051

0.041

0.034

W-2.9

6

0.192

0.029

0.098

10

0.174

0.116

0.087

0.058

0.044

0.035

0.029

W-2.5

7

0.177

0.025

0.084

10

0.150

0.100

0.075

0.050

0.038

0.030

0.025

W-2.1

8

0.162

0.021

0.070

10

0.126

0.084

0.062

0.042

0.032

0.025

0.021

W-1.7

9

0.148

0.017

0.059

10

0.102

0.068

0.051

0.034

0.026

0.020

0.017

W-1.4

10

0.135

0.014

0.049

10

0.084

0.056

0.042

0.028

0.021

0.017

0.014

W-4.9

Weight, lb/ft

Minimum side wire gage

2 in.

3 in.

4 in.

6 in.

8 in.

10 in.

12 in.

2" typical

a. This chart represents sizes typically used in double-tee stems. Larger sizes are available when considering use of WWR in other components. Consult welded wire manufacturers for local availability. b. Specify overall height, overall length, gage and spacing of vertical wires, gage of side wires, and finish. c. Standard length = 10 ft. Lengths up to 24 ft and heights up to 48 in. typically available. d. Plain, galvanized wire, hot-dip galvanized, and epoxy-coated finishes available.

Overhang typically 1 /2 spacing

Horizontal side wire (4 typical)

2" typical

Overall height

  15

1

Steel area, in.2

Area of steel, in.2, per lineal foot at indicated Main shear reinforcement spacing

Wire diameter, in.

15–44

Spacing

Vertical wire Overall length

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GENERAL DESIGN INFORMATION

CHAPTER 15

15.6 STANDARD BOLTS, NUTS, AND WASHERS Design Aid 15.6.1 Dimensions of Nuts and Bolts Bolt heads

F D

D H

F

C

D

C

H

C

H

Bolt head dimensions, rounded to nearest 1⁄16 in., are in accordance with ANSI B18.2.1 – 1972 (square and hex) and ANSI 18.5 – 1971 (countersunk). Standard thread lengths L are: L ≤ 6 in. = 2 x bolt diameter + 1/4 in. L > 6 in. = 2 x bolt diameter + 1/2 in. Standard dimensions for bolt heads Diameter of bolt D, in.

Square Width F, in.

⁄4

3

⁄8

9

1

3

Width C, in.

Hex Height H, in.

⁄8

1

⁄2

3

⁄16

13

⁄16

1

Width F, in.

⁄16

7

⁄4

9

Width C, in.

Heavy hex Height H, in.

Width F, in.

Width C, in.

Height H, in.

⁄16

...

...

...

1

...

11

⁄8

7

⁄16

1

⁄2

3

⁄16

5

⁄8

1

⁄4

...

...

7

⁄8

7

⁄2

3

⁄4

11⁄16

5

⁄16

3

⁄4

⁄8

15

⁄16

5

1 ⁄16

7

⁄16

15

⁄4

11⁄8

19⁄16

1

⁄2

7

⁄8

5

1 ⁄16

7

1 ⁄8

5

1

11⁄2

21⁄8

1

1 ⁄8

11

1 ⁄16

3

11⁄4

17⁄8

3

Countersunk

⁄8

3

⁄16

1

1 ⁄16

7

⁄8

1

3

⁄16

1

1 ⁄16

1

1 ⁄4

7

11⁄8

15⁄16

1

⁄2

11⁄4

17⁄16

1

⁄8

5

1 ⁄16

1

1 ⁄2

9

⁄16

7

1 ⁄16

11

1 ⁄16

9

11

⁄16

11⁄2

13⁄4

2 ⁄8

3

⁄4

11

1 ⁄16

15

11

⁄16

15⁄8

17⁄8

1 ⁄16

3

⁄4

13

1 ⁄16

1

25⁄8

7

⁄8

17⁄8

23⁄16

7

⁄8

2

1 ⁄8

1

2 ⁄16

2 ⁄16

15

⁄16

1

2 ⁄16

2 ⁄8

15

1

1 ⁄2

1

2 ⁄4

3

3 ⁄16

1

1

2 ⁄4

5

13⁄4

...

...

...

25⁄8

2 1

...

...

...

2 ⁄4

...

...

1

2 ⁄2

...

23⁄4

...

3 1

Diameter D, in.

Height H.

in.

⁄2

1

⁄16

3

⁄8

⁄16

⁄8

1

⁄16

1

1 ⁄8

5

⁄2

13⁄8

3

⁄16

1 ⁄16

7

11

⁄16

113⁄16

1

2 ⁄16

3

⁄4

1

2 ⁄16

9

25⁄16

7

⁄8

21⁄4

5

⁄16

3

2 ⁄16

2 ⁄2

15

⁄16

1

2 ⁄2

11

2 ⁄8

1

3

2 ⁄8

3

2 ⁄4

1

11

2 ⁄16

3

3

13⁄16

23⁄4

33⁄16

13⁄16

...

...

3

37⁄16

13⁄8

31⁄8

35⁄8

13⁄8

...

...

...

3

3 ⁄8

7

3 ⁄8

1

1 ⁄2

1

3 ⁄2

1

4 ⁄16

1

1 ⁄2

...

...

...

...

3

3 ⁄4

5

4 ⁄16

11

1 ⁄16

7

3 ⁄8

1

4 ⁄2

11

1 ⁄16

...

...

...

...

41⁄8

43⁄4

113⁄16

41⁄4

415⁄16

113⁄16

...

...

...

...

...

41⁄2

53⁄16

2

45⁄8

55⁄16

2

...

...

3 ⁄4

...

...

...

7

4 ⁄8

5

5 ⁄8

3

2 ⁄16

...

...

...

...

...

1

3 ⁄2

...

...

...

1

5 ⁄4

1

6 ⁄16

5

2 ⁄16

...

...

...

...

...

33⁄4

...

...

...

55⁄8

61⁄2

21⁄2

...

...

...

...

...

4

...

...

...

6

615⁄16

211⁄16

...

...

...

...

...

1

5 3

15

3

1

9

⁄4

⁄16 ⁄8

⁄16 ⁄2

⁄16 ⁄8 ⁄16 ⁄4

Source: American Institute of Steel Construction (AISC): Steel Construction Manual, thirteenth edition (Chicago, IL: AISC, 2005).

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

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  15

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.6.1 Dimensions of Nuts and Bolts (Cont.) Nuts

C

F C

F H

H

Nut dimensions, rounded to nearest 1⁄16 inch, are in accordance with ANSI B18.2.2 – 1972.

Dimensions for nuts Nut size, in.

Width F, in.

⁄4

7

⁄8

5

⁄2

13

1

Width C, in.

⁄16

5

⁄8

7

Hex Height H, in.

Width F, in.

Heavy square

Width C, in.

⁄8

1

⁄4

7

⁄16

1

Height H, in.

Width F, in.

⁄2

1

⁄4

1

⁄8

5

⁄16

11

⁄8

7

⁄16

7

1

1

⁄8

5

⁄16

9

⁄16

5

⁄16

11⁄8

7

⁄16

3

⁄4

7

⁄8

1

7

1 ⁄16

9

⁄16

15

⁄16

1 ⁄16

9

⁄4

1

1 ⁄8

9

1 ⁄16

11

⁄16

1 ⁄8

5

1 ⁄16

5

7

⁄8

15⁄16

17⁄8

3

⁄4

15⁄16

11⁄2

3

1

11⁄2

21⁄8

7

⁄8

11⁄2

13⁄4

7

1

1 ⁄8

11

1 ⁄16

3

2 ⁄8

1

11

1 ⁄16

15

11⁄4

17⁄8

25⁄8

11⁄8

13⁄8

21⁄16

215⁄16

1

1 ⁄2

1

2 ⁄4

3

13⁄4

⁄2

Width C, in. 11

⁄16

Heavy hex

Height H, in.

Width F, in.

⁄4

1

⁄8

11

⁄2

7

1

⁄16

1

3

⁄8

11⁄4

1

⁄16

1

1 ⁄16

1

1 ⁄2

5

⁄8

1

1 ⁄4

3

1 ⁄4

3

⁄4

17⁄16

21⁄16

⁄8

15⁄8

1 ⁄16

1

13

17⁄8

23⁄16

11⁄4

21⁄16

3 ⁄16

5

1 ⁄16

1

...

...

2

...

21⁄4

3

  15

Square

Width C, in.

⁄2

9

⁄16

13

Height H, in.

⁄16

1

⁄16

3

⁄4 ⁄8

⁄8

1

1

⁄8

1

1 ⁄16

1

1 ⁄4

5

⁄8

⁄4

1

1 ⁄4

7

1 ⁄16

3

⁄4

7

⁄8

17⁄16

111⁄16

7

⁄8

25⁄16

1

15⁄8

17⁄8

1

1 ⁄16

9

2 ⁄16

1

1 ⁄8

13

1 ⁄16

1

2 ⁄16

11⁄8

11⁄16

2

213⁄16

11⁄4

2

25⁄16

11⁄4

23⁄8

13⁄16

23⁄16

31⁄8

13⁄8

23⁄16

21⁄2

13⁄8

2 ⁄4

5

2 ⁄8

5

1 ⁄16

3

2 ⁄8

3

3 ⁄8

1

1 ⁄2

3

2 ⁄8

3

2 ⁄4

11⁄2

...

...

...

...

...

...

...

23⁄4

33⁄16

13⁄4

...

...

...

...

...

...

...

...

31⁄8

35⁄8

2

...

...

...

...

...

...

...

...

...

31⁄2

41⁄16

23⁄16

21⁄2

...

...

...

...

...

...

...

...

...

37⁄8

41⁄2

27⁄16

23⁄4

...

...

...

...

...

...

...

...

...

41⁄4

415⁄16

211⁄16

3

...

...

...

...

...

...

...

...

...

45⁄8

55⁄16

215⁄16

31⁄4

...

...

...

...

...

...

...

...

...

5

53⁄4

33⁄16

1

3 ⁄2

...

...

...

...

...

...

...

...

...

3

5 ⁄8

3

6 ⁄16

37⁄16

33⁄4

...

...

...

...

...

...

...

...

...

53⁄4

65⁄8

311⁄16

4

...

...

...

...

...

...

...

...

...

61⁄8

71⁄16

315⁄16

1 5 3

⁄2

Source: American Institute of Steel Construction (AISC): Steel Construction Manual, thirteenth edition (Chicago, IL: AISC, 2005).

15–46

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.6.2 Dimensions of Standard Washers Size of bolt

Size of hole

Outside diameter

Thickness wire gage number

Weight per 1000, lb

Size of bolt

Plain washers, U.S. standard, in.

Size of hole

Outside diam­eter

Thickness wire gage number

Plain washers, SAE standard, in.

1

⁄2

9

⁄16

13⁄8

12 (3⁄32)

38.4

1

⁄2

17

⁄32

11⁄16

3

⁄16

5

⁄8

1

1 ⁄2

12 ( ⁄32)

44.4

9

⁄16

19

⁄32

3

1 ⁄16

3

⁄8

11

⁄16

3

1 ⁄4

10 ( ⁄8)

77.0

5

⁄8

21

⁄32

5

1 ⁄16

3

⁄4

13

⁄16

2

10 (1⁄8)

111.0

3

⁄4

13

⁄16

11⁄2

1

7

⁄8

15

⁄16

1

2 ⁄4

5

9 ( ⁄32)

153.0

7

⁄8

15

⁄16

1 ⁄4

1

1

11⁄16

21⁄2

9 (5⁄32)

176.0

11⁄8

11⁄4

23⁄4

9 (5⁄32)

1 ⁄4

1 ⁄8

3

9 ( ⁄32)

9

5 3

1

3

3

1

3

⁄32 ⁄32 ⁄32 ⁄8 ⁄8

Narrow-gage washers, in.

5

1

⁄2

9

⁄16

11⁄4

12 (3⁄32)

⁄16

5

⁄8

13⁄8

12 (3⁄32)

⁄8

11

⁄16

11⁄2

10 (1⁄8)

⁄4

13

⁄16

3

1 ⁄4

10 (1⁄8)

7

⁄8

15

⁄16

9

5 3

2

9 (5⁄32)

1

1

1 ⁄16

1

2 ⁄4

9 (5⁄32)

11⁄8

11⁄4

21⁄2

9 (5⁄32)

11⁄4

13⁄8

23⁄4

9 (5⁄32)

1 ⁄8

1 ⁄2

3

8 (11⁄64)

3

1

w Note: SAE = Society of Automotive Engineers.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

15–47

  15

GENERAL DESIGN INFORMATION

CHAPTER 15

15.7 WELDING INFORMATION Design Aid 15.7.1 Weld Symbols Commonly Used in Precast Concrete Construction Basic welding symbols and their meanings Elements of a typical weld symbol

Weld symbol elements effective throat

length of weld

weld pitch (c/c spacing)

r

Reference line read left to right regardless of arrow tail orientation

Square edge of fillet, bevel, & flare Bevel always on left (typical)

Basic weld symbol - other side of joint (fillet shown)

Field weld symbol - flag always points to tail

Reference line Reference note(s)/process

Weld all around designation

(omit with no notes or processes) Basic weld symbol - arrow side of joint (fillet shown)

Arrow connecting reference line to “arrow side” of joint Location / position of symbol Type of weld

  15

Arrow side

weld size

o

Other side

Both sides

Supplemental symbols Field weld

Weld all around

Finishing contours

Fillet weld Side designation

Plug or slot weld

Not Applicable

Square

Arrow side

Other side

Maximum detailed fillet weld sizes at edges V

Groove welds

Base metal in. thick Base metal in. thick

Bevel

End returns

Flare– bevel 2t

t = weld thickness

Flare–V

Stud weld

No arrow or other side significance to the stud weld symbol.

Refer to AWS D1.1, section 2.19 regarding end returns at angles, brackets, and beam seats

For other basic and supplemental weld symbol and process information, refer to ANSI/AWS A2.4.

References: American Institute of Steel Construction (AISC): Steel Construction Manual, thirteenth edition (Chicago, IL: AISC, 2005). American Welding Society (AWS): Standard Symbols for Welding, Brazing and Nondestruction Examination (ANSI/AWS A2.4-86) (Miami, FL: AWS, 1986). AWS: Structural Welding Code – Steel (ANSI/AWS D1.1:2000), seventeenth edition (Miami, FL: AWS, 2000). 

15–48

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PCI DESIGN HANDBOOK/SEVENTH EDITION

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.7.2 Typical Welded Joints in Precast Concrete Construction Fillet weld

Fillet weld Weld on other side

Center-to-center spacing of weld segments (pitch)

Weld on other side

Weld on arrow side

Weld size

Length of individual weld segments

Weld on arrow side

2 in. of 5⁄16 fillet weld on 6 in. centers, each side

⁄4 in. fillet weld, 6 in. long, each side

1

Plug weld

Flare bevel with fillet weld

Depth of filling (size ommission indicates filling = thickness)

Weld size (hole diameter at root)

Weld length

Straight or normal leg always on left

Field weld points to tail HSS

4" c/c Center-to-center spacing of plug welds (pitch)

Flare bevel weld

1" diameter t

Fillet weld

First weld (flare bevel)

Weld size Second weld (fillet)

1 in. Ø plug welds 1⁄2 in. deep at 4 in. on-center

Flare bevel weld of tube to plate followed by an optional 1⁄4 in. fillet weld

Bevel with fillet weld

Square weld with fillet

Field weld (points to tail)

Bevel weld size

After setting spandrel panel AE6

Root opening 1st weld (bevel)

Root opening (omission = zero in present case)

Erection note

2nd weld (bevel)

Fillet weld size

Straight or normal leg always on left of symbol

Field weld (points to tail)

Root opening 2nd weld (fillet) 1st weld (square)

⁄4 in. bevel weld with 5⁄16 in. fillet weld reinforcement, one side

1

Root opening

On both sides of joint: square weld followed by fillet weld Fillet weld size

⁄8 in. square weld with 1⁄2 in. fillet weld reinforcement, both sides

3

Note: c/c = center to center; HSS = hollow structural section.

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

15–49

  15

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.7.2 Typical Welded Joints in Precast Concrete Construction (Cont.) Stud weld Stud diameter

Reinforcing bar weld

Center-to-center spacing of studs in one line (pitch)

S(E) S(E)

S(E) Effective weld size (E) = 0.48

Number of studs in one line

S

Effective weld size (E) = 0.48

S

1. Single

Six 1⁄2 in. φ studs spaced at 3 in. on-center in one line

2. Double (A) Flare-bevel-groove weld S(E) S(E)

S(E) S

S

1. Single

Effective weld size (E) = 0.68

2. Double

(B) Flare-V-groove weld

  15

Weld all around

Effective weld size (E) = 0.68

A706 reinforcing bar Steel plate

Weld size

Fillet

General notes: 1. Radius of reinforcing bar = S. 2. These are sectional views. Bar deformations are shown only for illustrative purposes. 3. Omission of S and (E) dimensions indicate that filling the entire gap from the edges of the reinforcing bar is required; omission of (E) indicates that filling the entire gap from the S dimensions is required.

15–50

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.7.3 Properties of Weld Groups Treated as Lines (tw = 1) Section b = width; d = depth

Distance to centroid

Section modulus about horizontal axis S=

d

(1)

Polar moment of inertia IP, about center of gravity

d2 6

Ip =

d3 12

b

S= 3

Ip =

d ( 3b 2 + d 2 ) 6

S = bd

Ip =

b ( 3d 2 + b 2 ) 6

d2

d

(2) b d

(3) x y d b

– y=

d2 2 (b + d )

– x=

2

b 2 (b + d )

Stop =

4bd + d 2 6

Sbott =

(b + d )4 − 6b 2d 2 12 (b + d )

Ip =

d ( 4b + d ) 6 (2b + d ) 2

(4)

  15

x d

– x=

b2 2b + d

d2

S = bd + 6

Ip =

b4 8b 3 + 6bd 2 + d 3 − 12 2b + d

Ip =

d4 b 3 + 6b 2d + 8d 3 − 12 2d + b

b

(5) 2 Stop = 2bd + d

b y

d

– y=

d2 b + 2d

(6)

3

d 2 ( 2b + d ) Sbott = 3 (b + d )

b d2

Ip =

S = bd + 3

d

(b + d )3 6

(7) b

2 Stop = 2bd + d

y

– y=

d

(8)

d2 b + 2d

3

d 2 ( 2b + d ) Sbott = 3 (b + d )

Ip =

b 3 + 8d 3 d4 − 12 b + 2d

b d2

S = bd + 3

d

Ip =

b 3 + 3bd 2 + d 3 6

(9) x

x r

S = πr 2

lp = 2πr 3

(10)

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

15–51

GENERAL DESIGN INFORMATION

CHAPTER 15

15.8 SECTION PROPERTIES Design Aid 15.8.1 Properties of Geometric Sections SQUARE Axis of moments through center

c

RECTANGLE Axis of moments on diagonal

A = d 2 c =

d 2

I =

d4 12

S =

d3 6

d

d

c

SQUARE Axis of moments on base A = d 2

  15

I =

d4 3

d3 S = 3

r =

SQUARE Axis of moments on diagonal c

d

d

d 3

c =

d 2

I =

d4 12

HOLLOW RECTANGLE Axis of moments through center

c d d1

d S = 6 2

c

b 2d 2 6 b2 + d 2

d 2

I =

bd 3 12

d 2

b

bd (b 2  sin2  a  + d 2  cos2  a ) 12

S =

bd (b 2  sin2  a + d 2  cos2  a ) 6 (b  sin a  + d  cos a )

(b 2  sin2  a + d 2  cos2  a )

c =

d 2

I =

bd 3 − b1d 13 12

S =

bd 3 − b1d 13 6d

r =

bd 3 − b1d 13 12A

A = b(d – d1) c =

d 2

I =

b (d 3 − d 13 ) 12

S =

b (d 3 − d 13 ) 6d

c d d1

d 12

12

A = bd – b1d1

b

r =

bd 6 (b 2 + d 2 )

I =

b

EQUAL RECTANGLES Axis of moments through center of gravity

c =

bd 6

S =

b1

d 12

A = bd

S =

b 3d 3 6 (b 2 + d 2 )

r =

3

RECTANGLE Axis of moments through center

I =

c = b sin a + d  cos a 2

b

d

A = d 2

r =

bd b2 + d 2

A = bd

c

a d

c =

r =

RECTANGLE Axis of moments any line through center of gravity

c = d c

b

d

d 12

r =

d

A = bd

r =

d 3 − d 13 12 (d − d 1 )

Source: American Institute of Steel Construction (AISC): Steel Construction Manual, thirteenth edition (Chicago, IL: AISC, 2005).

15–52

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.8.1 Properties of Geometric Sections (Cont.) A = bd RECTANGLE Axis of moments on base c = d I c

d

=

S =

UNEQUAL RECTANGLES Axis of moments through center of gravity

bd 3 3 bd 2 3

b

r

=

TRIANGLE bd A = Axis of moments through 2 center of gravity 2d c = 3 c

I

=

y

c

y1

c1

d d1 t1

d = 3

t1

b1

HALF CIRCLE Axis through moments of center of gravity

bd 3 36

bd 2 S = 24

r

b

0.5bt 2 + b1t 1 (d − 0.5t 1) A

I

bt 3 bt3 + bty 2 + 1 1 + b1t 1y 12 12 12

r

A =

c

d

d

PARTIAL CIRCLE Axis of moments through circle center

bd 3 12

=

R

c d

b

=

d 6

d 3 (b 2 + 4bb1 + b12 ) 36 (b + b1 )

d 2 (b 2 + 4bb1 + b12 ) S = 12 (2b + b1 ) r = d × 2 (b 2 + 4bb1 + b12 ) 6 (b + b1 )

8 ⎞ ⎛π = R4 ⎜ − ⎝ 8 9π ⎟⎠

=R

A =

  15

9π 2 − 64 6π

πR 2 − y 1 R 2 − y 12 2

⎛y ⎞ −R 2sin−1 ⎜ 1 ⎟ ⎝R⎠

y1 c

NOTE: Angles in radians

PARABOLA

2 (R 2 − y 12 ) /A 3 πR 4 y 1 = + (R 2 − y12 )3 8 2

c = I

d (b + b1 ) TRAPEZOID A = 2 Axis of moments through center of gravity d ( 2b + b1 ) c = 3 (b + b1) b1

I

πR 2 2

3/ 2

bd 2 S = 12

r

b

=

l A

4 ⎞ ⎛ c = R ⎜ 1− ⎝ 3π ⎟⎠

r

I

=

l l  S1 = c c1

⎡ R 3 ⎤ ⎡ ( 9π 2 − 64) ⎤ S = ⎢ ⎥ ⎢ ⎥ ⎣ 24 ⎦ ⎣ 3π − 4 ⎦

d = 18

TRIANGLE bd A = Axis of moments on base 2 c = d

=

S =

I

c

R

d

c = t

t

b

A = bt + b1t1

−

R2 ⎛ ⎜ y1 4 ⎝

A =

4 ab 3

m =

2 a 5

I1 =

16 3 ab 175

I2 =

4 ab 3 15

I3 =

32 3 ab 105

a

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

m b

(R 2 − y 12 ) + R 2sin−1

y1 ⎞ ⎟ R⎠

15–53

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.8.1 Properties of Geometric Sections (Cont.) CIRCLE Axis of moments through center

R

c

d

HALF PARABOLA A =

πd 2 = πR 2 4

c =

d R 2

S =

πd 3 πR 3 = 32 4

r =

d R = 4 2

π (d 2 − d 12 ) 4 d c = 2 I =

π (d 4 − d 14 ) 64

S =

π (d − d 32d

c

4

d d1

r =

PARABOLIC FILLET IN RIGHT ANGLE

a =

m

b

n

a

t

4 1

)

COMPLEMENT OF HALF PARABOLA n

a

1 2 t 6

t

b

n

m= n=

4 t 5

I1 = I 2 =

11 4 t 2100

a

m

b

* See note on next page.

15–54

3 b 8

I1 =

8 3 ab 175

I2 =

19 ab 3 480

I3 =

16 3 ab 105

I4 =

2 ab 3 15

m=

7 a 10

n =

3 b 4

I1 =

37 3 ab 2100

I2 =

1 ab 3 80

m

2 2

A =

n =

1 A = ab 3

*ELLIPTIC COMPLEMENT

t t 2

2 a 5

m

d 2 + d12 4

b =

m=

a

b

A =

  15

2 ab 3

n

4 4 I = π d = π R 64 4

HOLLOW CIRCLE Axis of moments through center

A =

First Printing/CD-ROM Edition

⎛ π⎞ A = ab ⎜ 1− ⎟ ⎝ 4⎠

m=

a ⎛ π⎞ 6 ⎜ 1− ⎟ ⎝ 4⎠

n =

b ⎛ π⎞ 6 ⎜ 1− ⎟ ⎝ 4⎠

⎛ ⎞ ⎜1 π ⎟ 1 I1 = a b ⎜ − − ⎟ ⎜ 3 16 36 ⎛ 1− π ⎞ ⎟ ⎟ ⎜⎝ ⎝⎜ 4 ⎠ ⎟⎠ 3

⎛ ⎞ ⎜1 π ⎟ 1 − I2 = ab 3 ⎜ − ⎟ ⎜ 3 16 36 ⎛ 1− π ⎞ ⎟ ⎜⎝ ⎟⎠ ⎟ ⎜⎝ 4 ⎠

PCI DESIGN HANDBOOK/SEVENTH EDITION

GENERAL DESIGN INFORMATION

CHAPTER 15

Design Aid 15.8.1 Properties of Geometric Sections (Cont.) *HALF ELLIPSE

A =

1 π ab 2

m =

4a 3π

m

φ =

a φ

R

1 I2 = π ab 3 8

R1

1 I3 = π a 3b 8

b

180° n

a = 2 R 2 − R12

8 ⎞ ⎛π I1 = a 3b ⎜ − ⎝ 8 9π ⎟⎠

a

n = number of sides

REGULAR POLYGON

R =

a 2sinφ

R1 =

a 2tanφ

A =

1 2 na cotφ 4

1 2 nR sin2φ = nR12 tanφ 2 A ( 6R 2 − a 2 ) I1 = I 2 = 24



=



=

A (12R12 + a 2 ) 48

r1 = r2 =

*QUARTER ELLIPSE

A =

1 π ab 4

m =

4a 3π

n

n =

4b 3π

4 ⎞ ⎛π I1 = a 3b ⎜ − ⎝ 16 9π ⎟⎠

a

m

b

F

F φ

1 π a 3b 16

I4 =

1 π ab 3 16

I4 = Ixcos2φ + Iysin 2φ

x

φ

x

⎞ ⎛y x fb = M ⎜ sinφ + cosφ ⎟ Iy ⎠ ⎝ Ix y y

4 ⎞ ⎛π I2 = ab 3 ⎜ − ⎝ 16 9π ⎟⎠

I3 =

12R1 + a 2 48

I3 = Ixsin 2φ + Iycos2φ

BEAMS AND CHANNELS

F

=

  15

6R 2 − a 2 24

Where M is bending moment due to force F.

* To obtain properties of half circles, quarter circle, and circular complement, substitute a = b = R.

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Design Aid 15.8.1 Properties of Geometric Sections (Cont.) ANGLE Axis of moments through center of gravity

tan2θ =

2k Iy − Ix

b a

t

θ y

c

d

K =

product of inertia about X−X & Y−Y ±

x

abcdt 4 (b + c )

Ix =

1⎡ 3 3 t (d − y ) + by 3 − a ( y − t ) ⎤⎦ 3⎣

Iy =

1⎡ 3 3 t (b − x ) + dx 3 − c ( x − t ) ⎤⎦ 3⎣

Iz =

Ixsin2θ + Iycos2θ + Ksin2θ

Iw =

Ixcos2θ + Iysin2θ – Ksin2θ

t

yy ==

d 2 + at 2 (b + c )

t(b + c)

=

xx ==

b 2 + ct 2 (b + c )

A =

ZZ is axis of minimum I

  15

K is negative when heel of angle, with respect to center of gravity, is in first or third quadrant, positive when in second or fourth quadrant.

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Design Aid 15.8.2 Plastic Section Moduli and Shape Factors Section

d

Plastic modulus Zs, in.3

Shape factor

bd 2 4

1.5

b

x−x axis t

bt (d − t ) +

x

w (d − 2t )2 4

1.12 (approximate)

d

w

y−y axis 1.55 (approximate)

b 2t (d − 2t )w 2 + 4 2

b

  15

t

w

d

bt (d − t ) +

w (d − 2t ) 4

2

1.12 (approximate)

b

d1

d

d3 6

d

d 3 − d 13 6

d1 d

b1

1.70

16d 3π

⎡ d 3 − h13 ⎤ ⎢d 4 − h4 ⎥ ⎣ 1 ⎦

3d ⎡ bd 2 − b1d 12 ⎤ 2 ⎢⎣ bd 3 − b1d 13 ⎥⎦ bd 2 − b1d 12 4

Note: For hollow structural shapes, refer to American Institute of Steel Construction, Steel Construction Manual, thirteenth edition.

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15.9 METRIC CONVERSION Design Aid 15.9.1 Metric Calculations and Example “Hard” SI (metric) calculations for precast concrete

Example:

Design Aid 15.9.2 shows direct conversion from inch-pound (U.S. customary) to SI units. Calculations made in SI units are usually rounded to even num­bers. These are known as “hard” metric calculations. The metric version of ACI 318-05 is ACI 318M-05. Some of the common SI units used are:

Given:

Concrete strength: 20 MPa is approximately equivalent to 3000 psi. 35 MPa is approximately equivalent to 5000 psi.

Reinforcement: Twelve 13-mm-diameter 1860 MPa low-relaxation strands (6 each stem). Area per strand = 99 mm2 Aps = 12(99) = 1188 mm2 As = 2 − #19 = 568 mm2 fy = 420 MPa

  15

Grade 420 reinforcing bar (fy = 420 MPa) is equivalent to Grade 60 reinforcing bar. Prestressing strand: Strand diameters and areas are rounded to the nearest mm. For example, 13 mm is equivalent to 1⁄2 in. diam­eter, area = 99 mm2. Relationships in SI: Structural engineering calculations in SI units involve forces that include gravitational effects, rather than just weights, or mass. Thus, one kilogram (kg) of mass converts to 9.8 newtons (N) of force. For example, a 50-mm-thick concrete topping 1 m wide weighs (50/1000) m × 1 m × 2400 kg/m3 = 120 kg/m. It exerts 120 × 9.8 = 1176 N/m or 1.18 kN/ m of force. Pressure or stress is expressed in pascals (P). 1P = 1N/m2. It is more common to work in megapas­cals (MPa). 1 MPa =1N/mm2. Bending moments are expressed in newton-meters (N-m) or kilonewton-meters (kN-m). Design Aid 15.9.2 lists quantities that are fre­quently encountered in the design of precast con­crete as well as in general structural engineering practice. Most U.S. government agencies that require SI unit dimensioning of contract documents will also require consistent use of the listed SI units given in the table. The equivalent U.S. customary units listed are those traditionally used by the design professions in the United States.

Concrete: Precast f'c = 35 MPa Topping f'c = 20 MPa

Problem: Find the design flexural strength of the composite section using Eq. 18-3 from ACI 318M-05.

dp

Reinforcement: Most U.S. reinforcing bar manufacturers mark bars with metric designations, although the actual sizes have not changed (see Design Aid 15.4.1).

Double-tee similar to PCI standard 8DT24+2

d

Concrete weight (or mass): Normalweight concrete may be assumed to weigh 2400 kg/m3 (149.8 lb/ft3). Lightweight concrete may be assumed to weigh 1900 kg/m3 (118.6 lb/ft3).

Use of Eq. 18-3 from ACI 318M-05 (similar to example 5.2.1.4)

Dimentions in millimeters (mm) ⎛ γ fps = fpu ⎜ 1− p β1 ⎝

⎡ fpu d ⎤⎞ ⎢ ρp ' + ω − ω ' ⎥ ⎟ ⎣ fp d p ⎦⎠

ω´ = 0 in this example A 1188 ρp = ps + = 0.00087 bd p 2400 ( 570 )

ω=

As bd

⎛ fy ⎞ 568 ⎛ 420 ⎞ ⎜⎝ f ' ⎟⎠ = 2400 ( 620) ⎜⎝ 20 ⎟⎠ = 0.0080 c

⎞ ⎛ 0.28 ⎡ 1860 620 fps = 1860 ⎜ 1− 0.00087 + ( 0.0080 )⎤⎥ ⎟ = 1805 MPa 20 570 ⎝ 0.85 ⎢⎣ ⎦⎠

a=

Apsfps + Asfy 1188 (1805 ) − 568 ( 420 ) = 0.85fc' b 0.85 (20 ) 2400

a = 47 mm a⎞ a⎞ ⎛ ⎛ M n = Apsfps ⎜ d p − ⎟ + Asfy ⎜ d − ⎟ ⎝ ⎝ 2⎠ 2⎠

⎛ 570 − 24 ⎞ ⎛ 620 − 24 ⎞ = 1188 (1805 ) ⎜ + 568 ( 420 ) ⎜ ⎝ 1000 ⎟⎠ ⎝ 1000 ⎟⎠ 2 ⎧ 2 d 2 −=2 1313 x ( d − x ) +N-m (c 2 + ekN-m ) − ⎡⎣e 2x + c 2 (d − x ) ⎤⎦ ⎫⎬ =× ⎨⎩1,312,991 d ⎭ φMn = 0.9(1313) = 1182 kN-m

Conversion of frequently encountered concrete stress coefficients used in ACI 318-05 and the PCI Handbook are tabulated in Design Aid 15.9.4.

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Design Aid 15.9.2 C  onversion from U.S. Customary Units to the International System of Units (SI) To Convert From

To

Multiply By

Length inch (in.)

millimeter (mm)

25.4

inch (in.)

meter (m)

0.0254

foot (ft)

meter (m)

0.3048

yard (yd)

meter (m)

0.9144

mile (mi)

kilometer (km)

1.6093

Area square foot (ft2)

square meter (m2)

0.09290

square inch (in. )

square millimeter (mm )

square inch (in. )

square meter (m )

square yard (yd2)

square meter (m2)

acre (A)

hectare (ha) = 10,000 m

square mile (mi2)

square kilometer (km2)

2

645.2

2

2

0.0006452

2

0.8361 2

0.4047 2.590

Volume cubic inch (in.3)

cubic meter (m3)

0.00001639

cubic foot (ft )

cubic meter (m3)

0.02832

cubic foot (ft3)

gallon (gal.)

6.22965

cubic yard (yd3)

cubic meter (m3)

3

a

liter (L)

a

gallon (gal.) Can. liquid

cubic meter (m )

gallon (gal.) U.S. liquida

liter (L)

gallon (gal.) Can. liquid

a

gallon (gal.) U.S. liquid

0.7646 4.546 0.004546

3

3.785

cubic meter (m )

0.003785

3

Force kip

kilogram (kgf)

453.6

kip

newton (N)

4448.0

pound (lb)

kilogram (kgf)

0.4536

pound (lb)

newton (N)

4.448

Pressure or stress kip/square inch (ksi)

megapascal (MPa)b b

pound/square foot (lb/ft2)

kilopascal (kPa)

pound/square inch (psi)

kilopascal (kPa)b

pound/square inch (psi) pound/square foot (lb/ft2)

6.895 0.04788 6.895

b

megapascal (MPa) kilogram/square meter (kgf/m2)

0.006895 4.882

Mass pound (avdp)

kilogram (kg)

0.4536

ton (short, 2000 lb)

kilogram (kg)

907.2

grain

kilogram (kg)

0.00006480

tonne (t)

kilogram (kg)

1000

a. One U.S. gallon equals 0.8321 Canadian gallon. b. One pascal equals one newton/square meter; 1 Pa = 1 N/m2. Note: To convert from SI units to U.S. customary units (except for temperature), divide by the factors given in this table.

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Design Aid 15.9.2 C  onversion from U.S. Customary Units to the International System of Units (SI) (Cont.) To Convert From

To

Multiply By

Mass (weight) per length kip/linear foot (kip/ft)

kilogram/meter (kg/m)

1488

pound/linear foot (lb/ft)

kilogram/meter (kg/m)

1.488

pound/linear foot (lb/ft)

newton/meter (N/m)

14.593

Mass per volume (density) pound/cubic foot (lb/ft3)

kilogram/cubic meter (kg/m3)

16.02

kilogram/cubic meter (kg/m )

0.5933

pound-inch (lb-in.)

newton-meter

0.1130

pound-foot (lb-ft)

newton-meter

1.356

kip-foot (kip-ft)

newton-meter

1356

pound/cubic yard (lb/yd ) 3

3

Bending moment or torque

Temperature

  15

degree Fahrenheit (°F)

degree Celsius (°C)

degree Fahrenheit (°F)

degree Kelvin (K)

tC = (tF – 32)/1.8 tK = (tF + 459.7)/1.8

Energy British thermal unit (Btu)

joule (j)

1056

kilowatt-hour (kwh)

joule (j)

3,600,000

Power horsepower (hp) (550 ft-lb/sec)

watt (W)

745.7

mile/hour (mph)

kilometer/hour

1.609

mile/hour (mph)

meter/second (m/s)

Velocity 0.4470

Other Section modulus (in.3)

mm3

16,387

Moment of inertia (in. )

mm4

416,231

4

Coefficient of heat transfer

(Btu/ft2/h/°F)

Modulus of elasticity (psi)

W/m2/°C MPa

5.678 0.006895

Thermal conductivity

(Btu/in./ft2/h/°F)

Wm/m2/°C

Thermal expansion (in./in./°F)

mm/mm/°C

Area/length (in.2/ft)

mm2/m

15–60

0.1442 1.800 2116.80

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Design Aid 15.9.3 Preferred SI Units and U.S. Customary Equivalents Quantity

SI

U.S. customary

Area, cross section

mm2

in.2

Area, plan dimension

mm

ft2

Bending moment Coefficient of thermal expansion

2

kN-m

kip-ft

mm/(mm-°C)

in./in./°F

Deflection

mm

in.

Density, linear

kg/m

lb/ft, kip/ft

Density, area

kg/m2

lb/ft2, kip/ft2

Density, mass

kg/m3

lb/ft3, kip/ft3

kN

lb, kip

Force Force, per unit length

kN/m

lb/ft, kip/ft

Force, per unit area

kN/m2

lb/ft2, kip/ft2

Length, cross section

mm

in.

Length, plan dimension

mm

ft

kg

lb, kip

Modulus of elasticity

MPa

psi, ksi

Moment of inertia

mm4

in.4

Section modulus

mm

in.3

Stress

MPa

psi, ksi

°C

°F

kN-m

lb-ft, kip-ft

Mass

Temperature Torque

3

  15

Design Aid 15.9.4 Concrete Stress Coefficients U.S. customary coefficient

SI coefficient

U.S. customary coefficient

SI coefficient

0.5

0.04

3.3

0.27

0.6

0.05

3.5

0.29

0.667

0.06

4.0

0.33

1.0

0.08

4.4

0.37

1.1

0.09

5.0

0.42

1.2

0.10

5.5

0.46

1.25

0.10

6.0

0.50

1.5

0.12

6.3

0.52

1.6

0.13

6.5

0.54

1.7

0.14

7.0

0.58

1.9

0.16

7.5

0.62

2.0

0.17

8.0

0.66

2.4

0.20

10.0

0.83

3.0

0.25

12.0

1.00

Examples: U.S. customary: 1.0 psi

SI equivalent: 0.08 MPa

U.S. customary: 10 psi

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SI equivalent: 0.83 MPa

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APPENDIX

APPENDIX IMPACT OF ACI 318-08 ON THIS HANDBOOK

The PCI Design Handbook 7th edition is based on the Building Code Requirements for Structural Concrete (ACI 318-05), Minimum Design Loads for Buildings and Other Structures (ASCE 7-05), and the International Building Code (IBC-2006). The IBC-2006 is the code adopted by most jurisdictions having legal authority over building construction at the time of publication of this edition of the handbook. The IBC-2006 references ACI 318-05 and ASCE 7-05. IBC-2009 was published in the spring of 2009 (IBC-2009) and references ACI 318-08 and ASCE 7-05. However, it is not clear how many jurisdictions will adopt IBC-2009 and if so, when. Many may choose to wait until IBC-2012 is released. Hence, if this handbook were to use IBC-2009 as its main model building code reference, some of its provisions may not be in conformance with the applicable codes in all jurisdictions. It is desirable that this handbook present the most current information available with respect to the design of precast/ prestressed concrete. This Appendix is intended to provide the user of the handbook an easy reference to chapters in the handbook and how ACI 318-08 affects those chapters. This is done on a chapter by chapter basis. References identified within the text are references to ACI 318-08 unless specified otherwise. Notation for the Appendix shown at the end of the section, includes only the notation used in this Appendix, and reflects notation used in ACI 318-08 unless noted otherwise. The material presented is directly from four articles1,2,3,4 written by SK Ghosh and published in the PCI Journal as special supplements for members.

Chapter 1 – Precast and Prestressed Concrete: Applications This chapter provides a general discussion of the applications of precast and prestressed concrete and is not affected by either ACI 318-08 or IBC 2009.

in Section 7.5.2.1. Design load combination is now defined in Chapter 2. Important new definitions have been added in Chapter 2 for equilibrium density, headed deformed bars, and headed shear stud reinforcement. Commentary to the definition for headed deformed bars points out important differences between such bars and headed shear stud reinforcement.

Chapter 3 – Preliminary Design of Precast, Prestressed Concrete Structures Chapter 3 presents a number of load tables for deck components and interaction curves for columns and wall panels. These may be influenced by changes in ACI 318-08 that are identified in the section in the appendix on Chapter 5. The user of the handbook should review the changes in Chapter 5 and use judgment in how it affects these load table and interaction diagrams.

Chapter 4 – Analysis and Design of Precast, Prestressed Concrete Structures General In Chapter 2, new definitions for shear cap, steel fiberreinforced concrete, and work have been added. A new Section 8.8, “Effective Stiffness to Determine Lateral Deflections,” has been added. Section 8.8.2 requires that the lateral deflections of reinforced-concrete building systems resulting from factored lateral forces be determined by either: • •

Chapter 2 – Notation and Definitions A new definition for specified concrete cover has been added in Chapter 2. The commentary to this definition points out that tolerances on specified concrete cover are provided

a detailed analysis considering the reduced stiffness of all members under the loading conditions; a linear analysis using (a) section properties defined in Section 10.10.4(a) through (c) (Section 10.10 deals with slenderness effects in compression members) or (b) 50% of stiffness values based on gross section properties.

The new commentary Section, R9.2.1(a), provides valuable and much-needed clarification. It points out that the

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APPENDIX load-factor modification of Section 9.2.1(a) is different from the live-load reduction based on the loaded area that is typically allowed in the legally adopted general building code. The live-load reduction in the code adjusts the nominal load L. The lesser load factor in Section 9.2.1(a) reflects the reduced probability of the occurrence of maximum values of multiple transient loads at the same time. The reduced live loads specified in the legally adopted general building code can be used simultaneously with the 0.5 load factor specified in Section 9.2.1(a). Commentary Section R14.8.4 states that “service-level load combinations are not defined in Chapter 9 of ACI 318.” However, they are discussed in Appendix C of ASCE/SEI 7-05, although, unlike ACI 318, “appendices to ASCE/SEI 7 are not considered to be mandatory parts of the standard.” Appendix C of ASCE 7-05 recommends the following load combination for calculating service-level lateral deflections of structures:

Overall changes to Chapter 21: Earthquake-Resistant Structures

D + 0.5L + 0.7W

“which corresponds to a 5% annual probability of exceedance.” Seismic Related

  A

Commentary Section R1.1.9, “Provisions for Earthquake Resistance” (formerly Section R1.1.8) has been completely rewritten with the introduction of SDC terminology into ACI 318. Table R1.1.9.1 (formerly Table 1.1.8.3), which provides correspondence between the new terminology and the terminology used in legacy model codes (seismic performance categories, seismic zones) and in prior editions of ACI 318 (regions of low, moderate, and high seismic risk), has been updated. The term seismic design category is defined in Chapter 2. Definitions for special precast structural wall and special structural wall were added. The term special structural wall is now defined, and it can be made of cast-in-place or precast concrete. Design requirements for earthquake-resistant structures have been rewritten in terms of SDC. The prior terminology of regions of low, moderate, and high seismic risk is gone. This change makes ACI 318 terminology the same as that used in the IBC and ASCE 7 Standard Minimum Design Loads for Buildings and Other Structures5 (since its 1998 edition). Because the IBC has emerged as the one model building code for the entire country on which the legal codes by most legal jurisdictions (such as cities, counties, and states) are based, this is a sensible and timely change. The IBC will no longer have to provide an interface between its own terminology and that of ACI 318, as it has in the past. The φ-factor modifications of Section 9.3.4(a)–(c) are now also applicable to structures that rely on intermediate precast concrete structural walls to resist earthquake effects in seismic design categories (SDC) D, E, or F. Previously, the modifications applied only to structures that rely on special moment frames or special structural walls to resist earthquake effects. A–2

The first paragraph of Section R9.3.4 of ACI 318-05 has been eliminated. In Section R9.4, it is clarified that the maximum specified yield strength of nonprestressed reinforcement fy in Section 21.1.5 is 60,000 psi in special moment frames and special structural walls. “For a compression member with a cross section larger than required by considerations of loading,” Section 10.8.4 permits the minimum reinforcement to be based on a reduced effective area Ag not less than one-half the total area. ACI 318-05 previously stated that the provision does not apply in regions of high seismic risk. ACI 318-08 now states that this provision does “not apply to special moment frames or special structural walls designed in accordance with Chapter 21.” According to Section R14.8.4, “if a slender wall is designed to resist earthquake effects, E, and E is based on strengthlevel seismic forces,” a conservative estimate of service-level seismic forces is 0.7E.

Title The title of the chapter has changed from “Special Provisions for Seismic Design” to “Earthquake-Resistant Structures.” Notation In previous editions of ACI 318, the format was to have all definitions in Chapter 2, with the exception of Chapter 21, which in ACI 318-05 contained definitions. Having definitions in two places is undesirable because there can be problems in updating the definitions consistently. Alternatively, having definitions in Chapter 21 but not Chapter 2 can create difficulties locating definitions. Thus, all definitions have been transferred from Chapter 21 to Chapter 2. In addition to the transfer, a few of the definitions have been modified. Detailing requirements by seismic design category ACI Committee 318 originally developed seismic design provisions for regions of high seismic risk. The design provisions were placed in Appendix A in earlier versions of ACI 318 and subsequently in Chapter 21. Provisions for regions of moderate seismic risk were added later. It has always been understood among the users of ACI 318 that the body of the document, excluding Chapter 21, provides design and detailing requirements for regions of low seismic risk. As long as the model building codes divided the United States into Seismic Zones 0 through 4, and seismic detailing requirements were triggered by seismic zones, it was relatively easy for the practicing engineer to correlate the regions of low, moderate, and high seismic risk of ACI 318 with the Seismic Zones 0 through 4 of the model codes. But then the model building codes started triggering seismic detailing requirements by seismic performance categories, which were a function of the seismic hazard at the site and the occupancy of the structure. The IBC6 now triggers seismic detailing requirements by seismic design catego-

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IMPACT OF ACI 318-08 ON THIS HANDBOOK ries (SDCs) that are additionally functions of the soil characteristics at the site. Thus, in recent times, ACI 318 has used the awkward language: “in regions of low seismic risk or for structures assigned to low seismic performance or design categories,” “in regions of moderate seismic risk or for structures assigned to intermediate seismic performance or design categories,” and “in regions of high seismic risk or for structures assigned to high seismic performance or design categories.” ACI 318-08 has dropped this cumbersome language. Instead, SDCs are now used directly in Section 1.1.9, “Provisions for Earthquake Resistance,” Section 21.1.1, “Scope,” and elsewhere. This is a significant positive development. Because the IBC will no longer have to provide an interface between the SDC and the regions of low, moderate, and high seismic risk of ACI 318, it will be possible to eliminate unnecessary amendments to ACI 318 requirements. More logical organization In ACI 318-05, design and detailing requirements for structures assigned to SDC A and B are located in Chapters 1 through 18. Additional detailing requirements for structures assigned to SDC C are given in Sections 21.12 and 21.13, and those for structures assigned to SDCs D, E, and F are given in Sections 21.2.2 through 21.2.8 and 21.3 through 21.10. This is obviously not the most logical arrangement. In ACI 318-08, seismic detailing requirements have been organized in the order of ascending SDCs. Chapter 21 starts with two new provisions for SDC B structures and the provisions for SDC C structures (commonly referred to as intermediate detailing) follow. Appearing last in Chapter 21 are the provisions for SDC D, E, and F structures (commonly referred to as special detailing). Table A.1 shows the section

APPENDIX number changes that have resulted in Chapter 21 from ACI 318-05 to 318-08. Deliberate use of special A primary use of the term special in Chapter 21 is to define structural systems in which the proportions and details make them suitable as primary lateral-force-resisting systems of structures assigned to high SDCs. However, the term special is also used throughout Chapter 21 of ACI 318-05 for other purposes, sometimes leading to confusion in code usage. Any unnecessary or confusing use of the term special has now been removed from all of Chapter 21, as well as from a few locations in Chapter 1 that refer to seismic design requirements. The term special transverse reinforcement, which refers to the confinement reinforcement within the region of potential plastic hinging at the ends of special-moment-frame columns, has been dropped. Specific changes to Chapter 21 Removal of commentary sentence When the committee was removing the word special, it was noted that the 2003 National Earthquake Hazards Reduction Program (NEHRP) provisions7 and ASCE 7-055 include intermediate precast concrete walls. Consequently, the nolonger-relevant commentary sentence, “Although new provisions are provided in 21.13 for design of intermediate precast structural walls, general building codes that address seismic performance or design categories do not include intermediate structural walls,” has been struck from ACI 318-08 commentary Section R21.1.1 (previously ACI 318-05 commentary Section R21.2.1).

Table A.1  ACI 318-05 and the corresponding ACI 318-08 Chapter 21 section numbers ACI 318-08 section numbers

ACI 318-05 section numbers

All definitions have moved to chapter 2

21.1 Definitions

21.1 General Requirements

21.2 Same title

21.2 Ordinary Moment Frames

Not included

21.3 Intermediate Moment Frames

21.12 Requirements for Intermediate Moment Frames

21.4 Intermediate Precast Structural Walls

21.13 Same title

21.5 Flexural Members of Special Moment Frames

21.3 Same title

21.6 S  pecial Moment-Frame Members Subjected to Bending and Axial Load

21.4 Same title

21.7 Joints of Special Moment Frames

21.5 Same title

21.8 S  pecial Moment Frames Constructed Using Precast Concrete

21.6 Same title

21.9 Special Structural Walls and Coupling Beams

21.7 S  pecial Reinforced Concrete Structural Walls and Coupling Beams

21.10 S  pecial Structural Walls Constructed Using Precast Concrete

21.8 Same title

21.11 Structural Diaphragms and Trusses

21.9 Same title

21.12 Foundations

21.10 Same title

21.13 M  embers Not Designated as Part of the Seismic-ForceResisting System

21.11 M  embers Not Designed as Part of the Lateral-ForceResisting System

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APPENDIX High-strength transverse reinforcement

  A

Section 21.2.5 of ACI 318-05 introduced a sentence that limits the yield strength of transverse reinforcement, including spirals, to 60,000 psi. The added sentence was part of a change that modified ACI 318-02 Sections 9.4 and 10.9.3 to allow the use of spiral reinforcement with specified yield strength up to 100 ksi. The added sentence specifically prohibits such use in members resisting earthquake-induced forces in structures assigned to SDC D, E, or F. This was largely a result of some misgiving that high-strength spiral reinforcement might be less ductile than conventional mild reinforcement and that spiral failure has been observed in earthquakes. There are fairly convincing arguments, however, against such specific prohibition. Spiral failure, primarily observed in bridge columns, has invariably been the result of insufficient spiral reinforcement. Also, prestressing steel, which is primarily the high-strength steel available on the U.S. market, is at least as ductile as welded-wire reinforcement, which is allowed to be used as transverse reinforcement. Under 2006 IBC Section 1908.1.5, the applicability of the ACI 318-05 restriction “The value of fyt for transverse reinforcement including spiral reinforcement shall not exceed 60,000 psi” is narrowed by the clause “for computing shear strength” in front of the requirement. Two of the functions of transverse reinforcement in a reinforcement concrete member are to confine the concrete and to act as shear reinforcement. There has been enough testing of columns8-10 with high-strength confinement reinforcement (fyt ranging up to 120 ksi and beyond) to show that there is no detriment to such use. The 2006 IBC, therefore, uses the ACI 318-05 upper limit on the yield strength of transverse reinforcement solely to limit the width of possible shear cracks to acceptable levels. This does not preclude the use of highstrength transverse reinforcement for confining the core of a concrete member. During discussion of this item within ACI 318 Subcommittee, H, Budek11 introduced research results that showed equivalent shear and confinement performance of 18-in.diameter columns with transverse reinforcement having roughly 200 ksi yield strength. Section 21.1.5.4 of ACI 318-08 now states, “The value of fyt used to compute the amount of confinement reinforcement shall not exceed 100,000 psi.” Section 21.5.5.5 of ACI 318-08 now states, “The value of fy or fyt used in design of shear reinforcement shall conform to 11.4.2.” Section 11.4.2 reads, “The values of fy and fyt used in design of shear reinforcement shall not exceed 60,000 psi, except the value shall not exceed 80,000 psi for welded deformed wire reinforcement.” Thus, unlike the 2006 IBC, ACI 318-08 imposes an upper limit of 100 ksi on the yield strength of high-strength confinement reinforcement in members resisting earthquake-induced forces in structures assigned to SDC D, E, or F. Also, ACI 318-08 requires such transverse reinforcement to conform to ASTM A1035.12 Section 3.5.3.1 requires deformed reinforcA–4

ing bars to conform to ASTM A61513 (carbon steel), ASTM A70614 (low-alloy steel), and ASTM A95515 (stainless steel). Ordinary moment frames Section 21.2, for the first time, contains specific detailing requirements for ordinary moment frames in buildings assigned to SDC B. Both SDC A and SDC B fall under the old designation of low seismic risk. Structures assigned to SDC A are required to satisfy Chapters 1 through 18 and Chapter 22 of ACI 318. Frames in buildings assigned to SDC B are required in both the 2003 NEHRP provisions7 and ASCE 7-055 to satisfy additional requirements. The additional requirements of ASCE 7-05 are: •

•

“In structures assigned to SDC B, flexural members of ordinary moment frames forming part of the seismic force-resisting system shall have at least two main flexural reinforcing bars continuously top and bottom throughout the beams through or developed within exterior columns or boundary elements.” “In structures assigned to SDC B, columns of ordinary moment frames having a clear height-to-maximumplan-dimension ratio of five or less shall be designed for shear in accordance with ACI 318-05 Section 21.12.3 (ACI 318-08 Section 21.3.3).”

Intermediate moment frames There are important changes in Section 21.3, “Intermediate Moment Frames.” Intermediate moment frames include beam-column as well as slab-column moment frames. When the requirements for intermediate moment frames were introduced in ACI 318-83, shear design requirements for beamcolumn and slab-column frames were grouped (Section 21.12.3 of ACI 318-05). However, it was never intended that nominal shear stresses due to shear and moment transfer in two-way slab-column frames be treated the same as beam shear in beam-column frames or one-way shear in two-way slabs, though the provisions appear to indicate such. The provisions of former Section 21.12.3 constrained slab-column designs in a way that was not intended and that was not supported by observations in laboratory tests. Analyses of laboratory tests11 indicate that the ductility or inelastic deformability of slab-column framing is better judged on the basis of the level of gravity shear stress and the presence of slab shear reinforcement. This has been recognized for gravity framing of buildings assigned to high SDCs (Section 21.13.6) and slab-column intermediate frames (Section 21.3.6.8). The purpose of a significant change to Section 21.3.6.8 is to clarify that the nominal shear stresses due to shear and moment transfer in two-way slabs do not need to satisfy the requirements of Section 21.3.3, but instead only need to satisfy the requirements of Section 21.3.6.8. In addition, Section 21.3.6.8 has been modified to make it more consistent with current understanding of the relationship between earthquake demands and strengths, as reflected in Section 21.13.6. ACI 318-05 permits the value of eccentric shear stress to reach

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IMPACT OF ACI 318-08 ON THIS HANDBOOK φVn for design load combinations including E, as long as the contribution of E does not exceed 0.5φVn. Considering that E is the linear earthquake action divided by a force-reduction factor R, ACI 318-05 is believed to permit unsafe levels of nominal shear stresses. A modification eliminates this provision in ACI 318-08 and replaces it with a more rational one. Specifically, in Section 21.3.6.8 (formerly Section 21.12.6.8), the second sentence has been changed from “It shall be permitted to waive this requirement if the contribution of the earthquakeinduced factored two-way shear stress transferred by eccentricity of shear in accordance with 11.12.6.1 and 11.12.6.2 at the point of maximum stress does not exceed one-half of the stress φVn permitted by 11.12.6.2” to “It shall be permitted to waive this requirement if the slab design satisfies requirements of 21.13.6.” Columns supporting discontinued shear walls Discontinuous shear walls and other stiff members can impose large axial forces on supporting columns during earthquakes. Section 21.4.4.5 of ACI 318-05 contains transverse reinforcement requirements for such columns in order to improve column toughness under anticipated demands. The requirements are triggered when “the factored axial compressive force in these members, related to earthquake effect, exceeds Ag f 'c /10.” The same requirements continue in Section 21.6.4.6 of ACI 318-08. However, the trigger has been adjusted by adding the following sentence: “Where design forces have been magnified to account for the overstrength of the vertical elements of the seismic-force-resisting system, the limit of Ag f 'c/10 shall be changed to Ag f 'c/4.” While Section 21.6.4.6 applies to columns of special moment frames, ACI 318-08 has added corresponding requirements for columns of intermediate moment frames. Section 21.3.5.6 requires the following: Columns supporting reactions from discontinuous stiff members, such as walls, shall be provided with transverse reinforcement at the spacing, s0, as defined in 21.3.5.2 over the full height beneath the level at which the discontinuity occurs if the portion of factored axial compressive force in these members related to earthquake effects exceeds Ag f 'c /10. Where design forces have been magnified to account for the overstrength of the vertical elements of the seismic-force-resisting system, the limit Ag f 'c /10 shall be increased to Ag f 'c /4. This transverse reinforcement shall extend above and below the columns as required in 21.6.4.6(b). It should be noted that the confinement that Section 21.3.5.6 requires is considerably less than that required by Section 21.6.4.6. Also, the 2006 IBC section 1908.1.12 modifies ACI 318-05 Section 21.12.5 to introduce a provision similar to that of ACI 318-08 Section 21.3.5.6. Beams and joints of special moment frames Changes have been made to Sections 21.5, “Flexural Members of Special Moment Frames,” and 21.7, “Joints of Special Moment Frames,” to clarify maximum beam width, joint confinement requirements, and design rules for joints having

APPENDIX beam stubs extending a short distance past the joint. Research16 has shown that the effective beam width is more closely related to the depth of the column than it is to the depth of the beam. A recommendation based on the column widths and beam widths tested to date has been adopted. Research17 has also indicated that extensions of beams (beam stubs) that project a short distance past the joint can also be considered as confining members to joints if they extend at least one effective depth beyond the joint face and meet the dimensional and reinforcement requirements for full flexural members. A change has been made to recognize this effect. Section 21.5.1.4 now reads, “Width of member, bw, shall not exceed width of supporting member, c2, plus a distance on each side of supporting member equal to the smaller of (a) and (b): (a) width of supporting member, c2, and (b) 0.75 times the overall dimension of supporting member, c1.” In ACI 318-05 it reads, “plus distances on each side of supporting member not exceeding three fourths of the depth of flexural member.” Sections 21.7.3.1, 21.7.3.2, and 21.7.3.3 on transverse reinforcement within beam-column joints of special moment frames has been rewritten for added clarity. Section 21.7.3.3, in particular, represents a major improvement. In ACI 318-05 it reads, “Transverse reinforcement as required by 21.4.4 (now 21.6.4) shall be provided through the joint to provide confinement for longitudinal beam reinforcement outside the column core if such confinement is not provided by a beam framing into the joint.” It now reads, “Longitudinal beam reinforcement outside the column core shall be confined by transverse reinforcement passing through the column that satisfies spacing requirements of 21.5.3.2, and requirements of 21.5.3.3 and 21.5.3.6, if such confinement is not provided by a beam framing into the joint.” An example of transverse reinforcement through the column provided to confine the beam reinforcement passing outside the column core is now shown in Fig. R21.5.1. This figure is a welcome addition (Fig. A.1). Finally, the following text has been added to Section 21.7.4.1: “Extensions of beams at least one overall beam thickness h beyond the joint face are permitted to be considered as confining members. Extensions of beams shall satisfy 21.5.1.3, 21.5.2.1, 21.5.3.2, 21.5.3.3, and 21.5.3.6.” Columns of special moment frames Significant changes have been made to Section 21.6.4 to improve the organization and expression of transverse reinforcement requirements for columns in special moment frames, as well as to eliminate one provision. The provisions of Section 21.6 are intended to apply to a column of a special moment frame for all load combinations if, for any load combination, the axial load exceeds Ag f 'c /10. The wording in ACI 318-05 is often misinterpreted as meaning that the provisions applied only for those load combinations for

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APPENDIX

• •

forcement be determined using (a) or (b) but does not require that (c), (d), and (e) always be satisfied. The term design strength of the member core is used in ACI 318-05 in Section 21.4.4.1(d), but that terminology is not well defined. ACI 318-05 Section 21.4.4 uses both bc and Ash to determine the required amount of special transverse requirement. However, bc is based on center-to-center dimensions and Ash is based on the out-to-out dimensions of the hoop. To make it easier for the user, these items have been made consistent. In Section 2.1 of ACI 318-08, both Ash and bc are “measured to the outside edges of transverse reinforcement.” This amounts to a small increase in Ash on the order of 2% to 3%.

Additional deliberations within ACI 318 Subcommittee H have led to additional changes, including: • •

  A

•

Fig. A.1 Maximum effective width of wide beam and required transverse reinforcement. Source: Reprinted by permission from Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R-08) (Farmington Hills, MI: ACI, 2008) p. 334, Figure R21.5.1.

which the axial load exceeded Ag f 'c/10. Thus, Section 21.6.1 of ACI 318-08 has been modified to read, “Requirements of this section apply to special moment frame members…that resist a factored axial compressive force Pu under any load combination exceeding Ag f 'c/10.” (emphasis added) Several areas for potential improvement of ACI 318-05 provisions related to columns of special moment-resisting frames were first identified by ACI 318 Subcommittee H-Seismic Provisions. These included the following: •

A–6

The items listed as (a) through (e) in ACI 318-05 Section 21.4.4.1 are not expressed in parallel language. ACI 318-05 requires that the area of transverse rein-

removing the terminology “special transverse reinforcement” to refer to the confinement reinforcement within the length lo of the column; eliminating ACI 318-05 Section 21.4.4.1(d), which allows the design of columns with less than the specified confinement reinforcement, if the column core satisfies design requirements; allowing crossties of diameter less than that of the hoops (Section 21.6.4.2).

ACI 318-05 Section 21.4.4 has been replaced with the new ACI 318-08 Section 21.6.4. The revision is outlined in Table A.2. Note that the revised Section 21.6.4 is made up of parts of ACI 318-05 Section 21.4.4, with some revisions and some reorganization. A two-sentence paragraph has been added to Section R21.6.4.4. “Equations (21-4) and (21-5) are to be satisfied in both cross-sectional directions of the rectangular core. For each direction, bc is the core dimension perpendicular to the tie legs that constitute Ash, as shown in Fig. R21.6.4.2 [Fig. A.2].” This figure replaces ACI 318-05 Fig. R21.4.4 and represents a significant improvement. Finally, the following sentence has been deleted from the commentary of ACI 318-05 Section 21.4.4.6 (now 21.6.4.5). “Field observations have shown significant damage to columns in the unconfined region near the midheight. The requirements of 21.4.4.6 are to ensure a relatively uniform toughness of the column along its length.” Special moment frames made with precast concrete A change has been made to commentary Section R21.8.4 to alert designers to ACI ITG-1.2,18 which provides an option to satisfy the provisions of Section 21.1.1.8. ACI 374.119 provides for the development of precast concrete special moment frames that can meet the requirements of Section 21.1.1.8. ACI ITG-1.2 is an industry standard that defines requirements, in addition to those of Section 21.8.4, for the design of one specific type of moment frame that con-

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APPENDIX

Table A.2  Reorganization of ACI 318-5 Section 21.4.4 into ACI 318-08 Section 21.6.4 ACI 318-08 section numbers

Consecutive crossties engaging the same longitudinal bar have their 90-degree hooks on opposite sides of column

ACI 318-05 section numbers

21.6.4.4

21.4.4.1

No change

21.4.4.1(a)

No change

21.4.4.1(b)

21.6.4.2

21.4.4.1(c)

Deleted

21.4.4.1(d)

21.6.4.7

21.4.4.1(e)

21.6.4.3

21.4.4.2

21.6.4.2

21.4.4.3

21.6.4.2

21.4.4.4

21.6.4.6

21.4.4.5

21.6.4.5

21.4.4.6

Eq. (21-3)

Eq. (21-2)

Eq. (21-4)

Eq. (21-3)

Eq. (21-5)

Eq. (21-4)

Eq. (21-2)

Eq. (21-5)

sists of precast concrete beams post-tensioned to precast or cast-in-place concrete columns. The columns are continuous through the joints, and each beam spans a single bay. The hybrid beam-to-column connection uses a system of post-tensioning strands that run through a duct at the center of the beam and through the column. Mild-steel reinforcement is placed in ducts in the center of the beam and through the column, and then grouted. A key feature of the hybrid frame connection is that the grouted mild reinforcing bars must be deliberately debonded for short distances in the beams adjacent to the beam-column interfaces in order to reduce the high cyclic strains that would otherwise occur at those locations. The amount of mild-steel reinforcement and post-tensioning steel are proportioned so that the frame recenters itself after a major seismic event. The University of Washington test results for the Third and Mission building in San Francisco, Calif., and the Precast Seismic Structural Systems (PRESSS) building test results for the frame direction can be used as a basis for special precast concrete hybrid moment frame designs in accordance with ITG-1.2. The results of the University of Washington tests are on file at ACI in conjunction with ITG-1.2. The results of the PRESSS building frame direction tests are available in a series of reports from PCI. The following sentence has been added at the end of section R21.8.4. “ACI ITG 1.2 defines design requirements for one type of special precast concrete moment frame for use in accordance with 21.8.4.” ACI ITG-1.2 has also been added to the Chapter 21 commentary reference list. Boundary elements of special shear walls Section 21.9.6.4 (c) has been changed to permit increased

6db extension 6db ≥ 3 in.

Ash2

xi bc2 xi Ash1 xi

xi

xi

bc1 The dimension xi from centerline to centerline of tie legs is not to exceed 14 inches. The term hx used in equation 21-2 is taken as the largest value of xi.

Fig. A.2 This is an example of transverse reinforcement in columns. Source: Reprinted by permission from Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R-08) (Farmington Hills, MI: ACI, 2008) p. 341, Figure R21.6.4.2.

spacing of transverse reinforcement in the boundary elements of walls with relatively thin boundary zones. ACI 318-05 Section 21.7.6.4(c) requires special boundary elements to satisfy ACI 318-05 Section 21.4.4.2, which limits the spacing of transverse reinforcement to no more than one quarter of the minimum member dimension. This was an unintended consequence of referring the wall transverse reinforcement requirements to those of columns of special moment frames. For a 12-in.-thick wall, the spacing requirements could not exceed 3 in. The Uniform Building Code,20 in its last two editions, relaxed the maximum spacing to the smaller of 6 in. and 6 times the longitudinal bar diameter, regardless of wall thickness. Wall specimens tested by Thomsen and Wallace21 included rectangular walls RW1 and RW2 with boundary transverse reinforcement spaced at three quarters of the wall thickness. The walls had lateral drift capacities in excess of 2% of the wall height. Section 21.9.6.4(c) now reads, “The boundary element transverse reinforcement shall satisfy the requirements of 21.6.4.2 through 21.6.4.4 except Eq. (21-4) need not be satisfied and the transverse reinforcement spacing limit of 21.6.4.3(a) shall be one-third of the least dimension of the boundary element.” A sentence has been added at the end of Section R21.9.6.4 that reads, “Tests show that adequate performance can be achieved using spacing larger than permitted by 21.6.4.3(a).”

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APPENDIX Table A.3  Coupling beam detailing requirements of ACI 318-08

ACI 318-08 section 21.9.7.1

21.9.7.3

21.9.7.2

Conditions

(ln /h) > 4, no limit on Vu

(ln /h) < 4, no limit on Vu

(ln /h) < 2 and Vu > 4 fc' Acw

Conventional reinforcement per ACI 318-08 Section 21.5

Required*

Not mentioned†

Not permitted

Diagonal reinforcement per ACI 318-08 Section 21.9.7.4

Not permitted

Permitted

Required

*The provisions of Sections 21.5.1.3 and 21.5.1.4 need not be satisfied if it can be shown that the beam has adequate lateral stability. † Only Sections 21.5.2 through 21.5.4 need be satisfied. Note: Acw = area of concrete section of an individual pier, horizontal wall segment, or coupling beam resisting shear; fc' = design compressive strength of concrete; h = overall thickness or height of member; ln = length of clear span measured face to face of supports; Vn = nominal shear strength; Vu = factored shear force at section.

Table A.4  Coupling beam detailing requirements of ACI 318-05 ACI 318-05 section 21.7.7.1

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21.7.7.2

21.7.7.3

Conditions

(ln /h) > 4, no limit on Vu

(ln /h) < 4, no limit on Vu

(ln /h) < 2 and Vu > 4 fc' Acw

Conventional reinforcement per ACI 318-05 Section 21.3

Required

Not mentioned

Not permitted

Diagonal reinforcement per ACI 318-05 Section 21.7.7.4

Not permitted

Permitted

Required

Note: Acw = area of concrete section of an individual pier, horizontal wall segment, or coupling beam resisting shear; fc' = design compressive strength of concrete; h = overall thickness or height of member; ln = length of clear span measured face to face of supports; Vn = nominal shear strength; Vu = factored shear force at section.

The Thomsen and Wallace paper21 has also been added to the Chapter 21 commentary reference list. Coupling beams In Section 21.9.7, a clarification has been provided that the provisions of Sections 21.5.2 through 21.5.4 can be applied to coupling beams of moderate aspect ratios (2 ≤ ln /h < 4). Conventional reinforcing details for coupling beams with moderate aspect ratios (2 ≤ ln /h < 4) have at times been disallowed by building departments, even though the intent of ACI 318 has always been to allow these details. The ACI 318-08 provisions for coupling beams that are part of the lateral-force-resisting system are summarized in Table A.3. It should be evident from Table A.3 that ACI 318 was inadvertently silent on the issue of whether conventional reinforcement could be used in beams with 2 ≤ ln /h < 4. ACI 318-05 Section 21.7.7.2 reads, “Coupling beams with (ln /h) < 4 shall be permitted to be reinforced with two intersecting groups of diagonally placed bars symmetrical about the midspan.” ACI 318-08 Section 21.9.7.3 now reads, “Coupling beams not governed by 21.9.7.1 or 21.9.7.2 shall be permitted to be reinforced either with two intersecting groups of diagonally placed bars symmetrical about the midspan or according to 21.5.2 through 21.5.4.” Significant changes have been made to Section 21.9.7 to A–8

relax the spacing requirements for transverse reinforcement confining diagonal reinforcement in coupling beams and to introduce an alternate detail involving confinement of the entire beam cross section (Fig. A.3). ACI 318-99 first introduced diagonal reinforcement in coupling beams. Among its provisions was the requirement that spacing not exceed one quarter of the minimum member dimension. For diagonally reinforced coupling beams, this dimension is defined as the cross section of the diagonal cage (out to out) plus nominal cover. This may result in a spacing as low as 2 in. in practical situations. This appears to be unnecessarily restrictive. Andres Lapage carried out a brief review of available diagonally reinforced coupling beam test results for the benefit of subcommittee H. Paulay and Binney22 had tested a 6 in. × 31 in. coupling beam with a span-to-depth ratio of 1.3 and a 6 in. × 39 in. beam with a span-to-depth ratio of 1.0. The spacing of transverse reinforcement around the diagonal reinforcement in both beams was 4 in. 4.6db, bw /1.5, and d1 /1.0. Tassios et al.23 have tested a 5 in. × 20 in. coupling beam with a span-to-depth ratio of 1.0 and a 5 in. × 12 in. beam with a span-to-depth ratio of 1.7. The spacing of transverse reinforcement around the diagonal reinforcement was 2 in. 5.0db, bw /2.5, and d1 /1.3. Setting aside the difference in loading protocol, all four specimens exhibited negligible strength degradation up to total rotations of 5%.

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Note: For clarity, only part of the required reinforcement is shown on each side of the line of symmetry.

Line of symmetry

A Horizontal beam reinforcement at wall does not develop fy

APPENDIX

Transverse reinforcement spacing measured perpendicular to the axis of the diagonal bars not to exceed 14 in.

Avd = total area of reinforcement in each group of diagonal bars α

h

≥ bw /2

Wall boundary reinforcement

A

bw

n

Elevation

Section A-A (a) Confinement of individual diagonals. Note: For clarity in the elevation view, only part of the total required reinforcement is shown on each side of the line of symmetry.

Horizontal beam reinforcement at wall does not develop fy

Note: For clarity, only part of the required reinforcement is shown on each side of the line of symmetry.

B Line of symmetry

Spacing not exceeding smaller of 6 in. and 6db

 

A

Transverse reinforcement spacing not to exceed 8 in.

Avd = total area of reinforcement in each group of diagonal bars α

h db

B

Transverse reinforcement spacing not to exceed 8 in.

Wall boundary reinforcement n

Elevation

Section B-B Note: Consecutive crossties engaging the same logitudinal bar have their 90-degree hooks on opposite sides of beam.

(b) Full confinement of diagonally oriented reinforcement. Wall reinforcement shown on one side only for clarity.

Fig. A.3. Coupling beams are shown with diagonally oriented reinforcement. Wall boundary reinforcement is shown on one side only for clarity. Source: Reprinted by permission from Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R-08) (Farmington Hills, MI: ACI, 2008) p. 355, Figure R21.9.7.

Galano and Vignoli24 had tested two 6 in. × 16 in. coupling beams with a span-to-depth ratio of 1.5. The spacing of transverse reinforcement around the diagonal reinforcement was 4 in., 10db, bw /1.5, and d1 /1.3. These specimens experienced buckling of the diagonal reinforcement at total rotations below 3%. It should be emphasized that the transverse reinforcement around the diagonal was spaced at 10db.

The results suggest that the transverse reinforcement around the diagonals need not be spaced at one quarter the minimum dimension of the confined section as long as the spacing does not exceed 6db. Thus some relaxation of the spacing requirement appears to be justified. See ACI 318-08 Section 21.9.7.4(c) for such relaxation.

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APPENDIX ACI 318 Subcommittee H also explored whether confinement of the entire beam section might be a suitable alternative. Examples of this detailing in practice were identified. It was noted that this was the approach used successfully in early PCA tests.25 This alternative detailing approach has now been incorporated into ACI 318-08 (see Section 21.9.7.4[d]). The organization and presentation of Section 21.9.7 have improved. Also, because the bars are diagonal (not longitudinal), and flexural reinforcement is not present, some sections that had been called out in earlier editions of ACI 318 were not strictly correct. These have been corrected. The following important commentary has been added to Section R21.9.7:

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Diagonal bars should be placed approximately symmetrically in the beam cross section, in two or more layers. The diagonally placed bars are intended to provide the entire shear and corresponding moment strength of the beam; designs deriving their moment strength from combinations of diagonal and longitudinal bars are not covered by these provisions. Two confinement options are described. The first option is found in Section 21.9.7.4(c). This option is not needed but revisions have been made in the 2008 Code to relax spacing of transverse reinforcement confining the diagonal bars, to clarify that confinement is required at the intersection of the diagonals, and to simplify design of the longitudinal and transverse reinforcement around the beam perimeter; beams with these revised details are expected to perform acceptably. Section 21.9.7.4(d) describes a second option for confinement of the diagonals introduced in ACI 318-08 (Figure R21.9.7(b)). This second option is to confine the entire beam cross section instead of confining the individual diagonals. This option can considerably simplify field placement of hoops, which can otherwise be especially challenging where diagonal bars intersect each other or enter the wall boundary. Special structural walls made with precast concrete A change made to Section 21.10 now allows the use of unbonded, post-tensioned precast concrete walls, coupled or uncoupled, as special structural walls, provided that the requirements of ACI ITG-5.126 are satisfied. Testing and analysis27-29 have shown that, with appropriate limitations, unbonded post-tensioned precast concrete walls, coupled or uncoupled, can exhibit seismic performance equal to or better than that of cast-in-place special reinforced concrete shear walls. ITG-5.1 defines the protocol necessary to establish a design procedure, validated by analysis and laboratory tests, for such precast concrete walls. Provided that the requirements of ITG-5.1 are satisfied, the requirements of Section 21.1.1.8 that such walls must “have strength and toughness equal to or exceeding those provided by a comparable monolithic reinforced concrete structure satisfying the chapter” are met. Since 2002, ACI 318 has permitted in Section 21.8.3 (previously 21.6.3) the use of special moment frames constructed A–10

using precast concrete, provided those frames met the requirements of ACI 374.1.19 The object of the recent change to Section 21.10 is to allow, in a similar manner, through a systematic program of analysis and laboratory testing, the use of one type of special precast concrete structural walls. For special precast concrete moment frames, Section 21.8.3 also contains two requirements related to the details and materials used in test specimens and the design procedure used to proportion test specimens. For walls, those latter two requirements are not needed because they are specifically included in ITG-5.1. The ITG-5.1 document has been adopted in Section 3.8.10 of ACI 318-08. Section 21.10.3 now reads, “Special structural walls constructed using precast concrete and unbonded post-tensioning tendons and not satisfying the requirements of 21.10.2 are permitted provided they satisfy the requirements of ACI ITG-5.1.” A new commentary section R21.10.3 has also been added. Structural diaphragms and trusses Terminology and design requirements for diaphragms and trusses have been updated through changes in Sections 21.1, “Definitions,” and 21.11, “Structural Diaphragms and Trusses.” ACI 318-05 Sections 21.9.2 and 21.9.3, as written, implies that a complete transfer of forces is required only for composite-topping slab diaphragms, not for non-composite diaphragms. A new Section, 21.11.3, has been added to clarify that this is required for all diaphragms. Structural trusses are separated from diaphragms because requirements differ and separating them clarifies the requirements. In Sections 21.1, in the definition of boundary elements, any reference to diaphragms has been eliminated. Boundary elements are now for structural walls only. The definition of collector element has been revised to “Element that acts in axial tension or compression to transmit seismic forces within a structural diaphragm or between a structural diaphragm and a vertical element of the lateralforce-resisting system.” The definition of structural diaphragm has been revised to clarify that it transmits forces to “the vertical elements of the lateral-force-resisting system,” rather than to “lateral-forceresisting members.” The definitions of strut and tie elements have been deleted. Section 21.11.2, “Design Forces,” which is new in ACI 318-08, reads, “The earthquake design forces for structural diaphragms shall be obtained from the legally adopted general building code using the applicable provisions and load combinations.” New Section 21.11.3, “Seismic Load Path,” reads: 21.11.3.1—All diaphragms and their connections shall be proportioned and detailed to provide for a complete transfer of forces to collector elements and to the vertical elements of the lateral-force-resisting system. 21.11.3.2—Elements of a structural diaphragm system that are subjected primarily to axial forces and used to transfer diaphragm shear or flexural forces around openings or other discontinuities, shall comply with the requirements

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IMPACT OF ACI 318-08 ON THIS HANDBOOK for collectors in 21.11.7.5 and 21.11.7.6. Any reference to continuous load path has been eliminated from Section 21.11.4, “Cast-in-Place Composite-Topping Slab Diaphragm,” because the topic is now covered in Section 21.11.3. Section 21.11.7.2 has been changed for clarity to “Bonded tendons used as reinforcement to resist collector forces or diaphragm shear or flexural tension.” Section 21.11.7.3 now reads, “All reinforcement used to resist collector forces, diaphragm shear, or flexural tension.” References to structural truss elements, struts, ties, and diaphragm chords have been eliminated from Section 21.11.7.5. The former Sections 21.9.8.1 and 21.9.8.2 have now been replaced by Section 21.11.8, “Flexural Strength,” which reads, “Diaphragms and portions of diaphragms shall be designed for flexure in accordance with 10.2 and 10.3 except that the nonlinear distribution of strain requirements of 10.2.2 for deep beams need not apply. The effects of openings shall be considered.” This is an important change because flexure is no longer supposed to be resisted by the boundary element reinforcement only, as is implied in earlier editions of ACI 318. The new Section 21.11.11, “Structural Trusses,” now reads: 21.11.11.1—Structural truss elements with compressive stresses exceeding 0.2 at any section shall have transverse reinforcement, as given in 21.6.4.2 through 21.6.4.4 and 21.6.4.7, over the length of the element. 21.11.11.2—All continuous reinforcement in structural truss elements shall be developed or spliced for fy in tension. A new commentary Section in R21.11.2 has been added. There are other significant additions to and deletions from the commentary on Section 21.11. Notable among these are the additions to Section R21.11.8. Diaphragm shear strength Studies of precast concrete parking structures following the 1994 Northridge earthquake30 indicate that composite topping slab diaphragms depend on shear friction to transmit inertial forces to the vertical elements of the lateral-forceresisting system. The results of this research were used to develop ACI 318-05 Eq. (21-11) and are summarized in ACI 318-05 commentary Section R21.9.7. However, ACI 318-05 Eq. (21-11) referred to distributed transverse reinforcement within the diaphragm (for consistency with ACI 318-05 Eq. [21-10]) rather than to distributed longitudinal reinforcement. When the provisions in ACI 318-05 Section 21.9.7.2 were originally developed, it was assumed that the sentence “The required web reinforcement should be distributed uniformly in both directions” was sufficient to ensure that the same amount of reinforcement be used in both the longitudinal and the transverse directions. There were subsequent indications that clarification was needed. ACI 318-05 Section 21.9.7.3 (now 21.11.9.3) has been revised to directly refer to shear friction reinforcement. Both

APPENDIX boundary and distributed reinforcement in the topping slab are assumed to contribute to the shear strength of the topping slab diaphragm, but connectors between the precast concrete elements are not included at this time. Section 21.11.9.1 (formerly 21.9.7.1) has added the following text below Eq. (21-10): “For cast-in-place topping slab diaphragms on precast floor or roof members, Acv shall be computed using the thickness of topping slab only for non-composite topping slab diaphragms and the combined thickness of cast-in-place and precast elements for composite topping slab diaphragms. For composite topping slab diaphragms, the value of f 'c used to determine Vn shall not exceed the smaller of f 'c for the precast members and f 'cfor the topping slab.” Sections 21.11.9.3 and 21.11.9.4 now read: 2 1.11.9.3—Above joints between precast elements in non-composite and composite cast-in-place topping slab diaphragms, Vn shall not exceed Vn = Avf fy µ



where Avf is total area of shear friction reinforcement within topping slab, including both distributed and boundary reinforcement, that is oriented perpendicular to joints in the precast system and coefficient of friction, µ, is 1.0λ where λ is given in 11.6.4.3. At least one-half of Avf shall be uniformly distributed along the length of the potential shear plane. Area of distributed reinforcement in topping slab shall satisfy 7.12.2.1 in each direction. 21.11.9.4—Above joints between precast elements in non-composite and composite cast-in-place topping slab diaphragms, Vn shall not exceed the limits in 11.6.5 where Ac is computed using the thickness of the topping slab only. Commentary Section R21.9.7 has been modified to explain the changes. Gravity columns An error has been corrected in Section 21.13, “Members Not Designated as Part of the Seismic-Force-Resisting System.” Consider the case of a gravity column where the effects of design displacements are not explicitly checked and the member has axial load exceeding Ag f 'c /10. According to ACI 318-05 Section 21.11.3.3, the member need not satisfy ACI 318-05 Section 21.4.3.2 and, therefore, the column lap splice might be located at the base of the column. However, if the effects of the design displacements were checked, then according to ACI 318-05 Section 21.11.2.2, the member must satisfy ACI 318-05 Section 21.4.3.2 and the location of the column splice must be within the center of the column length. In other words, if a gravity column might yield under the design displacements, the designer could splice the longitudinal reinforcement at any location, but if the column was not expected to yield, the splice has to be located near midheight. This does not make sense.

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APPENDIX This flaw traced back to ACI 318-95. Before the 1995 edition, lap-splice locations were not prescribed for members that were not proportioned to resist forces induced by earthquake motions. The flaw has been corrected in ACI 318-08. ACI 318-05 Section 21.11.2.2 requires members with factored gravity axial forces exceeding Ag f 'c /10 to satisfy Sections 21.4.3, 21.4.4.1(c), 21.4.4.3 and 21.4.5. ACI 318-08 Section 21.13.3.2 now requires such columns to satisfy Sections 21.6.3.1, 21.6.4.2, and 21.6.5. ACI 318-05 Section 21.11.3.3 requires members with factored gravity axial forces exceeding Ag/10 to satisfy Sections 21.4.3.1, 21.4.4, 21.4.5, and 21.5.2.1. ACI 318-08 Section 21.13.4.3 now requires such columns to satisfy Sections 21.6.3, 21.6.4, 21.6.5, and 21.7.3.1. Structural Integrity Related:

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In Section 7.13, “Requirements for Structural Integrity,” changes have been made to the anchorage and splice requirements for structural integrity reinforcement. Continuous top and bottom structural reinforcement is now required to pass through the column core. Also, the types of transverse reinforcement used to enclose structural integrity reinforcement in perimeter beams are more clearly specified. A new Section 12.1.3 has been added. The section specifically calls designers’ attention to the structural-integrity requirements in Section 7.13. There has been concern within ACI Committee 318 that many designers were simply not aware of these requirements, though they have existed since the 1989 edition of ACI 318.

Chapter 5 – Design of Precast and Prestressed Concrete Components In Section 9.3.2.2, the strength-reduction factor φ for spirally reinforced columns has been increased from 0.70 to 0.75. Commentary Section R9.3.2 notes that this increase is partly due to the superior performance of spirally reinforced columns when subjected to excessive loads or extreme excitations31 and is partly due to new reliability analyses.32 In Section 9.3.5, the φ factor for plain concrete has been increased from 0.55 to 0.60. As stated in commentary Section R9.3.5, this is partly due to recent reliability analysis and a statistical study of concrete properties.33 The most significant change in Chapter 10 is a rewriting of Sections 10.10 through 10.13 of ACI 318-05 into the new Section 10.10, “Slenderness Effects in Compression Members.” The slenderness provisions are reorganized to reflect “current practice where second-order effects are considered primarily using computer analysis techniques,” while the style of presentation used by ACI 318 since 1971 is retained. The moment magnifier method is also retained as an alternate procedure. Section 10.10.1 permits slenderness effects to be neglected “for compression members not braced against sidesway

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when: k u ≤ 22 in. 4

and “for compression members braced against sidesway when:

⎛M ⎞ k u ≤ 34 − 12 ⎜ 1 ⎟ ≤ 40 in. ⎝ M2 ⎠ r where k = effective length factor lu = unsupported length The font r = radius of gyration M1 = smaller factored end moment M2 = larger factored end moment M1/M2 = positive if a compression member is bent in single curvature A new feature permits a compression member to be considered braced against sidesway when “bracing elements have a total stiffness, resisting lateral movement of that story, of at least 12 times the gross stiffness of the columns within the story.” Section 10.10.2 requires that when slenderness effects are not neglected as permitted by Section 10.10.1, “the design of compression members, restraining beams, and other supporting members be based on the factored forces and moments from a second-order analysis satisfying [Section] 10.10.3, 10.10.4, or 10.10.5.” Section 10.10.3 is titled “Nonlinear Second-Order Analysis,” Section 10.10.4 contains requirements for elastic second-order analysis, and Section 10.10.5 details moment magnification procedure. The members being discussed are also required to satisfy Sections 10.10.2.1 and 10.10.2.2. Section 10.10.2.1 requires that second-order effects in compression members, restraining beams, or other structural members not exceed 40% of the moment due to first-order effects. Section 10.10.2.2 requires that second-order effects “be considered along the length of compression members.” This can be done using the nonsway moment magnification procedure outlined in Section 10.10.6. Section 10.10.4 on elastic second-order analysis includes new equations (10-8) and (10-9), which provide morerefined values of EI considering axial load, eccentricity, reinforcement ratio, and concrete compressive strength, as presented in the two Khuntia and Ghosh ACI Structural Journal articles. 34, 35 Commentary Section R10.13.8, “Tie Reinforcement around Structural Steel Core,” which is Section R10.16.8 in ACI 318-05, states: Concrete that is laterally confined by tie bars is likely to be rather thin along at least one face of a steel core section. Therefore, complete interaction between the core, the concrete, and any longitudinal reinforcement should not be assumed. Concrete will probably separate from smooth faces of the steel core. To maintain the concrete around the structural steel core, it is reasonable

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IMPACT OF ACI 318-08 ON THIS HANDBOOK to require more lateral ties than needed for ordinary reinforced concrete columns. Because of probable separation at high strains between the steel core and the concrete, longitudinal bars will be ineffective in stiffening cross sections even though they would be useful in sustaining compression forces. This text has now been replaced with, “Research has shown that the required amount of tie reinforcement around the structural steel core is sufficient for the longitudinal steel bars to be included in the flexural stiffness of the composite column.” The revisions to achieve a consistent treatment of lightweight concrete throughout ACI 318 (see discussion of Section 8.6 in “Significant Changes to ACI 318-08 Relative to Precast/Prestressed Concrete: Part 1”1) have led to the deletion of Section 11.2 of ACI 318-05. The revisions to ACI 318 also affect several of the equations in Chapter 11. Those equations are found in Sections 11.2, “Shear Strength Provided by Concrete for Non-prestressed Members”; 11.3, “Shear Strength Provided by Concrete for Prestressed Members”; 11.5.1, “Threshold Torsion”; 11.5.2, “Calculation of Factored Torsional Moment”; 11.9, “Provisions for Walls”; and 11.11, “Provisions for Slabs and Footings”. In addition, in Section 11.6.4.3 (11.6 is the section on shear friction), λ = 0.85 for sand-lightweight concrete has been changed to “Otherwise, λ shall be determined based on volumetric proportions of lightweight and normalweight aggregates as specified in [Section] 8.6.1, but shall not exceed 0.85.” Although the equations in the sections noted previously have different appearances, there have not been any significant changes related to the shear strength of structural members made of lightweight concrete. Significant changes have been made to the list of members in Section 11.4.6.1 for which minimum shear reinforcement is not required where Vu exceeds 0.5φVc. Solid slabs, footings, and joists are excluded from the minimum shear-reinforcement requirement because there is a possibility of load sharing between weak and strong areas.” Section 11.4.6.1, under item (a), has now clarified that the slabs must be solid. Based on experimental evidence,36 a new limit on the depth of hollow-core units of 12.5 in. is established in item (b) of Section 11.4.6.1. “Research has shown that deep, lightly reinforced oneway slabs and beams, particularly if constructed with highstrength concrete, or concrete with a small coarse aggregate size, may fail at shear demands less than Vc computed using Eq. (11-3) especially when subjected to concentrated loads.” 37-39 Because of this, “the exclusion for certain beam types in 11.4.6.1(e) is restricted to cases in which the total depth h does not exceed 24 in.” In Section 11.6.5, the upper limit on the nominal shear-friction strength Vn has been significantly increased for both monolithically placed concrete and concrete placed against intentionally hardened concrete. Commentary Section R11.6.5 points out that the increase is justified in view of test data.40, 41 Section 11.6.5 now clarifies that if a lower-strength concrete is cast against a higher-strength concrete, the value of f 'c

APPENDIX used to evaluate Vn must be the f 'c for the lower-strength concrete. The increase in the upper limit on the nominal shearfriction strength is also reflected in Section 11.8.3.2.1 (part of Section 11.8, “Provisions for Brackets and Corbels”). In all of the equations for development length of deformed bars and deformed wire in tension and compression, in Sections 12.2.2 and 12.2.3, respectively, the lightweightaggregate factor λ has been moved from the numerator to the denominator. At the same time, in Section 12.2.4(d), λ = 1.3 has been replaced by “λ shall not exceed 0.75 unless fct is specified (see [Section] 8.6.1).” All of this is consistent with the definition of λ in Section 8.6 and is explained clearly in commentary Section R12.2.4. Before ACI 318-08, Eq. (12-2) for Ktr included the yield strength of the transverse reinforcement fyt. The current expression assumes that fyt = 60 ksi and includes only the area and the spacing of the transverse reinforcement and the number of bars being developed or lap spliced. This is because tests have shown that transverse reinforcement rarely yields during bond failure. By far the most significant change in Chapter 12 is the introduction of Section 12.6, “Development of Headed and Mechanically Anchored Deformed Bars in Tension.” Use of headed deformed bars is attractive as an alternative to hooked bar anchorages in regions where reinforcement is heavily congested. The term development, as used in Section 12.6, indicates that “the force in the bar is transferred to the concrete through a combination of a bearing force at the head and bond forces along the bar.” The term anchorage, as used in Section 12.6, indicates that “the force in a bar is transferred to the concrete through bearing of the head alone.” Commentary Section R12.6 states that the “provisions for headed deformed bars were written with due consideration of the provisions for anchorage in Appendix D and the bearing strength provisions of [Section] 10.4. 42, 43 Appendix D contains provisions for headed anchors related to the individual failure modes of concrete breakout, side-face blowout, and pullout, all of which were considered in the formulation of [Section] 12.6.2. The restriction that the concrete must be normalweight, the maximum bar size of # 11, and the upper limit of 60,000 psi on fy are based on test data.44 Commentary Fig. R12.6(a) shows the length of headed deformed bar ldt measured from the critical section to the bearing face of the head, which is given in Section 12.6.2 for developing headed deformed bars. “For bars in tension, heads allow the bars to be developed in a shorter length than required for standard hooks.42-44 The minimum limits on clear cover, clear spacing, and head size are based on the lower limits on these parameters used in the tests to establish the expression for ldt in [Section] 12.6.2. … Headed bars with Abrg < 4Ab have been used in practice, but their performance may not be accurately represented by the provisions of [Section] 12.6.2.” Headed bars may be used only in compliance with the requirements of Section 12.6.4. “A factor of 1.2 is consistently used for epoxy-coated headed reinforcing bars, the same value as used for epoxy-

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coated standard hooks.” The upper limit of 6000 psi on the value of f 'c in Section 12.6.2 is based on the concrete strengths used in the Texas tests.42-44 “Because transverse reinforcement has been shown to be largely ineffective in improving the anchorage of headed deformed bars, additional reductions in development length … are not used for headed deformed reinforcing bars.” The sole exception to this is a reduction for excess reinforcement. Commentary Section R12.6 indicates that where longitudinal headed deformed bars from a beam or slab terminate at a column or other supporting member, as shown in Figure R12.6(b), “the bars should extend through the joint to the far face of the supporting member, allowing for cover and avoiding interference with column reinforcement, even though the resulting anchorage length exceeds ldt.” Extending the bar to the far face of the supporting member improves the performance of the joint. Section 12.6.3 requires that heads “not be considered effective in developing bars in compression” because there are no available test data demonstrating that “the use of heads adds significantly to anchorage strength in compression.” In Section 12.8, Eq. (12-3) for the development length of plain welded-wire reinforcement in tension now shows the lightweight-aggregate factor λ in a position that is consistent with its definition in section 8.6. In Section 12.13, the expression for the embedment length of web reinforcement between the midheight of a member and outside end of the hook now contains λ. In Section 12.15, “Splices of Deformed Bars and Deformed Wire in Tension,” Section 12.15.3 has been added. The section states that “when bars of different size are lap spliced in tension, splice length shall be the larger of ld of larger bar and tension lap splice length of smaller bar.” Section 14.3.7 of ACI 318-05 reads, “In addition to the minimum reinforcement required by 14.3.1, not less than (2) # 5 bars shall be provided around all window and door openings. Such bars shall be extended to develop the bar beyond the corner of the openings but not less than 24 in.” The section now reads, “In addition to the minimum reinforcement required by 14.3.1, not less than (2) # 5 bars in walls having two layers of reinforcement in both directions and (1) # 5 bar in walls having a single layer of reinforcement in both directions shall be provided around window, door, and similar sized openings. Such bars shall be anchored to develop fy in tension at the corners of the openings.” Section 14.8, “Alternative Design of Slender Walls,” was introduced in the 1999 edition of ACI 318, and the provisions are based on similar provisions in the Uniform Building Code (UBC),45 which in turn are based on experimental research.46 Changes have been made in the 2008 edition to reduce differences in the serviceability provisions between ACI 318 and the UBC to ensure that the intent of the UBC provisions is included in future editions of the IBC. Before the 2008 edition of ACI 318, under Section 14.8.3, the effective area of longitudinal reinforcement in a slender wall for obtaining an approximate cracked moment of inertia was calculated using an effective area of tension reinforcement defined by Eq. (14-7) without the h/2d modifier. The A–14

contribution of the axial load to the cracked moment of inertia was overestimated in many cases where two layers of reinforcement were used in a slender wall. The effective area of longitudinal reinforcement has been modified in 2008 by introducing the h/2d modifier. “The neutral axis depth c in Eq. (14-7) corresponds to this effective area of longitudinal reinforcement.” Section 14.8.4 has undergone significant changes. Prior to ACI 318-08, out-of-plane deflections of wall panels were calculated using the effective moment of inertia given in Section 9.5.2.3. “However, reevaluation of the original test data 46 indicates that out-of-plane deflections increase rapidly when the service-level moment exceeds 2/3Mcr. A linear interpolation between ∆cr (given by Eq. [14-10]) and ∆n (given by Equation [14-11]) is used to determine ∆s to simplify the design of slender walls” if the maximum moment in member due to service loads Ma exceeds 2/3Mcr. One important change in Section 18.4.1 permits an increase in the allowable concrete compressive stress immediately after prestress transfer at the ends of pretensioned, simply supported members from 0.60f 'c i to 0.70f 'c i. This change was made based on research results and common practice in the precast/prestressed concrete industry. The remainder of Section 18.4.1 was editorially rewritten.

Chapter 6 – Design of Connections The three significant changes in Appendix D are the following: • • •

New definitions of reinforcement types that cross the concrete breakout surface Important revisions to the requirements that ductile anchor failure precede any concrete failure mode in moderate to high seismic applications Addition of provisions for lightweight concrete, in the computation of concrete breakout strength of anchors

ACI 318-05 defines an anchor group as “a number of anchors of approximately equal effective embedment depth with each anchor spaced at less than three times its embedment depth [3hef] from one or more adjacent anchors.” This definition considers anchors subject to tension but not anchors subject to shear. This deficiency has now been corrected. The 31808 definition reads, “a number of anchors of approximately equal effective embedment depth with each anchor spaced at less than 3hef from one or more adjacent anchors when subjected to tension, or 3ca1 from one or more adjacent anchors when subjected to shear.” The distance from the center of an anchor shaft to the edge of concrete in one direction is represented by ca1. ACI 318-08 has also added to the definition, “only those anchors susceptible to the particular failure mode under investigation shall be included in the group.” An important new term, anchor reinforcement, is defined in Chapter 2 as “reinforcement used to transfer the full design load from the anchors into the structural member.” New Sections D.5.2.9 and D.6.2.9 contain provisions concerning anchor reinforcement.

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IMPACT OF ACI 318-08 ON THIS HANDBOOK ACI 318-05 defines supplementary reinforcement as “reinforcement proportioned to tie a potential concrete failure prism to the structural member.” ACI 318-08 has revised the supplementary reinforcement definition to read, “reinforcement that acts to restrain the potential concrete breakout but is not designed to transfer the full design load from the anchors into the structural member.” The second part of the revised definition clearly indicates that supplementary reinforcement is not anchor reinforcement. Section D.3.3 of ACI 318-05 reads, “When anchor design includes seismic loads, the additional requirements of D.3.3.1 through D.3.3.5 shall apply.” This wording has now changed to “when anchor design includes earthquake forces for structures assigned to Seismic Design Category C, D, E, or F, the additional requirements of D.3.3.1 through D.3.3.6 shall apply.” There are two differences: • •

Section D.3.3.6 has been added. The applicability of the ACI 318-05 provision included seismic design category (SDC) B, which is no longer the case.

The change in the SDC matters for Section D.3.3.1 only because subsequent ACI 318-05 language restricted the applicability of Sections D.3.3.2 through D.3.3.5 to structures assigned SDC C, D, E, or F. Section D.3.3.2 of ACI 318-08 specifically requires that “pullout strength Np and steel strength of the anchor in shear Vsa shall be based on the results of the ACI 355.2 Simulated Seismic Tests.” This specific requirement is not part of ACI 318-05. Section D.3.3.3 has undergone an important change. While the section in ACI 318-05 requires that “the design strength of anchors shall be taken as 0.75φNn and 0.75φVn,” the ACI 318-08 section requires that “the anchor design strength associated with concrete failure modes shall be taken as 0.75φNn and 0.75φVn.” The variables φ, Nn, and Vn represent the strength reduction factor, the nominal strength in tension, and the nominal shear strength, respectively. By making the seismic reduction apply only to concrete failure modes, it is significantly more difficult to meet the requirements of Section D.3.3.4 when anchors subjected to seismic forces in structures assigned to SDC C, D, E, or F have to be governed by the strength of a ductile steel element. Section D.3.3.4 of ACI 318-05 waives the ductile anchor failure requirement if Section D.3.3.5 can be satisfied. The same section in ACI 318-08 waives the ductile failure requirement if either section D.3.3.5 or Section D.3.3.6 can be satisfied. The 2006 IBC Section 1908.1.16 modified ACI 318-05 section D.3.3.5 to read, “Instead of D.3.3.4 . . . specified in D.3.3.3, or the minimum design strength of the anchors shall be at least 2.5 times the factored forces transmitted by the attachment.” The 2006 IBC includes the text of ACI 318-05 Section D.3.3.5 with the addition of “or the minimum design strength of the anchors shall be at least 2.5 times the factored forces transmitted by the attachment.” In other words, ductile anchor failure was declared unnecessary if the anchorage was overdesigned for concrete breakout. This concept has

APPENDIX been adopted into Section D.3.3.6 of ACI 318-08 with the wording, “as an alternative to D.3.3.4 [ductile anchor failure] and D.3.3.5 [yielding in the attachment], it shall be permitted to take the design strength of the anchors as 0.4 times the design strength determined in accordance with D.3.3.3.” For anchors of stud-bearing walls, the 0.4 factor may be taken as 0.5. Because ACI 318 is a material standard, the committee did not feel comfortable modifying the design load, as the 2006 IBC had done. It was decided instead, in effect, to modify the strength reduction factor. A 0.4 multiplier on φ is equivalent to a 2.5 multiplier on the design load. Section D.3.4 concerning anchors embedded in lightweight concrete is different—but mostly in appearance, not really in substance. A very important sentence has been added to Section D.4.2.1: “Where anchor reinforcement is provided in accordance with D.5.2.9 and D.6.2.9, calculation of the concrete breakout strength in accordance with D.5.2 and D.6.2 is not required.” This sentence was added because anchor reinforcement is reinforcement that carries all the design load when breakout failure occurs. The commentary concerning supplementary reinforcement has changed in Section RD.4.4. Important new points are, “An explicit design of supplementary reinforcement is not required. However, the arrangement of supplementary reinforcement should generally conform to that of the anchor reinforcement shown in Fig. RD.5.2.9 and RD.6.2.9 (b). Full development is not required [of the supplemental reinforcement].” The descriptions of conditions A and B in Section D.4.4 have been editorially modified for greater clarity. The descriptions now read, “Condition A applies where supplementary reinforcement is present except for pullout and pryout strengths. Condition B applies where supplementary reinforcement is not present, and for pullout or pryout strength.” A distinction is now made between the effective crosssectional area of anchor in tension Ase,N and the effective cross-sectional area of anchor in shear Ase,V. In ACI 315-05, there is only the effective cross-sectional area of anchor Ase. The change is reflected in ACI 318-08 Eq. (D-3), (D-19), and (D-20). Commentary Section RD.5.1.2 reproduces an equation from American National Standards Institute (ANSI)/ American Society of Mechanical Engineers (ASME) B1.1, Unified Inch Screw Threads (UN and UNR Thread Form)47 for Ase,N of threaded bolts. Commentary Section RD.6.1.2 reproduces an equation from ANSI/ASME B1.1 for Ase,V for threaded bolts. The two equations are identical. The difference in the value obtained from the two equations is evident for postinstalled mechanical anchors, particularly torquecontrolled expansion anchors with a tapered conical shape at the bottom. Approved postinstalled anchors give both effective areas in the product approval (in most cases, the areas provided are the same as those given by the equations in the ACI 318-08 commentary). In Eq. (D-7) for basic concrete breakout strength, a lightweight concrete factor λ was introduced. A very important new section, D.5.2.9, has been added to ACI 318-08. This section reads, “Where anchor reinforcement is developed in accordance with Chapter 12 on both

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Fig. A.4 Anchor reinforcement for tension. Source: Reprinted by permission from Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R08) (Farmington Hills, MI: ACI, 2008), p. 426, Fig. RD.5.3.

sides of the breakout surface, the design strength of the anchor reinforcement shall be permitted to be used instead of the concrete breakout strength in determining φNn. A strength reduction factor of 0.75 shall be used in the design of the anchor reinforcement.” An important new commentary Section RD.5.2.9 states that “for conditions where the factored tensile force exceeds the concrete breakout strength of the anchor(s) or where the breakout strength is not evaluated, the nominal strength can be that of anchor reinforcement.” The commentary includes Fig. RD.5.2.9, which is helpful and is reproduced here as Fig. A.4. The term d0, which represents the outside diameter or shaft diameter of a headed stud, headed bolt, or hooked bolt of ACI 318-05, has been replaced with da in ACI 318-08. This change is reflected in Eq. (D-16) for pullout strength in tension and in Section D.8.3. The lightweight concrete factor λ is introduced in Eq. (D-17) for the concrete side-face blowout strength of a single anchor in tension and in Eq. (D-18) for the concrete side-face blowout strength of a group of anchors in tension. A–16

Fig. A.5 Hairpin anchor reinforcement for shear. Source: Reprinted by permission from Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R08) (Farmington Hills, MI: ACI, 2008), p. 435, Fig. RD.6.2.9(a).

A new modification factor ψh,V has been added to Eq. (D-21) and (D-22) for concrete breakout strength of anchors in shear. The factor is defined by Eq. (D-29) and is for anchors located in a concrete member in which ha < 1.5ca1 and ha is the thickness of the member in which an anchor is located, measured parallel to anchor axis. The lightweight concrete factor λ is also introduced into Eq. (D-24) and (D-25) for the basic concrete breakout strength in shear.

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APPENDIX

Chapter 7 – Structural Considerations for Architectural Precast Concrete This chapter is not affected by ACI 318-08.

Chapter 8 – Component Handling and Erection Bracing This chapter is not affected by ACI 318-08.

Chapter 9 – Precast and Prestressed Concrete: Materials

Fig. A.6 Edge reinforcement and anchor reinforcement for shear. Source: Reprinted by permission from Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R08) (Farmington Hills, MI: ACI, 2008), p. 435, Fig. RD.6.2.9(b).

Paralleling Section D.5.2.9, another important new section, D.6.2.9, has been added to ACI 318-08. It reads, “Where anchor reinforcement is either developed in accordance with Chapter 12 on both sides of the breakout surface, or encloses the anchor and is developed beyond the breakout surface, the design strength of the anchor reinforcement shall be permitted to be used instead of the concrete breakout strength in determining φVn. A strength reduction factor of 0.75 shall be used in the design of the anchor reinforcement.” New commentary Section RD.6.2.9 explains the provision. It includes Fig. RD. 6.2.9(a) and RD.6.2.9(b), which are reproduced here as Fig. A.5 and A.6, respectively.

The definition of lightweight aggregate concrete in Chapter 2 now references ASTM C3307 and replaces “dry loose weight of 70 lb or less” with “loose bulk density of 70 lb/ft3 or less, determined in accordance with ASTM C29.” All-lightweight and sand-lightweight concretes are now defined separately, whereas they used to be part of the definition of lightweight concrete. Normalweight concrete is now also defined. In the definition of lightweight concrete, “equilibrium density not exceeding 115 lb/ft3” has been replaced with “equilibrium density between 90 and 115 lb/ft3.” Chapters 4 and 5 of earlier editions of ACI 318 were reformatted in 1989 to emphasize the importance of considering durability requirements before selecting f 'c and the specified concrete cover over the reinforcing steel. In ACI 318-08, the format of Chapter 4 is extensively revised by introducing exposure categories and classes, with applicable durability requirements given for the various classes in a unified format. ACI 318-08 defines exposure categories and classes for concrete structures in Section 4.2.1—specifically in Tables 4.2.1.a through 4.2.1.d. Tables A.6 through A.9 are adapted from those tables and the commentary to Section 4.2.1. Associated requirements for concrete relative to the exposure classes are provided in ACI 318 Section 4.3. Because of the concern that material properties may change with time, a limit of 12 months has been imposed on the age of the historical data used to qualify mixture proportions under Section 5.3, and proportioning on the basis of field experience or trial mixtures or both is allowed. Under Section 5.3.3.2, the requirements that must be met by trial mixtures for concrete proportions established from such mixtures to be acceptable have been revised as indicated: •

•

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Requirement (b) of Section 5.3.3.2 in 318-05 reads: “Trial mixtures having proportions and consistencies required for proposed work shall be made using at least three different water-cementitious materials ratios or cementitious materials contents that will produce a range of strengths encompassing f 'cr .” It now reads: “Trial mixtures with a range of proportions that will produce a range of compressive strengths encompassing f 'cr and meet the durability requirements of Chapter 4.” Requirement (c) of ACI 318-05 is: “Trial mixtures shall be designed to produce a slump within ±0.75 in. A–17

 

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APPENDIX Table A.5  ASTM reference standards added to ACI 318-08, Section 3.8 ASTM Standard

Title

A820/A820M-06

Standard Specification for Steel Fibers for Fiber-Reinforced Concrete

A955/A955M-07A

Standard Specification for Deformed and Plain Stainless-Steel Bars for Concrete Reinforcement

A970/A970M-06

Standard Specification for Headed Steel Bars for Concrete Reinforcement

A1022/A1022M-07

Standard Specification for Deformed and Plain Stainless Steel Wire and Welded Wire for Concrete Reinforcement

A1035/A1035M-07

Standard Specification for Deformed and Plain, Low-Carbon, Chromium, Steel Bars for Concrete Reinforcement

A1044/A1044M-05

Standard Specification for Steel Stud Assemblies for Shear Reinforcement of Concrete

C29/C29M-97 (revised 2003)

Standard Test Method for Bulk Density (Unit Weight) and Voids in Aggregate

C231-04

Standard Test Method for Air Content of Freshly Mixed Concrete by the Pressure Method

C1012-04

Standard Test Method for Length Change of Hydraulic-Cement Mortars Exposed to a Sulfate Solution

C1116-06/C1116M-06

Standard Specification for Fiber-Reinforced Concrete

C1602/C1602M-06

Standard Specification for Mixing Water Used in the Production of Hydraulic Cement Concrete

C1609/C1609M-06

Standard Test Method for Flexural Performance of Fiber-Reinforced Concrete (Using Beam with ThirdPoint Loading)

Table A.6  Exposure Category F based on freezing and thawing exposure Class

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Description

Condition

F0

Not applicable

Concrete not exposed to freezing and thawing cycles

F1

Moderate

Concrete exposed to freezing and thawing cycles and that may be occasionally exposed to moisture before freezing (for example, exterior walls, beams, girders, and slabs not in direct contact with soil)

F2

Severe

Concrete exposed to freezing and thawing cycles and that is in continuous contact with moisture before freezing (for example, water tanks)

F3

Very severe

Concrete exposed to freezing and thawing cycles, that is in continuous contact with moisture, and where exposure to deicing chemicals is anticipated (for example, parking structures in the northern United States)

Source: Data adapted from Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R-08) Table 4.2.1 and commentary Section R4.2.1.

Table A.7  Exposure Category S based on sulfate exposure Class

Description

Water-soluble sulfate in soil, % by weight

Sulfate in water, ppm

Commentary

S0

Not applicable

SO4 < 0.10

SO4 < 150

Injurious sulfate attack not common

S1

Moderate

0.10 ≤ SO4 < 0.20

150 ≤ SO4 < 1500 sea water

More critical value of measured water-soluble sulfate concentration in soil or the concentration of dissolved sulfate in water governs

S2

Severe

0.20 ≤ SO4 ≤ 2.00

1500 ≤ SO4 ≤ 10,000

Same as for S1

S3

Very severe

SO4 > 2.00

SO4 > 10,000

Same as for S1

Source: Data adapted from Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R-08) Table 4.2.1 and commentary Section R4.2.1. Note: ppm = parts per million.

of maximum permitted, and for air-entrained concrete, within ±0.5% of maximum allowable air content.” • It now reads: “Trial mixtures shall have slumps within the range specified for the proposed Work; for airA–18

entrained concrete, air content shall be within the tolerance specified for the proposed Work.” Requirement (d) of ACI 318-05 is: “For each water cementitious materials ratio or cementitious materials content, at least three test cylinders for each test age

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Table A.8  Exposure Category P based on requirements for low permeability Class

Description

Condition

Commentary

P0

Not applicable

Concrete not required to have low permeability to water

—

P1

Applicable

Concrete required to have low permeability to water

When the permeation of water into concrete might reduce durability or affect the intended function of the structural element

Source: Data adapted from Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R-08) Table 4.2.1 and commentary Section R4.2.1.

Table A.9 Class

Description

Condition

Commentary

C0

Not applicable

Concrete that will be dry or protected from moisture in service

No additional protection required against the corrosion of reinforcement

C1

Moderate

Concrete exposed to moisture but not to an external source of chlorides in service

—

C2

High

Concrete exposed to moisture and to an external source of chlorides in service

For example, deicing chemicals, salt, brackish water, seawater, or spray from these sources

Source: Data adapted from Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R-08) Table 4.2.1 and commentary Section R4.2.1.

shall be made and cured in accordance with ASTM C192, Standard Practice for Making and Curing Concrete Test Specimens in the Laboratory.28 Cylinders shall be tested at 28 days or at test age designated for determination of f 'c.” It now reads: “For each trial mixture, at least two 6 in. × 12 in. or three 4 in. × 8 in. cylinders shall be made and cured in accordance with ASTM C192. Cylinders shall be tested at 28 days or at test age designated for f 'c.” •

Requirements (e) and (f) of ACI 318-05 read: “From results of cylinder tests a curve shall be plotted showing the relationship between water-cementitious materials ratio or cementitious materials content and compressive strength at designated test age. Maximum water-cementitious materials ratio or minimum cementitious materials content for concrete to be used in proposed Work shall be that shown by the curve to produce f 'c required by 5.3.2, unless a lower water-cementitious materials ratio or higher strength is required by Chapter 4.”

All of this has been replaced by a new item (e), which reads: “The compressive strength results, at designated test age, from the trial mixtures shall be used to establish the composition of the concrete mixture proposed for the Work. The proposed concrete shall achieve an average compressive strength as required in 5.3.2 and satisfy the applicable durability criteria of Chapter 4.” It should be noted that ACI 318 has now recognized the use of three 4 in. × 8 in. cylinders as equivalent to the use

of two 6 in. × 12 in. cylinders. This change is also reflected in Section 5.6.2.4. The commentary clarifies that the confidence level of the average strength is preserved this way because 4 in. × 8 in. cylinders tend to have about 20% higher within-test variability than 6 in. × 12 in. cylinders. The commentary also points out that more than the minimum number of specimens may be desirable to allow for discarding an outlying individual cylinder strength in accordance with ACI 214R. Commentary Section R6.3.2 now points out that Section 6.3.2 prohibits calcium chloride or any admixture containing chloride from being used in concrete with aluminum embedments. Chapter 10 – Design for Fire Resistance of Precast and Prestressed Concrete This chapter is not affected by ACI 318-08. Chapter 11 – Thermal and Acoustical Properties of Precast Concrete This chapter is not affected by ACI 318-08. Chapter 12 – Vibration Design of Precast, Prestressed concrete Systems This chapter is not affected by ACI 318-08. Chapter 13 – Tolerances for Precast and Prestressed Concrete To permit a more consistent application of tolerances in ACI 318 and other ACI documents, specified cover has replaced minimum cover throughout Chapter 7. This change affects sections 7.7.1, 7.7.2, 7.7.3, 7.7.4, 7.7.5, and 7.7.6.

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APPENDIX Chapter 14 – Specifications and Standard Practices The term contract documents is now defined in Chapter 2 and reads “Documents, including the project drawings and project specifications, covering the Work.” The term registered design professional has been replaced with licensed design professional. Because registered design professional is the term used in the IBC, the ACI 318 definition for licensed design professional is as follows: “An individual who is licensed to practice structural design as defined by the statutory requirements of the professional licensing laws of the state of jurisdiction in which the project is to be constructed and who is in responsible charge of the structural design; in other documents, also referred to as registered design professional.” Chapter 15 – General Design Information This chapter is not affected by ACI 318-08. References: 1. G  hosh, S. K. 2008. “Significant Changes to ACI 318-08 Relative to Precast/Prestressed Concrete: Part 1.” PCI Journal, V. 53, No. 2 (March–April): supplement.

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2. G  hosh, S. K. 2008. “Significant Changes to ACI 318-08 Relative to Precast/Prestressed Concrete: Part 2.” PCI Journal, V. 53, No. 3 (May-June): supplement. 3. G  hosh, S. K. 2008. “Significant Changes to ACI 318-08 Relative to Precast/Prestressed Concrete: Part 3.” PCI Journal, V. 53, No. 5 (September-October): supplement. 4. G  hosh, S. K. 2009. “Significant Changes to ACI 318-08 Relative to Precast/Prestressed Concrete: Part 4.” PCI Journal, V. 54, No. 3 (Summer): supplement. 5. S  tructural Engineering Institute. 2005. Minimum Design Loads for Buildings and Other Structures. Reston, VA: American Society of Civil Engineers (ASCE). 6. I nternational Code Council. 2006. International Building Code. Falls Church, VA: International Code Council. 7. B  uilding Seismic Safety Council (BSSC). 2003. NEHRP Recommended Provisions for the Development of Seismic Regulations for New Buildings and Other Structures. Washington, DC: BSSC. 8. M  uguruma, H., and F. Watanabe. 1990. Ductility Improvement of High-Strength Concrete Columns with Lateral Confinement. In Proceedings, Second International Symposium on High-Strength Concrete, pp. 47–60. Detroit, MI: American Concrete Institute (ACI).

9. M  uguruma, H., M. Nishiyama, F. Watanabe, and H. Tanaka. 1991. Ductile Behavior of High-Strength Concrete Columns Confined by High-Strength Transverse Reinforcement. In Evaluation and Rehabilitation of Concrete Structures and Innovations in Design, pp. 877–891. Detroit, MI: ACI. 10. S  ugano, S., T. Nagashima, H. Kimura, A. Tamura, and A. Ichikawa. 1990. Experimental Studies on Seismic Behavior of Reinforced Concrete Members of High Strength Concrete. In Proceedings, Second International Symposium on High-Strength Concrete, pp. 61–87. Detroit, MI: ACI. 11. B  udek, A., M. Priestley, and C. Lee. 2002. Seismic Design of Columns with High-Strength Wire and Strand as Spiral Reinforcement. ACI Structural Journal, V. 99, No. 5 (September–October): pp. 660–670. 12. A  merican Society for Testing and Materials (ASTM) Subcommittee A01.05. 2006. Standard Specification for Deformed and Plain, Low-carbon, Chromium, Steel Bars for Concrete Reinforcement. ASTM A1035/ A1035M-06. West Conshohocken, PA: ASTM. 13. A  STM Subcommittee A01.05. 2006. Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete Reinforcement. ASTM A615/A615M-06A. West Conshohocken, PA: ASTM. 14. A  STM Subcommittee A01.05. 2006. Standard Specification for Low-Alloy Steel Deformed and Plain Bars for Concrete Reinforcement. ASTM A706/A706M06A. West Conshohocken, PA: ASTM. 15. A  STM Subcommittee A01.05. 2006. Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete Reinforcement. ASTM A615/A615M-06A. West Conshohocken, PA: ASTM. 16. A  CI-ASCE Committee 352. 2002. Recommendations for Design of Beam-Column Connections in Monolithic Reinforced Concrete Structures (ACI 352R-02). Farmington Hills, MI: ACI. 17. M  einheit, D. F., and J. O. Jirsa. 1981. Shear Strength of R/C Beam-Column Connections. Journal of the Structural Division, V. 107, No. ST11 (November): pp. 2227–2244. 18. A  CI Innovation Task Group 1. 2003. Special Hybrid Moment Frames Composed of Discretely Jointed Precast and Post-Tensioned Concrete Members (ITG1.2-03) and Commentary (ITG-1.2R-03). Farmington Hills, MI: ACI. 19. A  CI Committee 374. 2005. Acceptance Criteria for Moment Frames Based on Structural Testing (ACI 374.105) and Commentary (ACI 374.1R-05). Farmington Hills, MI: ACI. 20. I nternational Conference of Building Officials (ICBO). 1994, 1997. Uniform Building Code. Whittier, CA: ICBO.

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21. T  homsen, J. H., and J. W. Wallace. 2004. Displacement Design of Slender Reinforced Concrete Structural Walls—Experimental Verification. Journal of Structural Engineering, V. 130, No. 4: pp. 618–630.

34. K  huntia, M., and S. K. Ghosh. 2004. Flexural Stiffness of Reinforced Concrete Columns and Beams: Analytical Approach. ACI Structural Journal, V. 101, No. 3 (May– June): pp. 351–363.

22. P  aulay, T., and J. R. Binney. 1974. Diagonally Reinforced Coupling Beams of Shear Walls. In Shear in Reinforced Concrete, pp. 579–598. Detroit, MI: ACI.

35. K  huntia, M., and S. K. Ghosh. 2004. Flexural Stiffness of Reinforced Concrete Columns and Beams: Analytical Approach. ACI Structural Journal, V. 101, No. 3 (May– June): pp. 364–374.

23. T  assios, T., M. Moretti, and A. Bezas. 1996. On the Behavior and Ductility of Reinforced Concrete Coupling Beams of Shear Walls. ACI Structural Journal, V. 93, No. 6 (November–December): pp. 711–720.

36. H  awkins, N. M., and S. K. Ghosh. 2006. Shear Strength of Hollow-Core Slabs. PCI Journal, V. 51, No. 1 (January–February): pp. 110–114.

24. G  alano, L., and A. Vignoli. 2000. Seismic Behavior of Short Coupling Beams with Different Reinforcement Layouts. ACI Structural Journal, V. 97, No. 6, (November–December): pp. 876–885.

37. A  ngelakos, D., E. C. Bentz, and M. D. Collins. 2001. Effect of Concrete Strength and Minimum Stirrups on Shear Strength of Large Members. ACI Structural Journal, V. 98, No. 3 (May–June): pp. 290–300.

25. B  arney, G. B., Shiu, K. N., Rabbat, B. G., Fiorato, A. E., Russell, H. G., and Corley, W. G., Behavior of Coupling Beams under Load Reversals, RD 068.01B, Portland Cement Association, Skokie, IL, 1980.

38. L  ubell, A., E. C. Sherwood, E. C. Bentz, and M. P. Collins. 2004. Safe Shear Design of Large Wide Beams. Concrete International, V. 26, No. 1 (January): pp. 66–78.

26. A  CI Innovation Task Group 5. 2007. Acceptance Criteria for Special Unbonded Post-Tensioned Precast Walls Based on Validation Testing (ITG-5.1-07) and Commentary (ITG-5.1R-07). Farmington Hills, MI: ACI.

39. B  rown, M. D., O. Bayrak, and J. O. Jirsa. 2006. Design for Shear Based on Loading Conditions. ACI Structural Journal, V. 103, No. 4 (July–August): pp. 541–550.

27. P  riestly, M. J. N., S. Sritharan, J. Conley, and S. Pampanin. 1999. Preliminary Results and Conclusions from the PRESSS Five-Story Precast Concrete Test Building. PCI Journal, V. 44, No. 6 (November– December): pp. 42–67. 28. P  erez, F. J., S. Pessiki, R. Sause, and L. W. Lu. Lateral Load Tests of Unbonded Post-Tensioned Precast Concrete Walls. In Large Scale Structural Testing, pp. 161–182. Farmington Hills, MI: ACI.

40. K  ahn, L. F., and A. D. Mitchell. 2002. Shear Friction Tests with High-Strength Concrete. ACI Structural Journal, V. 99, No. 1 (January–February): pp. 98–103. 41. M  attock, A. H. 2001. Shear Friction and High-Strength Concrete. ACI Structural Journal, V. 98, No. 1 (January– February): pp. 50–59. 42. T  hompson, M. K., M. J. Ziehl, J. O. Jirsa, and J. E. Breen. 2005. CCT Nodes Anchored by Headed Bars— Part 1: Behavior of Nodes. ACI Structural Journal, V. 102, No. 6 (November–December): pp. 808–815.

29. R  estrepo, J. I. 2002. New Generation of Earthquake Resisting Systems. In Proceedings, Fifth fib Congress, Session 6, Osaka, Japan, pp. 41–60.

43. T  hompson, M. K., J. O. Jirsa, and J. E. Breen. 2006. CCT Nodes Anchored by Headed Bars—Part 2: Capacity of Nodes. ACI Structural Journal, V. 103, No. 1 (January– February): pp. 65–73.

30. W  ood, S. L., J. F. Stanton, and N. M. Hawkins. 2000. New Seismic Design Provisions for Diaphragms in Precast Concrete Parking Structures. PCI Journal, V. 45, No. 1, (January–February): pp. 50–65.

44. T  hompson, M. K., A. Ledesma, J. O. Jirsa, and J. E. Breen. 2006. Lab Splices Anchored by Headed Bars. ACI Structural Journal, V. 103, No. 2 (March–April): pp. 271–279.

31. M  lakar, P. F., ed. 2005. Special Section: Performance of the Pentagon: Terrorist Attack of September 11, 2001. Journal of Performance of Constructed Facilities, V. 15, No. 3 (August): pp. 187–221.

45. I nternational Conference of Building Officials (ICBO). 1997. Uniform Building Code. Whittier, CA: ICBO.

32. N  owak, A. S., N. M. Szerszen, E. K. Szeliger, A. Szwed, and P. K. Podhorecki. 2005. Reliability-Based Calibration for Structural Concrete. Report No. UNLCE 05-036. Lincoln, NE: University of Nebraska. 33. H  awkins, N. M., and S. K. Ghosh. 2006. Shear Strength of Hollow-Core Slabs. PCI Journal, V. 51, No. 1 (January–February): pp. 110–114.

46. A  they, J. W, ed. 1982. Test Report on Slender Walls. Los Angeles, CA: Southern California Chapter of the American Concrete Institute and Structural Engineers Association of Southern California. 47. A  merican Society of Mechanical Engineers (ASME). 1989. Unified Inch Screw Threads (UN and UNR Thread Form). American National Standards Institute (ANSI)/ASME B1.1. Fairfield, NJ: ASME.

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APPENDIX Notation:

  A

Abrg = net bearing area of the head of stud, anchor bolt, or headed deformed bar Ac = area of concrete section resisting shear transfer Acw = area of concrete section of an individual pier, horizontal wall segment, or coupling beam resisting shear Ag = gross area of concrete section Ase = effective cross-sectional area of anchor (ACI 318-05) Ase,N = effective cross-sectional area of anchor in tension Ase,V = effective cross-sectional area of anchor in shear Ash = total cross-sectional area of transverse reinforcement (including crossties) within spacing s and perpendicular to dimension bc Avd = total area of reinforcement in each group of diagonal bars in a diagonally reinforced coupling beam Avf = area of shear-friction reinforcement bc = cross-sectional dimension of member core measured to the outside edges of the transverse reinforcement composing area Ash bw = web width or diameter of circular section c1 = dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction of the span for which moments are being determined c2 = dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction perpendicular to c1 ca1 = distance from the center of an anchor shaft to the edge of concrete in one direction (if shear is applied to the anchor, ca1 is the maximum edge distance) ca2 = distance from the center of an anchor shaft to the edge of concrete in the direction perpendicular to ca1, in. d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement d1 = minimum dimension of confined section containing diagonal reinforcement da = outside diameter of anchor or shaft diameter of headed stud, headed bolt, or hooked bolt db = nominal diameter of bar, wire, or prestressing strand d0 = outside diameter of anchor or shaft diameter of headed stud, headed bolt, or hooked bolt (ACI 318-05) D = dead loads or related internal moments and forces E = load effects of earthquake or related internal moments and forces EI = flexural stiffness of compression member f 'c = specified compressive strength of concrete f 'ci = s pecified compressive strength of concrete at time of initial prestress fy = specified yield strength of nonprestressed reinforcement fyt = specified yield strength of transverse reinforcement h = overall thickness or height of member hef = effective embedment depth of anchor k = effective length factor for compression members Ktr = transverse reinforcement index ld = development length in tension of deformed bar, deformed wire, plain and deformed welded-wire reinforcement, or pretensioned strand, in. A–22

ldh = development length in tension of deformed bar or deformed wire with a standard hook, measured from critical section to outside end of hook (straight embedment length between critical section and start of hook [point of tangency] plus inside radius of bend and one bar diameter), in. ldt = development length in tension of headed deformed bar, measured from the critical section to the bearing face of the head ln = length of clear span measured face-to-face of supports lo = length, measured from joint face along axis of structural member, over which special transverse reinforcement must be provided lu = unsupported length of compression member L = live loads or related internal moments and forces M1 = smaller factored end moment on a compression member M2 = larger factored end moment on a compression member Ma = maximum moment in member due to service loads Mcr = cracking moment N = tensile force Nn = nominal strength in tension Np = pullout strength in tension of a single anchor in cracked concrete r = radius of gyration of cross section of a compression member so = center-to-center spacing of transverse reinforcement within the length lo V = shear force Vc = nominal shear strength provided by concrete Vn = nominal shear strength Vsa = nominal strength in shear of a single anchor or group of anchors as governed by the steel strength Vu = factored shear force at section W = wind load, or related internal moments and forces ∆ cr = computed out-of-plane deflection at midheight of wall corresponding to cracking moment ∆n = computed out-of-plane deflection at midheight of wall corresponding to nominal flexural strength ∆s = computed out-of-plane deflection at midheight of wall due to service loads λ = modification factor reflecting the reduced mechanical properties of lightweight concrete µ = coefficient of friction φ = strength-reduction factor ψh,V = factor used to modify shear strength of anchors located in concrete members with ha < 1.5ca1

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PCI DESIGN HANDBOOK/SEVENTH EDITION

Index A Accelerators 9–9 Acceptance 14–30 Access to jobsite 14–28 ACI 318-05 4–6 ACI 318-08, impact of A–1 Acid etching, finish 9–19 Acoustical properties of precast concrete 11–23 Acoustics, composite wall considerations 11–24 Acoustics, leaks and flanking 11–24 Adhesive anchors 6–8 Admixture 9–3 Admixtures 1–2 Affected zone 11–2 Aggregate 9–3 Aggregate, coarse 9–3 Aggregate, fine 9–3 Aggregate, lightweight 9–3 Aggregates 9–4 Aggregates, aesthetic considerations 9–5 Aggregates, grading 9–5 Aggregates, lightweight 9–5 Aggregates, normalweight 9–5 Aggregates, quality / durability 9–5 Aggregates, surface texture and shape 9–5 Aircraft-cable loops 8–10 Air entrainment 9–5 Alkali-carbonate reactions 9–15 Allowable story drift ∆a, in. 4–87 Analysis and design – ordinary moment frames 4–52 Analysis using ACI 318-05 equations 5–6 Analysis using strain compatibility 5–6 Anchorage of stone facing 7–33 Anchor bolts and bearing devices 14–28 Anchor reinforcement 6–60 Annual average ambient relative humidity, percent 4–88 Anodic index 9–21 Applications 1–8 Approval, of shop drawings or submittals 14–34 Architectural cladding component analysis 7–15 Architectural components coefficients 4–87 Architectural / decorative finishes 9–18 Architectural precast 7–1 Architectural precast concrete 1–9, 7–3 Architectural precast concrete, connections 7–14 Architectural precast concrete, crack control 7–12 Architectural precast concrete, design loads 7–7 Architectural precast concrete, handling, transporting, and erecting 7–11 Architectural precast concrete panel with earthquake loading, example 7–21 Architectural precast concrete, prestressing 7–13 Architectural precast concrete, reinforcement 7–12

Architectural precast concrete, shims 7–14 Architectural precast concrete, stacking non-load-bearing panels 7–13 Architectural precast concrete, support deflections and building movements 7–7 Architectural precast concrete, tolerances 7–11 Architectural precast concrete, volume changes 7–7 Architectural walls/spandrel erection tolerances 13–18 ASCE 7 1–4 ASCE 7-05 4–5 ASTM E119 10–2 Austenitic stainless steels 9–23 Authority 14–34

B Back edge 6–25 Base shear 4–10 Basic wind speed, mph 4–82 Beam-column framing 3–3 Beam design equations and diagrams 15–5 Beam erection tolerances 13–10 Beams with ledges 5–68 Bearing 5–77 Bearing area 5–112 Bearing on plain concrete 5–77 Bearing pads 6–64 Bearing pads, design 6–67 Bearing-wall construction 3–3 Bending of asymmetrical sections 5–41 Bilinear behavior 5–90 Blast loads 4–65 Blast resistance and structural integrity 1–4 Blast-resistant design 4–65 Blockouts, cuts, and alterations 14–29 Bolts and threaded connectors 6–7 Bond 7–31 Bond strength 9–10 Bowing 5–96, 13–2 Bowing, forces required to restrain 5–148 Box beam 1–5 Box girder segments 1–20 Braced frames 4–3 Brick 7–20 Bridges 1–20 British thermal unit (Btu) 11–2 Broom finish 9–17 Building envelope 11–2 Building lines and benchmarks 14–28 Build-up of restraint forces in beams kb 4–93 Bulb-tee 1–5 Bulb-tees 1–20 Bushhammered 7–32 Bush-hammering, finish 9–19

C Cable guys 8–26 Cable stays 1–20

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

INDEX–1

Calculating restraint forces 4–23 Camber 13–2, 15–23 Camber and deflection 5–87 Camber equations for typical strand profiles 5–146 Cambers 3–9 Cantilever beam design method 5–110 Cantilevered columns 4–3 Cantilevered column systems for seismic design 4–47 Cantilevers 5–133 Capacity 3–8 Carbonate aggregate concrete 10–2 Carbon fibers 1–4 Cazaly hanger 6–60 Cement 9–3 Cementitious materials 9–3 Charpy V-notch test 9–20 Chemical admixtures 9–5 Chemical resistance 9–14 Chord forces 4–55 Cladding 1–4, 1–9 Cladding connections, example 6–76 Class C 3–9 Class C (cracked) 5–18 Classifications for seismic considerations 4–51 Class T 3–9 Class T (transition) 5–18 Class U 3–9 Class U (uncracked) 5–18 Clay product–faced precast concrete 7–30 Clay-product properties 7–30 Clay-product selection 7–30 Clearance 13–2 Clearance examples 13–26 Clearances 13–26 Clear distance 13–2 Code-prescribed forces 4–60 Code provisions 3–8 Code references 4–5 Code requirements for structural loads 4–5 Collector forces 4–56 Column, anchor bolts 6–70 Column, base plates 6–68 Column bases 6–68 Column bases, fixity 4–50 Column connection, example 6–72 Column covers 7–13 Column covers and mullions 7–4 Column erection tolerances 13–14 Columns and load-bearing wall panels 3–10 Comparison of corbel design methods 5–115 Component handling 8–2 Component resistance-deflection function 4–69 Composite components 5–18 Compression components 5–99 Computer models for frame analysis 4–50 Concealed surface 13–2 Concrete 9–3 Concrete axial load 6–3 INDEX–2

Concrete brackets or corbels 5–110 Concrete capacity design (CCD) 6–7 Concrete, compressive strength 9–10 Concrete density 3–9, 3–10 Concrete, durability / reactivity 9–13 Concrete, modulus of elasticity 9–11 Concrete, normalweight 9–3 Concrete, physical properties 9–10 Concrete, Poisson's ratio 9–11 Concrete, sand-lightweight 9–3 Concrete strength 3–9 Concrete strength, breakout 6–11 Concrete strength, shear 6–15 Concrete strength, tension 6–11 Concrete, structural lightweight 9–3 Concrete, temperature effects 9–12 Concrete, tensile strength, magnitude 9–11 Concrete, volume changes 9–11 Condensation control 11–18 Condensation control, air barriers 11–19 Condensation control, vapor retarders 11–20 Condensation prevention on wall surfaces 11–22 Connection 13–2, 14–34 Connection design, constructibility 6–5 Connection design criteria 6–4 Connection design, ductility 6–4 Connection design, durability 6–4 Connection design, fire resistance 6–4 Connection design, strength 6–4 Connection design, volume change accommodation 6–4 Connection hardware 6–5 Connection materials 9–20 Connections, bearing pads 9–20 Connections, design considerations 7–14 Connections protection, bolts 9–22 Connections protection, embrittlement 9–23 Connections protection, galvanized steel 9–22 Connections, protection of 9–22 Connections protection, painted steel 9–22 Connections protection, stainless steel 9–23 Connections protection, welding 9–23 Connections, steel sections 9–20 Connections, structural bolts / anchor bolts 9–20 Construction manager 14–34 Continuity 5–133 Contract documents 13–2, 14–34 Contractor 14–34 Corners 6–18 Correction factors for prestress and concrete strength, creep only 4–89 Correction factors for relative humidity 4–90 Correction factors for volume-to-surface 4–90 Correction of errors 14–29 Corrosion and protection means 9–21 Corrosion inhibitors 9–8 Corrosion protection 9–3 Corrosion-resistant steels 9–28 Cracked concrete 6–10

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PCI DESIGN HANDBOOK/SEVENTH EDITION

Cracked-section analysis 5–18, 5–90 Cracking factor 6–11 Creep 1–4, 7–7 Creep and shrinkage strains 4–89 Critical section 5–5

D Damping, estimation 12–4 Dapped-end, anchorage of reinforcement 5–83 Dapped-end bearing 5–79 Dapped-end, diagonal tension at re-entrant corner 5–83 Dapped-end, diagonal tension in extended end 5–83 Dapped-end, direct shear 5–79 Dapped-end, flexure and axial tension in extended end 5–79 D-cracking 9–14 Dead loads 4–6, 15–2 Deadmen 8–26 Deck components, warping of 5–133 Deck panels 1–20 Decompression force 5–35 Decompression stress 5–20, 5–35 Deflections 3–9 Deformation limits 4–70 Deformed bar anchors 6–7 Deformed bar or reinforcing bar connection plate supporting steel beam, example 6–97 Deformed reinforcing bars 9–25 Deformed steel bars 9–24 Degree day 11–2 Delayed ettringite formation 9–16 Design (as a noun) 14–34 Design (as a transitive verb) 14–34 Design coefficients and factors for precast concrete seismic-force-resisting systems 4–86 Design considerations, additional 4–71 Design drawings 14–34 Design, heat transmission 10–5 Design of group weld, elastic vector method 6–49 Design of group weld, instantaneous center method 6–50 Design parameters 3–9 Design Parameters 3–9 Design practices, responsibility 14–35 Design strength interaction curves 3–50 Design strength of concrete brackets, corbels, or haunches 5–150 Design stress for underdeveloped strand 5–140 Design temperature strains, millionths 4–90 Detail (as a noun) 14–34 Detail (as a transitive verb) 14–34 Determining flexural design strength – bonded prestressing steel 5–139 Determining moments and restraining forces on eccentrically loaded columns braced against sidesway 5–149 Development length 5–115 Development of corbel reinforcement 5–115

Deviation 13–2 Dew-point temperature 11–2 Diaphragm 4–25 Diaphragm design 4–55 Diaphragm design forces 4–60 Diaphragm, detailing considerations 4–62 Diaphragm, general detailing requirements 4–63 Diaphragm over-strength factors 6–4 Diaphragm, performance-based design 4–62 Diaphragms 4–16 Diaphragms, elastic design of 4–60 Diaphragm-to-wall shear connection, example 6–82 Diaphragm, wind and low seismic hazard 4–62 Dimension, actual 13–2 Dimension, basic 13–2 Dimensions 3–2 Dimension, working 13–2 Discernible cracking 5–18 Distribution factor 7–21 Double-tee load tables 3–12 Double-tees 1–5 Draft 13–2 Drawings 13–2 Drift 4–28 Drift effects 4–7, 4–13 Drying shrinkage 7–31 Drypack 9–19 Durability 1–8 Dynamic material properties 4–66 Dynamic yield stress 4–67

E Earthquake loads 4–9 Eccentrically loaded columns 5–105 Eccentricity factor 6–11 Edge-distance factor 6–11 Educational facilities 1–15 Effective weight 12–5 Effective width of wall panels 5–116 Effects of fire, components restrained against thermal expansion 10–14 Effects of fire, continuous components 10–12 Effects of fire, simply supported components 10–11 Elastic deflections 5–88 Elastic deformation 7–31 Elastic vector method (EVM) 6–49 Emulative design 4–3 End-point criteria 10–3 End stresses at transfer 5–40 Engineer of Record (EOR) 14–34 Epoxy grouts 9–20 Equivalent volume change 4–22 Equivalent volume-change strains for typical building elements (non-prestressed components), millionths 4–94 Equivalent volume-change strains for typical building elements

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

INDEX–3

Force and loads 15–23 Force-resisting systems 4–3 Forcing frequency 12–2 Formed surface finishes 9–18 Foundations, piers, abutments, and other bearing surfaces 14–28 Framing 3–2 Free heat 11–2 Freezing and thawing 9–13

(prestressed components), millionths 4–94 Erection bracing 8–23 Erection, bracing equipment and materials 8–26 Erection drawings 13–2 Erection, factors of safety 8–26 Erection handling 8–21 Erection, handling equipment 8–25 Erection, loads 8–26 Erection requirements, special 14–28 Erection, surveying and layout 8–26 Erection tolerances 13–7 Erection tolerances, bearing 13–9 Erection tolerances, connections 13–9 Erection tolerances, mixed building systems 13–8 Erection tolerances, recommended 13–8 Erector 14–34 Estimated 3–9 Expansion anchors 6–7 Expansion joints 9–32 Expansion joints, spacing of 4–21 Expansion joints, width of 4–21

G

F Ferritic stainless steel 9–23 Fibers 9–24 Field assembly 14–29 Film or surface conductance 11–2 Finishes 9–17 Finite-element analysis 4–64 Fire dynamics simulator (FDS) 10–20 Fire endurance 10–2, 10–3 Fire endurance by rational design 10–11 Fire rating 10–3 Fire ratings, restraint 10–5 Fire resistance 10–2 Fire resistance, code and economic considerations 10–24 Fire resistance, floors 10–7 Fire resistance, multi-course assemblies 10–9 Fire-resistance rating 10–2 Fire resistance, ribbed panels 10–7 Fire resistance, roofs 10–7 Fire resistance, single course slabs 10–5 Fire resistance, wall panels 10–5 Fire resistance, walls faced with gypsum Wallboard 10–7 Fire tests 10–5 Fixed end, moments 15–25 Flanged components 5–3 Flatness 13–2 Flexural design strength 5–46 Flexure 5–3 Float finish 9–17 Floor and roof component erection tolerances 13–12 Floor vibrations, human response 12–2 Floor vibration, types 12–2 Flushness 13–2 Fly ash 9–4 For 3–9 INDEX–4

Galvanic series 9–21 General blast-design methods 4–67 General contractor 14–34 General design information 15–1 Geometric sections, properties 15–1 Glass-fiber-reinforced concrete (GFRC) 1–12 Granite 7–20 Granite veneers 7–32 Gravity 3–3 Gravity and lateral-forceresisting systems 3–3 Gravity and lateral loads 1–4 Gravity loads 4–6 Green buildings 1–4 Ground granulated blast-furnace slag 9–4 Grout 9–3, 9–19 Grout at bearing areas 14–29 Grouted anchors 6–8 Guide specification, architectural precast concrete 14–23 Guide specification, structural precast concrete 14–23

H Handling devices 8–10 Handling, lateral stability 8–18 Hanger connections 6–60 Headed concrete anchor (HCA) design 6–8 Headed concrete anchors 6–5, 6–9 Headed concrete anchors, concrete strength 6–9 Headed concrete anchors, steel strength 6–9 Heat capacity 11–2, 11–11 Heat transmittance 11–2 Hertz 11–23 Higher harmonics 12–6 High-range water reducers 9–8 High seismic hazard, untopped systems for 4–64 High-strength concrete 1–2 High-strength steels 1–4 High-strength threaded rods 6–7 History 1–2 Hollow-core decks, effective resisting widths for concentrated loads on 5–128 Hollow-core load tables 3–31 Hollow-core section properties 3–35 Hollow-core slabs 1–5 Horizontal shear transfer in composite components 5–52 Horizontal stirrups 5–112

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

Hot-dip galvanizing 9–22 Hydrogen embrittlement 9–23

I IBC 2006 4–5 I-beam 1–5 I-girder 1–20 IIC 11–23 Impact insulation class (IIC) 11–23 Impact noise reduction 11–23 Importance factor 7–18 Initial camber 5–88 In-service considerations, component strengthening 9–35 In-service considerations, connection repair 9–35 In-service considerations, cracking 9–33 In-service considerations, crack repair 9–35 In-service considerations, maintenance 9–39 In-service considerations, patching 9–34 In-service considerations, repair 9–34 Inspector 14–34 Instantaneous center method (ICM) 6–49 Interaction of tension and shear 6–25 Interface, characteristics 13–33 Interface tolerance design approach 13–32 Interface with other trades 14–30 Interfacing tolerances 13–32 Interior shear walls 3–3 International Building Code 1–4 International Building Code (IBC) 6–7 Interstory drift 4–9 In-the-field 6–25 Inverted-tee beam load tables 3–47

J Joint profile 9–30 Joint sealant considerations 9–31 Joint sealants 9–30 Justice facilities 1–13

L Large-panel bearing-wall structures 4–18 Lateral distribution 4–13 Lateral soil loads 4–14 L-beam load tables 3–45 Leadership in Energy and Environmental Design (LEED) 1–5 Ledge, attachment of to web 5–69 Ledge, longitudinal bending of 5–69 Ledge, shear strength of 5–68 Ledge, transverse (cantilever) bending of 5–68 LEED 1–4 Length of structure without use of expansion joints 4–92 LFRS considerations 4–5 Licensed design professional (LDP) 14–34 Life-cycle assessment or LCA 1–5 Lifting points 8–2, 8–6 Lightweight aggregate concrete 10–2

Limestone 7–20, 7–32 Lithium 9–9 Live loads 4–6 Load-bearing components 1–4, 7–6 Load combination factor 7–21 Load combinations 4–14 Load factors 6–3 Load factors, concrete anchorages 6–3 Load factors for diaphragms 4–15 Loads 6–3 Load tables 3–8 Load-transfer devices 6–5 Log-decrement damping 12–4 Long-line beds 1–2 Long-term camber/deflection 5–90 Loov hanger 6–64 Loss of prestress 5–83 Low-relaxation strand 1–2, 9–25

M Manner of delivery 14–27 Manufacturer 14–34 Marble 7–20, 7–32 Marking and shipping of materials 14–28 Materials of other trades 14–29 Maximum seasonal climatic temperature change, Farenheit 4–88 Member 14–34 Metakaolin, calcinated clay 9–4 Metal-inert gas (MIG) 9–23 Mixed structural materials 4–18 Modal damping 12–4 Modeling partially fixed bases 4–50 Modular products 1–5 Modulus of elasticity 9–3, 15–29 Modulus of rupture 5–18, 9–3 Moment connections 6–70 Moment frames 3–3 Moment of inertia of transformed section – prestressed components 5–147 Moment resistance, column bases 4–46 Moment-resisting building frames 4–46 Moment-resisting frames 4–3 Moments, shears, and deflections in beams with overhangs 15–28 Monorails 1–23 Mortar 9–19 Moving load placement for maximum moment and shear 15–27

N NEHRP 2000 and 2003 4–6 Noise insulation objectives 11–24 Non-emulative design 4–5 Non-load-bearing components 7–3 Non-prestressed component design 5–16 Non-shrink grouts 9–20

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

INDEX–5

Normalweight concrete 10–2 Note 4 3–9

O Office buildings 1–13 On responsibility for design and construction of precast concrete structures 14–34 Openings through decks 5–128 Openings through webs 5–129 Ordinary moment frame connection, example 6–96 Out-of-plane bending near beam end 5–70 Overload factors 6–3 Owner 14–34

P Painting, caulking, and closure panels 14–29 Parking structures 1–17 Partial interaction curves for precast, prestressed solid and sandwich wall panels 3–56 Partial interaction curves for precast, reinforced concrete solid and sandwich wall panels 3–57 Partial interaction curves for prestressed hollow-core and sandwich wall panels 3–55 Patch 9–3 Patching 14–29 Pavements 1–23 PCI-certified plants 1–4 PCI’s Plant certification program 1–7 PCI standard design practice 14–3 P-∆ effects 4–14 Perm 11–2 Permeability, water vapor 11–2 Permeance 11–2 Pigments 9–10 Piles 1–5, 1–23, 3–10, 5–116 Piles, service-load design 5–116 Piles, strength design 5–116 Plastic / drying shrinkage cracking 9–14 Plastic section moduli 15–1 Plate-and-bar diaphragm shear connection, example 6–80 Plate tolerances, architectural panels 13–7 Plate tolerances, bowing 13–7 Plate tolerances, smoothness 13–7 Plate tolerances, structural products 13–7 Plate tolerances, warping 13–7 Plumb 13–2 Pocketed spandrels 5–70 Point loads on double-tee flanges 5–128 Poles 1–23 Polymers 1–4 Post-grouting 6–6 Post-installed anchors 6–7 Post-tensioning precast 1–20 Precast concrete 14–34 Precast concrete column covers, fire 10–22 Precast concrete compression components, strength design of 5–99 INDEX–6

Precast concrete engineer 14–34 Precast concrete pavements 1–7 Precast concrete used as forms 7–35 Precast, prestressed concrete component 3–2 Precautions during delivery 14–28 Pre-grouting 6–6 Preliminary analysis 3–2 Prestressed component design 5–18 Prestressing bars 9–25, 15–31 Prestressing strand and wire 15–30 Prestressing-strand loops 8–10 Prestressing strands 3–10 Prestressing tendons 9–24 Prestress loss, anchorage seating loss and friction 5–83 Prestress loss, creep of concrete and relaxation of tendons 5–83 Prestress loss, elastic shortening of concrete 5–83 Prestress losses 3–10 Prestress loss, estimating prestress loss 5–84 Prestress loss, range of values for total loss 5–84 Prestress loss, shrinkage of concrete 5–83 Prestress transfer and strand development 5–35 Pretopped double-tee load tables 3–24 Pretopped systems 13–2 Production drawings 13–2 Production limitations 1–26 Production process 1–23 Product tolerances 13–4 Product tolerances, camber 13–4 Product tolerances, differential camber 13–4 Product tolerances, horizontal misalignment 13–4 Product tolerances, overall dimensions 13–4 Product tolerances, strands position 13–4 Product tolerances, sweep 13–4 Progressive failure 1–2 Protection of connections, fire 10–21 Pullout strength 6–15

Q Quality 13–2 Quality assurance 13–2 Quality control 13–2

R Railroad ties 1–23 Raker beams 1–5 Recommended maximum spans for precast concrete stairs 3–61 Rectangular beam load tables 3–44 Redundancy 4–14 Reinforced concrete bearing 5–77 Reinforcement 9–24 Reinforcement, limitations 5–5 Reinforcement protection, carbonation / cracking 9–27 Reinforcement protection, concrete cover 9–27 Reinforcement protection, corrosion mechanism / chlorides 9–26

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PCI DESIGN HANDBOOK/SEVENTH EDITION

Reinforcement protection, epoxy-coated reinforcement 9–28 Reinforcement protection, epoxy-coated strand 9–28 Reinforcement protection, galvanized reinforcement 9–27 Reinforcement, protection of 9–26 Reinforcing-bar couplers and splice devices 6–6 Reinforcing bars 6–5, 7–13, 15–34 Reinforcing bars in conduit 6–6 Relative alignment 13–2 Relative humidity 11–2 Relative humidity (RH) 11–18 Relevant standards and publications 9–40 Repair 9–3 Requirements for parking structures, fire 10–19 Residential buildings 1–12 Response modification coeffient 4–13 Responsibility 14–35 Retaining walls 1–23 Retarded / exposed aggregate finish 9–19 Retarders 9–9 Rigging 8–6 Rigid and flexible diaphragms 4–56 Rigid or flexible diaphragms, behavior and design considerations 4–57 Rigid or flexible diaphragms, defining 4–56 Riser erection tolerances 13–20 Rolling blocks 8–6 Room module erection tolerances 13–22 Rotation coefficients 15–23 R-value 1–15

S Safe Superimposed Loads 3–8 Safety 14–29 Sandblast, finish 9–18 Sand-cement mixtures 9–19 Sand-lightweight concrete 10–2 Sandwich panels 5–122, 10–10 Sandwich panels, composite during handling, but non-composite during service life 5–125 Sandwich panels, composite for full life cycle of panel 5–122 Sandwich panels, non-composite for full life cycle of panel 5–122 Sandwich panels, partially-composite for full life cycle of panel 5–125 Sandwich panels, structural design 5–122 Sandwich wall panel, connections 5–126 Sandwich wall panels, thermal bowing 5–128 Sandwich wall panels, Wythe connectors 5–127 Scaling 9–17 Sealant types 9–30 Second-order analysis of an uncracked component, example 5–107 Second-order (P-∆) analysis 5–106 Section properties 5–41 Section propertiesa and allowable service loads for pre-

stressed concrete piles 3–59 Section properties and allowable service loads of prestressed sheet piles 3–60 Security measures 14–30 Seismic cladding factor 7–21 Seismic design categories 4–10 Seismic design category D and higher – topped systems 4–63 Seismic hazard – topped and pretopped systems, moderate 4–63 Seismic loads 7–20 Selfconsolidating concrete 1–4 Sensitivity of connection to tolerances 6–4 Service load design 5–16 Service load stresses 5–41 Setup 13–3 Seven-wire strand 1–2 SFRS 4–11 Shear 5–46 Shear design, shallow drape 5–142 Shear design, steep drape 5–143 Shear design, straight strands 5–141 Shear friction 5–58 Shear reinforcement 5–145 Shear resistance, fire 10–19 Shear resistance of prestressed components 5–46 Shear strength 9–10 Shear transfer between components 4–55 Shear-wall buildings, principles of 4–23 Shear-wall, code requirements 4–23 Shear-wall deflection 4–97 Shear-wall, design guidelines for structures 4–24 Shear wall, frame interaction 4–54 Shear wall, intermediate precast concrete structural 4–23 Shear wall, ordinary structural 4–23 Shear walls 4–3, 5–122 Shear walls, coupled 4–28 Shear walls, distribution of lateral loads 4–26 Shear wall special precast concrete structural 4–24 Shear walls, proportioning 4–25 Shear walls, stiffness analysis 4–25 Shear walls with large openings 4–29 Shear-wall systems 4–23 Shear-wall systems, evaluation of 4–29 Shop drawings 13–2, 14–35 Shoring 5–18 Shrinkage 1–4, 7–7, 13–3 Shrinkage and temperature reinforcement 5–5 Side edge 6–20 Side-face blowout 6–15 Sign convention 5–18 Silanes 9–29 Silica fume 9–4 Siliceous aggregate concrete 10–2 Siloxanes 9–29 Simple diaphragm design, horizontal beam analogy 4–55 Single-, double-, and quad-cell modules 1–5

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

INDEX–7

Site classifications and coefficients 4–85 Slenderness effects in columns and wall panels 5–106 Smoothness 13–3 Snow drifting 4–81 Snow loading 4–80 Snow loads 4–7 Solid flat-slab load tables 3–41 Sound barriers 1–23 Sound levels 11–23 Sound transmission loss 11–23 Sources of stress loss 5–83 Spandrels 7–13 Spandrels, load-bearing 7–6 Spandrels, non-load-bearing 7–3 Span-to-depth ratios 3–2 Special design considerations 5–128 Specially finished structural precast concrete 13–3 Special moment frames for high seismic design categories 4–54 Special moment frames, seismic design category C 4–53 Specialty inserts 6–7 Specialty structural engineer (SSE) 14–35 Splitting tensile strength 9–3 Spreader beams 8–6 Stadium riser 5–42 Stadium riser allowable spans 3–62 Stadium risers 3–11 Stadium riser units 1–5 Stadiums/arenas 1–19 Stadium seating, vibration of 12–6 Stainless steel, dissimilar metal welding 6–45 Stainless steel, plate welding 6–45 Stainless steel, stud welding 6–45 Stainless-steel, welding 6–45 Stairs 3–11 Stair unit erection tolerance 13–24 Standard fire tests 10–2 Standard operations practice 14–24 Standard operations practice, architectural precast concrete 14–24 Standard operations practice, certification categories 14–24 Standard operations practice, contract administration 14–30 Standard operations practice, contract documents 14–25 Standard operations practice, delivery of materials 14–27 Standard operations practice, design responsibility 14–25 Standard operations practice, drawing approvals 14–26 Standard operations practice, drawing discrepancies 14–26 Standard operations practice, erection 14–28 Standard operations practice, erection drawings 14–26 Standard operations practice, finishes 14–27 Standard operations practice, fire-rated products 14–27 Standard operations practice, inspections 14–27 Standard operations practice, materials 14–27 Standard operations practice, production drawings 14–26 Standard operations practice, qualification of erector 14–25 Standard operations practice, qualification of manufacturer INDEX–8

14–24 Standard operations practice, samples and mockups 14–24 Standard operations practice, shop drawings 14–26 Standard operations practice, structural precast concrete 14–24 Standard operations practice, tests of materials 14–27 Standard operations practice, warranties 14–30 STC 11–23 Steam curing 1–2 Steel, built-up sections 6–30 Steel, combined loading 6–32 Steel, design flexural strength 6–30 Steel, design shear strength 6–30 Steel, design torsional strength 6–30 Steel, hollow structural sections (structural tubing) in torsion 6–32 Steel materials 6–9 Steel, non-triangular stiffener design 6–43 Steel plates and shapes 6–9 Steel, rectangular solid plates in torsion 6–30 Steel shapes 6–5 Steel, strength reduction 6–3 Steel, triangular stiffener design 6–35 Steel-trowel finish 9–18 Steel, unstiffened connection angles 6–32 Stirrups 4–54 Stone-faced panels 1–4 Stone properties 7–32 Stone sizes 7–33 Stone veneer–faced precast concrete 7–32 Storage 8–18 Storage tanks 1–23 Story-drift 7–10 Strain compatibility 5–3 Strand debonding 5–40 Strand placement 3–10 Strength analysis of weld group 6–51 Strength, concrete compressive 9–3 Strength design 5–3 Strength-reduction factors 5–5, 6–3 Strength-reduction factors, anchorages 6–3 Strength-reduction factors, concrete flexure 6–3 Stress block, depth 5–3 Stress loss, critical locations 5–87 Stress-relieved strand 9–25 Stress-strain 9–10 Stress-strain relationship 5–3 Stress-strain relationship – bonded strand 5–140 Stripping 8–2 Stripping, benefits of prestressing 8–9 Stripping design 8–8 Stripping, factors of safety 8–8 Stripping, stress limits and crack control 8–9 Structural design considerations 7–7 Structural engineer of record (SER) 14–35 Structural integrity 4–15 Structural-steel corbels 6–56 Structural-steel design 6–30

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION

Structural wall panel erection tolerances 13–16 Structural welded-wire reinforcement 9–26 Strut-and-tie design method 5–112 Strut-and-tie modeling 4–64 Studs 6–9 Sub-diaphragms 4–63 Submerged metal arc welding (SMAW) 9–24 Sulfate attack 9–17 Sunshine Skyway 1–2 Superimposed loads 3–8 Supplemental, reinforcement 6–10 Surface roughness 7–18 Surfaces to receive composite concrete 9–17 Sustainability 1–4 Sweep 13–3 System over-strength factor 6–4

Tolerances, wall panels 13–5 Tolerance, weld plates 13–5 Topographic factor 7–18 Torsion 4–13, 5–59 Torsion diagrams, reactions, and rotations 15–26 Total-precast-concrete systems 1–8 Transfer length 5–35 Transition sections 5–5 Transportation 8–19 Treatment of joints between wall panels, fire resistance 10–10 Trinitrotoluene (TNT) 4–66 Truss geometry 5–112 Tungsten-inert gas (TIG) 9–23

T

Ultra-high-strength concrete 1–4 Ultraviolet radiation (UV) exposure 9–22 Underwriters Laboratories 10–2 Unloading time allowance 14–28 Use of design aids 5–6 Utilities 14–29

Temperature 7–7 Temperature change 1–4 Temporary floors and access 14–29 Tensile strength 9–10 Tensile strength, flexural strength 9–11 Tensile strength, split cylinder test 9–11 Tension ties 4–16 Terra cotta 7–20 Thermal bridges 11–15 Thermal conductance 11–2 Thermal conductance of an air space 11–2 Thermal conductivity 11–2 Thermal fusible membrane 11–19 Thermal inertia 11–2 Thermal mass 1–4, 11–2 Thermal or flame finish 7–32 Thermal properties 11–2 Thermal resistance 11–2 Thermal storage (mass) effects 11–11 Thermal transmittance 11–3 Thin-set brick 1–4 Threaded inserts 8–10 Ties 4–54 Tile 7–20 Tipping 13–3 Tolerance 13–3 Tolerances 14–28 Tolerances, acceptability range 13–3 Tolerances, contractual 13–3 Tolerances, economical 13–3 Tolerances, erection 13–3 Tolerances, feasible 13–3 Tolerances, haunches of columns 13–5 Tolerances, interfacing 13–3 Tolerances, legal 13–3 Tolerances, product 13–3 Tolerances, responsibility 13–3 Tolerances, structural 13–3 Tolerances, visual 13–3

U

V Varying section properties of compression components 5–116 Veneered panels 7–20 Veneer jointing 7–35 Vertical distribution 4–13 Vibration, damping 12–4 Vibration, isolation for mechanical equipment 12–8 Vibration, minimum natural frequency 12–5 Vibration, natural frequency 12–2 Vibration, rhythmic excitation 12–5 Vibrations, harmonics 12–5 Vibrations, mixed-use structures with parking 12–8 Vibrations, walking 12–5 Viscosity modifying agents 9–8 Volume-change effects in moment-resisting frames 4–21 Volume-change forces 3–8 Volume changes 1–4, 4–18 Volume changes, shrinkage and creep 9–12 Volume-change strains for typical building elements (non-prestressed components), millionths 4–91 Volume-change strains for typical building elements (prestressed components), millionths 4–91

W Wall panels, load-bearing 7–7 Wall panels, non-load-bearing 7–6 Wall-to-wall shear connection with combined loading, example 6–91 Wall-to-wall tension connection, example 6–84 Walnut Lane Memorial Bridge 1–2

PCI DESIGN HANDBOOK/SEVENTH EDITION First Printing/CD-ROM Edition

INDEX–9

Warehouses and industrial buildings 1–14 Warping 13–3 Water, mixing 9–9 Waterproofing 9–3, 9–29 Waterproofing, clear surface sealers for architectural precast concrete panels 9–29 Waterproofing, coatings for horizontal deck surfaces 9–29 Waterproofing, surface coatings for architectural precast concrete 9–29 Weld design 6–46 Weld design, fillet 6–46 Weld design, full-penetration welds 6–46 Weld design, partial-penetration groove 6–46 Weld design, reinforcing bar 6–46 Welded-wire reinforcement 1–24, 7–12, 9–24 Welding 6–43 Welding, corrosion resistance of connections 6–43 Welding, cracking in concrete around welded connections 6–49 Welding, design of group welds 6–49 Welding, hot-dip galvanized 6–45 Welding, stainless steel 6–45 Weld, strength of reinforcing bar 6–47 Wind-load determination, example 7–16 Wind loads 4–7 Window panels, load-bearing 7–6 Window panels, non-load-bearing 7–5 Wire rope 8–26 Wire tie connectors 5–128 Working space and crane access 14–29

Y Yarding and storage 8–18

Z Zinc-rich primers 9–22

INDEX–10

First Printing/CD-ROM Edition

PCI DESIGN HANDBOOK/SEVENTH EDITION