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ARCHITECTURAL AND STRUCTURAL TOPICS WOOD-STEEL-CONCRETE • THE NEW LADDER TYPE CURRICULUM GEORGE SALINDA SAtVAN ... fuap • ASSISTANT PROFESSOR College of Engineering and Architecture Baguio Colleges Foundation 1980-1988 • First and lone graduate of B.S. Architecture, 1963 North of Manna, St. Louis University, Baguio City • Former instructor 1965-1969 at St. louis University • Recipient of various ACE certificates, Architects Continuing Education Program • A licensed Architect, active practitioner and a licensed building constructor, inventor and a board topnotcher • Past president of United Architects Phils. Baguio Chapter 1982 and 1983 • Elected National Director; UAP. Regional District I for the year 1987 • Conferred the title of "Fellow• United Architects Phils. College of Fellows, October, 1988
JOSELITO F. BUHANGIN • • • •
'
Bachelor of Science in Civil Engineering 1987, St. Louis University, Baguio City Associate Professor, Civil Engineering 1980 to Date Expertise: Structural Desig11, Consu~ancy, Construction Management Member: PICE- Phil. Institute of Civil Engrs. ACI - American Concrete Engineers Institute
.
JMC PRESS, INC. 388 Quezon Avenue, Quezon City
Copyright © 1996 by: JMC PRESS, INC. and GEORGE S. SALVAN JOSELITO F. BUHANGIN All rights reserved. No part of !his book may be reproduced in any manner without permission of the publisher.
FIRST EDITION ISBN: 971 -1,-0987-5 Published and Printed by: JMC PRESS, INC. 388 Quezon Avenue, Quezon City Distributed by: GOODWILL BOOKSTORE Main Office: Rizal Avenue, Manila P.O. Box 2942, Manila
Dedicated to all future Architects and Engineers The hope for a functional, comfortable And convenient designs for better living.
ACKNOWLEDGMENTS
The authors wish to acknowledge the helpful comments and reviews of a rumber of individuals and organizations during its writing. Our sincere thanks to friends, colleagues and reviewers for their suggestions for improvement, discussions of general approach, and other assistance. In particular, we wish to thank Mr. Arnel Astudillo, Mr. Fredelito Alvarado, Miss MymaAquinoand Miss Agnes Arceo, all graduates of St. Louis University class '94 and '95, for their fine and clear drafting of all the illustrations throughout the various chapters. likewise to Engr. Anastacio D. AngNay Jr. class 1995, Civil Engineering BCF for his untiring and patient editing the original manuscripts and proofreading the galley proofs, with the help of Mr. Sudhir Thapa, an architect from Nepal, and a graduate of B.S. Arch. Baguio Colleges Foundation, class 1993, who made some mustrations on Chapter 1 and likewise to Mr. Arthur B. Managdag Jr. a graduate of B.S. Civil Engineering, St. Louis University class 1995. To Mr. luis V. Canave who guided me on the complete process of publishing from pasted-up dummy, to final page proofs and up to the final printing, together with the patient laser typesetting of Mrs. Tess Espinoza Dulatre and Mr. Joseph P. Reate. Finally, to Mr. Roy Pagador, an AR student of Baguio Colleges Foundation, for developing and designing the chapter pages and the simple yet attractive cover design.
PREFACE The purpose of this book is to introduce architects and engineers to the structural design of concrete, wood and steel structures in one volume. It's production was undertaken because it was felt that much of the three structural topics has become too specialist and detailed in nature and does not offer an easily understood introduction to the subject. Simplified in its approach, this book is a useful and practical guide and reference volume in design offices and a suitable text for senior architectural and engineering students. Particular emphasis has been placed on the logical order and completeness of the design examples. The examples are done in a step-by-step order and every step is worked out completely from first principles, at least once. This book deals principally in the practical application of engineering principles and forrrulas and in the design of structural members. The derivations of the most commonly used formulas are given in order that the reader may comprehend fully why certain formulas are appropriate in the solution of specifk: problems. This text pulls together the design of the various element~ into ~ single reference. A large number of practical design examples are provided throughout the text. Because of their wide usage, buildings naturally form the basis of the majority of these examples. The main reason, however, for writing this book was the observation made by the authors during many years of practical work and university teaching, that most so-called design books are still basically concerned with analysis.
tt is the Author's conviction that a proper text must.demonstrate to the reader how to make his first assumptions, how to select initial sections, and what procedure to follow after making a first choice so as to arrive at a final design. Part of this emphasis on an aspects of design has resutt~d here in the discussion of several modern automatic design techniques as well as design optimization procedures. Chapter 1 sets the stages for the volume by providing definitions, structural and engineering concepts for Architecture and giving illustrations of the various types and methods of construction. Chapter 2 continues the introductory material with a discussion of the goals of structural design based, in part, on the limit states design concept. It deals comprehensively on the selection of structural system whether for wood, steel or concrete. Determining the loads acting on buildings is basic to structural analysis and design. These are presented in Chapter 3 as a basis for developing the flexural theory discussing time-dependent deflections, and so on. There are many types of loads on buildings. This chapter provides an overview of what the different types are, how they are determined and their effects on buildings and Architectural design. Chapter 4 deals with structural fundamentals like the conc~pt of force, stress, the properties of crosssections (centroid, moment of inertia, static moment of .area) and free body diagrams. Chapter 5 discusses the analysis of beams and columns. The corf1>lete analysis of beams would require the solution for shear and moment diagrams, while the principles of column analysis and require an understanding of radius of gyration and slenderness ratio as properties of the column.
v
Chapter 6 centers on truss analysis by the Methods of Joints, Sections, or by Maxwell's diagram. Chapter 7 is an introduction to soil mechanics with discussions on foundation systems and retaining wall structures. Chapter 8 gives a description of the different types of connections and their uses. A majority of structural failures occur in the connection of members and not in the members themselves, and may be caused by either of the following (a) the incorrect type of connector is used, (b) the connector is undersized, (c) too few in number, or (d) improperly installed. Chapter 9 discusses how building code provisions relate to structural design, how loads must be determined, what stresses are allowed in structural members, formulas for designing •members of various materials, and miscellaneous requirements for construction. Chapter 10 focuses on the basic concepts of Structural Timber Design. Chapter 11 is an overview of the principles of Structural Steel Design. Chapter 12 discusses the basic principles of Structural reinforced concrete design and show how to make some common, fairly simple design calculations. Chapter 13. Although the primary focus of.this chapter is the structural design of walls, there are other considerations, in selecting the optimum waH for a particular circumstance. The designer must exercise judgement in selecting the wall system to best satisfy all the requirements of the project. Chapter 14 is a discussion of wind forces and their effects on building. Chapter 15 discusses the basic principles of earthquakes and primary design and planning guidelines to make a structure earthquake-resistant. In addition, a basic review of the static analysis method is presented with some simplified problems to help explain the design concepts.
vi
TABLE OF CONTENTS Chapter
1
STRUCTURAL AND ENGINEERING CONCEPTS FOR ARCHITECTURE ..................................................................
1
1. Overall Approach to Structural Education, 1 2. Structure and Other Subsystems, 3 3. Construction Methods and Structures as Expression of Architectural Design, 13 A. Building, 13 B. Form, Shape and Appearance, 13 C. Structural Forms, 13 D. Concrete, 15
Chapter
2
SELECTION OF STRUCTURAL SYSTEMS ......................... 37 1. Standard Structural Systems, 38 A. Wood, 38 B. Steel, 40 C. Concrete, 41 D. Masonry, 45 E. Composite Construction, 46 F. Walls and the Building Envelope , 47 2. Complex Structural Systems , 47 A. Trusses, 47 B. Arches, 48 c. Rigid Frames, 49 D. Space Frames, 50 E. Folded Plates. 51 F. Thin Shell Structures, 51 G. Stressed-Skin Structures, 51 H. Suspension Structures, 52 I. Inflatable Structures, 53 3. Structural System Selection Criteria, 53 A. Resistance to Loads, 53 B. Building Use and Function, 54 C. Integration with Other Building Systems, 54 D. Cost Influences, 54 E. Fire Resistance, 55 F. Construction Limitations, 55 G. Style, 55 H. Social and Cultural Influences, 56
Chapter
3
LOADS ON BUILDING .......................................................... 57 1. Gravity Loads, 58 A. Dead Loads, 58 B. Live Loads, 60 C. Combination Loads, 63 vii
2. Lateral Loads, 63 A. Wind,63 B. Earthquake, 65 3. Miscellaneous Loads . 65 A. Dynamic Loads, 65 B. Temperature-Induced Loads, 67 C. Soil loads, 67 D. Water, 68
Chapter
4
STRUCTURAL FUNDAMENTALS ........................................ 69 . 1. Statics and Forces, 70 A. Statics. 70 B. Forces, 70 C. Stresses, 72 D. Thermal Stresses, 72 E: Strain and Deformation , 73 F . .Moment, 75 2. Properties of Sections, 76 A. Centroid, 76 B. Statical Moment of Area, 76 C. Moment of lneryia, 79 3. Structural Analysis, 61 A. Resultant Forces, 61 B. Components of a Force, 82 c. Free B_ody Diagrams, 63 ·
Chapter
5
BEAMS AND COLUMNS ...................................................... 85 1. Beams,86 A. Basic Principles . 86 B. Types of Beams, 89 C. Shear Diagrams, 91 D. Moment Diagrams, 94 2. Columns. 96 . A. Basic Principles, 96
Chapter
6
TRUSSES ... .... ... .. .. .... .. .. .. ... .. .. ..... .. .. ... .. .... ... ..... .. .. ............. ... 99 1. Basic Principles, 100 2. Truss Analysis, 102 A. Method of Joints, 103 B. Method of Sections, 106 C. Graphic Method, 108
Chapter
7
sOILS AND FOUNDATIONS ................................................ 111 1. Soil Properties, 112 A. Subsurface Exploration, 113 B. Soil Types and Bearing Capacities, 113 C. Water in Soil; 113
viii
D. Soil Treatment, 114 E. Other Considerations, 118 2. Foundation Systems, 119 A. Spread Footings, 119 B. Pile Foundations, 120 C. Designing Footings, 121 3. Retaining Walls, 123 A. Types of Retaining Walls, 123 B. Forces on Retaining Walls, 124 C. Design Considerations, 124
Chapter
8
CONNECTIONS ............................. .. ......... .... ........ ...... .......... 125 1. Wood Connections . 126 A General, 126 B. Type of Load, 126 C. Condition of Wood, 126 ;Q, Service Conditions, 127 E. Fire-Retardant Treatment, 127 F. Angle of Load, 127 G. Critical Net Section, 127 H. Type of Shear, 128 I. Spacing Connectors, 128 J . End and Edge Distances to Connectors. 128 K. Nails, 128 L. Screws, 129 M. Lag Screws, 130 N. Bolts. 130 0 . Timber Connectors, 136 P. Miscellaneous Connection Hardware , 136 2. Steel Connections, 136 A. Bolts, 137 B. Welds, 143 3. Concrete Connections, 146 A. Rebars and Keyed Sections, 146 B. Weld Plates, 147 C. Shear Connectors, 147
Chapter
9
BUILDING CODE REQUIREMENTS ON STRUCTURAL DESIGN ........ .............................. ................. 149 1. Loading, 150 A. Live Loads, 151 B. Dead Loads, 151 C . Lateral Loads, 151
2. Allowable Stresses , 152 A. Wood, 152 B. Steel. 153 C. Concrete , 154
ix
3. Construction Requirements, 154 A. Wood,154 B. Steel, 155 C. Concrete, 155 4. Fireproofing, 155
Chapter
10
WOOD CONSTRUCTION ..................................................... 157 1. Properties of Structural Lumber, 158 A. Sizes. 158 B. Grading, 158 C. Design Values, 160 D. Moisture Content. 160 2. Wood Beams, 162 A. Design for Bending, 162 B. Design for Horizontal Shear, 163 c. Design for Deflection, 163 3. Miscellaneous Provisions, 165 A. Notched Beams, 165 B. Size Factor, 166 C. Lateral Support, 166 D. Bearing, 166 4. Wood Columns, 167 5. Joists, 170 6. Glued Laminated Construction, 171 7. Planking, 172
Chapter
Chapter
11
STEEL CONSTRUCTION ..................................................... 173
12
CONCRETE CONSTRUCTION .......................................... ;. 193
1. Properties of ~tructural Steel, 174 A. Types and Composition of Steel, 175 B. Shapes and-Sizes of Structural Steel, 175 C . Allowable Stresses, 177 2. Steel Beams, 178 A. Lateral Support and Compact Sections, 178 B. Design for Bending, 179 C. Design for Shear, 162 D. Design for Deflection, 186 3. Steel Columns, 188 A. End Conditions. 188 B. Design for Axial Compression, 189 4. Built-Up Sections, 191 5. Open-Web Steel Joists, 191
1. Concrete Materials and Placement, 195 A. Composition of Concrete, 195 B. Admixtures, 196 C. Reinforcing Steel, 196
X
2.
3.
4.
5.
6.
Chapter
13
D. Placing and Curing, 196 E. Testing Concrete, 198 Safety Factors, 199 Concrete Beams, 199 A Basic Concepts of Design, 199 B. Design for Flexure, 202 C. Shear, 206 D. Compression Steel, 207 E. Development Length and Reinforcement Anchorage, 207 F. Deflections, 208 G. Continuity, 208 H. T-Beams, 211 Concrete Slabs, 212 Concrete Columns. 212 A. Tied Columns, 2~ 3 8 . Spiral Columns, 2~3 Prestressed Concrete, 214 A. Precast, Pretensioned, 214 B. Post-Tensioned, 214
WALL CONSTRUCTION ...................................................... 215 1. Masonry Walls, 216 A. Single Wythe Walls, 218 8 . Reinforced Hollow Unit Masonry, 2~8 C. Cavity Walls, 219 D. Reinforced Grouted Masonry, 2~9 E. Openings, 221 2. Stud Walls, 221 A. Wood Studs, 222 B. Metal Studs. 223 C. Openings, 223 3. Concrete Walls, 224 A. Cast-in Place, 224 8. Precast Concrete Walls, 225 4. Building Envelope, 226 A Attachment to Structural Members, 226 B. Movement, 227
Chapter
14
LATERAL FORCES- WIND ................................................. 229 1 . The Effect of Wind on Buildings, 230 B. Wind Measurement, 231 C. Variables Affecting Wind Loading , 232
2. Analysis of Wind Loading, 233 A. Ce Factor, 234 B. Cq Factor. 236 C. qs Factor, 236 D. Importance Factor, 237
xi
E. Load Combinations Required, 239 F. Special Areas and Components, 239 3. Design of Wind-Resisting Structures. 240 A. Lateral Force Distribution, 240 B. Building Shape and Framing Methods, 243 C. Diaphragm Design, 246 D. Chord Force, 246 E. Shear Walls and Overturning, 247 F. Drift, 249 G. Connections, 249
Chapter
15
LATERAL FORCES-EARTHQUAKES ................................. 251 1. Basic Principles, 253 A. Characteristics of Earthquakes, 253 B. Measurement of Earthquakes, 254 C. Seismic Zones, 254 D. The Effect of Earthquakes on Buildings, 255 2. Structural Systems to Resist Lateral Loads, 256 A. Bearing Wall Systems, 257 B. Building Frame Systems, 259 C. Moment-Resisting Frame Systems, 260 D. Dual Systems, 260 E. Horizontal Elements, 260 3. Building Configuration, 261 A. Torsion, 263 B. Plan Shape, 264 C. Elevation Design, 266 4. Analysis of Earthquake Loading, 268 A. Z Factor, 268 B. 1 Factor, 269 c. c Factor. 270 D. Rw Factor, 271 E. w Factor, 271 F. Distribution of Base Shear, 271 G. Parts of Buildings, 274 H. Load Combinations Required, 274 5. Additional Considerations, 274 A. Overturning Moment, 274 B. Drift, 274 C. The Rise and Fall of Buildings, 276 D. How Floors Damage Property, 278
Bibliography...........................................................................
279
Index ...................................................................................... 280
xii
I
STRUCTURAL and ENGINEERING CONCEPTS for ARCHITECTURE
STRUCTURAL AND ENGINEERING CONCEPTS FOR ARCHITECTURES 1. OVERALL APPROACH TO STRUCTURAL EDUCATION The objective of architectural d~ign is to create en effective environmental whole, a total system of interacting environmental subsystem. Since the architectural challenge is to deal in a coherent way, with organiZational, symbolic, a.nd constructi~e comple·xtty, fragmentation of techntca! knowledge does not contribute to a creative r~ by designers. This leads to an educational conclusion that the Ieamer must never be anowed to forget that his ability to conCeptualize overall space-form interactions will allow him to control the need for details, and not vice veBB. It a.tso suggests that a common educational strategy for students of both engineering and architecture would be to move deductively; from an.introduction to structures that cOnsiden. the schematic implications of buildings viewed as space-fonn
CENTRE GEORGES POMPIDOV- PARIS
SYDNEY OPERA HOUSE: AUSTRALIA
MUNICH ClYMPIC STADIUM
2
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to a logical elaboration of this basic undemanding. The basic understanding focusses on consideration of major structural subsystems and discrimination of key elements, whereas, the act of elaboration involves attention to the details required to realize the whole. The good sense of such an overall approacl') to education can be vividly characterized by considering what we often termed the nonstructural space enclosure and subdivision aspects of architectural design. The spatial organization and'8rticulation of the various properties of activity spaces calls for control of the external and intemal adjacency and interface potentials. Horizontal and vertical surfaces in the form of floors, walls, roofs, and penetrations through these surfaces must be provided to establish varying degrees of spatial differentiation, enclosu~, access, and geometric definition. Imagine that the physical components of a spatial organization scheme were designed with n~ thought for tt)eir structural implications. The probability for major revision of early·concepts due to structural requirements will be high. Now, in contrast, imagine that these components of spatial organization were organized from the beginning with overall structural impiications of the schematic spaee-form system in mind. The probability for major revision would be minimized, and the symbolic and physical integration of the structure with the overall architectural scheme would be insured. It became apparent that an ability for overall thinking can make it possible to apply structural knowledge to the 'total arc~itectural design effort from the very beginning and with a minimum of distraction by lower-level details. It alone can enable the architect to think of the physicat issues of a space-structure in a c.ontext that is inherently compatible with his mode of dealing with the many organizational and symbolic issues of space-forming. Thu~ it can assure that the emphasis on components conceived as acting together as total systems rather than separately, an independent parts. It is also apparent that much can be gained from applying this overall-to-specific model of educational management to a reconsideration of teaching and writing strategies in many specialized field of deaign-releted knowledge.
2. STRUCTURE AND OTHER SUBSYSTEMS· There are other important reasons for suggesting that structural thinking should be introduced at the very earliest stages of the design process. These derive from the need to provide buildings with mechanical and other environmental seNice subsystems that support horizontal and vertical movement of men and materials as well as provide for heating, ventilation, air-conditioning, power, water, and waste disposal.ln addition, provision for acoustical and lighting needs is often influenced by structural ~. VERTICAL CIRCULATION TOWERS ALSO RESIST HORIZONTAL FORCES
(a) VERTICAL
MOVEMENT SU8S'(STEMS CAN PLAY BASIC STROCTURAL ROLeS
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3
Vente:.! mowment of ~ through a building- requiree rath« large thafbl, end overetl thlndng c.n rMUtt in the uae of thele leMce components as ma;or structural ~ . The requirements for proviaions of heating, ventilation, air-conditioning, power, water, and weste services can be viauatized In the form of a Tree diagram. TheM services usually originlite at a centralized location and must trace their way horizontatly and vertically throughout the ibucture in order to eerve the activity spaces. Large trunk-chaee spaces rr.ay be. required, W1d their structural implications thoukj be considered early in the design procea. US!
UE
CENTRAL MECHANICAL AND OTHER SERVICES
In term1 of acoustics, it;. cleaF that the structural shape of a spatial organization can dtrectty
inftuence ecou8tiCIII ~. In addition, if a apetia) organization calls for heevy equipment to be located IUch that it !mpinges on a flexibte structure vibnltiorJ and acoustical diaturbancee C8fl be transmitted throughout the space because of an incompatible interfaCe between machines all(f stt.Ucture.
·
SOUND DISTRIBUTION 1S INFLUENCED BY THE OVERALL SHAPE OF SPACE
DOME ROOF CONCENTRATES
DISH
ROOF
DISBURSES
Mechaf'Hcal Equip~nt Sound is transmitted through structure. When the structUre is flexibfe, vibrations are
atao tran.mltted.
The raqtjirernent for artificial and naturallight:t>rings. up other considerations. Artificial lighting often calla for integrating conlideration of structural subsystems with considerations of the spatial qualmes of light and of the spatial requirements for housing and the lighting fixtures. Thtt ~cturat implications of natural ligthing are even more obvious. 4
ARTIFICIAL UGHT AND STRUCTURE INTERACT AT SUBSYSTEM LEVEL
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Lighting systems should be made to interface well with structural sub-systems GOOD INTERFACE MINIMIZES
STRUCTURAL DEPTH
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INTER~CE
MAXIMIZES
STRUCTURAL
DEPTH
LIGHTiNO · I'ION.I Nill.L'f PINNED SUPPORT
FRANK
LlOYD WRIGHT'S
JOHNSON WAX BUILDING
For example, consider a fully enclosed space-form with all lighting provided artificially. Then cons!der an open-top Spatial organization with a heavy reliance on natural lighting throughout the space.
NATURAL LIGHT AND STRUCTURE INTERACT AT OVERALL LEVEL a) Fully enclosed box represents simple structural problems but provides no natural light.
b) Fully transparent roof provides natural light but poses more complex structural design problems.
5
c) Bearing and shear wall design with few windows is simple but admits little light.
d) Frame design is more complex but allows up to ~%of the wall to be transparent for light and view.
BUILDING FORMS CONCEIVED AS SPACE-STRUCTURES 4 THiN VERTICAL PLANES JOINED TO FORM OPEN TOP TABLE
IF PL ANES ARE TOO iHIN , THE Y WILL BUCKLE AND THE FORM WILL COLLAPSE
"
6
TUBE ACTION CAN BE ACHIEVED FOR A VARIETY OF SECTIONAL SHAPES AND BY MEANS OF STRUCTURAL CORE DESIGNS
HORIZONTAL
SUB-SYSTEM
BALANCED FRAME ACTION REQUIRES THAT INTERIOR COLUMNS BE ABOUT TWO TIMES SiiFFER THAN EXTERIOR COLUMNS
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At conceptual stages, the designer need only keep in mind the four basic str~Jctural subsystem interactions that must be~provided in order to achieve overall integrity in the structural action of a building form:
1. Horizontal subsystems m.ust pick up and transfer vertical lo_ads in the vertical subsystems.
2. Horizontal subsystems must also pick up horizontal-loads accumulated along tt')e height of a building and distribute them to the vertical shear-resisting su~systems.
3 All of the vertical subsystems must carry the accumulated dead load and live loads, and some must be capable of transferring shear from the upper portions of a building to the foundation.
DEAD L.OAD
4. Key vertical subsystems that can resist bending and/or axial forces due to overturning moments must be provided. Wh.ere possible, th ~y should be interacted by horizontal subsystems.
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High Rise Building -Steel Framing
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3. CONSTRUCTION METHODS AND STRUCTURES AS EXPRESSION OF ARCHITECTURAL DESIGN A. BUILD_ING The purpose of a building is to provide a shelter for the performance of human activities. from the time .of the cave dwellers to the'present, one of the first needs of man has been a shelter from the elements. In a more general sense, the art of building encompasses all of man's efforts to control his environment and direct natural forceS to his own needs. This art includes, in addition to buildings all the civil engineering structures such as dams, canals, tunnels, aqueducts and bridges.
The form of a building is an outgrowth of its function, its environment and various soci9economic factors. An apartment building, an office buiiding, and a school differ in term because of the difference in function they fulfill. In an apartment building every habitable space such as living rooms and bedrooms, must have natural light from windows while bathrooms and kitchens can have artificial light an~ therefore can be in the interior of the building. In office buildings, on the other hand, artificial ligt}t is accepted for more uniform illumina-
tion, and therefore the depth of such buildings is not limited by need for natural light.
B. FORM, SHAPE AND APPEARANCE: Environment may affect both the shape and appearance of the building. An urba11 school may create its ow.n environme.nt by using blank walls to seal out the city completely, and a country school may develop as an integral part of the land scape even though both schools futfill the same function . The form of a building is affected by a variety of socio-economic factors, including land, costs, ·tenancy building budget, and zoning restrictions. High land costs in urban areas result in high buildings. A housing project for the rich wiil take a different form than a low cost housing project. A prestige office building will be more generously budgeted for than other office buildings. Buildings with similar functions ·therefore take on different forms.
C. STRUCTURAL FORMS: The· beam or arch have developed through the ages in relation to the availability of materials and the technology of the time. The arch developed on a result of the availability of the brick. In the Tec~nology of buildings, every structure must work against the gravity, which tends to pull everything down to the ground. A balance therefore must be attained between the force of gravity, the shape of the structure, and the strength of material used. To provide a cover over a sheltered space and permit openings in the walls that surround it. Builders have developed four technimiP.~> consistent with these balance between gravity. form and material.
WALL
a.
Post and Lintel
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·A HORIZONTAL BEAM BETWEEN TWO VERTICAL SUPPORTS
13
b. Arch Construction covering an open ·space by placing wedge-shaped units tOgether with their thick ends outward.
c. Corbel or Cantilever a projection .from the face of a wall fixed in position to support a weight.
d. Truss Construction
allowing for the use of a potnted roof.
14
D. CONCRETE Concrete is a conglomerate artifiCial stone. It is made by mixing a paste of cement and water -Mth $8nd and crushed stone, gravel, or other inert material. The chemically active substance in the mixture is the cement that unites physically and chemically with the water and, upon hardenirfg, binds the aggregates together to form a solid mass resembling stone.
A particular inherent property is that concrete may be made in any desired shape. "The wet mixture is placed in wood, plastic, cardboard or' metal forms in which it hardens or sets. Properly proportioned concrete is hard and durable materials. It is strong in compression but brittle and almost useless in resisting tensile stresses. MASS or PLAIN con~e is used .in members in which the stresses are almost entirely comp1818ive such as dams. piers. and certain types of footing . MASS CONCRETE BEAM
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c In order to avoid compression and tension. Teinforcement made of billet steel and rail steel, usually intermediate grade is introduced. This.. is called REINFORCED CONCRETE.
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REINFORCED CONCRETE is produced in different ways: 1. CAST IN PLACE - when: a concrete Is poured at the jobsite wh~e beams, slabs and columns are set in forms on scaffoldings and later on removed after !the·concrete is hard. Usually the minimum length of time f or w~lls is 12 days and for beams and columns;·7, to 11 days. A rule of thumb is to retain the bottom forms 2 days for each inch of thickness of concrete. For a 3,000 lb . concrete a ratio of 6 gallons of WATER per sack of cement will produce a watertight concrete. 6 l/2 gallons should be the maximum.
THE FORM OF THE SIDES OF BEAMS CAN BE
REMOVED EARUER .
Two Types of Mixture Tests: Sometimes, the mixture of concrete is too much cement· sand mortar caused by water, an(j sometimes insufficient cement-sand mortar which produces honey combed S\Jffaces. To test the consistency of mixes _o f plasticity,~ have the SLUMP TEST and to test the strength of the concrete, we have t he COMPRESSION CYLINDER TEST.
SLUMP TEST
·10
n
0::3 L
+
· 20
With an truncated cooe made of sheet metal, with dimensions shown as above,leave the top and bottom op8n. Freshiv mixed concrete is placed in·fhe mold in three layers, each being rodded separately 25 times with a 5/ 8" (16mm) diameter rod. When the mold is filfed and rodded the top is levelled off, and the mold is lifted at once. Immediately the slumping action of the concrete is measured taking the difference in height between the top of the mold and the top of the slumped mass of·concrete.
by
16
RECOMMENDED SLUMPS SLUMP METRIC
TYPES OF CONSTRucnON
MIN.
Reinforced Foundation walla and Footing
Plain Fcotil~gs, substructure
0.~
0.126 0.10
0.025
Slabs, beams, reinforced walts
0.15
0.075
Columns
0.15
0.075
Pavements
0.75
0.05
Heavy Mass ConstructiQn
0.75
0.025
waU8
COMPRESSION TEST This is the test given to concrete for strength. The specimens to b4 tested are cylindrical in shape and have a length twice the diametet'. The standard is 6 inch 10.15) in. diameter and 12 inch (0.30 in height.
-- --CYLIHDI'R
Freshly made concrete is then placed into the mold in these separate layers, each about one-third the volume of the mokt. Rodded with a 16 mm , bullet-pointed rod. After the top layer has been rodded, the surfaces is· leveted with a Trowel and covered with glass or planed metal. After 2 to 4 hours, when the concrete has· ceased settlirig, the specimens are capped with a th!n layer of neat cement paste and covered with glass or metal. It is customary to keep the specimens at the site of 24 hours. After which they are taken to the laboratory' and cured in a moist atmosphere at 70°F. Tests are usualty made at 7 and liday periods.
rPLAIH '-../'
.In making specimens~ extreme care should be taken to see that the ends are plane-parallel surfaces. After the spe.cimen is placed in the testing machine, a compressive load is applied until the specimen fails. The load causing the failure is recorded, and this load divided by the cross-sectional area of the cylinder gives the ultimate compressive unit; stress usually in psi.
2. PRECAST CONCRETE Prefabricated reinforced concrete which have been cast and cured in a factory rather than in place on the site. Then delivered by long trailer trucks and installed by welding together all the components. These include floor and roof slabs, columns, girders, beams and joists, wall panels and stairs. Whole wall sections are precast and later raised to position in what to be called TILT-UP Construction.
17
Advantages: 1. CaSting and curing conditions, as well as concrete design, can be rigidly controlled resutting in consistently high .quality concrete~
2. The cost of forms and scaffolding is reduced since they can be placed on ground rather than having to be suspended or supported in position.
3.. Where mass production of a unit is possible, forms can be made precisely of steel en~uring long use and very smooth surfaces.
4. Structural members can be mass-produced in a plant while excavations and foundation work are taking place at the site.
5. Pre-cast concrete members are then delivered as. called for in work schedules and in most cases erected directly from truck bed to the structure without rehandling at the site.
6. Close supervision and control of materials and a specialized work'force in a centralized plant result in
a high-quality product.
7. Finishing work ~n concrete surface$ can be done more easily in the plant than in position on the site.
8. Because of superior reinforcing techniques the dead load of the structural members themselves can be reduced.
9. Plant prqduction is not normally subject to delays due to adverse weather conditions as so often happens to jobsite operations. Two General Classifications of PRE·CAST Structural Members. 1. Normally reinforced
2. Prestressed a. Pre-tensioned b. Post-tensioned Normally reinforced precast concrete are deSigned according to accepted reinforced-concrete practice prestressed concrete unit is one in which engineered stresses have been ·placed before it has been subjected to a load. When PRE-TENSIONING is employed, the reinforcement, In the form of high-tensile steel strands, is first stretched through the form or casting bed between two end abut· rnents or anchorages. Concrete is then poured into the form, encasing the strands. As the concrete sets, it bonds to the tensioned steel; when it has reached a specified strength,.the ends.of the tenaion~rands are released . These prestresses the concrete, putting it under compression and creating built-in tensile atrongttl having been prestressed. Members hllve a.slight arch or camber.
---
CAMBE'R PLAIN
CONCftETE
1 1 1
UNLOADED
lEAN
1 18
-
-·
STRt:CWED
LOAD
LOADED
LOADED
POST TENSIONING involves placing and curing a precaat member which contains normal reinforcing and in addition, a number of ctlann* through which poststressing c8btes or rods (tendons) may be passed. Sometimes the tendons are wrapped in oiled paper for easy sliding. One side·is anchored ~urely at the find and one -side is held by a cone. After concrete has hardened tothe desired suet lgth. The cone is fitted to a hydraulic jack and is pulled to the allowable strength then a amall steel plate is wedge so as the tendons will not go back to its normal posttion. Post tensioning is usually carried out when the member is very large or when only one or a very few of one particular kind of unit are to be made. In general, post-tensioning will be used if the unit is CNer 46 feet (14 mllong or
over 7 tons is weight. BUM .
tri)(U) PLATE
. THIS PLAT!: 18 INIIIRTED WHf:N PULLID TO RQUUtl! ITRENGnt t OR Pit. 80 THAT Ttll! TI:NDON8 18 PI!RIIIANI!MTLY ITRI!CHI!O.
BEAM, COLUMNS, "'OtSTS, FLOORING
CHANNEL $L.AI
DOUIIl.E- T- ROOf" SLAB
L. IN · T
19
~--- .. ~---· -- - " SERIES f1F PR£ - CAST '...._ CURTAIH WAI.L ftLDED ' TO THE STRUCTURAL . . .MS f'- . . . _ WILL HASTEN CONSTRUCTION 1 ......_ TilliE AND £Llii1HATES IIIIOST l '-. ......_ OF THE I'ORNWORICS·
1
'
I
1
I l
WALL PANELS - ARE PRECASTED CUSTOM -DESIGNED ARCHITECTURAL PANELS WITH SPECIALLY DESIGNED WATERPROOf JOINTS ··THIS IS ALSO USED FOR INDIVIDUAL HOUSING UNITS ·
3. LIFT SLAB BUILPING SYSTEMS
lift slab is a systems approach to construction based on advanced Technology. But unlike some competitive systems, lift slab is deSigned to fit your requirements instead of trying to make you fit its requirements. In lift slab Building systems, floor and roof slabs are cast one on top of the other. After a short curing time, they are lifted_to their final positions by hydraOiic jacks and secured t~ vertical supports. The result efficient utilization of manpoWer and desing versatility. No large expenditure is. requjred on the part of the general contractor who uses lift slab. Nor does the architect or ·engineer need to limit his design creativity to fit a restrictive system.
How Uft Stab lowers Costa a) FORMS ARE REQUIRED ONLY ON THE OUTSIDE EDGE OF THE SLABS. Lift stab
eliminates 90 percent of the formwork req~ired for a cast-in-place concrete buikiing and reduces the number of carpenters to a minimum. With very littfe waste and trash, costly cleanup is eliminated. Irregularly shaped floor plans are easily formed. ~-
- ltl!AOY YIXl!:O COI'ICRt:T!
b) SLABS ARE CAST ONE ATOP ·THE OTHER. After the first slab is laid out, it serves as a template for su.bsequent slabs . This eliminates layout on all but the initial slab, and cuts mistakes to a minimum. EJectrical, plumbing, and mechanical work is fast and accurate; craftsmen are able to work more Elfficientty.
20
· ··- SPAC£ ALLOWANCE
CONCitETt: COl.UMN
POST
FORMS
Tt:HSIOHING TtNOONS
lllll.
CONCR£T~ - -
·1!'•· . •
SLA8
·'·.:
SLEI!:VIS (P"OA ELECTRICAL ANO PLUM81HO Plf>IS)
\______ TENnOftS
Here Pest-Tensioning Tendons, mild steel reinforcement rods and forms to block Ol openings in the slab are all in place, ready for next slab to be poured. There is no wait for erection of complex.elevated formworic. This shonens the timeinterval between pouring one slab and the next. The bottom of each slab is exceptionally smooth (just like the top); it is ready for finish paint or spraying without additional pr~paration.
c. Two Casting Systems are Available All slabs are cast and cured on the ground and then raised into position and secured. The ground-levet casting method is used for structural frame lift slab building· systems up to twelve floo•a and bearing wall lift stab building system up to four floors •
.. ••
• .
..
-~
QPEH
·,·
Sf'I'CE
21
E-~ oa•
•
'tO
Powerful hydraulic lifting tacks provide the muscle to lift up to 160,000 pounds (72, kg . l per tack at rates of eight to twelve feet (2.40-3.60 ml per hour or more. As many as 48 lifting jacks can be used at the same time.
m
First the designed footing is laid out and poured then the reinforced concrete column is enclosed in a form and poured. Up to a height of 3 1/ 2 floors. When all slabs had been lifted. The top of the columns is again smashed to expose the steel bars and another one and one half floors height of column is 'connected by welding and poured to a smoothened top finish . This will accomodate all the t)ydrauli.c jacks in one horizontal elevation.
STEEL. ENI!II! OPED TO CO L.UMN AHD Sl.A8 FOflt WELDING PURPOSES
22
!I R-
.,
....
R
·-
-lltiRD COLUNN StMe
7-...,
!S-
!J-
R -INITI.4L er. The stressing in the cables is calculated to provide the correct camber and strength for the anticipated loading so that when the member is in place, and live and dead loads are placed on it, the cant>er disappears or is greatly reduced . Post-tensioned concrete is yet another structural system that takes advantage of the. qualities of concrete and steel. In this system, the post-tensioning steel (sometimes called tendons) is stressed after the concrete has been poured and cured. Post-tensioning tendons can be small high-strength wires, sever-wire strands, or solid bars. They are stressed with hydraulic jacks pulling on one or both ends of the tendon with pressure about 0.70 mPa to 1.75 mPa of concrete area for slabs and 1.40
mPa to 3.50 mPa for beams. Post-tensioned structural systems are useful where high strength is required and where it may be too difficult to transport precast members to the job site.
44
D. Masonry A£ a structural system in conteff1)0rary construction, masonry is generalty limited to bearing wals. It has a high compressive strength but is unitized nature makes It inherently weak in tension and bending. There are three basic types of masonry bearing wall construction: single wythe, doubte wythe, and cavity (see Figure2.5). Both of the layers in double wythe construction may be of the same material or different materials. Cavity walts and double wythe walls may be either grouted and relnloreed or ungrouted. Single wythe walls no provisions for reinforcing or grouting.
have
Unh masonry bearing walls offerthe advantages of strength, design flexibility, appearance, res~ance to weathering, fire resistance, and sound insulation. In addition, their mass makes them Ideal for any passive solar energy applications.
TI£S
DOUILI WYTHI CONSTRUCTION
IINeU WYTHf CONSTRUCTION
HONZCWTAL I VERTICAL ~-~ IU'INFORCEM.ENT CAVITY FULLY
GROUTED
CAVITY WALL
CONSTft~CTlON
Figure 2.5 The joints of masonry units must be reinforced hOrizontally at regular intervals. This not only strengthens the walt, but also controls shrinkage cracks, ties ITlJiti·wythe walls together, and provides a way to anchor veneer facing to a structural backup wall. Horizontal joint reinforcement comes in a variety of forms and is generally placed 400 mm on center.
45
Vertical reinforcement is accomplished with standard reinforcing bars sized and spacedin.accordance with the structural requirements of the wall. Typically, horizontal bars are also used and tied to the vertical bars with the entire assembly being set in a grouted cavity space. In a single wythe concrete block wall, only venical reinforcing is used with fully grouted wall cavities. One if1l>Ortant consideration in utilizing masonry wall is the thickness of the wall, which determines three important properties; the slenderness ratio, the flexural strength, and the fire resistance . The ~Jenderness ratio is the ratio of the wall unsupported height to its thickness and is an indication of the ability of the wall to resist buckling when a compressive load is applied from above. The flexural strength is important when the wall is subjected to lateral forces such as from wind. Finally, the fire rating depends on both the material of the wall and its thickness. These topics will be discussed in more detail in Chapter 12.
HEADED STUD ANCHORS
HEADED
STUD
ANCHORS
-
-
CONCRETE CAST
CW FORMS
CONCRETE SLAB AND STEEL BEAM
COMPOSITE STEEL DECI< AND BEAM SYSTEM .
OPEN·W£8 STEEL. .JOISTS AND \11000 CHClftDS
Figure 2.6
E. Composite Construction Composite oonstruction is any structural system consisting of two or more materials designed to act together to resist loads. Composite construction is employed to utilize the best characteristics of each of the individUC\1 materials. Reinforced concrete construction is the most typical composite construction, but others include composite steel deck and concrete, concrete slab and steel beam systems, and open-web steel joists with wood chords. See Figure 2.6. In composite construction with concrete and steel beams, headed stud anchors are used to transfer load between the concrete and steel, making them act as one unit. Composite steel deck is designed with deformations or wires welded to the deck to serve the same purpose. Composite open-web joists are used to provide a nailable surface for the floor and ceiling while using the high strength-to-weight ratio of steel for the web members. There are many_other types of composite constructions that are less frequently used. These include trusses with wood for compression mermers and _ steelllbds for tensiOn members, and concrete-filed steel tube sectiOns.
F. Walls and the Building Envelope Nonbearing walls are generally not considered part of the structural system of a building, but there are two important structural considerations when deciding how to atach the exterior, non-structural envelope to the structural frame . The first is how the weight of the envelope itself will be supported, and the second is how exterior loads, primarily wind, will be transferred tothe structural frame without damaging the facing. How an exterior facing is attached depends, of course, on the specific material and the type of structural frame. Panel and curtain wall systems are attached wHh clips on the mullions at the structural frame. The size and spacing of the clips is determined by the structural capabilities of the curtain wall or panel system. Stone and masonry facings are attached with clip angles. Continuous angles, or special fastenings to the structural frame at the floor lines. If additional attachment is required, a grid of secondary steel framing Is attachedto the primary structure and then serves as a framework for the facing . Lightweight facings such as wood siding, shingles, and stucco need to be applied over continuous sheathing firmly secured to the structural wall framing. One of the most important considerations in attaching exterior facing to the structural frame is to allow for expansion and contraction due to the temperature changes and slight movement of the structural frame. Materials with a high coefficient of thermal expansion, such as aluminum, require space for movement within each panel, at the perimeter of large sections of the facing. Movement can be provided for by using clip angles with slotted holes, slip joints, and flexible sealants. Materials with a low coefficient of expansion, such as masonry, still require expansion jo ints at regular intervals and at changes in the plane of the wall. If these are not provide, the joints or masonry may crack or the facing itself may break away during extreme temperature changes. Usually, steel-framed buildings do not present many problems with movement of the structuralframe. but concrete and wood structures will move enough·to present problems. Concrete structures are especially subject to creep, a slight deformation of the concrete over time under continuous dead load. This condition must be accounted for when designing and detailing connections. Wood structures also deform over time due to shrinkage of the wood and long-term deflection. Sjnce most wood buildings are relatively small, this is not always a problem, but should be considered in attaching exterior facings. -
2. COMPLEX STRUCTURAL SYSTEMS A. Trusses Trusses are structures comprised of straight members forming a number of triangles with the connections arranged so that the stresses in the mer)'lbers are either in tension or compression. Trusses can be used horizontally. vertically , or diagonally to support various types of loads when it would be impossible to fabricate a single structural member to span a large distance. Although trusses are primarily tension/compression structural systems, some amount of bending is present in many otthe members. This is due to loads applied between the connections and secondary bending and shear stresses at the connections themselves caused by minor eccentric loading. Trusses can be field-fabricated or assembled in the factory as is the case with open-web steel joists and wood trussed rafters. The primary limiting factor is the abil~y to transport them from the factory
to the job s~e. Trusses are discussed in more detail in Chapter 5. 47
B. ARCHES Arches may be hinged or fixed supports. A hinged arch is a structural shape whiCh is primarily .subjected to compressive forces. For a given set of loads the shope of an arch to resist the loads only in compression is its funicular shape. This shape can be found by suspending the anticipated loads from a flexible cable and then turning the shape upside down, as Antonio Gandi did in many of his structural studies. For a hinged arch supporting a unifonn load across its span this shape is a parabola. However, no arch is subjected to just one set of loads, so there is always a combination of compression and some bending stresses. At the supports of a hinged arch there are two reactions: the vertical reactions and the horizontal reactions, or thrust, as shown in Figur9j2.7. Since the loads on the arch tend to force it to spread out, the thrust- must be resisted either with tie rods which hold the two tower portions of the arch together or with foundations which prevent the spread. For a given span, the thrust is inversely proportional to the rise, or height, of the arch; if the rise is reduced by one-half, the thrust doubles. Arches can be constructed of any material :steel, concrete, wood, or stone, ahhough each has its inherent limitations. Arches can also take a variety of shapes, from the classic half-round arch of the Romans, to the pointed Gothic arch, to the more decorate Arabic arches, to the functional parabolic shapes. Since the shape of a building arch is often selected tor its aesthetic appeal, it is not always the ideal shape and must be designed for the variety of loads it must carry in addition to simple compression. Wood arches typically span from 15m to 72 m, concrete arches from 6 m to 96 m, and stee I arches from 15 m to 150m. Although arches may' have fixed supports, they are usually hinged. This allows the arch to remain flexibte and avoids developing high bending stresses under live loading and lo~ding due to temperature changes and foundation settlement. Occasionally, an arch will have an additional hinge connection at the apex and is called a three-hinged arch. The addition of the third hinge makes the structure statically determinate whereas two hinged or fixed arches are statically indeterminate.
REACTIONS OF A HINGED ARCH
Figure 2.7
48
C. Rigid Frames In contrast to a simple post-and-beam system, a rigid frame is constructed so that the vertical and horizontal members wo!'1( as a single structural unit. This makes for a more efficient structure because au three members resist vertical and lateral loads together rather than singly. The beam portion is partially restrained by the columns and becomes more rigid to vertical bending forces, and both the columns can resist lateral forces because they are tied together by the beam. See Figure 2.8. Because the three members are rigidly attached, there are forces and reactions in a rigid frame unlike those in gjmpie post-and-beam system. This is shown in Figure 2.8 (b anc c) and results in the columns being subjected to both CO I11lressive and bending forces and a thrust, or outwa(d force, induced by . the action of the vertical loads on the beam transferred to the columns. As with an arch, this thrust must be resisted with tie rods as with appropriate foundations. The attachment of the columns to the foundations may be rigid or hinged. This results in slightly different loads on the columns. The fixed frame as shown in Figure 2.8- (c) is stiff~ r that the hinged frame and the thrust in the fixed frame is also greater. When a horizontal beam is not required, such as in a single-story structure. a rigid frame often takes on the appearance of a gabled frame a shown in Figure 2.9. This shape decreases the bending stresses in the two inclined mernbers and increases the compression, making the configuration a more efficient structure. Because rigid frames develop a high moment (see Chapter 3) at the connections between horizontal and vertical members, the amount of material is often increased near these points as shown in the tapered columflS and roof members in Figure 2.9.
I I
l
I I Il I II
j
(a)
SIN PL£ POST AND BEAM
RIGID FRAME WITH FlX£D CONNECTION Cot.U•
I ! I I I l I
Figure 2.8
49
AT 8AS!S
GABLED RIGIO FRAME
Figure 2.9
D. Space Frames In simplest terms, a space frame is a structural system consisting of trusses in two directions rigidly connected at their intersections. With this definition it is possible to have a rectangular space frame where the top and bottom chords of the trusses are directly above and below one another. The bays created by the intersection of the two sets of trusses then form squares or rectangles. The more common type of space frame is a triangulated space frame where the bottom chord is offset from the top chord by one half bay, and each is connected with inclined web members. See Figure 2.10. Space frames are very efficient structures for enclosing large rectangular areas because of the twoway action of the components acting as asingle unit. This results in a very stiff structure that may span up to 105 m. Span-to-depth ratios of space frames may be from 20:1 to 30:1. Other advantages include light weight andthe repetitive nature of connectors and struts so that fabrication and erection time is minimized. The structural design of a space frame is complex because they are statically indetermine s!ructures with numerous intersections. A computer is needed for analysis and design.
TYPICAL SPACE FRAME
Figure 2.10
50
E. Folded Plates A folded plate structure is one in which the loads are carried in two directions, first in the tansverse direction through each plate supported by adjacent plates and secondly in the longitudinal direction with each plate acting as a girder spanning between vertical supports. See F:igure 2.11. Since the plates act as beams between supports, there are compressive stresses above the neutral axis and tensile stresses below. Folded plates are usually constructed of reinforced concrete from 75 mm to 150 mm thick although structures made of wood or steel are possible. Typical longitudinal spansare9 m to30 mwith longer spans possible using reinforced concrete.
FOLDED PlATE CONSTRUCTfON Figure 2.11
F. Thin Shell Structures A thin shell structure is one with a curved surface that resists loads through tension. compression , and shear in the plane of the shell only. Theoretically, there are no bending or moment stresses in a thin shell structure. These structures derive part of their name (thin} because of the method of resisting loads; a thick structure is not necessary since there are no bending stresses. Since thin shells are composed of curved surfaces, the material is practically always reinforced concrete from about 75 mm to 150 mm. The forms can be domes, parabolas, barrel vaults, and the more complex shape of the saddle-shaped hyperbolic paraboloid. Thin shell domes can span from 12m to over 60 m while hyperbolic paraboloids may span from 9 m to 48 m.
G. Stressed-Skin Structures These structures comprise panels made of a sheathing material attached on one or both sides of intermediate web members in such a way that the panel acts as a series of !-beams with the sheathing being the flange and the intermediate members being the webs. Since the panel is constructed of two or more pieces, the connection between the skin and the interior web members must transfer all the horizontal stress developed. Stressed-skin panels are typically made of wood as shown in Figure 2.1 (g), but are also fabricated of steel and other composite mate rials. Although long-span steel stressedskin panels are possible, most panels of this type span intermediate distances from 3.6 m to 10.5 m.
51
H. Suspension Structures Suspension structures are most commonly seen in suspension bridges, but their use is increasing in buildings, most notably in large stadiums with suspended roofs. The suspension system was boldly used in the Federal Reserve Bank in Minneapolis where two sets of cables were draped from towers at the ends of the building. These, in turn, support the floors and walls, leaving the space on the grade level of columns. Cable suspension structures are similar to arches in that the loads they support must be resisted by both vertical reactions and horizontal thrust reactions. The difference is that the vertical reaction is outward since the sag tends to pull the ends together. As shown in Figure.2.12 (a), the horizontal reaction is dependent on the amount of sag in the cable . Shallow sags resuh in high reactions while deep sags result in lower reactions. Since suspension structures can only resist loads with tens~n. the shape of the cable used changes as the load changes . No bending stresses are possible. With a single. concentrated load, the cable assumes the shape of two straight lines (not counting the intermediate sag due to the weight ot.the cable). With two concentrated loads, the shape is three straight lines. and so on. If the cable is uniformly loaded horizontal, the shape of the curve is a parabola. If the cable is loaded along its length uniformly (such as supporting its own weight) the shape will be a catenary curve. See Figure 2.12 (b} and (c).
(a) tfORIZONTAL REACTIOH D£PD«l8 ON SAt
(b) ~ffORM HONZONTAL LOAD ft!SULTI W PMAIMlLIC CUAVE
(c) YI'IFOIUI LOAD ON CAlLa . .IULTS IN CATINAitY CUIWI
Figure2.12
52
The fact that a suspension structure can only resist loads in tension creates one of its disadvantages: instability due to wind and other types of loading. Suspension structures must be stabilized or stiffened with a heavy infill material, with cables attached to the ground or with a secondary grid of cables either above or below the primary set.
I. Inflatable Structures Inflatable structures are similar to suspension structures in that they can only resist loads in tensiOn. They are held in place with constant air pressure which is greater than the outside air pressure. The simplest inflatable structure is the single membrane anchored continuously at ground level and inflated. A variation of this is the double-skin inflatable structure in which the structure is created by inflation of a series of voids, much like an air mattress. With this system, the need for an "air-lock" for entry and exit is eliminated. Another variation is a double-skin structure with only one large air pocket supported on the bottom by a cable suspension system and with the top supported by air pressure. Like cable suspension buildings, inflatable structures are inherently unstable in the wind and cannot support concentrated loads. They are often stabilized with a network of cables over the top of the membrane. Inflatable structures are used for temporary enclosures and for large, single-space buildings such as spons arenas .
3. STRUCTURAL SYSTEM SELECTION CRITERIA The selection of an optimum structural system for a building c an be a complex task. In addition to the wide variety of structural systems available and their many variations and combination, there are dozens of other considerations that must be factored into making the full scope of the problem and find the best balance among often conflicting requirements. This section briefly outlines some of the major selection criteria you should be familiar with when analyzing possible systems.
A. Resistance to Loads Of course the primary consideration is the ability of the structural system to resist the anticipated and unanticipated loads that will be placed on it. These include the weight of the structure itself (dead load). loads caused by external factors such as wind and earthquakes, loads caused by the use of the building such as people, furniture, and equipment (live loads) , as well as others. These are discussed in more detail in Chapter 2. The anticipated loads can be calculated directly from known weights of m~terials and equipment and from requirements of building codes that set down what is statistically probable in a given situation, the load caused by peop le in a church , for example. Unanticipated loads are difficult to plan for but include such things as changes in the use of a building, overloading caused by extra people or equipment, pending of water on a roof, and degradation of the structure itself. When deciding on what material or system to use, there is always the consideration of what is reasonable for the particular circumstances. For example, wood can be made to support very heavy ~oads with long spans, but only at a very high cost with complex systems. A wood system doesn't make sense if other materials and systems such as steel and concrete are available. Often, very unusual loads will be the primary determinant of the structural system and its effect on the appearance of the bu ilding. Extremely tall high-rise build ings like the Sears Tower or the John Hanrock Building in Chicago w ith its exterior diagonal framing are examples of load-driven structural solutions.
53
B. Building User and Functions The type of occupance is one o1 the primary determinants of a structural system. A parking garage need spans long enough to allow the easy movement and storage of automobiles. An office building works well with spans in the 9 m to 12m foot range. Sports arenas need quite large open areas. Some buildings have a fixed use over their l~e span and may work with fixed bearing walls while others must remain flexible and require small columns widely spaced. These are all examples of somewhat obvious determinates of building systems. However, there are many other needs that are not so apparent. For example , in a location where building height is limited, a client may want to squeeze as many floors into a multistory building as possible. This may require the use of concrete flat plate construction with closely spaced columns although another system is more economical. In another instance, a laboratory building may need large spaces between usable floors in which to run mechanical services. This may suggest the use of deep span, open-web trusses. If the ~me laboratory were to house delicate, motion sensitive equipment, then the use of a rigid, massive concrete structure might be warranted.
C. Integration With Other Building Systems Although a building's structure is an important element. it dOes not exist alone. Exterior cladding must be attached to it, ductwork and pipes run around and through it, electrical wires among it, and interior finishes must cover it. Some materials and structural systems make it easy for other services to be integrated. For instance, a steel column-and-beam system with open-web steel joists and concrete floors over metal decking yields a fairly penetrable structure tor pipes, ducts, and wiring while stiR allowing solid attachment of ceilings, walls, and exterior cladding. On the other hand, reinforced prestressed concrete buildings may require more consideration as to how mechanical services will be run so there is not an excess of dropped ceilings, furred-out columns, and structure-weakening penetrations. Exposed structural systems, such as glued-laminated beams and wood decking or architectural concrete, present particularly difficult integration problems.
D. Cost Influences As with most contemporary construction, the concern over money drives many decisions. Structure is no exception. It is one portion of a building that is most susceptible to cost cutting because it quite often cannot be seen and the clien1 sees no reason to spend more on it than absolutely necessary. There are two primary elements of selecting a structural system based on cost. The first is selecting materials and systems that are most appropriate for the anticipated loads, spans required, style desired, integration needed, fire-resistance called for, and all the other factors that must be considered. This generally leads to major decisions such as using a concrete flat slab construction instead of steel, or using a steel arch system instead of glued-laminated beams. The second part is refining the selected system so that the most economical arrangement and use of materials is selected regardless of the system used. In a typical situation, for example, a steel system is selected but various framing options must be compared and evaluated. Changing the directions of the beams and girders or slightly altering the spacing of beams may result in a savings in the weight of steel and therefore a savings In money. Or, a concrete frame may be needed, but·the one with the simplest forming will generally cost less.
54
E. Fire Resistance Building codes dictate the fire resistance of structural system as well asotherparts of a building. These range from one hour to four hours; the time is an indication of how long the member can withstand a standard fire test before becoming dangerously weakened. The structure is, of course, the most important part of a building because it holds everything else up. As a consequence, required tire resistances are generally greater for structural members than for other components in the same occupancy type and building type. There are two-considerations in the fire resistance of a structural member. One is the combustibility of the framing itseH and the other is the loss of strength a merroer may experience wh~n subjected to intense heat. Steel, for instance, will not burn but will bend and collapse when subjected to high temperature. It must, therefore be protected with other noncombustible materials. Heavy timber, on the other hand, will burn slightly and char, but still maintain much of its strength in a fire before it bums completely. Some materials, such as concrete and masonry, are inherently fire, resistant and are not substantially weakened when subjected to fire {assuming any steel reinforcing is adequately protected). Other materials, such as wood and steel, must be protected for the time period required by building codes. Since it costs money to protect structural members from fire this rrust be factored into the decision to use one material instead of another. Even though steel may be a less expensive structural material to use than concrete, it may be more expensive to fireproof and in the long run cost more than a concrete-framed building.
F. Construction Limitations The realities of construction often are a decisive factor in choosing a structural system. Some of these include construction time, material and labor availability, and equipment availability. Construction time is almost always a factor due to fluctuations in material costs typical in the Philippines. However, other things influence the need to shorten the construction period as much as possible. The cost of financing requires that the term of construction loans be as short as feasible. This may dictate the use of large, prefabricated structural elements instead of slow, labor-intensive systems such as unit masonry. Another factor can be climate and weather. In locations with short construction seasons, buildings need to be erected as fast as possible. Material and labor are the two primary variables in all construction cost. Sometimes both are expensive, but usually one dominates the other. In the Philippines as in many developing countries, labor is extremely cheap while most modern materials are expensive or even unattainable. Related to the cost of labor are the skills of the work force. A sophisticated structural system may require a technically skilled workforce that is not available in a remote region. The cost to transport and house the needed workers could very well make such a system unfeasible. Finally, equipment needed to assemble a structural system may be unavailable or prohibitively expensive. The lack of heavy cranes near the job location, for example could suggest that large, prefabricated components not be used.
G. Style Some structural systems are more appropriate as an expression of a particular style than others. One of the most obvious examples is the International Style, which could only be achieved with a steel postand·beam system. Even when fireproofing requirements might have implied a concrete structure, steel was used. 55
The architect and client usually determine what style the building will be and then require that any structural solution adapt to that need. In some instances, the structural engine_er may devise a struCtural solution that becomes the style itself. Once again, there should be a balance between what styte may be desired and what is practical and reasonable from a structural point of view.
H. Social and Cultural Influences Related to the style of a building are the social and cultural influences on the architecture of a geographical location and particular time period. The architect must be sensitive to these influences. For example, in a historic area where most buildings are constructed of brick, a masonsy bearing wall structural system certainly should be considered. In a newly developing industrial park, more contemporary and daring structural systems might be appropriate.
56
.....
....
~
LOADS ON BUILDINGS
LOADS ON BUILDINGS Nomenclature A D L
p r R
v
area of floor or roof dead load live load direct wind pressure rate of reduction of live loads allowable reduction of live load wind velocity
M2 Pa Pa Pa
kph
Determining the loads acting on buildings is basic to structural analysis and design. An accurate determination of loads is necessary to design a safe building and satisfy building code requirements while not requiring a more costly structure than necessary. The probable magnitudes building loads have been determined over a long period of time based on successful experience and the statistical probability that a particular situation will result in a given load. They are also based on the worst case situation. For example , the common live load for residences of 2000 Pa in a house, but provides an allowance for safety and unusual circumstances. Typically, loads are defined by building codes and by common practice. Codes, tor example, give live load requirements, wind values, and earthquake values. Standard published tables provide accepted weights of building materials for dead load calculations. Occasionally, special situations may require custom load determination such as when building models are tested in a wind tunnel. Most loads on buildings are static, and those that are dynamic, such as wind, are assumed to have a static effect on the building structure so calculations are easier. There are many types ~f loads on buildings. This chapter provides an overview of what the different types are, how they are determined and their effects on buildings and architectural design. More detailed information concerning building code requirements is given in Chapter 9, while speciiic calculation procedures for lateral loads due to wind and earthquake are described in Chapters 14 and 15, respectively.
1. GRAVITY LOADS A. Dead Loads Dead loads are the vertical loads due to the weight of the building and any permanent structural and nonstructural components of a building. These include such things as beams, exterior and interior walls, floors, and fixed service equipment. Dead loads of structural elements cannot always be readily determined because the weight depends on the size, which in turn depends on the weight to be supported. Initially, the weight of the structure must be assumed to make a preliminary calculation of the size of the structural member. Then the actual weight can be used for checking the calculation. Most dead loads are easily calculated from published lists of weights of building materials found in standard reference sources. Some c~mmon weights are given in Table 3.1 In addition to this, the Uniform Building Code requ ires that floors in office buildings and other bu ildings where partition locations are subject to change be designed to support an extra 1000 Pa of dead load.
58
TABLE3.1 WEIGHTS OF ASSEMBLED ELEMENTS OF CONTRUCTION
Member or Element
Weight i Pa
Wood Floor (20 mm) and wood joists Concrete Slab, per em thick Steel Decking Floor finishes ~ment Finish, 2-3 em {aver.) V~rif ied t ile & mortar, 3 ems. (aver.) Cement tile & mortar, 4 ems Asphalt or Vinyl on cement mortar base {min) Parquet floor on cement mortar base G ranolithic or terrazo., casHn-place Granol~hic or terrazo tiles on mortar base 20 mmwood floor on sleepers wl cone. filler Partitions 6 mm plywood double wall on 50 x 100 studs 20 mm wood panels, double on SO x 100 studs Glass blocks, 100 mm thick Brick, 100 mm thick Brick, 150 mm thick Brick, 200 mm thick Curtain wall. aluminum & glass, (aver.) Concrete Hollow Blocks {1/2 of cells filled) 100 mm, CHB, no plaster 100 mm, CHB, plastered one face 100 mm, CHB, plastered both faces 150 mm, CHB, no plast er 150 mm, CHB, plastered one face 150 mm, CHB, plastered both faces 200 mm, CHB, no plaster 200 mm, CHB, plastered one face 20 mm, CHB, plastered both faces Ceilings, including joists and furrings 6 mm plywood 20 mm wo od boards 12 mm insulation or acoustical boards Metal lath and plaster 4.5 mm asbestos cement sheets 6 mm asbestos cement sheets Root Covering (Excludes purlins and/or rafters) Galvanized Corrugated (includes laps & fastenings) 22 U.S. Std gage 24 U.S. Std gage 26 U.S. Std gage Plain G. I. WI battens (includes sheathing boards) 22 U.S. Std gage 24 U.S. Std gage 26 U.S. Std gage Corrugated asbestos cement (includes laps and fastenings} 3.75 mm thick 4.50 mm thick 6.00 mm thick Clay roofing tiles with sheathing, membrane waterproofing and fastenings, no mortar Metal roof tiles with sheathing, membrane water proofing and faste nings Asphalt shingles Built-up Roofing, 5 ply
59
526.90 239.50 143.70 7 18.50 718.50
958.00 574.80 622.70 1437.00 1676.50
1437.00 335.30 431. 10 862,20 1916.00 2874.00
3832.00 718.50 1532.80
1820.20 2107.60 2155.50
2442.90 2730.30 2730.30
3017.70 3305.10
239.50 383.20 31 1.35 862.20 335.30 383 .20
114.96 95.80
76.64 335.30 325.72 316.14
153.28 182.02
239.50 1005.90
479.00 95.80 287.40
Example3.1 Find the uniform load on a typical interior beam supporting the floor shown in the diagram. Do not include the weight of the beam. 1-----------~:~ .."--.-
-
·--· --l QUARRY
..
2 .40
TILE
~OONM
BEAN
± soMN
2.
i
- ------
__ _j
ACOUSTICAL CEILING
SECTION
PLAN
From Table 3.1 determine the weight per square meter foot of the materials comprising the floor. Since the concrete is on fluted steel deck, take the average thickness of 125 mm. The total weight is therefore:
958.00 Pa
cement tile and mortar concrete (239.50 Pax 125 mm x 1 mm/1 0 em)
2993.75 Pa 143.70 Pa 239.50 Pa
steel deck 6 mm plywood ceiling Total
4334.95 Pa
The beam supports a portion of the floor half the distance of the beam spacing on either side of it, or 2.40 meters. 2.4 times 4334.95 is 10403.88 N/m. In practice, numbers such as 71.8 are rounded to the nearest whole number, so the weight in this case would be 72 pst and the load would be 576 plf.
B. Live Loads live loads are those imposed on the building by its particular use and occupancy, and are generally considered movable or temporary such as people, furniture, movable equipmern, and snow. It does not include wind loading or earthquake loading. Live loads are established by building codes for different occupancies. Table 3.2 gives the uniform live floor loads from the national structural code of the Philippines and Table 3.3.minimum roof live loads. The requirements for special conditions as cranes, elevators, and fire sprinkler structural support, among others. The code also requires that floors be designed to support concentrated loads if the specified load on an otherwise unloaded floor would produce stresses greater than those caused by the uniform load. The concentrated load is assumed to be located on any space 750 mm x 750 mm square. The concentrated load requirements are giveri in the last column in Table 3.2.
60
TABLE 3.2 UNIFORM AND CONCENTRATED LOADS
Use of Occupancy
Uniform load1 Description
Category
Pa
Concerntrated load N
7200
0
Fixed seating areas Movable seating and other areas
2400 4800
0 0
auditorium and balconies therewi1h" 3. Cornices, marquees ·and residential balconies 4. Exit facilities s
Stage areas and enclosed platforms
6000
0
5. Garages
General storage and/or repair
4800
:\
Private pleasure car storage
2400
3
6 . Hospitals
Wards and rooms
2000
45002
7. libraries
Reading rooms
3000
450()2
8. Manufacturing
Stack room s Light
6000 3600
67002 89002
Heavy
6000
134002
Press rooms Composing and linotype rooms
2400 7200 4800 2000
89002 112002 89002 06
4800
0
2000
45002 3
1. Armories 2. Assembly areas ~ and
9. Offices 10. Prir.ting Plants
3000 4800
11 . Residential6
oe 0
7
12. Rest rooms 13. Reviewing stands, grandstands and bleachers 14. Roo1 deck
Same as area served or for the type of occupancy accommodated
15. Schools
Classrooms
16. Sidewalks and driveways
Public access
12000
17. Storage
Light Heavv
6000 12000
18. Stores
Retail
3600
Whnl~!':al~
.4800
19. low cost housing unit11
1500
1
89002 1344002
oe
See Section 3.1 .4 for live load reductions. See Section 3.1.2.3, first paragraph, for area of load application 3 See Section 3.1.2.3, second paragraph, for concentrated loads. ~ Assembly are include such occupancies as dance halls. drill moms, gymnasiums, playgrounds, plazas, terraces and similar occupancies which are generally accessible to the public. 5 Exit facilities shall include such uses as corridors serving an occupant load of 10 or more persons, exterior exit balconies, stairways, fire escapes and similar uses. 6 Residential occupancies include private dwelling, apartment and hotel guest rooms. 7 Rest room loads shall be not less than the load for the occupancy with which they are associated, but not to &xceed 2400 Pa. · 8 Individual stair treads shall be designed to support a 1300 N c:oncentraled k>ad placed in position which would cause maximum stress, stair stringers may be designated for the uniform load set forth in the table. e Total floor area of a unit shall not exceed 60 .m2 2
61
TABLE 3.3 MINIMUM ROOF LIVE LOADS TRIBUTARY LOADED AREA FOR ANY STRUCTURAL MEMBER Roof Slope
0 to 20 sq.m.
21 to 60 sq.m.
Over 60 sq.m.
1000 Pa
800 Pa
600 Pa
horizontal to less than 1 horizontal; Arch or dome with rise 1/8 of span to less than 3/8 of span
800 Pa
700 Pa
600 Pa
3 Ris.e 1 vertical to 1 horizontal; Arch or dome with rise 3/8 of span or greater600 Pa
600 Pa
600 Pa
4 Awning, except cloth covered
250 Pa
250 Pa
1. Flat or rise less than 1 verlical to 3 horizontal; Arch or dome with rise less 1/8 of span 2 . Rise 1 vertical per 3
250 Pa
I
5 Green Houses, lathhouses and agricultural buildings
I
There are two instances when the national structural Code allows the live load to be reduced: when a structural member supports more than 14 sq meters (except for floors in places of public assembly) and for live loads greater than 4800 Pa. The allowable reduction from the load values shown in Table 3.2 is given by the formula: A = r (A- 14)
3:1
The rate of reduction, r, is equal to 0.08 for floors, 0.08 for roofs ranging from flat to less than4 inches rise per foot , and 0.06 for roof slopes ranging from 4/12 to 12/12. There are a few limitations, however. The reduction cannot exceed 40 percent for members receiving load from one level only, or 60 percent for other members, nor can the reduction exceed the percentage determined by the formula: R "'23.1 (1 + 0/L)
3:2
Where R = Reduction in percent r
= Ra1e of reduction equal to 0.86 percent for floors
A = Area of floor supported by member in sq. m. D
= Dead load per square meter of area supported by the members
L = Unit live load per square meter of area supported by the members
62
Example 3.2
What live load should be used to design a structural member that supports an area of 20 square meters of single-level office space, a live load of 2800 Pa and a dead load of 3400 Pa? Since the live load Is less than 4800 Pa and it is not a public assembly place , a reduction is permitted. First, determine the reduction and then check against the other two limitations and select the least one. A = r (A -150) = 0.86 (20- 14)
=6% =
40% for members receiving load from one floor
Check against formula 2.2 R "' 23.1 (1 + D/L)
= 23. 1 (1 R
= 51.15%
+ 3400/2800) --·-···--·-··--- (3)
Of the three values , 5.16% is the least, so the reduced live load will be 2800 - (5.16/100) (2800) or 2655.52 Pa
C. Combination Loads It is generally agreed that when calculating all the loads on a building, all of them probably will not act at once. The National Structural Code recognizes this and requires that several combinations of loads be calculated to find the most critical one (floor live load shall not be included where its inclusion results in lower stresses in the under investigation) These combination of loads are as follows: • dead plus floor live plus roof live • dead plus floor live • dead plus floor live plus seismic (or wind} • dead plus seismic (or wind)
2. LATERAL LOADS A. Wind Wind loading on buildings is a dynamic process. That is, the pressures. directions. and timing are constantly changing. For purposes of calculation, however, wind is considered a static force. There are several variables that affect wind loading. The first is the wind velocity itself. The pressure on a building varies as the square of the velocity according to the following formula :
p = 0.0000473V 2 The second variable is the height of the wind above the ground. Since wind acts as any fluid where a surface causes friction and slows the fluid, wind velocity is lower near the ground and increases with height. Wind speed values are taken at a standard height of 10 meters (33 feet) above the ground, so adjustments mu st be made when calculating pressure at different elevations.
63
WINO DIRECTION
'-~
"" '
........
,_,./
~/
/
/ / /
/
FORCES ON A BUILDING DUE TO WINO
Figure 3.1 A third variable is the nature of the building's surroundings. Other buildings, trees, and topography affect how the wind will finally strike the structure under consideration. Buildings in large, ope~ areas are subject to more wind force than those in protected areas. The type of surrounds is taken in account with multiplying factors found in the building codes. Finally, there are things like the size, shape, and surface texture of the building. Some buildings allow the wind to flow around them while others·channel or focus the wind. A building subjected to wind forces responds in several ways. These are shown diagrammatically in Figure 3.1. The~e is, of course , positive pressure on the windward side of the building. On the l~eward side and roof there is often a negative pressure, or suction. In addition to these, there are local areas where wind pressure is greater such at building corners, overhangs, parapets, and other projections. The method of calculating these is described on detail in Chapter 14.
Of particular interest to architects are building shapes and design features that may exacerbate wind problems. These include things such as closely spaced buildings or small openings at ground level that cause normally acceptable wind speeds to increase to unacceptable levels. Because wind is a fluid, forcing a given speed Into a smaller area causes the speed to increase. There have been instances, for example, where localized winds are so great that entry doors cannot be opened or an otherwise pleasant outdoor plaza is unusable. Other potential problem$ include building drift, which is the distance abuilding moves from side to side in the wind. This is particularly of concern in very tall buildings where the drift may be several feet. G~nerally . a building should be designed stiff enough so that the maximum drift does not exceed 1/ 500 of the height of the building.
64
B. Earthquake Like wind, an earthquake produces dynamic loads on a building. During an earthquake, the ground moves both vertically and laterally, but the lateral movement is usually most significant and the vertical movements is ignored. For some tall buildings or structures with complex shapes or unusual conditions, a dynamic structural analysis is required. With this method, a computer is used to model the building and earthquakes to study the response of the structure and what forces are developed. In most cases, however, building codes allow a static analysis of the loads produced,'"greatly simplifying structural design. With the static analysis method, the total horizontal shear at the base of the building is calculated according to a ·standard formula. Then. this total lateral force is distributed to the various floors of the building so the designer knows what force the structure must resist. Chapter~ 4 discusses calculat.ion of earthquake loads in more detail.
3. MISCELLANEOUS LOADS A. Dynamic Loads When a load is applied suddenly or changes rapidly, it is called a dynamic load. When a force is only applied suddenly, it is often called an impact load. Examples of dynamic loads are automobiles moving in a parking garage, elevators traveling in a shaft, or a helicopter landing on the roof of a building. Dynamic loads do not occur on every building but are important to analyze and design for. The Uniform Building Code lists minimum requirements for many of these types of loads. See table 2.4. In many cases, a dynamic load is simply a static load value multiplied by an impact factor. A unique type of dynamic load is a resonant load. This is a rhythmic application of a force to a structure with the same fundamental period as the structure itself. The fundamental period is the time it takes the structure to complete one full oscillation, such as a complete swing from side to side in a tall building in the wind or one up-and-down bou nee of a floor. Resonant loads are usually small compared to other types of loads but slowly build over time as the load repeatedly amplifies the motion ot the structure. The principle of resonant loading is what makes it possible for a few people to overturn a heavy car by bouncing it on its springs in time with the fundamental period of the springs. The rocking motion of the car eventually is great enough so a final push makes it overturn. Resonant loads can affect an entire structure, such as repeated gusts of wind on a tall building, or portions of a building. A common problem is a vibrating machine attached to a floor with the same period as the machine's vibrations. In such a situation, the floor can be subjected to forces larger that it was designed for. The problem can be alleviated by placing the machine on resilient pads or springs to dampen the vibration, or by stiffening the floor to change its fundamental period. Occasionally, a tuned dynamic damper is placed at the top of tall buildings to dampen the effects ot wind sway. This is a very heavy mass attached to the sides of the building with springs of the same period as the building. As the building oscillates in one direction, the spring-mounted mass moves in the opposite direction, effectively counteracting the action of the wind. With this approach, costly wind bracing normally required to stiffen the entire building can be minimized. Table 23- special loads
65
TABLE 3.4 SPECIAL LOADS1
u ~E
VERTICAL LOAD
LATERAL LOAD
Description
Category
(Pa. Unless OtheiWise noted) 1. Construction, public access at the site (live load} 2. Grandstands, reviewing stands and bleacher {live load)
Walkway, See Sec. 2.1.9
3. Stage accessories see
Gridirons and fly galleries Loft block wells" Head block wells and sheave beams' Over staaes
3600
All uses except over stages
500 5
Sec. 2.1.11 (live load)
4. Ceiling framing (live load)
Canopy, See Sec. 2.1.10 Seats and footboards
7200 7200 17502
See Footnote
3 3650
3650
3650 1000
3650
5. Partitions and interi o·r walls, see Sec. 2.1.7 (Uve load)
250 2 by Total loads
6. Elevators ano dumbwaiters (dead and live load)
7. Mechanical and
I
electrical equipment (dead load)
8. Cranes (dead and live load)6
9. Balcony railings, guardrails and handrails
10. Storage racks
I Total load including Impact increase
125 by Totalload 6
0.10 by Total load
Exit facilities serving an occupant load greater than 50
7508
Other
3008
Over 2.4 m.
Total loads9
See Chapter 2
' The tabulated loads are minimum loads. Where other vertical loads required by this cx.de or required by the design would cause greater stresses, they shall be used. 2 Newton per linear meter, N!m 3 Lateral sway bracing loads of 350 N/m parallel and 150N/m perpendicular to seat and footboards. 4 All loads are in N/m. Head block wells and sheave beams shall be designed for all loft block well loads tributary thereto. Sheave blocks shall be designed with a factor of safety of five. $ Does not apply to ceilings which have sufficient total access from below, such that access is not required within the space above the ceiling. Does not apply to ceiling. Does not apply to ceiling if the attic areas above the ceiling are not provided with access. This live load need not be considered acting simultaneously with other live loads imposed upon the ceiling framing or its supporting structure. 6 The impact factors included are for cranes with steel wheels riding on steel rails. They may be modified if substantiating technical data acceptable to the building official are submitted. Live loads on crane support girders .and their connection shall be taken as the maximum crane wheel loads. For pendant·operated traveling crane support girders and their connections, the impact factors shall be 1:10. 7 This applies in the direction parallel to the runway rails (longitudinal). The factor for forces perpendicular to the rail is 0.20 x the transverse traveling loads (trolly, cab. books and lifted loads). Forces shall be applied at top of rail and may be distributed among rails of multiple rail cranes and shall be distributed with tdue regard for lateral stijfness of the structures supporting these rails. 8 A load pet linear meter to be applied horizontally at right angles to the top rail. 9 Vertical members of storage racks shall be protected from impact forces of operating equipment or racks shall be designed so that failure of one vertical member will not cause collapse of more than the bay or bays directly supported by the member.
66
B. Temperature-Induced Loads All materials expand when they are heated and contract when they are cooled. The amount of the change is dependent on the material and is expressed as the coefficie11t of expansion measured in mm per mm per degree centegrade. Some materials, like wood, have a low coefficient of expansion while others, like plastic, have a high value. If a material is restrained so it cannot move and then subjected to a temperature change, a load is introduced on the material in addition to any other applied loads. In the worst case, temperature-induced loads can so overload a structural member that failure may occur. Most often, however, failing to account for temperature-induce loads causes other types of failures such as tight-fitting glass breaking when a metal frame contracts, or masonry walls cracking when expansion joints are not provided . In nearly all cases, the solution is fairly simple: the material or assembly of materials must be allowed to expand and contract fo rth~ expected distance. This is fairly easy to calculate and detailed methods are described in Chapter 4.
C. Soil Loads Retaining walls are required to resist the lateral pressure of the retained material in accordance with accepted engineering practice. The Uniform Building Code allows retaining drained earth to be designed for pressure equal to that exerted by a fluid weighing 4.7 kn/cu . meter and having a depth equal to that of the retained earth. This is in addition to any surcharge such as vertical loads near the top of the wall or other lateral loads. In addition, retaining walls must be designed to resist sliding or overturning by at least 1 .5 times the lateral force or overturning moment. To calculate the pressure at the bottom of the wall, simply multiply 4.7 kn/cu. meter by the depth of the wall to get kn per square meter. Since the pressure varies uniformly from zero at the very top of the wall where no earth is retained to a maximum at the bottom, the total load is found by calculating the area of the triangular distribution or the maximum earth pressure at the bottom times the height divided by two. This is the horizontal load per linear meter acting on the wall. See Figure 3.2
"I
''
LOAD FROM SOIL ON RETAINING WALL
Figure 3.2 Example 3.4 What is the total horizontal load exerted on a retaining wall 3m high? The pressure at the bottom is a 3 m times 4. 7 kn per cubic meter, or 14.1 kn per square meter. The total horizontal load is 14.1/2 times 3m, or 21.15 kn per linear meter of wall. It will be shown that this total load acts at the centroid of a triangle, or one-third the distance from the base.
67
D. Water Loads from water can occur in many situations: in water tanks, swimming pools, and against retaining walls hOlding back groundwater. The load developed from water and other fluids is equal to the unit weight of the fluid in kilonewton per cubic meter multiplied by its depth. For water, the weight is about 9.8 kilonewton per cubic· meter an.. ,
··.[}:
...
·;·:-· ·. ( .
.r.-.
. . .. ........
...
·. 0< ,.,
·.
;
...
''I'
•.· .· ·. ~
~:-.;;··.
.... . ~
,·,
bell
....:·.
~ ~ ·. ~b)
topen.d pile
Figure 7.8 Pile Types 120
(c) drt1*i and bell•d pier
C. Designing Footings There are three primary factors to investigate when designing footings. The first is the unit loading, so that the allowable bearing pressure of the soli is not exceeded and differential settlement in various parts of the structure is eliminated as much as possible. The other two are shear and bending. There are two kinds of shear failure. A footing fails in punching or two-way shear when the column or wall load punches through the footing. A footing can also fail in flexural shear or diagonal tension the same as regular beams. Footings fall in bending when the lower surface cracks under flexural loading. Simple spread footings act much like inverted beams with the upward soil pressure being a continuous load that is resisted by the downward column load (although ln reality, the column load is the action and the upward pressure is the reaction).See Figure 7.1 0. This tend to cause bending in the upward direction, which induces compression near the top of the footing and tension near the bottom of the footing. If the tension is great enough, tension reinforcing must be added near the bottom of the footing.
building column
pile cap
grade beam reinfot
57<
50"
76°
78"
67<
59"
761
891'
76<
68"
3ae
32'
40.5
48.5 72.5
40.5 60.5
35.1 52.5
24.0
20.0
36.5 30.3
Fu • 400 MPa 3
36.5 54.3
-5
26.2 45.4
3s.sTio.3 54.3 39.1
6 72.5 72.5 60.5 8 90.8 90.8 75.6 10 109.0 109.0 90.8 11. )126.8 126.8 105.9 1
41.4 61.8
42.3 63.6
35.1 52.9
30.7 45.8
60.5
52.5 82.8 84.5 70.7 61.0 60.5 97.0 80.5 69.8 48.5 65.4 1 103.2 105.9 88.4 76.5 101.0 121.0 101.0 87.2 60.5 78.71124.1 126.8 105.9 91.6 121.01 145.0 121.0 105.0 72.5 91.6 144.6 118.2 123.7 107.2 141.01 109.5 141.0 122.3 89.50
40.5 50.3 60.5 70.7
J1
145.0 145.0 121 .0 105.0 1165.5 169.5 141 .0 122.3 161.5 193.5 161.5 139.7E 97.0 80.5 163.3 163.0 136.1 117.5 186.0 190.4 158.8 137.0 181 .5 217.6 181 .5 157.1 109.0 90.8 166.4 199.1 227.3 232.7 194.8 168.2 221 .6 266.0 221 .6 192.2 133.0 110.8
20 21 22 24
157.0 211.8 183.3 21 1.8 183.3 242.0 290.5 242.0 209.5 145.0 121.0 170.4 229.1 198.9 262.0 262.0 227.3 157.0 131.5 214.0 282.1 282.1 244.7 69.5 141.0 262.0 181.5 151 .3
12 14
l
25 290.5 290.5 242.01209.5 330.6 338.6 282.1 244.7 322.6 387.1 322.6 279.4 193.5 161.5 • Usual spacing. b Minimum spacing to obtain full bearing (F = 1.5F). e Preferred minimum spacing (3d). P d Absolute minimum spacing (22/ad). • Preferred minimum end distance. 'Absolute minimmum end distance. 9 See AISC Specifications Formula (1.16-1). ~See AISC Specifications Formulas (1 .16·2) and (1.16-3). Notes: This table is applicable to all mechanical fasteners in both friction-type and bearing-type connections utilizing standard holes. Standard holes shall have a diameter nominally 1.6 mm larger than the nominal bolt diam· eter (d + 1.6 mm). For oversize or slotted holes, see AISC Spec.nicatioo. Sects. 1.16.4.2 and 1.16.5.4.
Fu is the specified minimum tensile strength of the base material of the connected part. Values for decimal thicknesses may be obtained by multiplying the decimal value of the unlisted thickness by the value given tor a 1" thickness in the appropriate table. Values are limited at the double shear capacity of A490-X fasteners.
Reprinted from Manual of StHf Construction 8th «i., American Institute of StHI Construction
134
Example8.2 A nominal1 00 mm x 150 mm redwood beam is to be supported by 50 mm x 150 mm members acting as a spaced column as shown in illustration. The minimum spacing and edge distances for 12-mm bolts are shown. How many 12-mm bobs will be required to safely carry a load 6.67 kn?
min. 11/ 2 times bolt diameter
-t---! -~--
min. row spacing 5 times bolt diameter
t __ _ i
min. 4 times bolt diameter
-·~···-·-···- ·1 I
Look In Table 8.1 under column labeled 12-mm bolt diameter. Since the length of the bolt in the main member 64 mm {1 00 mm nominal width), use that row and the portion of the row labeled double shear. The lower of the two values governs. so use this row. This is the load perpendicular to the grain. This value is 4.86 kn (4360 newton). Two bolts will allow for a load of 4.36 kn times 2, or 8. 72 kn, well above the 6.67 kn required. Using the spacing and edge distances given in the illustration, there must be a spacing of 64 mm, a
top edge distance of 20 mm and a bottom edge distance of 350 mm for a total of 134 mm, within the total actual depth of 140 mm of the 100 mm x 150 mm member.
135
0. Timber Connectors There are two types of timber connectors: split rings and shear plates. Split rings are either 37 mm or 100 mm in diameter and are cut through in one place in the circumference to form a tongue and slot. The ring is beveled from the central portion toward the edges. Grooves are cut in each piece of the wood members to be joined so that haH the ring is in each section. The members are held together with a bolt concentric with the ring as shown in Figure 8.4 (a). Shear plates are either 65.625 mm or 100 mm in diameter,and are flat plates with a flange extending from the face of the plate. There is a hole in the middle through which a either a 18 mm or 21 mm bolt is placed to hold the two members together. Shear plates are inserted in precut grooves in a piece of wood so that the plate is flush with one surface. See Figure 8.4 (b). Because of this configuration, shear plate connections can either hold two pieces of wood together or one piece of wood and a steel plate. Split ring connectors and shear plates can transfer larger loads than bolts or screws alone. and are often used in connecting truss members. Shear plates are particularly suited for constructions that must be dis-assembled. Tables of design values for loads, spacing, end and edge distances are published by the National Forest Products Association.
P. Miscellaneous Connection Hardware Because wood is such a common building material, there are dozens of types of special connectors especially designed to make assembly easy, fast. and structurally sound. Hardware is available for both standard sizes of wood members as well as special members like woodtruss joists. Manufacturers publish allowable design values for each of their pieces. Some of the common types of connection hardware are shown in Figure 8.5.
2 STEEL CONNECTIONS Bolting and welding are the two most common methods in use today for making steel connections. RiVeting was once widely used but has been generally replaced with bolting because bolting is less expensive and does not take such a large crew of skilled workers to accomplish.
jci~t hanger saddl~
hsnger
post c:ap
post base
Figure 8.5 Special Connection Hardware
136
A. Bolts There are two types of bolted connections: bearing type and friction type. Bearing-type connections resist the shear load on the bolt through direct bearing of the steel being fastened on the sides of the bolt. As with wood connections, the bolt may either be in single shear or double shear. Friction-type connections are made when the bolt is tightened to such an extent that friction develops between the connecting members and loads are transferred through this friction rather than through the bolt itself. Bolts are further classified as to whether the bolt threads are Included or excluded from the shear plane. This affects the strength of the connection because there is less area to resist the load through the threaded portion. See Figure 8.6. Bearing-type connections have the lowest load-carrying capacity of bolted joints and are used in noncritical or secondary connections. Because the holes are slightly larger than the bolts there is usually some movement as load is appUed. Where sUppage is undesirable or the joint may be subject to vibration or repeated reversal of load, friction-type connections must be used. There are three basic types of bolts used in modem steel construction. Bolts designated with the American Society of Testing and Materials (ASTM) number A307 are called unfinished bolts and have the lowest load-carrying capacity. They are used only forbearing-type connections. Bolts designated A325 and A490 are high-strength bolts and may be used in bearing-type connections but roost be used in 1riction-type connections. In friction connections, the nuts are tightened to develop a high tensile stress in the bolt, thus causing the connected members to develop a high friction between them which resists the shear. Bolts range in diameter from 12 mm to 38 mm in 3 mm increments, but the roost typically used diameters are 20 mm and 22 mm. Bolts are installed with a washerunderthe head and nut. In addition to the ASTM designations, there are standard codes for the condition of use:
• F: friction-type connection • N: Bearing-type connection with threads included in the shear plane * X: bearing-type connection with threads excluded from the shear plane
• S: bolt in single shear • 0: bolt in double shear The American Institute of Steel Construction (AISC) Manual of Steel Construction gives the allowable loads for various types of connectors in both shear and bearing. For bearing connections, different values are given based on the minimum tensile strength of the base material of the connected part. For A36 steel, this value is 400 MPa. The maximum allowable bearing stress between the bolt and the side of the hole is given by the equation. Fp
•
1.5 Fu
There are several types of holes for bolted connections. Standard round holes are 1.5 mm larger than the diameter of the bolt. Other kinds of holes as listed below may be used with high-strength holes 16 mm in diameter and larger. Oversize holes may have nominal diameters up to 4.5 mm larger than bolts 22 mm and less in diameter, 6 mm larger than 25 mm bolts, and 7.5 mm larger than bolts 27 mm and greater in diameter. These holes may only be used in friction type connections. Short slotted holes are 1.5 mm wider than the bolt diameter and have a length that does not exceed the oversize hole dimensions by more than 1.5 mm. They may be used in either bearing or.frictiontype connections , but if used in bearing,the slots have to be perpendicular to the direction of load. 137
Long slotted holes are 1.5 mm wider than the bolt diameter and a length not exceeding 2 1/2 times the bolt diameter. They may be used in friction-type connections without regard to direction of load. but must be perpendicular to the load direction in bearing-type connections. SloUed holes are used where some amount of adjustment is needed. Long sloUed holes can be used in one of the connected parts of a joint. The other part must use standard round holes or be welded. In addition to the load-carrying capacities of the bolts. the effect of reducing the cross-sectional area of the members must be checked. Figure 8.7 shows a \YPical example of this. In this case, a beam is framed into a girder with an angle welded to the girder bolted to the beam. With a load applied to the bt:am, there is a tendency for the web of the beam to tear where the area of the flange has been reduced by the bolt holes. This area is known as the net area. As shown in the figure, there is both shear failure parallel to the load and tension failure perpendicular to the load.
The AISC Specifications limit the allowable stress on the net tension area to : Ft = 0.50Fu
The allowable stress on the net shear area is limited to: Fv
=
0.30Fu
The total shearing force is the sum required to cause t"loth forms of failure. The stress on the net tension area must be compared with the allowable stress on the gross section which is: Ft
=
0.30Fy
(beam
girder\
shear
r-tl
pl~r.e
f. ___')__-...=~~
Q:
t hreads exc lu ded from chear plane. t h reads ;ncludcd i n shea: p_lane
Figure 8.6 Location of Bolt Threads in Relation to Shear Plane
Figure 8.7 Tearing Failures at Bohed Connection Example 8.3
A 10 mm A36 steel plate is suspended from a 12 mm plate with three 20 mm A325 bo Its in standard holes spaced as shown in the drawing. The threads are excluded from the shear plane and the connection is bearing type. What is the maximum toad-carrying capacity of the 10 mm plate?
138
First, check the shear capacity of the bons. From Table 8 .2, one bolt can carry a load of 59.2 kn or three bolts can carry 3 x 59.2 kn or 177.5 kn.
r--- -----I2..$-.
31.1) 115
I '--
Finally, determine the maximum str~s on the net section through the holes. Once again, the thinner materials is the most critical component. The allowable unit stress is:
115 ST.:I
I l
0 @ @ ---------f-
..,....... ,... ._
______
Next. check bearing capacity. The thinner material governs, so use the 10 mm row in Table 8.3. From this row, read under the 20 mm diameter column and under the 75 mm spacing. The allowable load is 109.0 kn . Three bolts will then carry 3 x 109.0 kn, or 327.0 kn.
F1 .,. O.SOFv
"'
0.50
x 400 Mpa :: 200 Mpa
The diameter of each hole is 1.6 mm larger than the bolt, or13116 inch, which is 20.6 mm. The net width of the 10 mm plate is:
net width - 22.5 mm- (3 x 20.0 mm) - 166 mm The allowable stress on the net section is: F1 = (166 mm x 10 mm} x 200 Mpa =317.4 kn
From these three loads, the minimum governs, which is the shear capacijy of the bolts, or 177.53 kn.
There are many kinds of framed connections depending on the type of connector being used, the size and shape of the connected members, and the magnitude of the loads that must be transferred. Figure 8 ~6 illustrates some of the more typical kinds of steel connections. In most cases, the angle use to connect one piece with another is welded to one member in the shop and bolted to the other member during field erection. Slotted holes are sometimes used to allow for minor field adjustment. If the top flange of one beam needs to be flush with another, the web is coped as shown in Figure 6.8 {b). Simple beam to column connections are often made as illustrated in figure 8.8 (c~. The seat angle carries most of the gravity load, and the clip angle is used to provide stability from rotation. If a moment connection is required, a detail similar to Figure 8.6 {d) is used, although welding is more suitable for moment connections. For tubes and round columns, a single plate can be welded to the column and connected with beams as shown in Figure 8.8 (f). When the loads are heavy, some engineers prefer to slot the column and run the shear plate through, welding it at the front and back of the column. Since connecting beams to columns and other beams with angles and bolts is such a common method of steel framing, the AISC Manual gives table of allowable loads for various types and diameters of bolts and lengths and thicknesses of angles. Two such tables are reproduced in Table 6.4 and 8.5. The first is for bearing type connections and the second is for friction type connections.
139
Allowable Loads for Framed Beam Connections-Bearing Type
FRAMED BEAM CONNECTIONS
Bolted Allowable loads in kips •
:: .
varies
i
-
. t
; ·- -
11age..: ..
TABLE 8.4
Framed Beam Connections For bohs in bearing·type connections with standard or slotted holes. · t
Boh type
A325-N
A490-N
A325-X
A490-X
F. (MPa)
145
193
207
275.8
20
Bolt Oiam. d (mm)
22
25
20
22
25
20
22
22
25
1606
d
1570 2015•
d
1446
d
1415 1815•
d
20
25
Angle Thickness t (mm) L l (mm) (mm)
750
n
10
828 1126
673
787 711
9
597 521
635 559
8
7
743 1010 658 899 578 787
444
488
6
368
406
292
1468 1099 1499 195SI' 1179 1321 992 1348 176~ 1063 1175 881 1187 1566'> 1943
676
5
494 413
1028 770 1050 137(1> 1828 881 658 899 1174b 707
561
734
330
4
330
449
216
254
3
248
140
178
2
165
1286 1126 961
d 1615< d d 1099 1410C 210C 943 121 ()C 121 ()C d
1259
747
9791'
592
801
010C
787
587
552 440
101()< 101 ()C
601
7~
472
641
8os•
627
337"
440
330
449" 5871'
354b
480
sos• 471!' sos•
aos• 60Se
2251>
294
220
2991' 391!'
236"
321
403"
31st'
403"
sos· 403•
• Tabulated load values are based on double shear of bolts unless noted. See AISC Specification, Appendix E. for other surface conditions. b
Capacity shown is based on double shear of the bolts; however, for length L, net shear on the angle thickness specified is critical. See Table 11-C.
• Capacity shown is based on bearing capacity of 32 mm (11/4j end distance {Specification Eq. (1.16-2)] on A36 angles of thickness specified; however, for length L, net shear on this angle is critical. See Table 11-C. d Capacity is governed by net shear on angles for lengths L and L'. See Table 11-C.
Reprinted from Manual of Steel Construction 8th ed., American Institute of Ste91 Construction
140
Allowable Loads for Framed Beam Connections-Friction Type FRAMED BEAM CONNECTIONS
Bohed Allowable loads in kips .:."!
-.
.I~'
varies
Note: FOI' L=211z use one half tt·,e tabular load value shovm for L • 5'h, fOI' the same bolt type, diameter, and thickness.
TABLE8.5
Framed Beam Connections Bolt type
A2.07
A325-F
A490-F
F. (MPa)
68.95
120.66
151.69
Bolt Diam.
20
22
25
20
22
25
20
22
25
6
6
6
6
8
12
8
12
16
d (mm)
Angle Thickn~ss t (mm)
L
L
(mm)
(mm)
n
750
787
10
393
534
698
690
934 1223
863
1179 1539
673
711
9
354
480
627
618
841
1099
779
1059 1384
597
635
428 375
979
489
552 480
747
559
315 275
561
521
8 7
659
854
694 605
943' 1228 823 1077
444
488
6
236
321
419
413
521
707
921
368
406
5
197
267
349
344
561 ·734 467 610
432
587
770
292
330
4
157
214
279
275
375
489
346
472
614
216
254
3
118
164
210
206
281
367
259
353
364
140
178
2
79
107
140
137
187
245
173
235
207
NOTE: For friction type oonnections with oversize or sloned holes, see Table 11 -B
• Tabulated load values are based on double shear of bolts unless noted. See AISC Specification, Appendix E, for other surface conditions. b
Capacity shown is based on double shear of the bolts; however, for length L. net shear on the angle thickness specified is cr~ical. See Table 11-C. Reprinted from Manual of Steel Construction 8th fld., American fnstitut9 of Ste91 Constn.Jction
141
1T
angle boltecr-..,. [;]•. o r welded to 'girdef
r1'=======~
(bl coped connection
(a1 beam to girder
tel column to bum connection
(d)
......
-
moment connec!ion
......
"--
~
f- steel pi ate welded to column
(f) beam. 10 round column
(e) beam over column
Figure 8.8 Typical Steel Framing Connections
One of the more important considerations in bolted steel connections, just as in wood connections, is the spacing of bolts and the edge distance from the last bolt to the edge of the member. The AISC specifies minimum dimensions. The absolute minimum spacing is 2~213 times the diameter of the batt being used with 3 times the diameter being the preferred dimension. Many times a dimension of 75 mm is used for all sizes of bolts up to 25 mm diameter. The required edge distance varies with the diameter of the bolt being used: at the edge of plates, shapes or bars the dimension is 25 mm for an 18 mm bolt and 31 for a 25 mm bolt. To simplify detailing, a dimension of 31 mm is often.used for all bolts up to 25 mm diameter. 142
B. Welds Welded connections are quite frequently used .in lieu of bolts for several reasons:
* The gross cross section of the members can be used instead of the net section. • Construction is often more efficient because there are no angles, bolts, or washers to deal with and no clearance problems with wrenches. • Welding is more practical for moment connections. Smce members must be held in place untn welding is completed, welding is often used in combination with bolting. Connection angles and other pieces are welded to one member in the shop with the outreach leg punched or slotted for field connection with bolts. There are several types of welding processes, but the one most commonly used in building construction is the electric arc process. One electrode from the power source is attached to the steel members being joined, and the other electrode is the welding rod the welder holds in his or her hand. The intense heat generated by the electr:c arc formed when the welding rod is brought close to the members causes some of the base metal and the end of the electrode to melt into the joint. So the material of the electrode and both pieces of the joint are fused together. Penetration refers to the depth from the surface of the basemetal to the point where fusion stops. Two types of electrodes are in common use today: the E60 and the E70. The allowable shear stress for E60 electrodes is 124 MPa, and for E70 electrodes it is 145 Mpa. There are many types of welds. Which one to use depends on the configuration of the joint; the magnitude and direction of the load, the cost of preparing the joint. and what the erection process will be. The three most common types of welded joints are the lap, the butt, and the tee. Some of the common welding conditions for these joints are shown in Figure 8.9 along with the standard welding symbol used on drawings. In addition to the welds shown, plug or slot welds are frequently used to join two pieces. In these welds, a hole is cut or punched in one of the members and the area filled with the weld.
(a)
tingle tilltt Ilt (c) tqllart Qroovt buu jaint
( j) aiaot• .1 ,.. joint
Figure 8.9 Types of Welded Connections
143
l>eo~tl
tee joint
(b) groove weld
FJgUre 8.10 Weld Dimensions
(a) fillet weld
The fillet weld is one of the most common types. In section, its form Is an isosceles triangle with the two equal legs of the triangle being the size of the weld. The perpendicular distance from the 90 degree comer to the hypotenuse of the triangle is called the throat. See Figure8.10(a). Because the angles are 45 degrees, the dimension of the throat is 0.707 times the leg dimension. For a butt Joint, the throat dimension is the thickness of the material if both pieces are the same thickness, or the size of the thinner of two materials if they are unequal as shown in Figure 8.1 O(b) There are comrron symbols used for welding. These are listed in the AISC Manual of Steel Construction. A few are reproduced in Figure 8.11 (a). The full range of symbols gives information regarding the type, siZe location, finish, welding process, angle for grooves. and other information. To indicat~ information about a weld, a horizontal line is connected to an arrowhead line which points to the weld. This is shown in Figure 8.11 (b). This type of weld is indicated with one of the standard symbols and placed below the fine if the weld is on the side near the arrow and above the line if it is on the side away from the arrow.lf the members are to be welded on both sides, the symbol is repeated above and below the line. Other data placed with we ld symbol are.the size, weld symbol, length of weld, and spacing, in that order, reading from left to right. Field welds are indicated with a flag placed at the Junction of the horizontal line and the arrowhead line and pointing toward the tail of the reference line. A circle at the same point indicates that the weld should be made all around. The perpendicular legs of the fillet, bevel, J, and flare bevel welds must be at the left.
iI
v
"vi
y u
bevel
fillet
(field weld
\ r J
flare vee
flare bevel
weld ·a ll
0
I(
around~ ,.
weld all around
lengrh o( weld ar>d ~;:>;~c !ng symbol
.----
11
3@4
\..
~weld
· size of weld
(bl typical weld ing symbol field weld
f!vs!l contour
convex contour
Ia) weld ing sy mbo ls
Figure 8.11 Welding Synbols
144
Designing a welded joint requires that you know the load to be resisted and the allowable stress In the weld. For fillet welds, the stress is considered as shear on the throat regardless of the direction of the load. For butt welds, the allowable stress Is the same as for the base metal. As previously mentioned, the allowable stress for fillet welds of E60 electrodes is 124 MPa and for E70 electrodes it is 145 MPa. These stresses apply to A36 steel. For any size fillet weld you can multiply the size by 0.070 and by the allowable stress to get the allowable working strength per linear mm of weld, but these have been tabulated for quicker calculations. The allowable strengths are listed in Table 8.6.
TABLE 8.6 Allowable Working Strengths of Fillet Welds auowable load (MPa)
size of weld, mm
EGO electrodes
E70 electrodes
5mm 6mm 8mm 10mm 12mm 16mm 20mm
16.55 22.06 27.58 33.10 44.13 55.16 65.50
19.31 25.51 31.72 38.61 51.02 64.12 76.53
Source: Manual of Steel Construction, 8th ed.• American Institute of Steel Construction
In addition to knowing the allowable stresses, some AISC Code provisions apply to weld design. The following are some of the requirements. * The maximum size of fillet weld is 1.5 mm less than the nominal thickness of the
material being joined if it is 6 mm thick or more. If the material is less than 6 mm thick, the maximum size is the same as the material. * The minimum size of the fillet welds is shown in Table 8.7 • The minimum lenght of fillet welds must not be less than 4 times the weld size plus 6 mm for starting and stopping the art. •For two or more welds parallel to each other, the length must be at least equal to the perpendicular distance between them • For intermittent welds, the length must be at least 36 mm
145
Table 8.7 Minimum Size of Fillet Welds material thickness of the thicker part hoined, mm to 6mm inclusive over 6mm to 12mm over 12mm to 18mm over 18mm
minimum size of fillet weld, mm
3 4.5 6
7.5
3 CONCRETE CONNECTIONS: ln most cast-in-place concrete construction there are generally no connectors as with wood or steel. Different pours of concrete are tied together with reinforcing bars of with keyed sections. For precast concrete construction, however, there must be some way of rigidly attaching one piece to another. This accomplished with weld pfates.
A. Rebars and Keyed Sections The most typical type of cast-in-place concrete joint is one where the reinforcing bars ar.e allowed to extend past the tormwork to become part of the next pour. Continuity is achieved through the bonding of the two pours of concrete with the bars that extend through the joint. These types of joints are found in many situations: footing to foundation wall or column walls to slabs, beam to beam, column to beam, and several others. When the reinforcing is ontyforthe purpose of tying two pours of concrete together rather than transmitting large loads, they are called dowels. Some conditions are shown in Figure 8.12. The length of the dowels or extensi.ons of rebar from one section of concrete to the next is determined by the minimum development length required to transmit the loads or by the ACI Code. Keyed connections are used either alone or with rebars to provide a stronger joint between two pours of concrete. Keyed sections are often used in footings and floor slabs as shown in Figure 8.13.
(a) footil'g to :ound~tion wall
(b) wall 10 slab (a) keyl!~j~ i nt in foo til'l9
r·Jow e\s
lbl keyec' joint ;,, s! aiJ
lc) coLumn to column
{d) bear.n to beam
Figure 8.1 2 Concrete Joints Tied with Rebats
146
Figure 8.13 Keyed Concrete .nections
B. Weld Plates Because precast structures are built in sections, there must be some way to transmit horizontal, vertical, and moment forces from one piece to the next. This is usually accomplished by casting.weld plates. angles, and other types of steel pieces into the concrete members at the factory. At the site, the members are placed in position and corresponding plates are welded together. Wnen allowance must be made for horizontal movement due to temperature changes, concrete shringkage, and the like, precast members often bear on elastomeric pads rather than being rigidly fastened. Figure 8.14 shows two of the many possible types of precast connections.
C. Shear Connectors Shear connectors are not really connectors in the usual sense. but are used to tie steel and concrete together in composHe sections so forces are transmHted from one to the other. They are available in diameters of 15 mm, 16 mm, and 21 mm. One of the rypical applications of shear connectors is with concrete slab/steel beam composite sections as shown in Figure 8.15. Here the connectors are welded to the top of the steel beam in the fabricating shop at a fairly close spacing which is determined by engineering calculations to transmit the forces created by the applied loads. When the beam is erected, forms are placed and the concrete is poured around the connectors (along with any tensile and temperature steel). The enlarged head of the connectors is provided to give extra bearing surface. These are often called headed anchor studs and abbreviated HAS on the drawings. Figure 8.15 shows a single row of studs but two rows may be used if required. Metal decking instead of removable forms is often used for forming the concrete.
f
beam
weld
column
em! view
weld .Plate v weld
·0= ·
,---- angle with anchor
·~rdt:t~h.~~().
bolt can in footing
·
sjde view
Figure 8.14 Precast Concrete Connections
147
Figure 8.1 5 Shear Connectors
IX
BUILDING CODE REQUIREMENTS ON STRUCTURAL DESIGN
BUILDING CODE REQUIREMENTS ON STRUCTURAL DESIGN Nomenclature
.d
depth of beam
mm
Fb
allowable bending stress
MPa
Ft
allowable axial tensile stress
Fv
allowable shear stress specified minimum yield stress of the type of steel being used
MPa MPa
Fy
MPa
Building code provisions related to stf!Jctural design deal with how loads must be determined, what stresses are allowed in structural members, formulas for designing members of various materials, and miscellaneous requirements· for construction. Specific provisions and calculation methods are presented in other chapters. Loads on buildings are covered in Chapter 3, wind loading and calculation methods in Chapter 14, and seismic design methods are reviewed in Chapter 15. The code provisions outliRed here are based on the National Structural Code of the Philippines.
1 LOADING Chapter 23 of the UBC details how loads must be calculated.ln general terms, the code requires that any construction method be based on a rational analysis in accordance with welt-established principle of mechanics, and that such an analysi~ provides a path for all loads and forces from their point of origin to the load resisting elements. The analysis must include distribution of horizontal shear, horizontal torsional moments, stability agains~ overturning, and anchorage. Horizontal torsional moment resu Its from torsion due to eccentricity between the center of application of a lateral force and the center of rigidity of the force-resisting system. Anchorage resists the uplift and sliding forces on a structure. The code also requires that various combination of loads be investigated and that the one resulting in the greatest effect on the structure be used in calculations. Since it is recognized that all types of loads will not be acting at once•. some modification is allowed in determining the various load combinations that must be Investigated. These combinations are:
* dead plus floor live plus roof live • dead plus floor live • dead plus floor live plus wind plus seismic (or wind) • dead plus seismic (or wind) In addition, lateral earth pressure rrust be included in the design when it results in a more critical combination.
150
A. Live Loads Required floor live loads are given in UBC Table 23-A, roof loads in Tables 23-C, and special loads in Table 23-B. These are reproduced in Tables 3.2, 3.3, and 3.4, respectively. Some reductions in live loads are permitted. The loads given in the National Structural Code may be reduced on any member supporting more than 14 sq. meters except for floors in places of public assembly and for live loads greater than 4800 Pa for determining these reductions are given in Chapter 3 in formulas 3.1 and 3.2, respectively, along with examples for their use. Additional code provisions related to live loads include the following. • Provisions must be made for designing floors to accommodate concentrated loads as shown in Figure 3.1 (UBC Table 23-A).If these loads, acting on any space 750 mm x 750 mm square feet square on an otheiWise unloaded floor, would result in stresses greater than those caused by the uniform load, then the floor must be designed accordingly. • Where uniform live floor and roof loads are involved, the design may be l.imited to full dead load on all spans in combination with fulllille load on adjacent spans and on alternate spans. This is particularly important where structural continuity of adjacent spans is involved. In any case, the code requires the investigation of loading conditions that would cause maximum shear and bending moments along continuous members. • Live loads for each floor or portion thereof in commercial or industrial buildings must be conspicuously posted. • Interior walls, permanent partitiqns, and temporary partitions over 1.8 m high must be designed to resist all loads on them but in no case less than a force of 250 Pascals applied perpendicular to the wall.
B. Dead Loads The UBC defines dead load as the vertical load due to the weight of all permanent structural and non· structural components of a building, such as walls, floors. roofs, and fixed service equipment. The code does not specifically state required dead loads; rather, the designer must use standard unit weights for various building materials published in standard reference sources. However, two specific provisions are mentioned. First, floors in office building where partition locations are subject to change must be designed to support a uniformly distributed dead load equal to 960 Pa. Second, access floor systems may be designed to support an additional480 Pa of uniformly distributed dead load over all other loads.
C. Lateral Loads lateral loads include wind loads and seismic loads. Wind is assumed to come from any direction, and the design wind pressure used for calculations is dependent on the height of the structure above the ground, exposure of the structure, a wind stagnation pressure at a standard height of 9.15 m above the ground, the portion of the structure under consideration, and a factor related to the importance of the building during an emergency, such as a fire station. These are established as values and coefficients given in tables at the end of Chapter 23 of the UBC. The formulas for determining design wind pressure and a full explanation of the factors involved are given in Chapter 14. When special conditions exist, such as structures sensitive to dynamic effects. structures sensitive to wind-excited oscillations, and buildings over 120m in height, the buildings must be designed in accordance with approved national standards. This basically means using accepted wind tunnel testing procedures to determine the actual wind forces on the structure. 151
a
For earthquake loads, the code requires that stresses be calculated as the effect of force applied horizontally at each floor or roof level above the base. The designer must assume that the force can come from any direction. Although the UBC gives detailed methods and concepts for designing structures to resist seismic forces, it does allow that other methods can be approved by the local building official if it can be shown that equivalent ductility and energy absorption can be provided. In the event that wind loads produce higher stresses, they must be used in place of those resu~ing from earthquake forces. Seismic forces and methods of design are discussed in more detail in Chapter 15.
2 ALLOWABLE STRESSES The Unlform Building code establishes basic allowable stresses for various types of construction materials. The design of any structural member must be such that these stresses are not exceeded. Although some provisions of the code are extremely complex (such as with concrete), this section outlines some of the more important provisions with which you should be familiar.
A. Wood Tables in Chapter 4 of the National Structural Code give allowable unit stresses in structural lumber. and glued-laminated timber. These include allowable stresses for extreme fiber In bending~ tension parallel to the grain, horizontal shear., and compression perpendicular and parallel to the grain. The stresses given are for normal loading and must be adiusted according to various conditions of use as follows: Single or. repetitive use: Two values for allowable stress in extremes fiber are given in UBC Tables 2-A·1 and 25-A-2. One is for a wood member used by itself, such as a beam, and one is for several members used together such a:s joists or rafters. Examples of these tables are shown in Chapter 10. The value for repetitive use is higher than for single use. In order to use the higher value, the member cannot be over 100 mm in nominal thickness, ·cannot be spaced more than 600 mm in nominal thickness, cannot be spaced f!10re than 600 mm on center, must be joined by transverse load-distributing elements (such as bridging or decking), and there must be at least three members in a group. Duration of load: The amount of stress a wood member can withstand is dependent on the time during which the load producing the stress acts. This relation of strength to duration of load is shnwn graphically In Figure 9.1, Allowable design loads are based on what is called normal duration of load which is assumed to be ten years. For duration of loads shorter than this, the allowable stress may be increased according to the following percentages:
• 15 percent for two months' duration,
• 25 percent for seven days' duration, as for roof loads • 33 1/3 percent for wind or earthquake loads
• 100 percent for impact loads If a structural member is fully stressed to the maximum aUowable stress for more than ten years under conditions of maximum design loads, the allowable stress cannot exceed 90 percent of those listed in the tables. Flre-ret$ldant treatment: allowable stress values must be decreased by 10 percent for lumber pressure Impregnated with approved fire-retardant chemicals. PlyWood values must be reduced by 16 percent.
152
Size-factor adjustment: When the depth of a rectangular sawn bending member exceedd 300 mm, the allowable unit must be multiplied by a size factor determined by the formula:
CF=
)t. (-l2 rl
There is also a slenderness factor adjustment for unsupported beams. However, most wood members are supported either with bridging or with continuous decking material, so this adjustment is not usually required. 2.0 impact 1.9 :::~ 1.8 ~ .. 1 7 ;;;.£ . ., - 1.G t:l
t---.,._ :cE s f ~ \. 1 - - -4--.>...
E c 1.4 1----+--~
iii 0
1 .3 1 -- - - t - --i---"'to... 0; 1. 2 t--+-+-t---=:::.,..._ .Q -!S 1.1 1----1---1----'!-----+----=::::........_ ~ £ t .0 t - --+--+-_..;f---+--+---=::::::...normal
0.9
1 see. 1 min.
i
hr. 1 day , · mo. 1 yr.
-- -- _ pe.rrnaner 10 y rs.
duration of meximum load
Figure 9.1 Relation of Strength to Duration of Load for
B. Steel Allowable stresses for structural steel are expressed as a fraction of the yield stress of the steel. They vary with the type of stress the member is under (shear, compression, bending, and tension) and with conditions such as unsupported lengths and geometry ofthe section. Some of the more common code requirements for allowable stress are: For tension on the gross area.
=
0.60 Fy
9.2
For tension on the net effective area, Ft = 0.50 Fy
9.3
Ft
For shear on gross sections,
9.4
Fv = 0.40 Fy
At beam end connections wh€re the top flange is coped, and similar conditions where failure might occur along a place through the fasteners, allowable shear stress is: Fv
=
0.30 Fy
9.5
For bending where the beam is laterally supported, and the section meets the requirements of a compact section and is loaded in the place of the minor axis, Fb
=
0.66 Fy
9.6
For bending where the beam is not a compact section, but where it is supported laterally. Fb ""
0.60 Fy
9.7
Allowable stresses for bolts, rivets, and threaded parts are based on the type of load placed on them and given as values MPa based on the ASTM designation of the fastener or as a fraction of the minimum tensile strength of the type of fastener. These are enumerated In UBC Table 27-A. and a detailed listing Is given in Tables 8.2 and 8.3 in Chapter 8. 153
Allowable stresses for welds are based either on the yield strength of the base metal or the nominal tensile strength of the weld metal. The allowable stress is then multipUed by the area of the weld. Chapter 27 of the Uniform Building Code along with UBC Table 27-B describe the requirements for welds in great detail. Table 8.6 in Chapter 8 summarizes the allowable working strengths for welds of various sizes.
C. Concrete Building code requirements for reinforced concrete are very complex and detailed. and cover all aspects of formwork, reinforcing, mixing, placing, and curing. NSCP Chapter 5 concerns concrete construction. It contains specific requirements too numerous to mention here. In addition. it makes reference to Building Code Requirements for Reinforced Concrete, ACI 318 , published by the American Concrete Institute. as well as to other ACI publicatons. Concrete construction is based on the specified compressive strength, f'c expressed in MPa. Many of the formulas for concrete design use this as a part of the equation. Because concrete is a highly variable material, the USC goes to great lengths to specify how concrete is to be mixed and then how quality control is to be maintained. This is to ensure that a building is actually constructed of concrete that meets or exceeds the original design strength. The UBC requires that samples for strength tests are taken for each class of concrete placed. Samples must be taken not less than once per day, not less than once for each 150 cubic yards of concrete, nor less than once for each 5,000 square feet of surface area for slabs or walls. The average of all sets of three consecutive strength tests must equal or exceed f'c, and no individual test can be less than 500 psi below the f'c value.
3 CONSTRUCTION REQUIREMENTS In addition to allowable stresses and other requirements related to structural calculations, the UBC places many restriction on how various materials may be used. The following sections outline some of the more important ones with which you should be familiar.
A. Wood Since the structural integrity of wood is dependent on such factors as moisture, fire, insect at1ack, and connections, the UBC goes to great lengths to specify wood construction techniques. You should be familiar with the following requirements. • The bot1om of wood joists must be at least 450 mm above exposed ground, and the bottom of v.oove this point, the wood is dimensionally stable, but as wood dries below this point it begins to shrink. When wood is used for structural framing and other construction purposes, it tend to absorb or lose moisture in response to the temperature and humidity of the surrounding air. As it loses moisture it shrinks , and as it gains moisture it swells. Ideally, the moisture content of wood when it is installed should be the same as the prevailing humidity to which it will be exposed. However, this is seldom possible, so lumber needs to be dried-either air dried or kiln dried-to reduce the moisture content to acceptable levels. To be considered dry lumber, moisture content cannot exceed 19 percent. To be grademark kiln dry, the maximum moisture content permitted is 15 percent. Design values found in tables assume that maximum moisture content will not exceed 19 percent. If it does, the allowable stresses must be decreased slightly. Wood shrinks most in the direction perpendicular to the grain and very little parallel t6 the grain. Perpendicular to the grain wood shrinks most in the direction of the annual growth rings {tangentially) and about half as much across the rings (radially). In developing wood details, an allowance must be made for the fact that wood will shrink and swell during use regardless of its initial moisture content. Of particular importance is the accumulated change in dimension of a series of wood members placed one on top of the next. The shrinkage of an individual member may not be significant, but the total shrinkage of several may result in problems such as sagging floors, cracked plaster, distortion of door openings, and nail pops in gypsum board walls.
2WOODBEAMS The design of wood beams is a fairly simple procedure. First, the loads and stresses on the beam are determined as described in Chapter 5. This includes finding the support reactions, vertical shear stresses. and bending moments. Then, the basic flexure formula is used to find the required section modulus needed to resist the bending moment. A beam size is then selected that has the required section modulus. Second, horizontal shear stresses are calculated and compacted withthe allowable horizontal shear for the species and grade of lumber being used. This is especially important because wood beams have a tendency to fail parallel to the grain where their strength is lowest. Finally, deflection is checked to see if it is within acceptable limits. This, too, is important because wood is not as stiff as steel or concrete. Even though a beam may be strong enough to resist bending moment, the deflection may be outside of tolerable limits.
A. Design for Bending To design wood beams for bending, the basic flexure formula is used: Fb
=
6M
~------
bd2
The allOwable extreme fiber stress in bending is found in Table 10.2 or similar tables in the building
code or from other reference sources. Since moment is usually calculated in kN-M, you must be sure to convert to n-mm by multiplying by 10' because the value of Fb is in mPa. Also, if any increase in stress is allowed due to short duration of loading, the value of Fb is multiplied by the allowable percentage increase.
162
B. Design for Horizontal Shear Because it is easy for wood to shear along the lines of the grain, actual horizontal shear must always be checked against the allowable unft shear stress. Fv. This is especially important for short spans with large loads. Frequently, a beam that is sufficient in size to resist bending stresses must be made larger to resist horizontal shear stresses. Because horizontal shear failure will always occur before vertical shear failure, it is not necessary to check for vertical shear except for beams notched at their supports. For rectangular beams, the maximum unit horizontal shear is: 3V
Fv = 2 bd When calculating the vertical shear, V, the loads within the distance from the supports equal to the depth of the member may be neglected.
Example 10.5
Using the beam found in Example 10.1, check nfor horizontal shear. The load is 5100 N per linear meter for 3.66 m or 18666 N total. The vertical shear at each reaction is 9333 N. Subtract the load within a distance equal to the depth of the beam, 294 mm. V=
9333- ( 294) 5100 =7833.6 N 1000
The value of bd is the area of the member which equals 27636 mrn2. Actual horizontal is:
Fv = 3(7833 ·6} 2(27636)
=
0.425 MP
a
Looking at Table 10.2, the allowable horizontal shear, Fv, is 0.586 MPa for Douglas fir-larch #2, so the beam is adequate to resist the imposed horizontal shear. If the actual value was greater than the allowable, a larger beam would be needed.
C. Design for Deflection Since wood is not as stiff as steel or concrete, deflection is always a concern. Detrimental effects of deflection can include nail popping In gysum ceilings, cracking of plaster, bouncy floors, and visible sagging. In many cases, a wood member can be selected that will satisfy bending requirements but will not satisfy deflection criteria. Therefore, the design of wood beams must always include a check for deflection. The formulas for deflection are the same ones used for other materials and are outlined in Figure 5.3. The criteria for maximum deflection is given in the Uniform Building Code and requires that two different conditions of loading be chacked. The first limits deflection due to live load only to U360 of the span. The second limits deflection due to live load and dead load for unseasoned wood to U240 of the span. In both cases, the units of deflection will be the same as the units used for the value of L.
163
The Uniform Building Code does allow a reduction by one-half of the dead load for the condition of live load and dead load if seasoned wood is used. Seasoned wood is defined as wood with a moisture content of less than 16 percent at the time of installation and used under dry conditions. This is typically the case, but since wood will deflect under long~term use beyond its initial deflection, it is common practice to use the full value of dead load and live load when checking deflection against the U240 criterion. This provides for the extra stiffness necessary to limit deflection under long-term loading.
Example 10.6 Using the same beam found In Example 10.1. check to see that its deflection is within the allowable limits. Assume that of the total load of 5100 N/m, dead load is 667 Nand liveload is 2920 N/m. From Figure 5.5, the deflection for a uniformly loaded beam is:
5wl4 fl.
;z
384EI
The modulus of elasticity of Douglas fir-larch #2 is 11720.503 MPa as found in Table 10.2 and the moment of inertia of a 100 mm x 300 mm 15 199062108 as found in Table 10.1 . In this case, it is important to keep units consistent in order for the answer to be in mm. Remember that w is the unit weight per unit length and I is the length. If I is in mm, the weight must be in Nlmm, not m. The beam length of 3.66 m. must be converted to mm and then raised to the fourth power; 5(5100)
.6.=
10~ 0
(3.66 X 103)•
384( 11720 .503)( 1990621 08)
... s.n mm
For deflection of liveload only,
O~Q (3.66 X 103) 4 1 384( 11720.503) (1990621 08) 5(2920)
A=
"'2.92 mm
Next, determine the allowable deflection limits. For liveload only 3 66
·
3~~
000
""10.17 mm
This is more than the actual deflection under live load only of 2.92 mm, so this is acceptable. For total load, 3.66 X 1000 240
=15.25 mm
This iS also more than the actual deflection under total load of 5.11 mm, so the 100 mm x 30 mm is acceptable for deflection requirements.
164
3 MISCELLANEOUS PROVISIONS
A. Notched Beams Notching of beams should be avoided, but if it is done, the UBC states that notches in sawn lumber bending members cannot exceed one-sixth the depth of the member and cannot be located in the middle third of the span. When the notches are at the supports as shown in Figure 10.2 the depth cannot exceed one-fourth of the beam depth.
If beams are notched, the vertical shear cannot exceed the value determined by the formula.
v=
2bd'FV
d
2bd'Fv
d
3
d
3
d
9.6
Figure 10.1 Notching of Beams
Example 10.7 tf the beam in Examp48 10.1 is notched 50 nvn, is it still an accept8t*t size?
The beam found in exai'Jl)le 10.1 is a 100 mm x 300 mm, so its actual depth Is 294 mm. Subtracting 50 mm gives a "d" value of 244 mm with a width of 87.5 nvn. From Table 10.2, the allowable horizontal shear for Douglas fir-larch 112 is 0.586 MPa. V
= 2(S7.S)(~)(0.586)
X :
•
6922.24 N
Fromexample10.5,theverticalshearwasfoundtobe9333N,sothisbeamcouldnotbenotched 50 mm without exceeding the allowable vertical shear limitation. I
165
B. Size Factor As the depth of a beam increases, there is a slight decrease in bending strength. The Uniform Building Code requires that the allowable unit stress in bending, Fb, be decreased by a size factor as determined by the formula.
300 119
Cf
= -----·····
10.7
d
This applies only to rectangular sawn bending members exceeding 300 mm in depth and does not apply to visually graded lumber 50 mm to 100 mm thick or to machine-stress-rated lumber. The size factor does not affect the allowable strenglh to any great amount. Cf for a 350 mm deep beam, for example, is only 0.987, and for a 400 mm deep beam, it is 0.972.
C. Lateral Support When a wood beam is loaded in bending there is atendency tor it to buckle laterally. The UBC provides that a decrease in allowable bending strength be made if certain conditions are not met. For the vast majority of wood construction, this is not required if proper lateral support is provided. lhis amount to providing continuous support at the compression edge, such as with sheathing or subflooring, and providing restraint against rotation at the-ends of the members and at intervals with bridging. Most wood construction meets these conditions, so adjustments are not required .
D. Bearing The load on a wood beam compresses the fibers where the weight is concentrateQ at the supports. To determine the required bearing area, the total reaction load is divided by the allowable compression perpedicularto grain, Fc1 , found in Table 10.2. For joists,the UBC states thatthere must be at least 36 mm bearing on wood or metal, and at least 75 mm bearing on masonry. Beams or girders supported on masonry must have at least 75 mm of bearing surface.
Example 10.8
What is the required bearing area for the beam selected in Example 10.1? The total reaction of the beam is: R"" 18666 ""9333 N 2
The required bearing area is:
A"'
9333 4.309
'"'2165.93 mm2
Since the beam is 87.5 mm wide, the required length of bearing is 2165.93187.5 or 24.75 mm. However, since this is less than the code requirement of 75 mm, 75 mm must be used.
166
4 WOOD COLUMNS As discussed in Chapter 4. columns have a tendency to buckle under a load, so even though a column may have enough cross-sectional area to resist the unit compressive forces, it may fail in buckling. For wood columns. the ratio of the column length to its width is just as important as it is for concrete and steel columns. However, for wood columns; the slenderness ratio is defined as the laterally unsupported length in mm divided by the least dimension of the column. This is a little different than the length divided by the radius of gyration as discussed in Chapter 5. but the same principles apply. Wood columns can be solid members of rectangular, round, or other shapes, or spaced columns buitt up from two or more individual solid members separated by blocking. Since almost all wood columns are solid rectangular sections, the method of design in this section will be limited to these types. As mentioned in Chapter 4, the load-carrying capacity of a wood column depends on the way the ends of the column are fixed. For design, the effective length must be determined. This is the total unsupported length multiplied by an effective buckling length factor, Kc. These factors for various and conditions are shown in Figure 10.2. Notice thatthis diagram is very similarto Figure 4.8, butthe values are slightly different. Ke VALUE
Z.IO
2.4
(
' '' I
I I I
'
' '
'\
''
~
..:.:; ·1
~
1T
n
,,,,/
OlD fREt: W111N.ISI..AT[ aJf llafAT.:JH fi)(EO
EMO F!£E TO AOT.\n Ao'ft> TIOANSL4T£
Figure 10.2 K. Values for Wood Columns Because of the way most wood construction is detailed, columns are usually fixed in translation but free to .rotate, so the K value is taken as the actual unsupported length. For the purposes of this chapter, the letter L will indicate the effective length of a column in Inches. Wood columns are divided into three categories: short Intermediate and long. The allowable compressive stress is different in each and must be calculated. Short columns are defined as those with a slenderness ratio, 1/d, of 11 or less. For short columns, the design vah.Je for compression parallel to grain, F'c Is the same as.the allowable design value 1or compression parallel to the grain, Fe, as given in Table 10.2.
167
Intermediate columns are defined as those with an Ud ratio of greater than 11 but less than k, where k Js given by the formula:
k::0.6714 For intermediate columns,
Fe'= Fe [1-1/3(~d)"]
Long colums are defined as those with an Ud ratio of k or greater but equal to or less than 50. The Ud ratio for a simple, solid column can not exceed 50. For long columns:
. Fc ""
0.3E
(Ud)2
The design of wood colurms is an iterative process. To support a given load, a least dimension, d, has to be assumed, the Ud ratio calculated, and Fe' values determined to find the required crosssectional area. Then a oolumn with the needed area is selected. If the column has a depth much greater than the assumed width, d, it is usually not an efficient column and the next size larger is tried. Gnerally, square or nearly square columns are most efficient.
Example 10.9 A wood column of Douglas fir-larch #1 is to support a load of 80 KN. If the column is 3.05 m long,
what is the most economical size to use? Try a column with a least nominal dimension of 100 mm (actual width of 94 mm). Since a 100 mm nominal member is being tried, to find the modulus of elasticity and the allowable compression parallelto the grain, use the grade grouping in Table 10.2 of 50 mmto 100 mmthick, 125 mm and wider.
-dL
::z:
k
=
3.05 X 1000 94 0.671
""32.45
~E/Fc =0.671 ~
12409.94 8.62
25.46 If the column size was 150 mm, the post and timber category would be used.
Since Ud is greater thanK, this is a long column and equation to be used is: Fe' ""
0 30 · E2
(Ud)
168
=3.54 MPa
The required area is then: A .. P/Fc'
=
80 X 100 3.54
,.. 22598.9 mm2 From Table 10.1 a 100 x 300 section has an area of 27636 mn~. so his size-column would work. However, a column of these dimensions is vey inefficient, so try a column with a nQ.rninal150- mm least dimension where d "' 144 m. .!:_., 3.05 X 1000 =21 18 d 144 . The value of K needs to be recalculated, because with a 150 mm member, a new grade category must be used where E =11031.05 and Fe= 6.89 MPa. k
k
=
0.671
~
11031.05 6.89
= 26.85
Now, the column is considered intennediate because Lid is greater than 11, but less thank.
Fe'
= [1 - ~ ( ~d ... 6.89 [ 1 -
)•]
~ ( ~d
)•]
= 6MPa The required area is now: A= 80 X 1000 6
=1333.33mni
From Table 10.1, a 150 mm x 150 mm has an area of 20736 mni, so this is more eoonomical size than the 100 mm x 300 mm.
169
TABLE 10.3
Allowable Spans for Floor Joists DESIGN CRITERIA: Deflection- For 1915.3 N per square meter. limited to span in mm. divided by 360. StrengthLiveload of 1915.3 N/m2 plus deaload of 478.8 N/m2 determines the required fiber stress value. JO!ST SIZE SPACING
Modulus of Elasticity, E in 6894.4 MPa
600
2.59 4.96 2.36 5.45 2.06 6.2
1.0 0.9 2.69 2.79 5.38 5.72 2.44 2.54 5.93 6.34 2.13 2.21 6.76 7.24
300
3.43 4.96
3.56 3.68 5.38 5.72
3.1
(mm) (mm} 0.8 300 50 X 150 400
3.45
3.23 3.35 5.86 6.34 2.82 2.92 6.76 7.24 4.55 4.7 5.38 5.72 4.11 4.27 5.86 6.34 3.61 3.73
600
6.2 5.31
6.76 7.24 5.51 5.71
300
4.96 4.83
5.38 5.72 5.0 5.18
400
5.45 4.22
5.93 6.34 4.37 4.55
600
6.2
6.26
50 X 200 400 660 300 50x250 400
sox 300
5.45 2.72 6.2 4.37 4.95 3.96 5.45
7.24
1.1 1.2 1.3 2.97 3.05 2.9 6.14 6.48 6.83 2.62 2.69 2.77 6.76 7.17 7.51 2.29 2.36 2.41
1A. 3.12 7.17 2.84 7.93 2.49
1.5
3.2 7.51 2.9 8.27 2.54 8.62 9.03 9.51 4.01 4.11 ·4.22
1.6
1.7
3.28 7.86 2.97 8.62 2.59 9.93 4.32
3.33 8.2 3.02 9.03 2.64 10.34
7.72 8.2 4.39 3.81 3.91 6.14 6.48 6.83 7.17 7.51 7.86 8.2 3.45 3.56 3.66 3.73 3.84 3.91 3.99 6.76 7.17 7.51 7.93 8.27 . 8.62 9.03 3.02 3.1 7.72 8.2
3.2 3.28 8.62 9.03
4.85 5 6.14 6.48 4.42 4.55 6.76 7.17 3.86 3.96
5.13 5.26 6.83 7.17 4.65 4.77 7.51 7.93 4.6 4.17
1.8 3.4 8.48 3.1 9.38 2.69 10.69
3.15 9.72 2.74 11.1
4.47
~.57
4.65
8.48 4.06
8.82 9.1 4.14 4.22
8.82
6.96 8.48 6.32 6.76 7.17 7.51 7.93 8.27 8.62 9.03 9.38 4.67 4.83 4.95 5.08 5.18 5.31 5.41 5.51 7.72 8.2 8.62 9.03 9.51 9.93 10.34 10.69
4.8 9.72 4.34
9.72 1Cl.7 10.69 3.63 3.68 3.81 11.1 11.51 12.27 5.82 5.92 8.82 9.1 5.28 5.38 9.72 10.07 4.62 4.7
'9.93 10.34 10.69 11:1 6.68 6.83 7.86 8.2 6.07 6.2
2.2
3.63 9.1 9.72 3.2 3.3 10.07 10.69 2.79 2.9 11.51 12.27
9.38 3.35 3.43 3.48 3.56 9.51 9.93 10.34 10.69 5.38 5.49 5.61 5.41 7.51 7.86 8.2 8.48 4.88 5 5.11 5.18 8.27 8.62 9.03 9.38 4.27 4.37 4.44 4.55
7.72 8.2 8.62 9.03 9.51 5.89 6.07 6.25 6.4 6.55 6.14 6.48 6.83 7.17 7.51 5.36 5.51 5.66 5.82 5.94
1.9 2.0 3.45 3.53
7.09 8.82 6.43
6.12 9.72 5.56 10.69 4.86
11.51 :12.27 7.19 7.44 9.1 9.72 6.55 6.76
9.72 10.07 10.69 5.61 5.71 5.89 11.1
11.51 .12.27
5JOISTS Joists are a very common type of wood construction. They are small, closely spaced members used to support floor, ceiling, and roof loads, and are usually lumber nominally 2 inches wide by 6, 8, 1o, and 12 inches deep, spaced 12, 16, or 24 inches on center. Of course, they are beams and can be designed using the methods described earlier in this section, but since they are used so frequently, their size and spacing is usually selected from tables. When they are designed as beams, the design value of Fb from Table 10.2 should be selected from the column selected from the column labeled "Repetitive Member Uses." The design value is slightly larger tor multiple member use than for single members. Table 10.3 shows one joisttable from the Uniform Building Code. Similar tables are published by the National Forest Products Association, the Southern Forest Products Association, other trade groups, and reference sources. For a given joist size and spacing, and a given modulus of elasticity, the table
170
gives the maximum allowable span when the deflection is the limiting factor. Below the span is the required extreme fiber stress in bending. Most tables are established for typical floor and roof loads, so if you have unusual circumstances you need to calculate the required size and spacing using methods of beam design. To use the table, you can either begin with a known span and lumber species and find the required size and spacing of joists, or begin with the span and joists design and determine what design values are required to satisfy your requirements. Then you can specify a lumber species and grade that have the design values you need. The design values are found in Table 10.2. Example 10.10
A floor must be designed to support a liveload of 191.3 N/..n2 and a deadload of 478.825 NJ..n2. The joist will span 3.96 m. If the most readily available grade of wood joist is Douglas fir-larch #2. What size and spacing is requ ired? Since joist are being used, they fall in the size classification of 50 mm to 100 mm thick, 125 mm and wider. From Table 10.2, Douglas fir-larch #2 has a modulus of elasticity of 11720.5 MPa and an Fb value for repetitive member use of 10 MPa. Table 10.3gives E in multiples of 6894.4 MPa, so look down the 1.7column until you find a span of 4.0 m corresponding to 50 mm x 200 mm joist 400 mm on center. Below the span is a value of 9 MPa for the minimum Pb. Since this is less than the actual value of 10 MPa, this size and spacing will work.
6 GLUED LAMINATED CONSTRUCTION Glued laminated wood members consist of a number of individual pieces of lumber glued together and finished under factosy conditions for use as beams, columns, purlins, and other structural uses. Glued laminated construction, or glue-lam as it is usually referred to, is used when larger wood members are required for heavy loads or long spans, and simple sawn timber pieces are not available or cannot meet the strength requirements. Glue-lam construction is also used where unusual structural shapes are required and appearance is a consideration. In addition to being fabricated in simple rectangular shapes, glue-lam members can be formed into arches, tapered forms, and pitched shapes. Glue-lam members are manufactured in standard sizes of width and depth. In most cases, 1 1/2 inch actual depth pieces are used, so the overall depth is some multiple of 1112 depending on how many laminations are used. Three-quarter Inch thick pieces are used if a tight curve must be formed. Standard widths and depths are shown in Figure 10.3. Because individual pieces can be selected free from certain defects and seasoned to the proper moisture content, and the entire manufacturing process is conducted under carefully controlled conditions, the allowable stresses for glue-lam construction are higher than for solid, sawn lumber. Although glue-lam beams are usually loaded in the direction perpendicular to the laminations, they can be loaded in either direction to suit the requirements of the design. Tables of design values give allowable stresses about both axes. For structural purposes, glue-lams are designaied by size and a commonly used symbol that specifies its stress rating. For design purposes, glue-lams are available in three appearance grades: Industrial, architectural, and premium. These do not affect the structural properties but only designate the final look and finishing of the member.lndustrial is used where appearance is not a primary concern, while premium is used where the finest appearance is important. Architectural grade ls used where appearance is a factor but the best grade is not required.
171
GLUED LAM&NATEt>
~AM
DEPTI( MULTII'LES
OF 18(1113T.IIM
NOMIIiAt.
ACTUAL
100 .....
Tl liM. IU
ItO
too
"'
no
Ill
:500
HI
3!10
101
Figure 10.3 ~ed Laminated Beam
7 PLANKING Wood planking, or decking as it is often called, is solid or laminated lumber laid on its face spanning between beams. Planking is available in nominal thicknesses of 2, 3, 4, and 51nches with actual sizes varying with manufacturer and whether the piece is solid or laminated. All planking has some type of tongue and groove edging, so the pieces fit solidly together and load can be distributed among adjacent pieces. The allowable span depends on the thickness of the planking and load to be supported, and ranges from4 teet to 20 feet. Planking is often used on heavy timber construction with glued laminated beams and purlins. Planking has the advantages of easy installation, attractive appearance, and efficient use of material since the planking serves as floor structure, finish floor, and finish ceiling below. Its primary disadvantages are that there Is no place to put additional insclation or conceal mechanical and electrical services. Wood framing, of course, Is combustible, but may be used ln certain types of construction I adequately protected. A unique property Of wood is that whUellls combusttie, thick pieces of wood exposed to fire will char but not lmmadlately loose struct1.1ral integrity. The UBC recognizes this by having a separate type of constructton, Type IV, for heavy timber construction. In thls type Of construction, columns must be at least 8 inches In any dlmen8Jon, beams and gilders must be at least 6 Inches wide and 10 inches deep. and floor decking must be at least 3 inches thick. (200 mm, 150 mm wide and 250 mm deep).
172
STEEL CONSTRUCTION
STEEL CONSTRUCTION Nomenclature A cross-sectional area d actual depth of beam De uniform load deflection constant E modulus of elasticity Fa allowable axial compressive stress Fb bending stress permitted in a member in the absence of axial force Ft allowable tensile stress Fv unit shear stress Fv allowable shear stress Fy specified minimum yield point of the type of steel being used 1 moment of inertia . K effective length factor 1 span L span or oolumn length Lc maximum unbraced length of the compression flange at which the allowable bending stress. may be taken at 0.66 Fy Lu maximum unbraced length of the compression flange at which the allowable bending stress may be taken at 0.60 Fy Lv span length below which shear, v, in beam web governs M moment MR resisting moment P concentrated load r governing radius of gyration R end beam reaction S section modulus tw thickness of web V maximum web shear w weight per foot W total uniform load on a beam We uniform load constant A deflection
mm2 mm mmlm2 mPa mPa mPa mPa mPa mPa mPa mi'Tt
mm meter meter meter meter N-m or kN-m kN-m newton or kllonewton
mm newton or kilonewton mrril mm kilonewton newton or kilonewton mm mm
mm
1 PROPERTIES OF STRUCTURAL STEEL Steel is on of the most widely used structural materials because of its many advantages, which include high strens;Jth, ductility, uniform~ of manufacture. variety of shapes and sizes, and ease speed of erection. Steel has a high strength-to-weight ratio. This makes it possible to reduce a building's dead load and to minimize the space taken up by structural elements. In addition, steel has a high modulus of elasticity, which means it is very stiff. Ductility of steel is a property that allows It to withstand excessive deformations due to high tensile stresses without failure. This property makes it useful for earthquake-resistant structures. 174
Because steel is manufactured under carefully controlled conditions, the composition. size, and strength can be uniformly predicted so that structures do not have to be overdesigned to compensate for manufacturing or erection variables as with concrete. The variety of available sizes and shapes of steel also allows the designer to select a member that is the most efficient fort he job and that is not larger than it needs to be. These properties make possible a cost-efficient structure. Finally, because most of the cutting and preparation of members can occur in the fabricating plant, steel structures can be erected very quickly and easily. thus reducing overall construction time. In spite of the advantages, however, steel does have negative properties that must be accounted for. Most notable are its reduction in strength when subjected to fire and the tendency to corrode in the presence of moisture. Steel itself does not bum. but defonns in the presence of high temperatures. As a result. steel must be protected with fire-resistance materials such as sprayed-on cementitious material or gysum board, or it must be encased in concrete. This adds to the overall cost, but is usually justified when the many advantages are considered. As with any ferrous material, steel will rust and otherwise corrode if not protected. This can be accomplished by including alloys in the steel to protect it (e.g., stainless steel). or by covering it with paint or other protective coatings.
A. Types and Composition of Steel Steel is composed primarily of iron with small amounts of carbon and other elements that are part of the alloy, either as impurities left over from manufacturing or deliberately added to impart certain desired qualities to the alloy. In medium-carbon steel used in construction. these other elements include manganese (from 0.5 to 1.0 percent}, silicon (from 0.25 to 0.75 percent}, phosphorus, and sulfur. Phosphorus and sulfur in excessive amounts are harmful in that they affect weldability and make steel brittle. The percentage of carcon present affects the strength and ductility of steel. As carbon is added, the
strength increases bu the ductility decreases. Percentage of carbon range from about 0.15 percent for very mild steel to 0.70 percent for high-carbon steel. Standard structural steel has from 0.20 to 0.50 percent carbon. The most common type of steel for structural use is ASTM A36 which means that the steel ts manufactured according to the American Society for Testing and Materials (ASTM} specification number A36. The yield point for this steel is 248 Mega Pascals (MPa). Other high-strength steels include A242, A440, and M41 steel, which have yield points of 317 MPa or 345 MPa.
B. Shapes and Sizes of Structural Steel Structural steel comes in a variety of shapes, sizes. and weights. This gives the designer a great deal of flexibility In selecting an economical member that is geometrically correct for any given situation. Figure 11.1 shows the most common shapes of structural steel.
Wide flange members are H-shaped sections used for both beams and columns. They are called "Wide flange" because the width of the flange is greater than that of standard 1-beams. The outside and Inside faces of the flanges are parallel. Many of the wide flange shapes are particularly suited for columns because the width of the flange is very nearly equal to the depth of the section, so they have about the same rigidity in both axes. 350 mm deep wide flange sections are offen used for colurMs on high-rise multistory structures. On low-rise and mid-rise multistory .buildings, usually the smallest column used is a 200 ryun deep wide flange. · f75
W1DTH
CEPTH
~A---W£8
SLOPE I Ill 6
FLANGE
--=-=c
AMERICAN STAN04RD BfAM
WfDE FLANGE
"s" SHAPES
"W" SHAPES
r
L
STRUCTURAL TEE
At.'ERICAN STANDARD CHANNEL
"c"SHAPES
"WT" SHAPES
"sT "
ANGLE UNEQUAL LEGS
OR SHAPES
ANGLE 1EQUAI.. L£GS
"L" SHAPES
"L" SHAPES
Figure ·11.1 Structural Steel Shapes
176
Wide flange sections are designated with the latter W followed by the nominal depth in mm and the mass in kglm. For example, a w 460 x 95 a wide flange nominally 460 mm deep and has a mass of 95 kg/m. Because of the way these sections are rolled in the mill, the actual depth varies slightly from the nominal depth. American Standard 1-beams have a relatively narrow flange width in relation tot heir depth, and the inside face of the flanges have a slope of 16 213 percent, or 1/6. Unlike the wide flanges, the actual depth of an 1-beam In any size group Is also the nominal depth. Heavier sections are made by adding thickness to the flanges on the inside face only. The designation of depth and mass per meter these sections is preceded with the letterS. These sections are usually usef for beams only. American Standard channel sections have a flange on one side of the web only and are designated with the letter C followed by the depth and mass per meter. Like the American Standard 1-beams, the depth is constant for any size group. Extra weight is added by increasing the thickness of the web, and the inside face of the flanges. Channel sections are typically used to frame openings, form stair stringers, or in other applicatons where a flush side is required. They are seldom used by themselves as beams or columns because they tend to buckle due to their shape. Structural tees are made by cutting either a wide flange section or 1-beam in half. If cut from a wide flange section, a tee is given the pref ix designation WT, and if cut from an American Standard 1-beam, it is given the designation ST. A WT 230 x 47.5, for example, is cut from a W 460 x 95. Because they are symmetrical about one axis and have an open flange, tees are often used for chords of steel ·trusses. Steel angles are available either with equal or unequal legs. They are designated by the letter L followed by the lengths of the angles. and then followed by the thickness of the legs. Angles are used in pairs for members for steel trusses or singly as lintels in a variety of applications. They are used for miscellaneous-bracing of other structural members. Square and rectangulartube sections and round pipe are also available. These are often used for tight columns and as members of large trusses or space frames. Structural tubing of various sizes Is available in several different wall thicknesses, while structural pipe is available in standard weight, extra strong, and double-extra strong. Each of the three weights has a standard wall thickness depending on the size. Pipe is designated by its nominal diameter, but the actual outside dimension is slightly larger, while the size designation for square or rectangular tubing refers to its actual outside dimensions. Finally, steel is available in bars and plates. Bars are considered any rectangular section 150 mm or less in width with a thickness of 5.75 mm and greater, or sections 150 to 200 mm in width with a thickness of 5.75 and greater. Plates are considered any section over 200 mm in width with a thickness of 5.75 mm and over, or sections over 1200 mm in width with a thickness of 4.50 mm and over. Table 11.1 summarizes the standard designations for structural steel shapes.
· C. Allowable Stresses Allowable unit stesses for structural steel are expressed as percentages of the minimum specified yield point of the grade of steel used. For A36 steel, the yield point is 248 MPa. The percentages used depend on the type of stress, the condition of use, and other factors. Allowable unit stresses are established by the American Institute of Steel Construction (AISC) and are commonly adopted by reference by model codes such as the Uniform Building Code and by local codes. Table 11.2 summarizes some of the more common AISC values for A36 steel.
Table 11.1 Standard Oesign()tions for Structural Shapes wide flange shapes American Standard beams miscellaneous shapes American Standard channels miscellaneous channels angles, equal legs angles, unequal legs structural tees-cut from wide flange shapes· structural tees~ut from American Standard beams plate structural tubing, square pipe
W
310
x
97
S
310
x
74
M
310
x
25
C
380
x
50
MC
310
X
46
L
75
X
75
l.
75
X
100 X 12
WT ST
230
X
47.5
155
X
37
PL
12
x
250
TS
200
X
200 X 9.4
X 10
100 mm"
2 STEEL BEAMS The design of steel beams involves finding the lightest weight section (and therefore the least expensive) :hat will resist bending and shear forces within allowable li~its of stress, and one that will not have excessive deflection for the condition of use. Beam design can be accomplished either through the use of the standard formulas for flexure, shear, and deflection, or by using tables in the Manual of steel Construction published by the AISC. Both methods will be reviewed in the following sections.
A. Lateral Support and Compact Sections Before proceeding with methods for steel design, you should have a firm understanding of two important concepts: lateral support .and compact sections. When a simply supported beam is subjected to a load, the top flange is in compression and the bottom flange is in tension as discussed in Chapter 5. At the compression flange, there is a tendency for it to buckle under load, just as a column can buckle under an axial load. For overhanging beams, when the bottom flange is in compression the same potential problem exists. To resist this tendency, either the compression flange needs to be supported or the beam needs to be made larger. In many cases, steel beams are automatically laterally supported because of standard construction methods. This occurs with beams supporting steel decking welded to the beams, beams with the top flange embedded in a concrete slab, or composite construction. In some instances, a girder is only supported laterally with intermittent beams. It a beam is continuously supported or supported at intervals not greater than Lc, the full allowable stress of 0.66 Fy may be used. If the support is greater than Lc, but not greater than Lu. then the allowable stress must be reduced to 0.60 Fy. The value of Lc, and Lu are given in tables in the AISC manual and will be illustrated in later example problems.
178
Table 11.2 Selected Allowable Stresses for A36 Steel
TYPE OF STRESS AND CONDITION
STRESS NOMENClATURE
AISC SPECS
VALUE F.OR A36 STEEL
Fb
0.66f=y
165 MPa
Fb
0.60Fy
152 MPa
Solid round and Square bars bending about their weak axis and doubly symnetrical I and H shapes bent about their minor axis
Fb
0.75Fy
186 MPa
Shear on gross section
Fu
0.40Fy
100MPa
On net section
Ft
0.60Fy
152MPa
On effective net area except at pin hoks
Ft
0.50Fy
200MPa
•BENDING Tension and compression on extreme fibers of laterally supported compact sections symmetrical about ancl loaded in the plane of their minor axis. Tension and compression on extreme fibers of other rolled shapes braced laterally.
•TENSION
Sections are determined to be either compact or non·compact based on the yield strength of the steel and the width·to-thickness ratios of the web and flanges. If a section Is non-compact, a lower allowable bending stress must be used. Identification of non-compact sections and the reduced stresses are incorporated into the design tables in the AISC manual.
B. Design for Bending There are two approaches to designing steel beams: with the fie xure formula as discussed in Chapter 4 or with the tables found in the AISC manual. Both will be discussed here. The basic flexure formula is:
s
M
11.1
= ----
fb
This formula from Chapter 5 is the same for steel design, except that the AISC uses the nomenclature Fb for the allowable bending stress instead of fb, which it reserves for computed bending stress. The basic formula is used in two forms to either select a beam by finding the required section modulus, S, or to calculate the maximum resisting moment, M, when a beam is being analyzed. These two forms are, respectively:
s
=
M
fb
--·····
1~ .2
and 179
M "'
S (Fb) •••••• 11 .3
Table11.3 Properties of Wide FJange Shapes y
- .,_k, k
It-
c•.
-
X
t.,-
l
-
T
X
W SHAPES Dimensions
!-
~~J
k Web
Desio· nation
Area
Depth
Thickness
A
d
t,.,
..,
ln.
ln.
ln.2
W12lC3W 88.8
x3os• x27t'
8U
x252' 74.1
)(2,30'
e1.1 k211)11 81.8
x190 X170 X162 X138
55.8 50.0 44.7 39.9
X120 35.3 )11()6 31.2 xee 282 )( 17 25.6 X79 23.2 X72 21.1 x.es 19.1
W 12x 58 17.0
x53
1$.6
W 12x 50 14.7 )(~
)(4()
13.2 11.8
16.82 16% 1..775 1V• 16.32 1.625 1~ 15.85 15'-' 1.530 1'h. 15.w proper placement of the concrete. For a 300 mm beam (assaming no. 4 bars for shear reinforcement) the clearance requirement leave a width of only 200 mm for the tension steel. This only leaves room for four no. 8 bars; an addilional125 mm would be needed to accomodate seven no. 8 bars. Actually, the beam would probably be made 450 mm rather than 425 mm, because widths are multiple of 50 mm. Either the beam must be increased in wiclth, or the percentage of steel must be reduced. h wou1d be more economical to reduce the steel percentage and increase the depth of the beam, so try a new percentage and recalculate. Try 0.0130 percentage. 4 14 ) 538.61 X 10' =0.90 (0.0130)414bcf{1-0.59(0.01300) 2 7.6. ·tx¥"" 125.652
since at this point we know that the width of the beam is important simply to accomodate the steel, try a width of 350 mm this time. 350d2 • 125.652 X 108 d= 599.17 mm
..
--
..
!: ~
~·
..
4. 4
I>
d
.,
..
4 - D 32 (fRO )
_L 40 mm
T
... .
!
.. 200111m
85111111
~
lS00111m
Rounding up to 600 mm and assuming a cover of 65 mm gives a total beam depth of 665 mm. A 350 mm x 665 mm is reasonable, but then we may use 350 mm x 700 mm. Find the actual area of the steel with this new size and
As
new assumed percentage of steel.
=pbd =0.0130(350)(600) -2730mni
This can be satisfied with four no. 10 bars (A= 3217 mrW! or, five no. 9 bars (A = 3078.75 mni). These will fit in a 350 mm wide beam (use either four no. 10 bars or five no. 9 bars) in a 350 mm x 700 mm beam.
C. Shear In the previOus section only, stresses due to bending were discussed. However, forces caused by shear can also be significant and rrust be checked and provided for with additional reinforcement if the conerete itself is not capable of resisting them. It is especially important that concrete beams be adequately designed for shear, because, like compressive failure, shear collapse.occurs suddenly and without warning. Actually, what is commonly referred to as shear stress is really diagonal tension stress caused by the combination of shear and longitudinal flexural stress. The result is a characteristic diagonal cracking of the concrete beam in the areas of high shear forces, usually close to the beam supports as shown in Figure 12.2. SHEAR REINFORCEMENT
CRITICAL SECTION
d
FACE OF SUPPORT
Figure 12.3 Typical Shear Cracking Pattern Near End of Beam When calculating for shear forces , the critical section is usually taken at the distance, d, from the support. This is because the reactions from the supports orfrom a monolithic column introduce vertical compressive into the beam which mitigates excessive shear in that area. There are two ways shear reinforcement, correctly called web reinforcement, is provided for. One way is to bend up some of tHe tension steel near the supports at a 45 degree angle as shown in Figure 12.4 (a). This is possible since most of the tension steel is required in the center of the beam where the moment is the greatest. The other, more common way, is to use vertical stirrups as shown in Figure 12.4 (b). These are small diameter bars (usually no. 3, no. 4, or no. 5 bars) that form a lJ.shaped cage around the tension steel.
(d) INCLINED WEB RSNFORCEMENT
(b) VERTICAl STIAAUP . F~re
12.4 Methods of Providing Web Reinforcement
206
The theories behind shear and diagonal tension in beams are still not completely understood. Exact, rational-analysis formulas do not exist. The existing formulas are based on tests, experience, and some mathematical analysis, and can become quite complicated. The following fofl'OOias are a few of the basic ones with which you should be familiar. Vc= 2..Jf'cb,.d
12.11
The minirrum area of web reinforcement required by the ACI code is given by the formula
Av"' 50 b;S
12.12
y
This formula must be used if the actual shear stress.Vu, is more than one-half of the shear capacity, which is Vc times the strength reduction factor, e. For shear, 11 is 0.85. To design the area of steel required for vertical stirrups the following formula is used: S=
0 Avfyd -0 V
V
u
12.13
c
D. Compression Steel In most reinforced concrete construction, reinforcement is added to the top, compression side of a beam or other section. Such beams are often called doubly reinforced besms. There are several reasons for this. First, the concrete alone may not be able to resist the compressive forces. This is especially true if the concrete is of low strength or if the cross-sectional area is small is proportion to the applied loads. Second, compression steel reduces long-term deflections caused by concrete creep. Third, steel in the compression zone may simply be used to support stirrups before the concrete is poured. Finally, it may be included to provide for expected or unexpected negative moment in a member normally stressed with only positive moment. This can happen when an i~osed load on one portion of a continuous span causes an adjacent unloaded span to bend upward. If the member is designed for compression, the steel must be restrained to prevent its buckling outward just as with a column. Lateral ties are used for this purpose and rrust encircle the compression and tension steel on all four sides and be spaced for the entire length of the member. The shear reinforcement can serve part of this purpose, but instead of being U·shaped bars, it must continue across the top of the compression reinforcement to form a secure tie.
E. Development Length and Reinforcement ANCHORAGE In order for concrete reinforcement to do its job, there must be a firm bond between the two materials so that they act together to resist loads. As mentioned earlier, this is accomplished by mechanical bonding due to the deformations of the tebars and through chemical bonding betwe~n the two materials. One of the primary requirements for safety is that there is a sufficient length of steel barfrom any point of stress to the end of the bar to develop the necessary bond. The required length is primarily dependent on the strength of the concret~. the strength of the steel, and the size of the bar. The basic formula for minirrum development length for steel in tension is: 1db = 0.04 AbFy
.Jfc
207
12.14
However, the ACI code requires thatthe length not be less than 0.0004dbfy, where db is the diameter of the bar. The ACI code also requires that in no case shall the length be less than 300 mm. Formula 12.1 4 holds for no. 11 bars and smaller.larger bars require a slightly shorter development length. There are also some other variables that aifect development length: · ~the amount of concrete cover over the steel and the spacing of thebars.lf rebarsare spaced at least 150 mm on center and there is at least 75 mm clear from the edge bar to the face of the concrete, the development length may be reduced by a factor of 0.8.
"pressence of lateral reinforcement. If spiral reinforcement of not less than 6 mm and not more than 4 pitch enclosses the tensile bars, the development length may be reduced by a factor of 0.75. "lightweight aggregate. lightweight aggregates required longer development length than those determined by formula 12.14. •top reinforcement. If there is more than 300 mm of co.ncrete cast in a merrber below the bar in question, the development length must be increased by a factor of 1.4. This is because excess water tends to rise during pouring and curing, so that air and water accumulate near the underside of the bars, weakening the bond a little. "high-strength reinforcing steel. Steels with yield stresses greater 413.7 mPa require longer development lengths.
F. Deflectlons Anhough concrete may seem to be a very stiff material and not subject to much deflection, this is not the case. This is true because the strength design method of design. and higher strength concretes and steels, both resuh in smaller structural members that are less stiff than In the past. Controlling deflection in concrete structures is important to avoid cracking partitions, glass, and other building components attached to the concrete, to avoid sagging o: roofs and subsequent ponding of water, and to prevent noticeable deflection of visible members. As with other aspects of concrete design, predicting deflection is not as easy as it is with hOmogeneous materials such as steel and wood. Design is further complicated by the fact that concrete has two phases of deflection: Immediate deflection caused by normal dead and live loads. and long-tenn deflection caused by shrinkage and creep. Long-term deflection may be two or more times the initial deflection.
There are formulas and procedures that give the approximate initial and long-term deflections. These deflections can then be compared with deflection limitations in the ACI code for various types of members and conditions of deflection. These limitations are expressed in terms of fractions of the total span. See table 12.3. If certain conditions are met, the ACI code gives minimum depths of members in the form of spanto-depth ratios for various conditions. These are shown in Table 12.4.
G. Continuity Since continuity is such a typical conditiM in concrete construction, you should be familiar with the basic principles. Continuity is an extension of a structural member over one or more supports. An example of a continuity member is placing a 9 meter steel beam over four supports, each 3m on center. Since concrete is typically poured in forms extending across several columns {or a slab extending over several beams), concrete structures are inherently continuous. Concrete structures are typically continuous in the vertical direction as well as the horizontal direction. 208
N
~
But not greater 1han tolerance provided for nonstructural elements. Limit may be exceeded if oamber is provided so that total deflection minus camber does not exceed limit.
long-lime deflection shall be determined in accordance with Section 9.5.2.5 or 9.5.4.2 but may be reduced by amount of deflection calculated to occur before attachment of nonstruaural elements. This amount shall be detennined on basis of accepted engineering data relating to time-deflection characteristics of members similar to those being considered.
limit may be exceeded if adequate measures are taken to prevent damage to supported or attached elements.
Limit not intended to safeguard against pondiog. Ponding should be checked by suitable calculations of deflection, including added dellections due to ponded water, and considering long-time effects of all sustained loads, camber, conslrUction tolerances and reliability of provisions for drainage.
Root or floor construction supporting or attached to nonstructural elements not likely to be damaged by large deflections
That part of the total deflection occurring aftet atttachment of nonstructural elements (sum of the long-time deflection due to all sustained loads and the immediate deflection due to any additional live load)
Immediate deflection due to live load L
Floors not supporting or attached to nonstructural elements likely to be damaged by large deflections
Roof or floor construction supporting or attached to nonstructural elements likely to be damaged by large deflections
Immediate deflection due to live load L
Deflection to be considered
Flat roofs not supporting or attached to nonstructural elements likely to be damaged by large deflect:Ons
Type of member
TABLE 12.3(b)-MAXIMUM PERMISSIBLE COMPUTED DEFLECTIONS
BUILDING-CODE REQUIREMENTS
TABLE 12.3 Maximum Computed Deflections
240
I
l 480
360
l
l 180
Deflection limitation
318-35
TABLE 12.4
Mlnlmum Thickness of Non-Prestressed Beams or One-Way Slabs Unless Deflections Are COmputed Minimum thickness, h Simply supported Member
One end continuous
Both ends continuous
Canti-lever
Members. not supporting or attached to partitions or other construction likely to be damaged by large deflections.
Solid-one way slabs Beams or ribbed oneway slabs
V20
V24
V28
V10
V16
1/18.5
V21
V8
•span lengltl I is in inches.
Values given shall be used directly for members with normal weight concrete (w< = 145 pet) and Grade 60 reinforcement. For oltler conditions, the values shall be modified as follows. {a) For Slrueturalllghtwelght concrete having unit .weights in the range 00.120 lb per cu ft. tie values shall be multipljed by (1.65 O.OOSW) but notl&ss 1tlan 1.09 where we is the unit weight in lb per cu. It (b) For fy, other than 60,000 psi, !he values shall be multiplied by (0.4 + f/1 00,000).
A portion of an exaggerated concrete structure is shown in Figure .12.5 (a) with deflections due to vertical aoo lateral loads also shown exaggerated. In the mid-spans of the beams, there is positive moment as discussed in Chapter 4. Over the center column support, however. the loads tend to cause the beam to bend upward with negative moment, while at the outer columns, the .beam is fixed. Contiruous beams and columns are statically indeterminate, meaning that they cannot be solved wUl the principles or equations of equilibrium discussed in Chapter 4. A few of the typical conditions for shear. moment and deflection for continuous beams are shown in Figure4. 12. Continuous beams are more efficient than simply supported beams because the maximum moment for a given load and span is less than the moment for the corresponding simple beam. This is because the loads in adjacent spans effectively counteract each other to a certain extent. For concrete structures, the negative moment causes the top of the beam to experience tension rather than the usual compression, so reinforcing steel must be added to counteract the forces just as in the bottom of a simply supported beam. In some cases, straight rebars are added over the supports to act as tension reinforcement. In other cases, some of the bottom tension steel is bent upward at the point of inflection to serve as negative reinforcement. See Figure 12.5 (b).
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ADDITIONAL STRAIGHT BAR FOR TENSION AS REQUIRED I I
I I
-. -
I
-....... _______ ,.., -
...... _ ... ___ .... __,. ...
I
_____.____ ... _..
I
\
''
I I
(a) DEFLECliONS
--
TENSION STEEL FOR NEGATIVE MOMENT
-
CLEAR DISTANCE TENSION STEEL FOR __ POSITIVE MOMENT (b) REINFORCEMENT PATIERN (STIRRUPS AND COLUMN REINFORCEMENT NOT SHOWN)
Figure 12.5 Continuity in Concrete Construction
H. T-Beams Since floor and roof slabs are always poured with the beams that support them, the two elements act integrally with a portion of the slab acting as the top portion of the beam. In effect, then, what looks like a simple rectangular beam becomes aT-beam with a part of the slab resisting compressive forces. The horizontal portion is called the flange, and the vertical portion below the flange is called the web or stem. For an isolated T-section, the entire top flange acts in compression. However. for stems that are in the middle of slabs or edge beams, the effective flange width is smaller than what is actually available. The various conditions are shown in Figure 12.6. The ACI code limits the effective flange widths as follows:
•••
211
For isolated beams, the flange thickness shall not be less than one-half the width of the web,·and the total flange width shall not be more than four times the web width. See Figure 12.6 (a). For symmetrical T-beams (such as interior beams poured with the slab) the smallest of three conditions determine the effective width. This width shall not exceed one-fourth of the span of the beam, nor shall the overhanging slab width on either side of the beam web exceed 8 times the thickness of the slab, nor shall it exceed one-half the clear distance to the next beam. See Figure 12.6 · (b).
For edge beams, the effective overhanging slab portion shall not exceed one-twelfth the span of the beam, nor shall the overhanging slab exceed six times the thickness of the slab, nor shall it exceed one-half the clear distance to the next beam. See Figure 12.6 (c). If the neutral axis is equal to or leSs than the slab thickness, the section is designed as though it were a solid beam with a width equal to the effective width of the flange. If the neutral axis is in the web, special T-beam analysis is required.
4 CONCRETE SLABS As part of a structural system of column and beams, slabs can either span (structurally) in one direction or ·two directions. The former is called a one-way slab, aLld the latter is called a two-way slab. In a one-way slab, reinforcement is run in one direction perpendicular to the beams supporting the slab. Two-way slabs have rebars in both directions and are more efficient because the applied loads are distributed in all directions. However, in order for two-way slabs to work as intended, the column bays supporting them should be square or nearly square . When the ratio of length to width of one slab bay approaches 2:1, the slab begins to act as a one-way slab regardless of the reinforcement or edge supports. One-way slabs need extra reinforcement to counteract the effects of shrinkage and temperature changes. Often called temperature steel, the minimum amount of reinforcements is set by ACI code by percentage as tension steel is, but in no case can the rebars be placed farther apart-than five times the slab thickness or more than 450 mm. The minimum·steel ratio in any case is 0.0018 .
5 CONCRETE COLUMNS Columns are the most typical of several types of concrete compressive members. In addition to columns, these include arch ribs, compressive members of trusses, and portions of rigid frames. The design of concrete compressive members is complex, especially when eccentric loading is involded or when the member supports both axial and bending stresses. This sector will cover the basics of the two most typical types of concrete compressive members: tied columns and spiral columns. Composite compressive members, which co·nsist of concrete reinforced with structural steel shapes, are sometimes used, but are not included here. As with other types of columns, one of the primary considerations in design is the effect of buckling of the column caused by the axial load. The overall size of concrete columns usually result in lengthto-width ratios of from 8 to 12, so slenderness is often not a critical consideration. However, since the steel reinforcement is very slender, it tends to fail by buckling and pushing out the concrete cover at the faces of the column. To prevent this, lateral ties are required, either as individual tied bars or a continuous spiral as discussed iO the next two sections. Ties also hold the longitudinal steel in place before the concrete is poured. If oolumns are slender, either by design or by using higher strength concretes and reinforcement, then special calculations are required.
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The ACI code limits the percentage of longitudinal steel to from 0.01 minimum to 0.08 maximum of the gross concrete cross section. It further requires there be at least four bars for tied columns and six for spiral columns. One reason for a limited percentage of steel is that large numbers or bars create a congested column form, and make proper placing of the concrete difficult.
A. Tied Columns Tied columns consist of vertical steel running parallel to the length of the column near its faces, with lateral reinforcement consisting of individual rebars tied to the vertical reinforcement at regular intervals. See Figure 12.7 (a). The ACI code requires that the lateral ties be at least no. 3 rebars for longitudinal bars up to no. 10and at least no. 4rebars for no. 11, no. 14, and no. 18bars. No.4 rebars must also be used for bundled reinforcement. Tied columns are most often used for square or rectangular shapes. The spacing of the ties cannot exceed 16 diameters of vertical bars, 48 diameters of tie bars, nor the least dimension of the column. The ties must be arranged so that every corner and alternate vertical bar has lateral support on both directions. No bar can be more than __ inches clear from such a laterally supported bar. The strength reduction factor, o, is 0.70 for tied columns.
B. Spiral Columns Spiralcolumns have a continuous spiral of steel in lieu of individual latera!ties as shown in Figure 12.7 (b). The spiral must be at least 9.4 mm in diameter and the clear spacing between turns cannot be less than 25 mm nor more than 75 mm. The distance between the center lines of the tums is called the pitch of the spiral. Figure 12.7 shows a square spiral column, but they may also be round.
PITCH
CLEAR SPACING 25mm. min 75mm. max
(a,) TIED COLUMN
(b) SPIRAL COLUMN
Figure 12.7 CONCRETE COLUMNS
The strength reduction factor, 0, for spiral ooklmns ts 0.75, reflec:ting the fact that spiral oolumns are slightly stronger than tied oolumns of the same size and reinforcement. Another ifl1)0rtant difference to note Isthat spk'aloolumnsare more ductile, meaningthattheyfaia in agradual mannerwtththe outer covering of ooncrete spalllng before the oolumn fails. Tied oolumns tend to fail· suddenly without warning.
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6 PRESTRESSED CONCRETE Prestressed concrete consists of members that have internal stresses applied to them before they are subjected to servive toads. The prestressing consists of compressive forces applied where normally the memberwould be intension which effectively eliminates or greatly reduces tensile forces that the member is not capable of carrying. In addition to making a more efficient and economical structure section. prestressing reO.Jces cracking and deflection, increases shear strength, and allows lOnger spans and greater loads. Prestressing is accomplished in one of two ways: pretensioning or post-tensioning.
A. Precast, Pretensloned With this system, concrete members are produced in a pre casting plant. High-strength pretensioning stranded cable or wire is draped in forms according to the required stress pattern needed and a tensile force is applied. The concrete is then poured and allowed to cure. Once cured, the cables are cut and the resulting compressive force is transmitted to the concrete through the bond between cable and concrete.
B. Post-Tensioned For post-tensioning, hollow sleeves or conduit are placed in the forms on the site and concrete poured around them. Within the conduit is the prestressing steel, called tendons, which are stressed with hydraulic jaCks or other means after the concrete has cured. In some cases, the spaces between the tendons and the conduit is grouted. The resulting stress is transferred to the concrete through the plates in the concrete member. (please refer to page 18 and 19 of Chapter I)
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WALL CONSTRUCTION
WALL CONSTRUCTION Nomenclature Ag gross area of concrete wall
mm2
As area of reinforcing
mm2
f'c
specified compressive strength of concrete
mPa
I'm compressive strength of masonry at 28 days
mPa
Fa allowable average axial compressive stress for centroidally applied axial load
mPa
h
height of wall
mm
k
effective length factor
lc
vertical distance between supports
Pn nominal axial load strength
newtons
effective thickness of wythe or wall 0
mm mm
strength reduction factor (0.70 for concrete bearing walls)
The two primary classifications of walls are loadbearlng and non-loadbearlng. Loadbearing walls support their own weight in addition to vertical and lateral loads. They can be further classified into vertlcalloadbearfng walls, shear walls, and retaining walls. Verticalloadbearingwalls support the weight of other walls above, in addition to floor and roof loads. Shear walls are structural walls that resist lateral loads acting in the plane of the wall. Retaining walls,as discussed in Chapter 7, are structural walls that resist the movements of soil. Non-loading walls support only their own weight, and are used to enclose a building or to divide space within a building. When used for a building enclosure, they do serve to transfer wind forces to the primary structural frame. A non-loadbearing exterior wall is called a curtain wall. Although the primary focus of this chapter is the structural design of walls, there are other consideration in selecting the optimum wall for a particular circumstance. In addition to load-carrying ability, a wall must provide for openings, keep out the weather. be cost effective. satisfy the a.:;sthetic requirement of the job, resist heat loss and gain, and be easy to maintain. The architect must exe;·cise judgment in sele
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