Prestressed Concrete - Edward Nawy

FIFTH EDITION UPDATE ACI, AA~ IBC 2009 Codes Version

~QIO A •

a

= depth of equivalent rectangular stress block.

cp

= area enclosed by outside perimeter of con-

b,

the closed stirrups resisting torsion.

crete cross section.

o.:J L5

= width of that part of cross section containing

bv

= width of cross section at contact surface being investigated for horizontal shear.

Ag = gross area of section, in. 2 Ah

ura! tension reinforcement, in. Aj

bw

= area of shear reinforcement parallel to flex2

e

neutral axis, in.

in. in a plane parallel to plane of reinforcement generating shear in the joint. The joint depth shall be the overall depth of the column. Where a beam frames into a support of larger width, the effective width of the joint shall not exceed the smaller of: (a) beam width plus the joint depth (b) twice the smaller perpendicular distan ce from the longitudinal axis of the beam to the column side. total area of longitudinal reinforcement to resist torsion, in. 2

A 0h

Nuc'

in.

2

= area enclosed by centerline of the outermost = area of prestressed reinforcement in tension

= distance from extreme compression fiber to

column, capital, or bracket measured transverse to the direction of the span for which moments are being determined, in. centroid of tension reinforcement, in.

d'

= distance from extreme compression fiber to centroid of compression reinforcement, in.

= nominal diameter of bar, wire, or prestressing

area of compression reinforcement, in.

treme tension fiber to center of bar or wire located closest thereto, in. dP

= distance from extreme compression fiber to centroid of prestressed reinforcement.

e

= eccentricity of load parallel to axis of member measured from centroid of cross section.

Ec

= modulus of elasticity of concrete, psi.

Es

= modulus of elasticity of bar reinforcement, psi. = modulus of elasticity of prestressing reinforce-

Eps

= area of one leg of a closed stirrup resisting torforcement (stirrup or tie) within a spacing s and perpendicular to plane of bars being spliced or developed, in. 2

= area of shear reinforcement within a distance s, or area of shear reinforcement perpendicular to flexura! tension reinforcement within a distance s for deep flexura! members, in. 2

Av¡

= area of shear-friction reinforcement, in. 2

Avh

= area of shear reinforcement parallel to flexura! tension reinforcement within a distance 2 Sz, in.

= width of compression face of member, in.

= perimeter of critica! section for slabs and footings, in.

= thickness of concrete cover measured from ex-

2

A,, = total cross-sectional area of transverse rein-

b0

d

de

sion within a distance s, in. 2

b

= size of rectangular or equivalent rectangular

2

total cross-sectional area of transverse reinforcement (including cross-ties) within spacing s and perpendicular to dimension h 0 .

Av

c2

strand, in.

area of nonprestressed tension reinforcement, in. 2

A,

column, capital, or bracket measured in the direction of the span for which moments are being determined, in.

db

zone, in. 2

A's

= size of rectangular or equivalent rectangular

= gross area enclosed by shear flow path, in. 2 closed transverse torsional reinforcement, in.

Aps

c1

= area of reinforcement in bracket or corbel resisting tensile force

A0

= distance from extreme compression fiber to

= Effective cross-sectional area within a joint, 2

An

= web width, or diameter of circular section, in.

ment.

f; = specified 28-day compressive strength of concrete, psi.

fer

= average strength to be used as basis for selecting concrete proportions, psi.

f~, =

V f~

required average compressive strength of concrete used as the basis for selection of concrete proportions, psi.

= square root of specified compressive strength

of concrete, psi. f~; =

V f~;

compressive strength of'cóncrete at time of initial prestress, psi.

= square root of compressive strength of con-

crete at time of initial prestress, psi.

Íci = average splitting tensile strength of lightweight aggregate concrete, psi. 1

J;1 = stress due to unfactored dead load, at extreme fpc

/¡,,

f,

¡; fy

Íyt h

I lb fer

le

Ig

k

Kb Kc Kec Ks K1 ldh

Mª

fiber of section where tensile stress is caused by externally applied loads, psi. = compressive stress in concrete due to effective prestress forces only (after allowance for ali prestress losses) at extreme fiber of section where tensile stress is caused by externally applied loads, psi. = stress in prestressed reinforcement at nominal strength. = specified tensile strength of prestressing tendons, psi. = specified yield strength of prestressing tendons, psi. = modulus of rupture of concrete, psi. = tensile strength of concrete, psi. = specified yield strength of nonprestressed reinforcement, psi. = specified yield strength of transverse, reinforcement, psi. = overall thickness of member, in. = moment of inertia of section resisting externally applied factored loads, in. 4 = moment of inertia about centroidal axis of gross section of beam, in. 4 = moment of inertia of cracked section transformed to concrete, in. 4 = effective moment of inertia for computation of deflection, in. 4 = moment of inertia of gross concrete section about centroidal axis, neglecting reinforcement, in. 4 = effective length factor for compression members. = flexura! stiffness of beam; moment per unit rotation. = flexura! stiffness of column; moment per unit rotation. = flexura! stiffness of equivalent column; moment per unit rotation. = flexura! stiffness of slab; moment per unit rotation. = torsional stiffness of torsional member; moment per unit rotation. = development length of standard hook in tension, measured from critica! section to outside end of hook (straight embedment length between critica! section and start of hook [point of tangency] plus radius of bend and one bar diameter). in. = lhb x applicable modification factors. = maximum moment in member at stage deflection is computed.

Me

= factored moment to be used for design of compression member.

= moment dueto dead load. Mcr = cracking moment. Mn = nominal moment strength. Mm- = maximum factored moment at section dueto Md

externally applied loads. Mu

n

= factored moment at section.

= modular ratio of elasticity. = E/ Ec or Ep/ Ec

Nu

= facto red axial load normal to cross section occurring simultaneously with Vu; to be taken as positive for compression, negative for tension, and to include effects of tension due to creep and shrinkage.

Nuc

= factored tensile force applied at top of bracket or corbel acting simultaneously with Vu, to be taken as positive for tension.

Pb

= nominal axial load strength at balanced strain conditions.

= critica! buckling load. Pn = nominal axial load strength at given eccentricPe

ity. Pcp

= outside perimeter of the concrete cross-section Acp; in.

Ph

= perimeter of centerline of outermost closed

r

= radius of gyration of cross section of a com-

transverse torsional reinforcement, in. pression member.

s

= spacing of shear or torsion reinforcement in ?irect parallel to longitudinal reinforcement, m.

= thickness of a wall of a hollow section, in. Tu = factored torsional moment at section. Ve = nominal shear strength provided by concrete. vci

= nominal shear strength provided by concrete when diagonal cracking results from combined shear and moment.

Vcw = nominal shear strength provided by concrete when diagonal cracking results from excessive principal tensile stress in web. Vd

= shear force at section dueto unfactored dead load.

VP = vertical component of effective prestress force at section.

Vs

= nominal shear strength provided by shear reinforcement.

Vu

= factored shear force at section.

PRESTRESSED CONCRETE

PRESTRESSED CONCRETE A Fundamental Approach

Fifth Edition Update ACI, AASHTO, IBC 2009 Codes Version

Edward G. Nawy Distinguished Professor Emeritus Department of Civil and Environmental Engineering Rutgers, The State University of New Jersey

Prentice Hall Upper Saddle River Boston Columbus San Francisco New York Indianapolis London Toronto Sydney Singapore Tokyo Montreal Dubai Madrid Hong Kong Mexico City Munich Paris Amsterdam Cape Town

Vice Presiden! and Editorial Director, ECS: Marcia J. Horron Senior Editor: Holly Srark Associate Editor: Dee Bemlwrd Editorial Assistant: Wi/liam Opaluch Director ofTeam-Based Project Management: Vince O'Brien Senior Managing Editor: Scou Disan110 Production Editor: Jane Bonnelll Patty Donova11 Senior Operations Supervisor: Atan Fischer Operations Specialist: Lisa McDoivel/ Senior Marketing Manager: Ti111 Galligt111 Marketing Assistant: Mack Pa1terso11 Art Director, Cover: Jayne Come Cover Designer: Bruce Kenselanr Art Editor: Greg Dulles Media Editor: Daniel Sandin Media Project Manager: Daniel/e Leone Composition: Laserwords Maine

Abow rhe Cover: The new T-35W bridge, Minneapolis, Minnesota. Designed for the Minnesota Departmem of Transportation by FTGG, this new bridge incorpora tes aesthetics selccted by the communüy using a theme of "Arches-WaterReílection" to complement the sitc across tbe Mississipi Ri ver. Curved, 70' tall concrete piers meet thc swceping parabolic arch of the 504' precast, prcstresscd concre te main span ovcr thc river to create a modern bridge. Tbc new 10-lane intcrstalc bridge was constructcd by Flatiron-Manson, N and opcned to traffic on September 18, 2008. The bridge was dcsigned and buill in l l months. The bridge incorporales the first use of LED highway lighting, the fírst major use in the Unitcd States of nanotechnology cernen! that cleans the air (gateway sculptures) and "smart bridge" technology with 323 sensors embedded lhroughout thc concrete to provide valuable data for the future. The photograph of the new I-35W bridge is courtcsy of FlGG. Copyright 2010, 2006, 2003, 2000, 1996, 1989 by Pearson Education, lnc., Upper Saddle River, New J ersey 07458. AlJ rights rcserved. Manufacrurcd in the United States of Amcrica. This publication is protected by Copyright and pcrmissions should be obtaincd from thc publisher prior to any prohibited reproduction, storagc in a rctrieval system, or transmissioo in any form or by any means, electronic, mechanical, pho tocopying, recording, or likewise. To obtain pcrmission(s) to use matcrials frorn this work, pleasc submit a written request to Pearson Higher Education. Pcrmissions Department, l Lakc Strcet, Upper Saddle River, NJ 07458. The au thor and publishcr of this book have used their best efforts in preparing this book. Thcsc cfforts include the dcvclopment. research, and testing of the theories and programs to determine their eífectiveness. Thc author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book. Thc author and publisher shall not be liablc in any event for incidental or consequential damages in connection with, or arising out of. the furnishing, performance. or the use of thesc programs. Library of Congress Cataloging-in-Publication Data Nawy, Edward G. Prcstressed concrete: a fundamental app roach I Edward G. Nawy.- 5th ed. p. cm. ISBN 0-13-608150-9 1. Prestressed concrete. l. Title.

T A683.9.N39 2009 624. l '83412-dc22 2009024405

Prentice Hall is an imprint of

----

l09 8 7 6 5 4 3 2 1

PEARSON www.pearsonhlghered.com

ISBN-13: 978-0-13-608150-0 0-13-608150-9 ISBN-10:

To Rachel E. Nawy For her high-limit state of stress endurance over the years, which made the writing of this book in its severa/ editions a reality.

CONTENTS

PREFACE

1

BASIC CONCEPTS 1.1

1.2 1.3

1.4 1.5 1.6 1.7

2

xix 1

lntroduction 1 1.1.1 Comparison with Reinforced Concrete 2 1.1.2 Economics of Prestressed Concrete 4 Historical Development of Prestressing 5 Basic Concepts of Prestressing 7 1.3.1 lntroduction 7 1.3.2 Basic Concept Method 1O 1.3.3 C-Line Method 12 1.3.4 Load-Balancing Method 15 Computation of Fiber Stresses in a Prestressed Beam by the Basic Method C-Line Computation of Fiber Stresses 21 Load-Balancing Computation of Fiber Stresses 22 SI Working Stress Concepts 23 Selected References 28 Problems 28

MATERIALS ANO SYSTEMS FOR PRESTRESSING 2.1

2.2 2.3

2.4

2.5 2.6 2.7

Concrete 31 2.1.1 lntroduction 31 2.1.2 Parameters Affecting the Quality of Concrete 31 2.1.3 Properties of Hardened Concrete 32 Stress-Strain Curve of Concrete 36 Modulus of Elasticity and Change in Compressive Strength with Time 2.3.1 High-Strength Concrete 38 2.3.2 lnitial Compressive Strength and Modulus 39 Creep 43 2.4.1 Effects of Creep 45 2.4.2 Rheologial Models 45 Shrinkage 48 Nonprestressing Reinforcement 50 Prestressing Reinforcement 53 2.7.1 Types of Reinforcement 53 2.7.2 Stress-Relieved and Low-Relaxation Wires and Strands 54 2.7.3 High-Tensile-Strength Prestressing Bars 55 2.7.4 Steel Relaxation 56 2.7.5 Corrosion and Deterioration of Strands 58

19

31

36

vii

Contents

viii

2.8

2.9

2.10

2.11 2.12

3

PARTIAL LOSS OF PRESTRESS 3.1 3.2

3.3

3.4 3.5 3.6

3.7 3.8 3.9 3.10 3.11 3.12

4

ACI Maximum Permissible Stresses in Concrete and Reinforcement 59 2.8.1 Concrete Stresses in Flexure 59 2.8.2 Prestressing Steel Stresses 59 AASHTO Maximum Permissible Stresses in Concrete and Reinforcement 60 2.9.1 Concrete Stresses before Creep and Shrinkage Losses 60 2.9.2 Concrete Stresses at Service Load after Losses 60 2.9.3 Prestressing Steel Stresses 60 2.9.4 Relative Humidity Values 60 Prestressing Systems and Anchorages 61 2.10.1 Pretensioning 61 2.10.2 Post-Tensioning 62 2.10.3 Jacking Systems 63 2.10.4 Grouting of Post-Tensioned Tendons 64 Circular Prestressing 70 Ten Principies 70 Selected References 70

73

lntroduction 73 Elastic Shortening of Concrete (ES) 75 3.2.1 Pretensioned Elements 75 3.2.2 Post-Tensioned Elements 78 Steel Stress Relaxation (R) 78 3.3.1 Relaxation Loss Computation 80 3.3.2 ACl-ASCE Method of Accounting for Relaxation Loss 80 Creep Loss (GR) 80 3.4.1 Computation of Creep Loss 82 Shrinkage Loss (SH) 83 3.5.1 Computation of Shrinkage Loss 84 Losses Dueto Friction (F) 85 3.6.1 Curvature Effect 85 3.6.2 Wobble Effect 86 3.6.3 Computation of Friction Loss 87 Anchorage-Seating Losses (A) 88 3.7.1 Computation of Anchorage-Seating Loss 89 Change of Prestress Due to Bending of a Member (Mp8 ) 90 Step-by-Step Computation of Ali Time-Dependent Losses in a Pretensioned Beam 90 Step-by-Step Computation of Ali Time-Dependent Losses in a Post-Tensioned Beam 96 Lump-Sum Computation of Time-Dependent Losses in Prestress 99 SI Prestress Loss Expressions 100 13.12.1 SI Prestress Loss Example 101 Selected References 104 Problems 105

FLEXURAL DESIGN OF PRESTRESSED CONCRETEELEMENTS 106 4.1 4.2

lntroduction 106 Selection of Geometrical Properties of Section Components 4.2.1 General Guidelines 108 4.2.2 Minimum Section Modulus 108

108

Contents

ix 4.3

4.4

4.5

4.6

4.7 4.8 4.9

4.1 O 4.11

4.12

4.13 4.14 4.15 4.16 4.17

Service-Load Design Examples 115 4.3.1 Variable Tendon Eccentricity 115 4.3.2 Variable Tendon Eccentricity with No Height Limitation 122 4.3.3 Constant Tendon Eccentricity 126 Proper Selection of Beam Sections and Properties 128 4.4.1 General Guidelines 128 4.4.2 Gross Area, the Transformed Section, and the Presence of Ducts 130 4.4.3 Envelopes for Tendon Placement 130 4.4.4 Advantages of Curved or Harped Tendons 131 4.4.5 Limiting-Eccentricity Envelopes 132 4.4.6 Prestressing Tendon Envelopes 136 4.4. 7 Reduction of Prestress Force Near Supports 138 End Blocks at Support Anchorage Zones 139 4.5.1 Stress Distribution 139 4.5.2 Development and Transfer Length in Pretensioned Members and Design of Their Anchorage Reinforcement 141 4.5.3 Post-Tensioned Anchorage Zones: Linear Elastic and Strut-and-Tie Theories 144 4.5.4 Design of End Anchorage Reinforcement for Post-Tensioned Beams 153 Flexura! Design of Composite Beams 158 4.6.1 Unshored Slab Case 159 4.6.2 Fully Shored Slab Case 161 4.6.3 Effective Flange Width 161 Summary of Step-by-Step Trial-and-Adjustment Procedure for the Service-Load Design of Prestressed Members 162 Design of Composite Post-Tensioned Prestressed Simply Supported Section 165 Ultimate-Strength Flexura! Design 178 4.9.1 Cracking-Load Moment 178 4.9.2 Partial Prestressing 179 4.9.3 Cracking Moment Evaluation 180 Load and Strength Factors 181 4.10.1 Reliability and Structural Safety of Concrete Components 181 ACI Load Factors and Safety Margins 184 4.11.1 General Principies 184 4.11.2 ACI Load Factors Equations 185 4.11.3 Design Strength vs. Nominal Strength: Strength-Reduction Factor 187 Limit State in Flexure at Ultimate Load in Bonded Members: Decompression to Ultimate Load 188 4.12.1 lntroduction 188 4.12.2 The Equivalent Rectangular Block and Nominal Moment Strength 189 4.12.3 Strain Limits Method for Analysis and Design 191 4.12.4 Negative Moment Redistribution in Continuous Beams 193 4.12.5 Nominal Moment Strength of Rectangular Sections 194 Preliminary Ultimate-Load Design 202 Summary Step-by-Step Procedure for Limit-State-at-Failure Design of the Prestressed Members 204 Ultimate-Strength Design of Prestressed Simply Supported Beam by Strain Compatibility 209 Strength Design of Bonded Prestressed Beam Using Approximate Procedures 212 SI Flexura! Design Expression 216 4.17.1 SI Flexura! Design of Prestressed Beams 218 Selected References 220 Problems 221

Contents

X

5

SHEAR ANO TORSIONAL STRENGTH DESIGN 5.1 5.2 5.3 5.4

5.5

5.6

5.7

5.8 5.9 5.1 O 5.11 5.12 5.13 5.14 5.15

5.16

5.17

5.18 5.19

223

lntroduction 223 Behavior of Homogeneous Beams in Shear 224 Behavior of Concrete Beams as Nonhomogeneous Sections 227 Concrete Beams without Diagonal Tension Reinforcement 228 5.4.1 Modes of Failure of Beams without Diagonal Tension Reinforcement 229 5.4.2 Flexura! Failure [F] 229 5.4.3 Diagonal Tension Failure [Flexure Shear, FS] 229 5.4.4 Shear Compression Failure [Web Shear, WS] 231 Shear and Principal Stresses in Prestressed Beams 232 5.5.1 Flexure-Shear Strength [Ve¡] 233 5.5.2 Web-Shear Strength [ Vewl 236 5.5.3 Controlling Values of Vei and Vew for the Determination of Web Concrete Strength Ve 237 Web-Shear Reinforcement 238 5.6.1 Web Steel Planar Truss Analogy 238 5.6.2 Web Steel Resistance 238 5.6.3 Limitation on Size and Spacing of Stirrups 241 Horizontal Shear Strength in Composite Construction 242 5.7.1 Service-Load Level 242 5.7.2 Ultimate-Load Level 243 5.7.3 Design of Composite-Action Dowel Reinforcement 245 Web Reinforcement Design Procedure for Shear 246 Principal Tensile Stresses in Flanged Sections and Design of Dowel-Action Vertical Steel in Composite Sections 249 Dowel Steel Design for Composite Action 250 Dowel Reinforcement Design for Composite Action in an lnverted T-Beam 251 Shear Strength and Web-Shear Steel Design in a Prestressed Beam 253 Web-Shear Steel Design by Detailed Procedures 256 Design of Web Reinforcement for a PCI Double T-Beam 259 Brackets and Corbels 263 5.15.1 Shear Friction Hypothesis for Shear Transfer in Corbels 264 5.15.2 Horizontal Externa! Force Effect 266 5.15.3 Sequence of Corbel Design Steps 269 5.15.4 Design of a Bracket or Corbel 270 5.15.5 SI Expressions for Shear in Prestressed Concrete Beams 272 5.15.6 SI Shear Design of Prestressed Beams 27 4 Torsional Behavior and Strength 278 5.16.1 lntroduction 278 5.16.2 Pure Torsion in Plain Concrete Elements 279 Torsion in Reinforced and Prestressed Concrete Elements 284 5.17 .1 Skew-Bending Theory 285 5.17 .2 Space Truss Analogy Theory 287 5.17 .3 Compression Field Theory 289 5.17.4 Plasticity Equilibrium Truss Theory 293 5.17.5 Design of Prestressed Concrete Beams Subjected to Combined Torsion, Shear, and Bending in Accordance with the ACI 318-08 Code 298 5.17.6 Sl-Metric Expressions for Torsion Equations 303 Design Procedure for Combined Torsion and Shear 304 Design of Web Reinforcement for Combined Torsion and Shear in Prestressed Beams 308

Contents

xi 5.20

5.21

6

INDETERMINATE PRESTRESSED CONCRETE STRUCTURES 340 6.1 6.2 6.3 6.4

6.5

6.6

6.7

6.8 6.9 6.10 6.11 6.12

6.13

7

Strut-and-Tie Model Analysis and Design of Concrete Elements 317 5.20.1 lntroduction 317 5.20.2 Strut-and-Tie Mechanism 318 5.20.3 ACI Design Requirements 321 5.20.4 Example 5.10: Design of Deep Beam by Strut-and-Tie Method 324 5.20.5 Example 5.11: Design of Corbel by the Strut-and-Tie Method 328 SI Combined Torsion and Shear Design of Prestressed Beam 332 Selected References 335 Problems 337

lntroduction 340 Disadvantages of Continuity in Prestressing 341 Tendon Layout for Continuous Beams 341 Elastic Analysis for Prestress Continuity 344 6.4.1 lntroduction 344 6.4.2 Support Displacement Method 344 6.4.3 Equivalent Load Method 347 Examples lnvolving Continuity 347 6.5.1 Effect of Continuity on Transformation of C-Line for Draped Tendons 347 6.5.2 Effect of Continuity on Transformation of C-Line for Harped Tendons 352 Linear Transformation and Concordance of Tendons 354 6.6.1 Verification of Tendon Linear Transformation Theorem 355 6.6.2 Concordance Hypotheses 358 Ultimate Strength and Limit State at Failure of Continuous Beams 358 6. 7 .1 General Considerations 358 6.7.2 Moment Redistribution 361 Tendon Profile Envelope and Modifications 362 Tendon and C-Line Location in Continuous Beams 362 Tendon Transformation to Utilize Advantages of Continuity 373 Design for Continuity Using Nonprestressed Steel at Support 378 lndeterminate Frames and Portals 379 6.12.1 General Properties 379 6.12.2 Forces and Moments in Portal Frames 382 6.12.3 Application to Prestressed Concrete Frames 386 6.12.4 Design of Prestressed Concrete Bonded Frame 389 Limit Design (Analysis) of lndeterminate Beams and Frames 401 6.13.1 Method of lmposed Rotations 402 6.13.2 Determination of Plastic Hinge Rotations in Continuous Beams 405 6.13.3 Rotational Capacity of Plastic Hinges 408 6.13.4 Calculation of Available Rotational Capacity 411 6.13.5 Check for Plastic Rotation Serviceability 412 6.13.6 Transverse Confining Reinforcement for Seismic Design 413 6.13.7 Selection of Confining Reinforcement 414 Selected References 415 Problems 417

CAMBER, DEFLECTION, ANO CRACK CONTROL 7 .1 7 .2

1ntroduction

418 Basic Assumptions in Deflection Calculations

419

418

Contents

xii

7.3

7.4 7.5 7.6 7.7

7.8 7.9 7.1 O 7.11 7.12 7 .13

7.14 7 .15 7.16 7.17 7.18 7.19 7.20 7.21

8

Short-Term (lnstantaneous) Deflection of Uncracked and Cracked Members 420 7.3.1 Load-Deflection Relationship 420 7.3.2 Uncracked Sections 423 7.3.3 Cracked Sections 427 Short-Term Deflection at Service Load 433 7.4.1 Example 7.3 Non-Composite Uncracked Double T-Beam Deflection 433 Short-Term Deflection of Cracked Prestressed Beams 439 7.5.1 Short-Term Deflection of the Beam in Example 7.3 if Cracked 439 Construction of Moment-Curvature Diagram 440 Long-Term Effects on Deflection and Camber 446 7.7.1 PCI Multipliers Method 446 7.7.2 Incremental Time-Steps Method 448 7.7.3 Approximate Time-Steps Method 450 7.7.4 Computer Methods for Deflection Evaluation 452 7.7.5 Deflection of Composite Beams 452 Permissible Limits of Calculated Deflection 453 Long-Term Camber and Deflection Calculation by the PCI Multipliers Method 454 Long-Term Camber and Deflection Calculation by the Incremental Time-Steps Method 458 Long-Term Camber and Deflection Calculation by the Approximate Time-Steps Method 469 Long-Term Deflection of Composite Double-T Cracked Beam 472 Cracking Behavior and Crack Control in Prestressed Beams 4 79 7.13.1 lntroduction 479 7.13.2 Mathematical Model Formulation for Serviceability Evaluation 479 7 .13.3 Expressions for Pretensioned Beams 480 7.13.4 Expressions for Post-Tensioned Beams 481 7.13.5 ACI New Code Provisions 483 7.13.6 Long-Term Effects on Crack-Width Development 484 7.13.7 Tolerable Crack Widths 485 Crack Width and Spacing Evaluation in Pretensioned T-Beam Without Mild Steel 485 Crack Width and Spacing Evaluation in Pretensioned T-Beam Containing Nonprestressed Steel 486 Crack Width and Spacing Evaluation in Pretensioned 1-Beam Containing Nonprestressed Mild Steel 487 Crack Width and Spacing Evaluation for Post-Tensioned T-Beam Containing Nonprestressed Steel 488 Crack Control by ACI Code Provisions 490 SI Deflection and Cracking Expressions 490 SI Deflection Control 491 SI Crack Control 496 Selected References 496 Problems 497

PRESTRESSED COMPRESSION ANO TENSION MEMBERS 8.1 8.2 8.3 8.4

lntroduction 500 Prestressed Compression Members: Load-Moment lnteraction in Columns and Piles 501 Strength Reduction Factor cf> 507 Operational Procedure for the Design of Nonslender Prestressed Compression Members 508

500

xiii

Contents 8.5 8.6 8.7

8.8 8.9 8.1 O 8.11

8.12

8.13 8.14

8.15

8.16 8.17

9

Construction of Nominal Load-Moment (Pn-Mn) and Design (Pu-Mu) lnteraction Diagrams 509 Limit State at Buckling Failure of Slender (Long) Prestressed Columns 515 8.6.1 Buckling Considerations 519 Moment Magnification Method: First-Order Analysis 520 8.7.1 Moment Magnification in Non-Sway Frames 521 8.7.2 Moment Magnification in Sway Frames 522 Second-Order Frames Analysis and the P - ~ Effects 523 Operational Procedure and Flowchart for the Design of Slender Columns 525 Design of Slender (Long) Prestressed Column 525 Compression Members in Biaxial Bending 531 8.11.1 Exact Method of Analysis 531 8.11.2 Load Contour Method of Analysis 532 8.11.3 Step-by-Step Operational Procedure for the Design of Biaxially Loaded Columns Practica! Design Considerations 537 8.12.1 Longitudinal or Main Reinforcement 537 8.12.2 Lateral Reinforcement for Columns 537 Reciproca! Load Method for Biaxial Bending 540 Modified Load Contour Method for Biaxial Bending 542 8.14.1 Design of Biaxially Loaded Prestressed Concrete Column by the Modified Load Contour Method 542 Prestressed Tension Members 544 8.15.1 Service-Load Stresses 544 8.15.2 Deformation Behavior 546 8.15.3 Decompression and Cracking 547 8.15.4 Limit State at Failure and Safety Factors 547 Suggested Step-by-Step Procedure for the Design of Tension Members 548 Design of Linear Tension Members 548 Selected References 551 Problems 552

TWO-WAY PRESTRESSED CONCRETE FLOOR SYSTEMS 9.1

9.2

9.3

9.4 9.5

lntroduction: Review of Methods 554 9.1.1 The Semielastic ACI Code Approach 557 9.1.2 The Yield-Line Theory 557 9.1.3 The Limit Theory of Plates 557 9.14 The Strip Method 557 9.1.5 Summary 558 Flexura! Behavior of Two-Way Slabs and Plates 558 9.2.1 Two-Way Action 558 9.2.2 Relative Stiffness Effects 558 The Equivalent Frame Method 559 9.3.1 lntroduction 559 9.3.2 Limitations of the Direct Design Method 560 9.3.3 Determination of the Statical Moment M0 561 9.3.4 Equivalent Frame Analysis 563 9.3.5 Pattern Loading of Spans 566 Two-Directional Load Balancing 567 Flexura! Strength of Prestressed Plates 569 9.5.1 Design Moments Mu 569

554

535

xiv

Contents 9.6

9.7 9.8 9.9

9.1 O 9.11 9.12

9.13 9.14

9.15

10

CONNECTIONS FOR PRESTRESSED CONCRETE ELEMENTS 632 10.1 10.2 10.3 10.4 10.5

10.6 10.7 10.8

11

Banding of Prestressing Tendons and Limiting Concrete Stresses 572 9.6.1 Distribution of Prestressing Tendons 572 9.6.2 Limiting Concrete Tensile Stresses at Service Load 573 Load-Balancing Design of a Single-Panel Two-Way Floor Slab 577 One-Way Slab Systems 582 Shear-Moment Transfer to Columns Supporting Flat Plates 583 9.9.1 Shear Strength 583 9.9.2 Shear-Moment Transfer 583 9.9.3 Deflection Requirements for Minimum Thickness: An lndirect Approach 586 Step-by-Step Trial-and-Adjustment Procedure for the Design of a Two-Way Prestressed Slab and Plate System 587 Design of Prestressed Post-Tensioned Flat-Plate Floor System 592 Direct Method of Deflection Evaluation 61 O 9.12.1 The Equivalent Frame Approach 610 9.12.2 Column and Middle Strip Deflections 611 Deflection Evaluation of Two-Way Prestressed Concrete Floor Slabs 613 Yield-Line Theory for Two-Way-Action Plates 616 9.14.1 Fundamental Concepts of Hinge-Field Failure Mechanisms in Flexure 617 9.14.2 Failure Mechanisms and Moment Capacities of Slabs of Various Shapes Subjected to Distributed or Concentrated Loads 622 Yield-Line Moment Strength of a Two-Way Prestressed Concrete Plate 628 Selected References 629 Problems 630

lntroduction 632 Tolerances 633 Composite Members 633 Reinforced Concrete Bearing in Composite Members 634 10.4.1 Reinforced Bearing Design 638 Dapped-End Beam Connections 640 10.5.1 Determination of Reinforcement to Resist Failure 641 10.5.2 Dapped-End Beam Connection Design 644 Reinforced Concrete Brackets and Corbels 647 Concrete Beam Ledges 647 10.7.1 Design of Ledge Beam Connection 649 Selected Connection Details 651 Selected References 659 Problems 659

PRESTRESSED CONCRETE CIRCULAR STORAGE TANKS ANO STEEL ROOFS 660 11.1 11.2

lntroduction 660 Design Principies and Procedures 661 11.2.1 Interna! Loads 661 11.2.2 Restraining Moment M0 and Radial Shear Force Q0 at Freely Sliding Wall Base Due to Liquid Pressure 664 11.2.3 General Equations of Forces and Displacements 669 11.2.4 Ring Shear Q0 and Moment M0 Gas Containment 673

Contents

xv Moment M0 and Ring Force 0 0 in Liquid Retaining Tank 67 4 Ring Force Oy at lntermediate Heights of Wall 676 Cylindrical Shell Membrane Coefficients 677 Prestressing Effects on Wall Stresses for Fully Hinged, Partially Sliding and Hinged, Fully Fixed, and Partially Fixed Bases 679 11.6.1 Freely Sliding Wall Base 694 11.6.2 Hinged Wall Base 694 11.6.3 Partially Sliding and Hinged Wall Base 695 11.6.4 Fully Fixed Wall Base 695 11.6.5 Partially Fixed Wall Base 699 11.7 Recommended Practice for Situ-Cast and Precast Prestressed Concrete Circular Storage Tanks 704 11.7.1 Stresses 704 11.7.2 Required Strength Load Factors 705 11.7.3 Minimum Wall-Design Requirements 706 11.8 Crack Control in Walls of Circular Prestressed Concrete Tanks 708 11.9 Tank Roof Design 708 11.9.1 Membrane Theory of Spherical Domes 709 11.1 O Prestressed Concrete Tanks with Circumferential Tendons 715 11.11 Seismic Design of Liquid Containment Tank Structures 715 11.12 Step-by-Step Procedure for the Design of Circular Prestressed Concrete Tanks and Dome Roofs 720 11.13 Design of Circular Prestressed Concrete Water-Retaining Tank and lts Domed Roof 727 Selected References 7 40 Problems 7 41

11.3 11.4 11.5 11.6

12

LRFD ANO STANDARD AASHTO DESIGN OF CONCRETE BRIDGES 742 12.1 12.2

12.3

12.4

12.5 12.6

lntroduction: Safety and Reliability 7 42 AASHTO Standard (LFD) and LRFD Truck Load Specifications 744 12.2.1 Loads 745 12.2.2 Wheel Load Distribution on Bridge Decks: Standard AASHTO Specifications (LFD) 748 12.2.3 Bending Moments in Bridge Deck Slabs: Standard AASHTO Specifications (LFD) 12.2.4 Wind Loads 751 12.2.5 Seismic Forces 751 12.2.6 AASHTO LFD Load Combinations 751 12.2.7 LRFD Load Combinations 753 Flexura! Design Considerations 758 12.3.1 Strain E and Factor Variations: The Strain Limits Approach 758 12.3.2 Factored Flexura! Resistance 760 12.3.3 Flexura! Design Parameters 760 12.3.4 Reinforcement Limits 761 Shear Design Considerations 762 12.4.1 The Modified Compression Field Theory 762 12.4.2 Design Expressions 763 Horizontal Interface Shear 768 12.5.1 Maximum Spacing of Dowel Reinforcement 770 Combined Shear and Torsion 770

750

xvi

Contents 12.7 12.8 12.9 12.1 O 12.11 12.12 12.13 12.14

13

AASHTO-LRFD Flexural-Strength Design Specifications vs. ACI Code Provisions 773 Step-by-Step Design Procedure (LRFD) 775 LRFD Design of Bulb-Tee Bridge Deck 780 LRFD Shear and Deflection Design 793 Standard AASHTO Flexura! Design of Prestressed Bridge Deck Beams (LFD) 801 Standard AASHTO Shear-Reinforcement Design of Bridge Deck Beams 809 Shear and Torsion Reinforcement Design of a Box-Girder Bridge 813 LRFD Major Design Expressions in SI Format 819 Selected References 820 Problems for Solution 821

SEISMIC DESIGN OF PRESTRESSED CONCRETE STRUCTURES 824 13.1

13.2

13.3

13.4

13.5

13.6

13. 7

lntroduction: Mechanism of Earthquakes 824 13.1 .1 Earthquake Ground Motion Characteristics 826 13.1 .2 Fundamental Period of Vibration 827 13.1.3 Design Philosophy 828 Spectral Response Method 829 13.2.1 Spectral Response Acceleration Maps 829 13.2.2 Seismic Design Parameters 829 13.2.3 Earthquake Design Load Classifications and Seismic Categories 833 13.2.4 Redundancy 835 13.2.5 General Procedure Response Spectrum 835 Equivalent Lateral Force Method 837 13.3.1 Horizontal Base Shear 837 13.3.2 Vertical Distribution of Forces 840 13.3.3 Horizontal Distribution of Story Shear Vx 841 13.3.4 Rigid and Flexible Diaphragms 841 13.3.5 Torsion 841 13.3.6 Story Drift and the P-Delta Effect 841 13.3.7 Overturning 843 13.3.8 Simplified Analysis Procedure for Seismic Design of Buildings 843 13.3.9 Other Aspects in Seismic Design 844 Seismic Shear Forces in Beams and Columns of a Frame: Strong Column-Weak Beam Concept 845 13.4.1 Probable Shears and Moments 845 13.4.2 Strong Column Weak Beam Concept 847 ACI Confining Reinforcements for Structural Concrete Members 849 13.5.1 Longitudinal Reinforcement in Compression Members 849 13.5.2 Transverse Confining Reinforcement 851 13.5.3 Horizontal Shear at the Joint of Beam-Column Connections 852 13.5.4 Development of Reinforcement 854 13.5.5 Allowable Shear Stresses in Structural Walls, Diaphragms, and Coupling Beams Seismic Design Concepts in High-Rise Buildings and Other Structures 858 13.6.1 General Concepts 858 13.6.2 Ductility of Elements and Plastic Hinging 858 13.6.3 Ductility Demand Due to Drift Effect 859 Structural Systems in Seismic Zones 860 13.7.1 Structural Ductile Frames 860 13.7.2 Dywidag Ductile Beam-Column Connection: DDC Assembly 864

854

Contents

xvii

13.8 13.9 13.1 O 13.11 13.12 13.13 13.14 13.15

13.7.3 Structural Walls in High-Seismicity Zones (Shear Walls} 867 13.7.4 Unbonded Precast Post-Tensioned Walls 869 Dual Systems 872 Design Procedure for Earthquake-Resistant Structures 872 SI Seismic Design Expressions 876 Seismic Base Shear and Lateral Forces and Moments by the IBC Approach 879 Seismic Shear Wall Design and Detailing 882 Example 13.3 Structural Precast Wall Base Connection Design 888 Design of Precast Prestressed Ductile Frame Connection in a High-Rise Building in High-Seismicity Zone Using Dywidag Ductile Connection Assembly (DDC) 890 Design of Precast Prestressed Ductile Frame Connection in a High-Rise Building in High-Seismicity Zone Using a Hybrid Connector System 895 Selected References 900 Problems for Solution 902

APPENDIX A UNIT CONVERSIONS, DESIGN INFORMATION, PROPERTIES OF REINFORCEMENT 905 APPENDIX B SELECTED TYPICAL STANDARD PRECAST DOUBLE TEES, INVERTED TEES, HOLLOW CORE SECTIONS, ANO AASHTO BRIDGE SECTIONS 929 INDEX

943

PREFACE

Prestressed concrete is a widely used material in construction. Hence, graduates of every civil engineering program must have, as a minimum requirement, a basic understanding of the fundamentals of linear and circular prestressed concrete. The high technology advancements in the science of materials have made it possible to construct and assemble large-span systems such as cable-stayed bridges, segmenta! bridges, nuclear reactor vessels, and offshore oil drilling platforms-work impossible to undertake in the past. Reinforced concrete's tensile strength is limited, while its compressive strength is extensive. Consequently, prestressing becomes essential in many applications in arder to fully utilize that compressive strength and, through proper design, to eliminate or control cracking and deflection. Additionally, design of the members of a total structure is achieved only by trial and adjustment: assuming a section and then analyzing it. Hence, design and analysis are combined in this work in arder to make it simpler for the student first introduced to the subject of prestressed concrete design. This completely updated fifth edition of the book revises the previous text so as to conform to the new ACI 318-08 Code and the International Building Code, IBC 2006-2009, for seismic design, stressing the strain limits approach, sometimes termed as the "unified method" in the code. The text is the outgrowth of the author's lecture notes developed in teaching the subject at Rutgers University over the past 45 years and the experience accumulated over the years in teaching and research in the areas of reinforced and prestressed concrete inclusive of the Ph.D. level, and the consulting engineering and forensic work that the author has been engaged in over the years. The material is presented in such a manner that the student can become familiarized with the properties of plain concrete, both normal and high strength, and its components prior to embarking on the study of structural behavior. The book is uniquely different from other textbooks on the subject in that the majar tapies of material behavior, prestress loss, flexure, shear, and torsion are selfcontained and can be covered in one semester at the senior level and the graduate level. The in-depth discussions of these tapies permit the advanced undergraduate and graduate student, as well as the design engineer, to develop with minimum effort a profound understanding of fundamentals of prestressed concrete structural behavior and performance. The concise discussion presented in Chapters 1 through 3 on basic principles, the historical development of prestressed concrete, the properties of constituent materials, the long-term basic behavior of such materials, and the evaluation of prestress losses should give an adequate introduction to the subject of prestressed concrete. They should also aid in developing fundamental knowledge regarding the reliability of performance of prestressed structures, a concept to which every engineering student should be exposed today. Chapters 4 and 5 on flexure, shear, and torsion, with the step-by-step logic of trial and adjustment as well as the flowcharts shown, give the student and the engineer a basic understanding of both the service load and the limit state of load at failure, using the new xix

XX

Preface

ACI 318-08 Code requirements for ultimate load design, thereby producing a good feel for the reserve strength and safety factors inherent in the design expressions. Chapter 4 in this edition contains the latest design procedure with numerical examples for the design of end anchorages of post-tensioned members as required by the latest ACI and AASHTO codes. An extensive Chapter 5 presents, with design examples, the provisions on torsion combined with shear and bending, which include a unified approach to the topic of torsion in reinforced and prestressed concrete members. SI Units examples are included in the text in addition to having equivalent SI conversions for the major steps of examples throughout the book. Additionally, a detailed theoretical discussion is presented on the mechanisms of shear and torsion, the various approaches to the torsional problem and the plastic concepts of the shear equilibrium and torsional equilibrium theories and their interaction. A totally new section is added on the strut-and-tie modeling of forces in deep beams and corbels, with detailed design examples as required by the latest ACI Code provisions. Furthermore, inclusion in this edition of design examples in SI Units anda listing of the relevant equations in SI format extends the scope of the text to cover wider applications by the profession. In this manner, the student as well as the practicing engineer can avail themselves with the tools for using either the lb-in. (PI) system or the international (SI) system. Chapter 6 on indeterminate prestressed concrete structures covers in detail continuous prestressed beams as well as portal frames, consistent with the increased use of continuous members in bridge structures. Numerous detailed examples illustrate the use of the basic concepts method, the C-line method, and the balancing method presented in Chapter l. Chapter 7 discusses in detail the design for camber, deflection, and crack control, considering both short- and long-term effects using three different approaches: the PCI multipliers method, the detailed incremental time steps method, and the approximate time steps method. A state-of-the-art discussion is presented, based on the author's work, of the evaluation and control of flexura} cracking in partially prestressed beams. Severa! design examples are included in the discussion. Chapter 8 covers the proportioning of prestressed compression and tension members, including the buckling behavior and design of prestressed columns and piles and the P-Li effect in the design of slender columns. Chapter 9 presents a thorough analysis of the service load behavior and yield-line behavior of two-way action prestressed slabs and plates. The service load behavior utilizes, with extensive examples, the equivalent frame method of flexura! design (analysis) and deflection evaluation. A detailed discussion is presented on the shear-moment transfer at column support section in two-way action prestressed concrete plates, and on deflection of two-way plates. Extensive coverage is presented of the yield-line failure mechanisms of all the usual combinations of loads on floor slabs and boundary conditions, including the design expressions for these various conditions. Chapter 10 on connections for prestressed concrete elements covers the design of connections for dapped-end beams, ledge beams, and bearing, in addition to the design of the beams and corbels presented in Chapter 5 on shear and torsion. It is revised to accommodate the new load and strength reduction factors required in the ACI 318-08 Code. This book is also unique in that Chapter 11 gives a detailed account of the analysis and design of prestressed concrete tanks and their shell roofs. Presented are the basics of the membrane and bending theories of cylindrical shells for use in the design of prestressed concrete tanks for the various wall boundary conditions of fixed, semi-fixed, hinged, and sliding wall bases, as well as the incorporation of vertical prestressing, using wrapped wires as well as tendons. Chapter 11 also discusses the theory of axisymmetrical shells and domes that are used in the design of domed roofs for circular tanks.

Preface

xxi

The extensive Chapter 12, added to the previous edition, has been updated to accommodate the latest LRFD and Standard AASHTO 2009 specifications far the design of prestressed bridge deck girders far flexure, shear, torsion, and serviceability, including the design of anchorage blocks. Several extensive examples are given using bulb-tees and box girder sections. It also includes the AASHTO requirements far truck and lane loadings and load combinations as stipulated both by the LRFD and the Standard specifications. Chapter 13, dealing with the seismic design of prestressed precast structures in high seismicity zones, has been updated based on the new ACI 318-08 and the significantly modified International Building Code, IBC 2009, on seismic design of reinfarced and prestressed concrete structures. It contains several design examples and a detailed discussion of ductile moment-resistant connections in high-rise buildings and parking garages in high seismicity zones. A unique approach far the design of such ductile connections in precast beam-column joints in high-rise building structures was extended and updated to confarm to the new load and strength reduction factors. It also contains examples of the design of shear walls and hybrid connections-all based on the state of the art in this field. Selected photographs involving various areas of the structural behavior of concrete elements at failure are included in all the chapters. They are taken from research work conducted and published by the author with many of his MS and PhD students at Rutgers University over the past faur decades. Additionally, photographs of sorne majar prestressed concrete landmark structures are included throughout the book to illustrate the versatility of design in pretensioned and post-tensioned prestressed concrete. Appendices have also been included, with monograms and tables on standard properties, sections and charts of flexural and shear evaluation of sections, as well as representative tables far selecting sections such as PCI double-tees, PCI/AASHTO bulb-tees, box girder and AASHTO standard sections far bridge decks. Conversion to SI metric units is included in the examples throughout most chapters of the book. In summary, the tapies of this updated fifth edition of the book have been presented in as concise a manner as possible without sacrificing the need far instructional details. The majar portions of the text can be used without difficulty and equally in an advanced senior level and at the graduate level far any student who has had a prior course in reinfarced concrete. The contents should also serve as a valuable guideline far the practicing engineer who has to keep abreast of the state-of-the-art in prestressed concrete and the latest provisions of the ACI 318-08 Building Code and PCI Standards, AASHTO 2009 Standards, and the International Building Code (IBC 2009), as well as the designer who seeks a concise treatment of the fundamentals of linear and circular prestressing. ACKNOWLEDGMENTS

Grateful acknowledgment is due to the American Concrete Institute, the Prestressed Concrete Institute and the Post-Tensioning Institute far their gracious support in permitting generous quotations from the ACI 318 and other relevant Codes and Reports and the numerous illustrations and tables from so many PCI and PTI publications. Special mention has to be made of the author's original mentor, the late Professor A. L. L. Baker of London University's Imperial College of Science, Technology and Medicine, who inspired him with the affection that he has developed far systems constructed of reinfarced and prestressed concrete. Grateful acknowledgment is also made to the author's many students, both undergraduate and graduate, who have had much to do with generating the writing of this book and to the many who assisted in his research activities over the past 50 years. Thanks are also due to the many professors who have been continuously

Preface

xxii

using this textbook since 1988 in major universities in the United States and their valuable comments, and to the engineers worldwide who have adopted this book as a standard reference on the up-to-date analysis and design of prestressed concrete structures. Acknowledgment is also made to the many experts who reviewed the manuscript of the first edition including Professors Carl E. Ekberg of Iowa State University; Thomas T. C. Hsu of the University of Houston; Daniel P. Jenny, formerly of the PCI; and Clifford L. Freyrmuth, formerly of the PTI. Thanks are also due to Robert M. Nawy, BA, BS, MBA, Rutgers Engineering class of 1983, who assisted in the work on the first edition, and to Engineer Gregg Romano, MS Rutgers 1999, for his contribution to the last edition's Chapter 12 on LRFD design of bridge decks. For the third edition of this book, particular thanks are dueto Professor Thomas Hsu for again reviewing the revised portions on torsional theory and examples and the shear LRFD section; Professor Alex Aswad of Pennsylvania State University at Harrisburg for his valuable input on precast shear walls in seismic regions; George Nasser, formerly Editor-in-Chief, and Paul Johal, Research Director, both of the Precast/Prestressed Concrete Institute, for their support; Mr. Khalid Shawwaf, Vice President-Engineering, Dywidag Systems International, for his cooperation and advice; and Dr. Robert E. Englekirk, President, Englekirk Consulting Engineers, and Visiting Professor at the Universities of California, Los Angeles, and San Diego, for his extensive input, discussions and advice on the subject of ductile moment-resisting frame connections in high sesimicity zones. Thanks also go to Ms. Linda Figg, President and CEO, FIGG Bridge Engineers, for her input into this and previous editions of this book. Grateful acknowledgment is also made to the Prentice Hall officers and staff: Marcia Horton, Vice President and Editorial Director, and Vincent O'Brien, Director of Team-Based Project Management, who both have given me continuous encouragement and support over the years; Holly Stark, Senior Engineering Editor, for her cooperation in processing this updated version; Scott Disanno, Senior Managing Editor, for his continuous guidance in the successful and prompt production of the book; Jane Bonnell, Production Liaison, for her coordinating efforts; Bruce Kenselaar, of the Prentice Hall Art Department, for his admirable artwork on the book cover for this and prior editions of the textbook; and Patty Donovan, Senior Project Coordinator, Laserwords Maine, for commendable efforts over the years in bringing to fruition the several editions of this book. Last but not least, the author is grateful to Mayrai Gindy, Nakin Suksawang, and James Giancastro, all PhD, Rutgers, for their assistance in the fifth edition, and to Joseph Davis, PhD, Rutgers, for his past help and diligent computational and processing work in the new sections of this edition. EDWARD

G.

NAWY

Rutgers University The State University of New Jersey Piscataway, New Jersey

PRESTRESSED CONCRETE

BASIC CONCEPTS

1.1 INTRODUCTION

Concrete is strong in compression, but weak in tension: its tensilc strenglh varies from 8 to 14 perccnt of ils compressive strength. Due to such a low tcnsile capacity. tlexural cracks develop at early slages of loading. In order to reduce or prevent such cracks from devcloping, a conccnlric or eccentric force is imposed in lhc longitudinal direction of the structural ciernen t. This force prevents the cracks from dcvcloping by climinating or considerably reducing thc tensile stresses at the critica! midspan and support scctions at service load, thcreby raising lhe bending, sbear, and torsional capacities of thc sectioos. Tbe sections are then a ble lo behave elastically, and almosl lhc full capacity of lhe concrete in comprcssion can be efficiently utilized across lhe entire dcpth of the concrete sections whcn ali loads act on the structure. Such an imposed longitudinal force is called a prestressing force, i.e., a compressive force that prestresses the sections along the span of the structural element prior to the application of the Lransverse gravily dead and live loads or transienl horizontal live loads. Thc lype of prestressing force involved, together with its magnilude, are determined mainly on the basis of the type of system to be constructed and the span length and slenderncss dcsired. Since the prestressing force is applied longitudinally along or parallel to The Diamond Baseball Stadium. Richmond, Virginia. Situ cast and precast post-tensioned prestressed structure. (Courresy, Prestressed Concrete Tnslitutc.) 1

2

~

¡

:

Individual

~

blocks

:

-o:c='~~~! L=-LI_.l--__,_____=J=:====:==,I __.__...__ =:==¡j~

.;...,...p

\

= =' -..L_=r-

A

Chapter 1 Basic Concepts

1

fe

Longitudina1 prestressing force

fe

Sec. C

Elevation

Sec. A, B (b)

(a)

staves pressure

Metal bands

F

F

A wooden barre! (e)

(d)

(e)

Figure 1.1 Prestressing principie in linear and circular prestressing. (a) Linear prestressing of a series of blocks to form a beam. (b) Compressive stress on midspan section C and end section A or B. (c) Circular prestressing of a wooden barrel by tensioning the metal bands. (d) Circular hoop prestress on one wooden stave. (e) Tensile force Fon half of metal band dueto interna! pressure, to be balanced by circular hoop prestress.

the axis of the member, the prestressing principie involved is commonly known as linear prestressing. Circular prestressing, used in liquid containment tanks, pipes, and pressure reactor vessels, essentially follows the same basic principies as 18,000 PSI Superplasticizer

Coarse aggregate (iin.) (lb)

Fine aggregate (paving sand) (lb)

Cement (lb)

Water (lb)

Silica fume (gal)

1872 1894 (1805)

1165 1165 (1100)

957 956 (950)

217 217 (w/c = 0.22)

13 13 (70 lb)ª

W. R. Grace Dartard Mighty 40 150 (oz/100 lb cement)

2.1 2.1 (6.0)

9.8 16.4 (Up to 24)

ªWeight of solid silica fume only. Water contained as part of the emulsion must be subtracted from the total water allowed.

Chapter 2

40

Materials and Systems for Prestressing

21

20 19

o

o X ·¡¡;

c.

18

17

.;:; e °' 16

~ "'> ·~

"'5. E o

u ~

15 14

-e e

;;.. 13 (.)

12 11

Age at test (days)

Figure 2.5

where

Compressive strength versus age of high-strength concrete.

f~

= 28 days' compressive strength t =time in days

a= factor depending on type of cement and curing conditions = 4.00 for moist-cured type-1 cement and 2.30 for moist-cured type-111 cement = 1.00 for steam-cured type-1 cement and 0.70 for steam-cured type-111 cement 13 = factor depending on the same parameters for a giving corresponding values of 0.85, 0.92, 0.95, and 0.98, respectively Hence, for a typical moist-cured type-I cement concrete,

f~;

Table 2.2

=

J:' t 4.00 + 0.85t e

Mixture Proportions in lb/yd3 For Composite Beams f~ > 13,000 PSI

Water

Powder silica fume force10,000

Liquid super plasticizer (Grace)

(3)

(4)

(5)

(6)

720

288

180

54

3• 0m.

Fine aggregate (natural sand)

Portland cement type 111

(1)

(2)

1851

1100

Coarse aggregate

(2.4b)

1 lb/yd3 = 0.59 Kg/m3

so·

60#

48.

48"

p

p

B 4 #3@4•

p

B

6.o·

1os.ow

1os.o·

:iJ.~-

1:·14 3 #5

I

2 rxrprism I 1 #5

6.o•

·14:1 ( 2

'

3 2•x2•prism )

r

2

;

b Ñ

~

A-A(C-1)

A-A(C-2)

A-A (C-3, C-4)

~

....

~

B-B (C-1, C-2, C-3)

Figure 2.6 (Ref. 2.37).

..... ""'

B-~

(C-4)

High-strength flanged sections reinforced with prestressed concrete prisms instrumented with fiber-optic sensors

Chapter 2

42

Materials and Systems for Prestressing

Photo 2.4 Scanning electron microscope photograph of concrete fracture surface. (Tests by Nawy. Sun, and Sauer.)

The effective modulus of concrete,

E' = '"

E~

is

stress elastic strain + creep strain

(2.5)

and the uJtimate effective modulus is given by E,

Ec,,

= 1 + "11

(2.6a)

where 'Yi is the creep ratio defined as 'Yt =

ultimate crcep strain elastic strain

The creep ratio y, has upper and lower limits as follows for prcstressed quality concrete: Upper:

"11

Lower:

'Yt

H) = 0.75 + 0.75 ( 10050- H)

= 1.75 + 2.25 ( 10065-

(2.6b}

(2.6c}

where H is the mean humidity in percent. lt has to be pointed out tbat tbese expressions are val id only in general terms, sioce the value of the modulus of elasticity is affected by factors othcr than loads, sucb as moisture in the concrete specimen, the water/cement ratio, the age of thc concrete, and temperature. Therefore. for speciaJ structures such as arches, tunnels, and tanks, the modulus of e lasticity needs to be determined from test results.

43

2.4 Creep

Limited work exists on the determination of the modulus of elasticity in tension because the low-tensile strength of concrete is normally disregarded in calculations. It is, however, valid to assume within those limitations that the value of the modulus in tension is equal to that in compression.

2.4 CREEP Creep, or lateral material flow, is the increase in strain with time dueto a sustained load. The initial deformation due to load is the elastic strain, while the additional strain due to the same sustained load is the creep strain. This practica! assumption is quite acceptable, since the initial recorded deformation includes few time-dependent effects. Figure 2.7 illustrates the increase in creep strain with time, and as in the case of shrinkage, it can be seen that creep rate decreases with time. Creep cannot be observed directly and can be determined only by deducting elastic strain and shrinkage strain from the total deformation. Although shrinkage and creep are not independent phenomena, it can be assumed that superposition of strains is valid; hence,

Total strain (E1)

=

elastic strain (Ee) + creep (Ec) + shrinkage (Esh)

An example of the relative numerical values of strain due to the foregoing three factors for a normal concrete specimen subjected to 900 psi in compression is as follows: Immediate elastic strain, Ee Shrinkage strain after 1 year, Esh Creep strain after 1 year, Ec

=

E1

=

= =

250 X 10- 6 in./in. 500 X 10- 6 in./in. 750 X 10- 6 in./in. 1,500 X 10 6 in./in.

These relative values illustrate that stress-strain relationships for short-term loading lose their significance and long-term loadings become dominant in their effect on the behavior of a structure. Figure 2.8 qualitatively shows, in a three-dimensional model, the three types of strain discussed that result from sustained compressive stress and shrinkage. Since creep is time dependent, this model has to be such that its orthogonal axes are deformation, stress, and time. Numerous tests have indicated that creep deformation is proportional to applied stress, but the proportionality is valid only for low-stress levels. The upper limit of the relationship cannot be determined accurately, but can vary between 0.2 and 0.5 of the ulti-

..

e'

~

E,

eE

(elastic strain)

Time, t

Figure 2.7

Strain-time curve.

Chapter 2

44

Materials and Systems for Prestressing

Three-dimensional model of time-dependent structural behavior.

Figure 2.8

mate strength f ~· This range in the limit of the proportionality is due to the large extent of microcracks at about 40 percent of the ultimate load. Figure 2.9a shows a section of the three-dimensional model in Figure 2.8 parallel to the plane containing the stress and deformation axes at time t 1. It indicates that both elastic and creep strains are linearly proportional to the applied stress. In a similar manner, Figure 2.9b illustrates a section parallel to the plane containing the time and strain axes at a stress f 1; hence, it shows the familiar relationships of creep with time and shrinkage with time. As in the case of shrinkage, creep is not completely reversible. If a specimen is unloaded after a period under a sustained load, an immediate elastic recovery is obtained which is less than the strain precipitated on loading. The instantaneous recovery is followed by a gradual decrease in strain, called creep recovery. The extent of the recovery

Total deformation under a stress f 1 at a time t 1

e:

o

·~

E

~

o Static strain

-----~--t----"'"""'"--~~~+-~~~1---+~~~~~~~~~

Stress

Time

1 1 Shrinkage

Shrinkage f---------+++l . . . _ • - - - - 1 2 ' - o " - - - -..~1t>-