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The Design of Prestressed

Concrete Bridges

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The Design of Prestressed

Concrete Bridges

Concepts and principles

Robert Benaim

First published 2008

By Taylor & Francis

2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN

Simultaneously published in the USA and Canada

By Taylor & Francis

270 Madison Avenue, New York, NY 10016

Taylor & Francis is an imprint of the Taylor & Francis Group, an informa

business

© 2008 Robert Benaim

All rights reserved. No part of this book may be reprinted or reproduced or

utilised in any form or by any electronic, mechanical, or other means, now

known or hereafter invented, including photocopying and recording, or in

any information storage or retrieval system, without permission in writing

from the publishers.

The publisher makes no representation, express or implied, with regard to

the accuracy of the information contained in this book and cannot accept

any legal responsibility or liability for any efforts or omissions that may be

made.

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

Library of Congress Cataloging-in-Publication Data

Benaim, Robert.

The design of prestressed concrete bridges : concepts and principles /

Robert Benaim.

p. cm.

Includes bibliographical references and index.

1. Bridges, Concrete–Design and construction. 2. Reinforced concrete

construction. I. Title.

TG340.B3975 2007

624.2–dc22 2007004615

ISBN10: 0–415–23599–5 (hbk)

ISBN10: 0–203–96205–2 (ebk)

ISBN13: 978–0–415–23599–0 (hbk)

ISBN13: 978–0–203–96205–3 (ebk)

This edition published in the Taylor & Francis e-Library, 2007.

“To purchase your own copy of this or any of Taylor & Francis or Routledge’s

collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.”

ISBN 0-203-96205-2 Master e-book ISBN

I would like to dedicate this book to my wife Simone who has supported me in all the

phases of my professional life, from the initial decision to take the risk of starting my

own practice, through the tensions and crises that are an integral part of the major

international projects in which we were involved, to the long drawn out preparation

of this book.

Figures xiii

Acknowledgements xxii

Disclaimer xxiii

Introduction 1

1 The nature of design 4

1.1 Design and analysis 4

1.2 A personal view of the design process 5

1.3 Teamwork in design 6

1.4 The specialisation of designers 7

1.5 Qualities required by a bridge designer 8

1.6 Economy and beauty in design 9

1.7 Expressive design 14

1.8 Bridges as sculpture 19

1.9 Engineering as an art form 23

2 Basic concepts 28

2.1 Introduction 28

2.2 Units 28

2.3 Loads on bridge decks 28

2.4 Bending moments, shear force and torque 29

2.5 Limit states 32

2.6 Statical determinacy and indeterminacy 33

3 Reinforced concrete 35

3.1 General 35

3.2 The historical development of reinforced concrete 35

3.3 General principles of reinforced concrete 37

3.4 Reinforced concrete in bending 40

3.5 The cracking of reinforced concrete 47

3.6 The exothermic reaction 51

Contents

viii Contents

3.7 The ductility of reinforced concrete 57

3.8 Imposed loads and imposed defl ections 58

3.9 Creep and relaxation of concrete 60

3.10 Truss analogy 61

3.11 Strut-and-tie analogy 70

3.12 Continuity between the concepts of bending and arching

action 77

4 Prestressed concrete 80

4.1 Introduction 80

4.2 A comparison between reinforced concrete and prestressed

concrete 84

4.3 Pre-tensioning and post-tensioning 89

4.4 Conclusion 90

5 Prestressing for statically determinate beams 91

5.1 General 91

5.2 Materials employed for the example 91

5.3 Section properties 91

5.4 Central kern and section effi ciency 93

5.5 Loads 95

5.6 Bending moments, bending stresses and shear force 95

5.7 Centre of pressure 96

5.8 Calculation of the prestress force 97

5.9 Table of stresses 100

5.10 Non-zero stress limits 101

5.11 Compressive stress limits 102

5.12 Sign convention 103

5.13 Arrangement of tendons at mid-span 103

5.14 Cable zone 104

5.15 The technology of prestressing 107

5.16 Cable profi le 111

5.17 Losses of prestress 116

5.18 The concept of equivalent load 120

5.19 Internal and external loads 125

5.20 Prestress effect on shear force 125

5.21 Anchoring the shear force 126

5.22 Defl ections 126

5.23 The shortening of prestressed members 128

5.24 Forces applied by prestress anchorages 129

5.25 Following steel 135

5.26 The introduction of prestress forces 137

5.27 Bonded and unbonded cables 137

Contents ix

6 Prestressing for continuous beams 139

6.1 General 139

6.2 The nature of prestress parasitic moments 139

6.3 Parasitic moments at the ULS 142

6.4 The effect of parasitic moments on the beam reactions 143

6.5 Concordant cables 144

6.6 Straight cables in built-in beams 144

6.7 Cable transformations 145

6.8 Control of prestress parasitic moments 145

6.9 Details of the sample bridge deck 146

6.10 Section properties 147

6.11 Comment on the accuracy of calculations 149

6.12 Dead and live loads 150

6.13 Bending moments 150

6.14 Considerations on the choice of tendon size 164

6.15 Calculating the prestress force 165

6.16 Prestress scheme 1 167

6.17 Prestress scheme 2 174

6.18 Non-zero stress limits 175

6.19 Very eccentric cross sections 177

6.20 Design of the parasitic moments 177

6.21 Modifi cation of bending moments due to creep 179

6.22 Modifi cation of bending stresses due to creep following

change of cross section 184

6.23 Bursting out of tendons 185

6.24 The anchorage of tendons in blisters 187

6.25 Checks at the ULS 187

7 Articulation of bridges and the design of substructure 191

7.1 General 191

7.2 Design parameters 191

7.3 Bearings: general design considerations 194

7.4 Mechanical bearings 194

7.5 Elastomeric bearings 197

7.6 Concrete hinges 198

7.7 Design of foundations 199

7.8 The design of piers 208

7.9 The articulation of decks with mechanical bearings 212

7.10 Deck on laminated rubber bearings 222

7.11 Piers built into the deck 223

7.12 Split piers 223

7.13 Integral bridges 226

7.14 Continuity versus statical determinacy 227

7.15 Examples of bridge articulation 231

x Contents

8 The general principles of concrete deck design 238

8.1 General 238

8.2 Transverse bending 238

8.3 Transverse distribution of live loads 240

8.4 Material quantities and costs 243

8.5 Choice of most economical span 248

9 The design of bridge deck components 250

9.1 General 250

9.2 Side cantilevers 250

9.3 Top slabs 264

9.4 Bottom slabs 270

9.5 Webs 278

9.6 Diaphragms 294

9.7 Deck drainage 303

9.8 Waterproofi ng 306

9.10 Expansion joints 307

10 Precast beams 308

10.1 General 308

10.2 Standard precast beams 308

10.3 Customised precast beams 312

11 Solid slabs, voided slabs and multi-cell box girders 327

11.1 Slab bridges, general 327

11.2 Reinforced concrete slab bridges 327

11.3 Prestressed concrete slab bridges 328

11.4 Solid slab portal bridges 333

11.5 Voided slabs 340

11.6 Case history: River Nene Bridge 344

11.7 Multi-cell box girders 346

12 Ribbed slabs 349

12.1 General 349

12.2 Behaviour of twin rib decks 351

12.3 The use of diaphragms 355

12.4 Proportioning of twin rib decks 357

12.5 Ribbed slabs and skew bridges 362

12.6 Heat of hydration effects on twin rib decks 362

12.7 Prestress layout 365

12.8 Substructure for twin rib bridges 365

12.9 Construction technology 365

12.10 The development of ribbed slabs 367

Contents xi

13 Box girders 369

13.1 General 369

13.2 Cast-in-situ construction of boxes 369

13.3 Evolution towards the box form 371

13.4 Shape and appearance of boxes 372

13.5 The number of webs per box 378

13.6 Number of boxes in the deck cross section 379

14 Counter-cast technology for box section decks 386

14.1 General 386

14.2 Long line casting 387

14.3 Short line casting 388

15 The construction of girder bridges 414

15.1 General 414

15.2 Cast-in-situ span-by-span construction of continuous beams 414

15.3 Precast segmental span-by-span erection 422

15.4 Cast-in-situ balanced cantilever construction 428

15.5 Precast segmental balanced cantilever construction 439

15.6 Progressive erection of precast segmental decks 458

15.7 Construction programme for precast segmental decks 459

15.8 Incremental launching 460

15.9 Prefabrication of complete spans 475

16 The effect of scale on the method of construction 484

16.1 General 484

16.2 A bridge length of 130 m on four spans 484

16.3 A bridge length of 130 m on three spans 485

16.4 The bridge is 500 m long 487

16.5 A series of short bridges totalling typically 1,000 m 490

16.6 The bridge is 1,000 m long 491

16.7 The bridge is 2,000 m long 492

16.8 The bridge is 10,000 m long 494

17 The design and construction of arches 498

17.1 General 498

17.2 Line of thrust 498

17.3 Unreinforced concrete and masonry arches 501

17.4 Flat arches 502

17.5 Reinforced concrete arches 503

17.6 Short-span reinforced concrete arches with earth fi ll 504

17.7 Longer span reinforced concrete arches supporting bridge

decks 509

17.8 Construction of arches 512

xii Contents

17.9 Progressive collapse of multi-span arch bridges 516

17.10 Tied arches 516

18 Cable-supported decks 519

18.1 General 519

18.2 Extradosed bridge decks 519

18.3 Undertrussed bridges 521

18.4 Cable-stayed bridges 522

18.5 Stressed ribbon bridges 552

18.6 Steel cable catenary bridges 560

18.7 Flat suspension bridges 561

Appendix 564

References 568

Index 572

1.1 Cross sections of slip road merging with main carriageway 10

1.2 Options for bridge pier 11

1.3 Options for fl ared column 12

1.4 STAR Viaduct: typical pier 13

1.5 Byker Viaduct: pier fi nishes 13

1.6 Fish belly beams: simply supported beams of Maracaibo Bridge 15

1.7 Beam or arch? 16

1.8 Byker Viaduct under construction 16

1.9 Ah Kai Sha Bridge towers 17

1.10 Alex Fraser Bridge towers 18

1.11 Hungerford Footbridge 20

1.12a Runnymede Bridge: original Lutyens design 21

1.12b Long section of Lutyens bridge 21

1.12c New Runnymede Bridge 21

1.12d New Runnymede Bridge: load testing the bridge model 22

1.13 Hampton Court Bridge by Lutyens 22

1.14 Pantheon, Rome 24

1.15 Beauvais Cathedral 25

1.16 Saltash Bridge by Brunel 26

1.17 Palazzetto dello Sport by Nervi 26

1.18 Salginatobel Bridge by Maillart 27

2.1 Bending moment and shear force on cantilever 30

2.2 Rectangular cross section cantilever 31

2.3 Section unsymmetrical about a horizontal axis 31

2.4 Eccentric load creating torsion 32

2.5 Statically determinate and indeterminate beams 33

3.1 Hagia Sophia in Constantinople 36

3.2 Stress–strain curve for concrete 38

3.3 Stress–strain curve for high yield reinforcing steel 40

3.4 Beam in bending at working load 41

3.5 Beam in bending at the ULS 43

3.6 Examples 1 and 2 44

3.7 Typical highway tunnel below the water table 49

3.8 Jacking head 50

3.9 Diagrammatic representation of temperature rise and strength gain

of setting concrete 52

Figures

xiv List of fi gures

3.10 Typical heat of hydration cracking of walls 54

3.11 Singapore Central Expressway 55

3.12 Alternative reinforcement of two-way slab with beam strips 58

3.13 Imposed loads and imposed defl ections on a cantilever 59

3.14 Creep and relaxation of concrete 60

3.15 Truss analogy for beams 62

3.16 Opening in beam web 64

3.17 Halving joint 65

3.18 Load applied close to support 66

3.19 Curtailment of reinforcement 67

3.20 Hanging steel 68

3.21 Shear fi elds 69

3.22 Tiered strut-and-tie brackets 70

3.23 Stress diagrams for deep beam 71

3.24 Deep beams 73

3.25 Shear friction 74

3.26 Bond of bars and plates 76

3.27 Arching action in beams 77

3.28 Arching action in reinforced concrete fl oor 79

4.1 Prestressing of two pinned arch 81

4.2 Greek temple 81

4.3 Plain concrete beam 82

4.4 Centrally prestressed beam 83

4.5 Eccentrically prestressed beam 83

4.6 Tied arch 85

5.1 Statically determinate beam 92

5.2 The central kern 93

5.3 Effi ciency of typical deck types 94

5.4 Centre of pressure 96

5.5 Calculation of prestress force using kern and centre of pressure 98

5.6 Arrangement of tendons 104

5.7 Plotting the cable zone 105

5.8 Elevation of cable zone 106

5.9a Typical prestress anchors: CCL slab anchor for 6 strands 107

5.9b Typical prestress anchors: CCL anchor for 19 No 15.7 mm strands 108

5.9c Typical prestress anchors: CCL anchor for 37 No 15.7 mm strands 108

5.9d Typical prestress anchors: bar anchors 109

5.9e Typical prestress anchors: buried dead anchors 109

5.10 Prestressing jack 110

5.11 Cable arrangements 112

5.12 Cables in a typical beam 113

5.13 Eccentricity of cables within their ducts 113

5.14 Arrangement of swept up anchors 114

5.15 Loss of prestress due to friction and anchor set 118

5.16 The concept of equivalent load for a ‘V’ profi le cable 121

5.17 Equivalent load for a parabolic cable 122

5.18 Equivalent loads for general case 123

5.19 Equivalent loads; straight cable and defl ected neutral axis 124