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BRIDGEDECKANALYSISSECOND EDITION

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BRIDGEDECKANALYSISSECOND EDITION
Eugene J. OBrien and Damien L. Keogh
Department of Civil Engineering
University College Dublin, Ireland
Alan J. O’Connor
Trinity College Dublin, Ireland
Chapter 4 written in collaboration with the authors by
Barry M. Lehane
Department of Civil, Structural and Environmental Engineering
Trinity College Dublin, Ireland

CRC Press
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Version Date: 20140819
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This book is dedicated to Sheena, Margaret and Mette.
Thank you for your endless patience.

vii
Contents
Preface xiii
Acknowledgements xv
Disclaimer xvii
Authors xix
1 Introduction 1
1.1 Introduction 1
1.2 Factors affecting structural form 1
1.3 Cross sections 2
1.3.1 Solid rectangular 2
1.3.2 Voided rectangular 3
1.3.3 T-section 4
1.3.4 Box sections 5
1.3.5 Older concepts 6
1.4 Bridge elevations 7
1.4.1 Simply supported beam/slab 8
1.4.2 Series of simply supported beams/slabs 8
1.4.3 Continuous beam/slab with full propping during construction 8
1.4.4 Partially continuous beam/slab 9
1.4.5 Continuous beam/slab: Span-by-span construction 12
1.4.6 Continuous beam/slab: Balanced cantilever construction 13
1.4.7 Continuous beam/slab: Push-launch construction 16
1.4.8 Arch bridges 16
1.4.9 Frame or box culvert (integral bridge) 19
1.4.10 Beams/slabs with drop-in span 21
1.4.11 Cable-stayed bridges 22
1.4.12 Suspension bridges 24
1.5 Articulation 24
1.6 Bearings 27
1.6.1 Sliding bearings 27
1.6.2 Pot bearings 28
1.6.3 Elastomeric bearings 28
1.7 Joints 29
1.7.1 Buried joint 30

viii Contents
1.7.2 Asphaltic plug joint 30
1.7.3 Nosing joint 30
1.7.4 Reinforced elastomeric joint 31
1.7.5 Elastomeric in metal runners joint 31
1.7.6 Cantilever comb or tooth joint 32
1.8 Bridge aesthetics 32
1.8.1 Single-span beam/slab/frame bridges of constant depth 33
1.8.2 Multiple spans 34
2 Bridge loading 39
2.1 Introduction 39
2.2 Dead loading 40
2.3 Imposed traffic loading 41
2.3.1 Pedestrian traffic 41
2.3.2 Nature of road traffic loading 41
2.3.3 Code models for road traffic 44
2.3.4 Imposed loading due to rail traffic 45
2.4 Shrinkage and creep 46
2.4.1 Shrinkage 47
2.4.2 Creep 47
2.5 Thermal loading 47
2.5.1 Uniform changes in temperature 48
2.5.2 Differential changes in temperature 50
2.6 Impact loading 56
2.7 Dynamic effects 57
2.8 Prestress loading 61
2.8.1 Equivalent loads and linear transformation 61
2.8.2 Prestress losses 67
2.8.3 Non-prismatic bridges 69
3 Introduction to bridge analysis 73
3.1 Introduction 73
3.2 Positioning the traffic load model on the bridge 73
3.3 Differential settlement of supports 77
3.4 Thermal expansion and contraction 78
3.4.1 Equivalent loads method 81
3.5 Differential temperature effects 83
3.5.1 Temperature effects in three dimensions 93
3.6 Prestress 96
3.7 Analysis for the effects of creep 102
4 Integral bridges 109
4.1 Introduction 109
4.1.1 Integral construction 109

Contents ix
4.1.2 Lateral earth pressures on abutments 111
4.1.3 Stiffness of soil 114
4.2 Contraction of bridge deck 116
4.2.1 Contraction of bridge fully fixed at the supports 116
4.2.2 Contraction of bridge on flexible supports 116
4.3 Conventional spring model for deck expansion 120
4.4 Modelling expansion with an equivalent spring at deck level 123
4.4.1 Development of general expression 123
4.4.2 Expansion of frames with deep abutments 126
4.4.3 Expansion of bank-seat abutments 128
4.5 Run-on slab 131
4.6 Time-dependent effects in composite integral bridges 133
5 Slab bridge decks: Behaviour and modelling 137
5.2 Thin-plate theory 137
5.2.1 Orthotropic and isotropic plates 137
5.2.2 Bending of materially orthotropic thin plates 138
5.2.3 Stress in materially orthotropic thin plates 144
5.2.4 Moments in materially orthotropic thin plates 146
5.2.5 Shear in thin plates 153
5.3 Grillage analysis of slab decks 155
5.3.1 Similitude between grillage and bridge slab 156
5.3.2 Grillage member properties: Isotropic slabs 158
5.3.3 Grillage member properties: Geometrically orthotropic slabs 162
5.3.4 Computer implementation of grillages 164
5.3.5 Sources of inaccuracy in grillage models 164
5.3.6 Shear force near point supports 166
5.3.7 Recommendations for grillage modelling 166
5.4 Planar finite element analysis of slab decks 168
5.4.1 FE theory: Beam elements 168
5.4.2 FE theory: Plate elements 171
5.4.3 Similitude between plate FE model and bridge slab 175
5.4.4 Properties of plate finite elements 176
5.4.5 Shear forces in plate FE models 178
5.4.6 Recommendations for FE analysis 179
5.5 Wood and Armer equations 182
5.5.1 Resistance to twisting moment 186
5.5.2 New bridge design 187
6 Application of planar grillage and finite element methods 189
6.2 Simple isotropic slabs 189
6.3 Edge cantilevers and edge stiffening 192
6.4 Voided slab bridge decks 200

x Contents
6.5 Beam-and-slab bridges 206
6.5.1 Grillage modelling 207
6.5.2 Finite element modelling 213
6.5.3 Transverse local behaviour of beam-and-slab bridges 215
6.6 Cellular bridges 215
6.7 Skew and curved bridge decks 222
6.7.2 FE modelling 224
7 Three-dimensional modelling of bridge decks 225
7.2 Shear lag and effective flange width 225
7.2.1 Effective flange width 226
7.3 Three-dimensional analysis using brick elements 228
7.3.1 Interpretation of results of brick models 228
7.4 Upstand grillage modelling 239
7.5 Upstand finite element modelling 240
7.5.1 Upstand finite element modelling of voided slab bridge decks 244
7.5.2 Upstand FE modelling of other bridge types 247
7.5.3 Prestress loads in upstand FE models 248
8 Probabilistic assessment of bridge safety 251
8.2 Code treatment of probability of failure 252
8.2.1 Eurocode 1990 253
8.2.2 ISO/CD 13822:2010 254
8.2.3 Nordic Committee on Building Regulations 255
8.2.4 International Federation for Structural Concrete Bulletin 65 255
8.2.5 AASHTO 256
8.3 Calculation of the probability of failure, Pf 256
8.3.1 Basic statistical concepts 258
8.4 Resistance modelling 262
8.4.1 Reinforced concrete 263
8.4.2 Prestressed concrete 265
8.4.3 Structural steel 265
8.4.4 Soils 266
8.4.5 Material model uncertainty 266
8.5 Deterioration modelling 268
8.6 Load modelling 273
8.6.1 Permanent and quasi-permanent loads 273
8.6.2 Variable imposed loads 274
8.7 Probabilistic assessment of LS violation 274
8.8 Component vs. system reliability analysis 275

Contents xi
9 Case studies 277
9.2 Reinforced concrete beam-and-slab deck 277
9.2.1 Bridge model 277
9.2.2 Probabilistic classification and modelling 280
9.2.3 Results of probabilistic assessment 285
9.3 Post-tensioned concrete slab deck 287
9.4 Steel truss bridge 293
9.5 Conclusion 301
References 303
Appendix A: Stiffness of structural members and associated bending
moment diagrams 309
Appendix B: Location of centroid of a section 311
Appendix C: Derivation of shear area for grillage member representing
cell with flange and web distortion 313
Index 315

xiii
Preface
This edition arose from a suggestion by Alan O’Connor that our book should include chap-
ters on reliability theory. However, when we took a closer look, we found that the entire book
was in need of a major update; and what started as minor revisions became a big undertak-
ing. New research has changed the way that soil/structure interaction is treated in Chapter
4. We decided to drop the text on moment distribution in Chapter 3 and added a new section
to give examples of how to analyse for the effects of creep. A lot has changed over the years.
Grillage analysis is surely declining in popularity as plate finite-element (FE) programs are
widely available, and most engineers are now familiar with the basics of FE theory. We have
retained grillage analysis for now, but we de-emphasise it and have greatly expanded the
sections on 3-D brick finite elements. The old references to the British Standard BS5400 are
now gone, and the text is consistent with the Eurocodes and AASHTO standards. We have
kept with our tradition of taking the reader through big examples in considerable detail. The
feedback we get is that young engineers find this really useful.
In many ways, we have grown up with this book. Damien Keogh was just a graduate
when we wrote the first edition, and he is now a project engineer with the international firm
of consultants, Rambøll. Eugene OBrien was a junior lecturer when he was working on the
first edition, and he is now a professor and a company director at Roughan O’Donovan
Innovative Solutions. It has been a pleasure to update the book to reflect the many changes
that have happened since the 1990s. We hope that the readers will agree that it has been
worthwhile.

xv
Acknowledgements
Several people helped us in the preparation of the second edition. Dr. Donya Hajializadeh,
in particular, invested a great deal of time in running the analyses for examples in Chapters
3, 4 and 7, and she was particularly patient when the numbers changed and re-analysis was
required. Rachel Harney, Cathal Leahy and Jennifer Keenahan also contributed analysis
and figures essential to the explanation of complex concepts. On technical issues, Marcos
Sanchez Sanchez was an immense resource; he is an outstanding bridge engineer, and he
gave most generously of his time. Aonghus O’Keeffe, Arturo González, Bernard��Enright,
Colin�� Caprani and�� Cathal�� Leahy were also most helpful on technical questions. The
Ministry of Infrastructure and the Environment of the Netherlands, Rijkswaterstaat, is
acknowledged for making available weigh-in-motion data. Dr. Ib Enevoldsen of Rambøll
Consulting Engineers is specifically thanked for his contribution and for making available
the examples in Chapter 9, which form such an important part of the new edition. Finally,
we would like to thank Dr. Arturo González for taking on extra lectures and Dr. Atorod
Azizinamini with Florida International University for hosting a sabbatical in Miami, where
much of the work for the second edition was completed. The cover photograph is provided
courtesy of Roughan and O’Donovan Consulting Engineers.

xvii
Disclaimer
This publication presents many advanced techniques, some of which are novel and have not
been exposed to the rigours of time. The material represents the opinions of the authors and
should be treated as such. Readers should use their own judgement as to the validity of the
information and its applicability to particular situations and check the references before
relying on them. Sound engineering judgement should be the final arbiter in all stages of the
design process. Despite the best efforts of all concerned, typographical or editorial errors
may occur, and readers are encouraged to bring errors of substance to our attention. The
publisher and authors disclaim any liability, in whole or in part, arising from information
contained in this publication.

xix
Authors
Dr. Eugene OBrien is professor of civil engineering at the University College Dublin (UCD),
Ireland. After completing his PhD, Dr. OBrien worked for 5 years in the industry before
becoming a lecturer in 1990 at Trinity College Dublin. Since 1998, he has been a profes-
sor of civil engineering at UCD. He has personally supervised 26 PhDs to completion and
has published 220 technical papers and one other book. He has a significant track record
of participation in European framework projects since the mid-1990s and, at the time of
writing, leads a €2 million national project, PhD in Sustainable Development, funded by
the Irish Research Council. He is also the UCD Principal Investigator on Next Generation
Bridge Weigh-in-Motion, a $1 million project funded jointly by the Science Foundation
Ireland, Invest Northern Ireland and the American National Science Foundation (NSF).
As well as his academic work, Dr. OBrien is involved in the commercialisation of research
as the director of Roughan O’Donovan Innovative Solutions. In that role, he leads the FP7
projects, Long Life Bridges and InfraRisk, and is a partner in the Research for SME project,
BridgeMon.
Dr. Damien Keogh, BSc Eng, PhD, is a senior bridge design engineer and project manager
in the International Bridges Department with Rambøll in Copenhagen, Denmark. He is a
chartered engineer and member of the Institution of Engineers of Ireland. He has exten-
sive international experience in bridge design and project management, having worked in
Ireland, the Middle East, India and Denmark. His experience varies from single-span pre-
cast concrete road bridges up to large composite steel and concrete cable stayed bridges. At
the time of writing, he is working on the Queensferry Crossing: a new 2.7 km road bridge
across the Firth of Forth in Scotland where Rambøll are the lead designers.
Prof. Alan O’Connor, BA, BAI, PhD, is an associate professor in the Department of Civil
Engineering at Trinity College Dublin, Ireland. He is a chartered engineer and a fellow of
the Institution of Engineers of Ireland. He has extensive national/international experience
in infrastructural risk analysis and probabilistic safety assessment. He has advised clients
such as Irish Rail, The Irish National Roads Authority, The Danish Roads Directorate,
Danish Railways, Swedish Railways, The Norwegian Roads Authority and the Ministry
of Infrastructure and the Environment of the Netherlands. At Trinity College Dublin, the
research group that he leads is focused on investigating infrastructural asset management
and optimised whole life management, cross asset maintenance optimisation, structural
health monitoring, stochastic modelling of engineering systems, risk analysis of critical
infrastructure for extreme weather events and structural reliability analysis.

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