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Bridge Design

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Bridge Design
Concepts and Analysis

António J. Reis

IST – University of Lisbon and Technical Director GRID Consulting Engineers
Lisbon
Portugal

José J. Oliveira Pedro

IST – University of Lisbon and GRID Consulting Engineers
Lisbon
Portugal

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This edition first published 2019
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Library of Congress Cataloging‐in‐Publication Data
Names: Reis, António J., 1949– author. | Oliveira Pedro, José J., 1968– author.
Title: Bridge design : concepts and analysis / António J. Reis, IST – University of Lisbon and Technical
Director GRID Consulting Engineers, Lisbon, José J. Oliveira Pedro, IST – University of Lisbon and GRID
Consulting Engineers, Lisbon.
Description: First edition. | Hoboken, NJ : John Wiley & Sons, Ltd, 2019. | Identifiers: LCCN 2018041508
(print) | LCCN 2018042493 (ebook) | ISBN 9781118927656 (Adobe PDF) | ISBN 9781118927649 (ePub) |
ISBN 9780470843635 (hardback)

Subjects: LCSH: Bridges–Design and construction.
Classification: LCC TG300 (ebook) | LCC TG300 .R45 2019 (print) | DDC 624.2/5–dc23
LC record available at />Cover Design: Wiley
Cover Image: © Ana Isabel Silva
Set in 10/12pt Warnock by SPi Global, Pondicherry, India
Printed in the UK by Bell & Bain Ltd, Glasgow
10 9 8 7 6 5 4 3 2 1

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v

Contents
About the Authors  xiii
Preface  xv
Acknowledgements  xvii
1Introduction 
1

1.1­Generalities  1
1.2­Definitions and Terminology  1
1.3­Bridge Classification  4
1.4­Bridge Typology  6
1.5­Some Historical References  16
1.5.1 Masonry Bridges  16
1.5.2 Timber Bridges  18
1.5.3 Metal Bridges  18
1.5.4 Reinforced and Prestressed Concrete Bridges  24
1.5.5 Cable Supported Bridges  28

­References  30
Bridge Design: Site Data and Basic Conditions  31
2.1­Design Phases and Methodology  31
2.2­Basic Site Data  32
2.2.1Generalities 
32
2.2.2 Topographic Data  32
2.2.3 Geological and Geotechnical Data  35
2.2.4 Hydraulic Data  36
2.2.5 Other Data  38
2.3­Bridge Location. Alignment, Bridge Length and Hydraulic Conditions  38
2.3.1 The Horizontal and Vertical Alignments  42
2.3.2 The Transverse Alignment  46
2.4­Elements Integrated in Bridge Decks  49
2.4.1 Road Bridges  49
2.4.1.1 Surfacing and Deck Waterproofing  50
2.4.1.2 Walkways, Parapets and Handrails  50
2.4.1.3 Fascia Beams  53
2.4.1.4 Drainage System  54

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2.4.1.5 Lighting System  55

2.4.1.6 Expansion Joints  55
2.4.2
Railway Decks  58
2.4.2.1 Track System  59
2.4.2.2 Power Traction System (Catenary System)  61
2.4.2.3 Footways, Parapets/Handrails, Drainage and Lighting Systems  61
­References  61
Actions and Structural Safety  63
3.1­Types of Actions and Limit State Design  63
3.2­Permanent Actions  65
3.3­Highway Traffic Loading – Vertical Forces  68
3.4­Braking, Acceleration and Centrifugal Forces in Highway Bridges  72
3.5­Actions on Footways or Cycle Tracks and Parapets, of Highway Bridges  74
3.6­Actions for Abutments and Walls Adjacent
to Highway Bridges  75
3.7­Traffic Loads for Railway Bridges  76
3.7.1General 
76
3.7.2
Load Models  76
3.8­Braking, Acceleration and Centrifugal Forces in Railway Bridges:
Nosing Forces  77
3.9­Actions on Maintenance Walkways and Earth Pressure Effects
for Railway Bridges  78
3.10­Dynamic Load Effects  79
3.10.1
Basic Concepts  79
3.10.2
Dynamic Effects for Railway Bridges  82
3.11­Wind Actions and Aerodynamic Stability of Bridges  84

3.11.1
Design Wind Velocities and Peak Velocities Pressures  84
3.11.2
Wind as a Static Action on Bridge Decks and Piers  89
3.11.3
Aerodynamic Response: Basic Concepts  91
3.11.3.1 Vortex Shedding  94
3.11.3.2 Divergent Amplitudes: Aerodynamic Instability  95
3.12­Hydrodynamic Actions  98
3.13­Thermal Actions and Thermal Effects  99
3.13.1
Basic Concepts  99
3.13.2
Thermal Effects  102
3.13.3
Design Values  107
3.14­Shrinkage, Creep and Relaxation in Concrete Bridges  109
3.15­Actions Due to Imposed Deformations. Differential Settlements  117
3.16­Actions Due to Friction in Bridge Bearings  119
3.17­Seismic Actions  119
3.17.1
Basis of Design  119
3.17.2
Response Spectrums for Bridge Seismic Analysis  121
3.18­Accidental Actions  124
3.19­Actions During Construction  124
3.20­Basic Criteria for Bridge Design  125
­References  125

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4
Conceptual Design and Execution Methods  129
4.1­Concept Design: Introduction  129
4.2­Span Distribution and Deck Continuity  131
4.2.1 Span Layout  131
4.2.2 Deck Continuity and Expansion Joints  132
4.3­The Influence of the Execution Method  134
4.3.1 A Prestressed Concrete Box Girder Deck  134
4.3.2 A Steel‐Concrete Composite Steel Deck  136
4.3.3 Concept Design and Execution: Preliminary Conclusions  136
4.4­Superstructure: Concrete Bridges  138
4.4.1 Options for the Bridge Deck  138
4.4.2 The Concrete Material – Main Proprieties  139
4.4.2.1Concrete 139
4.4.2.2 Reinforcing Steel  140
4.4.2.3 Prestressing Steel  140
4.4.3 Slab and Voided Slab Decks  142
4.4.4 Ribbed Slab and Slab‐Girder Decks  144
4.4.5 Precasted Slab‐Girder Decks  152
4.4.6 Box Girder Decks  155
4.5­Superstructure: Steel and Steel‐Concrete Composite Bridges  160
4.5.1 Options for Bridge Type: Plated Structures  160
4.5.2 Steels for Metal Bridges and Corrosion Protection  166
4.5.2.1 Materials and Weldability  166

4.5.2.2 Corrosion Protection  172
4.5.3 Slab Deck: Concrete Slabs and Orthotropic Plates  173
4.5.3.1 Concrete Slab Decks  174
4.5.3.2 Steel Orthotropic Plate Decks  176
4.5.4 Plate Girder Bridges  179
4.5.4.1 Superstructure Components  179
4.5.4.2 Preliminary Design of the Main Girders  182
4.5.4.3 Vertical Bracing System  188
4.5.4.4 Horizontal Bracing System  191
4.5.5 Box Girder Bridges  192
4.5.5.1General 192
4.5.5.2 Superstructure Components  193
4.5.5.3 Pre‐Design of Composite Box Girder Sections  196
4.5.5.4 Pre‐Design of Diaphragms or Cross Frames  199
4.5.6 Typical Steel Quantities  201
4.6­Superstructure: Execution Methods  202
4.6.1 General Aspects  202
4.6.2 Execution Methods for Concrete Decks  203
4.6.2.1General 203
4.6.2.2 Scaffoldings and Falseworks  203
4.6.2.3 Formwork Launching Girders  206
4.6.2.4 Incremental Launching  206
4.6.2.5 Cantilever Construction  212
4.6.2.6 Precasted Segmental Cantilever Construction  221

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4.6.2.7 Other Methods  222
4.6.3 Erection Methods for Steel and Composite Bridges  223
4.6.3.1 Erection Methods, Transport and Erection Joints  223
4.6.3.2 Erection with Cranes Supported from the Ground  224
4.6.3.3 Incremental Launching  224
4.6.3.4 Erection by the Cantilever Method  227
4.6.3.5 Other Methods  227
4.7­Substructure: Conceptual Design and Execution Methods  229
4.7.1 Elements and Functions  229
4.7.2 Bridge Piers  229
4.7.2.1 Structural Materials and Pier Typology  229
4.7.2.2 Piers Pre‐Design  232
4.7.2.3 Execution Method of the Deck and Pier Concept Design  233
4.7.2.4 Construction Methods for Piers  240
4.7.3Abutments 
241
4.7.3.1 Functions of the Abutments  241
4.7.3.2 Abutment Concepts and Typology  241
4.7.4 Bridge Foundations  245
4.7.4.1 Foundation Typology  245
4.7.4.2 Direct Foundations  245
4.7.4.3 Pile Foundations  246
4.7.4.4 Special Bridge Foundations  247
4.7.4.5 Bridge Pier Foundations in Rivers  250
­References  251
5

Aesthetics and Environmental Integration  255

5.1­Introduction  255
5.2­Integration and Formal Aspects  256
5.3­Bridge Environment  256
5.4­Shape and Function  258
5.5­Order and Continuity  260
5.6­Slenderness and Transparency  262
5.7­Symmetries, Asymmetries and Proximity
with Other Bridges  266
5.8­Piers Aesthetics  267
5.9­Colours, Shadows, and Detailing  268
5.10­Urban Bridges  272
­References  277

6
Superstructure: Analysis and Design  279
6.1­Introduction  279
6.2­Structural Models  280
6.3­Deck Slabs  283
6.3.1General 
283
6.3.2 Overall Bending: Shear Lag Effects  283
6.3.3 Local Bending Effects: Influence Surfaces  287
6.3.4 Elastic Restraint of Deck Slabs  295

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6.3.5 Transverse Prestressing of Deck Slabs  297
6.3.6 Steel Orthotropic Plate Decks  300
6.4­Transverse Analysis of Bridge Decks  301
6.4.1 Use of Influence Lines for Transverse Load Distribution  301
6.4.2 Transverse Load Distribution Coefficients for Load Effects  302
6.4.3 Transverse Load Distribution Methods  303
6.4.3.1 Rigid Cross Beam Methods: Courbon Method  304
6.4.3.2 Transverse Load Distribution on Cross Beams  307
6.4.3.3 Extensions of the Courbon Method: Influence of Torsional Stiffness
of Main Girders and Deformability of Cross Beams  307
6.4.3.4 The Orthotropic Plate Approach  308
6.4.3.5 Other Transverse Load Distribution Methods  313
6.5­Deck Analysis by Grid and FEM Models  313
6.5.1 Grid Models  313
6.5.1.1Fundamentals 313
6.5.1.2 Deck Modelling  315
6.5.1.3 Properties of Beam Elements in Grid Models  317
6.5.1.4 Limitations and Extensions of Plane Grid Modelling  318
6.5.2 FEM Models  318
6.5.2.1Fundamentals 318
6.5.2.2 FEM for Analysis of Bridge Decks  323
6.6­Longitudinal Analysis of the Superstructure  329
6.6.1 Generalities – Geometrical Non‐Linear Effects: Cables and Arches  329
6.6.2 Frame and Arch Effects  332
6.6.3 Effect of Longitudinal Variation of Cross Sections  334
6.6.4 Torsion Effects in Bridge Decks – Non‐Uniform Torsion  336
6.6.5 Torsion in Steel‐Concrete Composite Decks  343
6.6.5.1 Composite Box Girder Decks  343

6.6.5.2 Composite Plate Girder Decks  345
6.6.5.3 Transverse Load Distribution in Open Section Decks  348
6.6.6 Curved Bridges  350
6.6.6.1 Statics of Curved Bridges  350
6.6.6.2 Simply Supported Curved Bridge Deck  352
6.6.6.3 Approximate Method  353
6.6.6.4 Bearing System and Deck Elongations  353
6.7­Influence of Construction Methods on Superstructure Analysis  355
6.7.1 Span by Span Erection of Prestressed Concrete Decks  356
6.7.2 Cantilever Construction of Prestressed Concrete Decks  357
6.7.3 Prestressed Concrete Decks with Prefabricated Girders  360
6.7.4 Steel‐Concrete Composite Decks  361
6.8­Prestressed Concrete Decks: Design Aspects  364
6.8.1Generalities 
364
6.8.2 Design Concepts and Basic Criteria  364
6.8.3Durability 
364
6.8.4 Concept of Partial Prestressed Concrete (PPC)  364
6.8.5 Particular Aspects of Bridges Built by Cantilevering  365
6.8.6 Ductility and Precasted Segmental Construction  366

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6.8.6.1 Internal and External Prestressing  367
6.8.7
Hyperstatic Prestressing Effects  367
6.8.8
Deflections, Vibration and Fatigue  368
6.9­Steel and Composite Decks  373
6.9.1Generalities 
373
6.9.2
Design Criteria for ULS  373
6.9.3
Design Criteria for SLS  375
6.9.3.1 Stress Limitations and Web Breathing  376
6.9.3.2 Deflection Limitations and Vibrations  377
6.9.4
Design Criteria for Fatigue Limit State  377
6.9.5
Web Design of Plate and Box Girder Sections  383
6.9.5.1 Web Under in Plane Bending and Shear Forces  383
6.9.5.2 Flange Induced Buckling  385
6.9.5.3 Webs Under Patch Loading  387
6.9.5.4 Webs under Interaction of Internal Forces  389
6.9.6
Transverse Web Stiffeners  390
6.9.7
Stiffened Panels in Webs and Flanges  391
6.9.8Diaphragms 
394
6.10­Reference to Special Bridges: Bowstring Arches and Cable‐Stayed

Bridges  395
6.10.1Generalities 
395
6.10.2
Bowstring Arch Bridges  396
6.10.2.1 Geometry, Slenderness and Stability  396
6.10.2.2 Hanger System and Anchorages  402
6.10.2.3 Analysis of the Superstructure  403
6.10.3
Cable‐Stayed Bridges  404
6.10.3.1 Basic Concepts  404
6.10.3.2 Total and Partial Adjustment Staying Options  408
6.10.3.3 Deck Slenderness, Static and Aerodynamic Stability  411
6.10.3.4 Stays and Stay Cable Anchorages  414
6.10.3.5 Analysis of the Superstructure  416
­References  418
Substructure: Analysis and Design  423
7.1­Introduction  423
7.2­Distribution of Forces Between Piers and Abutments  423
7.2.1
Distribution of a Longitudinal Force  423
7.2.2
Action Due to Imposed Deformations  424
7.2.3
Distribution of a Transverse Horizontal Force  425
7.2.4
Effect of Deformation of Bearings and Foundations  429
7.3­Design of Bridge Bearings  430
7.3.1
Bearing Types  430

7.3.2
Elastomeric Bearings  430
7.3.3
Neoprene‐Teflon Bridge Bearings  434
7.3.4
Elastomeric ‘Pot Bearings’  435
7.3.5
Metal Bearings  437
Concrete Hinges  439
7.3.6

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7.4­Reference to Seismic Devices  441
7.4.1Concept 
441
7.4.2 Seismic Dampers  441
7.5­Abutments: Analysis and Design  444
7.5.1 Actions and Design Criteria  444
7.5.2 Front and Wing Walls  446
7.5.3 Anchored Abutments  448
7.6­Bridge Piers: Analysis and Design  449
7.6.1 Basic Concepts  449
7.6.1.1Pre‐design 449
7.6.1.2 Slenderness and Elastic Critical Load  449

7.6.1.3 The Effect of Geometrical Initial Imperfections  450
7.6.1.4 The Effect of Cracking in Concrete Bridge Piers  450
7.6.1.5 Bridge Piers as ‘Beam Columns’  451
7.6.1.6 The Effect of Imposed Displacements  452
7.6.1.7 The Overall Stability of a Bridge Structure  453
7.6.1.8 Design Bucking Length of Bridge Piers  453
7.6.2 Elastic Analysis of Bridge Piers  454
7.6.3 Elastoplastic Analysis of Bridge Piers: Ultimate Resistance  459
7.6.4 Creep Effects on Concrete Bridge Piers  465
7.6.5 Analysis of Bridge Piers by Numerical Methods  465
7.6.6 Overall Stability of a Bridge Structure  471
­References  473
Design Examples: Concrete and Composite Options  475
8.1­Introduction  475
8.2­Basic Data and Bridge Options  475
8.2.1 Bridge Function and Layout  475
8.2.2 Typical Deck Cross Sections  476
8.2.3 Piers, Abutments and Foundations  477
8.2.4 Materials Adopted  477
8.2.4.1 Prestressed Concrete Deck  478
8.2.4.2 Steel‐concrete Composite Deck  481
8.2.5 Deck Construction  481
8.3­Hazard Scenarios and Actions  481
8.3.1 Limit States and Structural Safety  482
8.3.2Actions 
482
8.3.2.1 Permanent Actions and Imposed Deformations  482
8.3.2.2 Variable Actions  484
8.4­Prestressed Concrete Solution  486
8.4.1 Preliminary Design of the Deck  486

8.4.2 Structural Analysis and Slab Checks  486
8.4.3 Structural Analysis of the Main Girders  492
8.4.3.1 Traffic Loads: Transverse and Longitudinal Locations  493
8.4.3.2 Internal Forces  497
8.4.3.3 Prestressing Layout and Hyperstatic Effects  497
8.4.3.4 Influence of the Construction Stages  498

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8.4.4 Structural Safety Checks: Longitudinal Direction  498
8.4.4.1 Decompression Limit State – Prestressing Design  498
8.4.4.2 Ultimate Limit States – Bending and Shear Resistance  501
8.5­Steel–Concrete Composite Solution  502
8.5.1 Preliminary Design of the Deck  502
8.5.2 Structural Analysis and Slab Design Checks  503
8.5.3 Structural Analysis of the Main Girders  503
8.5.3.1 Traffic Loads Transverse and Longitudinal Positioning  504
8.5.3.2 Internal Forces  505
8.5.3.3 Shrinkage Effects  505
8.5.3.4 Imposed Deformation Effect  506
8.5.3.5 Influence of the Construction Stages  506

8.5.4 Safety Checks: Longitudinal Direction  507
8.5.4.1 Ultimate Limit States – Bending and Shear Resistance  507
8.5.4.2 Serviceability Limit States – Stresses and Crack Widths Control  509
­References  510
Annex A: Buckling and Ultimate Strength of Flat Plates  511
A.1­Critical Stresses and Buckling Modes of Flat Plates  511
A.1.1 Plate Simply Supported along the four Edges and under
a Uniform Compression (ψ = 1)  511
A.1.2 Bending of Long Rectangular Plates Supported at both Longitudinal Edges or
with a Free Edge  513
A.1.3 Buckling of Rectangular Plates under Shear  513
A.2­Buckling of Stiffened Plates  514
A.2.1 Plates with One Longitudinal Stiffener at the Centreline under Uniform
Compression  515
A.2.2 Plate with Two Stiffeners under Uniform Compression  516
A.2.3 Plates with Three or More Longitudinal Stiffeners  517
A.2.4 Stiffened Plates under Variable Compression. Approximate Formulas  518
A.3­Post‐Buckling Behaviour and Ultimate Strength of Flat Plates  518
A.3.1 Effective Width Concept  519
A.3.2 Effective Width Formulas  520
­References  523
Index 
525

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About the Authors

António J. Reis became a Civil Engineer at IST – University of Lisbon in 1972 and
obtained his Ph.D at the University of Waterloo in Canada in 1977. He was Science
Research Fellow at the University of Surrey, UK, and Professor of Bridges and Structural
Engineering at the University of Lisbon for more than 35 years. Reis was also Visiting
Professor at EPFL Lausanne Switzerland in 2013 and 2015. In 1980, he established his
own design office GRID where he is currently Technical Director and was responsible
for the design of more than 200 bridges. The academic and design experience were
always combined in developing and supervising research studies and innovative design
aspects in the field of steel and concrete bridges, cable stayed bridges, long span roofs
and stability of steel structures. A. Reis has design studies and projects in more than
20 countries, namely in Europe, Middle East and Africa and presented more than 150
publications. He received several awards at international level from IABSE, ECCS, ICE
and Royal Academy of Sciences of Belgium.
José J. Oliveira Pedro became a Civil Engineer at IST – University of Lisbon in 1991,
concluding his Master’s degree in 1995 and Ph.D in 2007, with the thesis “Structural
analysis of composite steel-concrete cable-stayed bridges”. He joined the Civil
Engineering Department of IST in 1990, as a Student Lecturer, and is currently Assistant
Professor of Bridges, Design of Structures and Special Structures. In 1999, he was
Researcher at Liège University / Bureau d’Etudes Greisch and, in 2015, Visiting Professor
at EPFL Lausanne. In 1991, he joined design office GRID Consulting Engineers, and
since then is very much involved in the structural design of bridges and viaducts, stadiums, long span halls and other large structures. He is the author/co-author of over
seventy publications in scientific journals and conference proceedings. In 2013, he
received the Baker medal, and in 2017 the John Henry Garrood King Medal, from the
Institute of Civil Engineers, for the best papers published in Bridge Engineering journal.

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Preface
About 15 years ago, the first author, A. J. Reis, was invited by Wiley to write a book on
Bridge Design that could be adopted as textbook for bridge courses and as a guideline
for bridge engineers. The author’s bridge course notes from the University of Lisbon,
updated over almost 30 years, were the basis for this book. For different reasons, the
completion of the book was successively postponed until a final joint effort with the
second author, J. J. Oliveira Pedro, made this long project a reality. The book mainly
reflects the long design experience of the authors and their academic lecturing and
research activities.
Bridge design is a multidisciplinary activity. It requires a good knowledge and understanding of a variety of aspects well beyond structural engineering. Road and railway
design, geotechnical and hydraulic engineering, urban planning or environmental
impact and landscape integration are key aspects. Architectural, aesthetic and environmental aspects are nowadays recognized as main engineering issues for bridge designers. However, these subjects cannot be studied independently of structural and
construction aspects, such as the bridge erection method. On the other hand, what
differentiates bridge design from building design, for example, is generally the role of
the bridge engineer as a leader of the design process. Hence, the first aim of this book is
to present an overview on all these aspects, discussing from the first bridge concepts to
analysis in a unified approach to bridge design.
The choice of structural materials and the options for a specific bridge type are part
of the design process. Therefore, the second aim of the book is to discuss concepts and
principles of bridge design for the most common cases – steel, concrete or composite
bridges. Good bridge concepts should be based on simple models, reflecting the structural behaviour and justifying design options. Sophisticated modelling nowadays adopts
available software, most useful at advanced stages of the design ­process. However, it
should be borne in mind that complex modelling does not make necessarily a good
bridge concept.
The methodology to select the appropriate bridge typology and structural material is
discussed in the first four chapters of this book. Examples, mainly from the authors’
design experiences, are included. General aspects and bridge design data are presented
in Chapter  2. Actions on bridges are included in Chapter  3 with reference to the
Eurocodes. Structural safety concepts for bridge structures and limit state design
criteria are also outlined in this chapter. Chapter 4 includes the conceptual design of

bridge super‐ and substructures. Basic concepts for prestressed concrete, steel or steel

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Preface

concrete composite bridges, with slab, slab‐girder and box girder decks are dealt with.
These topics are discussed in relation to superstructures and execution methods such
as classical falsework, formwork launching girders, incremental launching and balanced
cantilevering. Bridge substructures are referred to in Chapter 4 as well, namely for the
basic typologies of bridge piers, abutments and foundations.
Architectural, environmental, and aesthetic aspects that could be adopted as primary
guidelines when developing a bridge concept are addressed in Chapter 5. Principles are
explained on the basis of design cases from the authors’ design practices. Of course, this
could have been done on the basis of many other bridges. However, it is sometimes
difficult to comment on bridge aesthetics while not being aware of design, cost or
­execution constraints faced by other designers.
Specific aspects of structural analysis and design are dealt with in Chapters 6 and 7.
Particular reference is made in Chapter 6 to simplified approaches to the preliminary
superstructure design. These approaches can also be adopted to check results from
sophisticated numerical models at the detailed design stages. The influence of the
­erection method on structural analysis and design of prestressed concrete, steel and
composite bridge superstructures is considered in Chapter  6. Particular reference is
made to safety during construction stages and redistribution of internal forces due to
time dependent effects. Chapter  6 ends with some design concepts and analysis for
bowstring arch bridges and cable-stayed bridges. Of course, due to the scope of the
book, the aspects dealt with for these specific bridge types are introductory in nature.

The substructure structural analysis and design is presented in Chapter 7. The distribution of horizontal forces between piers and abutments due to thermal, wind and
earthquake actions is discussed. Stability of bridge piers and reinforced concrete design
aspects are dealt with. Bridge bearing typologies and specifications are introduced.
Particular reference is made to bridge seismic isolation and different types of seismic
isolation devices are presented.
The book ends with Chapter 8, which presents a simple design case with two different
superstructure solutions – a prestressed concrete deck and a steel‐concrete composite
deck. The application of design principles presented throughout the book is outlined.
The authors expect readers may find this book useful and in some way it will contribute to bridges reflecting the ‘art of structural engineering’.
António J. Reis and José J. Oliveira Pedro
Lisbon, May 2018

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xvii

Acknowledgements
This book is the result of the authors’ activities at IST–University of Lisbon and at
GRID  Consulting Engineers. The support of both institutions is a pleasure to
­acknowledge and special thanks are due to Professor Francisco Virtuoso from IST and
to our colleagues from GRID.
During 45 years of professional life as designer, the first author, A. Reis, had the
­privilege of meeting a few outstanding bridge engineers. Particular reference is made to
Jean Marie Cremer, from Bureau d’Études Greisch, with whom A. Reis had the pleasure
of working with on a few bridge projects but, most important, developing a friendship with.
Part of this book was written by the first author, A. Reis, during his stays in 2013 and
2015 as Visiting Professor at EPFL École Polytechnique Féderale de Lausanne,
Switzerland. The second author, J. Pedro, had a similar opportunity in 2015. Thanks are
due to EPFL and, in particular, to Professor Alain Nussbaumer for these opportunities.

The authors are also grateful to all sources and organizations allowing the reproduction of some figures and pictures with due credit referenced in the text.
Last, but not least, thanks are due to our families for the time this book has taken
from being with them.
António J. Reis and José J. Oliveira Pedro
Lisbon, May 2018

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1

1
Introduction
1.1 ­Generalities
Bridges are one of the most attractive structures in the field of Civil Engineering, creating
aesthetical judgements from society and deserving, in many cases, the Latin designation
in the French language of Ouvrages d’Art.
Firstly, a set of definitions and appropriated terminology related to bridge structures
is established before discussing bridge design concepts. A short historical view of the
topic is included in this chapter to introduce the reader to the bridge field, going from
basic concepts and design methods to construction technology.
A bridge cannot be designed without an appropriated knowledge of general
concepts that go well beyond the field of structural analysis and design. The concept
for a bridge requires from the designer a general knowledge of other aspects, such as
environmental and aesthetic concepts, urban planning, landscape integration,
hydraulic and geotechnical engineering.
The designer very often has to discuss specific problems for a bridge design concept
with specialists in other fields, such as the ones previously mentioned, as well as from
aspects of more closely related fields like highway or railway engineering.
Introducing the reader to the relationships between all the fields related to bridge

design, from the development of the bridge concept to more specific aspects of bridge
construction methods, is one of the aims of this book.
Most of the bridge examples are based on design projects developed at the author’s
design office. Some of these design cases have been summarized in the chapters in
order to illustrate the basic concepts developed throughout the book.

1.2 ­Definitions and Terminology
A bridge may be defined as a structure to traverse an obstacle, namely a river, a valley, a
roadway or a railway. The general term bridge is very often left for the first case, that is,
a structure over a river leaving the more specific term of viaduct for bridges over valleys
or over other obstacles. So, the relevance of the structure very often related to its length
or main span has nothing to do with the use of the terms bridge or viaduct. One may
have bridges of only 20 m length and viaducts 3 or 4 km long. In highway bridge
terminology, it is usual to differentiate between viaducts passing over or under a main
Bridge Design: Concepts and Analysis, First Edition. António J. Reis and José J. Oliveira Pedro.
© 2019 John Wiley & Sons Ltd. Published 2019 by John Wiley & Sons Ltd.

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2

Bridge Design: Concepts and Analysis

road by designating them as overpasses or underpasses. So, one shall adopt the term
‘bridge’ to designate bridges in particular, or viaducts. Figure 1.1 shows a bridge over the
river Douro that is 703 m long, 36 m width for eight traffic lanes and has a main span of
150 m, and also a viaduct in Madeira Island, 600 m long for four traffic lanes and with a
typical span of 45 m. The decks of these structures are made of two parallel box girders
supported by independent piers.

(a)

(b)

Figure 1.1  (a) The Freixo Bridge over the river Douro in Oporto, 1993, and (b) a viaduct in Madeira
Island, Portugal, 1997 (Source: Courtesy GRID, SA).

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Introduction

In Europe, important bridges have been built over the sea in recent years, such as
fixed links across large stretches of water, for example, the Öresund Bridge (7.8 km long)
between Sweden and Denmark, and the Vasco da Gama Bridge (12 km long) in the
Tagus river estuary, Lisbon, shown in Figure 1.2.
Many of these structures include main spans as part of cable‐stayed or suspension bridges and many typical spans repeated along offshore or inland areas. If
that occurs over the riversides, it is usual to designate that part of the bridge the
approach viaduct.

(a)

(b)

Figure 1.2  (a) The Öresund link between Sweden and Denmark, 2000 (Source: Soerfm, http://
commons.wikimedia.org/wiki/File:Öresund_Bridge_‐_Öresund_crop.jpg#mediaviewer/File:Öresund_
Bridge_‐_Öresund_crop.jpg. CC BY‐SA 3.0.), and (b) the Vasco da Gama Bridge, in Lisbon, Portugal,
1998 (Source: Photograph by José Araujo).

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4

Bridge Design: Concepts and Analysis

A bridge integrates two main parts:
●●
●●

the superstructure; the part traversing the obstacle and
the substructure; the part supporting the superstructure and transferring its loads to
the ground through the foundations.

The superstructure is basically made of a deck transferring the loads to the piers by
bearings or by a rigid connection between the deck and the pier; the substructure
includes the piers, foundations and the abutments, as shown in Figure 1.3. The piers
transfer the loads from the superstructure due to permanent and variable actions,
namely dead weight, traffic loads, thermal, wind and earthquake action, to the foundations.
The abutments establish the transition between the superstructure and the earthfill of the
highway or the railway and retain the filling material. The abutments transfer the loads
induced by the superstructure, generally transmitted by the bearings, and supporting the
soil impulses generated by the embankments.
The deck is, in general, supported by a set of bearings, some located at the abutments,
as previously referred to, and others located at the top of the piers as shown in Figure 1.3.
Nowadays, these bearings are generally made of elastomeric materials (natural rubber
or synthetic rubber – chloroprene) and steel.
The foundations of the bridge piers and abutments may be by footings, as in Figure 1.3

(shallow foundations) or by piles (deep foundations). A different type of foundation
include caissons made by lowering precasted segmental elements in a previous excavated soil, a method adopted sometimes for deep bridge piers foundations in rivers.

1.3 ­Bridge Classification
Bridges may be classified according several criteria namely:
●●

●●

●●

the bridge function, dependent on the type of use of the bridge, giving rise to designations of highway or railway bridges, canal bridges for the transportation of water,
quay bridges in ports, runway or taxiway bridges in airports, pedestrian bridges or
pipeline bridges. The function of the bridge may be twofold as for example in the case
of the Oresund Bridge, for railway and highway traffic (Figure 1.2).
the bridge structural material, like masonry bridges, as used in the old days since the
Romans, timber bridges, metal bridges in steel or aluminium or in iron as adopted in
the nineteenth century, concrete bridges either in reinforced concrete or prestressed
concrete (more precisely, partially prestressed concrete as preferred nowadays) and,
more recently, composite steel‐concrete bridges.
the bridge structural system, which may be distinguished by:
–– the longitudinal structural system;
–– the transversal structural system.

The former, the longitudinal system, gives rise to beam bridges, frame bridges,
arch bridges and cable supported bridges; namely, cable‐stayed bridges and suspension bridges. The last, the transversal structural system, is characterized by the type
adopted for the cross section of the superstructure, namely slab, girder or box girder
bridges. A preliminary discussion on bridge structural systems is presented in next
section.

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(a)

Superstructure

270.00

P1 (SOUTH)
116.99

30.00
SPAN 1

P2
117.14

35.00
SPAN 2

P3
117.31

104.0

104.0

105.0

35.00
SPAN 3

P4
117.49

ORIGINAL
EARTHFILL

35.00
SPAN 4

P5
117.66

35.00
SPAN 5

P6
117.84

P7
118.01

104.0

104.0

102.0

35.00
SPAN 6

104.0

35.00
SPAN 7

P8

30.00
SPAN 8
118.19

P9 (NORTH)
118.34

103.7
103.0

AVERAGE
ROCK LEVEL
[m]

Abutment

Piers and foundations

(b)
11.40 m

0.50

3.60
Carriageway
HOR. ALIGN.

1.60
Sidewalk

2.05

0.50

0.40

0.96

0.75

2.5%

2.12

2.05

2.5%

C
L

0.40

3.60
Carriageway

0.30

0.50

0.20

1.60
Sidewalk

0.60

Main girder

2.80

2.80

Bearing

Cross girder

Figure 1.3  Section elevation and typical cross section of a bridge – The Lugela bridge in Mozambique, 2008. Superstructure (deck) and Substructure
(piers, abutments and foundations).

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6

Bridge Design: Concepts and Analysis
●●

Another type of classification is often adopted, according to:
–– the predicted lifetime of the bridge, namely temporary (made in general in wood or
steel) or definitive bridges.
–– the fixity of the bridge, namely fixed or movable bridges, like lift bridges if the deck
may be raised vertically rolling bridges if the deck rolls longitudinally, or swing
bridges if the deck rotates around a vertical axis.
–– the in‐plan geometry of the bridge, like straight, skew or curved bridges.

1.4 ­Bridge Typology
Different bridge typologies, namely concerning the longitudinal structural system or
the deck cross section, may be adopted with different structural materials. The concept
design of a bridge is developed mainly in Chapters 4 and 5, but a brief description of the
variety of bridge options is presented here in order to introduce the topics of Chapters 2
and 3 concerning the basic data and conditions for design.
Nowadays, a beam bridge is the most usual type where the deck is a simple slab, a beam
and slab (Figure 1.3) or a box girder deck. Beam bridges may be adopted in reinforced
concrete for small spans (l), generally up to 20 m, or in prestressed concrete or in steel‐
concrete composite decks (Figure 1.4) for spans up to 200 m or even more. The superstructure may have a single span, simply supported at the abutments, or multiple
continuous spans (Figure 1.5). Between these two cases, some other bridge solutions are
possible like multiple span decks, in which most of the spans are continuous, but some
spans have internal hinges like in the so called ‘Gerber’ type beam bridges, shown in
Figure 1.6. However, the general trend nowadays is to adopt, as far as possible, fully continuous superstructures, to reduce maintenance of the expansion joints and to improve
the earthquake resistance of the bridge if located in a seismic region. Continuous decks

more than 2000 m long have been adopted for beam bridges, either for road or rail bridges.
Yet, in long continuous bridges, the distance between expansion joints is generally
restricted to 300–600 m to reduce displacements at the expansion joints. In a beam bridge,
the connection between the superstructure and the piers is made by bearings, as in
Figure 1.3, which allow the relative rotations between the deck and the piers; the relative
longitudinal displacements between the deck and the piers may or may not be restricted,
depending on the flexibility and slenderness of the piers, as discussed in Chapters 4 and 7.
If the deck is rigidly connected to the piers, one has a frame bridge (Figure 1.7). The
superstructure may be rigidly connected to some piers and standing in some bearings,
allowing rotations, or rotations and displacements, between the deck and some of
other piers.
In frame bridges, the piers are in most cases vertical. However, frame bridges with
slant legs, exemplified in Figure 1.8a, are a possible option. For a frame bridge with slant
legs or arch bridges, the main condition for adopting these typologies is the load bearing capacity of the slopes of the valley to accommodate, with very small displacements,
the horizontal component H (the thrust of the arch) of the force reactions induced by
the structure, as shown in Figure 1.8b.
An arch is likely to be a very efficient type of structure, an aesthetically pleasant solution for long spans in deep valleys, provided the geological conditions are appropriate.
The ideal shape of the arch, if the load transferred from the deck is considered as a

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Introduction

Figure 1.4  Steel‐concrete composite plate girder decks: Approach viaducts three‐dimensional model
of the Sado River railway crossing, in Portugal (Figure 1.12).

uniformly distributed load q (valid for closed posts), is a second degree parabola because
the arch for the permanent load is free from bending moments. In this case, the arch is
only subjected to axial forces; that is, the arch follows the ‘pressure line’. It is easy to

show using simple static equilibrium (bending moment condition equal to zero at the
2
crown) that the thrust is given by H ql / 8 f .
Arch bridges may have different typologies and be made of different structural materials. In the old days, masonry arches made of stones were very often adopted for small
to medium span bridges. More recently, iron, steel and reinforced concrete bridges
replaced these solutions with spans going up to several hundred metres. One of the

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8

Bridge Design: Concepts and Analysis

(a)

l

(b)

l1

l2

l3

l4

l5

Figure 1.5  Beam bridges – Elevation and longitudinal model: (a) single span and (b) multiple spans.

Expansion joint
Internal hinge

Figure 1.6  Beam bridge – Gerber type.

(a)

(b)

(c)

Figure 1.7  Beam bridges – elevation view and longitudinal structural model: (a) single span, (b) and
(c) multiple spans.

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Introduction

(a)

(b)

H

H

Figure 1.8  A frame bridge with inclined (slant) legs: (a) Reis Magos Bridge and (b) longitudinal
structural model.

most beautiful arch bridges is Arrábida Bridge, in Oporto (Figure 1.9), designed at the
end of the 1950s, the beginning of the 1960s and opened to traffic in 1963. The bridge,
at the time the longest reinforced concrete arch bridge in the world, has a span of 270 m
and a rise of 54 m (  f/l = 1/5).
The arch bridge may have the deck working from above or from below, as shown in
Figures 1.10 and 1.11. This last solution is adopted for traversing rivers at low levels
above the water, with particular restrictions for the vertical clearance h for navigation
channels. The horizontal component of the reaction at the base of the arch, at the connection between the arch and the deck, is taken by the deck. A bowstring arch bridge is
the designation for this bridge type, in which the deck has a tie effect, together with its
beam behaviour. Figure 1.12 shows a multiple bowstring arch bridge, with a continuous
deck composed of a single steel box section. The deck, with spans of 160 m, is a steel‐
concrete composite box girder to allow the required torsion resistance under eccentric
traffic loading. However, the classical solution for bowstring arches is made of a beam
and slab deck suspended from above by two vertical or inclined arches, as presented in
Chapter 6.
The main restriction nowadays for the construction of arches is the difficulty of the
execution method, when compared to a long span frame bridge with vertical piers, built
by the balanced cantilever method referred to in Chapter 4.
For spans above 150 m and up to 1000 m, cable‐stayed bridges, as previously shown in
Figure 1.2, are nowadays generally preferred to beam or frame bridges, for which the

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10

Bridge Design: Concepts and Analysis

Figure 1.9  The Arrabida Bridge in Oporto, Portugal, 1963 (Source: Photograph by Joseolgon / https://
commons.wikimedia.org / Public Domain).

(a)

(b)
f (rise)

H

H

Spring line
l

(c)
crown
post

(d)

(e)

Figure 1.10  Arch bridges: (a) the classical parabolic two hinges arch bridge; (b) structural longitudinal
model; (c) independent arch and deck at the crown; (d) segmental arch and (e) low rise arch for a
pedestrian bridge without posts.

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