Bridge Design

Bridge Design

Concepts and Analysis

António J. ReisIST – University of Lisbon and Technical Director GRID Consulting EngineersLisbonPortugal

José J. Oliveira PedroIST – University of Lisbon and GRID Consulting EngineersLisbonPortugal

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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–dc23LC record available at https://lccn.loc.gov/2018041508

Cover Design: WileyCover Image: © Ana Isabel Silva

Set in 10/12pt Warnock by SPi Global, Pondicherry, India

Printed in the UK by Bell & Bain Ltd, Glasgow

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v

About the Authors xiiiPreface xvAcknowledgements xvii

1 Introduction 11.1 Generalities 11.2 Definitions and Terminology 11.3 Bridge Classification 41.4 Bridge Typology 61.5 Some Historical References 161.5.1 Masonry Bridges 161.5.2 Timber Bridges 181.5.3 Metal Bridges 181.5.4 Reinforced and Prestressed Concrete Bridges 241.5.5 Cable Supported Bridges 28 References 30

2 Bridge Design: Site Data and Basic Conditions 312.1 Design Phases and Methodology 312.2 Basic Site Data 322.2.1 Generalities 322.2.2 Topographic Data 322.2.3 Geological and Geotechnical Data 352.2.4 Hydraulic Data 362.2.5 Other Data 382.3 Bridge Location. Alignment, Bridge Length and Hydraulic Conditions 382.3.1 The Horizontal and Vertical Alignments 422.3.2 The Transverse Alignment 462.4 Elements Integrated in Bridge Decks 492.4.1 Road Bridges 492.4.1.1 Surfacing and Deck Waterproofing 502.4.1.2 Walkways, Parapets and Handrails 502.4.1.3 Fascia Beams 532.4.1.4 Drainage System 54

Contents

Contentsvi

2.4.1.5 Lighting System 552.4.1.6 Expansion Joints 552.4.2 Railway Decks 582.4.2.1 Track System 592.4.2.2 Power Traction System (Catenary System) 612.4.2.3 Footways, Parapets/Handrails, Drainage and Lighting Systems 61 References 61

3 Actions and Structural Safety 633.1 Types of Actions and Limit State Design 633.2 Permanent Actions 653.3 Highway Traffic Loading – Vertical Forces 683.4 Braking, Acceleration and Centrifugal Forces in Highway Bridges 723.5 Actions on Footways or Cycle Tracks and Parapets, of Highway Bridges 743.6 Actions for Abutments and Walls Adjacent

to Highway Bridges 753.7 Traffic Loads for Railway Bridges 763.7.1 General 763.7.2 Load Models 763.8 Braking, Acceleration and Centrifugal Forces in Railway Bridges:

Nosing Forces 773.9 Actions on Maintenance Walkways and Earth Pressure Effects

for Railway Bridges 783.10 Dynamic Load Effects 793.10.1 Basic Concepts 793.10.2 Dynamic Effects for Railway Bridges 823.11 Wind Actions and Aerodynamic Stability of Bridges 843.11.1 Design Wind Velocities and Peak Velocities Pressures 843.11.2 Wind as a Static Action on Bridge Decks and Piers 893.11.3 Aerodynamic Response: Basic Concepts 913.11.3.1 Vortex Shedding 943.11.3.2 Divergent Amplitudes: Aerodynamic Instability 953.12 Hydrodynamic Actions 983.13 Thermal Actions and Thermal Effects 993.13.1 Basic Concepts 993.13.2 Thermal Effects 1023.13.3 Design Values 1073.14 Shrinkage, Creep and Relaxation in Concrete Bridges 1093.15 Actions Due to Imposed Deformations. Differential Settlements 1173.16 Actions Due to Friction in Bridge Bearings 1193.17 Seismic Actions 1193.17.1 Basis of Design 1193.17.2 Response Spectrums for Bridge Seismic Analysis 1213.18 Accidental Actions 1243.19 Actions During Construction 1243.20 Basic Criteria for Bridge Design 125 References 125

Contents vii

4 Conceptual Design and Execution Methods 1294.1 Concept Design: Introduction 1294.2 Span Distribution and Deck Continuity 1314.2.1 Span Layout 1314.2.2 Deck Continuity and Expansion Joints 1324.3 The Influence of the Execution Method 1344.3.1 A Prestressed Concrete Box Girder Deck 1344.3.2 A Steel‐Concrete Composite Steel Deck 1364.3.3 Concept Design and Execution: Preliminary Conclusions 1364.4 Superstructure: Concrete Bridges 1384.4.1 Options for the Bridge Deck 1384.4.2 The Concrete Material – Main Proprieties 1394.4.2.1 Concrete 1394.4.2.2 Reinforcing Steel 1404.4.2.3 Prestressing Steel 1404.4.3 Slab and Voided Slab Decks 1424.4.4 Ribbed Slab and Slab‐Girder Decks 1444.4.5 Precasted Slab‐Girder Decks 1524.4.6 Box Girder Decks 1554.5 Superstructure: Steel and Steel‐Concrete Composite Bridges 1604.5.1 Options for Bridge Type: Plated Structures 1604.5.2 Steels for Metal Bridges and Corrosion Protection 1664.5.2.1 Materials and Weldability 1664.5.2.2 Corrosion Protection 1724.5.3 Slab Deck: Concrete Slabs and Orthotropic Plates 1734.5.3.1 Concrete Slab Decks 1744.5.3.2 Steel Orthotropic Plate Decks 1764.5.4 Plate Girder Bridges 1794.5.4.1 Superstructure Components 1794.5.4.2 Preliminary Design of the Main Girders 1824.5.4.3 Vertical Bracing System 1884.5.4.4 Horizontal Bracing System 1914.5.5 Box Girder Bridges 1924.5.5.1 General 1924.5.5.2 Superstructure Components 1934.5.5.3 Pre‐Design of Composite Box Girder Sections 1964.5.5.4 Pre‐Design of Diaphragms or Cross Frames 1994.5.6 Typical Steel Quantities 2014.6 Superstructure: Execution Methods 2024.6.1 General Aspects 2024.6.2 Execution Methods for Concrete Decks 2034.6.2.1 General 2034.6.2.2 Scaffoldings and Falseworks 2034.6.2.3 Formwork Launching Girders 2064.6.2.4 Incremental Launching 2064.6.2.5 Cantilever Construction 2124.6.2.6 Precasted Segmental Cantilever Construction 221

Contentsviii

4.6.2.7 Other Methods 2224.6.3 Erection Methods for Steel and Composite Bridges 2234.6.3.1 Erection Methods, Transport and Erection Joints 2234.6.3.2 Erection with Cranes Supported from the Ground 2244.6.3.3 Incremental Launching 2244.6.3.4 Erection by the Cantilever Method 2274.6.3.5 Other Methods 2274.7 Substructure: Conceptual Design and Execution Methods 2294.7.1 Elements and Functions 2294.7.2 Bridge Piers 2294.7.2.1 Structural Materials and Pier Typology 2294.7.2.2 Piers Pre‐Design 2324.7.2.3 Execution Method of the Deck and Pier Concept Design 2334.7.2.4 Construction Methods for Piers 2404.7.3 Abutments 2414.7.3.1 Functions of the Abutments 2414.7.3.2 Abutment Concepts and Typology 2414.7.4 Bridge Foundations 2454.7.4.1 Foundation Typology 2454.7.4.2 Direct Foundations 2454.7.4.3 Pile Foundations 2464.7.4.4 Special Bridge Foundations 2474.7.4.5 Bridge Pier Foundations in Rivers 250 References 251

5 Aesthetics and Environmental Integration 2555.1 Introduction 2555.2 Integration and Formal Aspects 2565.3 Bridge Environment 2565.4 Shape and Function 2585.5 Order and Continuity 2605.6 Slenderness and Transparency 2625.7 Symmetries, Asymmetries and Proximity

with Other Bridges 2665.8 Piers Aesthetics 2675.9 Colours, Shadows, and Detailing 2685.10 Urban Bridges 272 References 277

6 Superstructure: Analysis and Design 2796.1 Introduction 2796.2 Structural Models 2806.3 Deck Slabs 2836.3.1 General 2836.3.2 Overall Bending: Shear Lag Effects 2836.3.3 Local Bending Effects: Influence Surfaces 2876.3.4 Elastic Restraint of Deck Slabs 295

Contents ix

6.3.5 Transverse Prestressing of Deck Slabs 2976.3.6 Steel Orthotropic Plate Decks 3006.4 Transverse Analysis of Bridge Decks 3016.4.1 Use of Influence Lines for Transverse Load Distribution 3016.4.2 Transverse Load Distribution Coefficients for Load Effects 3026.4.3 Transverse Load Distribution Methods 3036.4.3.1 Rigid Cross Beam Methods: Courbon Method 3046.4.3.2 Transverse Load Distribution on Cross Beams 3076.4.3.3 Extensions of the Courbon Method: Influence of Torsional Stiffness

of Main Girders and Deformability of Cross Beams 3076.4.3.4 The Orthotropic Plate Approach 3086.4.3.5 Other Transverse Load Distribution Methods 3136.5 Deck Analysis by Grid and FEM Models 3136.5.1 Grid Models 3136.5.1.1 Fundamentals 3136.5.1.2 Deck Modelling 3156.5.1.3 Properties of Beam Elements in Grid Models 3176.5.1.4 Limitations and Extensions of Plane Grid Modelling 3186.5.2 FEM Models 3186.5.2.1 Fundamentals 3186.5.2.2 FEM for Analysis of Bridge Decks 3236.6 Longitudinal Analysis of the Superstructure 3296.6.1 Generalities – Geometrical Non‐Linear Effects: Cables and Arches 3296.6.2 Frame and Arch Effects 3326.6.3 Effect of Longitudinal Variation of Cross Sections 3346.6.4 Torsion Effects in Bridge Decks – Non‐Uniform Torsion 3366.6.5 Torsion in Steel‐Concrete Composite Decks 3436.6.5.1 Composite Box Girder Decks 3436.6.5.2 Composite Plate Girder Decks 3456.6.5.3 Transverse Load Distribution in Open Section Decks 3486.6.6 Curved Bridges 3506.6.6.1 Statics of Curved Bridges 3506.6.6.2 Simply Supported Curved Bridge Deck 3526.6.6.3 Approximate Method 3536.6.6.4 Bearing System and Deck Elongations 3536.7 Influence of Construction Methods on Superstructure Analysis 3556.7.1 Span by Span Erection of Prestressed Concrete Decks 3566.7.2 Cantilever Construction of Prestressed Concrete Decks 3576.7.3 Prestressed Concrete Decks with Prefabricated Girders 3606.7.4 Steel‐Concrete Composite Decks 3616.8 Prestressed Concrete Decks: Design Aspects 3646.8.1 Generalities 3646.8.2 Design Concepts and Basic Criteria 3646.8.3 Durability 3646.8.4 Concept of Partial Prestressed Concrete (PPC) 3646.8.5 Particular Aspects of Bridges Built by Cantilevering 3656.8.6 Ductility and Precasted Segmental Construction 366

Contentsx

6.8.6.1 Internal and External Prestressing 3676.8.7 Hyperstatic Prestressing Effects 3676.8.8 Deflections, Vibration and Fatigue 3686.9 Steel and Composite Decks 3736.9.1 Generalities 3736.9.2 Design Criteria for ULS 3736.9.3 Design Criteria for SLS 3756.9.3.1 Stress Limitations and Web Breathing 3766.9.3.2 Deflection Limitations and Vibrations 3776.9.4 Design Criteria for Fatigue Limit State 3776.9.5 Web Design of Plate and Box Girder Sections 3836.9.5.1 Web Under in Plane Bending and Shear Forces 3836.9.5.2 Flange Induced Buckling 3856.9.5.3 Webs Under Patch Loading 3876.9.5.4 Webs under Interaction of Internal Forces 3896.9.6 Transverse Web Stiffeners 3906.9.7 Stiffened Panels in Webs and Flanges 3916.9.8 Diaphragms 3946.10 Reference to Special Bridges: Bowstring Arches and Cable‐Stayed

Bridges 3956.10.1 Generalities 3956.10.2 Bowstring Arch Bridges 3966.10.2.1 Geometry, Slenderness and Stability 3966.10.2.2 Hanger System and Anchorages 4026.10.2.3 Analysis of the Superstructure 4036.10.3 Cable‐Stayed Bridges 4046.10.3.1 Basic Concepts 4046.10.3.2 Total and Partial Adjustment Staying Options 4086.10.3.3 Deck Slenderness, Static and Aerodynamic Stability 4116.10.3.4 Stays and Stay Cable Anchorages 4146.10.3.5 Analysis of the Superstructure 416 References 418

7 Substructure: Analysis and Design 4237.1 Introduction 4237.2 Distribution of Forces Between Piers and Abutments 4237.2.1 Distribution of a Longitudinal Force 4237.2.2 Action Due to Imposed Deformations 4247.2.3 Distribution of a Transverse Horizontal Force 4257.2.4 Effect of Deformation of Bearings and Foundations 4297.3 Design of Bridge Bearings 4307.3.1 Bearing Types 4307.3.2 Elastomeric Bearings 4307.3.3 Neoprene‐Teflon Bridge Bearings 4347.3.4 Elastomeric ‘Pot Bearings’ 4357.3.5 Metal Bearings 4377.3.6 Concrete Hinges 439

Contents xi

7.4 Reference to Seismic Devices 4417.4.1 Concept 4417.4.2 Seismic Dampers 4417.5 Abutments: Analysis and Design 4447.5.1 Actions and Design Criteria 4447.5.2 Front and Wing Walls 4467.5.3 Anchored Abutments 4487.6 Bridge Piers: Analysis and Design 4497.6.1 Basic Concepts 4497.6.1.1 Pre‐design 4497.6.1.2 Slenderness and Elastic Critical Load 4497.6.1.3 The Effect of Geometrical Initial Imperfections 4507.6.1.4 The Effect of Cracking in Concrete Bridge Piers 4507.6.1.5 Bridge Piers as ‘Beam Columns’ 4517.6.1.6 The Effect of Imposed Displacements 4527.6.1.7 The Overall Stability of a Bridge Structure 4537.6.1.8 Design Bucking Length of Bridge Piers 4537.6.2 Elastic Analysis of Bridge Piers 4547.6.3 Elastoplastic Analysis of Bridge Piers: Ultimate Resistance 4597.6.4 Creep Effects on Concrete Bridge Piers 4657.6.5 Analysis of Bridge Piers by Numerical Methods 4657.6.6 Overall Stability of a Bridge Structure 471 References 473

8 Design Examples: Concrete and Composite Options 4758.1 Introduction 4758.2 Basic Data and Bridge Options 4758.2.1 Bridge Function and Layout 4758.2.2 Typical Deck Cross Sections 4768.2.3 Piers, Abutments and Foundations 4778.2.4 Materials Adopted 4778.2.4.1 Prestressed Concrete Deck 4788.2.4.2 Steel‐concrete Composite Deck 4818.2.5 Deck Construction 4818.3 Hazard Scenarios and Actions 4818.3.1 Limit States and Structural Safety 4828.3.2 Actions 4828.3.2.1 Permanent Actions and Imposed Deformations 4828.3.2.2 Variable Actions 4848.4 Prestressed Concrete Solution 4868.4.1 Preliminary Design of the Deck 4868.4.2 Structural Analysis and Slab Checks 4868.4.3 Structural Analysis of the Main Girders 4928.4.3.1 Traffic Loads: Transverse and Longitudinal Locations 4938.4.3.2 Internal Forces 4978.4.3.3 Prestressing Layout and Hyperstatic Effects 4978.4.3.4 Influence of the Construction Stages 498

Contentsxii

8.4.4 Structural Safety Checks: Longitudinal Direction 4988.4.4.1 Decompression Limit State – Prestressing Design 4988.4.4.2 Ultimate Limit States – Bending and Shear Resistance 5018.5 Steel–Concrete Composite Solution 5028.5.1 Preliminary Design of the Deck 5028.5.2 Structural Analysis and Slab Design Checks 5038.5.3 Structural Analysis of the Main Girders 5038.5.3.1 Traffic Loads Transverse and Longitudinal Positioning 5048.5.3.2 Internal Forces 5058.5.3.3 Shrinkage Effects 5058.5.3.4 Imposed Deformation Effect 5068.5.3.5 Influence of the Construction Stages 5068.5.4 Safety Checks: Longitudinal Direction 5078.5.4.1 Ultimate Limit States – Bending and Shear Resistance 5078.5.4.2 Serviceability Limit States – Stresses and Crack Widths Control 509 References 510

Annex A: Buckling and Ultimate Strength of Flat Plates 511A.1 Critical Stresses and Buckling Modes of Flat Plates 511A.1.1 Plate Simply Supported along the four Edges and under

a Uniform Compression (ψ = 1) 511A.1.2 Bending of Long Rectangular Plates Supported at both Longitudinal Edges or

with a Free Edge 513A.1.3 Buckling of Rectangular Plates under Shear 513A.2 Buckling of Stiffened Plates 514A.2.1 Plates with One Longitudinal Stiffener at the Centreline under Uniform

Compression 515A.2.2 Plate with Two Stiffeners under Uniform Compression 516A.2.3 Plates with Three or More Longitudinal Stiffeners 517A.2.4 Stiffened Plates under Variable Compression. Approximate Formulas 518A.3 Post‐Buckling Behaviour and Ultimate Strength of Flat Plates 518A.3.1 Effective Width Concept 519A.3.2 Effective Width Formulas 520 References 523

Index 525

xiii

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, stadi-ums, 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.

About the Authors

xv

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 under-standing 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 environ-mental aspects are nowadays recognized as main engineering issues for bridge design-ers. 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 struc-tural 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

Preface

Prefacexvi

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 distri-bution 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 contrib-ute to bridges reflecting the ‘art of structural engineering’.

António J. Reis and José J. Oliveira PedroLisbon, May 2018

xvii

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 friend-ship 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 reproduc-tion 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 PedroLisbon, May 2018

Acknowledgements

1

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.

1

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

Introduction

Bridge Design: Concepts and Analysis2

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).

Introduction 3

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 suspen-sion 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).

Bridge Design: Concepts and Analysis4

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 exca-vated 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 designa-tions 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 suspen-sion 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.

35.00 35.00 35.00 35.00 35.00 30.0035.0030.00

270.00

116.99 117.14 117.31 117.49 117.66 117.84 118.01 118.19 118.34

105.0 104.0 102.0104.0 104.0 104.0 103.7

103.0

SPAN 2 SPAN 3 SPAN 4 SPAN 5 SPAN 6 SPAN 7 SPAN 8SPAN 1P3 P4 P5 P6 P7 P8P1 (SOUTH) P9 (NORTH)

P2

AVERAGEROCK LEVEL

ORIGINALEARTHFILL

104.0

[m]

Superstructure

Piers and foundations Abutment

(a)

1.60 1.60

2.12

0.30

0.20

2.05

2.05

0.40

0.40

0.75

2.5% 2.5%

11.40 m

3.60

HOR. ALIGN.LC

0.50 3.60 0.500.

500.

96

Sidewalk Carriageway SidewalkCarriageway

0.60

2.80 2.80Main girder BearingCross girder

(b)

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).

Bridge Design: Concepts and Analysis6

● 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 super-structure 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 con-tinuous 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 bear-ing 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 solu-tion 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

Introduction 7

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 crown) that the thrust is given by H ql f2 8/ .

Arch bridges may have different typologies and be made of different structural mate-rials. 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

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).

Bridge Design: Concepts and Analysis8

(a)

(b)

l1 l3 l5l2 l4

l

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

Internal hinge

Expansion joint

Figure 1.6 Beam bridge – Gerber type.

(b)

(c)

(a)

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

Introduction 9

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 con-nection 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

HH

(b)

(a)

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

Bridge Design: Concepts and Analysis10

(a)

crownpost

(c)l

H Hf (rise)

(b)

(d)

(e)

Spring line

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.

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