Design of Highway Bridges An LRFD Approach Third Edition Richard M Barker Jay A Puckett Cover Design: Elizabeth Brooks Cover Photograph: Courtesy of the National Steel Bridge Alliance This book is printed on acid-free paper Copyright © 2013 by John Wiley & Sons, Inc All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the web at www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at www.wiley.com/go/permissions Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with the respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation You should consult with a professional where appropriate Neither the publisher nor the author shall be liable for damages arising here from For general information about our other products and services, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002 Wiley publishes in a variety of print and electronic formats and by print-on-demand Some material included with standard print versions of this book may not be included in e-books or in print-on-demand If this book refers to media such as a CD or DVD that is not included in the version you purchased, you may download this material at http://booksupport.wiley.com For more information about Wiley products, visit www.wiley.com ISBN 978-0-470-90066-6; ISBN 978-1-118-33010-4 (ebk); ISBN 978-1-118-33283-2 (ebk); ISBN 978-1-118-33449-2 (ebk); ISBN 978-1-118-41112-4 (ebk); ISBN 978-1-118-41113-1 (ebk); ISBN 978-1-118-41115-5 (ebk) Printed in the United States of America 10 CONTENTS Preface Preface to the Second Edition Preface to the First Edition PART I GENERAL ASPECTS OF BRIDGE DESIGN CHAPTER INTRODUCTION TO BRIDGE ENGINEERING 1.1 1.2 CHAPTER xi xiii xv A Bridge Is the Key Element in a Transportation System Bridge Engineering in the United States 1.2.1 Stone Arch Bridges 1.2.2 Wooden Bridges 1.2.3 Metal Truss Bridges 1.2.4 Suspension Bridges 1.2.5 Metal Arch Bridges 1.2.6 Reinforced Concrete Bridges 1.2.7 Girder Bridges 1.2.8 Closing Remarks 1.3 Bridge Engineer—Planner, Architect, Designer, Constructor, and Facility Manager References Problems 3 10 12 13 14 SPECIFICATIONS AND BRIDGE FAILURES 17 2.1 2.2 17 18 18 Bridge Specifications Implication of Bridge Failures on Practice 2.2.1 Silver Bridge, Point Pleasant, West Virginia, December 15, 1967 2.2.2 I-5 and I-210 Interchange, San Fernando, California, February 9, 1971 2.2.3 Sunshine Skyway, Tampa Bay, Florida, May 9, 1980 2.2.4 Mianus River Bridge, Greenwich, Connecticut, June 28, 1983 2.2.5 Schoharie Creek Bridge, Amsterdam, New York, April 5, 1987 2.2.6 Cypress Viaduct, Loma Prieta Earthquake, October 17, 1989 14 15 15 19 21 22 24 25 iii iv CONTENTS 2.2.7 2.2.8 References Problems CHAPTER CHAPTER CHAPTER I-35W Bridge, Minneapolis, Minnesota, August 1, 2007 Failures During Construction 26 30 30 31 BRIDGE AESTHETICS 33 3.1 3.2 Introduction Nature of the Structural Design Process 3.2.1 Description and Justification 3.2.2 Public and Personal Knowledge 3.2.3 Regulation 3.2.4 Design Process 3.3 Aesthetics in Bridge Design 3.3.1 Definition of Aesthetics 3.3.2 Qualities of Aesthetic Design 3.3.3 Practical Guidelines for Medium- and Short-Span Bridges 3.3.4 Computer Modeling 3.3.5 Web References 3.3.6 Closing Remarks on Aesthetics References Problems 33 33 33 34 34 35 36 36 37 47 55 56 59 59 60 BRIDGE TYPES AND SELECTION 61 4.1 4.2 4.3 4.4 4.5 Main Structure below the Deck Line Main Structure above the Deck Line Main Structure Coincides with the Deck Line Closing Remarks on Bridge Types Selection of Bridge Type 4.5.1 Factors to Be Considered 4.5.2 Bridge Types Used for Different Span Lengths 4.5.3 Closing Remarks References Problems 61 61 64 66 66 66 69 72 72 73 DESIGN LIMIT STATES 75 5.1 5.2 75 75 75 76 76 77 77 77 79 80 81 81 82 82 82 Introduction Development of Design Procedures 5.2.1 Allowable Stress Design 5.2.2 Variability of Loads 5.2.3 Shortcomings of Allowable Stress Design 5.2.4 Load and Resistance Factor Design 5.3 Design Limit States 5.3.1 General 5.3.2 Service Limit State 5.3.3 Fatigue and Fracture Limit State 5.3.4 Strength Limit State 5.3.5 Extreme Event Limit State 5.4 Closing Remarks References Problems CONTENTS CHAPTER CHAPTER v PRINCIPLES OF PROBABILISTIC DESIGN 83 6.1 Introduction 6.1.1 Frequency Distribution and Mean Value 6.1.2 Standard Deviation 6.1.3 Probability Density Functions 6.1.4 Bias Factor 6.1.5 Coefficient of Variation 6.1.6 Probability of Failure 6.1.7 Safety Index β 6.2 Calibration of LRFD Code 6.2.1 Overview of the Calibration Process 6.2.2 Calibration Using Reliability Theory 6.2.3 Calibration of Fitting with ASD 6.3 Closing Remarks References Problems 83 83 83 84 85 85 86 87 89 89 89 93 94 94 94 GEOMETRIC DESIGN CONSIDERATIONS 95 7.1 Introduction to Geometric Roadway Considerations 7.2 Roadway Widths 7.3 Vertical Clearances 7.4 Interchanges References Problem 95 95 96 96 97 97 PART II LOADS AND ANALYSIS CHAPTER LOADS 101 8.1 8.2 101 101 101 102 114 114 118 122 127 127 129 129 129 129 129 129 129 130 130 131 Introduction Gravity Loads 8.2.1 Permanent Loads 8.2.2 Transient Loads 8.3 Lateral Loads 8.3.1 Fluid Forces 8.3.2 Seismic Loads 8.3.3 Ice Forces 8.4 Forces Due to Deformations 8.4.1 Temperature 8.4.2 Creep and Shrinkage 8.4.3 Settlement 8.5 Collision Loads 8.5.1 Vessel Collision 8.5.2 Rail Collision 8.5.3 Vehicle Collision 8.6 Blast Loading 8.7 Summary References Problems vi CONTENTS CHAPTER CHAPTER 10 CHAPTER 11 CHAPTER 12 INFLUENCE FUNCTIONS AND GIRDER-LINE ANALYSIS 133 9.1 9.2 9.3 Introduction Definition Statically Determinate Beams 9.3.1 Concentrated Loads 9.3.2 Uniform Loads 9.4 Muller–Breslau Principle 9.4.1 Betti’s Theorem 9.4.2 Theory of Muller–Breslau Principle 9.4.3 Qualitative Influence Functions 9.5 Statically Indeterminate Beams 9.5.1 Integration of Influence Functions 9.5.2 Relationship between Influence Functions 9.5.3 Muller–Breslau Principle for End Moments 9.5.4 Automation by Matrix Structural Analysis 9.6 Normalized Influence Functions 9.7 AASHTO Vehicle Loads 9.8 Influence Surfaces 9.9 Summary References Problems 133 133 134 134 136 137 137 138 139 139 142 143 145 146 147 149 156 157 157 157 SYSTEM ANALYSIS—INTRODUCTION 161 10.1 Introduction 10.2 Safety of Methods 10.2.1 Equilibrium for Safe Design 10.2.2 Stress Reversal and Residual Stress 10.2.3 Repetitive Overloads 10.2.4 Fatigue and Serviceability 10.3 Summary References Problem 161 162 162 165 165 169 170 170 170 SYSTEM ANALYSIS—GRAVITY LOADS 171 11.1 Slab–Girder Bridges 11.2 Slab Bridges 11.3 Slabs in Slab–Girder Bridges 11.4 Box-Girder Bridges 11.5 Closing Remarks References Problems 171 194 198 206 212 213 213 SYSTEM ANALYSIS—LATERAL, TEMPERATURE, SHRINKAGE, AND PRESTRESS LOADS 215 12.1 Lateral Load Analysis 12.1.1 Wind Loads 12.1.2 Seismic Load Analysis 12.2 Temperature, Shrinkage, and Prestress 12.2.1 General 12.2.2 Prestressing 215 215 216 221 221 221 CONTENTS 12.2.3 Temperature Effects 12.2.4 Shrinkage and Creep 12.3 Closing Remarks References vii 222 225 225 225 PART III CONCRETE BRIDGES CHAPTER 13 REINFORCED CONCRETE MATERIAL RESPONSE AND PROPERTIES 229 13.1 13.2 13.3 13.4 Introduction Reinforced and Prestressed Concrete Material Response Constituents of Fresh Concrete Properties of Hardened Concrete 13.4.1 Short-Term Properties of Concrete 13.4.2 Long-Term Properties of Concrete 13.5 Properties of Steel Reinforcement 13.5.1 Nonprestressed Steel Reinforcement 13.5.2 Prestressing Steel References Problems 229 229 230 232 232 238 242 242 244 246 246 BEHAVIOR OF REINFORCED CONCRETE MEMBERS 249 14.1 Limit States 14.1.1 Service Limit State 14.1.2 Fatigue Limit State 14.1.3 Strength Limit State 14.1.4 Extreme Event Limit State 14.2 Flexural Strength of Reinforced Concrete Members 14.2.1 Depth to Neutral Axis for Beams with Bonded Tendons 14.2.2 Depth to Neutral Axis for Beams with Unbonded Tendons 14.2.3 Nominal Flexural Strength 14.2.4 Ductility, Maximum Tensile Reinforcement, and Resistance Factor Adjustment 14.2.5 Minimum Tensile Reinforcement 14.2.6 Loss of Prestress 14.3 Shear Strength of Reinforced Concrete Members 14.3.1 Variable-Angle Truss Model 14.3.2 Modified Compression Field Theory 14.3.3 Shear Design Using Modified Compression Field Theory 14.4 Closing Remarks References Problems 249 249 252 255 256 257 257 259 260 262 264 265 270 271 272 278 289 289 290 CONCRETE BARRIER STRENGTH AND DECK DESIGN 291 15.1 Concrete Barrier Strength 15.1.1 Strength of Uniform Thickness Barrier Wall 15.1.2 Strength of Variable Thickness Barrier Wall 15.1.3 Crash Testing of Barriers 15.2 Concrete Deck Design References Problems 291 291 293 293 293 311 311 CHAPTER 14 CHAPTER 15 viii CONTENTS CHAPTER 16 CONCRETE DESIGN EXAMPLES 313 16.1 Solid Slab Bridge Design 16.2 T-Beam Bridge Design 16.3 Prestressed Girder Bridge References 313 321 340 359 PART IV STEEL BRIDGES CHAPTER 17 STEEL BRIDGES 363 17.1 Introduction 17.2 Material Properties 17.2.1 Steelmaking Process: Traditional 17.2.2 Steelmaking Process: Mini Mills 17.2.3 Steelmaking Process: Environmental Considerations 17.2.4 Production of Finished Products 17.2.5 Residual Stresses 17.2.6 Heat Treatments 17.2.7 Classification of Structural Steels 17.2.8 Effects of Repeated Stress (Fatigue) 17.2.9 Brittle Fracture Considerations 17.3 Summary References Problem 363 363 363 365 365 365 365 366 366 370 372 374 374 375 LIMIT STATES AND GENERAL REQUIREMENTS 377 18.1 Limit States 18.1.1 Service Limit State 18.1.2 Fatigue and Fracture Limit State 18.1.3 Strength Limit States 18.1.4 Extreme Event Limit State 18.2 General Design Requirements 18.2.1 Effective Length of Span 18.2.2 Dead-Load Camber 18.2.3 Minimum Thickness of Steel 18.2.4 Diaphragms and Cross Frames 18.2.5 Lateral Bracing References Problems 377 377 378 389 389 390 390 390 390 390 390 391 391 STEEL COMPONENT RESISTANCE 393 19.1 Tensile Members 19.1.1 Types of Connections 19.1.2 Tensile Resistance—Specifications 19.1.3 Strength of Connections for Tension Members 19.2 Compression Members 19.2.1 Column Stability—Behavior 19.2.2 Inelastic Buckling—Behavior 19.2.3 Compressive Resistance—Specifications 19.2.4 Connections for Compression Members 393 393 393 396 396 396 398 399 401 CHAPTER 18 CHAPTER 19 CONTENTS ix 19.3 I-Sections in Flexure 19.3.1 General 19.3.2 Yield Moment and Plastic Moment 19.3.3 Stability Related to Flexural Resistance 19.3.4 Limit States 19.3.5 Summary of I-Sections in Flexure 19.3.6 Closing Remarks on I-Sections in Flexure 19.4 Shear Resistance of I-Sections 19.4.1 Beam Action Shear Resistance 19.4.2 Tension Field Action Shear Resistance 19.4.3 Combined Shear Resistance 19.4.4 Shear Resistance of Unstiffened Webs 19.5 Shear Connectors 19.5.1 Fatigue Limit State for Stud Connectors 19.5.2 Strength Limit State for Stud Connectors 19.6 Stiffeners 19.6.1 Transverse Intermediate Stiffeners 19.6.2 Bearing Stiffeners References Problems 402 402 405 411 421 424 424 427 427 429 431 432 432 433 434 438 438 440 441 442 STEEL DESIGN EXAMPLES 443 20.1 Noncomposite Rolled Steel Beam Bridge 20.2 Composite Rolled Steel Beam Bridge 20.3 Multiple-Span Composite Steel Plate Girder Beam Bridge References 443 452 461 499 APPENDIX A INFLUENCE FUNCTIONS FOR DECK ANALYSIS 501 APPENDIX B TRANSVERSE DECK MOMENTS PER AASHTO APPENDIX A4 503 APPENDIX C METAL REINFORCEMENT INFORMATION 505 APPENDIX D REFINED ESTIMATE OF TIME-DEPENDENT LOSSES References 512 NCHRP 12-33 PROJECT TEAM Task Groups 513 LIVE-LOAD DISTRIBUTION—RIGID METHOD 515 CHAPTER 20 APPENDIX E APPENDIX F INDEX 507 513 517 PREFACE The objective of the third edition is the same as the first two editions, that is, to provide the student or practitioner a meaningful introduction to the design of medium-and short-span girder bridges However, the manner in which the material is presented has changed Instead of the eight chapters of the second edition, the content has been spread out over twenty shorter chapters This organization should lead to easier reading and simpler organization of classroom assignments To help understand how these changes have come about, it is informative to see how the process all started It was in August 1990 that the two authors were at an International Conference on Short and Medium Span Bridges in Toronto, Canada, where both were presenting papers They had often met at these bridge conferences and were familiar with each other’s work—Puckett’s on analysis and software development and Barker’s fundamental application of LRFD to geotechnical materials Both were classroom teachers in structural engineering At the time, a number of major changes were taking place in the design of highway bridges Philosophically the most dramatic was the change from a deterministic (allowable stress) design approach to a probabilistic (limit state) design concepts The other big change was a government edict that highway bridges that were built with federal dollars had to be constructed and designed in the metric system starting in 1997 The timing was right for a comprehensive textbook on the design of highway bridges The American Association of State Highway and Transportation Officials (AASHTO) were in the midst of a complete rewriting of their Bridge Design Specifications in a LRFD format Finite-element analysis tools had matured, truck loads were better understood through weigh-in-motion studies, material behavior was being unified for prestressed and non-prestressed concrete by the American Concrete Institute (ACI), postbuckling strength of plate girder webs and fatigue strength of weld details were better understood The two professors decided that someone needed to write a textbook to present these changes to students and practicing civil engineers So over dinner and a major league baseball game, they realized they could be the ones to the writing Puckett took his sabbatical with Barker at Virginia Tech in 1993, they wrote trial chapters, prepared a proposal that was accepted by John Wiley & Sons, and the first edition with ten chapters was published in 1997 It was not long before the metric system requirement was dropped and the highway bridge designers needed a textbook written in U.S Customary Units Therefore, it became necessary to make revisions and to prepare a second edition of the book Besides the units change, the LRFD specifications were in their third edition and the textbook needed to be updated As new material was added, the number of pages was deemed too large and two chapters were dropped—Wood Bridges and Substructure Design These two topics are found only in the metric system units of the first edition The remaining eight chapters of the second edition have been divided into four parts: General Aspects of Bridge Design (Chapters 1–7), Loads and Analysis (Chapters 8–12), Concrete Bridges (Chapters 13–16), and Steel Bridges (Chapters 17–20) Another change in the layout of the third edition is the addition of an insert of mainly color bridge photos These photos have been selected to illustrate bridges of historical significance; the ones most aesthetically pleasing that are most beautiful in their surroundings, and noteworthy as the longest, tallest, or highest bridges of their type We suggest that a first course in bridges be based on Chapters 1–7 with Chapters 5, 6, and compulsory reading Loads and analysis should follow with required reading in Chapter and selected portions of Chapter and 10 depending upon the students’ background and instructor’s interest Design can be addressed with either the chapters on concrete (Chapters 13–16) or those on steel (Chapters 17–20) Instructor guidance is required to lead the student through these chapters and to address the topics of most interest For example, concrete bridges could be addressed with nonprestressed bridges which would simplify the topic However, teaching prestressed concrete within a bridge context could be an excellent way for students to gain xi 514 E NCHRP 12-33 PROJECT TEAM Steel Structures Frank D Sears, Chair John Barsom Karl Frank Wei Hsiong William McGuire Dennis R Mertz Roy L Mion Charles G Schilling Ivan M Viest Michael A Grubb Wood Structures Andrzej S Nowak, Chair Baidar Bakht R Michael Caldwell Donald J Flemming Hota V S Gangarao Joseph F Murphy Michael A Ritter Raymond Taylor Thomas G Williamson Bridge Railings Ralph W Bishop, Chair Eugene Buth James H Hatton, Jr Teddy J Hirsch Robert A Pege Joints, Bearings and Accessories Charles W Purkiss, Chair Ian G Buckle John J Panak David Pope Charles W Roeder John F Stanton Earthquake Provisions Advisory Group Ian Buckle, Chair Robert Cassano James Cooper James Gates Roy Imbsen Geoffrey Martin Aluminum Structures Frank D Sears, Chair Teoman Pekoz Foundations J Michael Duncan, Co-Chair Richard M Barker, Co-Chair Deck Systems Paul F Csagoly, Chair Barrington deVere Batchelor Daniel H Copeland Gene R Gilmore Richard E Klingner Roman Wolchuk Buried Structures James Withiam, Chair Edward P Voytko Walls, Piers and Abutments J Michael Duncan, Co-Chair Richard M Barker, Co-Chair James Withiam Calibration Andrzej S Nowak, Chair C Allin Cornell Dan M Frangopol Theodore V Galambos Roger Green Fred Moses Kamal B Rojiani NL = number of lanes loaded xi = location of beam i in the cross section et = location of truck/lane in the cross section X ext = location of the exterior girder of interest APPENDIX F Consider one loaded lane positioned to the left side of the bridge: Live-Load Distribution— Rigid Method SE gmoment = NL Nb = Xext + + et trucks xi2 Nb 20 (17) + 122 + 202 = 0.470 The multiple presence factor is m = 1.2, therefore SE mgmoment = 1.2 (0.470) = 0.564 The live-load distribution factor method for moment to the exterior girders is provided in [A 4.6.2.2.d] Unlike the other equations and methods for other actions and locations of analysis, this article specifies the so-called rigid method Here the bridge cross section is assumed to be rigid as illustrated in Figure F.1 It is possible under this assumption that the distribution factor could be greater than that based upon lever rule or formulas This appendix demonstrates the rigid method computation without undue distraction from the other more commonly used methods The AASHTO requirements for the rigid method are outlined in [C4.6.2.2.2d-1], which is summarized below The procedure parallels that commonly used for load distribution to piles topped with a rigid cap, to bolts in a group connected with a stiff plate, or shear walls joined by a rigid floor diaphragm in a building: R= NL Nb Xext + et trucks xi2 Nb where: R = reaction to the exterior girder Nb = number of beams/girders in the bridge cross section Note the formula value from Example 6.2 is 0.55 lanes/girder Thus, the rigid method controls, slightly over the formula in this case Next consider two trucks positioned to the left side of the bridge The rigid method distribution factor is ME gmoment = NL Nb = Xext + + et trucks xi2 Nb 20 (17 + 9) 42 + 122 + 202 = 0.780 The multiple presence factor for two lanes loaded is m = 1.0, therefore SE mgmoment = 1.0 (0.780) = 0.780 The formula method of Example 6.2 for multiple lanes loaded is 0.71 The addition of a third truck combined with the multiple presence factor of m = 0.85 will not control over the two-lane case The rigid method controls slightly over the formula in this case Design of Highway Bridges , Third Edition Richard M Barker and Jay A Puckett © 2013 John Wiley & Sons, Inc Published 2013 by John Wiley & Sons, Inc 515 516 F LIVE-LOAD DISTRIBUTION—RIGID METHOD 2'-0" 3'-3" 6'-0" 2'-0" 6'-0" 8'-0" 8'-0" 6'-0" 4'-0" 20'-0" Fig F.1 (a) Slab–girder bridge cross section (same as Example 6.2) INDEX AASHO, see American Association of State Highway Officials Abutments: integral, 51–52, 55–58 for medium- and short-span bridges, 51–55 Addis, W., 35 ADT (average daily traffic), 107 Advanced first-order second-moment (AFOSM) method, 90–91 Aerodynamic instability, 63 Aesthetics, 36–59 and computer modeling, 56–59 contrast and texture in, 44–46 defined, 36–37 function in, 37–38 harmony in, 41–43 light and shadow in, 44, 46–47 for medium- and short-span bridges, 47–55 abutments, 51–55 deck overhangs, 49–50 girder span/depth ratio, 49–50 integral abutments and jointless bridges, 51–52, 55–58 piers, 50–53 resolution of duality, 47–49 order and rhythm in, 43–44 proportion in, 38–41 in selection of bridge type, 67 symmetry in, 147 Web references on, 56, 59 AISC (American Institute for Steel Construction), 149 Allowable stress design (ASD), 17 calibration with ASD criteria, 93–94 evolution of specifications, 75–76 shortcomings of, 76–77 and variability of loads, 76 Alvord Lake Bridge, San Francisco, 12 Ambassador Bridge, Detroit, Michigan, 9, 10 American Association of State Highway and Transportation Officials (AASHTO), 17 distribution factors, 175–178 and margin of safety, 75 A Policy on the Geometric Design of Highways and Streets, 95 strip widths, 198–199 American Association of State Highway Officials (AASHO), 17 American Bridge Company, American Institute for Steel Construction (AISC), 149 American Railroad Engineering Association (AREA), 17 American Railway Engineering and Maintenance of Way Association, 18 American Society of Civil Engineers (ASCE), 17 Anchorage set loss of prestress (concrete), 266 Arch bridges: for long spans, 71 with main structure below deck line, 61, 62 Marsh rainbow arch, 13 metal, 10–12 reinforced concrete, 12–13 span lengths for, 67 stone, 3–4 wooden, Arched trusses, 4, AREA (American Railroad Engineering Association), 17 Arlington Memorial Bridge, Washington DC, 12 ASCE (American Society of Civil Engineers), 17 Aspdin, Joseph, 17 Assumptions: in composite rolled steel beam bridge design problem, 460–461 in noncomposite rolled steel beam bridge design problem, 452 in system analysis, 161–162 Average daily traffic (ADT), 107 Average daily truck traffic (ADTT), 107 Axial strain: in flexibility and stiffness formulations, 223–225 temperature-gradient-induced, 222–223 Barriers: concrete barrier strength, 291–293 concrete deck design problem, 304–311 bending moment force effects, 295 critical length of yield line failure pattern, 306–307 flexural resistance of wall about axis parallel to longitudinal axis of bridge, 306 about vertical axis, 305–306 length of additional deck overhang bars, 310 nominal resistance to transverse load, 307 shear transfer between barrier and deck, 307–308 top reinforcement in deck overhang, 309–310 crash testing of, 293 traffic barrier design loads, 108–109 for uniform thickness barrier wall, 291–293 for variable thickness barrier wall, 293 Bayonne Arch Bridge, New Jersey, 11 Beam action shear resistance (I-sections), 427, 429 Beam columns, 396, 402 Beam-line analysis: box-girder bridges, 208–211 slab-girder bridges, 174–182 Bearing stiffeners: multiple-span composite steel plate girder beam bridge design problem, 490–493 steel bridges, 440–441 Bear Mountain Bridge, New York, Bending moment: concrete deck design problem, 294–295 barrier, 295 deck slab, 294–295 future wearing surface, 295 overhang, 295 of I-sections, 405 Bending stress profile, 161 Ben Franklin Bridge, Philadelphia, Pennsylvania, 9, 10 Betti’s theorem, 137 Bias factor, 85 Billner, K R., 12 Bixby Creek Bridge, Carmel, California, 13 Blast loading, 129–130 BMS (bridge management systems), 15 Bosporus Straits Bridge, Istanbul, Turkey, 37–38 Bowstring arch, 10 Bowstring arch trusses, Box-girder bridges, 64–67 configurations, 206–207 gravity load analysis, 206–212 beam-line methods, 208–211 behavior, structural idealization, and modeling, 206–208 finite-element method, 208, 211–212 modeling, 173–174 Braking forces, gravity loads from, 113 Bridges, classification of, 61–72 as key transportation system elements, subsystems of, 161 Bridge Aesthetics Around the World (Burke), 36 Bridge engineers, 14–15 Design of Highway Bridges , Third Edition Richard M Barker and Jay A Puckett © 2013 John Wiley & Sons, Inc Published 2013 by John Wiley & Sons, Inc 517 518 INDEX Bridge engineering, 3–30 failure of bridges, 18–30 during construction, 30 Cypress Viaduct, California, 25–26 I-5 and I-210 interchange, San Fernando, California, 19–21 I-35W Bridge, Minneapolis, Minnesota, 26–30 Mianus River Bridge, Greenwich, Connecticut, 22–23 Schoharie Creek Bridge, Amsterdam, New York, 24–25 Silver Bridge, Point Pleasant, West Virginia, 18–19 Sunshine Skyway, Tampa Bay, Florida, 21–22 girder bridges, 13–14 metal arch bridges, 10–12 metal truss bridges, 6–7 reinforced concrete bridges, 12–13 specifications, 17–18 stone arch bridges, 3–4 suspension bridges, 8–10 wooden bridges, 4–6 Bridge management systems (BMS), 15 Bridgescape (Gottemoeller), 36 Bridge types, 61–72 for different span lengths, 69–72 girder bridges, 13–14 with main structure: above the deck line, 61, 63–64 below the deck line, 61, 62 coinciding with deck line, 64–67 metal arch bridges, 10–12 metal truss bridges, 6–7 reinforced concrete bridges, 12–13 selection of, 66–69 specifications, 17–18 stone arch bridges, 3–4 suspension bridges, 8–10 wooden bridges, 4–6 Brittle fracture (steel bridges), 372–373 Broadway Bridge, Daytona, Florida, 55, 56 Brooklyn Bridge, New York, 8, 9, 11, 45, 61, 68 BT Beam-LRFD Analysis, 154 Buckling, 398–399 global, 411 lateral torsional, 411, 417–420 local, 411–417 compression flange, 416–417 web bend buckling, 414–415 web buckling load shedding, 415–416 web vertical buckling, 413–414 Burr, Theodore, Cable-stayed bridges: for extra-large spans, 71–72 with main structure above deck line, 61, 63–64 span lengths for, 67 CAD (computer-aided drafting), 33 Calibration of LRFD code, 89–94 for fitting with ASD, 93–94 using reliability theory, 89–93 Caltrans, 113–114 Camber: composite rolled steel beam bridge design problem, 460, 461 noncomposite rolled steel beam bridge design problem, 452 prestressed concrete girder bridge design problem, 350–352 steel bridges, 390 T-beam bridge design problem, 331–333 Canyon Padre Bridge, Flagstaff, Arizona, 12 Carbon structural steel, 368–369 Casey, Edward, 12 Cast-in-place (CIP) concrete: box girders, 229 bridges, 229 posttensioned concrete box girder bridges, 70, 71 reinforced concrete box girder bridges, 70 Cedar Creek Bridge, Elgin, Kansas, 13 Centrifugal forces, gravity loads from, 112–113 Charettes, 55 Chenoweth, Lemuel, Cincinnati Suspension Bridge, Ohio, 8, Coefficient of variation, 85 Collision loads, 129 Colorado Street Bridge, Pasadena, California, 12 Columns, 396 compressive resistance, 399–401 stability of, 396–398 Combined shear resistance (I-sections), 431–432 Compatibility, 161, 229–230 Composite rolled steel beam bridges: design problem, 452–461 checking assumptions, 460–461 dead-load camber, 460, 461 design sketch, 461 dimensions and details requirements, 460 flexural design, 454–459 force effects from non-live loads, 453–454 shear connectors, 459–460 shear design, 459 for medium spans, 70 Composite sections, 404 defined, 404 ductility of, 421 noncompact, 42 plastic moment of, 408–409 plastic neutral axis of, 407–408 yield moment of, 405–407 Composite steel bridges: box girder, 70–71 plate girder: multiple-span, bridge design problem, 462–499 for small and medium spans, 70–71 Compression field theory, 273 Compression flange: local buckling, 416–417 requirements for specifications, 417 section requirement for, 416–417 slenderness specifications, 417 Compression members: defined, 396 steel bridges, 396–401 column stability behavior, 396–398 compressive resistance, 399–401 connections for, 401 inelastic buckling behavior, 398–399 Compression softening (concrete), 233, 276 Compressive resistance (steel bridges), 399–401 Compressive strength: of aged concrete, 238 of confined hardened concrete, 233–236 of hardened concrete, 232–242 testing, of very-high-strength concrete, 231 Computer-aided drafting (CAD), 33 Computer modeling, aesthetics with, 56–59 Concentrated loads: axle, 17 influence functions for statically determinate beams, 134–136 Concentric loading, 161 Conceptual design stage, 35 Concrete, 229 classes of, 230 compression softening of, 276 creep in, 129, 225, 508–511 fatigue of, 252–253 fresh, 230–232 hardened, 232–242 compressive strength and behavior, 232–233 concrete tensile strength and behavior, 236–237 confined concrete compressive strength and behavior, 233–236 long-term properties of, 238–242 modulus of elasticity for, 241–242 short-term properties of, 232–237 high-performance, 231–232 modulus of elasticity for, 233 shrinkage in, 225 stress limitations for, 250–251 stress limits for, 344–345 very-high-strength, 231 water/cement ratio, 230–231 Concrete arch bridges, 71 Concrete barrier strength, 291–293 concrete deck design problem, 304–311 critical length of yield line failure pattern, 306–307 flexural resistance of wall about axis parallel to longitudinal axis of bridge, 306 about vertical axis, 305–306 length of additional deck overhang bars, 310 nominal resistance to transverse load, 307 shear transfer between barrier and deck, 307–308 top reinforcement in deck overhang, 309–310 crash testing of, 293 for uniform thickness barrier wall, 291–293 external virtual work by applied loads, 292 internal virtual work along yield lines, 292–293 nominal railing resistance to transverse load, 293 for variable thickness barrier wall, 293 Concrete bridges, 229–359 box girder, 64–67 concrete barrier strength, 291–293 crash testing of, 293 for uniform thickness barrier wall, 291–293 for variable thickness barrier wall, 293 design problems, 293–311 concrete deck, 293–311 prestressed girder bridge, 340–359 solid slab bridge, 313–321 T-beam bridge, 321–339 flexural strength of reinforced concrete members, 257–270 depth to neutral axis for beams with bonded tendons, 257–259 depth to neutral axis for beams with unbonded tendons, 259–260 INDEX ductility, maximum tensile reinforcement, and resistance factor adjustment, 262–264 loss of prestress, 265–270 minimum tensile reinforcement, 264–265 nominal flexural strength, 260–262 fresh concrete constituents, 230–232 hardened concrete properties, 232–242 long-term, 238–242 short-term, 232–237 limit states, 249–252 extreme event limit state, 256 fatigue limit state, 252–255 service limit state, 249–252 strength limit state, 255–256 for long spans, 71 for medium spans, 70 reinforced and prestressed concrete material response, 229–230 reinforced concrete, 12–13 shear strength of reinforced concrete members, 270–288 modified compression field theory, 272–278 shear design using modified compression field theory, 278–288 variable-angle truss model, 271–272 for small spans, 69–70 steel-reinforced concrete properties, 242–246 nonprestressed steel reinforcement, 242–244 prestressing steel, 244–246 Concrete deck design problem, 293–311 bending moment force effects, 294–295 barrier, 295 deck slab, 294–295 future wearing surface, 295 overhang, 295 concrete barrier strength, 304–311 critical length of yield line failure pattern, 306–307 flexural resistance of wall about axis parallel to longitudinal axis of bridge, 306 about vertical axis, 305–306 length of additional deck overhang bars, 310 nominal resistance to transverse load, 307 shear transfer between barrier and deck, 307–308 top reinforcement in deck overhang, 309–310 cracking control, 300–302 deck overhang design, 303–304 extreme event limit state, 304 strength limit state, 303–304 deck thickness, 294 empirical design of deck slabs, 302–303 design conditions, 302–303 reinforcement requirements, 303 fatigue limit state, 302 reinforcement quantifies, comparison of, 303 reinforcement selection, 298–300 distribution reinforcement, 300 negative moment reinforcement, 300 positive moment reinforcement, 299–300 shrinkage and temperature reinforcement, 300 strength limit state, 297–298 barrier, 298 deck slab, 298 future wearing surface, 298 live load, 298 overhang, 298 strength I limit state, 298 traditional design for interior spans, 302 vehicular live load, 296–297 maximum interior negative live-load moment, 297 maximum live-load reaction on exterior girder, 297 maximum positive live-load moment, 296–297 overhang negative live-load moment, 296 weights of components, 294 Construction: failure of bridges during, 30 as type selection criterion, 68 Contrast, in aesthetic design, 44–46 Cooper, Theodore, 17 Cooper series loading, 17, 18 Covell, Vernon R., 13 Cracking control: in concrete bridges, 249–250 concrete deck design problem, 300–302 solid slab bridge design problem, 316–317 T-beam bridge design problem, 327–330 Crash testing (concrete barriers), 293 Creative design stage, 35 Creep, 129, 225, 240–241 deformations due to, 129 girder concrete between transfer and deck placement, 508–511 in system analysis, 225 Critical load placement, 149 Cross frames: multiple-span composite steel plate girder beam bridge design problem, 496–499 steel bridges, 390 Culverts: precast, 229 for small spans, 69 Curvature: in flexibility and stiffness formulations, 223–225 temperature-gradient-induced, 223 Cyclic loads, 166–167 Cypress Viaduct, California, 25–26 Data gathering design stage, 35 Dead load: of earth fills, 102 of structural components and nonstructural attachments, 101–102 of wearing surface, 102 Dead-load camber: composite rolled steel beam bridge design problem, 460, 461 noncomposite rolled steel beam bridge design problem, 452 Deck: gravity loads, 107–109 multiple-span composite steel plate girder beam bridge design problem, 462 noncomposite rolled steel beam bridge design problem, 443 prestressed concrete girder bridge design problem, 340–341 thickness of, in concrete deck design problem, 294 transverse deck moments, 503–504 Deck analysis, influence functions for, 501–502 519 Deck overhang: concrete deck design problem, 303–304 bending moment force effects, 295 extreme event limit state, 304 length of additional overhang bars, 310 strength limit state, 303–304 top reinforcement in, 309–310 design loads, 108 for medium- and short-span bridges, 49–50 Deck slabs: bending moment force effects, 294–295 empirical design of, 302–303 design conditions, 302–303 reinforcement requirements, 303 Deductive reasoning, 34 Deflection: prestressed concrete girder bridge design problem, 350–352 steel bridges, 377 T-beam bridge design problem, 331–333 Deformations: concrete bridges, 250 forces due to, 127–129 from creep and shrinkage, 129 from settlement, 129 from temperature, 127–129 solid slab bridge design problem, 317–319 steel bridges, 377–378 Delafield, Richard, 10 De Miranda, F., 35–36 Density, 102 Department of Transportation in California (Caltrans), 113–114 Department of Transportation of Pennsylvania (PennDOT), 113 Depth to neutral axis (reinforced concrete): for beams with bonded tendons, 257–259 for beams with unbonded tendons, 259–260 Description of design, 33 Design-bid-build model, 68 Design-build, 68 Designer sign conventions, 133 Design lanes, 103 Design lane load, influence functions for, 150–152 Design loads, 103–106 deck overhangs, 108 lane, 150–152 tandem, 103–105, 150, 151–152 traffic barrier, 108–109 truck, 103–106, 149–154 vehicular, 103–106 Design of bridges , 75–97 calibration of LRFD code, 89–94 for fitting with ASD, 93–94 using reliability theory, 89–93 geometric design, 95–97 goals of, 75 historic procedures for, 75–77 justification stage of, 75 limit states in, 75, 77–82 basic design expression for, 77 ductility factor, 77–78 extreme event limit state, 81–82 fatigue and fracture limit state, 80–81 load combinations and load factors, 79–80 load designation, 78–79 operational importance factor, 78 redundancy factor, 78 service limit state, 79–80 strength limit state, 81 520 INDEX Design of bridges (continued) modeling in, 162, 163 probabilistic, 83–88 bias factor, 85 coefficient of variation, 85 frequency distribution and mean value, 83 levels of, 83 probability density functions, 84–85 probability of failure, 86 safety index, 86–88 standard deviation, 83–84 safety in, 75 structural design process, 33–36 description and justification in, 33–34 input to, 34 model of, 33 and regulation, 34–35 Design problems: composite rolled steel beam bridge, 452–461 concrete bridges, 293–311 concrete deck, 293–311 multiple-span composite steel plate girder beam bridge, 461–499 noncomposite rolled steel beam bridge, 443–452 prestressed girder bridge, 340–359 solid slab bridge, 313–321 steel bridges, 443–499 T-beam, bridge, 321–339 Design vehicular loads, 103–106 Diaphragms: multiple-span composite steel plate girder beam bridge design problem, 496–499 steel bridges, 390 Distributed loads, 136, 161 Distribution factors: for moment: multiple-span composite steel plate girder beam problem, 462–463 noncomposite rolled steel beam bridge design problem, 444–445 prestressed concrete girder bridge design problem, 341–342 T-beam bridge design problem, 323–325 for shear: multiple-span composite steel plate girder beam problem, 463–465 noncomposite rolled steel beam bridge design problem, 445–446 prestressed concrete girder bridge design problem, 342 T-beam bridge design problem, 325–326 slab-girder systems, 173–178 Distribution reinforcement, in solid slab bridge design problem, 321 DLA, see Dynamic load allowance Dominance, in aesthetic design, 44 Double-intersection Pratt truss, Double-plate transverse stiffener design, 489–490 Downdrag, 102 Drag coefficient, 116 Drip groove, 50 Duality: for medium- and short-span bridges, 47–49 unresolved, 47 Ductility: of composite sections, 421 in limit states, 77–78 in reinforced concrete, 262–264 steel, 363 and stress, 165–167 Dunlap’s Creek bridge, Brownsville, Pennsylvania, 10 Durability: solid slab bridge design problem, 316 T-beam bridge design problem, 327 Dynamic horizontal ice forces, 125–126 Dynamic load allowance (DLA): defined, 109 multiple-span composite steel plate girder beam bridge design problem, 462 noncomposite rolled steel beam bridge design problem, 444 prestressed concrete girder bridge design problem, 341 T-beam bridge design problem, 323 Dynamic load effect, 109–112 global, 111 impact factor parameters, 110–111 studies of, 109–110 Eads, James B., 10–11 Eads Bridge, St Louis, Missouri, 10–11 Earthquake failures: Cypress Viaduct, California, 25–26 and extreme event limit state, 81 I-5 and I-210 interchange, San Fernando, California, 19–21 and operational importance factor, 78 Earth surcharge load, 102 East Huntington Bridge, Huntington, West Virginia, 45, 61 Economics, in selection of bridge type, 67–68 Eden Park Bridge, Cincinnati, Ohio, 12 Effective strength of ice, 122–123 Einstein, Albert, 35 Elastic seismic response spectrum, 218–220 Elastic shortening, loss of prestressing from (concrete), 267–268 Ellet, Charles, Elliot, A L., 51 Elmira Bridge Company, 13 Empirical approach, in gravity load analysis, 198 End moments, Muller-Breslau principle for, 145–146 Equilibrium, 161 and compatibility/material response, 229–230 for safe design, 162–165 Erection, as type selection criterion, 68 Erie Canal bridge, Utica, New York, Esthetics in Concrete Bridge Design (Watson and Hurd), 36 Euclid, 38 Exclusion vehicles, in live-load model, 104–106 Expansion joints, maintenance problem with, 51–52 Experience, judgment and, 34 Extra large (long) span bridges, 71–72 Extreme event limit state, 81–82 concrete bridges, 256 concrete deck design problem, 304 steel bridges, 389–390 Factored loads, in noncomposite rolled steel beam bridge design problem, 447 Failure of bridges, 18–30 during construction, 30 Cypress Viaduct, California, 25–26 defined, 86 I-5 and I-210 interchange, San Fernando, California, 19–21 I-35W Bridge, Minneapolis, Minnesota, 26–30 Mianus River Bridge, Greenwich, Connecticut, 22–23 prior to specifications, 17 probability of, 86 Schoharie Creek Bridge, Amsterdam, New York, 24–25 Silver Bridge, Point Pleasant, West Virginia, 18–19 Sunshine Skyway, Tampa Bay, Florida, 21–22 Fatigue: defined, 252 and safety of analysis methods, 169–170 solid slab bridge design problem, 319 steel, 370–372 T-beam bridge design problem, 330–331 Fatigue and fracture limit state, 80–81 composite rolled steel beam bridge design problem, 458 multiple-span composite steel plate girder beam bridge design problem, 484 steel bridges, 378–388 detail categories, 379 fatigue design criteria, 378 fatigue load, 379 fatigue resistance, 379, 387 fracture toughness requirements, 387–388 load-induced fatigue, 378, 380–386 Fatigue limit state: concrete bridges, 252–255 fatigue of plain concrete, 252–253 fatigue of prestressing tendons, 254 fatigue of reinforcing bars, 253–254 fatigue of welded or mechanical splices of reinforcement, 255 concrete deck design problem, 302 I-sections in flexure, 421–423 prestressed concrete girder bridge design problem, 349–350 steel bridge shear connectors, 433–434 stud connectors (steel bridges), 433–434 T-beam bridge design problem, 330–331 Fatigue loads, 106–107, 379 Federal Aid Highway Act of 1968, 18 Fernandez-Ordóđez, J A., 44 FIGG Engineering Group, 55 Finite-element analysis: box-girder bridges, 208, 211–212 slab bridges, 195, 197, 198 slab-girder bridges, 187–192 slabs, 201–202 Finite-strip analysis: slab-girder bridges, 191–194 slabs, 201–202 Finley, James, First-order second-moment (FOSM) method, 83, 89–91 Flexibility: and axial strain, 223–225 and curvature, 223–225 Flexural resistance of wall, in concrete deck design problem: about axis parallel to longitudinal axis of bridge, 306 about vertical axis, 305–306 INDEX Flexural section properties, in multiple-span composite steel plate girder beam bridge design problem: for negative moment, 472–477 for positive flexure, 476–482 Flexural strength (reinforced concrete members), 257–270 depth to neutral axis for beams with bonded tendons, 257–259 depth to neutral axis for beams with unbonded tendons, 259–260 ductility, maximum tensile reinforcement, and resistance factor adjustment, 262–264 loss of prestress, 265–270 minimum tensile reinforcement, 264–265 nominal flexural strength, 260–262 Flexure: concrete bridges, 249–250 prestressed concrete girder bridge design problem, 352–353 steel bridge I-sections, 402–428 composite and noncomposite sections, 404 depth of web in compression, 410 hybrid strength reduction, 410–411 limit states, 421–428 moment redistribution, 403–404 plastic moment, 402–403, 405, 408–409 plastic neutral axis, 407–408 stability related to flexural resistance, 411–421 stiffness properties, 404 yield moment, 405–407 T-beam bridge design problem, 334–335 Flooding failure, 24–25 Fluid forces, 114–118 water, 118 wind, 116–118 Forces: braking, 113 centrifugal, 112–113 due to deformations, 127–129 from creep and shrinkage, 129 from settlement, 129 from temperature, 127–129 fluid, 114–118 ice, 122–127 rail collision, 129 vehicle collision, 129 vessel collision, 22, 81–82, 101, 129 water, 118 wind, 116–118 Fort Morgan Bridge, Colorado, 13 Fort Sumner Railroad Bridge, New Mexico, 14 FOSM (first-order second-moment) method, 83, 89–91 Fracture critical, 81 Frankford Avenue Bridge, Pennypack Creek, Franklin Institute of Philadelphia, Freezing degree days, 124 Frequency distribution, 83 Fresh concrete constituents, 230–232 Freyssinet, Eugene, 13 Friction loss of prestress, 266–267 Function: in aesthetic design, 37–38 in selection of bridge type, 67 General Theory of Bridge Construction (Herman Haupt), Genessee Road Bridge, Colorado, 48 Geometric design, 95–97 interchanges, 96–97 roadway widths, 95–96 vertical clearances, 96 George Washington Bridge, New York, 9, 10 George Westinghouse Memorial Bridge, North Versailles, Pennsylvania, 12–13 Girders: and proportion, 39 span/depth ratio for, 49–50 Girder bridges, 13–14 cantilever span, suspended span, cantilever span systems, 78 limit states for, 75 for long spans, 71 with main structure coinciding with deck line, 64–67 for medium spans, 70–71 span lengths for, 67 Global buckling (steel bridges), 411 Global load dynamic effects, 111 Golden Gate Bridge, San Francisco, California, 8–10, 14 Golden ratio/proportion/section/ number, 38 Gottemoeller, F., 36 Grant, A., 44 Gravity loads, 101–114 analysis of, 171–212 for box-girder bridges, 206–212 for slab bridges, 194–198 for slab-girder bridges, 171–194 for slabs in slab-girder bridges, 198–206 braking forces, 113 centrifugal forces, 112–113 deck and railing loads, 107–109 defined, 101 design lanes, 103 dynamic effects, 109–112 fatigue loads, 106–107 multiple presence, 109 pedestrian loads, 107 permanent, 101–102 permit vehicles, 113–114 transient, 102–114 vehicular design loads, 103–106 Greater New Orleans Through-Truss Bridge, 64 Grillage analysis: slab bridges, 195–196 slab-girder bridges, 182–189 slabs, 201–202 Hardened concrete properties, 232–242 compressive strength of aged concrete, 238 creep of concrete, 240–241 long-term, 238–242 compressive strength of aged concrete, 238 creep of concrete, 240–241 modulus of elasticity for permanent loads, 241–242 shrinkage of concrete, 238–240 short-term, 232–237 compressive strength and behavior, 232–233 concrete tensile strength and behavior, 236–237 confined concrete compressive strength and behavior, 233–236 shrinkage of concrete, 238–240, 507–508, 510–512 Hardness, steel, 363 Harmony, in aesthetic design, 41–43 521 Haupt, Herman, Heat-treated low-alloy steel, 369 Heat treatments (steel), 366 Hell Gate Bridge, New York, 11 High-performance concrete, 231–232 High-strength heat-treated alloy steel, 369–371 High-strength low-alloy steel, 369 Hildenbrand, Wilhelm, Hilton, Charles, 17 HL-93, 103 Holston River Bridge, Tennessee, 55 Hoover Dam Bypass, Arizona-Nevada, 38 Horizontal ice forces: dynamic, 125–126 static, 127 Howe, William, Howe truss, H series loading (AASHO), 17 Hybrid sections (steel bridges), 410–412 I-5 and I-210 interchange, San Fernando, California, 19–21 I-15 West Lilac Road overpass, California, 43 I-35W Bridge, Minneapolis, Minnesota, 26–30 I-82 Hinzerling Road undercrossing, Prosser, Washington, 44, 46, 47 I-90 Cedar Falls Road overpass, King County, Washington, 48 I-beam girder bridges, 64–67 Ice forces, 122–127 dynamic horizontal, 125–126 effective strength of ice, 122–123 field measurement of, 123–124 snow loads on superstructure, 127 static horizontal, 127 thickness of ice, 124–125 vertical, 127 Ice load, extreme event limit state and, 81–82 Imposed support deformations, 129 Incremental collapse, 167, 168 Inductive reasoning, 34 Inelastic buckling (steel bridges), 398–399 Influence functions (lines), 133–157 AASHTO vehicle loads, 149–156 for deck analysis, 501–502 defined, 133–134 influence surfaces, 156–157 integration of, 142–143 Muller-Breslau principle, 137–139 Betti’s theorem, 137 qualitative influence functions, 139 theory of, 138 normalized, 147–149 relationship between, 143–145 for statically determinate beams, 134–137 concentrated loads, 134–136 uniform loads, 136–137 for statically indeterminate beams, 139–147 automation by matrix structural analysis, 146–147 integration of influence functions, 142–143 Muller-Breslau principle for end moments, 145–146 relationship between influence functions, 143–145 Influence surfaces, 156–157 Integral abutments, 51–52, 55–58 Integral piers, 51 Interchanges, in geometric design, 96–97 522 INDEX I-sections (steel bridges), 424, 427–432 beam action shear resistance, 427, 429 combined shear resistance, 431–432 in flexure, 402–428 composite and noncomposite sections, 404 depth of web in compression, 410 hybrid strength reduction, 410–411 limit states, 421–428 moment redistribution, 403–404 plastic moment, 402–403, 405, 408–409 plastic neutral axis, 407–408 stability related to flexural resistance, 411–421 stiffness properties, 404 yield moment, 405–407 shear resistance of, 424, 427–432 beam action shear resistance, 427, 429 combined shear resistance, 431–432 tension field action shear resistance, 429–431 for unstiffened webs, 432 tension field action shear resistance, 429–431 for unstiffened webs, 432 Jacob’s Creek bridge, Uniontown, Pennsylvania, James J Hill Stone Arch Bridge, Minneapolis, Minnesota, Jaminet, Alphonse, 11 Jointless bridges, medium- and short-span, 51–52, 55–58 Judgment, experience and, 34 Justification of design, 34, 75 Key Bridge, Washington, DC, 12 Keystone Bridge Works, Knight’s Key Bridge, Florida, 14 Lancaster, S C., 12 Lane loads, design, 150–152 Lateral bracing (steel bridges), 390–391 Lateral loads, 114–127 analysis of, 215–221 seismic loads, 216–221 wind loads, 215–217 fluid forces, 114–118 ice forces, 122–127 seismic loads, 118–122 water forces, 118 wind forces, 116–118 Lateral torsional buckling (LTB), 411, 417–420 Lattice truss, 5–6 Lee Roy Selmon Crosstown Expressway, Tampa Florida, 56, 57 Legal issues, in selection of bridge type, 68–69 Leonard P Zakim Bunker Hill Memorial Bridge, Boston, Massachusetts, 44 Leonhardt, F., 35, 47 Lever rule, 175 Light, in aesthetic design, 44, 46–47 Limit states, 75, 77–82 basic design expression for, 77 concrete bridges, 249–256 extreme event limit state, 256 fatigue limit state, 252–255 service limit state, 249–252 strength limit state, 255–256 ductility factor, 77–78 extreme event limit state, 81–82 fatigue and fracture limit state, 80–81 I-sections in flexure, 421–428 fatigue limit state, 424 service limit state, 421–423 strength limit state, 424 load combinations and load factors, 79–80 load designation, 78–79 operational importance factor, 78 redundancy factor, 78 service limit state, 79–80 steel bridges, 377–390 extreme event limit state, 389–390 fatigue and fracture limit state, 378–388 I-sections in flexure, 421–428 service limit state, 377–378 strength limit state, 389 strength limit state, 81 Linear elastic method, for gravity load analysis, 198–199 Linear material response, 162–163 Linn Cove Viaduct, North Carolina, 42, 43 Live loads: concrete deck design problem, 298 multiple-span composite steel plate girder beam bridge design problem, 462–465 distribution factor for moment, 462–463 distribution factor for shear, 463–465 dynamic load allowance, 462 multiple presence, 462 number of lanes, 462 reactions to substructure, 465 stiffness, 465 wind effects, 465 noncomposite rolled steel beam bridge design problem, 444–446 distribution factor for moment, 444–445 distribution factor for shear, 445–446 dynamic load allowance, 444 multiple presence, 444 reactions to substructure, 446 stiffness, 446 wind effects, 446 prestressed concrete girder bridge design problem, 341–343 distribution factors for moment, 341–342 distribution factors for shear, 342 dynamic load allowance, 341 multiple presence factor, 341 shears and moments due to live loads, 342–343 rigid method with, 515–516 solid slab bridge design problem, 314–316 T-beam bridge design problem, 323–327 distribution factors for moment, 323–325 distribution factors for shear, 325–326 dynamic load allowance, 323 multiple presence, 323 number of lanes, 323 reactions to substucture, 326 Live-load model, 104–106 Live-load strip width (solid slab bridge design problem), 313–314 multiple lanes loaded, 314 one lane loaded, 314 Loads, 101–130 blast loading, 129–130 collision, 129 designations for, 78–79 forces due to deformations, 127–129 from creep and shrinkage, 129 from settlement, 129 from temperature, 127–129 gravity, 101–114 braking forces, 113 centrifugal forces, 112–113 deck and railing loads, 107–109 design lanes, 103 dynamic effects, 109–112 fatigue loads, 106–107 multiple presence, 109 pedestrian loads, 107 permanent, 101–102 permit vehicles, 113–114 transient, 102–114 vehicular design loads, 103–106 lateral, 114–127 fluid forces, 114–118 ice forces, 122–127 seismic loads, 118–122 water forces, 118 wind forces, 116–118 permanent, 101 seismic: analysis of, 216–221 combination of seismic forces, 121–122 lateral loads from, 118–122 minimum seismic design connection forces, 120–121 seismic design procedure, 119–120 transient, 101 variability of, 76 Load and resistance factor design (LRFD), 17–18, 77 advantages and disadvantages of, 77 calibration of LRFD code, 89–94 for fitting with ASD, 93–94 using reliability theory, 89–93 Load combinations: load factors for, 79–80 noncomposite rolled steel beam bridge design problem, 444 prestressed concrete girder bridge design problem, 341 service limit state, 79–80 solid slab bridge design problem, 315 strength limit state, 81 T-beam bridge design problem, 323 Load factors: calculating, 92–93 for load combinations, 79–80 multiple-span composite steel plate girder beam bridge design problem, 462 noncomposite rolled steel beam bridge design problem, 444 vehicular live load, 80–81 Load factor design, 17 Load modifiers: multiple-span composite steel plate girder beam bridge design problem, 462 noncomposite rolled steel beam bridge design problem, 443 prestressed concrete girder bridge design problem, 341 solid slab bridge design problem, 315 T-beam bridge design problem, 323 Local buckling (steel bridges), 411–417 compression flange, 416–417 web bend buckling, 414–415 web buckling load shedding, 415–416 web vertical buckling, 413–414 Locked-in erection stresses, 102 Lognormal probability density functions, 84–85 Loma Prieta earthquake, 25–26 INDEX Long, Stephen H., 5–6 Long-span bridges: girder, 13–14 reinforced concrete, 12–13 span lengths for, 71–72 steel arch, 10–11 stone arch, 3–4 suspension, 8–10 wooden, 4–5 Lower bound theorem, 162–165 shakedown load, 167 ultimate strength limit state, 169 LRFD Bridge Design Specifications (AASHTO), 18 basic design expression in, 77 compression behavior, 412–413 cross section resistance to bending and shear, 229 NCHRP projects related to, 231–232 temperature effects in, 225 Luten, Daniel, 12 MacCauley’s notation, 140 McComas, William, McCullough, Conde B., 12 McKim, Mead, and White, 12 Magnan Viaduct, Nizza, France, 39 Maintenance, as bridge type selection criterion, 67–68 Mancunian Way Bridge, Manchester, England, 38 Manhattan Bridge, New York, 10 Manual for Assessing Safety Hardware (AASHTO), 109 Marsh, James B., 13 Marsh rainbow arch bridges, 13 Material properties, 161 densities, 102 hardened concrete, 232–242 long-term, 238–242 short-term, 232–237 steel bridges, 363–374 brittle fracture, 372–373 classification of structural steels, 366–371 heat treatments, 366 production of finished products, 365 repeated stress (fatigue) effects, 370–372 residual stresses, 365–366 steel-making processes, 363–365 steel-reinforced concrete, 242–246 nonprestressed steel reinforcement, 242–244 prestressing steel, 244–246 typical resistance statistics, 85 Material response: and equilibrium/ compatibility, 229–230 linear, 162–163 nonlinear, 162–163 reinforced and prestressed concrete, 229–230 Mathematical models, 162–163 Matrix structural analysis, 146–147 Maximum negative moment, 139 MCFT, see Modified compression field theory Mean value, 83 Mechanical splices of reinforcement, fatigue of, 255 Medium-span bridges, 47–55 abutments, 51–55 deck overhangs, 49–50 girder bridges, 13 girder span/depth ratio, 49–50 integral abutments and jointless bridges, 51–52, 55–58 piers, 50–53 resolution of duality, 47–49 span lengths for, 70–71 Meigs, Montgomery, 10 Melan, Joseph, 12 Mendota Bridge, Mendota, Minnesota, 12 Mentalities for design process, 35–36 Metal bridges: arch, 10–12 truss, 6–7 Metal reinforcement, 505–506 Mianus River Bridge, Greenwich, Connecticut, 22–23, 78, 81 Michael Baker, Jr., Inc., 11 Mike O’Callaghan–Pat Tillman Memorial Bridge, Arizona-Nevada, 38 Millau Viaduct, France, 51 Millen, T., 12 Mini mills (steel), 365 Models: design-build, 68 mathematical vs numerical, 162–163 and safety of methods, 162–170 of structural design process, 33 Modeling: box-girder bridges, 173–174 computer, 56–59 slab-girder systems, 173–174 Modified compression field theory (MCFT), 6, 272–278 constitutive considerations, 276–277 equilibrium considerations, 275–276 shear design using, 278–288 longitudinal strain, 279–281 Method 1, 286–287 Method 2, 282–286 Method 3, 287–288 specifications, shear resistance, 281–282 strain considerations, 273–275 stress considerations, 273 Modulus of elasticity (concrete), 233, 241–242 Mohr strain circle, 274–275 Mohr stress circle, 272–273 shear design using, 278–288 stresses, 276–278 Moisseiff, Leon, 10 Moment diagrams, sign conventions for, 133, 144 Moment gradient correction factor, 420 Monier, Joseph, 12 Morison, George, 12 Moseltal-brücke, Germany, 41 Muller-Breslau principle, 137–139 Betti’s theorem, 137 end moments of statically indeterminate beams, 145–146 qualitative influence functions, 139 theory of, 138 Multiple king-post truss, Multiple presence: gravity loads, 109, 178 multiple-span composite steel plate girder beam bridge design problem, 462 noncomposite rolled steel beam bridge design problem, 444 prestressed concrete girder bridge design problem, 341 T-beam bridge design problem, 323 523 Multiple-span composite steel plate girder beam bridge design problem, 461–499 bearing stiffeners, 490–493 constructibilitiy, 482–483 deck, 462 design sketch, 499 diaphragms and cross frames, 496–499 dimension and detail requirements, 496–499 double-plate transverse stiffener design, 489–490 fatigue and fracture limit state, 484 flexural section properties for negative moment, 472–477 flexural section properties for positive flexure, 476–482 force effects from non-live loads, 466–473 exterior girders, 466 interior girders, 466 uniformly distributed load, 466–473 general section, 461–462 live-load force effects, 462–465 distribution factor for moment, 462–463 distribution factor for shear, 463–465 dynamic load allowance, 462 multiple presence, 462 number of lanes, 462 reactions to substructure, 465 stiffness, 465 wind effects, 465 load factors, 462 load modifiers, 462 resistance factors, 462 service limit state, 483–484 shear connectors, 492–496 shear design, 484–487 strength limit state, 484 transition points, 482 transverse intermediate stiffener design, 487–489 typical section, 462 Munro, T., 47 Napa River Bridge, California, 14, 42 National Bridge Inspection Standards (NBIS), 18, 22 National Bridge Inventory (NBI), 18 National Cooperative Highway Research Program (NCHRP): AASHTO LRFD specification revisions projects, 231–232 TL level definitions, 109 12–33 Project Team, 513–514 NBI (National Bridge Inventory), 18 Negative space, 38 New River Gorge Bridge, West Virginia, 11, 12, 61, 62 Niagara River Bridge, 8, Nominal flexural strength (reinforced concrete), 260–262 Noncomposite rolled steel beam bridge design problem, 443–452 checking assumptions, 452 dead-load camber, 452 deck, 443 design sketch, 452 dimensions and details, 451–452 factored loads, 447 force effects from non-live loads, 446–447 general section, 443 live-load force effects, 444–446 distribution factor for moment, 444–445 524 INDEX Noncomposite rolled steel beam bridge design problem (continued) distribution factor for shear, 445–446 dynamic load allowance, 444 multiple presence, 444 reactions to substructure, 446 stiffness, 446 wind effects, 446 load combination, 444 load factors, 444 load modifiers, 443 resistance factor, 443 shear design, 451 trial section, 447–451 typical section, 443 Noncomposite sections, 404 compactness requirements, 42 defined, 404 plastic moment of, 408, 409 plastic neutral axis of, 408 yield moment of, 407 Nonlinear material response, 162–163 Non-live load force effects: composite rolled steel beam bridge design problem, 453–454 multiple-span composite steel plate girder beam bridge design problem, 466–473 exterior girders, 466 interior girders, 466 uniformly distributed load, 466–473 noncomposite rolled steel beam bridge design problem, 446–447 prestressed concrete girder bridge design problem, 343–345 solid slab bridge design problem, 316 T-beam bridge design problem, 326–327 Nonprestressed steel reinforcement, 242–244 Normalized influence functions, 147–149 Normal probability function, 84 Notation, span point, 139–140 Numerical models, 162–163 Oakland-Bay Bridge, California, 10 Operational category, 119, 121, 122 Operational importance factor, 78 Order, in aesthetic design, 43–44 Overloads, repetitive, 165–169 Palmer, Timothy, 4–5 Paneled bridge truss: metal, wooden, Panhorst, F W., 13 Panther Hollow Bridge, Pittsburgh, Pennsylvania, 10 Peak ground acceleration (PGA), 119 Pedestrian loads, 107 PennDOT, 113–114 People factor, in bridge design, Permanent loads, 78–79, 101 defined, 101 gravity, 101–102 lateral, 101 load factors for, 79–80 Permit vehicles, gravity loads and, 113–114 Personal knowledge, in design process, 34 PGA (peak ground acceleration), 119 Philippi Covered Bridge, West Virginia, 4, Piers: integral, 51 for medium- and short-span bridges, 50–53 proportions for, 41 styles of, 50 Pigeon Key Bridge, Florida, 14 Plastic moment (steel bridge I-sections), 402–403, 405, 408–409 Plastic neutral axis (steel bridge I-sections), 407–408 Plate girders, 13–14 Poisson’s effect, 161 A Policy on the Geometric Design of Highways and Streets (AASHTO), 95 Portland cement, 12 Portland Company, 13 Posttensioned concrete segmental construction, 71 Pratt, Caleb, Pratt, Thomas, Pratt truss, 6–7 Precast concrete bridges: for medium spans, 70 for small spans, 69–70 Prestressed concrete: loss of prestress, 265–270 anchorage set loss, 266 approximate estimate of time-dependent losses, 268–269 elastic shortening loss, 267–268 friction loss, 266–267 lump-sum estimate of time-dependent losses, 269–270 refined estimate, 507–512 total loss, 265–266 material response, 229–230 Prestressed concrete girder bridges, 13, 14 design problem, 340–359 conventionally reinforced concrete deck, 340–341 design sketch, 359 fatigue limit state, 349–350 force effects from non-live loads, 343–345 general section, 292–293 live-load force effects, 341–343 distribution factors for moment, 341–342 distribution factors for shear, 342 dynamic load allowance, 341 multiple presence factor, 341 number of lanes, 341 shears and moments due to live loads, 342–343 load combinations, 341 load modifiers, 341 resistance factors, 341 service limit state, 344–352 choices of prestressing tendons, 345–347 deflection and camber, 350–352 fatigue limit state, 349–350 girder stresses at transfer, 348 prestress loss evaluation, 347–348 stress limits for concrete, 344–345 stress limits for prestressing tendons, 344 strength limit state, 352–358 flexure, 352–353 shear, 352–358 typical section, 292–293 Sunshine Skyway, Tampa Bay, Florida failure, 21–22 Prestressed concrete girder bridges: design problem: service limit state girder stresses after total losses, 349 Prestress effects, in system analysis, 221–222 Prestressing steel, 244–246 Prestressing tendons, fatigue of, 254 Probabilistic design, 83–88 bias factor, 85 coefficient of variation, 85 frequency distribution and mean value, 83 levels of, 83, 90 probability density functions, 84–85 probability of failure, 86 safety index, 86–88 standard deviation, 83–84 Probability density functions, 84–85 Probability of failure, 86–88 Proportion, in aesthetic design, 38–41 Public knowledge, in design process, 34 Purcell, C H., 13 Qualitative influence functions, 139 Rail collision forces, 129 Railing loads, 107–109 Ransome, Ernest, 12 Red Mountain Freeway–U.S 60 interchange, Mesa, Arizona, 44 Redundancy factor, 78 Regulation of design, 34–35 Reinforced concrete: fatigue of reinforcing bars, 253–254 fatigue of welded or mechanical splices of reinforcement, 255 flexural strength of members, 257–270 depth to neutral axis for beams with bonded tendons, 257–259 for beams with unbonded tendons, 259–260 ductility, maximum tensile reinforcement, and resistance factor adjustment, 262–264 loss of prestress, 265–270 minimum tensile reinforcement, 264–265 nominal flexural strength, 260–262 material response, 229–230 shear strength of members, 270–288 modified compression field theory, 272–278 shear design using modified compression field theory, 278–288 variable-angle truss model, 271–272 stress-strain response for, 276–277 Reinforced concrete bridges, 12–13 Reinforced concrete deck, 322 Reinforcement quantities, comparison of, 303 Reinforcement selection, 298–300 distribution reinforcement, 300 negative moment reinforcement, 300 positive moment reinforcement, 299–300 shrinkage and temperature reinforcement, 300 Relaxation loss, 509, 511 Reliability analysis, failure in, 86 Reliability theory, in calibration of LRFD code, 89–93 Repetitive overloads, 165–169 Residual stresses: columns, 397–398 from rolling, 161 and safety of methods, 165–167 steel bridges, 365–366 Resistance, typical statistics for, 85 INDEX Resistance factors: calculating, 92–94 multiple-span composite steel plate girder beam bridge design problem, 462 noncomposite rolled steel beam bridge design problem, 443 prestressed concrete girder bridge design problem, 341 in reinforced concrete, 262–264 solid slab bridge design problem, 315 T-beam bridge design problem, 322 Rhetorical design stage, 35–36 Rhythm, in aesthetic design, 43–44 Rigid method (live-load distribution), 515–516 Roadway widths, in geometric design, 95–96 Rock Creek bridge, Maryland, 10 Roebling, John A., 8, 9, 68 Roebling, Washington, 11, 68 Rolled steel beam bridges: composite, 452–461 checking assumptions, 460–461 dead-load camber, 460, 461 design sketch, 461 dimensions and details requirements, 460 flexural design, 454–459 force effects from non-live loads, 453–454 for medium spans, 70 shear connectors, 459–460 shear design, 459 noncomposite, 443–452 checking assumptions, 452 dead-load camber, 452 deck, 443 design sketch, 452 dimensions and details, 451–452 factored loads, 447 force effects from non-live loads, 446–447 general section, 443 live-load force effects, 444–446 load combination, 444 load factors, 444 load modifiers, 443 resistance factor, 443 shear design, 451 trial section, 447–451 typical section, 443 for small spans, 70 Roman bridge builders, 3–4 Rouge River Bridge, Gold Beach, Oregon, 12 Route 8/805 interchange, San Diego, California, 53 Safety: of analysis methods, 162–170 and equilibrium, 162–165 fatigue and serviceability, 169–170 repetitive overloads, 165–169 stress reversal and residual stress, 165–167 in design, 75 quantitative measure of, 86 Safety index, 87–88 estimating, 90–91 observing variation of, 91 target, selecting, 91–92 St Regis River Bridge, New York, 123 Salginatobel Bridge, Switzerland, 61, 62 Schematic design stage, 35–36 Schoharie Creek Bridge, Amsterdam, New York, 24–25 Scour, 118 SDOF (single-degree-of-freedom) systems, 218–220 Seismic design response spectra, 220–221 Seismic loads: analysis of, 216–221 elastic seismic response spectrum, 218–220 minimum requirements for, 217–218 seismic design response spectra, 220–221 combination of seismic forces, 121–122 lateral loads from, 118–122 minimum seismic design connection forces, 120–121 seismic design procedure, 119–120 Seismic performance zones, 121 Serviceability, safety of analysis and, 169–170 Service limit state, 79–80 composite rolled steel beam bridge design problem, 457–458 concrete bridges, 249–252 control of flexural cracking in beams, 249–250 deformations, 250 stress limitations for concrete, 250–251 stress limitations for prestressing tendons, 251–252 I-sections in flexure, 421–423 load combinations for, 79–80 multiple-span composite steel plate girder beam bridge design problem, 483–484 prestressed concrete girder bridge design problem, 344–352 choices of prestressing tendons, 345–347 deflection and camber, 350–352 fatigue limit state, 349–350 girder stresses after total losses, 349 girder stresses at transfer, 348 prestress loss evaluation, 347–348 stress limits for concrete, 344–345 stress limits for prestressing tendons, 344 solid slab bridge design problem, 316–319 cracking control, 316–317 deformations, 317–319 durability, 316 fatigue, 319 steel bridges, 377–378 T-beam bridge design problem, 327–333 crack control, 327–330 deflection and camber, 331–333 durability, 327 fatigue, 330–331 Settlement, deformations due to, 129 Seven Mile Bridge, Florida, 14 Shadow, in aesthetic design, 44, 46–47 Shakedown load, 167–169 Shear: concrete deck design problem, 307–308 prestressed concrete girder bridge design problem, 342–343, 352–358 steel bridges, 433–437 fatigue limit state for, 433–434 strength limit state for, 434–437 T-beam bridge design problem, 337–339 Shear connectors: composite rolled steel beam bridge design problem, 459–460 multiple-span composite steel plate girder beam bridge design problem, 492–496 Shear design: composite rolled steel beam bridge design problem, 459 multiple-span composite steel plate girder beam bridge design problem, 484–487 525 noncomposite rolled steel beam bridge design problem, 451 using modified compression field theory, 278–288 Method 1, 286–287 Method 2, 282–286 Method 3, 287–288 Shear diagrams, sign conventions for, 133 Shear resistance of I-sections, 424, 427–432 beam action shear resistance, 427, 429 combined shear resistance, 431–432 tension field action shear resistance, 429–431 for unstiffened webs, 432 Shear strength (reinforced concrete members), 270–288 modified compression field theory, 272–278 shear design using modified compression field theory, 278–288 variable-angle truss model, 271–272 Shepperd’s Dell Bridge, Latourell, Oregon, 12 Short-span bridges, 47–55 abutments, 51–55 deck overhangs, 49–50 girder bridges, 13 girder span/depth ratio, 49–50 integral abutments and jointless bridges, 51–52, 55–58 piers, 50–53 resolution of duality, 47–49 span lengths for, 69–70 Shrinkage: analyzing effects of, 221, 225 of concrete, 225, 238–240, 507–508, 510–512 deformations due to, 129 solid slab bridge design problem, 321 Sign conventions, 133 for moment diagrams, 133, 144 for shear diagrams, 133 for slabs, 199 for strains and stresses, 229 Silver Bridge, Point Pleasant, West Virginia, 18–19, 78, 81 Single-degree-of-freedom (SDOF) systems, 218–220 Single-load paths, 78 Slabs (slab-girder bridges), gravity load analysis, 198–206 analytical strip method, 198–202 empirical approach, 198 linear elastic method, 198–199 yield-line analysis, 202–206 Slab bridges: gravity load analysis, 194–198 for small spans, 69 solid slab bridge design problem, 313–321 design sketch, 321 distribution reinforcement, 321 force effects from other loads, 316 live-load force effects, 315, 316 live load for decks and deck systems, 314–315 live-load strip width, 313–314 load combinations, 315 load modifiers, 315 minimum recommended depth, 313 resistance factors, 315 service limit state, 316–319 shrinkage and temperature reinforcement, 321 strength limit state, 320 span lengths for, 67 526 INDEX Slab-girder bridges, gravity load analysis, 171–194 beam-line method, 174–182 behavior, structural idealization, and modeling, 173–174 finite-element method, 187–192 finite-strip method, 191–194 grillage method, 182–189 Slenderness ratio: columns, 397 tensile members, 396 Smart Road Bridge, Blacksburg, Virginia, 38, 56, 58 Smeared steel tensile stresses, 273 Smith, Andrew H., 11 Snow loads on superstructure, 127 Soil profiles, 120 Solar radiation zones, 128 Solid slab bridge design problem, 313–321 design sketch, 321 distribution reinforcement, 321 force effects from other loads, 316 live-load force effects, 315, 316 live load for decks and deck systems, 314–315 live-load strip width, 313–314 multiple lanes loaded, 314 one lane loaded, 314 load combinations, 315 load modifiers, 315 minimum recommended depth, 313 resistance factors, 315 service limit state, 316–319 cracking control, 316–317 deformations, 317–319 durability, 316 fatigue, 319 shrinkage and temperature reinforcement, 321 strength limit state, 320 Span/depth ratio (girders), 49–50 Span lengths, 66, 67 bridge types for, 69–72 extra large span bridges, 71 long-span bridges, 71–72 long-span wooden bridges, 4–5 medium-span bridges, 70–71 ratios for, 149 small-span bridges, 69–70 steel bridges, 390 Span point notation, 139–140 Specifications, 17–18 calibrating, 89 evolution of, 75–77 influence of bridge failures on, 18–30 LRFD Bridge Design Specifications, 18 Standard Specifications for Highway Bridges, 18 Spring Street Bridge, Chippewa Falls, Wisconsin, 13 Stagnation pressure, 115–116 Standard deviation, 83–84 Standard Specifications for Highway Bridges (AASHTO), 18 Standard Specifications for Highway Bridges and Incidental Structures (AASHO), 17 Starrucca Viaduct, Lanesboro, Pennsylvania, Statically determinate beams, influence functions for, 134–137 concentrated loads, 134–136 uniform loads, 136–137 Statically indeterminate beams, influence functions for, 139–147 automation by matrix structural analysis, 146–147 integration of influence functions, 142–143 Muller-Breslau principle for end moments, 145–146 relationship between influence functions, 143–145 Static horizontal ice forces, 127 Steel: heat treatments of, 366 structural, 366–371 carbon steel, 368–369 chemical composition of, 368 classification of, 366–371 heat-treated low-alloy, 369 high-strength heat-treated alloy, 369–371 high-strength low-alloy, 369 mechanical properties of, 366–368 tensile strength, 363, 393 Steel bridges, 363–499 arch, 71 box girder, 64–67 compression members, 396–401 column stability behavior, 396–398 compressive resistance, 399–401 connections for, 401 inelastic buckling behavior, 398–399 design problems, 443–499 composite rolled steel beam bridge, 452–461 multiple-span composite steel plate girder beam bridge, 461–499 noncomposite rolled steel beam bridge, 443–452 general design requirements, 390–391 I-sections in flexure, 402–428 composite and noncomposite sections, 404 depth of web in compression, 410 hybrid strength reduction, 410–411 limit states, 421–428 moment redistribution, 403–404 plastic moment, 402–403, 405, 408–409 plastic neutral axis, 407–408 stability related to flexural resistance, 411–421 stiffness properties, 404 yield moment, 405–407 limit states, 377–390 extreme event limit state, 389–390 fatigue and fracture limit state, 378–388 service limit state, 377–378 strength limit state, 389 for long spans, 71–72 material properties, 363–374 brittle fracture, 372–373 classification of structural steels, 366–371 heat treatments, 366 production of finished products, 365 repeated stress (fatigue) effects, 370–372 residual stresses, 365–366 steel-making processes, 363–365 for medium spans, 70–71 plate girder, 64–67 shear connectors (stud connectors), 433–437 fatigue limit state for, 433–434 strength limit state for, 434–437 shear resistance of I-sections, 427–432 beam action shear resistance, 427, 429 combined shear resistance, 431–432 tension field action shear resistance, 429–431 for unstiffened webs, 432 for small spans, 70 stiffeners, 438–441 bearing stiffeners, 440–441 transverse intermediate stiffeners, 438–440 tensile members, 393–396 strength of connections, 396 tensile resistance, 393–396 types of connections for, 393 truss, 71, 72 Steel-making processes, 363–365 Steel-reinforced concrete properties, 242–246 nonprestressed steel reinforcement, 242–244 prestressing steel, 244–246 Stiffeners: bearing: multiple-span composite steel plate girder beam bridge design problem, 490–493 steel bridges, 440–441 multiple-span composite steel plate girder beam bridge design problem: bearing stiffeners, 490–493 double-plate transverse stiffener design, 489–490 transverse intermediate stiffener design, 487–489 transverse intermediate stiffeners, 487–489 steel bridges, 438–441 bearing stiffeners, 440–441 transverse intermediate stiffeners, 438–440 for webs, 438–441 bearing stiffeners, 440–441 transverse intermediate stiffeners, 438–440 Stiffening, tension, 243 Stiffness: and axial strain, 223–225 and curvature, 223–225 multiple-span composite steel plate girder beam bridge design problem, 465 noncomposite rolled steel beam bridge design problem, 446 steel bridge I-sections, 404 Stone arch bridges, 3–4 Strain: axial: in flexibility and stiffness formulations, 223–225 temperature-gradient-induced, 222–223 Mohr strain circle, 274–275 reinforced concrete stress-strain response, 276–277 sign conventions for, 229 Strength limit state, 81 composite rolled steel beam bridge design problem, 458–459 concrete bridges, 255–256 concrete deck design problem, 297–298 barrier, 298 deck overhang design, 303–304 deck slab, 298 future wearing surface, 298 live load, 298 overhang, 298 strength I limit state, 298 ductility factor, 77–78 I-sections in flexure, 424 multiple-span composite steel plate girder beam bridge design problem, 484 operational importance factor for, 78 INDEX prestressed concrete girder bridge design problem, 352–358 flexure, 352–353 shear, 353–358 redundancy factor for, 78 solid slab bridge design problem, 320 steel bridges, 389 steel bridge shear connectors, 434–437 T-beam bridge design problem, 334–339 flexure, 334–335 shear, 337–339 Stress(es): allowable stress design, 17 calibration with ASD criteria, 93–94 evolution of specifications, 75–76 shortcomings of, 76–77 and variability of loads, 76 bending stress profile, 161 and ductility, 165–167 locked-in erection stresses, 102 modified compression field theory, 276–278 repeated, for steel bridges, 370–372 residual stresses, 365–366 columns, 397–398 from rolling, 161 and safety of methods, 165–167 sign conventions for, 229 smeared steel tensile stresses, 273 steel bridges: repeated stress (fatigue) effects, 370–372 residual stresses, 365–366 working stress design, 17 Stress limits: for concrete, 250–251, 344–345 for prestressing tendons, 251–252, 344 Stress relieving, 244 Stress reversal, safety of methods and, 165–167 Strip method (gravity load analysis), 198–202 Structural analysis, 146–147 Structural design process, 33–36 description and justification in, 33–34 input to, 34 model of, 33 and regulation, 34–35 stages of, 35–36 Structural steels: carbon steel, 368–369 chemical composition of, 368 classification of, 366–371 heat-treated low-alloy, 369 high-strength heat-treated alloy, 369–371 high-strength low-alloy, 369 mechanical properties of, 366–368 minimum thickness of, 390 Subsurface conditions, 67 Subsystems of bridges, 161 Sunshine Skyway, Tampa Bay, Florida, 21–22 Superstructure: continuity of, 39–41 deformations due to temperature change, 127–129 piers integral with, 51 snow loads on, 127 Suspension bridges, 8–10 for extra-large (long) spans, 71 failure of: Silver Bridge, Point Pleasant, West Virginia, 18–19 Tacoma Narrows Bridge, 9, 117–118 Wheeling Suspension Bridge, West Virginia, 8–9 with main structure above deck line, 61, 63–64 span lengths for, 67 Symmetry, 147 System analysis, 161–213 assumptions in, 161–162 creep, 225 gravity load, 171–212 for box-girder bridges, 206–212 for slab bridges, 194–198 for slab-girder bridges, 171–194 for slabs in slab-girder bridges, 198–206 lateral load, 215–221 seismic load analysis, 216–221 wind loads, 215–217 mathematical models for, 162–163 numerical models for, 162–163 prestress effects, 221–222 safety of methods used in, 162–170 and equilibrium, 162–165 fatigue and serviceability, 169–170 repetitive overloads, 165–169 stress reversal and residual stress, 165–167 shrinkage effects, 221, 225 temperature effects, 221–225 AASHTO temperature specifications, 222 temperature-gradient-induced axial strain, 222–223 temperature-gradient-induced curvature, 223 using strain and curvature formulas, 223–225 Tacoma Narrows Bridge, 9, 10, 117–118 Taft Bridge, Washington, DC, 12 Tandem loads: design, 103–106 influence functions, 150, 151–152 Taylor, D O., 12 T-beam bridges: design problem, 321–339 fatigue limit state, 330–331 force effects from non-live loads, 326–327 general section, 321, 322 live-load force effects, 323–327 distribution factors for moment, 323–325 distribution factors for shear, 325–326 dynamic load allowance, 323 multiple presence, 323 number of lanes, 323 reactions to substructure, 326 load combinations, 323 load modifiers, 323 reinforced concrete deck, 322 resistance factors, 322 service limit state, 327–333 crack control, 327–330 deflection and camber, 331–333 durability, 327 fatigue, 330–331 strength limit state, 334–339 flexure, 334–335 shear, 337–339 typical section and design basis, 322 girder, 64–67 for small spans, 69–70 Temperature: analyzing effects of, 221–225 AASHTO temperature specifications, 222 temperature-gradient-induced axial strain, 222–223 527 temperature-gradient-induced curvature, 223 using strain and curvature formulas, 223–225 deformations due to, 127–129 Temperature-gradient-induced axial strain, 222–223 Temperature-gradient-induced curvature, 223 Temperature reinforcement, in solid slab bridge design problem, 321 Temperature specifications, 222 Tensile (tension) members: net area, 395 slenderness requirements, 396 steel bridges, 393–396 strength of connections, 396 tensile resistance, 393–396 types of connections for, 393 Tensile reinforcement (concrete): maximum, 263–264 minimum, 264–265 Tensile strength: hardened concrete, 236–237 steel, 363, 393 testing, Tension field action, Tension field action shear resistance, 429–431 Tension field theory, 272 Tension stiffening, 243 Texture, in aesthetic design, 44–46 Thickness of ice, 124–125 3D finite-element model, 190 Through-truss bridges, 61, 63–64 Tied-arch design, 10 Time-dependent prestress losses (concrete): approximate estimate of, 268–269 lump-sum estimate of, 269–270 refined estimate, 507–512 Total loss of prestressing (concrete), 265–266 Toughness, steel, 363 Town, Ithiel, 4, Traffic barrier system design loads, 108–109 Traffic lanes, 103 Transient loads, 78–79, 101 gravity, 101, 102–114 lateral, 101 Transition points, in multiple-span composite steel plate girder beam bridge design problem, 482 Transportation Research Board (TRB), 103 Transportation systems, bridges in, Transverse deck moments, 503–504 Transverse intermediate stiffeners: multiple-span composite steel plate girder beam bridge design problem, 487–489 steel bridges, 438–440 Transverse intermediate stiffeners: steel bridges: slenderness, 438 stiffness, 438–439 TRB (Transportation Research Board), 103 Truck loads, 18 design, 103–106 fatigue limit state for, 80–81 influence functions, 149–154 Truck train loads, 17 Trusses : arch, 4–5 bowstring arch, Howe, lattice, 5–6 528 INDEX Trusses (continued) metal truss bridges, 6–7 multiple king-post, Pratt, 6–7 for suspension bridges, variable-angle truss model, 271–272 for wooden bridges, 4–6 Truss-arched bridges, 61–62 Truss bridges: for long spans, 71, 72 with main structure above deck line, 61, 63–64 span lengths for, 67 TS & L (type, size, and location) report, 66 Tunkhannock Creek Viaduct, Nicholson, Pennsylvania, 12, 44 Turner, C A P., 12 2D finite-element model, 188, 190 Type, size, and location (TS & L) report, 66 “Typical Specifications for the Fabrication and Erection of Steel Highway Bridges” (USDA), 18 Uniform loads: influence functions for statically determinate beams, 136–137 multiple-span composite steel plate girder beam bridge design problem, 466–473 repetitive overloads, 165–167 U.S Army Corps of Engineers, 10 U.S Department of Agriculture, Office of Public Roads, 18 Unresolved duality, 47 Unstiffened webs, shear resistance for, 432 Upper bound theorem, 167, 169 Variability of loads, 76 Variable-angle truss model, 271–272 Variation, coefficient of, 85 Vehicle collisions: concrete barrier strength, 291–293 crash testing of, 293 for uniform thickness barrier wall, 291–293 for variable thickness barrier wall, 293 and extreme event limit state, 81–82 Vehicle collision forces, 129 Vehicle loads: AASHTO, 103–108, 149–156 design fatigue load, 106–107 design lane load, 103–106, 150–152 design tandem load, 103–106, 150, 151–152 design truck load, 103–106, 149–154 concrete deck design problem, 296–297 maximum interior negative live-load moment, 297 maximum live-load reaction on exterior girder, 297 maximum positive live-load moment, 296–297 overhang negative live-load moment, 296 design gravity loads, 103–106 fatigue limit state for live loads, 80–81 live loads, fatigue limit state for, 80–81 repetitive overloads, 165–169 Velocity profile, 116–117 Verrazano-Narrows Bridge, New York, Vertical clearances, in geometric design, 96 Vertical ice forces, 127 Very-high-strength concrete, 231 Vessel collision forces, 22, 81–82, 101, 129 Von Emperger, Fritz, 12 Web (Internet) resources, for aesthetics, 56, 59 Webs (steel bridge I-sections): cross-sectional shape classifications, 411–412 depth of, in compression, 410 stiffeners for, 438–441 bearing stiffeners, 440–441 transverse intermediate stiffeners, 438–440 unstiffened, 432 Weigh-in-motion (WIM) studies, 104 Welded splices of reinforcement, fatigue of, 255 Wernwag, Lewis, Wheeler, Walter, 12 Wheeling Suspension Bridge, West Virginia, 8–9 Whipple, Squire, Wide-flange beam girder bridges, 64–67 Widths, roadway, in geometric design, 95–96 William Sallers and Company, Williamsburg Bridge, New York, 9–10 WIM (weigh-in-motion) studies, 104 Wind forces: lateral loads from, 116–118, 215–217 multiple-span composite steel plate girder beam bridge design problem, 465 noncomposite rolled steel beam bridge design problem, 446 Wobble effect, 266–267 Wood bridges, 4–6 creep in, 129 for small spans, 69 Working stress design, 17 A Work on Bridge Building (Squire Whipple), Wyeth, Nathan C., 12 Waddell and Harrington, 12 Walnut Lane Bridge, Philadelphia, Pennsylvania, 13 Washington Bridge, New York, 10 Water forces, lateral loads from, 118 Yield, 161 Yield-line analysis, 202–206 Yield-line failure pattern, 306–307 Yield moment, 405–407 Yield strength, steel, 363 ... textbook on the design of highway bridges The American Association of State Highway and Transportation Officials (AASHTO) were in the midst of a complete rewriting of their Bridge Design Specifications... second edition are a discussion of integral abutment bridges and a section on the use of computer modeling in planning and design Chapter presents the basics on load and resistance factor design (LRFD) ... engineers who have an interest in the design of highway bridges The objective is to provide the reader a meaningful introduction to the design of medium- and short-span girder bridges This objective