# Design of Highway Bridges : An LRFD Approach

**by**Barker, Richard M.; Puckett, Jay A.

### 9780470900666

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## Summary

## Author Biography

The late **RICHARD M. BARKER, PhD, PE,** was Professor Emeritus of Civil and Environmental Engineering at Virginia Polytechnic Institute and State University. Dr. Barker spent more than fifty years as a structural designer, project engineer, researcher, and teacher.

**JAY A. PUCKETT, PhD, PE,** is V. O. Smith Professor of Civil and Architectural Engineering at the University of Wyoming and President of BridgeTech, Inc., a consulting firm that specializes in software development for bridge engineering. With over thirty years of experience in bridge research and development, he has developed software for the analysis and rating of bridge systems that is currently in use at over forty transportation agencies. Dr. Puckett was a subconsultant to Michael Baker Jr. Inc. for the development of AASHTO's new rating and design systems (Virtis/Opis). His research has involved several National Academy NCHRP projects.

## Table of Contents

Preface to the Second Edition xiii

Preface to the First Edition xv

**PART I GENERAL ASPECTS OF BRIDGE DESIGN**

**CHAPTER 1 INTRODUCTION TO BRIDGE ENGINEERING 3**

1.1 A Bridge Is the Key Element in a Transportation System 3

1.2 Bridge Engineering in the United States 3

1.2.1 Stone Arch Bridges 3

1.2.2 Wooden Bridges 4

1.2.3 Metal Truss Bridges 6

1.2.4 Suspension Bridges 8

1.2.5 Metal Arch Bridges 10

1.2.6 Reinforced Concrete Bridges 12

1.2.7 Girder Bridges 13

1.2.8 Closing Remarks 14

1.3 Bridge Engineer—Planner, Architect, Designer, Constructor,

and Facility Manager 14

References 15

Problems 15

**CHAPTER 2 SPECIFICATIONS AND BRIDGE FAILURES 17**

2.1 Bridge Specifications 17

2.2 Implication of Bridge Failures on Practice 18

2.2.1 Silver Bridge, Point Pleasant, West Virginia, December 15, 1967 18

2.2.2 I-5 and I-210 Interchange, San Fernando, California,

February 9, 1971 19

2.2.3 Sunshine Skyway, Tampa Bay, Florida, May 9, 1980 21

2.2.4 Mianus River Bridge, Greenwich, Connecticut, June 28, 1983 22

2.2.5 Schoharie Creek Bridge, Amsterdam, New York, April 5, 1987 24

2.2.6 Cypress Viaduct, Loma Prieta Earthquake, October 17, 1989 25

2.2.7 I-35W Bridge, Minneapolis,Minnesota, August 1, 2007 26

2.2.8 Failures During Construction 30

References 30

Problems 31

**CHAPTER 3 BRIDGE AESTHETICS 33**

3.1 Introduction 33

3.2 Nature of the Structural Design Process 33

3.2.1 Description and Justification 33

3.2.2 Public and Personal Knowledge 34

3.2.3 Regulation 34

3.2.4 Design Process 35

3.3 Aesthetics in Bridge Design 36

3.3.1 Definition of Aesthetics 36

3.3.2 Qualities of Aesthetic Design 37

3.3.3 Practical Guidelines for Medium- and Short-Span Bridges 47

3.3.4 Computer Modeling 55

3.3.5 Web References 56

3.3.6 Closing Remarks on Aesthetics 59

References 59

Problems 60

**CHAPTER 4 BRIDGE TYPES AND SELECTION 61**

4.1 Main Structure below the Deck Line 61

4.2 Main Structure above the Deck Line 61

4.3 Main Structure Coincides with the Deck Line 64

4.4 Closing Remarks on Bridge Types 66

4.5 Selection of Bridge Type 66

4.5.1 Factors to Be Considered 66

4.5.2 Bridge Types Used for Different Span Lengths 69

4.5.3 Closing Remarks 72

References 72

Problems 73

**CHAPTER 5 DESIGN LIMIT STATES 75**

5.1 Introduction 75

5.2 Development of Design Procedures 75

5.2.1 Allowable Stress Design 75

5.2.2 Variability of Loads 76

5.2.3 Shortcomings of Allowable Stress Design 76

5.2.4 Load and Resistance Factor Design 77

5.3 Design Limit States 77

5.3.1 General 77

5.3.2 Service Limit State 79

5.3.3 Fatigue and Fracture Limit State 80

5.3.4 Strength Limit State 81

5.3.5 Extreme Event Limit State 81

5.4 Closing Remarks 82

References 82

Problems 82

**CHAPTER 6 PRINCIPLES OF PROBABILISTIC DESIGN 83**

6.1 Introduction 83

6.1.1 Frequency Distribution and Mean Value 83

6.1.2 Standard Deviation 83

6.1.3 Probability Density Functions 84

6.1.4 Bias Factor 85

6.1.5 Coefficient of Variation 85

6.1.6 Probability of Failure 86

6.1.7 Safety Index β 87

6.2 Calibration of LRFD Code 89

6.2.1 Overview of the Calibration Process 89

6.2.2 Calibration Using Reliability Theory 89

6.2.3 Calibration of Fitting with ASD 93

6.3 Closing Remarks 94

References 94

Problems 94

**CHAPTER 7 GEOMETRIC DESIGN CONSIDERATIONS 95**

7.1 Introduction to Geometric Roadway Considerations 95

7.2 Roadway Widths 95

7.3 Vertical Clearances 96

7.4 Interchanges 96

References 97

Problem 97

**PART II LOADS AND ANALYSIS**

**CHAPTER 8 LOADS 101**

8.1 Introduction 101

8.2 Gravity Loads 101

8.2.1 Permanent Loads 101

8.2.2 Transient Loads 102

8.3 Lateral Loads 114

8.3.1 Fluid Forces 114

8.3.2 Seismic Loads 118

8.3.3 Ice Forces 122

8.4 Forces Due to Deformations 127

8.4.1 Temperature 127

8.4.2 Creep and Shrinkage 129

8.4.3 Settlement 129

8.5 Collision Loads 129

8.5.1 Vessel Collision 129

8.5.2 Rail Collision 129

8.5.3 Vehicle Collision 129

8.6 Blast Loading 129

8.7 Summary 130

References 130

Problems 131

**CHAPTER 9 INFLUENCE FUNCTIONS AND GIRDER-LINE ANALYSIS 133**

9.1 Introduction 133

9.2 Definition 133

9.3 Statically Determinate Beams 134

9.3.1 Concentrated Loads 134

9.3.2 Uniform Loads 136

9.4 Muller–Breslau Principle 137

9.4.1 Betti’s Theorem 137

9.4.2 Theory of Muller–Breslau Principle 138

9.4.3 Qualitative Influence Functions 139

9.5 Statically Indeterminate Beams 139

9.5.1 Integration of Influence Functions 142

9.5.2 Relationship between Influence Functions 143

9.5.3 Muller–Breslau Principle for End Moments 145

9.5.4 Automation by Matrix Structural Analysis 146

9.6 Normalized Influence Functions 147

9.7 AASHTO Vehicle Loads 149

9.8 Influence Surfaces 156

9.9 Summary 157

References 157

Problems 157

**CHAPTER 10 SYSTEM ANALYSIS—INTRODUCTION 161**

10.1 Introduction 161

10.2 Safety of Methods 162

10.2.1 Equilibriumfor Safe Design 162

10.2.2 Stress Reversal and Residual Stress 165

10.2.3 Repetitive Overloads 165

10.2.4 Fatigue and Serviceability 169

10.3 Summary 170

References 170

Problem 170

**CHAPTER 11 SYSTEM ANALYSIS—GRAVITY LOADS 171**

11.1 Slab–Girder Bridges 171

11.2 Slab Bridges 194

11.3 Slabs in Slab–Girder Bridges 198

11.4 Box-Girder Bridges 206

11.5 Closing Remarks 212

References 213

Problems 213

**CHAPTER 12 SYSTEM ANALYSIS—LATERAL, TEMPERATURE, SHRINKAGE,**

**AND PRESTRESS LOADS 215**

12.1 Lateral Load Analysis 215

12.1.1 Wind Loads 215

12.1.2 Seismic Load Analysis 216

12.2 Temperature, Shrinkage, and Prestress 221

12.2.1 General 221

12.2.2 Prestressing 221

12.2.3 Temperature Effects 222

12.2.4 Shrinkage and Creep 225

12.3 Closing Remarks 225

References 225

**PART III CONCRETE BRIDGES**

**CHAPTER 13 REINFORCED CONCRETE MATERIAL RESPONSE AND PROPERTIES 229**

13.1 Introduction 229

13.2 Reinforced and Prestressed Concrete Material Response 229

13.3 Constituents of Fresh Concrete 230

13.4 Properties of Hardened Concrete 232

13.4.1 Short-Term Properties of Concrete 232

13.4.2 Long-Term Properties of Concrete 238

13.5 Properties of Steel Reinforcement 242

13.5.1 Nonprestressed Steel Reinforcement 242

13.5.2 Prestressing Steel 244

References 246

Problems 246

**CHAPTER 14 BEHAVIOR OF REINFORCED CONCRETE MEMBERS 249**

14.1 Limit States 249

14.1.1 Service Limit State 249

14.1.2 Fatigue Limit State 252

14.1.3 Strength Limit State 255

14.1.4 Extreme Event Limit State 256

14.2 Flexural Strength of Reinforced Concrete Members 257

14.2.1 Depth to Neutral Axis for Beams with Bonded Tendons 257

14.2.2 Depth to Neutral Axis for Beams with Unbonded Tendons 259

14.2.3 Nominal Flexural Strength 260

14.2.4 Ductility,Maximum Tensile Reinforcement,

and Resistance Factor Adjustment 262

14.2.5 Minimum Tensile Reinforcement 264

14.2.6 Loss of Prestress 265

14.3 Shear Strength of Reinforced Concrete Members 270

14.3.1 Variable-Angle Truss Model 271

14.3.2 Modified Compression Field Theory 272

14.3.3 Shear Design Using Modified Compression Field Theory 278

14.4 Closing Remarks 289

References 289

Problems 290

**CHAPTER 15 CONCRETE BARRIER STRENGTH AND DECK DESIGN 291**

15.1 Concrete Barrier Strength 291

15.1.1 Strength of Uniform Thickness Barrier Wall 291

15.1.2 Strength of Variable Thickness Barrier Wall 293

15.1.3 Crash Testing of Barriers 293

15.2 Concrete Deck Design 293

References 311

Problems 311

**CHAPTER 16 CONCRETE DESIGN EXAMPLES 313**

16.1 Solid Slab Bridge Design 313

16.2 T-Beam Bridge Design 321

16.3 Prestressed Girder Bridge 340

References 359

PART IV STEEL BRIDGES

**CHAPTER 17 STEEL BRIDGES 363**

17.1 Introduction 363

17.2 Material Properties 363

17.2.1 Steelmaking Process: Traditional 363

17.2.2 Steelmaking Process: Mini Mills 365

17.2.3 Steelmaking Process: Environmental Considerations 365

17.2.4 Production of Finished Products 365

17.2.5 Residual Stresses 365

17.2.6 Heat Treatments 366

17.2.7 Classification of Structural Steels 366

17.2.8 Effects of Repeated Stress (Fatigue) 370

17.2.9 Brittle Fracture Considerations 372

17.3 Summary 374

References 374

Problem 375

**CHAPTER 18 LIMIT STATES AND GENERAL REQUIREMENTS 377**

18.1 Limit States 377

18.1.1 Service Limit State 377

18.1.2 Fatigue and Fracture Limit State 378

18.1.3 Strength Limit States 389

18.1.4 Extreme Event Limit State 389

18.2 General Design Requirements 390

18.2.1 Effective Length of Span 390

18.2.2 Dead-Load Camber 390

18.2.3 Minimum Thickness of Steel 390

18.2.4 Diaphragms and Cross Frames 390

18.2.5 Lateral Bracing 390

References 391

Problems 391

**CHAPTER 19 STEEL COMPONENT RESISTANCE 393**

19.1 Tensile Members 393

19.1.1 Types of Connections 393

19.1.2 Tensile Resistance—Specifications 393

19.1.3 Strength of Connections for Tension Members 396

19.2 Compression Members 396

19.2.1 Column Stability—Behavior 396

19.2.2 Inelastic Buckling—Behavior 398

19.2.3 Compressive Resistance—Specifications 399

19.2.4 Connections for Compression Members 401

19.3 I-Sections in Flexure 402

19.3.1 General 402

19.3.2 Yield Moment and Plastic Moment 405

19.3.3 Stability Related to Flexural Resistance 411

19.3.4 Limit States 421

19.3.5 Summary of I-Sections in Flexure 424

19.3.6 Closing Remarks on I-Sections in Flexure 424

19.4 Shear Resistance of I-Sections 427

19.4.1 Beam Action Shear Resistance 427

19.4.2 Tension Field Action Shear Resistance 429

19.4.3 Combined Shear Resistance 431

19.4.4 Shear Resistance of UnstiffenedWebs 432

19.5 Shear Connectors 432

19.5.1 Fatigue Limit State for Stud Connectors 433

19.5.2 Strength Limit State for Stud Connectors 434

19.6 Stiffeners 438

19.6.1 Transverse Intermediate Stiffeners 438

19.6.2 Bearing Stiffeners 440

References 441

Problems 442

**CHAPTER 20 STEEL DESIGN EXAMPLES 443**

20.1 Noncomposite Rolled Steel Beam Bridge 443

20.2 Composite Rolled Steel Beam Bridge 452

20.3 Multiple-Span Composite Steel Plate Girder Beam Bridge 461

References 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 507

References 512

APPENDIX E NCHRP 12-33 PROJECT TEAM 513

Task Groups 513

APPENDIX F LIVE-LOAD DISTRIBUTION—RIGIDMETHOD 515

INDEX 517