Highway Bridge

SuperstructureEngineering

LRFD Approachesto Design and Analysis

Narendra Taly

CRC PressTaylor& Francis Group

Boca Raton London New York

CRC Press is an imprint of the

Taylor & Francis Croup, an informa business

Contents

Preface x'x

Acknowledgments xxiii

Chapter 1 Introduction 1

1.1 Structural Design Philosophies 1

1.2 General Design Concepts 1

1.3 Fundamentals of Structural Design Philosophies 2

1.3.1 Design Philosophies Based on Elastic Behavior: Allowable/

Working Stress Design 2

1.3.2 Design Philosophies Based on Inelastic Behavior: Plastic

Design Method 3

1.4 Limit States Design Philosophies 8

1.4.1 Concepts of Limit States 8

1.4.1.1 Strength Limit States 9

1.4.1.2 Serviceability Limit States 10

1.4.1.3 Fatigue Limit States 12

1.4.2 Strength Limit States versus Serviceability Limit Stales 13

1.4.3 Strength Design, Load Factor Design, and Load and Resistance

Factor Design 14

1.4.4 Strength Design Philosophy 14

1.4.4.1 Strength Design Concept 14

1.4.4.2 Load Factor Design 15

1.4.4.3 Load and Resistance Factor Design 15

1.5 LRFD Specifications for Highway Bridges 16

1.5.1 Evolution of LRFD Specifications for the Design of Steel

Buildings in the United States 16

1.5.2 Evolution of LRFD Specifications for Highway Bridges in the

United States 16

1.5.2.1 Why the Change from AASHTO Standard

Specifications? 16

1.5.2.2 Why Probability-Based Design Philosophy? 17

1.5.3 Issues and Considerations for the Development of AASHTO

LRFD Criteria 18

1.5.4 Probabilistic Basis of AASHTO LRFD Bridge Design

Specifications 18

1.5.5 Statistical Nature of Loads and Resistances 19

1.5.5.1 Random Variables, Normal and Lognormal

Distributions, and Probability 19

1.5.5.2 Properties and Applications of Normal (Gaussian)

Distribution 26

1.5.5.3 Linear Functions of Random Variables: Central Limit

Theorem (CLT, Normal Convergence Theorem) 37

1.5.6 Probabilistic Determination of Safety Factors 39

1.5.6.1 Probabilistic Concept of Safety: Limit State Function

(Performance Function) 39

viii Contents

1.5.6.2 Development of AISC LRFD Criteria 40

1.5.6.3 Development of AASHTO LRFD Criteria 44

1.5.6.4 Calibration Procedure 52

1.5.6.5 Calibration of Load and Resistance Factors 55

1.5.7 AASHTO LRFD Specifications Format of Load and Resistance

Relationship 56

1.5.7.1 Loads, Resistance, and Factor of Safety 56

1.6 Differences between Various Design Methods: Summary 63

1.6.1 Difference between the Design Methods Based on the Elastic

and Inelastic Material Behavior 63

1.6.2 Difference between Plastic Design, Strength Design,

Load Factor Design, and Load and Resistance Factor Design 64

1.7 Historical Review of AASHTO Specifications for Highway Bridges 64

1.8 AASHTO LRFD Highway Bridge Design Specifications and Design

Philosophies 65

1.9 AASHTO Interim Specifications 65

1.10 Scope of the AASHTO LRFD Bridge Design Specifications 66

1.11 Commentary to AASHTO LRFD Specifications 67

1.12 General Comments 67

l.A Appendix 68

References 70

Chapter 2 Highway Bridge Superstructure Systems 73

2.1 Introduction 73

2.2 AASHTO LRFD Spec.-Speci fic Highway Bridge Superstructures 73

2.3 Description and Design Characteristics of Superstructure Systems

in Table 2.1 81

2.3.1 RC Deck over Steel Wide Flange Beams of Plate Girders (Type a).... 81

2.3.2 Spread-Box Beam Superstructure (Type b) 83

2.3.3 Open Steel or Precast Concrete Box Superstructure (Type c) 83

2.3.4 Cast-in-Place Concrete Multicell Box Girder (Type d) 84

2.3.5 Cast-in-Place RC T-Beam Superstructure (Type e) 85

2.3.6 Adjacent-Prestressed Concrete Box Superstructure (Typef) 85

2.3.7 Adjacent-Prestressed Concrete Box Superstructure with

Integral Concrete Deck with or without Transverse

Posttensioning (Type g) 85

2.3.8 Precast Concrete Channel Sections with Shear Keys

and Concrete Overlay (Type h) 86

2.3.9 Precast Concrete Double-T Girders with Shear Keys, and with

or without Transverse Posttensioning and Integral Concrete

Deck (Type i) 87

2.3.10 Precast Concrete Single-T Girders with Shear Keys, and with or

without Transverse Posttensioning and Integral Concrete Deck

(Type./) 87

2.3.11 RC Deck over Prestressed I-Beams or Bulb-T Girders (Type k) 87

2.3.12 Fiber-Reinforced Polymer Highway Superstructure Systems 89

2.4 Diaphragms 91

2.4.1 Definition of a Diaphragm 91

2.4.2 Diaphragms in Building Structures 91

Contents lx

2.4.3 Diaphragms in Bridge Superstructures 91

2.4.3.1 ASSHTO Standard Specifications for Diaphragms 92

2.4.3.2 AASHTO LRFD Specifications for Diaphragms and

Cross-Frames 93

2.5 Bridge Site and Geometry 94

2.5.1 Bridge Type, Size, and Location 94

2.5.2 Bridge Width 95

2.5.3 Normal and Skewed Bridges 95

2.6 Deflections 97

2.6.1 Historical Review of Deflection Limitations 97

2.6.2 Purpose of Limiting Bridge Deflections 98

2.6.3 Criteria for Live Load Deflections 99

2.6.4 Optional Criteria for Span-to-Depth Ratios 101

2.6.4.1 Optional Deflection Criteria for Constant Depth

Superstructures 101

2.6.4.2 Optional Deflection Criteria for Curved Steel

Superstructures 102

2.6.5 Deflections Due to Dead Loads 102

2.6.6 Calculation of Live Load Deflections 103

2.7 Consideration of Future Widening 106

2.8 Constructabil ily 106

2.9 Bridge Esthetics 107

References 107

Chapter 3 Loads on Highway Bridge Structures 109

3.1 Introduction 109

3.2 AASHTO LRFD Highway Bridge Design Philosophy 110

3.2.1 Limit States Concept 110

3.2.2 Loads and Load Designations 114

3.2.3 Load Factors and Load Combinations for Design Loads 114

3.2.4 Selection of Design-Specific Limit States, Load Modifiers,

Load Combinations, and Load Factors 120

3.3 Load Factors and Load Combinations for Construction Loads 120

3.3.1 Evaluation at the Strength Limit States 120

3.3.2 Evaluation of Deflection at the Service Limit State 120

3.3.3 Load Factors for Jacking and Posttensioning Forces 121

3.3.3.1 Jacking Forces 121

3.3.3.2 Force for Posttensioning Anchorage Zones 121

3.4 Components of a Highway Bridge Structure 121

3.5 Dead Loads on a Highway Bridge Superstructure 122

3.5.1 General 122

3.5.2 Dead Load Due to Deck Slab 124

3.5.3 Dead Load Due to Girders 124

3.6 Construction Loads 130

3.7 Live Loads on Highway Bridge Superstructures 130

3.7.1 Historical Perspective 130

3.7.2 Development of AASHTO Standard Specifications Live Load

Model 131

X Contents

3.7.3 Description of AASHTO LRFD Notional Live Load Model 135

3.7.4 Understanding the Development of AASHTO LRFD Notional

Live Load Model 139

3.7.4.1 Concept of Notional Load: What Is It? 139

3.7.4.2 Commercial Vehicular Loads 140

3.7.4.3 Development of AASHTO LRFD Notional Live

Load: A Brief History 146

3.7.4.4 Permit Loads 156

3.7.5 Application of Design Vehicular Live Loads on Bridge

Superstructures 158

3.7.5.1 Position of Live Load on Simple Spans 158

3.7.5.2 Position of Vehicular Live Loads on

Continuous Spans 160

3.7.6 Bending Moments and Shears Due to Moving Loads on Simple

Spans 160

3.7.6.1 Bending Moments 160

3.7.6.2 Influence Lines for Absolute Maximum Bending

Moments in Simple Spans 161

3.7.7 Generalized Expressions for Maximum Moment and Maximum

Shear at a Section in a Simple Span Due to HS20 Truck 175

3.7.7.1 Maximum Moment and Shear: HS20 Truck Movingfrom Left to Right 175

3.7.7.2 Maximum Moment and Shear: HS20 Truck Movingfrom Right to Left 176

3.7.8 Absolute Maximum Bending Moment in Spans Due to Loads

Other than AASHTO HS20 Truck 178

3.7.9 Governing Span Lengths for Maximum Live Load Shear in

Simple Spans Due to AASHTO LRFD Live Load: HS20 Truck

and Tandem 183

3.7.10 Influence Lines for Beams with Other Support Conditions

and for Other Types of Structures 184

3.8 Dynamic Effects of Vehicular Live Load 185

3.8.1 General Considerations for Dynamic Force Effects: Dynamic

Load Allowance 185

3.8.2 Research on Quantification of Dynamic Load Effects 185

3.8.3 AASHTO LRFD Specifications for Dynamic Load Allowance 193

3.8.4 Exceptions to Application of Dynamic Load Effects 197

3.9 Fatigue Loading 198

3.9.1 Fatigue Phenomenon 198

3.9.2 Magnitude and Configuration of Live Load for Fatigue

Considerations 198

3.9.3 Formulas for Maximum Moment and Shear for Fatigue Limit

State Loading 199

3.9.3.1 Maximum Moment for Fatigue Limit State 199

3.9.3.2 Maximum Shear for Fatigue Limit State 202

3.9.4 Frequency of Loading for Fatigue Design Considerations 206

3.9.5 Application of ADTTS, for Determination of FatigueLimit State 209

3.10 Pedestrian Loads 210

3.10.1 Significance of Pedestrian Loading 210

3.10.2 Live Load Due to Sidewalks on Vehicular Bridges 210

Contents xl

3.10.3 Live Load on Pedestrian and/or Bicycle Bridges 210

3.11 Application of Design Live Loads on a Bridge Superstructure 212

3.11.1 Design Live Loads for Longitudinal Beams 212

3.11.2 Live Load for Deflection Considerations 214

3.11.3 Design Live Load for Decks, Deck Systems, and Top Slabs

of Box Culverts 214

3.11.4 Live Load on Deck Overhangs 215

3.11.5 Force Effects Due to Live Load in Multiple Traffic Lanes:

Multiple Presence of Live Load 216

3.12 Design Live Loads in Longitudinal Girders Supporting Bridge Decks 218

3.13 Envelopes for Moment and Shear Values 218

3.14 Tire Contact Area 235

3.14.1 Point Load versus Distributed Load 235

3.14.2 AASHTO LRFD Specifications for Tire Contact Area 245

3.15 Rail Transit Loads 247

3.16 Centrifugal Force (CE) 247

3.17 Braking Force (BR) 251

3.17.1 Magnitude of Braking Force 251

3.17.2 Application of Braking Forces on a Bridge 254

3.18 Vehicular Collision Force (CT) 255

3.18.1 Nature, Causes, and Magnitude of Collision Forces 255

3.18.2 Protection of Structures from Vehicular Collision Force, C7" 256

3.18.3 Protection of Structures from Vessel Collision Force, CV 256

3.19 Ice and Snow Loads 259

3.19.1 Ice Loads: General 259

3.19.2 Dynamic Ice Forces on Piers 260

3.19.2.1 Ice Floes and Modes of Failures 260

3.19.2.2 Effective Ice Crushing Strength 260

3.19.2.3 Horizontal Force from Flexing of Moving Ice 261

3.19.2.4 Influence of Directionality of Ice Forces and the Pier

Nose Profile on the Magnitude of Forces Acting on

the Pier 262

3.19.3 Snow Loads 263

3.20 Wind Loads (WL and WS) 264

3.20.1 Wind Effects on Structures 264

3.20.2 Magnitude of Horizontal Wind Pressure 265

3.20.3 Variation in Wind Velocity with Height 266

3.20.4 Estimation of Wind Loads 268

3.20.5 Wind Pressure on Structure (WS) 270

3.20.6 Wind Pressure on Live Load (WL) 271

3.21 Earthquake Forces (EQ) 272

3.21.1 Evolution of Earthquake-Resistant Design Provisions

in AASHTO Bridge Design Specifications 272

3.21.2 Philosophy for Design Basis Earthquake Forces 273

3.21.3 Determination of Seismic Forces: Fundamental Concepts 275

3.21.4 AASHTO LRFD Specifications Provisions for Seismic Designof Bridges 277

3.21.4.1 Seismic Design Philosophy 277

3.21.4.2 Site Class Characterization 278

3.21.4.3 Determination of Elastic Seismic Response

Coefficient, C,„, 278

xii Contents

3.21.4.4 Determination of Acceleration Coefficients 280

3.21.4.5 Design Basis Earthquake 284

3.21.4.6 Seismic Hazard Characterization: Design Response

Spectrum 285

3.21.4.7 Operational Classification 293

3.21.4.8 Response Modification Factors 294

3.21.5 Application of Earthquake Forces for Design of Structural

Members and Connections in Highway Bridges 296

3.21.6 Determination of Design Basis Earthquake Forces 298

3.21.6.1 General 298

3.21.6.2 Single-Span Bridges 298

3.21.6.3 Calculation of Design Connection Forces for Bridgesin Various Seismic Zones 300

3.21.7 Determination of Fundamental Period, T 305

3.21.7.1 Single-Mode Spectral Analysis Method (SM):

Procedure 1 305

3.21.7.2 Other Methods of Analysis 308

3.22 Earth Pressure: EH, ES, LS, and DD 308

3.22.1 General 308

3.22.2 Determination of Earth Pressure 308

3.22.2.1 Basic Concepts of Earth Pressure 309

3.22.3 Theories and Calculations of Earth Pressures 311

3.22.3.1 Theories of Earth Pressures 311

3.22.3.2 Calculations of Coefficients of Earth Pressures 312

3.22.4 Equivalent-Fluid Method of Estimating Rankine's Lateral Earth

Pressures 313

3.22.5 Selection of Backfill Material 313

3.22.6 Effects of Surcharge Loads: ES and LS 316

3.22.6.1 Nature of Surcharge Loads 316

3.22.6.2 Uniform Surcharge Loads (ES) 316

3.22.6.3 Point, Line, and Strip Loads (ES) 317

3.22.6.4 Effects of Live Load Surcharge Loads: LS 319

3.22.6.5 Downdrag: DD 324

3.22.7 Seismic Earth Pressure 324

3.23 Force Effects Due to Superimposed Deformations: TU, TG, SH,

CR, SE, and PS 325

3.23.1 General 325

3.23.2 Temperature-Induced Forces 325

3.23.3 Temperature-Induced Forces Due to Uniform Temperature 325

3.23.4 AASHTO LRFD Provisions for Design Unidirectional Thermal

Movements 327

3.23.5 Forces Induced by Temperature Gradient 327

3.23.5.1 Nature of Heat Flow Problem: Thermal Gradient 327

3.23.5.2 Effect of Nonlinear Temperature Variation 334

3.23.5.3 AASHTO LRFD Provisions for Thermal Gradient

Analysis 335

3.24 Miscellaneous Forces for Design Considerations 338

3.25 Friction Forces: FR 338

3.A Appendix 339

References 346

Contents xiii

Chapter 4 Structural Analysis of Highway Bridge Superstructures 353

4.1 Introduction 353

4.2 Load Path in Bridge Structures 354

4.3 Analysis for Dead Load on Bridge Superstructures 356

4.4 Methods of Structural Analysis for Live Load on Bridge Superstructures ...357

4.5 Approximate Analysis Methods for Live Loads: The Distribution

Factor Concept 358

4.6 Considerations for Live Load Distribution Factors for Common Typesof Bridge Superstructures 360

4.6.1 General Approach 360

4.6.2 Lever Rule 360

4.6.3 Applicability Criteria for LRFD Live Load Distribution Factors.... 363

4.6.3.1 Superstructures with Constant Deck Width

and Parallel Girders 363

4.6.3.2 Superstructures with Varying Deck Width

and Splayed Girders 364

4.6.4 Influence of Multiple Loaded Lanes 365

4.6.4.1 Number of Design or Traffic Lanes on a Bridge 365

4.6.4.2 Influence of Multiple Design/Traffic Lanes on Girders

Supporting the Deck 365

4.6.4.3 Position of Wheel Loads on Bridge Deck with Respectto Girders 366

4.7 Calculations of Distribution Factors for Beams/Girders of TypicalSuperstructures 366

4.7.1 Formulas for Distribution Factors 366

4.7.2 Distribution Factors for Interior Girders 366

4.7.2.1 Bending Moment 366

4.7.2.2 Live Load Distribution Factors for Shear 375

4.7.3 Live Load Distribution Factors for Exterior Girders 375

4.7.3.1 Influence of Diaphragms on Distribution Factors

for Exterior Girders 375

4.7.3.2 Distribution Factors for Bending Moment 375

4.7.3.3 Distribution Factors for Shear 377

4.8 Special Analysis for Distribution Factors for Bending Moments

and Shears in Exterior Girders 379

4.9 Correction Factors for Bridge Skew 380

4.10 Distribution Factors for Fatigue Limit State 382

4.11 Distribution Factors for Deflection Limit State 382

4.12 Illustrative Examples: Distribution Factors for Bending Moment and Shear 382

4.13 Application of Live Distribution Factors for Design Purposes 417

4.14 Distribution Factors for Special Loads with Other Traffic Loads 421

4.15 Live Load Distribution Factors for Bending Moments and Shear

in Transverse Floor Beams 421

4.16 Methods of Refined Analysis 421

4.17 Distribution of Lateral Loads in Multibeam Bridges 422

4.17.1 General 422

4.17.2 Lateral Wind Load Distribution in Multibeam Bridges 422

4.17.2.1 Load Path for Lateral Wind Load 422

4.17.2.2 Determination of Forces and Bending Moments Due

to Lateral Wind Load 423

Contents

4.17.3 Seismic Load Distribution in Multibeam Bridges 424

4.17.3.1 Load Path for Earthquake Forces in Multibeam

Bridges 424

4.17.3.2 Design Criteria 425

4.17.3.3 Earthquake Load Distribution 425

4.18 Analysis of Concrete Slabs and Slab-Type Bridges for LRFD Live Loads 425

4.18.1 General 425

4.18.1.1 Slab-Type Bridges 426

4.18.1.2 Concrete Decks 426

4.18.2 Analysis of Slab-Type Bridges 426

4.18.2.1 General 426

4.18.2.2 LRFD Provisions for the Analysis of Slab-Type

Bridges: The Approximate Strip Model 430

4.18.3 Analysis of Deck Systems 433

4.18.3.1 General 433

4.18.3.2 Calculation of Force Effects 433

4.18.4 Deflection Analysis of Slab Bridges 434

4.18.4.1 General 434

4.18.4.2 Influence of Cracking of Concrete Sections under

Service Loads 435

4.18.4.3 Long-Term Deflections 435

4.A Appendix 436

References 446

Chapter 5 Concrete Bridges 449

5.1 Introduction 449

5.2 Concrete Bridges and Aesthetics 449

5.3 Corrosion of Concrete Bridges 452

5.3.1 Reinforcing Bar Corrosion Problem 452

5.3.2 Mitigation of Corrosion Problem 453

5.3.2.1 Treated Reinforcing Steel 453

5.3.2.2 Concrete Cover for Reinforcing Steel 453

5.3.3 General Protective Requirements 454

5.4 Material Properties 455

5.4.1 Concrete for Bridge Construction 455

5.4.1.1 General 455

5.4.1.2 Normal-Weight and Structural Lightweight Concrete 456

5.4.1.3 Coefficient or Thermal Expansion 458

5.4.1.4 Shrinkage and Creep 458

5.4.1.5 Modulus of Elasticity of Concrete 459

5.4.1.6 Modulus of Rupture 461

5.4.2 High-Strength Concrete and Bridge Span Capabilities 462

5.4.3 Reinforcing Steel (Art. 5.4.3) 462

5.4.3.1 General 462

5.4.3.2 Reinforcing Bars 464

5.4.4 Prestressing Steel: Art. 5.4.4 467

5.4.4.1 General 467

5.4.4.2 Modulus of Elasticity of Prestressing Steels: Art. 5.4.4.2 469

5.4.4.3 Relaxation of Steel 470

Contents xv

5.4.5 Strength Limit State 471

5.4.5.1 General 471

5.4.5.2 Resistance Factors (^-factors) 471

5.5 Design Procedures for Flexure in Section 5 of LRFD Specifications 473

5.5.1 Assumption for Service and Fatigue Limit Stales: Art. 5.7.1 476

5.5.2 Assumptions for Strength and Extreme-Event Limit Slates 476

5.5.2.1 General 476

5.5.2.2 Rectangular Stress Distribution: Art. 5.7.2.2 478

5.5.3 Flexural Members 479

5.5.3.1 General 479

5.5.3.2 Nominal Flexural Resistance of Concrete Members

with Nonprestressed Reinforcement 479

5.5.3.3 Nominal Flexural Resistance of Prestressed Concrete

Members 481

5.5.3.4 Flexural Resistance: Art. 5.7.3.2 484

5.6 Limits of Reinforcement: Art. 5.7.3.3 485

5.6.1 Provisions for Maximum Reinforcement 485

5.6.2 Provisions for Minimum Reinforcement: Art. 5.7.3.3.2 486

5.7 Control of Cracking by Distribution of Reinforcement: Art. 5.7.3.4 487

5.8 Service Limit State 488

5.8.1 Service Load Analysis of Reinforced Concrete Sections 488

5.8.2 Deformations: Art. 5.7.3.6 490

5.8.2.1 General Requirements 490

5.8.3 Deflection and Camber 490

5.9 Fatigue Limit State 491

5.9.1 General 491

5.9.2 Stress Limits for Stresses Due to Fatigue 492

5.9.2.1 Reinforcing Bars 492

5.9.2.2 Prestressing Tendons 492

5.9.2.3 Welded or Mechanical Splices 492

5.10 Shear 493

5.10.1 General 493

5.10.2 Check for Shear near Supports 494

5.10.3 Nominal Shear Resistance of a Concrete Section 494

5.10.3.1 General 494

5.10.3.2 LRFD Procedures for Designing for Shear 495

5.10.4 Reinforcement for Shear Resistance: Regions Requiring

Transverse Reinforcement 497

5.10.5 Minimum Transverse Reinforcement 498

5.10.6 Maximum Spacing of Transverse Reinforcement 499

5.10.7 Shear Stress on Concrete 499

5.10.8 Tensile Capacity of Longitudinal Reinforcement: Art. 5.8.3.5 500

5.11 Estimating the Area of Required Nonprestressed Tensile Reinforcement

in Concrete Sections 500

5.12 Slab-Type Concrete Bridges and Concrete Decks 501

5.13 Concrete Decks 503

5.13.1 General 503

5.13.2 Minimum Depth and Cover Requirements 503

5.13.3 Composite Action between Decks and Supporting Beams 505

5.13.4 Skewed Decks 507

xvi Contents

5.13.5 Edge Support Requirements 507

5.13.6 Design of Cantilever Slabs 507

5.13.7 Design Procedures for Deck Slabs 508

5.13.7.1 Empirical Design Method 508

5.13.7.2 Traditional Design Method 513

5.13.8 Empirical Design versus Traditional Design 513

5.14 Design Examples 514

5.15 Design of Reinforced Concrete T-Beam Superstructures 539

5.16 Design of Deck Overhang and Barrier Walls 592

5.16.1 General 592

5.16.2 Traffic Railing Design Forces and Design Criteria 592

5.16.3 Yield Line Analysis for Concrete Traffic Barriers or Parapets 595

5.17 Slab-Precast, Prestressed Concrete Bridges 611

5.17.1 Introduction 611

5.17.2 Characteristics of Prestressed Concrete Bridges 612

5.17.2.1 Use of High-Strength Concrete 612

5.17.2.2 Shapes, Sizes, and Uses of Precast, Prestressed

Concrete Girders 612

5.17.3 Concepts of Prestressing 617

5.17.4 Pretensioned and Posttensioned Girders 627

5.17.5 Layout and Location of the Center of Gravity of Multiple

Strands in a Prestressed Girder 627

5.17.6 Design of a Prestressed Concrete Girder for a Highway Bridge 630

5.A Appendix 682

References 690

Chapter 6 Slab-Steel Girder Bridges 693

6.1 Introduction 693

6.2 Structural Forms and Characteristics of Steel Bridges 693

6.2.1 Common Forms of Slab-Steel Beam Bridges 693

6.2.2 Orthotropic Steel Bridges 693

6.2.3 Composite Steel Box Girder Bridges 696

6.2.4 Delta Frame Steel Bridges 699

6.3 Corrosion of Steel Bridges 699

6.4 Construction Considerations 702

6.5 Mechanical Properties of Steel for Highway Bridges 703

6.6 Hybrid Steel Girders 704

6.7 Noncomposite and Composite Sections 706

6.7.1 Noncomposite Sections 706

6.7.2 Composite Sections 706

6.7.3 Section Properties of Noncomposite and Composite Sections 706

6.8 Shored and Unshored Construction 707

6.8.1 Sequence of Loading during Construction 707

6.8.2 Shored Construction 707

6.8.3 Unshored Construction 708

6.9 Resistance Factors 708

6.10 Design Provisions for I-Section Flexural Members 709

6.10.1 General 709

6.10.1.1 General Format for LRFD Specifications for Steel

Superstructures 709

6.10.1.2 Sequence of Loading and Elastic Stresses 714

6.10.1.3 Flange-Strength Reduction Factors 714

6.10.2 Cross-Section Proportion Limits 716

6.10.2.1 Minimum Metal Thickness (LRFD Art. 7.7.3) 716

6.10.2.2 Web Proportion Limits (LRFD 6.10.2.1) 717

6.10.2.3 Flange Proportion (LRFD Art. 6.10.2.2) 717

6.10.3 Constructibility Requirements (LRFD Art. 6.10.3) 718

6.10.3.1 General 718

6.10.3.2 Dead Load Deflection and Camber 719

6.10.3.3 Instability of I-Beams: The Lateral-Torsional-

Buckling Phenomenon 719

6.10.3.4 Lateral-Torsional Buckling and Bracing of Beams 721

6.10.3.5 Flange Stresses and Member Bending Moments 721

6.10.3.6 Moment Gradient Modifier, Ch 722

6.10.3.7 Flange Stresses and Member Bending Moments:

Critical Stages of Construction 726

6.10.4 Considerations for Service Limit State 729

6.10.4.1 Permanent Deformations 729

6.10.4.2 General 729

6.10.4.3 Flange Stresses 729

6.10.5 Special Fatigue Requirements for Webs 730

6.10.6 Design Requirements for Strength Limit Slate 731

6.10.6.1 General 731

6.10.6.2 Composite Sections in Positive Flexure 731

6.10.6.3 Composite Sections in Negative Flexure

and Noncomposite Sections 732

6.10.7 Flexural Resistance of Composite and Noncomposite Sections

in Positive Flexure: Strength Limit State 732

6.10.7.1 Compact Sections in Positive Flexure 732

6.10.7.2 Noncompact Sections 733

6.10.7.3 Ductility Requirements: Art. 6.10.7.3 734

6.10.8 Flexural Resistance: Compact Sections in Negative Flexure

and Noncomposite Sections—Strength Limit State 734

6.10.8.1 General Requirements 734

6.10.8.2 Compression Flange Flexural Resistance: Art. 6.10.8.2.1... 736

6.10.9 Shear Resistance 739

6.10.9.1 General: Shear Strength of Steel Girders 739

6.10.9.2 Nominal Resistance of Unstiffencd Webs 741

6.10.9.3 Nominal Resistance of Stiffened Webs: Interior Panels 743

6.10.9.4 Shear Resistance of End Panels 743

6.10.10 Shear Connectors 743

6.10.10.1 Role of Shear Connectors 743

6.10.10.2 Types and Sizes of Shear Connectors 744

6.10.10.3 Fatigue Limit State: Loads for Fatigue Limit State 746

6.10.10.4 Fatigue Resistance of Shear Connectors: LRFD

Art. 6.10.10.2 746

6.10.10.5 Pitch of Shear Connectors (Art. 6.10.10.1.2) 748

6.10.10.6 Design of Shear Connectors for Strength Limit Slate

(Art. 6.10.10.4) 750

6.10.10.7 Strength of Shear Connectors 753

6.10.10.8 LRFD Provisions for Providing Shear Connectors 754

xviii Contents

6.10.11 Stiffeners 766

6.10.11.1 Definitions and Description of Stiffeners 766

6.10.11.2 Web Bend-Buckling Resistance 768

6.10.11.3 Design of Transverse Stiffeners 769

6.10.11.4 Design for Bearing Stiffeners 772

6.10.11.5 Design for Longitudinal Stiffeners 775

6.10.12 Cover Plates 778

6.11 Fatigue and Fracture Considerations 779

6.11.1 General 779

6.11.2 Classification of Fatigue 779

6.11.3 Design for Load-Induced Fatigue 779

6.11.3.1 Design Considerations 779

6.11.3.2 Design Criteria 780

6.11.3.3 Detail Categories 780

6.11.3.4 Detailing to Reduce Constraint 783

6.11.3.5 Fatigue Resistance 783

6.12 Design of Noncomposite Slab-Steel Girder Superstructures 785

6.13 Composite Slab-Steel Beam Superstructures 812

6.13.1 Introduction to Composite Construction 812

6.13.2 Flexural Strength of Composite Sections 812

6.13.2.1 Stress Distribution in Composite Beams in Positive

Flexure 812

6.13.2.2 Stress Distribution in Composite Beams in Negative

Flexure 815

6.13.2.3 Locating Plastic Neutral Axis of a Composite

Section in Positive Flexure 815

6.13.3 Effective Flange Width 816

6.13.4 AASHTO Procedure for Determining the Plastic Neutral Axis

and Plastic Moment Strength of a Composite Section: LRFD

Appendix D6, Art. D6.1 817

6.13.5 Examples on Determination of Plastic Moment Strength, Mp 825

6.13.5.1 Yield Moment of Noncomposite Sections: LRFD

Art. 6.2.1 839

6.13.5.2 Yield Moment of Composite Sections in Positive

Flexure: LRFD Art. D6.2.2 839

6.13.5.3 Yield Moment of Composite Sections in Negative

Flexure: LRFD Art. D6.2.3 845

6.13.5.4 Yield Moment of Composite Sections with Cover

Plates: LRFD Art. D6.2.4 845

6.13.6 Depth of the Web in Compression: LRFD Art. D6.3 846

6.13.6.1 Depth of the Web in Compression in the Elastic

Region (Dc): LRFD Art. D6.3.1 846

6.13.6.2 Depth of the Web in Compression at Plastic

Moment (Dcp): LRFD Art. D6.3.2 848

6.14 Design of Composite Slab-Girder Superstructures 849

6.A Appendix 906

References 922

Index 925