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1 Principles of Limit State Design1

1.1 Design Philosophies for Steel Structures3

1.2 Considerations in Limit State Design3

1.2.1 Serviceability Limit State Design4

1.2.2 Ultimate Limit State Design4

1.2.3 Fatigue Limit State Design5

1.2.4 Accidental Limit State Design9

1.3 Material Behavior of Structural Steels11

1.3.1 Monotonic Tensile Stress-Strain Curve11

1.3.2 Yield Condition under Multiple Stress Components15

1.3.3 Effect of Temperature16

1.3.4 The Bauschinger Effect - Cyclic Loading18

1.3.5 Limits of Cold Forming18

1.3.6 Lamellar Tearing19

1.3.7 Variability in Mechanical Properties19

1.4 Strength Member Types for Steel-Plated Structures20

1.5 Types of Loads21

1.6 Basic Types of Structural Failure22

1.7 Fabrication-related Initial Imperfections24

1.7.1 Weld Distortions24

1.7.2 Welding-induced Residual Stresses29

1.8 Age-related Structural Degradation33

1.8.1 Corrosion Damage33

1.8.2 Fatigue Cracks41

1.9 Accident-induced Damage41

1.10 Ultimate Limit State Design Format41

References43

2 Buckling and Ultimate Strength Behavior of Plate-Stiffener Combinations：Beams，Columns and Beam-Columns45

2.1 Structural Idealizations of Plate-Stiffener Assemblies45

2.2 Geometric and Material Properties47

2.3 Modeling of End Conditions49

2.4 Loads and Load Effects50

2.5 Effective Breadth/Width of Attached Plating51

2.5.1 Shear-lag-induced Ineffectiveness53

2.5.2 Buckling-induced Ineffectiveness56

2.5.3 Combined Shear-lag- and Buckling-induced Ineffectiveness58

2.6 Plastic Cross-sectional Capacities58

2.6.1 Axial Capacity58

2.6.2 Shear Capacity58

2.6.3 Bending Capacity59

2.6.4 Capacity under Combined Bending and Axial Load62

2.6.5 Capacity under Combined Bending，Axial Load and Shearing Force65

2.7 Ultimate Strength of Beams65

2.7.1 Cantilever Beams66

2.7.2 Beams Simply Supported at Both Ends67

2.7.3 Beams Simply Supported at One End and Fixed at the Other End68

2.7.4 Beams Fixed at Both Ends70

2.7.5 Beams Elastically Restrained at Both Ends72

2.7.6 Tripping under Lateral Load74

2.8 Ultimate Strength of Columns74

2.8.1 Large-deflection Behavior of Straight Columns75

2.8.2 Elastic Buckling of Straight Columns77

2.8.3 Effect of End Conditions78

2.8.4 Effect of Initial Imperfections80

2.8.5 Collapse Strength of Columns83

2.8.6 Local Web or Flange Buckling under Axial Compression87

2.8.7 Lateral -Torsional Buckling under Axial Compression87

2.9 Ultimate Strength of Beam-Columns87

2.9.1 Modified Perry-Robertson Formula87

2.9.2 Lateral-Torsional Buckling under Combined Axial Compression and Lateral Load90

2.10 Ultimate Strength of Plate-Stiffener Combinations and Their Design Considerations93

2.11 Axial Stress-Strain Relationships of Beam-Columns93

2.11.1 Pre-ultimate Strength Regime93

2.11.2 Ultimate Limit State94

2.11.3 Pos-ultimate Strength Regime95

2.11.4 Verification Examples96

References100

3 Elastic and Inelastic Buckling of Plates under Complex Circumstances103

3.1 Fundamentals of Plate Buckling103

3.2 Geometric and Material Properties104

3.3 Loads and Load Effects104

3.4 Boundary Conditions105

3.5 Linear Elastic Behavior106

3.6 Elastic Buckling of Simply Supported Plates under Single Types of Loads106

3.7 Elastic Buckling of Simply Supported Plates under Two Load Components107

3.7.1 Biaxial Compression/Tension107

3.7.2 Longitudinal Axial Compression and Longitudinal In-plane Bending110

3.7.3 Transverse Axial Compression and Longitudinal In-plane Bending110

3.7.4 Longitudinal Axial Compression and Transverse In-plane Bending111

3.7.5 Transverse Axial Compression and Transverse In-plane Bending111

3.7.6 Biaxial In-plane Bending111

3.7.7 Longitudinal Axial Compression and Edge Shear112

3.7.8 Transverse Axial Compression and Edge Shear112

3.7.9 Longitudinal In-plane Bending and Edge Shear113

3.7.10 Transverse In-plane Bending and Edge Shear113

3.8 Elastic Buckling of Simply Supported Plates under More than Three Load Components114

3.9 Elastic Buckling of Clamped Plates116

3.9.1 Single Types of Loads116

3.9.2 Combined Loads116

3.10 Elastic Buckling of Elastically Restrained Plates116

3.10.1 Rotational Restraint Parameters118

3.10.2 Longitudinal Axial Compression119

3.10.3 Transverse Axial Compression122

3.10.4 Combined Loads125

3.11 Effect of Welding-induced Residual Stresses125

3.12 Effect of Lateral Pressure127

3.13 Effect of Openings129

3.13.1 Longitudinal Axial Compression129

3.13.2 Transverse Axial Compression130

3.13.3 Edge Shear132

3.13.4 Combined Loads135

3.14 Elastic-Plastic Buckling135

3.14.1 Single Types of Loads135

3.14.2 Combined Loads141

3.15 Computer Software ALPS/BUSAP141

References142

4 Post-Buckling and Ultimate Strength Behavior of Plates145

4.1 Fundamentals of Plate Collapse Behavior145

4.2 Geometric and Material Properties146

4.3 Loads and Load Effects147

4.4 Fabrication-related Initial Imperfections148

4.5 Boundary Conditions148

4.6 Ultimate Strength by Gross Yielding151

4.7 Nonlinear Governing Differential Equations of Plates152

4.8 Elastic Large-deflection Behavior152

4.8.1 Combined Longitudinal Axial Load and Lateral Pressure153

4.8.2 Combined Transverse Axial Load and Lateral Pressure164

4.8.3 The Concept of the Effective Shear Modulus for a Plate Buckled in Edge Shear169

4.8.4 Average Stress-Strain Relationship under Combined Loads171

4.9 Ultimate Strength172

4.9.1 Basic Concepts to Derive the Ultimate Strength Formulations173

4.9.2 Combined Longitudinal Axial Load and Lateral Pressure174

4.9.3 Combined Transverse Axial Load and Lateral Pressure175

4.9.4 Lateral Pressure177

4.9.5 Edge Shear178

4.9.6 Combined Edge Shear and Lateral Pressure181

4.9.7 Combined Biaxial Loads，Edge Shear and Lateral Pressure181

4.10 Post-ultimate Behavior184

4.10.1 Average Stress-Strain Relationship184

4.10.2 Verification Examples186

4.11 Effect of Openings187

4.11.1 Longitudinal Axial Compression188

4.11.2 Transverse Axial Compression189

4.11.3 Edge Shear190

4.11.4 Combined Loads192

4.11.5 Effect of Opening Shapes196

4.12 Effect of Age-related Structural Degradation200

4.12.1 Corrosion Damage200

4.12.2 Fatigue Cracks204

4.13 Computer Software ALPS/ULSAP204

References204

5 Elastic and Inelastic Buckling of Stiffened Panels and Grillages207

5.1 Fundamentals of Stiffened Panel Buckling207

5.2 Geometric and Material Properties208

5.3 Loads and Load Effects210

5.4 Boundary Conditions211

5.5 Fabrication-related Initial Imperfections212

5.6 Linear Elastic Behavior212

5.7 Overall Buckling Versus Local Buckling213

5.8 Elastic Overall Buckling213

5.8.1 Longitudinal Axial Compression214

5.8.2 Transverse Axial Compression215

5.8.3 Edge Shear216

5.8.4 Combined Biaxial Compression/Tension216

5.8.5 Combined Axial Compression and Edge Shear218

5.9 Elastic Local Buckling of Plating between Stiffeners218

5.10 Elastic Local Buckling of Stiffener Web218

5.10.1 Governing Differential Equation219

5.10.2 Exact Web Buckling Characteristic Equation220

5.10.3 Closed-form Web Buckling Strength Expressions223

5.11 Elastic Local Buckling of Stiffener Flange225

5.12 Lateral-Torsional Buckling of Stiffeners226

5.12.1 Fundamentals of Lateral -Torsional Buckling226

5.12.2 Closed-form Tripping Strength Expressions228

5.12.3 Verification Examples232

5.13 Elastic-Plastic Buckling234

5.14 Computer Software ALPS/BUSAP234

References234

6 Post-buckling and Ultimate Strength Behavior of Stiffened Panels and Grillages237

6.1 Fundamentals of Stiffened Panel Collapse Behavior237

6.2 Classification of Panel Collapse Modes238

6.3 Modeling of Stiffened Panels242

6.4 Nonlinear Governing Differential Equations of Stiffened Panels242

6.4.1 Large-deflection Orthotropic Plate Theory after Overall Grillage Buckling243

6.4.2 Large-deflection Isotropic Plate Theory after Local Plate Buckling246

6.5 Elastic Large-deflection Behavior after Overall Grillage Buckling246

6.5.1 Combined Longitudinal Axial Load and Lateral Pressure246

6.5.2 Combined Transverse Axial Load and Lateral Pressure250

6.5.3 Average Stress-Strain Relationship under Combined Loads252

6.6 Elastic Large-deflection Behavior after Local Plate Buckling253

6.6.1 Combined Longitudinal Axial Load and Lateral Pressure253

6.6.2 Combined Transverse Axial Load and Lateral Pressure253

6.6.3 Average Stress-Strain Relationship under Combined Loads254

6.7 Ultimate Strength254

6.7.1 Overall Collapse （Mode Ⅰ）254

6.7.2 Biaxial Compressive Collapse （Mode Ⅱ）258

6.7.3 Beam-Column-type Collapse （Mode Ⅲ）260

6.7.4 Collapse by Local Buckling of Stiffener Web （Mode Ⅳ）262

6.7.5 Collapse by Tripping of Stiffener （Mode Ⅴ）264

6.7.6 Gross Yielding （Mode Ⅵ）266

6.8 Post-ultimate Behavior267

6.8.1 Average Stress-Strain Relationship267

6.8.2 Verification Examples269

6.9 Computer Software ALPS/ULSAP271

6.9.1 Outline of the Computer Software271

6.9.2 Application Examples271

References281

7 Ultimate Strength of Plate Assemblies：Plate Girders，Box Columns/Girders and Corrugated Panels283

7.1 Introduction283

7.2 Ultimate Strength of Plate Girders284

7.2.1 Ultimate Strength under Shearing Force284

7.2.2 Ultimate Strength under Bending Moment288

7.2.3 Ultimate Strength under Combined Shearing Force and Bending Moment291

7.2.4 Ultimate Strength under Patch Load293

7.2.5 Ultimate Strength under Combined Patch Load，Shearing Force and Bending Moment294

7.3 Ultimate Strength of Box Columns/Girders294

7.3.1 Ultimate Strength under Axial Compression295

7.3.2 Ultimate Strength under Bending Moment296

7.3.3 Ultimate Strength under Shearing Force297

7.3.4 Ultimate Strength under Combined Shearing Force and Bending Moment298

7.4 Ultimate Strength of Corrugated Panels298

7.4.1 Ultimate Strength under Axial Compression298

7.4.2 Ultimate Strength under Shearing Force298

7.4.3 Ultimate Strength under Lateral Pressure299

References301

8 Ultimate Strength of Ship Hulls303

8.1 Fundamentals of Hull Girder Collapse303

8.2 Hull Girder Loads305

8.2.1 Characteristics of Ship Structural Loads305

8.2.2 Calculations of Hull Girder Loads305

8.3 Basic Properties of Ship Hull Cross-sections310

8.3.1 Section Moduli310

8.3.2 Full Plastic Bending Capacity314

8.4 Progressive Collapse Behavior of Ship Hulls315

8.4.1 Single Hull Tanker315

8.4.2 Double Hull Tanker with Two Side-Longitudinal Bulkheads318

8.4.3 Single Skin-sided Bulk Carrier320

8.4.4 9000 TEU Container321

8.4.5 Effect of Lateral Pressure on Ultimate Vertical Moment323

8.4.6 Effect of Horizontal Moment on Ultimate Vertical Moment329

8.5 Closed-form Ultimate Hull Girder Strength Design Formulations329

8.5.1 Ultimate Vertical Moment329

8.5.2 Ultimate Horizontal Moment333

8.5.3 Ultimate Vertical Sectional Shear333

8.5.4 Ultimate Strength under Combined Hull Girder Loads336

8.5.5 Effect of Torsion on Ultimate Vertical Moment339

8.5.6 Effect of Age-related Structural Degradation on Ultimate Vertical Moment340

8.5.7 Effect of Accident-related Structural Damage on Ultimate Vertical Moment342

8.6 Computer Software ALPS/USAS345

References346

9 Impact Mechanics and Structural Design for Accidents349

9.1 Fundamentals of Structural Impact Mechanics349

9.2 Load Effects Due to Impact351

9.3 Material Constitutive Equation of Structural Steels under Impact Loading354

9.3.1 The Malvern Constitutive Equation355

9.3.2 Dynamic Yield Strength - the Cowper-Symonds Equation356

9.3.3 Dynamic Fracture Strain358

9.3.4 Inertia Effects358

9.3.5 Friction Effects359

9.4 Collapse Strength of Beams under Impact Lateral Loads359

9.5 Collapse Strength of Columns under Impact Axial Compressive Loads361

9.5.1 Oscillatory Response362

9.5.2 Dynamic Buckling Response362

9.6 Collapse Strength of Plates under Impact Lateral Pressure Loads364

9.6.1 Analytical Formulations - Small-deflection Theory364

9.6.2 Analytical Formulations - Large-deflection Theory366

9.6.3 Empirical Formulations368

9.7 Collapse Strength of Stiffened Panels under Impact Lateral Loads368

9.8 Crushing Strength of Thin-walled Structures369

9.8.1 Fundamentals of Crushing Behavior369

9.8.2 Crushing Strength of Plates and Stiffened Panels372

9.8.3 Crushing Strength of L-，T- and X-Shaped Elements375

9.9 Tearing Strength of Plates and Stiffened Panels376

9.9.1 Fundamentals of Tearing Behavior376

9.9.2 Analytical Formulations378

9.9.3 Empirical Formulations380

9.9.4 Concertina Tearing381

9.10 Numerical Simulation for Structural Impact Mechanics383

9.11 Some Considerations for the Quasi-Static Approximation385

9.12 Application to Ship Collision and Grounding Accidents386

9.12.1 Fundamentals of Ship Accident Mechanics386

9.12.2 Ship Collision387

9.12.3 Ship Grounding391

9.12.4 Design Standards for Ship Collision and Grounding396

References399

10 Fracture Mechanics and Ultimate Strength of Cracked Structures403

10.1 Fundamentals of Fracture Mechanics403

10.2 Basic Concepts for Fracture Mechanics Analysis406

10.2.1 Energy-based Concept406

10.2.2 Stress Intensity Factor Concept407

10.3 More on LEFM and the Modes of Crack Extension409

10.3.1 Useful K Solutions412

10.3.2 Fracture Toughness Testing413

10.4 Elastic-Plastic Fracture Mechanics414

10.4.1 Crack Tip Opening Displacement414

10.4.2 Other EPFM Measures：J-integral and Crack Growth Resistance Curve419

10.5 Fatigue Crack Growth Rate and its Relationship to the Stress Intensity Factor422

10.6 Ultimate Strength of Cracked Structures under Monotonic Extreme Loading425

10.6.1 Crack Damage Model425

10.6.2 Ultimate Strength of Plates with Existing Crack425

10.6.3 Ultimate Strength of Stiffened Panels with Existing Crack427

References429

11 A Semi-analytical Method for the Elastic-Plastic Large-deflection Analysis of Plates under Combined Loading433

11.1 Features of the Method433

11.2 Analysis of Elastic Large-deflection Behavior434

11.2.1 The Traditional Approach435

11.2.2 The Incremental Approach437

11.3 Application to the Elastic Large-deflection Analysis of Simply Supported Plates439

11.4 Treatment of Plasticity444

11.5 Computer Software ALPS/SPINE444

11.5.1 Outline of the Computer Software444

11.5.2 Application Examples445

References454

12 The Nonlinear Finite Element Method455

12.1 Introduction455

12.2 Solution Procedures for Nonlinear Problems455

12.2.1 The Direct Method456

12.2.2 The Incremental Method457

12.2.3 The Newton-Raphson Method458

12.2.4 The Modified Newton-Raphson Method459

12.2.5 The Arc Length Method459

12.3 Features of the Plastic Node Method460

12.4 Formulation of Nonlinear Rectangular Plate-Shell Element461

12.4.1 Nodal Forces and Nodal Displacements461

12.4.2 Strain-Displacement Relationship462

12.4.3 Stress-Strain Relationship463

12.4.4 Elastic Tangent Stiffness Matrix464

12.4.5 Displacement （Shape） Function466

12.4.6 Yield Condition467

12.4.7 Elastic-Plastic Tangent Stiffness Matrix469

12.4.8 Treatment of the Bauschinger Effect473

12.4.9 Local to Global Transformation Matrix474

12.5 Computer Software NATS474

12.5.1 Outline of the Computer Software474

12.5.2 Application Examples475

References477

13 The Idealized Structural Unit Method479

13.1 Features of the Method479

13.2 ISUM Modeling Strategies for Steel-plated Structures481

13.3 Procedure for Development of the ISUM Units482

13.4 The ISUM Beam-Column Unit483

13.5 The ISUM Rectangular Plate Unit for Analysis of Ultimate Strength485

13.6 The ISUM Rectangular Plate Unit for Analysis of Collision and Grounding Mechanics487

13.7 The ISUM Stiffened Panel Unit for Analysis of Ultimate Strength489

13.8 The ISUM Stiffened Panel Unit for Analysis of Collision and Grounding Mechanics490

13.9 The ISUM Gap/Contact Unit491

13.10 Treatment of Dynamic/Impact Load Effects492

13.11 Computer Software ALPS/ISUM493

13.11.1 Outline of the Computer Software493

13.11.2 Application Examples494

References505

Appendices507

A.1 How to Download the Computer Programs Presented in This Book507

A.2 Source Listing of the FORTRAN Computer Program CARDANO507

A.3 SI Units508

A.3.1 Conversion Factors508

A.3.2 SI Unit Prefixes510

A.4 Density and Viscosity of Water and Air510

Index511