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Chapter 1 Introduction 1

1.1 Types of Instability 1

1.2 Methods of Stability Analysis 6

1.3 Stability of PerfeCt Mechanical Models 8

1.4 Stability of Imperfect Mechanical Models 18

1.5 Stability of Snap-Through Mechanical Model 22

1.6 Mechanical Properties of Structural Steel 26

1.7 Residual Stress Distributions in Steel Members 32

1.8 Behavior and Steel Structure Design 36

Problem 49

References 51

Chapter 2 Flexural Buckling of Centrally Compressed Members 55

2.1 Introduction 55

2.2 Elastic Flexural Buckling of Centrally Compressed Members 56

2.3 Centrally Compressed Members with End Restrain 57

2.4 Effective Length Factors of Centrally Compressed Members 64

2.5 Elastic Large Deflection Analysis of Centrally Compressed Members 80

2.6 Effect of Initial Geometrical Imperfections on Centrally Compressed Members 84

2.7 Inelastic Flexural Buckling of Centrally Compressed Members 90

2.8 Effect of Residual Stresses on Centrally Compressed Members 99

2.9 Application of Stability Theory of Centrally Compressed Members on Steel Structure Design 105

Problems 131

References 133

Chapter 3 In-Plane Stability of Beam-Columns 136

3.1 Introduction 136

3.2 Deformations and Internal Forces of Simply Supported Elastic Beam-Columns under Transverse Loads 138

3.3 Deformations and Internal Forces of Fixed Ended Elastic Beam-Colunms under Transverse Loads 146

3.4 Deformations and Internal Forces of Elastic Beam-Column under end Moments 151

3.5 Equivalent Moment and Equivalent Moment Factor of Beam-Column 155

3.6 Slope-Deflection Equations of Elastic Beam-Column without Sway 159

3.7 Slope-Deflection Equations of Elastic Beam-Column with Sway 163

3.8 Slope-Deflection Equations of Elastic Beam-Column under Transverse Loads 164

3.9 In-Plane Ultimate Load of Beam-Column 167

3.10 Application of In-Plane Stability Theory of Beam-Columns on Steel Structure Design 181

3.11 Further Investigations of In-Plane Strength of Non-Sway Beam-Columns 202

Problems 209

References 210

Chapter 4 In-Plane Stability of Frames 213

4.1 Types of Instability of Frames 213

4.2 Elastic Buckling Loads of Frames by Equilibrium Method 216

4 3 Elastic Buckling Loads of Frames by Slope-Deflection Method 220

4.4 Elastic Buckling of Multi-Story Frames 228

4.5 Elastic Buckling Loads of Multistory Frames by Approximate Method 230

4.6 Stability of Frames under Primary Bending Moment 243

4.7 Elastic-Plastic Stability of Frames 249

4.8 Ultimate Loads of Sway Frames 251

4.9 Application of Stability Theory of Frames on Steel Structure Design 268

4.10 Overall Design Method of In-Plane Stability of Frame—Direct Analysis（Advanced Analysis）Method 300

4.11 Moment Rotation Curves of Beam-to-Column Connections and Design of Semi-Rigid Frames 318

4.12 Overall In-Plane Buckling of Single-Story Multi-Bay Pitched-Roof Frames 359

Problems 365

References 367

Chapter 5 Approximate Methods of Stability Analysis 372

5.1 Introduction 372

5.2 Principle of Energy Conservation 373

5.3 Principle of Stationary Value of Potential Energy and Principle of Minimum Potential Energy 377

5.4 Rayleigh-Ritz Method 383

5.5 Galerkin Method 387

5.6 Finite Difference Method 389

5.7 Finite Integral Method 395

5.8 Finite Element Method 402

5.9 Using Finite Element Method to Determine Effective Length Factors of The Unbraced Tapered Portal Framed Column 414

Problems 420

References 421

Chapter 6 Torsional Buckling and Flexural-Torsional Buckling of Compression Members 422

6.1 Introduction 422

6.2 Shear Center of Thin-Walled Open Section Members 424

6.3 Torsion of Thin-Walled Open Section Members 427

6.4 Elastic Torsional Buckling of Centrally Compressed Members 441

6.5 Elastic-Plastic Torsional Buckleng of Centrally Compressed Members 451

6.6 Elastic Flexural-Torsional Buckling of Centrally Compressed Members 456

6.7 Elastic-Plastic Flexural-Torsional Buckling of Centrally Compressed Members 465

6.8 Application of Torsional and Flexural-Torsional Buckling Theories of Centrally Compressed Members on Steel Structure Design 473

Problem 482

References 483

Appendix-Derivations of Ixf,Iyf,Ixyf,Ix,Iy,and ωfor Sloping Lipped Channel 484

Chapter 7 Flexural-Torsional Buckling of Beams 489

7.1 Introduction 489

7.2 Elastic Flexural-Torsional Buckling of Beams under Uniform Bending 491

7.3 Beams under Unequal end Moments 499

7.4 Beams under Transverse Loads 501

7.5 Elastic Flexural-Torsional Buckling of Beams with Varying Cross-Section 512

7.6 Elastic-Plastic Flexural-Torsional Buckling of Beams 518

7.7 Application of Flexural-Torsional Buckling Theory of Beams on Steel Structure Design 526

7.8 Ultimate Capacities and Design Formulas of Biaxial Bending Beams 565

7.9 Single Angle Flexural Members 575

Problems 580

References 581

Chapter 8 Flexural-Torsional Buckling of Beam-Columns 585

8.1 Introduction 585

8.2 Flexural-Torsional Buckling of Beam-Column by Energy Method 591

8.3 Elastic-Plastic Flexural-Torsional Buckling of Beam-Column 595

8.4 Application of Flexural-Torsional Buckling Theories of Beam-Columns on Steel Design 599

Problem 607

References 608

Chapter 9 Beam-Columns under Biaxial Bending 609

9.1 Elastic Differential Equilibrium Equations of Beam-Columns under Biaxial Bending 609

9.2 Flexural-Torsional Buckling Interaction Curves of Uniform Biaxial Bending Beam-Columns 612

9.3 Application of Biaxial Bending Theory of Beam-Columns for Steel Structural Design 615

References 623

Chapter 10 I-Section Beams and Beam-Columns under Bending and Torsion 625

10.1 Governing Differential Equations of Biaxial Bending Beam with Torsion 625

10.2 Testing Investigations for Steel Combined Flexure and Torsion of I-Shape Beams 641

10.3 Design Methodolgyo for Ultimate Limit States and Serviceability limit States 653

10.4 Summary and Conclusions 654

References 655

Chapter 11 Distortional Buckling of Steel I-Section Beams and Beam-Columns 657

11.1 Distortional Buckling of Steel Bi-Symmetric I-Section Beams 657

11.2 Theoretical Analysis on Distortional Buckling of Bi-Symmetric I-Section Beams 659

11.3 Theoretical Analysis on Distortional Buckling of Mono-symmetric I-Section Beams 661

11.4 Distortional Buckling of Steel Bi-Symmetric I-Section Beam-Columns 666

References 667

Chapter 12 Steel Beams with Corrugated Webs 669

12.1 Introduction 669

12.2 The Types of Corrugated Web Beams 669

12.3 Recent Application of Corrugated Steel Web I-Girders in Buildings and Bridges 669

12.4 A Review on Corrugated Steel Web I-Girder 670

12.5 Passing Bridges and Buildings with Corrugated Steel Web I-Girder 671

12.6 Flange Normal Stresses Due to In-Plane Bending 673

12.7 Shear Strength Capacity of Corrugated Webs I-Girder 675

12.8 Flexural-Torsional Buckling of Corrugated Webs I-Girder 678

12.9 Calculate I-Section Properties 684

12.10 Considering Point Load Height Effects,Determine Moment Modification Factor 684

12.11 Transplant Theoretical and Pratical Design Method to GB 50017—2014 694

12.12 Moment Gradient Correction Factor and Inelastic Flexural-Torsional Buckling of I-Girder with Corrugated Steel Webs 697

12.1 3 Conclusion 699

References 700

Chapter 13 Buckling of Thin Plates 702

13.1 Introduction 702

13.2 Equilibrium Equations of a Plate by Small Defection Theory 703

13.3 Elastic Buckling Loads of Simply Supported Plates under Uniform Compression in One Direction 709

13.4 Elastic Buckling Loads of Plates by Energy Method 712

13.5 Elastic Buckling of Simply Supported Plates under Non-Uniform Bending 717

13.6 Elastic Buckling of Simply Supported Plates under Uniform Shear 720

13.7 Differential Equations of Plates by Large Deflection Theory 722

13.8 Post-Buckling Strength of Simply Supported Plates under Uniform Compression 727

13.9 Elastic-Plastic Buckling Analysis of Plates 733

13.10 Application of Buckling Theory of Plates on Steel Structure Design 742

13.11 Plate Elements in a Centrally Compressed Member 744

13.12 Web in Beam and Stability Design of Plate Girder 752

13.13 Plate Elements in Beam-Columns 782

13.14 Provisions of Classification and Recommendation for Limit State Design of Steel Structures in Architectural Institute of Japan 792

13.15 Effective Width of Plate Elements in Cold-Formed Steel Sections 811

13.16 Design of Axially Loaded Slender Compression Members 846

13.17 Utilization of Web Post-Buckling Strength in Slender I-Section Beam-Columns 859

13.18 Buckling Tests on Cold-Formed Hollow Section of Beam-Columns 869

Problems 876

References 877

Chapter 14 Buckling of Cold-Formed Steel Members 883

14.1 Buckling of Cold-Formed Steel Columns and Beams with Holes 883

14.2 Global Flexural Buckling of Cold-Formed Steel Perforated Columns 883

14.3 Flexural-Torsional Buckling of Cold-Formed Steel Perforated Beams 886

14.4 Distortional Buckling Load of Cold-Formed Steel Perforated Columns and Beams 886

14.5 Local Buckling Load of Cold-Formed Steel Perforated Columns and Beams 887

14.6 Cold-Formed web Crippling 897

14.7 Tests and Design of Cold-Formed Channels under web Crippling 898

14.8 Behaviour of Stainless Steel Oval Hollow Section（OHS）Members 906

14.9 Structural Response of Stainless Steel Oval Hollow Section Members under Compression 908

14.10 Direct Strength Method（DSM）of Cold-Formed Member Design 913

14.11 Direct Strength Method for Buckling Capacity of Cold-Formed Steel Members with Uniform and Non-Uniform Elevated Temperatures 928

14.12 Direct Strength Method for Buckling Capacity of Cold-Formed Steel Beams with Uniform and Non-Uniform Elevated Temperature 936

14.13 Conclusions 953

14.14 Recent Investigations on Lateral-Torsional Buckling of Beams in Fire 954

14.15 Lateral-Torsional Buckling Behaviour of Cellular Beams 960

14.16 Lateral-Torsional Buckling Behaviour of Cellular Beams in Case of Fire 977

14.17 Conclusions 984

References 984

Chapter 15 Buckling of Cylindrical Sheels 990

15.1 Introduction 990

15.2 Equilibrium Equations of Cylinderical Shell by Small Deflection Theory 990

15.3 Elastic Buckling of Cylindrical Sheel under Axial Compression 994

15.4 Differential Equations on Large Deflection Theory of Cylindrical Shell 996

15.5 Buckling of Imperfect Cylindrical Shell 998

15.6 Elastic Buckling of Cylindrical Shell under Uniform Hoop Compression 1005

15.7 Cylindrical Buckling under Combined Axial and Hoop Loadings 1009

15.8 Elastiuc Buckling of Cylindrical Shell under Torsion 1013

15.9 Further Investigations for Imperfect Cylindrical Shells under External Pressure 1017

15.10 Conculusions 1021

References 1022

Answers to Some Selected Problems 1025

APPENDIX A 1033

AUTHOR INDEX 1180

SUBJECT INDEX 1188

POSTSCRIPT 1200