Preface ........................................................ ix
Authors Biography .............................................. xi
1 Buckling of Columns .......................................... 1
1.1 Introduction ............................................ 1
1.2 Neutral Equilibrium ..................................... 3
1.3 Euler Load .............................................. 4
1.4 Differential Equations of Beam-Columns .................. 8
1.5 Effects of Boundary Conditions on the Column
Strength ............................................... 15
1.6 Introduction to Calculus of Variations ................. 18
1.7 Derivation of Beam-Column GDE Using Finite Strain ...... 24
1.8 Galerkin Method ........................................ 27
1.9 Continuous Beam-Columns Resting on Elastic Supports .... 29
1.10 Elastic Buckling of Columns Subjected to Distributed
Axial Loads ............................................ 38
1.11 Large Deflection Theory (The Elastica) ................. 44
1.12 Eccentrically Loaded Columns—Secant Formula ............ 52
1.13 Inelastic Buckling of Straight Column .................. 56
1.14 Metric System of Units ................................. 66
General References .......................................... 67
References .................................................. 68
Problems .................................................... 69
2 Special Topics in Elastic Stability of Columns .............. 75
2.1 Energy Methods ......................................... 76
2.2 Stability Criteria ..................................... 89
2.3 Rayleigh-Ritz Method ................................... 92
2.4 The Rayleigh Quotient .................................. 95
2.5 Energy Method Applied to Columns Subjected to
Distributed Axial Loads ................................ 99
2.6 Elastically Supported Beam-Columns .................... 115
2.7 Differential Equation Method .......................... 120
2.8 Methods of Successive Approximation ................... 124
2.9 Matrix Method ......................................... 133
2.10 Free Vibration of Columns under Compressive Loads ..... 138
2.11 Buckling by a Nonconservative Load .................... 142
2.12 Self-Adjoint Boundary Value Problems .................. 146
References ................................................. 149
Problems ................................................... 150
3 Beam-Columns ............................................... 155
3.1 Transversely Loaded Beam Subjected to Axial
Compression ........................................... 155
3.2 Beam-Columns with Concentrated Lateral Loads .......... 161
3.3 Beam-Columns with Distributed Lateral Loads ........... 163
3.4 Effect of Axial Force on Bending Stiffness ............ 164
3.5 Ultimate Strength of Beam-Columns ..................... 185
3.6 Design of Beam-Columns ................................ 192
References ................................................. 195
Problems ................................................... 196
4 Continuous Beams and Rigid Frames .......................... 199
4.1 Introduction .......................................... 199
4.2 Continuous Beams ...................................... 199
4.3 Buckling Modes of Frames .............................. 203
4.4 Critical Loads of Frames .............................. 205
4.5 Stability of Frames by Matrix Analysis ................ 216
4.6 Second-order Analysis of a Frame by Slope-Deflection
Equations ............................................. 220
4.7 Effect of Primary Bending and Plasticity on the
Behavior of Frames .................................... 228
4.8 Stability Design of Frames ............................ 230
References ................................................. 240
Problems ................................................... 241
5 Torsion in Structures ...................................... 245
5.1 Introduction .......................................... 246
5.2 Uniform Torsion and St. Venant Theory ................. 247
5.3 Membrane Analogy ...................................... 251
5.4 Twisting of Thin Rectangular Bars ..................... 253
5.5 Torsion in the Inelastic Range ........................ 255
5.6 Torsion in Closed Thin-Walled Cross Sections .......... 260
5.7 Nonuniform Torsion of W Shapes ........................ 265
5.8 Nonuniform Torsion of Thin-Walled Open Cross
Sections .............................................. 280
5.9 Cross-Section Properties .............................. 287
References ................................................. 298
Problems ................................................... 298
6 Torsional and Flexural-Torsional Buckling .................. 303
6.1 Introduction .......................................... 303
6.2 Strain Energy of Torsion .............................. 305
6.3 Torsional and Flexural-Torsional Buckling of
Columns ............................................... 307
6.4 Torsional and Flexural-Torsional Buckling under
Thrust and End Moments ................................ 317
References ................................................. 325
Problems ................................................... 326
7 Lateral-Torsional Buckling ................................. 327
7.1 Introduction .......................................... 327
7.2 Differential Equations for Lateral-Torsional
Buckling .............................................. 328
7.3 Generalization of Governing Differential Equations .... 336
7.4 Lateral-Torsional Buckling for Various Loading and
Boundary Conditions ................................... 337
7.5 Application of Bessel Function to Lateral-Torsional
Buckling Problems ..................................... 343
7.6 Lateral-Torsional Buckling by Energy Method ........... 347
7.7 Design Simplification for Lateral-Torsional
Buckling .............................................. 362
References ................................................. 368
Problems ................................................... 369
8 Buckling of Plate Elements ................................. 373
8.1 Introduction .......................................... 373
8.2 Differential Equation of Plate Buckling ............... 374
8.3 Linear Equations ...................................... 390
8.4 Application of Plate Stability Equation ............... 401
8.5 Energy Methods ........................................ 418
8.6 Design Provisions for Local Buckling of Compression
Elements .............................................. 431
8.7 Inelastic Buckling of Plate Elements .................. 432
8.8 Failure of Plate Elements ............................. 433
References ................................................. 434
Problems ................................................... 437
9 Buckling of Thin Cylindrical Shell Elements ................ 441
9.1 Introduction .......................................... 441
9.2 Large-Deflection Equations (Donnell Type) ............. 442
9.3 Energy Method ......................................... 446
9.4 Linear Stability Equations (Donnell Type) ............. 450
9.5 Applications of Linear Buckling Equations ............. 455
9.6 Failure of Cylindrical Shells ......................... 465
9.7 Postbuckling of Cylindrical Shells .................... 466
References ................................................. 472
Problems ................................................... 473
10 Buckling of General Shell Elements ......................... 475
10.1 Introduction .......................................... 475
10.2 Nonlinear Equilibrium Equations ....................... 476
10.3 Linear Stability Equations (Donnell Type) ............. 490
10.4 Applications .......................................... 498
References ................................................. 514
Problems ................................................... 515
Author Index .................................................. 517
Subject Index ................................................. 521
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