Exact Solutions for Buckling of Structural Members (CRC Series in Computational Mechanics and Applied Analysis)

EXACT SOLUTIONS FOR BUCKLING OF STRUCTURAL MEMBERS......Page 1
Dedication......Page 5
About the Authors......Page 6
Preface......Page 7
Contents......Page 9
1.1 What Is Buckling?......Page 12
1.2 Importance of Buckling Load......Page 14
1.3 Historical Review......Page 16
1.4 Scope of the Book......Page 17
REFERENCES......Page 18
2.1.1 Governing Equations and Boundary Conditions......Page 19
2.1.2 Columns with Classical Boundary Conditions......Page 21
2.1.3 Columns with Elastic End Restraints......Page 22
2.2 Euler Columns under End Load Dependent on Direction......Page 24
2.3 Euler Columns with an Intermediate Axial Load......Page 26
2.4 Euler Columns with an Intermediate Restraint......Page 31
2.5.1 Columns with an Internal Hinge......Page 40
2.5.2 Columns with a Rotational Restrained Junction......Page 42
2.6 Euler Columns with a Continuous Elastic Restraint......Page 45
2.7.1 Infinite Hanging Heavy Column with Bottom Load......Page 50
2.7.2 Heavy Column with Top Load......Page 52
2.7.3 Two-Segment Heavy Column – General Formulation......Page 54
2.7.4 Heavy Column Partially Submerged in Liquid......Page 57
2.7.5 Standing Two-Segment Heavy Column......Page 59
2.8.1 Introduction......Page 61
2.8.2 Columns under End Concentrated Load......Page 62
2.8.3 Columns under Distributed Axial Load......Page 67
2.9.1 Columns under End Axial Load......Page 68
2.9.2 Columns under Intermediate and End Axial Loads......Page 74
2.10 Flexural–Torsional Buckling of Columns......Page 77
2.11 Inelastic Buckling of Columns......Page 79
REFERENCES......Page 81
3.1.2 Beams of Rectangular Cross-Section......Page 86
3.1.3 I-Beams......Page 90
3.2.1 Governing Equations......Page 94
3.2.2 Circular Rings under Uniform Pressure......Page 95
3.2.3 Circular Rings with Hinges......Page 96
3.2.4 Circular Rings with Distributed Resistance......Page 98
3.2.5 General Circular Arch......Page 99
3.2.6 Symmetrical Circular Arch......Page 101
3.2.7 Symmetrical Arches with a Central Torsional Hinge......Page 104
3.3 Flexural-Torsional Buckling of Arches under Equal End Moments......Page 106
REFERENCES......Page 108
4.2 Governing Equations in Rectangular Coordinates......Page 110
4.3 Governing Equations in Polar Coordinates......Page 113
4.4.1 General Solution for Axisymmetric Buckling......Page 117
4.4.2 Axisymmetric Buckling of Clamped Plates......Page 119
4.4.4 Axisymmetric Buckling of Simply Supported Plates with Rotational Restraint......Page 120
4.4.5 General Solution for Nonaxisymmetric Buckling......Page 121
4.4.6 Buckling of Plates with Internal Ring Support......Page 122
4.4.7 Axisymmetric Buckling of Plates under Intermediate and Edge Radial Loads......Page 125
4.4.8 Buckling of Annular Plates under Uniform Compression......Page 129
4.5.1 Preliminary Comments......Page 135
4.5.2 Simply Supported Biaxially Loaded Plates......Page 136
Biaxially Compressed Plate......Page 137
Biaxially Loaded Plate......Page 138
Uniaxially Compressed Plate......Page 139
4.5.3 Plates Simply Supported along Two Opposite Sides and Compressed in the Direction Perpendicular to These Sides......Page 142
Buckling of SSSF Plates......Page 144
Buckling of SSCF Plates......Page 146
Buckling of SSCC Plates......Page 148
4.5.4 Plates with Abrupt Changes in Geometry or Material Properties......Page 150
Plates with an Internal Line Hinge......Page 154
Plates with Internal Line Supports......Page 155
Plates with Intermediate Inplane Load......Page 156
4.6 Simply Supported Isosceles Triangular Plates......Page 157
4.7.1 Governing Equations of Rectangular Plates......Page 159
4.7.2 Buckling Loads of Rectangular Plates......Page 161
4.7.3 Buckling Loads of Circular Plates......Page 163
4.8.1 Introduction......Page 167
4.8.2 Governing Equations of Circular Plates......Page 168
4.8.3 Buckling Solutions of Circular Plates......Page 170
4.8.4 Governing Equations of Rectangular Plates......Page 171
Simply Supported Rectangular Plates......Page 176
Rectangular Plates with Two Opposite Sides Simply Supported......Page 179
4.8.6 Buckling of Simply Supported Polygonal Plates......Page 185
REFERENCES......Page 189
5.2 Axisymmetric Buckling of Circular Cylindrical Shells under Uniform Axial Compression......Page 194
5.3 Nonaxisymmetric Buckling of Circular Cylindrical Shells under Uniform Axial Compression......Page 196
5.4 Buckling of Circular Cylindrical Panels under Uniform Axial Compression......Page 203
5.5 Buckling of Circular Cylindrical Shells under Lateral Pressure......Page 204
5.6 Buckling of Spherical Shells under Hydrostatic Pressure......Page 207
5.7 Buckling of Truncated Conical Shells under Axial Vertex Load......Page 209
REFERENCES......Page 212