Theory of Elastic Stability (Dover Civil and Mechanical Engineering) [2 ed.] 0486472078, 9780486472072

Table of contents :
Front Matter
Prefaces
Preface to the Second Edition
Table of Contents
1. Beam-Columns
1.1 Introduction
1.2 Differential Equations for Beam-Columns
1.3 Beam-Column with a Concentrated Lateral Load
1.4 Several Concentrated Loads
1.5 Continuous Lateral Load
1.6 Bending of a Beam-Column by Couples
1.7 Approximate Formula for Deflections
1.8 Beam-Columns with Built-in Ends
1.9 Beam-Columns with Elastic Restraints
1.10 Continuous Beams with Axial Loads
1.10.1 Continuous Beams on Rigid Supports
1.10.2 Continuous Beams with Supports Not on a Straight Line
1.10.3 Continuous Beams Rigidly Connected to Columns
1.10.4 Continuous Beams on Elastic Supports
1.11 Application of Trigonometric Series
1.12 The Effect of Initial Curvature on Deflections
1.12.1 Solution by Equivalent Lateral Load
1.12.2 The Phenomenon of Reversal of Deflections
1.12.3 Bar with Lateral Loading
1.12.4 Bar with Fixed Ends
1.13 Determination of Allowable Stresses
2. Elastic Buckling of Bars and Frames
2.1 Euler's Column Formula
2.2 Alternate Form of the Differential Equation for Determining Critical Loads
2.2.1 Column with One End Fixed and the other Free
2.2.2 Column with One End Fixed and the other Pinned
2.2.3 Fixed-End Column
2.2.4 Column with Load through a Fixed Point
2.2.5 Bar with Rounded Ends
2.3 The Use of Beam-Column Theory in Calculating Critical Loads
2.4 Buckling of Frames
2.5 Buckling of Continuous Beams
2.6 Buckling of Continuous Beams on Elastic Supports
2.7 Large Deflections of Buckled Bars The Elastics
2.8 The Energy Method
2.9 Approximate Calculation of Critical Loads by the Energy Method
2.10 Buckling of a Bar on an Elastic Foundation
2.11 Buckling of a Bar with Intermediate Compressive Forces
2.12 Buckling of a Bar under Distributed Axial Loads
3. Inelastic Buckling of Bars
3.1 Inelastic Bending
3.2 Inelastic Bending Combined with Axial Load
3.3 Inelastic Buckling of Bars. Fundamental Case
3.4 Inelastic Buckling of Bars with other End Conditions
4. Experiments and Design Formulas
4.1 Column Tests
4.2 Ideal-Column Formulas as a Basis of Column Design
4.3 Empirical Formulas for Column Design
4.4 Assumed Inaccuracies as a Basis of Column Design
4.5 Various End Conditions
4.6 The Design of Built-up Columns
5. Torsional Buckling
5.1 Introduction
5.2 Pure Torsion of Thin-Walled Bars of Open Cross Section
5.3 Nonuniform Torsion of Thin-Walled Bars of Open Cross Section
5.4 Torsional Buckling
5.5 Buckling by Torsion and Flexure
5.5.1 Bar with Built-in Ends
5.5.2 Cross Section with One Axis of Symmetry
5.6 Combined Torsional and Flexural Buckling of a Bar with Continuous Elastic Supports
5.6.1 Cross Section with Two Axes of Symmetry
5.6.2 Cross Section with One Axis of Symmetry
5.6.3 Bar with Prescribed Axis of Rotation
5.6.4 Bar with Prescribed Plane of Deflection
5.7 Torsional Buckling under Thrust and End Moments
6. Lateral Buckling of Beams
6.1 Differential Equations for Lateral Buckling
6.2 Lateral Buckling of Beams in Pure Bending
6.2.1 I Beam
6.2.2 Narrow Rectangular Beam
6.3 Lateral Buckling of a Cantilever Beam
6.3.1 I Beam
6.3.2 Narrow Rectangular Beam
6.4 Lateral Buckling of Simply Supported I Beams
6.4.1 Concentrated Load at the Middle
6.4.2 Uniform Load
6.5 Lateral Buckling of Simply Supported Beam of Narrow Rectangular Cross Section
6.6 Other Cases of Lateral Buckling
6.6.1 Beams with Intermediate Lateral Support
6.6.2 Beams with Lateral Constraint at the Ends
6.7 Inelastic Lateral Buckling of I Beams
7. Buckling of Rings, Curved Bars, and Arches
7.1 Bending of a Thin Curved Bar with a Circular Axis
7.2 Application of Trigonometric Series in the Analysis of a Thin Circular Ring
7.3 Effect of Uniform Pressure on Bending of a Circular Ring
7.4 Buckling of Circular Rings and Tubes under Uniform External Pressure
7.5 The Design of Tubes under Uniform External Pressure on the Basis of Assumed Inaccuracies
7.6 Buckling of a Uniformly Compressed Circular Arch
7.7 Arches of other Forms
7.7.1 Parabolic Arch
7.7.2 Catenary Arch
7.8 Buckling of Very Flat Curved Bars
7.9 Buckling of a Bimetallic Strip
7.10 Lateral Buckling of a Curved Bar with Circular Axis
8. Bending of Thin Plates
8.1 Pure Bending of Plates
8.2 Bending of Plates by Distributed Lateral Load
8.2.1 Built-in Edge
8.2.2 Simply Supported Edge
8.2.3 Free Edge
8.2.4 Elastically Supported and Elastically Built-in Edge
8.3 Combined Bending and Tension or Compression of Plates
8.4 Strain Energy in Bending of Plates
8.4.1 Pure Bending
8.4.2 Bending of a Plate by Lateral Load
8.4.3 Combined Bending and Tension or Compression of Plates
8.5 Deflections of Rectangular Plates with Simply Supported Edges
8.6 Bending of Plates with a Small Initial Curvature
8.7 Large Deflections of Plates
9. Buckling of Thin Plates
9.1 Methods of Calculation of Critical Loads
9.2 Buckling of Simply Supported Rectangular Plates Uniformly Compressed in One Direction
9.3 Buckling of Simply Supported Rectangular Plates Compressed in Two Perpendicular Directions
9.4 Buckling of Uniformly Compressed Rectangular Plates Simply Supported along Two Opposite Sides Perpendicular to the Direction of Compression and Having Various Edge Conditions along the other Two Sides
9.5 Buckling of a Rectangular Plate Simply Supported along Two Opposite Sides and Uniformly Compressed in the Direction Parallel to Those Sides
9.6 Buckling of a Simply Supported Rectangular Plate under Combined Bending and Compression
9.7 Buckling of Rectangular Plates under the Action of Shearing Stresses
9.8 Other Cases of Buckling of Rectangular Plates
9.9 Buckling of Circular Plates
9.10 Buckling of Plates of other Shapes
9.10.1 Oblique Plates with Clamped Edges under Uniform Compression
9.10.2 Oblique Plate with Clamped Edges under Pure Shear
9.10.3 Triangular Plate
10. Bending of Thin Shells
10.1 Deformation of an Element of a Shell
10.2 Symmetrical Deformation of a Circular Cylindrical Shell
10.3 Inextensional Deformation of a Circular Cylindrical Shell
10.4 General Case of Deformation of a Cylindrical Shell
10.5 Symmetrical Deformation of a Spherical Shell
11. Buckling of Shells
11.1 Symmetrical Buckling of a Cylindrical Shell under the Action of Uniform Axial Compression
11.2 Inextensional Forms of Bending of Cylindrical Shells due to Instability
11.3 Buckling of a Cylindrical Shell under the Action of Uniform Axial Pressure
11.3.1 General Case
11.4 Experiments with Cylindrical Shells in Axial Compression
11.5 Buckling of a Cylindrical Shell under the Action of Uniform External Lateral Pressure
11.6 Bent or Eccentrically Compressed Cylindrical Shells
11.7 Axial Compression of Curved Sheet Panels
11.8 Curved Sheet Panels under Shear or Combined Shear and Axial Stress
Notations
Appendix
Table A.1 Table of the Functions phiu, psiu, chiu
Table A.2 Table of the Functions etau and lambdau
Table A.3 Properties of Sections
Name Index
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Subject Index
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B
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