Structural Stability Theory and Practice Buckling of Columns, Beams, Plates, and Shells

• Main Author: Jerath, Sukhvarsh
• Format: eBook
• Language: English
• Published: Newark Wiley 2020; John Wiley & Sons, Incorporated; Wiley-Blackwell
• Edition: 1
• Subjects: Buckling (Mechanics)

Discover the theory of structural stability and its applications in crucial areas in engineering Structural Stability Theory and Practice: Buckling of Columns, Beams, Plates, and Shells combines necessary information on structural stability into a single, comprehensive resource suitable for practici...

Table of Contents:

• 5.5.3 Inelastic Buckling of Frames -- Problems -- References -- Chapter 6 Torsional Buckling and Lateral Buckling of Beams -- 6.1 Introduction -- 6.2 Pure Torsion of Thin‐Walled Cross‐Sections -- 6.3 Non‐uniform Torsion of Thin‐Walled Open Cross‐Sections -- 6.3.1 I‐section -- 6.3.2 General Thin‐Walled Open Cross‐Sections -- 6.3.3 Warping Constant Cw of a Channel Section -- 6.4 Torsional Buckling of Columns -- 6.5 Torsional Buckling Load -- 6.5.1 Thin‐Walled Open Sections with Rectangular Elements Intersecting at a Point -- 6.5.2 Thin‐Walled Open Doubly Symmetric Sections -- 6.5.2.1 Pinned‐pinned Columns -- 6.5.2.2 Fixed‐fixed Columns -- 6.6 Torsional Flexural Buckling -- 6.6.1 Pinned‐pinned Columns -- 6.6.2 Fixed‐fixed Columns -- 6.6.3 Singly Symmetric Sections -- 6.6.3.1 Pinned‐pinned Columns -- 6.6.3.2 Fixed‐fixed Columns -- 6.7 Torsional Flexural Buckling: The Energy Approach -- 6.7.1 Strain Energy of Torsional Flexural Buckling -- 6.7.2 Potential Energy of External Loads in Torsional Flexural Buckling -- 6.8 Lateral Buckling of Beams -- 6.8.1 Lateral Buckling of Simply Supported, Narrow Rectangular Beams in Pure Bending -- 6.8.2 Lateral Buckling of Simply Supported I Beams in Pure Bending -- 6.8.3 Lateral Buckling of Simply Supported I Beams: Concentrated Load at the Mid‐Span -- 6.8.4 Lateral Buckling of Cantilever I Beams: Concentrated Load at the Free End -- 6.8.4.1 Lateral Buckling of Cantilever Narrow Rectangular Beams: Concentrated Load at the Free End -- 6.8.5 Lateral Buckling of Narrow Rectangular Cantilever Beams Acted on by Uniform Moment -- 6.9 The Energy Method -- 6.9.1 Lateral Buckling of Simply Supported I Beams: Concentrated Load at the Mid‐Span -- 6.9.1.1 Lateral Buckling of Simply Supported, Narrow Rectangular Beams: Concentrated Load at the Mid‐Span -- 6.9.2 Lateral Buckling of Simply Supported I Beams: Uniformly Distributed Load
• 2.4.1 Pinned‐Pinned Column with Intermediate Compressive Force -- 2.4.2 Cantilever Column with Intermediate Compressive Force -- 2.4.2.1 Case 1 -- 2.4.2.2 Case 2 -- 2.5 Higher‐Order Governing Differential Equation -- 2.5.1 Boundary Conditions for Different Supports -- 2.5.1.1 Pinned Support -- 2.5.1.2 Fixed Support -- 2.5.1.3 Free End -- 2.5.1.4 Guided Support -- 2.5.2 Pinned‐Pinned Column -- 2.5.3 Cantilever Column -- 2.5.4 Pinned‐Guided Column -- 2.6 Continuous Columns -- 2.7 Columns on Elastic Supports -- 2.7.1 Column Pinned at One End and Elastic Support at the Other End -- 2.7.2 Column Fixed at One End and Elastic Support at the Other End -- 2.8 Eccentrically Loaded Columns -- 2.8.1 The Secant Formula -- 2.9 Geometrically Imperfect Columns -- 2.9.1 The Southwell Plot -- 2.10 Large Deflection Theory of Columns -- 2.10.1 Pinned‐Pinned Column -- 2.10.2 Cantilever Column -- 2.10.3 Effective Length Approach -- 2.10.3.1 Pinned‐Pinned Column -- 2.10.3.2 Cantilever Column -- 2.10.3.3 Fixed‐Fixed Column -- 2.10.3.4 Fixed‐Pinned Column -- 2.11 Energy Methods -- 2.11.1 Calculus of Variations -- 2.11.2 The Rayleigh‐Ritz Method -- 2.11.3 The Galerkin Method -- Problems -- References -- Chapter 3 Inelastic and Metal Columns -- 3.1 Introduction -- 3.2 Double Modulus Theory -- 3.2.1 Rectangular Section -- 3.3 Tangent Modulus Theory -- 3.4 Shanley's Theory for Inelastic Columns -- 3.5 Columns with Other End Conditions -- 3.6 Eccentrically Loaded Inelastic Columns -- 3.7 Aluminum Columns -- 3.7.1 North American and Australian Design Practice -- 3.8 Steel Columns -- 3.8.1 Buckling of Idealized Steel I‐Section -- 3.8.1.1 Strong Axis Bending -- 3.8.1.2 Weak Axis Bending -- 3.8.2 Column Strength Curves for Steel Columns -- 3.8.3 Column Research Council Curve -- 3.8.4 Structural Stability Research Council Curves -- 3.8.5 European Multiple Column Curves
• 6.9.2.1 Lateral Buckling of Simply Supported, Narrow Rectangular Beams: Uniformly Distributed Load along the Centroidal Axis
• Cover -- Title Page -- Copyright -- Contents -- Foreword -- Preface -- About the Companion Website -- Chapter 1 Structural Stability -- 1.1 Introduction -- 1.2 General Concepts -- 1.2.1 Bifurcation of Equilibrium -- 1.2.2 Limit Load Instability -- 1.2.3 Finite Disturbance Instability -- 1.3 Rigid Bar Columns -- 1.3.1 Rigid Bar Supported by a Translational Spring -- 1.3.1.1 The Displaced Shape Equilibrium Method -- 1.3.1.2 The Energy Method -- 1.3.2 Two Rigid Bars Connected by Rotational Springs -- 1.3.2.1 The Displaced Shape Equilibrium Method -- 1.3.2.2 The Energy Method -- 1.3.3 Three‐Member Truss -- 1.3.3.1 The Energy Method -- 1.3.4 Three Rigid Bars with Two Linear Springs -- 1.3.4.1 The Displaced Shape Equilibrium Method -- 1.3.4.2 The Energy Method -- 1.4 Large Displacement Analysis -- 1.4.1 Rigid Bar Supported by a Translational Spring -- 1.4.1.1 The Displaced Shape Equilibrium Method -- 1.4.1.2 The Energy Method -- 1.4.2 Rigid Bar Supported by Translational and Rotational Springs -- 1.4.2.1 The Displaced Shape Equilibrium Method -- 1.4.2.2 The Energy Method -- 1.4.3 Two Rigid Bars Connected by Rotational Springs -- 1.4.3.1 The Energy Method -- 1.5 Imperfections -- 1.5.1 Rigid Bar Supported by a Rotational Spring at the Base -- 1.5.1.1 The Displaced Shape Equilibrium Method -- 1.5.1.2 The Energy Method -- 1.5.2 Two Rigid Bars Connected by Rotational Springs -- 1.5.2.1 The Displaced Shape Equilibrium Method -- 1.5.2.2 The Energy Method -- Problems -- References -- Chapter 2 Columns -- 2.1 General -- 2.2 The Critical Load According to Classical Column Theory -- 2.2.1 Pinned‐Pinned Column -- 2.2.2 Fixed‐Fixed Column -- 2.2.2.1 Symmetric Mode -- 2.2.2.2 Anti‐Symmetric Mode -- 2.2.3 Cantilever Column -- 2.2.4 Fixed‐Pinned Column -- 2.3 Effective Length of a Column -- 2.4 Special Cases
• 3.8.6 AISC Design Criteria for Steel Columns -- Problems -- References -- Chapter 4 Beam columns -- 4.1 Introduction -- 4.2 Basic Differential Equations of Beam Columns -- 4.3 Beam Column with a Lateral Concentrated Load -- 4.3.1 Concentrated Lateral Load at the Mid‐span -- 4.3.2 Beam Columns with Several Concentrated Loads -- 4.3.3 Beam Column with Lateral Uniformly Distributed Load -- 4.3.4 Beam Columns with Uniformly Distributed Load Over a Portion of Their Span -- 4.3.5 Beam Columns with Uniformly Increasing Load Over a Portion of Their Span -- 4.4 Beam Columns Subjected to Moments -- 4.4.1 Span Moment on Beam Column -- 4.4.2 End Moment on a Beam Column -- 4.4.3 Moments at Both Ends of Beam Column -- 4.4.3.1 Two Equal Moments -- 4.4.3.2 Moments at Both Ends of the Beam Column: Alternate Method -- 4.4.3.3 End Moments of the Same Sign Giving Double Curvature -- 4.5 Columns with Elastic Restraints -- 4.6 Beam Columns with Different End Conditions and Loads -- 4.6.1 Pinned‐fixed Beam Columns with a Concentrated Load -- 4.6.2 Pinned‐fixed Beam Columns Subjected to Uniformly Distributed Load -- 4.6.3 Fixed‐fixed Beam Column with Concentrated Force -- 4.6.4 Fixed‐fixed Beam Column with Uniformly Distributed Load -- 4.7 Alternate Method Using Basic Differential Equations -- 4.7.1 Fixed‐fixed Beam Column with Uniformly Distributed Load -- 4.7.2 Pinned‐fixed Beam Column with Uniformly Distributed Load -- 4.8 Continuous Beam Columns -- 4.9 Slope Deflection Equations for Beam Columns -- 4.9.1 Matrix Inversion -- 4.9.2 Beam Columns Subjected to Rotations and Relative Displacement at the Ends -- 4.9.3 Beam Columns Having One End Hinged -- 4.9.4 Beam Columns with Transverse Loading -- 4.9.5 Beam Columns in Single Curvature -- 4.10 Inelastic Beam Columns -- 4.10.1 Case 1: Yielding on the Compression Side Only
• 4.10.2 Case 2: Yielding on Both the Compression and Tension Sides -- 4.11 Design of Beam Columns -- 4.11.1 Concept of Equivalent Moment and Factor Cm -- 4.11.2 AISC Design Criteria for Steel Beam Columns -- 4.11.2.1 Doubly and Singly Symmetric Members Subjected to Flexure and Compression -- 4.11.2.2 Unsymmetric and Other Members Subject to Flexure and Axial Force -- 4.11.3 Eurocode 3 (ECS, 1993) Design Criteria -- 4.11.4 Canadian Standards Association (CSA 1994 - CSA‐S16.1) -- 4.11.5 Australian Standard AS4100‐1990 -- Problems -- References -- Chapter 5 Frames -- 5.1 Introduction -- 5.2 Critical Loads by the Equilibrium Method -- 5.2.1 Portal Frame Without Sidesway -- 5.2.1.1 Portal Frame Without Sidesway with Rigid or Extremely Flexible Beam -- 5.2.2 Portal Frame with Sidesway -- 5.2.2.1 Portal Frame Having Sidesway with a Rigid or Extremely Flexible Beam -- 5.2.3 Frame with Prime Bending and Without Sidesway -- 5.3 Critical Loads by Slope Deflection Equations -- 5.3.1 Portal Frame Without Sidesway -- 5.3.2 Portal Frame with Sidesway -- 5.3.3 Two‐Story Frame Without Sidesway -- 5.3.4 Two‐Bay Frame Without Sidesway -- 5.3.5 Frames with Prime Bending and Without Sidesway -- 5.3.5.1 Frame with Hinged Supports -- 5.3.5.2 Frame with Fixed Supports -- 5.3.6 Frames with Prime Bending and Sidesway -- 5.3.7 Box Frame Without Sidesway -- 5.3.8 Multistory‐Multibay Frames Without Sidesway -- 5.4 Critical Loads by Matrix and Finite Element Methods -- 5.4.1 Formation of the Element Stiffness Matrix -- 5.4.2 Formation of the Structure Stiffness Matrix -- 5.4.3 In Span Loading -- 5.4.4 Buckling of a Frame Pinned at the Base and with Sidesway Permitted -- 5.4.5 Nonlinear Geometric or Large Deflection Analysis (Second‐Order Elastic Analysis) -- 5.5 Design of Frame Members -- 5.5.1 Braced Frames (Sidesway Inhibited) -- 5.5.2 Unbraced Frames (Sidesway Not Inhibited)