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

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 practicing engineers and students alike. Written in both US and SI units, this invaluable guide is perfect for readers within and outside of the US. Structural Stability Theory and Practice: Buckling of Columns, Beams, Plates, and Shell offers:

• Detailed and patiently developed mathematical derivations and thorough explanations
• Energy methods that are incorporated throughout the chapters
• Connections between theory, design specifications and solutions
• The latest codes and standards from the American Institute of Steel Construction (AISC), Canadian Standards Association (CSA), Australian Standards (SAA), Structural Stability Research Council (SSRC), and Eurocode 3
• Solved and unsolved practice-oriented problems in every chapter, with a solutions manual for unsolved problems included for instructors

Ideal for practicing professionals in civil, mechanical, and aerospace engineering, as well as upper-level undergraduates and graduate students in structural engineering courses, Structural Stability Theory and Practice: Buckling of Columns, Beams, Plates, and Shell provides readers with detailed mathematical derivations along with thorough explanations and practical examples.

SUKHVARSH JERATH, PH.D., P.E., F.ASCE, is Professor Emeritus of Civil Engineering at the University of North Dakota. Dr. Jerath has over 40 years of experience teaching and researching structural design and analysis, structural mechanics, and properties of civil engineering materials. He is a fellow of the American Society of Civil Engineers and a member of the ASME and ASEE.

Dedication

Foreword

Preface

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 Displaced shape equilibrium method

1.3.1.2 Energy Method

1.3.2 Two Rigid Bars Connected by Rotational Springs

1.3.3 Three Member Truss

1.3.3.1 Energy method

1.3.4 Three Rigid Bars with Two Linear Springs

1.3.4.1 Displaced shape equilibrium method

1.3.4.2 Energy method

1.4 LARGE DISPLACEMENT ANALYSIS

1.4.1 Rigid bar Supported by a Translational Spring

1.4.1.1 Displaced shape equilibrium method

1.4.1.2 Energy method

1.4.2 Rigid Bar Supported by Translational and Rotational Springs

1.4.2.1 Displaced shape equilibrium method

1.4.2.2 Energy method

1.4.3 Two Rigid Bars Connected by Rotational Springs

1.4.3.1 Energy method

1.5 IMPERFECTIONS

1.5.1 Rigid bar Supported by a Rotational Spring at the Base

1.5.1.1 Displaced shape equilibrium method

1.5.1.2 Energy method

1.5.2 Two Rigid Bars Connected by Rotational Springs

1.5.2.1 Displaced shape equilibrium method

1.5.2.2 Energy method

PROBLEMS        

REFERENCES

CHAPTER 2  COLUMNS

 2.1 GENERAL

 2.2 CRITICAL LOAD BY CLASSICAL COLUMN THEORY

  2.2.1 Pinned – pinned Column

  2.2.2 Fixed – fixed Column

  2.2.3 Cantilever Column

  2.2.4 Fixed – pinned Column

 2.3 EFFECTIVE LENGTH OF A COLUMN

 2.4 SPECIAL CASES

  2.4.1 Pinned – pinned Column with Intermediate Compressive Force   Force

  2.4.2 Cantilever Column with Intermediate Compressive Course  Course

 2.5 HIGHER-ORDER GOVERNING DIFFERENTIAL EQUATIONS

  2.5.1 Boundary Conditions for Different Supports

  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 SUPOORTS

  2.7.1 Column Pinned at One End and Elastic Support at the other End  other End

  2.7.2 Column Fixed at One end and Elastic Support at the Other End  other End

 2.8 ECCENTRICALLY LOADED COLUMNS

  2.8.1 Secant Formula

 2.9 GEOMETRICALLY IMPERFECT COLUMNS

  2.9.1 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

 2.11 ENERGY METHODS

  2.11.1 Calculus of Variations

  2.11.2 Rayleigh - Ritz Method

  2.11.3 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

  3.8.2 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

  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 COLUMNS WITH A LATERAL CONCENTRATED LOAD

  4.3.1 Concentrated lateral Load at the Mid-span

  4.3.2 Beam Columns with Several Concentrated Loads

4.4 BEAM COLUMN WITH LATERAL UNIFORMLY DISTRIBUTED LOAD

4.4.1 Beam Columns with Uniformly Distributed Load Over a Portion of Their span

4.4.2 Beam Columns with Uniformly Increasing Load Over a portion of their Span

 4.5 BEAM COLUMNS SUBJECTED TO MOMENTS

  4.5.1 Span Moment on Beam Columns

  4.5.2 End moment on a Beam Column

  4.5.3 Moments at Both Ends of Beam Column

 4.6 COLUMNS WITH ELASTIC CONSTRAINTS

4.7 BEAM COLUMNS WITH DIFFERENT END CONDITIONS AND LOADS

 4.7.1 Pinned-Fixed Beam Columns with a Concentrated Load

4.7.2 Pinned-Fixed Beam Columns Subjected to Uniformly Distributed Load

4.7.3 Fixed-Fixed Beam Column with Concentrated Force

4.7.4 Fixed-Fixed Beam Column with Uniformly Distributed Load

4.8 ALTERNATE METHOD USING BASIC DIFFERENTIAL EQUATIONS

 4.8.1 Fixed-Fixed Beam Column with Uniformly Distributed Load

 4.8.2 Pinned-Fixed Beam Column with Uniformly Distributed Load

 4.9 CONTINUOUS BEAM COLUMNS

 4.10 SLOPE DEFLECTION EQUATIONS FOR BEAM COLUMNS

4.10.1 Beam Columns Subjected to Rotations and Relative        

   Relative Displacements at the Ends

4.10.2 Beam Columns Having One End Hinged

4.10.3 Beam Columns with Transverse Loading

4.10.4 Beam Columns in Single curvature

 4.11 INELASTIC BEAM COLUMNS

  4.11.1 Case 1: Yielding on the Compression Side Only

  4.11.2 Case 2; Yielding on Both the Compression and Tension Sides  Tension Sides

 4.12 DESIGN OF BEAM COLUMNS

  4.12.1 Concept of Equivalent Moment and Factor Cm

  4.12.2 AISC Design Criteria for steel Beam Columns

  4.12.3 Eurocode 3 (ECS, 1993) Design Criteria

  4.12.4 Canadian Standards Association (CSA 194-CSA-S16.1)

  4.12.5 Australian standard AS4100-1990

 PROBLEMS         REFERENCES

CHAPTER 5  FRAMES

 5.1 INTRODUCTION

 5.2 CRITICAL LOAD BY EQUILIBRIUM METHOD

  5.2.1 Portal Frame without Sidesway

  5.2.2 Portal Frame with Sidesway

  5.2.3 Frame with Prime Bending and without Sidesway

 5.3 CRITCAL LOAD 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

  5.3.6 Frames with Prime bending and Sidesway

  5.3.7 Box Frame without Sidesway

  5.3.8 Multistory – Multibay Frames Without Sidesway

5.4 CRITICAL LOAD BY MATRIX AND FINITE ELEMENT METHODS

 5.4.1 Formulation of Element Stiffness Matrix

 5.4.2 Formulation of Structure Stiffness Matrix

 5.4.3 In Span loading

5.4.4 Buckling of Frame Pinned at the Base and 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)

  5.5.3 Inelastic Buckling of Frames

 PROBLEMS       

 REFERENCES

CHAPTER 6 TORSIONAL BUCKLING AND LATERAL BUCKLING OF BEAMS

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 Wall Open Sections with Rectangular Elements Intersecting at a Point

6.5.2 Thin Wall 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 – 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

6.8.5 Lateral Buckling of Narrow Rectangular Beams Acted on by Uniform Moment

 6.9 ENERGY METHOD

6.9.1 Lateral Buckling of Simply Supported I Beams – Concentrated Load at the Mid Span

6.9.2 Lateral Buckling of Simply Supported I Beams - Uniformly Distributed Load

6.9.3 Lateral Buckling of Cantilever Rectangular Beams – Concentrated Load at the Free end

6.10 BEAMS WITH DIFFERENT SUPPORT AND LOADING CONDITIONS

 6.10.1 Different Support Conditions

 6.10.2 Different Loading Conditions

6.11 DESIGN FOR TORSIONAL AND LATERAL BUCKLING

 6.11.1 AISC Design Criteria for Steel Beams

PROBLEMS        

REFERENCES

CHAPTER 7  BUCKLING OF PLATES

 7.1 INTRODUCTION

 7.2 THEORY OF PLATE BENDING

 7.3 BUCKLING OF THIN PLATES

  7.3.1 In Plane Forces

 7.4 BOUNDARY CONDITIONS

  7.4.1 Simply Supported Edge

  7.4.2 Built-in Edge

  7.4.3 Free Edge

  7.4.4 Elastically Supported and Elastically Built-in Edge

7.5 BUCKLING OF RECTANGULAR PLATES UNIFORMLY COMPRESSED IN ONE DIRECTION

7.5.1 Buckling of Rectangular Plates with Simply Supported Edges

7.5.2 Buckling of Rectangular Plates with Other Boundary Conditions

7.5.3 Loading Edges Simply Supported, the Side y = 0 is Clamped, and the Side y = b is Free

7.5.4 Loading Edges Simply Supported and the Sides y = 0 and y = b are Clamped

7.5.5 Loading Edges Simply Supported, the Side y = 0 is Simply Supported, and the Side y = b is Free

7.5.6 Loading Edges Simply Supported, the Side y = 0 is elastically Built-In and the Side y= b is Free

7.5.7 Loading Edges Simply Supported, the Sides y = ± b/2 are Elastically Built-In

7.5.8 Loading Edges Simply Supported, the Sides y = 0 and y = b are Supported by Elastic Beams

 7.6 ENERGY METHOD

  7.6.1 Strain Energy Due to Bending in Plates

  7.6.2 Potential Energy of the External Forces in Plates

7.6.3 Rectangular plates Subjected to Uniaxial Compressive Force and Fixed on All Edges

7.6.4 A Rectangular Plate with Clamped Edges under Compressive Pressure in Two Perpendicular Directions

7.6.5 Buckling of Simply Supported Rectangular Plates under the Action of Shear Forces

7.6.6 Buckling of Simply Supported Rectangular Plates under Combined Bending and Compression

7.6.7 Buckling of Plates with Stiffeners

7.6.8 Simply Supported Rectangular Plates with Longitudinal Stiffeners

7.6.9 Simply Supported Rectangular Compressed Plate with Transverse Stiffeners

7.6.10 Simply Supported Rectangular Plates with   Stiffeners in Both the Longitudinal and Transverse Directions

 7.7 BUCKLING OF CIRCULAR PLATES

  7.7.1 Clamped Plate

  7.7.2 Simply Supported Plate

 7.8 FINITE DIFFERENCE METHOD

7.8.1 Critical Load for a Simply Supported Plate Subjected to Biaxial Loading

 7.9 FINITE ELEMENT METHOD

 7.10 LARGE DEFLECTION THEORY OF PLATES

  7.10.1 Post-buckling Behavior of Plates

 7.11 INELASTIC BUCKLING OF PLATES

  7.11.1 Rectangular plates with Simply Supported Edges

7.11.2 Plate with Loading Edges Simply Supported and the Sides y = 0 and y = b are Clamped

 7.12 ULTIMATE STRENGTH OF PLATES IN COMPRESSION

 7.13 LOCAL BUCKLING OF COMPRESSION ELEMENTS – DESIGN

 PROBLEMS       

 REFERENCES

CHAPTER 8  BUCKLING OF SHELLS

 8.1 INTRODUCTION

 8.2 LARGE DEFLECTION THEORY OF CYLINDRICAL SHELLS

 8.3 LINEAR THEORY OF CYLINDRICAL SHELLS

  8.3.1 Linear Membrane Equations for Cylindrical Shells

8.4 DONNELL LINEAR EQUATIONS OF STABILITY OF CYLINDRICAL SHELLS

8.5 ENERGY METHOD

8.6  APPLICATIONS OF LINEAR STABILITY EQUATIONS

 8.6.1 Circular Cylinders Under Axial Compression

 8.6.2 Circular Cylinders Under Uniform Lateral Pressure

8.6.2.1 Critical pressures for cylinders subjected to     External Pressure  

8.6.3 Cylinders Subjected to Torsion

8.6.4 Cylinders Subjected to Combined Axial Compression and Uniform External Lateral Pressure

8.6.5 Cylindrical Shells with Different End Conditions

 8.7 FAILURE AND POST BUCKLING BEHAVIOR OF CYLINDRICAL SHELLS

  8.7.1 Post Buckling Behavior of Cylindrical Shells

  8.7.2 Post Buckling Behavior of Cylindrical Panel

 8.8  GENERAL SHELLS

  8.8.1 Nonlinear Equations of Equilibrium

  8.8.2 Linear Equations of Stability (Donnell Type)

 8.9 SHELLS OF REVOLUTION

  8.9.1 Stability Equations where Pre-Buckling Rotations Retained  Retained

  8.9.2 Stability Equations with Pre-Buckling Rotations Neglected   Neglected

  8.9.3 Circular Flat Plates

  8.9.4 Shallow Spherical Caps

  8.9.5 Conical Shells

  8.9.6 Toroidal Shells

 PROBLEMS       

 REFERENCES

APPENDIX A Slope Deflection Coefficients for Beam Column Buckling

APPENDIX B: Torsion Properties of Thin Wall Open Cross-sections

APPENDIX C: Calculus of Variations

APPENDIX D: Euler equations

APPENDIX E: Differential Geometry in Curvilinear Coordinates  

Index

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