The Stability of Elastic Systems

The Stability of Elastic Systems

Pergamon Unified Engineering Series

1st Edition - January 1, 1973

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  • Author: S. J. Britvec
  • eBook ISBN: 9781483185170

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The Stability of Elastic Systems presents some of the most important aspects of the stability and the non-linear behavior at finite deformations of several types of structural elastic systems, which are important for a more precise understanding of the static performance of such systems. This book is divided into eight chapters that aim to complete parts of classical, eigenvalue, theories of buckling and to demonstrate the important role played by finite deformations in the theoretical analyses of stability. Other chapters discuss the properties of prismatic members and the post-buckling behavior of plane frameworks. A chapter describes the elastic buckling and stability of statically determinate space frameworks. The remaining chapters cover the elastic buckling of statically indeterminate pin-jointed systems and space frameworks. These chapters also examine the non-conservative aspects of structural systems. This book will be of great value to practicing engineers and students.

Table of Contents

  • Preface


    Chapter 1 Principal Forms of Equilibrium Paths and their Stability

    1-1 Conservative Elastic Systems—Generalized Coordinates

    1-2 The Total Potential Energy Function—Principal Orthogonal Coordinates of Deformation

    1-3 Equilibrium States and Stability—Critical States—Critical and Non-Critical Coordinates

    1-4 Branching of Equilibrium Paths at a Critical Point—The Buckling Behavior

    1-5 Stability of Equilibrium Near a Simple Branching Point

    1-6 Symmetry in the Critical Coordinate at a Simple Branching Point

    1-7 Perfect Elastic Systems Depending on Several Load Parameters—Equilibrium Hyper-Surfaces

    1-8 Elastic Structural Systems with Non-Orthogonal Generalized Coordinates—Solution of the Non-Linear Equilibrium Equations at a Branching Point

    1-9 Several Critical Coordinates—Branching Points of Systems with Several Degrees of Freedom

    1-10 Symmetrical Elastic Structural Systems—Complete Symmetry

    1-11 Buckling of Geometrically Imperfect Elastic Systems—Equilibrium Paths of Imperfect Systems

    1-12 Equilibrium Paths of Imperfect Symmetrical Systems

    1-13 Adjacent Branching Points—Coupled Modes of Elastic Buckling

    Chapter 2 Analysis of Prismatic Members as Constitutive Elements of a System

    Exact Theory

    2-1 Buckling of Compressive Members in a Plane—Flexural Elastica

    2-2 Transverse Deformations

    2-3 Geometrical Compatibility

    2-4 Coordinates of Deformation of Compressive Members

    2-5 Internal Forces

    2-6 Internal Energy

    2-7 Summary of Basic Equations for Compressive Members—Generalized Equilibrium Equations

    2-8 Inflectional Elastica of Tensile Members

    2-9 Summary of Basic Equations for Inflectional Tensile Members

    2-10 Non-Inflectional Elastica of Tensile Members—Non-Symmetrical Cases

    2-11 Summary of Basic Equations for Non-Symmetrical, Noninflectional—Tensile Members

    2-12 Summary of Basic Equations for Symmetrical Tensile Members

    Approximate Theory

    2-13 Categories of Practical Deformations

    2-14 Generalized Equilibrium Equations for Single Members—Buckling of Prismatic Bars

    2-15 The First-Order Theory

    2-16 Pin-Ended Members or Columns

    The Post-Buckling Behavior of Plane Frameworks

    Chapter 3 Elastic Buckling and Stability of Statically Determinate Plane Frameworks

    3-1 General Forms of the Force-Displacement Relationships for Perfect Members

    3-2 Elastic Buckling of Isostatic Frames in Equilibrium—General Theory

    3-3 Elastic Stability in Statical Equilibrium

    3-4 Applications of the Theory—Tests on Model Frames

    3-5 Experimental Determination of Critical States. The Southwell Plot

    3-6 The Energy Method—The Total Potential Energy Surfaces of Statically Determinate Frameworks

    3-7 Graphical Solution

    Chapter 4 Elastic Buckling of Continuous Rigidly-Jointed Plane Frameworks

    4-1 Critical States—Distinctions Between Braced and Unbraced Frames

    4-2 Critical Loading Systems of Unbraced Frames

    4-3 Geometrical Compatibility Conditions of Unbraced Frames

    4-4 Continuity Conditions of Unbraced Frames

    4-5 Statical Equilibrium of the Unbuckled Frame

    4-6 Statical Equilibrium of the Buckled Frame

    4-7 The Non-Linear Equations of Post-Critical Equilibrium States

    4-8 Solution of the Non-Linear Equations of Post-Critical Equilibrium States

    Chapter 5 Elastic Buckling of Rigidly-Jointed Plane Trusses

    5-1 The First-Order Theory—Statical Equilibrium of the Unbuckled Truss

    5-2 Statical Equilibrium of the Buckled Truss

    5-3 The Initial Buckling Condition and the Post-Critical Equilibrium States

    5-4 Tests on Model Frames

    5-5 An Alternative Solution of the Non-Linear Equilibrium Equations

    5-6 Axially-Hyperstatic Rigidly-Jointed Braced Frameworks—Compatibility Conditions of Flexural Contractions of the Members

    The Post-Buckling Behavior of Space Frameworks

    Chapter 6 Elastic Buckling and Stability of Statically Determinate Space Frameworks

    6-1 General Force-Displacement Equilibrium Paths for Perfect Members

    6-2 Geometrical Compatibility Conditions in Space

    6-3 Critical Equilibrium States

    6-4 Statical Equilibrium of the Buckled Framework

    6-5 The Post-Critical Equilibrium Paths

    6-6 Stability of Critical Equilibrium States

    6-7 Model Isostatic Space Frames

    6-8 Two Examples of Statical Equilibrium in the Elastic Post-Buckling of Isostatic Space Frames

    6-9 The Energy Method—The Total Potential Energy Surfaces of Statically Determinate Space Frameworks

    Axially-Hyperstatic Elastic Systems

    Chapter 7 Elastic Buckling of Statically Indeterminate Pin-Jointed Systems and Space Frameworks

    7-1 Flexural Buckling of Hyperstatic Pin-Jointed Frameworks

    7-2 Ultimate Critical States

    7-3 Statical Determination of Ultimate Critical Loads

    7-4 Determination of Ultimate Critical Loads by the Principle of Virtual Work

    7-5 Ultimate Critical States in the Case of Several Load Parameters

    7-6 Elements of Elastic Limit-Design

    7-7 Geometry and Kinematics of Spherical Reticulated Shells and Some Space Elements

    7-8 Some Three-Dimensional Symmetrical Elements and Their Combinations

    7-9 The Snap-Through Problem

    7-10 Dimensional Model Analysis of the Elastic Stability of Structures

    The Post-Buckling Behavior

    7-11 Geometrical Compatibility Conditions in Hyperstatic Systems

    7-12 Equilibrium of Hyperstatic Pin-Jointed Systems in Post-Buckling

    7-13 Test of a Hyperstatic Model Frame

    7-14 The Total Potential Energy Surfaces of Hyperstatic Frameworks

    Chapter 8 Non-Conservative Aspects of Structural Systems

    8-1 Plastic Flexural Buckling of Columns at Finite Deformations—Column Model

    8-2 Statical Equilibrium of the Buckled Column

    8-3 Initial Plastic Buckling Stress

    8-4 Plastic Post-Buckling of Columns or Pin-Jointed Members—Post-Critical Equilibrium Surfaces

    8-5 Plastic Buckling of Pin-Jointed Structural Systems

    8-6 Buckling of Imperfection-Sensitive Structures Under Dynamic Loading—Existing Models and Estimates

    8-7 Dynamic Buckling of Rigidly-Jointed Frameworks and Similar Systems Under Step-Loading

    8-8 Quasi-Static Criteria

    Appendix I

    Appendix II

    Appendix III

    Appendix IV

    Appendix V

    Appendix VI

    Appendix VII

    References and Related Bibliography


Product details

  • No. of pages: 480
  • Language: English
  • Copyright: © Pergamon 1973
  • Published: January 1, 1973
  • Imprint: Pergamon
  • eBook ISBN: 9781483185170

About the Author

S. J. Britvec

About the Editors

Thomas F. Irvine

Affiliations and Expertise

Department of Mechanical Engineering State University of New York at Stony Brook Stony Brook, New York

James P. Hartnett

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