Stability of Structures

Principles and Applications

Chai Yoo
Sung Lee

The current trend of building more streamlined structures has made stability analysis a subject of extreme importance. It is mostly a safety issue because Stability loss could result in an unimaginable catastrophe. Written by two authors with a combined 80 years of professional and academic experience, the objective of Stability of Structures: Principles and Applications is to provide engineers and architects with a firm grasp of the fundamentals and principles that are essential to performing effective stability analysts.

Concise and readable, this guide presents stability analysis within the context of elementary nonlinear flexural analysis, providing a strong foundation for incorporating theory into everyday practice. The first chapter introduces the buckling of columns. It begins with the linear elastic theory and proceeds to include the effects of large deformations and inelastic behavior. In Chapter 2 various approximate methods are illustrated along with the fundamentals of energy methods. The chapter concludes by introducing several special topics, some advanced, that are useful in understanding the physical resistance mechanisms and consistent and rigorous mathematical analysis. Chapters 3 and 4 cover buckling of beam-columns. Chapter 5 presents torsion in structures in some detail, which is one of the least well understood subjects in the entire spectrum of structural mechanics. Strictly speaking, torsion itself does not belong to a topic in structural stability, but needs to be covered to some extent for a better understanding of buckling accompanied with torsional behavior. Chapters 6 and 7 consider stability of framed structures in conjunction with torsional behavior of structures. Chapters 8 to 10 consider buckling of plate elements, cylindrical shells, and general shells. Although the book is primarily devoted to analysis, rudimentary design aspects are discussed.

The accompanying website will include additional formulas and problems based on the authors on software which is currently being used in corporations. The website will also include equations and examples based on there personal experiences. In addition, the website will include a solutions manual for those who wish to use the book as a text book for a two-semester course. Engineers, Architects, designers, and researcher will find this print/website combination a valuable guide both in terms of its applications of verification of design of structures.

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CONTENTS

PREFACE XI

1 Buckling Of Columns

2 Special Topics in Elastic Stability of Columns

3 Beam-Columns

4 Continuous Beams and Rigid Frames

5 Torsion in Structures

6 Torsional and Flexural-Torsional Buckling

7 Lateral-Torsional Buckling

8 Buckling of Plate Elements

9 Buckling of Thin Cylindrical Shell Elements

10 Buckling of General Shell Elements

Index

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Hardbound, 536 Pages

Published: March 2011

Imprint: Butterworth Heinemann

ISBN: 978-0-12-385122-2

CONTENTS
PREFACE XI
1 Buckling Of Columns
1 1.1 Introduction
1 1.2 Neutral Equilibrium
1.3 Euler Load
1.4 Differential Equations of Beam-columns
1.5 Effects of Boundary Conditions on the Column Strength
1.6 Introduction to Calculations of Variations
1.7 Derivation of Beam-column GDE Using Finite Strain
1.8 Galerkin method
1.9 Continuous Beam Columns Resting on Elastic Supports
1.10 Elastic Buckling of Columns Subjected to Distributed Axial Loads
1.11 Large Deflection Theory (The Elastica)
1.12 Eccentrically Loaded Columns - Secant Formula
1.13 Inelastic Buckling of Straight Columns
1.14 Metric System Units
1.15 General References
2 Special Topics in Elastic Stability of Columns
2.1 Energy Methods
2.2 Stability Criteria
2.3 Rayleigh-Ritz Method
2.4 The Rayleigh Quotient
2.5 Energy Method Applied to Columns Subjected to Distributed Axial Loads
2.6 Elastically Supported Beam-Columns
2.7 Differential Equation Method
2.8 Methods of Successive Approximation
2.9 Matrix Method
2.10 Free Vibration of Columns
2.11 Buckling by a Nonconservative Load
2.12 Self-Adjoint Boundary Value Problems
3 Beam-Columns
3.1 Transversely Loaded Beam Subjected to Axial Compression
3.2 Beam-Columns with Concentrated Lateral Loads
3.3 Beam-Columns with Distributed Lateral Loads
3.4 Effect of Axial Force on Bending Stiffness
3.5 Ultimate Strength of Beam-Columns
3.6 Design of Beam-Columns
4 Continuous Beams and Rigid Frames
4.1 Introduction
4.2 Continuous Beams
4.3 Buckling Modes of Frames
4.4 Critical Loads of Frames
4.5 Stability of Frames by Matrix Analysis
4.6 Second-order Analysis of Frames by Slope-Deflection Equations
4.7 Effect of Primary Bending and Plasticity on the Behavior of Frames
4.8 Stability Design of Frames
5 Torsion in Structures
5.1 Introduction
5.2 Uniform Torsion and St. Venant Theory
5.3 Membrane Analogy
5.4 Twisting of Thin Rectangular Bars
5.5 Torsion in the Inelastic Range
5.6 Torsion in Closed Thin-Walled Cross Sections
5.7 Non-Uniform Torsion of W Shapes
5.8 Non-Uniform Torsion of Thin-Walled Open Cross Sections
5.9 Cross Section Properties 323
6 Torsional and Flexural-Torsional Buckling
6.1 Introduction
6.2 Strain Energy of Torsion
6.3 Torsional and Flexural-Torsional Buckling of Columns
6.4 Torsional and Flexural-Torsional Buckling under Thrust and End Moments
7 Lateral-Torsional Buckling
7.1 Introduction
7.2 Differential Equations for Lateral-Torsional Buckling
7.3 Generalization of Governing Differential Equations
7.4 Lateral-Torsional Buckling under Transverse Loads
7.5 Lateral-Torsional Buckling by Energy Method
7.6 Design Specification for Lateral-Torsional Buckling
8 Buckling of Plate Elements
8.1 Introduction
8.2 Differential Equations of Plate Buckling
8.3 Linear Equations
8.4 Application of Plate Stability Equation
8.5 Energy Methods
8.6 Design Provisions for Local Buckling
8.7 Inelastic Buckling of Plate Elements
8.8 Failure of Plate Elements
9 Buckling of Thin Cylindrical Shell Elements
9.1 Introduction
9.2 Large Deflection Equations (Donnell Type)
9.3 Energy Method
9.4 Linear Stability Equations (Donnell Type)
9.5 Applications of Linear Buckling Equations
9.6 Failure of Cylindrical Shells
9.7 Postbuckling of Cylindrical Shells
10 Buckling of General Shell Elements
10.1 Introduction
10.2 Nonlinear Equilibrium Equations
10.3 Linear Stability Equations (Donnell Type)
10.4 Applications
Index

Stability of Structures

Principles and Applications

Contents