Matrix Methods of Structural Analysis - 2nd Edition - ISBN: 9780080188881, 9781483148915

Matrix Methods of Structural Analysis

2nd Edition

Pergamon International Library of Science, Technology, Engineering and Social Studies

Authors: R. K. Livesley
eBook ISBN: 9781483148915
Imprint: Pergamon
Published Date: 1st January 1975
Page Count: 290
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Matrix Methods of Structural Analysis, 2nd Edition deals with the use of matrix methods as standard tools for solving most non-trivial problems of structural analysis. Emphasis is on skeletal structures and the use of a more general finite element approach. The methods covered have natural links with techniques for automatic redundant selection in elastic analysis. This book is comprised of 11 chapters and begins with an introduction to the concepts and notation of matrix algebra, along with the value of a systematic approach; structure as an assembly of elements; boundaries and nodes; linearity and superposition; and how analytical methods are built up. The discussion then turns to the variables which form the basis of much of structural analysis, as well as the most important relationships between them. Subsequent chapters focus on the elastic properties of single elements; the equilibrium or displacement method; the equilibrium equations of a complete structure; plastic analysis and design; transfer matrices; and the analysis of non-linear structures. The compatibility or force method is also described. The final chapter considers the limits imposed by the size and accuracy of the computer used in structural analysis and how they can be extended. This monograph will be of interest to structural engineers and students of engineering.

Table of Contents

Preface to the Second Edition

Chapter 1. Introduction

1.1. The Value of a Systematic Approach

1.2. A Structure as an Assembly of Elements

1.3. Boundaries and Nodes

1.4. Linearity and Superposition

1.5. How Analytical Methods are Built up

Chapter 2. The Main Variables and Relationships

2.1. Nodal Variables—Loads and Displacements

2.2. Element Variables—Stress-Resultants and Deformations

2.3. Equilibrium and Compatibility Conditions: Virtual Work

2.4. Coordinate Transformations

Chapter 3. The Elastic Properties of Single Elements (a) Line Elements

3.1. Stress-Resultant and Deformation Vectors for a General Plane Member

3.2. The Straight Uniform Beam: Two Dimensional Analysis

3.3. The Straight Uniform Beam: Three-Dimensional Analysis

3.4. Straight Uniform Members with Pinned Ends

3.5. Straight Uniform Members in Plane Grillages

3.6. Curved and Non-Uniform Plane Members

3.7. Segmented Members

3.8. The Effect of Joints of Finite Size

3.9. Flexible Joint Connections

3.10. The Calculation of Equivalent Joint Loads

3.11. The Replacement of Distributed Mass

Chapter 4. The Elastic Properties of Single Elements (b) An Introduction to Area and Volume Elements

4.1. The Basic Equations of Plane Stress

4.2. The Simple Triangular Element

4.3. The Simple Rectangular Element

4.4. Body Forces and Initial Strains

4.5. Transformation of Axes

4.6. The Replacement of Distributed Mass

4.7. More Complex Elements

Chapter 5. The Equilibrium or Displacement Method

5.1. The Analysis of a Plane Pin-Jointed Truss

5.2. The Analysis of a Plane Rigid-Jointed Truss

5.3. The Assembly of the Stiffness Matrix of a Structure

5.4. Settlement and Partial Restraint

5.5. Dynamic Problems

Chapter 6. The Equilibrium Equations of a Complete Structure

6.1. Setting up the Equilibrium Equations

6.2. An Alternative Form of the Equilibrium Method

6.3. The Analysis of Determinate Structures

6.4. Determinate Structures with Rigid Joints: Tree Structures

Chapter 7. Plastic Analysis and Design

7.1. Ideal Rigid-Plastic Behavior

7.2. Setting up the Equilibrium Equations

7.3. Plastic Collapse under Proportional Loading

7.4. Duality and the Mechanism Approach

7.5. The Shakedown Problem

7.6. Minimum-Weight Design for Single and Multiple Loadings

7.7. A Compact Procedure for Finding the Collapse Load Factor

Chapter 8. The Compatibility or Force Method

8.1. The Analysis of a Pin-Jointed Truss

8.2. The Analysis of a Rigid-Jointed Frame

8.3. Applications to More Complex Skeletal Structures

8.4. Axial Forces in Rigid-Jointed Frames

8.5. An Algebraic Procedure for Transforming the Equilibrium Equations

Chapter 9. Transfer Matrices

9.1. Transfer Matrices for Single Structural Elements

9.1.1. The Equations for a Line Element

9.1.2. The Equations for a Joint

9.2. An Example of the Use of Transfer Matrices

9.3. A Problem Involving Intermediate Supports

9.4. A Comparison Between the Transfer Matrix and Equilibrium Methods

9.5. Rigid Supports and Flexible Joints

9.6. Vibration Problems

Chapter 10. The Analysis of Non-linear Structures

10.1. Stiffness Matrices for a Straight Uniform Member with Axial Thrust

10.2. The Determination of Elastic Critical Loads

10.3. A General Method for Analyzing Non-linear Structures

10.4. The Analysis of Guyed Masts

10.5. Non-linear Problems Associated with Plastic Collapse Analysis

10.6. Elastic-Plastic Analysis

Chapter 11. Problems of Size and Accuracy

11.1. The Solution of Large Sets of Load/Displacement Equations

11.2. The Use of Sub-Structures

11.3. Numerical Checks for Computer Analyses

11.4. Ill-Conditioning in Structural Analysis

A Summary of the Main Equations

Appendix. Vectors and Matrices

A.1. Vectors

A.2. Matrices

A.3. Matrix Inversion

A.4. Coordinate Transformations

A.5. The Principal Axes Problem

A.6. The Solution of Linear Equations and the Inversion of Matrices

A.7. The Linear Programming Problem




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About the Author

R. K. Livesley

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