Matrix Methods of Structural Analysis

1st Edition - January 1, 1964
Author: R. K. Livesley
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 1 - 3 6 2 6 - 4

Matrix Methods of Structural Analysis presents how concepts and notations of matrix algebra can be applied to arriving at general systematic approach to structure analysis. The… Read more

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Matrix Methods of Structural Analysis presents how concepts and notations of matrix algebra can be applied to arriving at general systematic approach to structure analysis. The book describes the use of matrix notation in structural analysis as being theoretically both compact and precise, but also, quite general. The text also presents, from the practical point of view, matrix notation as providing a systematic approach to the analysis of structures related to computer programming. Matrix algebraic methods are useful in repeated calculations where manual work becomes tedious. The Gaus-Seidel method and linear programming are two methods to use in solving simultaneous equations. The book then describes the notation for loads and displacements, on sign conventions, stiffness and flexibility matrices, and equilibrium and compatibility conditions. The text discusses the formulation of the equilibrium method using connection matrices and an alternative method. The book evaluates the compatibility method as programmed in a computer; and it discusses the analysis of a pin-jointed truss and of a rigid-jointed truss. The book presents some problems when using computers for analyzing structures, such as decision strategy, accuracy, and checks conducted on handling large matrices. The text also analyzes structures that behave in a non-linear manner. The book is suitable for structural engineers, physicist, civil engineers, and students of architectural design.

Preface

Chapter 1. Introduction

1.1. The Aim of Matrix Methods

1.2. Linearity

1.3. Superposition

1.4. Methods of Structural Analysis

Chapter 2. Vectors and Matrices

2.1. Vectors

2.2. Matrices

2.3. Matrix Inversion

2.4. Coordinate Transformations

2.5. The Principal Axes Problem

2.6. The Solution of Simultaneous Equations and the Inversion of Matrices

2.7. The Linear Programming Problem

Chapter 3. Basic Relationships and Definitions

3.1. Notation for Loads and Displacements

3.2. A Note on Sign Conventions

3.3. Stiffness and Flexibility Matrices

3.4. Equilibrium and Compatibility Conditions: Virtual Work

Chapter 4. The Equilibrium Method

4.1. The Analysis of a Plane Pin-Jointed Truss

4.2. The Analysis of a Plane Rigid-Jointed Truss

4.3. The Assembly of the Stiffness Matrix of a Structure

4.4. Stiffness Matrices for a Straight Uniform Member in a Space Structure

4.5. The Analysis of Plane Grillages

4.6. The Analysis of Pin-Jointed Space Trusses

4.7. Pin-Joints in Rigid-Jointed Structures

4.8. Temperature Stresses and Lack of Fit

4.9. Dynamic Problems

Chapter 5. Stiffness, Flexibility and Equilibrium Matrices for Single Members

5.1. Equilibrium Equations and Rigid-Body Displacements

5.2. Products of Equilibrium Matrices

5.3. Flexibility and Stiffness Matrices for a General Linear Member

5.4. Coordinate Transformations of Flexibility and Equilibrium Matrices

5.5. Members Formed From Elements Connected in Series

5.6. The Effect of Joints of Finite Size

5.7. Semi-Rigid Joint Connections

Chapter 6. Connection Matrices and Determinate Systems

6.1. Formulation of the Equilibrium Method Using Connection Matrices

6.2. an Alternative Formulation of the Equilibrium Method

6.3. The Analysis of Determinate Structures

6.4. Determinate Structures with Rigid Joints: Tree Structures

Chapter 7. The Compatibility Method

7.1. The Analysis of a Pinpointed Truss

7.2. The Analysis of a Rigid-Jointed Frame

7.3. General Features of the Compatibility Method

7.4. Axial Forces in Rigid-Jointed Frames

7.5. A Derivation of the Compatibility Equations by Virtual Work

7.6. Combinations of Release Systems

7.7. The Collapse Load of a Rigid-Plastic Structure

Chapter 8. Transfer Matrices

8.1. The Transfer Matrix of a Single Member

8.2. an Example of the Use of Transfer Matrices

8.3. The Effect of Intermediate Supports

8.4. a Comparison of the Transfer Matrix Method and the Equilibrium Method

8.5. Rigid Supports and Flexible Joints

8.6. The Application of Transfer Matrices to Vibration Problems

Chapter 9. Computational Problems

9.1. Single and Repetitive Problems

9.2. Ill-Conditioning in Matrix Processes

9.3. Numerical Checks in Matrix Processes

9.4. Operations on Banded Matrices

9.5. The Use of Sub-Structures

Chapter 10. The Analysis of Non-linear Structures

10.1. Stiffness Matrices for a 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. Some Problems of Collapse Analysis