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Matrix Methods of Structural Analysis
Pergamon International Library of Science, Technology, Engineering and Social Studies
- 2nd Edition - January 1, 1975
- Author: R. K. Livesley
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 4 8 9 1 - 5
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… Read more
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Request a sales quoteMatrix 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.
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
References
Index
- No. of pages: 290
- Language: English
- Edition: 2
- Published: January 1, 1975
- Imprint: Pergamon
- eBook ISBN: 9781483148915
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