Analysis of Structures by Matrix Methods

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
List of Symbols
Chapter 1: Introduction to Matrix Algebra
	1.1: Matrix Operations
	1.2: Solution of Simultaneous Equations
		1.2.1: Direct Methods
		1.2.2: Iterative Methods
	1.3: Matrix Inverse
	1.4: Eigenvalues and Eigenvectors
		1.4.1: The Algebraic Method
		1.4.2: The Direct Evaluation of Determinant
Chapter 2: General Principles
	2.1: Bar Element Subjected to an Axial Force
		2.1.1: Derivation of Stiffness Matrix
		2.1.2: The Overall Structure Matrix
		2.1.3: Bar Elements with Variable Cross Section
		2.1.4: Some Important Properties of the Stiffness Matrix
	2.2: Coordinate Systems
	2.3: Extension of Bar Stiffness Matrix to Other Types of Structural Elements
	2.4: Banded Matrix
Chapter 3: Pin-Connected Plane Frames
	3.1: Derivation of Stiffness Matrix
	3.2: Transformation from Local to Global Coordinates
		3.2.1: Transformation of Displacements
		3.2.2: Transformation of Forces
	3.3: Stiffness Matrix Relative to Global Coordinates
Chapter 4: Bending of Beams
	4.1: Derivation of Beam Stiffness Matrix
	4.2: Load Vector
	4.3: Beams with Elastic Supports
		4.3.1: Helical Spring
		4.3.2: Spiral Spring
Chapter 5: Rigidly Connected Plane Frames
	5.1: Derivation of Stiffness Matrix
	5.2: Transformation from Local to Global Coordinates
		5.2.1: Transformation of Displacements
		5.2.2: Transformation of Actions
	5.3: Members with a Pin at One End
Chapter 6: Arches
	6.1: Derivation of Stiffness Matrix
	6.2: Transformation of Coordinates
	6.3: Calculation of Actions Developed in the Elements
Chapter 7: Grillage Analysis
	7.1: Derivation of Stiffness Matrix
	7.2: Transformation from Local to Global Coordinates
Chapter 8: Beams Curved in Plan
	8.1: Derivation of Stiffness Matrix
	8.2: Transformation from Local to Global Coordinates
	8.3: Calculation of Actions Developed in the Elements
Chapter 9: Pin-Connected Space Frames
	9.1: Derivation of the Stiffness Matrix
	9.2: Transformation of Coordinates
		9.2.1: Rotation about the ȳ-axis by an Angle φȳ
		9.2.2: Rotation about the z̅ -axis by an Angle φz̅
Chapter 10: Rigidly Connected Space Frames
	10.1: Derivation of Stiffness Matrix
	10.2: Transformation to Global Coordinates
Chapter 11: Stability of Struts and Frames
	11.1: Derivation of Strut Buckling Matrix
	11.2: Stability of Struts
	11.3: Nonlinear Analysis of Struts
	11.4: Stability of Frames
	11.5: Nonlinear Analysis of Frames
Chapter 12: Vibration of Beams and Frames
	12.1: Systems with a Single Degree of Freedom
		12.1.1: Free Undamped Vibration
		12.1.2: Free Damped Vibration
		12.1.3: Forced Vibration Due to Harmonic Force Excitation
		12.1.4: Forced Vibration Due to Base Motion Excitation
	12.2: Systems with Multi-degrees of Freedom
	12.3: Mass Matrix
	12.4: Matrix Condensation
	12.5: Free Vibration of Pin-Connected Plane Frames
	12.6: Vibration of Beams
		12.6.1: Free Vibration of Beams
		12.6.2: Vibration of Beams Due to Harmonic Force Excitation
	12.7: Vibration of Rigidly Connected Plane Frames
Appendix 1 Bar Stiffness Matrix
Appendix 2 Beam Stiffness Matrix
Appendix 3 Bar Torsion Matrix
Appendix 4 Strut Stiffness Matrix
Appendix 5 Fixed End Moments and Forces
Bibliography
Index