The analysis of engineering structures has always been a challenge to engineers, and in the past, classical methods were used to quantify the response of a structure to the applied forces. These methods were suitable for the analysis of relatively simple structures that could be solved by hand calculations but complicated structures had to be simplified to a model that could be solved by classical methods. The results, however, were approximations depending on the modifications made to the structure as well as on the experience and judgement of the analyst. These limitations led to the derivation of the slope-deflection equations for continuous beams, and later, formulation of the moment distribution method. With the advent of electronic computers, systematic procedures for the analysis of structures have been developed. Computer programs help in obtaining required solutions to the simultaneous equations in the case of structures where the number of equations is large and hand calculations are not suitable. The detailed work with simultaneous equations can be made in a general and compact form by using matrix notation, leading to the development of the matrix methods of structural analysis.
This book deals with the analysis of engineering structures made of skeletal members and covers the type of structures that are commonly used in practice. It builds up on the subject matter dealing with matrix algebra, analysis of bar elements, special forms of members, stability and vibration of structures, and pin-connected, rigid-plane, and 3D frames. It treats the important step of formulating the overall stiffness matrix of a structure in a systematic and straightforward manner and uses simple mathematical approaches wherever possible. The book is reader friendly, particularly for beginners who have no prior knowledge in this subject and can also be used as a textbook by undergraduate and postgraduate students studying for a degree in civil, structural, or mechanical engineering as well as by practicing engineers who have not studied this subject but are using software packages that deal with the analysis of engineering structures.
Author(s): Fathi Al-Shawi
Publisher: Jenny Stanford Publishing
Year: 2023
Language: English
Pages: 542
City: Singapore
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
