This note is simple and logical and is made generally for civil engineering, building, architecture, or mechanical engineering students who are offering structural analysis or theory of structures courses at the elementary level or particularly for structural engineering students at the same level. Beyond the elementary knowledge in the analysis of structures offered by studies of the strength of materials, this note would be quite helpful to enable students to grasp concepts of the theory of structures easily. It would definitely help them to achieve excellence in the course modules at higher levels of study. It has brief explanations of topics and many practical solutions. It was drawn mainly and compiled from a number of lecture notes.
Table of Contents
List of Tables …………………………………………………………………………………………………………………….. v
List of Figures…………………………………………………………………………………………………………………….vi
Preface ………………………………………………………………………………………………………………………….viii
1.0 Introduction ………………………………………………………………………………………………………………… 1
1.1 Classes of Structures……………………………………………………………………………………………………1
1.1.1 Purpose of Structural Analysis…………………………………………………………………………………… 4
1.2 Types of Supports……………………………………………………………………………………………………….4
1.3 Equations of equilibrium………………………………………………………………………………………………6
1.4 Stability and Indeterminacy …………………………………………………………………………………………6
1.4.1 Alternative Method of Checking Degree of Indeterminacy …………………………………………… 11
2.0 Structural Analysis Problems……………………………………………………………………………………… 14
2.1 Analysis of Trusses…………………………………………………………………………………………………….14
2.1.1 Method of Joints…………………………………………………………………………………………………… 15
2.1.2 Method of Sections……………………………………………………………………………………………….. 23
2.1.3 Method of Tension Coefficients ………………………………………………………………………………. 31
2.1.4 Graphical Method …………………………………………………………………………………………………. 35
2.2 Structural Analysis of Arches: Three-hinged Arch…………………………………………………………43
2.3 Structural Analysis of Beams………………………………………………………………………………………54
2.4 Structural Analysis of Frames……………………………………………………………………………………..57
2.5 Structural Analysis of Cables………………………………………………………………………………………77
2.5.1 Equation of the Cable…………………………………………………………………………………………….. 78
2.5.2 Horizontal Tension in the Cable……………………………………………………………………………….. 79
2.5.3 Tension in Cable Supported at Different Levels …………………………………………………………80
3.0 Influence Lines…………………………………………………………………………………………………………..87
3.1 Influence Lines for Bending Moment and Shearing Forces …………………………………………..88
4.0 Introduction to Deflection …………………………………………………………………………………………..91
4.1 Determination of Deflection using Energy Methods……………………………………………………….91
4.2 External Work done by Force…………………………………………………………………………………….. 92
4.2.1 Methods of Virtual Work………………………………………………………………………………………… 92
4.2.2 Method of Virtual Work for Beams and Frames………………………………………………………..94
4.2.3 Method of Virtual Work for Trusses ……………………………………………………………………….. 102
5.0 Methods of Analysis of Indeterminate Structures ……………………………………………………….113
5.1 The Force Method …………………………………………………………………………………………………….. 113
5.1.1 Force Method of Analysis of Trusses ………………………………………………………………………. 115
5.1.2 Force Method of Analysis of Beams ……………………………………………………………………….. 122
5.2 The Displacement Method of Analysis……………………………………………………………………… 129
5.2.1 The Slope Deflection Method………………………………………………………………………………… 129
5.2.2 The Moment Distribution Method …………………………………………………………………………. 130
6.0 Computer Applications in Theory of Structures…………………………………………………………. 132
6.1 Software………………………………………………………………………………………………………………….. 132
6.2 Artificial Intelligence ………………………………………………………………………………………………..132
References……………………………………………………………………………………………………………………. 133
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