Theory of Structures

Theory of Structures
Prof. Metwally Abd-elaziz Ahmed
Contents
Preface Iii
Contents .v
1. Introduction
1.1 Structural Engineering 1
1.2 Structure Definition and Purpose 2
1.3 Structural Elements and Structural Forms 3
1.4 Structural Systems 7
1.5 Schematical Representation of Structures 9
1.6 Loads on Structures 10
1.6.1 Types of Loads 11
1.6.2 Intensity of Loads 12
1.7 Structural Analysis and Mechanics 15
Exercise 1 16
2. ELEMENTS OF PLANE STATICS
2.1 Introduction 17
2.2 The Force 17
2.2.1 Definition and Representation of a Force 17
2.2.2 Resolution of a Force 18
2.2.3 Moment of Forces and Couples 20
2.3 Resultant of a Concurrent Force System 22
2.3.1 Case of Two Forces 22
2.3.2 Case of Several Forces 23
2.4 Resultant of a Non-Concurrent Force System 25
2.5 Conditions of Equilibrium 27
Exercise 2 31vi
3. REACTIONS OF PLANAR STRUCTURES
3.1 Introduction 35
3.2 Types of Supports 35
3.2.1 Roller Supports 35
3.2.2 Hinged (Pinned) Supports 36
3.2.3 Fixed Supports 38
3.2.4 Link Support 38
3.3 Determination of Reactions 40
3.4 Condition Equation 43
3.5 Stability of Plane Structures 49
3.6 Redundant Systems 51
Exercise 3 55
4. ANALYSIS OF TRUSSES
4.1 Definitions 61
4.2 Stability and Statical Determinacy of Plane Trusses 65
4.3 Classification and Common Pattern of Plane Trusses 71
4.4 Methods of Analysis 74
4.4.1 The Method of Joints 76
4.4.2 The Method of Sections 81
4.4.3 Zero Members 87
4.4.4 The Method of Tension Coefficients 89
4.5 The Graphical Method (Maxwell Diagram) 93
4.6 Analysis of Simple Space Trusses 96
Exercise 4 99
5. ANALYSIS OF BEAMS
5.1 Introduction 103
5.2 Internal Forces in a Beam Element 104
5.2.1 Definition of Internal Force 104
5.2.2 Components of Internal Force 105
5.2.3 Sign Convention 106vii
5.3 Internal Force Diagrams 110
5.4 Relationship between Load, Shearing Force
and Bending Moment 112
5.5 Standard Cases of S.F.D. and B.M.D. 116
5.6 Multi-span Statically Determinate Beams 122
5.7 Principle of Superposition 127
Exercise 5 129
6. ANALYSIS OF FRAMES AND ARCHES
6.1 Introduction 135
6.2 Determinacy and Stability of Frames 136
6.3 Remarks on the Analysis of Frames 139
Exercise 6 155
References
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