Analysis of Structures


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Table of Contents

Chapter (1): Introduction to Structural Engineering Concepts .............................................. 1

1.1 Engineering Design Process ............................................................................................ 1

1.2 Structural Analysis ......................................................................................................... 2

1.3 Structural Form .............................................................................................................. 2

1.4 Structural Elements: ....................................................................................................... 2

1.4.1 Tie Rods: .................................................................................................................. 2

1.4.2 Beams: ...................................................................................................................... 2

1.4.3 Columns: .................................................................................................................. 3

1.5 Types of Structures: ....................................................................................................... 3

1.5.1 Trusses: .................................................................................................................... 4

1.5.2 Cables and arches: .................................................................................................... 4

1.5.3 Frames: ..................................................................................................................... 4

1.5.4 Surface Structures: ................................................................................................... 5

1.6 Codes and Loads types and categories: .......................................................................... 5

1.6.1 Codes: ....................................................................................................................... 5

1.6.2 Load Types:.............................................................................................................. 6

1.6.3 Load Categories: ....................................................................................................... 8

Chapter (2): Beam Analysis ................................................................................................. 17

2.1 Loading on Beams: ....................................................................................................... 17

2.2 Loading Types: ............................................................................................................. 17

2.3 Support Types: ............................................................................................................. 18

2.4 Beam Types: ................................................................................................................. 20

2.5 Beam Reactions: ...........................................................................................................21

2.6 Sign Convention: ..........................................................................................................21

2.7 Examples: ..................................................................................................................... 22

2.8 Internal Forces in Beams: ............................................................................................. 24

2.8.1 Procedure for Analysis ........................................................................................... 25

2.8.2 Examples: ...............................................................................................................26

2.9 Shear Force and Bending Moment Diagrams:.............................................................. 29

2.9.1 Procedure for Analysis ........................................................................................... 29

2.9.2 Examples: ...............................................................................................................32

2.10 Problems: .................................................................................................................... 39

Chapter (3): Truss Analysis ................................................................................................. 41

3.1 Introduction: ................................................................................................................. 41

3.2 Assumptions for Analysis of Trusses: ........................................................................... 42

3.3 Method of Joints: .........................................................................................................42

3.3.1 Procedure for Analysis ........................................................................................... 42

3.3.2 Examples: ...............................................................................................................44

3.4 Problems: ...................................................................................................................... 48

3.5 Method of Sections: ...................................................................................................... 51

3.5.1 Procedure for Analysis: .......................................................................................... 51

3.5.2 Examples: ...............................................................................................................52

3.6 Problems: ...................................................................................................................... 56

Chapter (4): Frame Analysis ............................................................................................... 58

4.1 Types of Frame Structures: .......................................................................................... 58

4.1.1 Rigid Structural Frame .......................................................................................... 58

4.1.2 Braced Structural Frames ...................................................................................... 59

4.1.3 Load path in Frame Structure: .............................................................................. 61

4.1.4 Comparison of Frame structures with Normal Load bearing Traditional High Rise

Building: ......................................................................................................................... 61

4.1.5 Frame Reactions: ................................................................................................... 62

4.1.6 Examples: ...............................................................................................................62

4.2 Internal Forces in Frames: ........................................................................................... 66

4.2.1 Examples: ...............................................................................................................66

4.3 Shear Force and Bending Moment Diagrams:.............................................................. 69

4.3.1 Procedure for Analysis: .......................................................................................... 69

4.3.2 Examples: ...............................................................................................................72

4.4 Problems: ...................................................................................................................... 76

Chapter (5): Beam Deflection .............................................................................................. 78

5.1 Introduction: ................................................................................................................. 78

5.2 Factors Affecting Beam Deflections ............................................................................. 78

5.3 Calculating Beam Deflections: ...................................................................................... 78

5.4 Examples: ..................................................................................................................... 78

5.5 Problems: ...................................................................................................................... 82

Chapter (6): Loads on Structures ........................................................................................ 83

6.1 Live Load Reduction: ................................................................................................... 83

6.1.1 Floors: .................................................................................................................... 83

6.1.2 Roofs: ..................................................................................................................... 86

6.2 Tributary Areas for beams and columns: ..................................................................... 86

6.2.1 Approximate Methods: ........................................................................................... 88

6.3 Concepts in Structural Design: ..................................................................................... 90

6.3.1 LRFD: .................................................................................................................... 90

6.3.2 Load Combinations: ............................................................................................... 91

6.3.3 LRFD Load Combinations: .................................................................................... 92

6.3.4 Examples: ...............................................................................................................93

6.4 Problems: .................................................................................................................... 104

Chapter (7): Useful Formulas ............................................................................................ 105

7.1 Beam Design Formulas with Shear and Moment Diagrams ...................................... 105

7.2 Bending Moment Diagrams and Equations for Frames ............................................. 121

7.3 Geometric Properties of Line and Area Elements: ..................................................... 124

7.4 Center of Gravity and Mass Moment of Inertia of Homogenous Solids: .................... 127

7.5 Fundamental Equations of Statics: ............................................................................ 128

7.6 SI Prefixes: ................................................................................................................. 129

7.7 Conversion Factors (FPS) to (SI) .............................................................................. 129

7.8 Conversion Factors (FPS): ......................................................................................... 129

7.9 Conversion Factors Table: ......................................................................................... 130

7.10 Cheat Sheet: ............................................................................................................. 131

Glossary ............................................................................................................................. 135