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Chapter 1 Stresses and Strains 1

1.1 What Is Mechanics of Materials 1

1.2 Basic Assumptions of Materials 2

1.3 External Forces 2

1.4 Internal Forces 3

1.5 Stresses 6

1.6 Strains 11

1.7 Deformations of Members 13

Problems 15

Chapter 2 Mechanical Properties of Materials 16

2.1 Tensile or Compressive Test 16

2.2 Tension of Low-Carbon Steel 16

2.3 Ductile and Brittle Materials 19

2.4 Stress-Strain Curve of Ductile Materials Without Distinct Yield Point 20

2.5 Percent Elongation and Percent Reduction in Area 21

2.6 Hooke's Law 21

2.7 Mechanical Properties of Materials in Compression 22

Chapter 3 Axial Tension and Compression of Bars 23

3.1 Definition of Axial Tension and Compression 23

3.2 Axial Force 24

3.3 Normal Stress on Cross Section 24

3.4 Saint-Venant's Principle 26

3.5 Normal and Shearing Stresses on Oblique Section 26

3.6 Normal Strain 29

3.7 Deformation of Axially Loaded Bar 31

3.8 Statically Indeterminate Axially Loaded Bar 33

3.9 Design of Axially Loaded Bar 34

3.10 Stress Concentrations 35

Problems 36

Chapter 4 Torsion of Shafts 39

4.1 Definition of Torsion 39

4.2 Twisting Moment 39

4.3 Hooke's Law in Shear 40

4.4 Shearing Stress on Cross Section of Circular Shaft 41

4.5 Normal and Shearing Stresses on Oblique Section of Circular Shaft 44

4.6 Angle of Twist 45

4.7 Statically Indeterminate Circular Shaft 47

4.8 Design of Circular Shaft 48

Problems 49

Chapter 5 Shearing Force and Bending Moment of Beams 53

5.1 Definition of Bending 53

5.2 Shearing-Force and Bending-Moment Diagrams 54

5.3 Relations Among Distributed Load,Shearing Force,and Bending Moment 58

5.4 Relations Among Concentrated Load,Shearing Force,and Bending Moment 61

Problems 63

Chapter 6 Normal Stress and Shearing Stress in Beams 66

6.1 Types of Bending 66

6.2 Normal Stresses on Cross Section in Pure Bending 67

6.3 Normal and Shearing Stresses on Cross Section in Transverse-Force Bending 72

6.4 Design of Prismatic Beams in Bending 77

Problems 78

Chapter 7 Deflection and Slope of Beams 81

7.1 Deformation of Beams 81

7.2 Method of Integration 83

7.3 Method of Superposition 85

7.4 Statically Indeterminate Beams 86

Problems 88

Chapter 8 Analysis of Stresses and Theories of Strength 92

8.1 State of Stress 92

8.2 Transformation of Plane Stress 93

8.3 Principal Stresses for Plane Stress 95

8.4 Maximum Shearing Stress for Plane Stress 98

8.5 Stresses in Pressure Vessels 100

8.6 Generalized Hooke's Law 102

8.7 Theories of Strength Under Plane Stress 105

Problems 112

Chapter 9 Combined Loadings 115

9.1 Definition of Combined Loadings 115

9.2 Stress in Bar Subjected to Eccentric Tension or Compression 116

9.3 Stress in I-Section Beam Subjected to Transverse Bending 118

9.4 Stress in Beam Subjected to Bending and Axial Tension/Compression 122

9.5 Stress in Shaft Subjected to Torsion and Bending 125

Problems 128

Chapter 10 Stability of Columns 131

10.1 Definition of Buckling 131

10.2 Critical Load of Long Slender Columns Under Centric Load with Pin Supports 132

10.3 Critical Load of Long Slender Columns Under Centric Load with Other Supports 134

10.4 Critical Stress of Long Slender Columns Under Centric Load 136

10.5 Critical Stress of Intermediate Length Columns Under Centric Load 137

10.6 Design of Columns Under Centric Load 139

Problems 140

Chapter 11 Energy Methods 143

11.1 External Work 143

11.2 Stain-Energy Density 145

11.3 Strain Energy 146

11.4 Principle of Work and Energy 151

11.5 Castigliano's Theorem 153

11.6 Unit Load Method 157

11.7 Applications of Energy Methods 160

Problems 162

Chapter 12 Dynamic Loadings 166

12.1 Definition of Impact Loadings 166

12.2 Vertical Impact 166

12.3 Horizontal Impact 169

Problems 172

Chapter 13 Statically Indeterminate Structures 175

13.1 Concept of Statically Indeterminate Structures 175

13.2 External and Internal Indeterminacy 175

13.3 Force Method for Analysis of Statically Indeterminate Structures 177

13.4 Force Method for Analysis of Symmetrical Indeterminate Structures 182

Problems 185

AppendixⅠ Geometrical Properties of Areas 191

Ⅰ.1 First Moment and Centroid 191

Ⅰ.2 First Moment and Centroid of a Composite Area 192

Ⅰ.3 Moment of Inertia and Polar Moment of Inertia 193

Ⅰ.4 Radius of Gyration and Polar Radius of Gyration 194

Ⅰ.5 Product of Inertia 194

Ⅰ.6 Parallel-Axis Theorem 195

AppendixⅡ Geometrical Properties of Rolled-Steel Shapes 196

Ⅱ.1 I-Steel 196

Ⅱ.2 Channel Steel 198

Ⅱ.3 Equal Angle Steel 200

Ⅱ.4 Unequal Angle Steel 203

AppendixⅢ Moment of Inertia and Polar Moment of Inertia of Commonly-Used Areas 206

AppendixⅣ Deflections and Slopes of Commonly-Used Beams 207

Glossaries 208

References 221