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Chapter 1 Stresses and Strains1

1.1 What Is Mechanics of Materials1

1.2 Basic Assumptions of Materials2

1.3 External Forces2

1.4 Internal Forces3

1.5 Stresses6

1.6 Strains11

1.7 Deformations of Members13

Problems15

Chapter 2 Mechanical Properties of Materials16

2.1 Tensile or Compressive Test16

2.2 Tension of Low-Carbon Steel16

2.3 Ductile and Brittle Materials19

2.4 Stress-Strain Curve of Ductile Materials Without Distinct Yield Point20

2.5 Percent Elongation and Percent Reduction in Area21

2.6 Hooke's Law21

2.7 Mechanical Properties of Materials in Compression22

Chapter 3 Axial Tension and Compression of Bars23

3.1 Definition of Axial Tension and Compression23

3.2 Axial Force24

3.3 Normal Stress on Cross Section24

3.4 Saint-Venant's Principle26

3.5 Normal and Shearing Stresses on Oblique Section26

3.6 Normal Strain29

3.7 Deformation of Axially Loaded Bar31

3.8 Statically Indeterminate Axially Loaded Bar33

3.9 Design of Axially Loaded Bar34

3.10 Stress Concentrations35

Problems36

Chapter 4 Torsion of Shafts39

4.1 Definition of Torsion39

4.2 Twisting Moment39

4.3 Hooke's Law in Shear40

4.4 Shearing Stress on Cross Section of Circular Shaft41

4.5 Normal and Shearing Stresses on Oblique Section of Circular Shaft44

4.6 Angle of Twist45

4.7 Statically Indeterminate Circular Shaft47

4.8 Design of Circular Shaft48

Problems49

Chapter 5 Shearing Force and Bending Moment of Beams53

5.1 Definition of Bending53

5.2 Shearing-Force and Bending-Moment Diagrams54

5.3 Relations Among Distributed Load,Shearing Force,and Bending Moment58

5.4 Relations Among Concentrated Load,Shearing Force,and Bending Moment61

Problems63

Chapter 6 Normal Stress and Shearing Stress in Beams66

6.1 Types of Bending66

6.2 Normal Stresses on Cross Section in Pure Bending67

6.3 Normal and Shearing Stresses on Cross Section in Transverse-Force Bending72

6.4 Design of Prismatic Beams in Bending77

Problems78

Chapter 7 Deflection and Slope of Beams81

7.1 Deformation of Beams81

7.2 Method of Integration83

7.3 Method of Superposition85

7.4 Statically Indeterminate Beams86

Problems88

Chapter 8 Analysis of Stresses and Theories of Strength92

8.1 State of Stress92

8.2 Transformation of Plane Stress93

8.3 Principal Stresses for Plane Stress95

8.4 Maximum Shearing Stress for Plane Stress98

8.5 Stresses in Pressure Vessels100

8.6 Generalized Hooke's Law102

8.7 Theories of Strength Under Plane Stress105

Problems112

Chapter 9 Combined Loadings115

9.1 Definition of Combined Loadings115

9.2 Stress in Bar Subjected to Eccentric Tension or Compression116

9.3 Stress in I-Section Beam Subjected to Transverse Bending118

9.4 Stress in Beam Subjected to Bending and Axial Tension/Compression122

9.5 Stress in Shaft Subjected to Torsion and Bending125

Problems128

Chapter 10 Stability of Columns131

10.1 Definition of Buckling131

10.2 Critical Load of Long Slender Columns Under Centric Load with Pin Supports132

10.3 Critical Load of Long Slender Columns Under Centric Load with Other Supports134

10.4 Critical Stress of Long Slender Columns Under Centric Load136

10.5 Critical Stress of Intermediate Length Columns Under Centric Load137

10.6 Design of Columns Under Centric Load139

Problems140

Chapter 11 Energy Methods143

11.1 External Work143

11.2 Stain-Energy Density145

11.3 Strain Energy146

11.4 Principle of Work and Energy151

11.5 Castigliano's Theorem153

11.6 Unit Load Method157

11.7 Applications of Energy Methods160

Problems162

Chapter 12 Dynamic Loadings166

12.1 Definition of Impact Loadings166

12.2 Vertical Impact166

12.3 Horizontal Impact169

Problems172

Chapter 13 Statically Indeterminate Structures175

13.1 Concept of Statically Indeterminate Structures175

13.2 External and Internal Indeterminacy175

13.3 Force Method for Analysis of Statically Indeterminate Structures177

13.4 Force Method for Analysis of Symmetrical Indeterminate Structures182

Problems185

AppendixⅠ Geometrical Properties of Areas191

Ⅰ.1 First Moment and Centroid191

Ⅰ.2 First Moment and Centroid of a Composite Area192

Ⅰ.3 Moment of Inertia and Polar Moment of Inertia193

Ⅰ.4 Radius of Gyration and Polar Radius of Gyration194

Ⅰ.5 Product of Inertia194

Ⅰ.6 Parallel-Axis Theorem195

AppendixⅡ Geometrical Properties of Rolled-Steel Shapes196

Ⅱ.1 I-Steel196

Ⅱ.2 Channel Steel198

Ⅱ.3 Equal Angle Steel200

Ⅱ.4 Unequal Angle Steel203

AppendixⅢ Moment of Inertia and Polar Moment of Inertia of Commonly-Used Areas206

AppendixⅣ Deflections and Slopes of Commonly-Used Beams207

Glossaries208

References221