Advanced Mechanics of Materials [Hardcover]

CHAPTER 1 INTRODUCTION 1

1.1 Review of Elementary Mechanics of Materials 1

1.2 Methods of Analysis 5

1.3 Stress–Strain Relations 8

1.4 Failure and Limits on Design 16

Problems 22

References 24

CHAPTER 2 THEORIES OF STRESS AND STRAIN 25

2.1 Definition of Stress at a Point 25

2.2 Stress Notation 26

2.3 Symmetry of the Stress Array and Stress on an Arbitrarily Oriented Plane 28

2.4 Transformation of Stress, Principal Stresses, and Other Properties 31

2.5 Differential Equations of Motion of a Deformable Body 50

2.6 Deformation of a Deformable Body 54

2.7 Strain Theory, Transformation of Strain, and Principal Strains 55

2.8 Small-Displacement Theory 61

2.9 Strain Measurement and Strain Rosettes 70

Problems 72

References 78

CHAPTER 3 LINEAR STRESS–STRAIN–TEMPERATURE RELATIONS 79

3.1 First Law of Thermodynamics, Internal-Energy Density, and Complementary Internal-Energy Density 79

3.2 Hooke’s Law: Anisotropic Elasticity 84

3.3 Hooke’s Law: Isotropic Elasticity 85

3.4 Equations of Thermoelasticity for Isotropic Materials 91

3.5 Hooke’s Law: Orthotropic Materials 93

Problems 101

References 103

CHAPTER 4 INELASTIC MATERIAL BEHAVIOR 104

4.1 Limitations on the Use of Uniaxial Stress–Strain Data 104

4.2 Nonlinear Material Response 107

4.3 Yield Criteria: General Concel“B