Resistance and Deformation of Solid Media

Preface

Introduction

Concepts and Definitions

The Particulate and the Continuum

Chapter 1 Elasticity


1-1 Coulomb's Law


1-2 Electrostatic Repulsion


1-3 Small Deformations, Hooke's Law


1-4 Stress and Strain


1-5 Bulk Modulus B


1-6 Ionic Crystals


1-7 Lateral Contraction: Poisson's Ratio


1-8 Bulk Modulus B and Young's Modulus E


1-9 Anisotropy of E: The Quasi-Isotropy


1-10 Shear Modulus G


1-11 Modulus of Elasticity and Periodic Table


1-12 Work of Deformation and Elastic Energy


1-13 Concluding Remarks


1-14 Problems

Chapter 2 Plasticity


2-1 Perfect Crystals


2-2 Defective Crystal: Dislocation


2-3 Strain Hardening


2-4 Mechanism of Slip in Uniaxial Tension


2-5 Relation between Shear Strain and Axial Strain


2-6 Relation between Shear Stress and Axial Stress


2-7 Plastic Stress-Strain Diagram


2-8 Actual Stress-Strain Diagram


2-9 Conventional and True Stress


2-10 Work of Deformation


2-11 The Dissipative and Recoverable Components

of Work of Deformation


2-12 Concluding Remarks


2-13 Problems

Chapter 3 Viscosity and Creep


3-1 Laminar Flow and Newton's Law of Viscosity


3-2 Coefficient of Viscosity


3-3 Poise and Centipoise


3-4 Range of Variation


3-5 Effect of Temperature


3-6 Coefficient of Fluidity: Kinematic Viscosity


3-7 Illustrative Example


3-8 Non-Newtonian Liquids


3-9 Viscoelasticity


3-10 Stress Relaxation: Relaxation Time


3-11 Illustrative Examples


3-12 Recoverable Creep (Delayed Elasticity)


3-13 Permanent Creep


3-14 Power of Deformation


3-15 Concluding Remarks


3-16 Problems

Chapter 4 Basic Principles


4-1 Principles of Equilibrium of Forces and Moments


4-2 Principle of Continuity of Deformation


4-3 Assumption of Small Deformations


4-4 Problems

Chapter 5 Homogeneous State


5-1 Stress at a Point: Macroscopic Approach


5-2 Prismatic Bars Under Axial Loading


5-3 Statically Determinate and Statically Indeterminate Structures


5-4 Illustration of a Statically Indeterminate Structure


5-5 Composite Bars


5-6 Thermal Stresses in Bars


5-7 Thin-Wall Pressure Vessels


5-8 Spherical Pressure Vessels


5-9 Torsion of Thin-Wall Tubes


5-10 Problems

Chapter 6 Uniaxial State: Plane Bending


6-1 Pure Bending


6-2 Bernouilli's Hypothesis


6-3 Equilibrium of Forces and Moments


6-4 Elastic Bending


6-5 Viscous Bending


6-6 Viscoelastic Bending


6-7 Recoverable Creep in Bending


6-8 Incipient Plastic Deformation


6-9 Distortion of the Cross Section: Anticlastic Surface


6-10 Bending by Transverse Forces


6-11 Bending by Distributed Forces


6-12 Illustrative Examples


6-13 Beams of Variable Cross Section


6-14 Deflection of Beams


6-15 Work of Deformation in Bending


6-16 Virtual Work in Bending


6-17 Virtual Work and Beam Deflection


6-18 Virtual Work and Statically Indeterminate Beams


6-19 Problems

Chapter 7 Uniaxial State (Continued): Torsion of Circular Cylinders


7-1 Stresses and Angle of Twist


7-2 Work of Deformation in Torsion


7-3 Virtual Work


7-4 Problems

Chapter 8 Uniaxial State (Concluded): Linear Beam Theory


8-1 General Expression of Bernouilli's Hypothesis


8-2 Conditions of Equilibrium


8-3 Elastic Deformation


8-4 Unsymmetrical Bending: Principal Axes and Moments of Inertia


8-5 The Most Economical Utilization of a Beam in Bending


8-6 Deflection in Unsymmetrical Bending


8-7 Thermal Stresses


8-8 Composite Beam


8-9 Problems

Chapter 9 Biaxial State of Stress


9-1 Notations


9-2 Sign Convention


9-3 Stresses at a Point


9-4 Reciprocity of Shear Stresses


9-5 Principal Planes: Directions and Stresses


9-6 Mohr Circle of Stress


9-7 Sign of the Shear Stress


9-8 Maxima and Minima of the Normal and Shear Stresses: Invariants


9-9 Illustrative Examples


9-10 Stress Tensor


9-11 Illustrative Example: Tensor of Moment of Inertia


9-12 Problems

Chapter 10 Biaxial State of Strain


10-1 Notations


10-2 Strain at a Point


10-3 Tensor of Strain


10-4 Principal Directions and Strains


10-5 Use of the Mohr Circle of Strain


10-6 Shear Strain ?xy and Distortion Angle ?xy


10-7 Sign Convention


10-8 Maximum Shear Strain


10-9 Problems

Chapter 11 Elementary Application of a Biaxial State of Stress and Strain


11-1 States of Stress and Strain near the Surface the Triplet of Mohr Circles


11-2 Uniaxial Tension


11-3 Torsion of Circular Shafts


11-4 Shear Stresses in Bending


11-5 Combined Shear and Bending


11-6 Combined Torsion and Bending


11-7 Problems

Chapter 12 Three-Dimensional State of Stress


12-1 Notations


12-2 Three-Dimensional Stress Tensor


12-3 Principal Stresses and Directions


12-4 Magnitude and Directions of Any Stress Vector in Terms of Principal Stresses


12-5 Any Normal Stress in Terms of Principal Stresses


12-6 Total Shear Stress ?nn in Plane n


12-7 Maximum and Minimum Values of the Normal Stress


12-8 Maximum Value of the Shear Stress


12-9 Octahedral Stresses


12-10 Existence of Principal Stresses and Direction


12-11 Uniqueness of the Principal Stresses


12-12 Problems

Chapter 13 Three-Dimensional State of Strain and Strain Rate


13-1 Tensor of Strain


13-2 Any Strain Vector in Terms of Principal Strains


13-3 Any Normal Strain in Terms of Principal Strains


13-4 Total Shear Strain and Distortion Angle


13-5 Maximum and Minimum Values of Normal Strain


13-6 Principal Values of the Distortion Angle


13-7 Octahedral Strain and Distortion Angle


13-8 Mohr Circle of Strain


13-9 Tensor of Strain Rate


13-10 Problems

Chapter 14 Stress-Strain Relations


14-1 Generalized Hooke's Law


14-2 Generalized Newton's Law of Viscosity


14-3 Viscoelasticity


14-4 Problems

Chapter 15 Stress-Strain (Strain-Rate) Relations in Plastic Fields


15-1 Criterion of Yielding


15-2 Plasticity Laws


15-3 Problems

Chapter 16 Stress-Strain Relations in Monotonically Increasing Plastic Fields


16-1 True Stress and Strain


16-2 Stress-Strain Relations


16-3 Illustrative Examples


16-4 Relations Between Linear and Natural Strain Components


16-5 Problems

Chapter 17 Particular Solutions of Three-Dimensional Heterogeneous States of Stress and Strain: Thick-Wall Cylinders


17-1 Types of Deformation in Pressure Vessels


17-2 Compatibility of Strains and Strain Rates


17-3 Equilibrium of Forces


17-4 Elastic Vessel


17-5 Viscous Vessel


17-6 Plastic Vessel


17-7 Partly Plastic Tube


17-8 Problems

Chapter 18 Structural Instability


18-1 The Snap-Through Instability


18-2 Tensile Plastic Instability


18-3 Elastic


18-4 Critical Buckling Stress


18-5 Effect of Initial Eccentricity


18-6 Incidence of Plastic Deformation


18-7 Strain Hardening


18-8 Viscous Column


18-9 Viscoelastic Column


18-10 Recoverable Creep in Buckling


18-11 Plastic Instability of Thin-Wall Pressure Vessels


18-12 Plastic Instability of Thick-Wall Pressure Vessels: No Strain Hardening


18-13 Problems

Chapter 19 Material Instability and Fracture


19-1 Theoretical Fracture Stress


19-2 Brittle Fracture


19-3 Incipient Plastic Deformation


19-4 Fatigue Fracture

References

Index