| |

| |

| |

Introduction | |

| |

| |

| |

Force systems | |

| |

| |

| |

Units | |

| |

| |

| |

Characterization of force systems | |

| |

| |

| |

Distributed forces | |

| |

| |

| |

Equivalent forces systems | |

| |

| |

| |

Work and power | |

| |

| |

| |

Conservative forces | |

| |

| |

| |

Conservative systems | |

| |

| |

| |

Static equilibrium | |

| |

| |

| |

Equilibrium of a body | |

| |

| |

| |

Virtual work and virtual power | |

| |

| |

| |

Equilibrium of subsets: Free-body diagrams | |

| |

| |

| |

Internal force diagram | |

| |

| |

| |

Dimensional homogeneity | |

| |

| |

Exercises | |

| |

| |

| |

Tension-Compression Bars: The One-Dimensional Case | |

| |

| |

| |

Displacement field and strain | |

| |

| |

| |

Units | |

| |

| |

| |

Strain at a point | |

| |

| |

| |

Stress | |

| |

| |

| |

Units | |

| |

| |

| |

Pointwise equilibrium | |

| |

| |

| |

Constitutive relations | |

| |

| |

| |

One-dimensional Hooke's Law | |

| |

| |

| |

Additional constitutive behaviors | |

| |

| |

| |

A one-dimensional theory of mechanical response | |

| |

| |

| |

Axial deformation of bars: Examples | |

| |

| |

| |

Differential equation approach | |

| |

| |

| |

Energy methods | |

| |

| |

| |

Stress-based design | |

| |

| |

Chapter summary | |

| |

| |

Exercises | |

| |

| |

| |

Stress | |

| |

| |

| |

Average normal and shear- stress | |

| |

| |

| |

Average stresses for a bar under axial load | |

| |

| |

| |

Design with average stresses | |

| |

| |

| |

Stress at a point | |

| |

| |

| |

Nomenclature | |

| |

| |

| |

Internal reactions in terms of stresses | |

| |

| |

| |

Equilibrium in terms of stresses | |

| |

| |

| |

Polar and spherical coordinates | |

| |

| |

| |

Cylindrical/polar stresses | |

| |

| |

| |

Spherical stresses | |

| |

| |

Chapter summary | |

| |

| |

Exercises | |

| |

| |

| |

Strain | |

| |

| |

| |

Shear strain | |

| |

| |

| |

Pointwise strain | |

| |

| |

| |

Normal strain at a point | |

| |

| |

| |

Shear strain at a point | |

| |

| |

| |

Two-dimensional strains | |

| |

| |

| |

Three-dimensional strain | |

| |

| |

| |

Polar/cylindrical and spherical strain | |

| |

| |

| |

Number of unknowns and equations | |

| |

| |

Chapter summary | |

| |

| |

Exercises | |

| |

| |

| |

Constitutive Response | |

| |

| |

| |

Three-dimensional Hooke's Law | |

| |

| |

| |

Pressure | |

| |

| |

| |

Strain energy in three dimensions | |

| |

| |

| |

Two-dimensional Hooke's Law | |

| |

| |

| |

Two-dimensional plane stress | |

| |

| |

| |

Two-dimensional plane strain | |

| |

| |

| |

One-dimensional Hooke's Law: Uniaxial state of stress | |

| |

| |

| |

Polar/cylindrical and spherical coordinates | |

| |

| |

Chapter summary | |

| |

| |

Exercises | |

| |

| |

| |

Basic Techniques of Strength of Materials | |

| |

| |

| |

One-dimensional axially loaded rod revisited | |

| |

| |

| |

Thinness | |

| |

| |

| |

Cylindrical thin-walled pressure vessels | |

| |

| |

| |

Spherical thin-walled pressure vessels | |

| |

| |

| |

Saint-Venant's principle | |

| |

| |

Chapter summary | |

| |

| |

Exercises | |

| |

| |

| |

Circular and Thin-Wall Torsion | |

| |

| |

| |

Circular bars: Kinematic assumption | |

| |

| |

| |

Circular bars: Equilibrium | |

| |

| |

| |

Internal torque-stress relation | |

| |

| |

| |

Circular bars: Elastic response | |

| |

| |

| |

Elastic examples | |

| |

| |

| |

Differential equation approach | |

| |

| |

| |

Energy methods | |

| |

| |

| |

Torsional failure: Brittle materials | |

| |

| |

| |

Torsional failure: Ductile materials | |

| |

| |

| |

Twist-rate at and beyond yield | |

| |

| |

| |

Stresses beyond yield | |

| |

| |

| |

Torque beyond yield | |

| |

| |

| |

Unloading after yield | |

| |

| |

| |

Thin-walled tubes | |

| |

| |

| |

Equilibrium | |

| |

| |

| |

Shear flow | |

| |

| |

| |

Internal torque-stress relation | |

| |

| |

| |

Kinematics of thin-walled tubes | |

| |

| |

Chapter summary | |

| |

| |

Exercises | |

| |

| |

| |

Bending of Beams | |

| |

| |

| |

Symmetric bending: Kinematics | |

| |

| |

| |

Symmetric bending: Equilibrium | |

| |

| |

| |

Internal resultant definitions | |

| |

| |

| |

Symmetric bending: Elastic response | |

| |

| |

| |

Neutral axis | |

| |

| |

| |

Elastic examples: Symmetric bending stresses | |

| |

| |

| |

Symmetric bending: Elastic deflections by differential equations | |

| |

| |

| |

Symmetric multi-axis bending | |

| |

| |

| |

Symmetric multi-axis bending: Kinematics | |

| |

| |

| |

Symmetric multi-axis bending: Equilibrium | |

| |

| |

| |

Symmetric multi-axis bending: Elastic | |

| |

| |

| |

Shear stresses | |

| |

| |

| |

Equilibrium construction for shear stresses | |

| |

| |

| |

Energy methods: Shear deformation of beams | |

| |

| |

| |

Plastic bending | |

| |

| |

| |

Limit cases | |

| |

| |

| |

Bending at and beyond yield: Rectangular cross-section | |

| |

| |

| |

Stresses beyond yield: Rectangular cross-section | |

| |

| |

| |

Moment beyond yield: Rectangular cross-section | |

| |

| |

| |

Unloading after yield: Rectangular cross-section | |

| |

| |

Chapter summary | |

| |

| |

Exercises | |

| |

| |

| |

Analysis of Multi-Axial Stress and Strain | |

| |

| |

| |

Transformation of vectors | |

| |

| |

| |

Transformation of stress | |

| |

| |

| |

Traction vector method | |

| |

| |

| |

Maximum normal and shear stresses | |

| |

| |

| |

Eigenvalues and eigenvectors | |

| |

| |

| |

Mohr's circle of stress | |

| |

| |

| |

Three-dimensional Mohr's circles of stress | |

| |

| |

| |

Transformation of strains | |

| |

| |

| |

Maximum normal and shear strains | |

| |

| |

| |

Multi-axial failure criteria | |

| |

| |

| |

Tresca's yield condition | |

| |

| |

| |

Henky-von Mises condition | |

| |

| |

Chapter summary | |

| |

| |

Exercises | |

| |

| |

| |

Virtual Work Methods: Virtual Forces | |

| |

| |

| |

The virtual work theorem: Virtual force version | |

| |

| |

| |

Virtual work expressions | |

| |

| |

| |

Determination of displacements | |

| |

| |

| |

Determination of rotations | |

| |

| |

| |

Axial rods | |

| |

| |

| |

Torsion rods | |

| |

| |

| |

Bending of beams | |

| |

| |

| |

Direct shear in beams (elastic only) | |

| |

| |

| |

Principle of virtual forces: Proof | |

| |

| |

| |

Axial bar: Proof | |

| |

| |

| |

Beam bending: Proof | |

| |

| |

| |

Applications: Method of virtual forces | |

| |

| |

Chapter summary | |

| |

| |

Exercises | |

| |

| |

| |

Potential-Energy Methods | |

| |

| |

| |

Potential energy: Spring-mass system | |

| |

| |

| |

Stored elastic energy: Continuous systems | |

| |

| |

| |

Castigliano's first theorem | |

| |

| |

| |

Stationary complementary potential energy | |

| |

| |

| |

Stored complementary energy: Continuous systems | |

| |

| |

| |

Castigliano's second theorem | |

| |

| |

| |

Stationary potential energy: Approximate methods | |

| |

| |

| |

Ritz's method | |

| |

| |

| |

Approximation errors | |

| |

| |

| |

Types of error | |

| |

| |

| |

Estimating error in Ritz's method | |

| |

| |

| |

Selecting functions for Ritz's method | |

| |

| |

Chapter summary | |

| |

| |

Exercises | |

| |

| |

| |

Geometric Instability | |

| |

| |

| |

Point-mass pendulum: Stability | |

| |

| |

| |

Instability: Rigid links | |

| |

| |

| |

Potential energy: Stability | |

| |

| |

| |

Small deformation assumption | |

| |

| |

| |

Euler buckling of beam-columns | |

| |

| |

| |

Equilibrium | |

| |

| |

| |

Applications | |

| |

| |

| |

Limitations to the buckling formulae | |

| |

| |

| |

Eccentric loads | |

| |

| |

| |

Rigid links | |

| |

| |

| |

Euler columns | |

| |

| |

| |

Approximate solutions | |

| |

| |

| |

Buckling with distributed loads | |

| |

| |

| |

Deflection behavior for beam-columns with combined axial and transverse loads | |

| |

| |

Chapter summary | |

| |

| |

Exercises | |

| |

| |

| |

Virtual Work Methods: Virtual Displacements | |

| |

| |

| |

The virtual work theorem: Virtual displacement version | |

| |

| |

| |

The virtual work expressions | |

| |

| |

| |

External work expressions | |

| |

| |

| |

Axial rods | |

| |

| |

| |

Torsion rods | |

| |

| |

| |

Bending of beams | |

| |

| |

| |

Principle of virtual displacements: Proof | |

| |

| |

| |

Axial bar: Proof | |

| |

| |

| |

Beam bending: Proof | |

| |

| |

| |

Approximate methods | |

| |

| |

Chapter summary | |

| |

| |

Exercises | |

| |

| |

| |

Additional Reading | |

| |

| |

| |

Units, Constants, and Symbols | |

| |

| |

| |

Representative Material Properties | |

| |

| |

| |

Parallel-Axis Theorem | |

| |

| |

| |

Integration Facts | |

| |

| |

| |

Integration is addition in the limit | |

| |

| |

| |

Additivity | |

| |

| |

| |

Fundamental theorem of calculus | |

| |

| |

| |

Mean value | |

| |

| |

| |

The product rule and integration by parts | |

| |

| |

| |

Integral theorems | |

| |

| |

| |

Mean value theorem | |

| |

| |

| |

Localization theorem | |

| |

| |

| |

Divergence theorem | |

| |

| |

| |

Bending without Twisting: Shear Center | |

| |

| |

| |

Shear center | |

| |

| |

Index | |