© 2003 by CRC Press LLC
46
Mechanics of Materials
46.1
Introduction
46.2
Stress
Method of Sections • Definition of Stress • Stress Tensor •
Differential Equations for Equilibrium • Stress Analysis of
Axially Loaded Bars
46.3
Strain
Normal Strain • Stress–Strain Relationships • Hooke’s Law •
Constitutive Relations • Deformation of Axially Loaded Bars •
Poisson’s Ratio • Thermal Strain and Deformation • Saint
Venant’s Principle and Stress Concentrations • Elastic Strain
Energy for Uniaxial Stress
46.4
Generalized Hooke’s Law
Stress–Strain Relationships for Shear • Elastic Strain Energy for
Shear Stress • Mathematical Definition of Strain • Strain Tensor
• Generalized Hooke’s Law for Isotropic Materials • E, G, and
Relationship • Dilatation and Bulk Modulus
46.5
Torsion
Torsion of Circular Elastic Bars • AngleofTwist of Circular
Members • Torsion of Solid Noncircular Members • Warpage
of ThinWalled Open Sections • Torsion of ThinWalled
Hollow Members
46.6
Bending
The Basic Kinematic Assumption • The Elastic Flexure Formula
• Elastic Strain Energy in Pure Bending • Unsymmetric Bending
and Bending with Axial Loads • Bending of Beams with
Unsymmetric Cross Section • Area Moments of Inertia
46.7
Shear Stresses in Beams
Shear Flow • ShearStress Formula for Beams • Shear Stresses
in a Rectangular Beam • Warpage of Plane Sections Due to
Shear • Shear Stresses in Beam Flanges • Shear Center
46.8
Transformation of Stress and Strain
Transformation of Stress • Principal Stresses • Maximum Shear
Stress • Mohr’s Circle of Stress • Principal Stresses for a General
State of Stress • Transformation of Strain • Yield and Fracture
Criteria
46.9
Stability of Equilibrium: Columns
Governing Differential Equation for Deflection • Buckling
Theory for Columns • Euler Loads for Columns with Different
End Restraints • Generalized Euler Buckling Load Formulas •
Eccentric Loads and the Secant Formula • Differential
Equations for BeamColumns
Austin D.E. Pan
University of Hong Kong
Egor P. Popov
University of California at Berkeley
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46.1 Introduction
The subject of
mechanics of materials
involves analytical methods for determining the
strength
,
stiffness
(deformation characteristics), and
stability
of the various members in a structural system. Alternatively,
the subject may be called the strength of materials, mechanics of solid deformable bodies, or simply
mechanics of solids. The behavior of a member depends not only on the fundamental laws that govern
the equilibrium of forces, but also on the mechanical characteristics
of the material. These mechanical
characteristics come from the laboratory, where materials are tested under accurately known forces and
their behavior is carefully observed and measured. For this reason, mechanics of materials is a blended
science of experiment and Newtonian postulates of analytical mechanics.
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 Spring '10
 Thorton
 Strain, Stress, CRC Press LLC, Civil Engineering Handbook

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