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Mechanics of Materials - 46 Mechanics of Materials 46.1...

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© 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 • Angle-of-Twist of Circular Members • Torsion of Solid Noncircular Members • Warpage of Thin-Walled Open Sections • Torsion of Thin-Walled 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 • Shear-Stress 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 Beam-Columns 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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