Part I Basic tools and concepts; 1 Basic Equations of Linear Elasticity .1.1 The concept of stress; 1.1.1 The state of stress at a point; 1.1.2 Volume equilibrium equations; 1.1.3 Surface equilibrium equations; 1.2 Analysis of the state of stress at a point; 1.2.1 Stress components acting on an arbitrary face; 1.2.2 Principal stresses; 1.2.3 Rotation of stresses; 1.2.4 Problems; 1.3 The state of plane stress; 1.3.1 Equilibrium equations; 1.3.2 Stresses acting on an arbitrary face within the sheet; 1.3.3 Principal stresses;1 ...
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Part I Basic tools and concepts; 1 Basic Equations of Linear Elasticity .1.1 The concept of stress; 1.1.1 The state of stress at a point; 1.1.2 Volume equilibrium equations; 1.1.3 Surface equilibrium equations; 1.2 Analysis of the state of stress at a point; 1.2.1 Stress components acting on an arbitrary face; 1.2.2 Principal stresses; 1.2.3 Rotation of stresses; 1.2.4 Problems; 1.3 The state of plane stress; 1.3.1 Equilibrium equations; 1.3.2 Stresses acting on an arbitrary face within the sheet; 1.3.3 Principal stresses;1.3.4 Rotation of stresses; 1.3.5 Special states of stress; 1.3.6 Mohr's circle for plane stress; 1.3.7 Lam???'s ellipse; 1.3.8 Problems; 1.4 The concept of strain; 1.4.1 The state of strain at a point; 1.4.2 The volumetric strain; 1.5 Analysis of the state of strain at a point; 1.5.1 Rotation of strains 1.5.2 Principal strains; 1.6 The state of plane strain; 1.6.1 Strain-displacement relations for plane strain; 1.6.2 Rotation of strains; 1.6.3 Principal strains; 1.6.4 Mohr's circle for plane strain; 1.7 Measurement of strains; 1.7.1 Problems; 1.8 Strain compatibility equations; 2 Constitutive Behavior of Materials; 2.1 Constitutive laws for isotropic materials; 2.1.1 Homogeneous, isotropic, linear elastic materials; 2.1.2 Thermal effects; 2.1.3 Problems; 2.1.4 Ductile materials; 2.1.5 Brittle materials; 2.2 Allowable stress; 2.3 Yielding under combined loading; 2.3.1 Tresca's criterion; 2.3.2 Von Mises' criterion; 2.3.3 Comparing Tresca's and von Mises' criteria;2.3.4 Problems; 2.4 Material selection for structural performance; 2.4.1 Strength design; 2.4.2 Stiffness design 2.4.3 Buckling design; 2.5 Composite materials; 2.5.1 Basic characteristics;2.5.2 Stress diffusion in a composite; 2.6 Constitutive laws for anisotropic materials; 2.6.1 Constitutive laws for a lamina in the fiber aligned triad; 2.6.2 Constitutive laws for a lamina in an arbitrary triad; 2.7 Strength of a transversely isotropic lamina; 2.7.1 Strength of a lamina under simpleloading conditions; 2.7.2 The Tsai-Wu failure criterion; 2.7.3 The reserve factor; 3 Linear Elasticity Solutions; 3.1 Solution procedures; 3.1.1 Displacement formulation; 3.1.2 Stress formulation; 3.1.3 Solutions to elasticity problems; 3.2 Plane strain problems; 3.3 Plane stress problems; 3.4 Plane strain and plane stress in polar coordinates; 3.5 Problem featuring cylindrical symmetry; 3.5.1 Problems; 4 Engineering Structural Analysis; 4.1 Solution approaches; 4.2 Bar under constant axial force; 4.3 Hyperstatic systems; 4.3.1 Solution procedures; 4.3.2 The displacement or stiffness method; 4.3.3 The force or flexibility method; 4.3.4 Problems; 4.3.5 Thermal effects in hyperstatic system; 4.3.6 Manufacturing imperfection effects in hyperstatic system; 4.3.7 Problems; 4.4 Pressure vessels; 4.4.1 Rings under internal pressure; 4.4.2 Cylindrical pressure vessels; 4.4.3 Spherical pressure vessels; 4.4.4 Problems; 4.5 Saint-Venant's principle; Part II Beams and thin-wall structures5 Euler-Bernoulli Beam Theory; 5.1 The Euler-Bernoulli Assumptions; 5.2 Implications of the Euler-Bernoulli assumptions; 5.3 Stress resultants; 5.4 Beams subjected to axial loads; 5.4.1 Kinematic description; 5.4.2 Sectional constitutive law; 5.4.3 Equilibrium equations; 5.4.4 Governing equations; 5.4.5 The sectional axial stiffness; 5.4.6 The axial stress distribution; 5.4.7 Problems; 5.5 Beams subjected to transverse loads; 5.5.1 Kinematic description; 5.5.2 Sectional constitutive law; 5.5.3 Equilibrium equations; 5.5.4 Governing equations; 5.5.5 The sectional bending stiffness; 5.5.6 The axial stress distribution; 5.5.7 Rational design of beams under bending; 5.5.8 Problems; 5.6 Beams subjected to axial and transverse loads; 5.6.1 Kinematic description; 5.6.2 Sectional constitutive law; 5.6.3 Equilibrium equations; 5.6.4 Governing equations; 6 Three-Dimensional Beam Theory; 6.1 Kinematic description; 6.2 Sectional constitutive law; 6.3 Sectional equilibrium equations; 6.4 Governing equati
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