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Preface | |

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Stress and Strain | |

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Overview | |

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Stress on a Surface | |

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Stress at a Point | |

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Sign Convention for Stress | |

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Stress Elements | |

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Construction of a Stress Cube | |

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Plane Stress | |

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Stress Transformation in Two Dimensions | |

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Matrix Method in Two Dimensions | |

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Principal Stresses | |

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Maximum Shear Stress | |

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Stress Transformation in Three Dimensions | |

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Principal Stresses | |

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Principal Stress Convention | |

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Characteristic Equation and Stress Invariants | |

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Octahedral Stresses | |

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Average Normal and Shear Strains | |

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Units of Average Strains | |

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Strain at a Point and Strain-Displacement Equations | |

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Plane Strain | |

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Finite Difference Approximation of Strains | |

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Strain Transformation | |

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Principal Strains | |

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Closure | |

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Material Description | |

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Overview | |

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Linear Material Model | |

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Monoclinic Materials | |

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Orthotropic Materials | |

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Transversely Isotropic Materials | |

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Isotropic Materials | |

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Plane Stress and Plane Strain | |

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Failure Theories | |

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Maximum Shear Stress Theory | |

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Maximum Octahedral Shear Stress Theory | |

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Maximum Normal Stress Theory | |

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Modified Mohr's Theory | |

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Saint-Venant's Principle | |

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Stress Concentration Factor | |

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Stress Intensity Factor | |

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Analysis Procedure | |

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Fatigue | |

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Closure | |

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Basic Structural Members | |

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Overview | |

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Logic in Structural Analysis | |

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Basic Theories of One-Dimensional Structural Members | |

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Limitations | |

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Elementary Theories of One-Dimensional Structural Members | |

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Shear Stress in Thin Symmetric Beams | |

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Stresses and Strains | |

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Discontinuity Functions | |

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Definition of Discontinuity Functions | |

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Boundary Value Problems | |

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Axial Displacement | |

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Torsional Rotation | |

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Beam Deflection | |

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Symmetric Bending of Curved Beams | |

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Kinematics | |

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Material Model | |

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Static Equivalency | |

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Location of the Neutral Axis | |

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Stress Formula | |

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Combined Loading | |

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Closure | |

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Composite Structural Members | |

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Overview | |

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Composite Axial Members | |

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Composite Shafts | |

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Composite Symmetric Beams | |

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Normal Bending Stress in Composite Beams | |

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Location of the Neutral Axis (Origin) in Composite Beams | |

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Bending Shear Stress in Composite Beams | |

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Cross Section Transformation Method | |

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Introduction to the Micromechanics of Composites | |

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Orthotropic Composite Laminae | |

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Unit Cell Approximation | |

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Longitudinal Modulus of Elasticity E[Subscript x] | |

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Poisson's Ratio v[Subscript xy] | |

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Transverse Modulus of Elasticity E[Subscript y] | |

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Shear Modulus G[Subscript xy] | |

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Closure | |

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Inelastic Structural Behavior | |

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Overview | |

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Effects of Temperature | |

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Initial Stress or Strain in Axial Members | |

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Temperature Effects in Axial Members | |

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Nonlinear Material Models | |

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Elastic-Perfectly Plastic Material Models | |

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Linear Strain-Hardening Material Model | |

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Power Law Model | |

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Elastic-Perfectly Plastic Axial Members | |

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Elastic-Perfectly Plastic Circular Shafts | |

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Residual Shear Stress | |

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Elastic-Perfectly Plastic Beams | |

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Material Nonlinearity in Structural Members | |

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Viscoelasticity | |

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Maxwell Model | |

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Kelvin Model | |

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Creep Test | |

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Relaxation Test | |

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Generalized Viscoelastic Linear Models | |

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Closure | |

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Thin-Walled Structural Members | |

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Overview | |

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Theory of Unsymmetric Bending of Beams | |

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Deformation | |

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Strain Distribution | |

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Material Model | |

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Internal Forces and Moments | |

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Sign Convention | |

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Bending Formulas | |

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Location of Origin | |

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Neutral Axis | |

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Equilibrium Equations | |

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Shear Stress in Thin Open Sections | |

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Shear Center | |

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Shear Stresses in Thin Closed Sections | |

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Shear Centers of Thin Closed Sections | |

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Torsion of Thin-Walled Tubes | |

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Torsional Deformation | |

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Torsion of Multicell Tubes | |

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Combined Loading | |

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Closure | |

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Energy Methods | |

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Overview | |

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Strain Energy | |

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Linear Strain Energy Density | |

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Axial Strain Energy | |

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Torsional Strain Energy of Circular Shafts | |

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Bending Strain Energy | |

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Work | |

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Virtual Work | |

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Types of Boundary Conditions | |

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Kinematically Admissible Functions | |

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Statically Admissible Functions | |

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Virtual Displacement Method | |

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Virtual Force Method | |

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Dummy Unit Load Method | |

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Axial Members | |

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Torsion of Circular Shafts | |

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Symmetric Bending of Beams | |

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Castigliano's Theorems | |

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Deflection of Curved Beams | |

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Minimum Potential Energy | |

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Rayleigh-Ritz Method | |

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Axial Members | |

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Torsion of Circular Shafts | |

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Symmetric Bending of Beams | |

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Functionals | |

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Closure | |

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Elasticity and the Mechanics of Materials | |

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Overview | |

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Elasticity Equations | |

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Compatibility Equations | |

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Plane Stress and Plane Strain | |

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Equilibrium Equations | |

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Boundary Conditions | |

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Axisymmetric Problems | |

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Axisymmetric Plane Strain | |

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Axisymmetric Plane Stress | |

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Rotating Disks | |

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Thick Hollow Cylinders | |

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Internal Pressure Only | |

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External Pressure Only | |

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Thin Disks | |

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Internal Pressure Only | |

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External Pressure Only | |

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Shrink Fitting | |

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Airy Stress Function | |

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Solution by Polynomials | |

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Quadratic Polynomials | |

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Cubic Polynomials | |

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Fourth-Order Polynomials | |

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Torsion of Noncircular Shafts | |

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Saint-Venant's Method | |

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Prandtl's Method | |

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Procedure for Solving Problems of Torsion of Noncircular Shafts | |

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Closure | |

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Finite Element Method | |

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Overview | |

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Terminology | |

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Lagrange Polynomials | |

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Axial Elements | |

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Element Stiffness Matrix | |

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Element Load Vector | |

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Assembly of Global Matrix and Global Load Vector | |

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Incorporating the External Concentrated Forces | |

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Incorporating the Boundary Conditions on Displacements | |

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Element Strain Energy | |

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Transformation Matrix | |

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Linear and Quadratic Axial Elements | |

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Procedural Steps in the Finite Element Method | |

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Circular Shaft Elements | |

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Symmetric Beam Elements | |

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Finite Element Equations in Two-Dimensions | |

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Constant Strain Triangle | |

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Closure | |

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Statics and Mechanics of Materials Review | |

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Overview | |

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Types of Forces and Moments | |

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External Forces and Moments | |

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Reaction Forces and Moments | |

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Internal Forces and Moments | |

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Free Body Diagrams | |

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Trusses | |

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Centroids | |

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Statically Equivalent Load Systems | |

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Distributed Force on a Line | |

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Distributed Force on a Surface | |

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Area Moments of Inertia | |

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Principal Moments of Inertia | |

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Mohr's Circle for Stress | |

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Construction of Mohr's Circle for Stress | |

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Principal Stresses and Maximum Shear Stress | |

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Stresses on an Inclined Plane | |

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Mohr's Circle for Strain | |

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Construction of Mohr's Circle for Strain | |

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Principal Strains and Maximum Shear Strain | |

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Strains in a Specified Coordinate System | |

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Strain Gages | |

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Thin-Walled Pressure Vessels | |

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Additional Details on Elementary Structural Theories | |

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Deformation | |

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Strains | |

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Stress | |

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Internal Forces and Moments | |

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Location of the Origin | |

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Stress and Deformation Formulas | |

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Sign Conventions | |

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Equilibrium Equations | |

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Differential Equations | |

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Basic Matrix Algebra | |

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Basic Definitions | |

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Addition of Matrices | |

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Multiplication of Matrices | |

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A Matrix Transpose | |

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Determinant of a Matrix | |

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Cramer's Rule | |

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Inverse of a Matrix | |

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Information Charts and Tables | |

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Stress Concentration Factor for a Finite Plate with a Central Hole | |

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Stress Concentration Factor for Stepped Axial Circular Bars with Fillet | |

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Stress Concentration Factor for Stepped Circular Shafts with Fillet | |

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Stress Concentration Factor for a Stepped Circular Beam with Fillet | |

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Reactions at the Support | |

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Areas, Centroids, and Second Area Moments of Inertia | |

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Deflections and Slopes of Beams | |

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Properties of Traditional Materials (FPS units) | |

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Properties of Traditional Materials (metric units) | |

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Properties of Typical Fiber and Matrix Materials | |

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Geometric Properties of Wide-Flange Sections (FPS units) | |

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Geometric Properties of Wide-Flange Sections (metric units) | |

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Geometric Properties of S-Shaped Sections (FPS units) | |

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Geometric Properties of S-Shaped Sections (metric units) | |

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Bibliography | |

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Index | |