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Introduction | |
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Force systems | |
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Units | |
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Characterization of force systems | |
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Distributed forces | |
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Equivalent forces systems | |
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Work and power | |
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Conservative forces | |
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Conservative systems | |
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Static equilibrium | |
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Equilibrium of a body | |
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Virtual work and virtual power | |
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Equilibrium of subsets: Free-body diagrams | |
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Internal force diagram | |
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Dimensional homogeneity | |
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Exercises | |
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Tension-Compression Bars: The One-Dimensional Case | |
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Displacement field and strain | |
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Units | |
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Strain at a point | |
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Stress | |
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Units | |
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Pointwise equilibrium | |
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Constitutive relations | |
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One-dimensional Hooke's Law | |
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Additional constitutive behaviors | |
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A one-dimensional theory of mechanical response | |
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Axial deformation of bars: Examples | |
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Differential equation approach | |
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Energy methods | |
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Stress-based design | |
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Chapter summary | |
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Exercises | |
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Stress | |
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Average normal and shear- stress | |
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Average stresses for a bar under axial load | |
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Design with average stresses | |
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Stress at a point | |
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Nomenclature | |
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Internal reactions in terms of stresses | |
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Equilibrium in terms of stresses | |
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Polar and spherical coordinates | |
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Cylindrical/polar stresses | |
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Spherical stresses | |
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Chapter summary | |
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Exercises | |
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Strain | |
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Shear strain | |
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Pointwise strain | |
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Normal strain at a point | |
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Shear strain at a point | |
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Two-dimensional strains | |
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Three-dimensional strain | |
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Polar/cylindrical and spherical strain | |
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Number of unknowns and equations | |
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Chapter summary | |
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Exercises | |
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Constitutive Response | |
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Three-dimensional Hooke's Law | |
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Pressure | |
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Strain energy in three dimensions | |
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Two-dimensional Hooke's Law | |
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Two-dimensional plane stress | |
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Two-dimensional plane strain | |
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One-dimensional Hooke's Law: Uniaxial state of stress | |
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Polar/cylindrical and spherical coordinates | |
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Chapter summary | |
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Exercises | |
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Basic Techniques of Strength of Materials | |
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One-dimensional axially loaded rod revisited | |
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Thinness | |
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Cylindrical thin-walled pressure vessels | |
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Spherical thin-walled pressure vessels | |
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Saint-Venant's principle | |
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Chapter summary | |
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Exercises | |
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Circular and Thin-Wall Torsion | |
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Circular bars: Kinematic assumption | |
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Circular bars: Equilibrium | |
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Internal torque-stress relation | |
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Circular bars: Elastic response | |
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Elastic examples | |
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Differential equation approach | |
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Energy methods | |
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Torsional failure: Brittle materials | |
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Torsional failure: Ductile materials | |
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Twist-rate at and beyond yield | |
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Stresses beyond yield | |
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Torque beyond yield | |
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Unloading after yield | |
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Thin-walled tubes | |
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Equilibrium | |
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Shear flow | |
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Internal torque-stress relation | |
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Kinematics of thin-walled tubes | |
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Chapter summary | |
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Exercises | |
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Bending of Beams | |
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Symmetric bending: Kinematics | |
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Symmetric bending: Equilibrium | |
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Internal resultant definitions | |
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Symmetric bending: Elastic response | |
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Neutral axis | |
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Elastic examples: Symmetric bending stresses | |
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Symmetric bending: Elastic deflections by differential equations | |
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Symmetric multi-axis bending | |
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Symmetric multi-axis bending: Kinematics | |
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Symmetric multi-axis bending: Equilibrium | |
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Symmetric multi-axis bending: Elastic | |
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Shear stresses | |
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Equilibrium construction for shear stresses | |
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Energy methods: Shear deformation of beams | |
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Plastic bending | |
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Limit cases | |
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Bending at and beyond yield: Rectangular cross-section | |
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Stresses beyond yield: Rectangular cross-section | |
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Moment beyond yield: Rectangular cross-section | |
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Unloading after yield: Rectangular cross-section | |
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Chapter summary | |
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Exercises | |
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Analysis of Multi-Axial Stress and Strain | |
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Transformation of vectors | |
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Transformation of stress | |
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Traction vector method | |
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Maximum normal and shear stresses | |
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Eigenvalues and eigenvectors | |
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Mohr's circle of stress | |
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Three-dimensional Mohr's circles of stress | |
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Transformation of strains | |
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Maximum normal and shear strains | |
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Multi-axial failure criteria | |
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Tresca's yield condition | |
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Henky-von Mises condition | |
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Chapter summary | |
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Exercises | |
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Virtual Work Methods: Virtual Forces | |
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The virtual work theorem: Virtual force version | |
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Virtual work expressions | |
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Determination of displacements | |
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Determination of rotations | |
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Axial rods | |
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Torsion rods | |
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Bending of beams | |
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Direct shear in beams (elastic only) | |
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Principle of virtual forces: Proof | |
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Axial bar: Proof | |
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Beam bending: Proof | |
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Applications: Method of virtual forces | |
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Chapter summary | |
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Exercises | |
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Potential-Energy Methods | |
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Potential energy: Spring-mass system | |
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Stored elastic energy: Continuous systems | |
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Castigliano's first theorem | |
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Stationary complementary potential energy | |
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Stored complementary energy: Continuous systems | |
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Castigliano's second theorem | |
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Stationary potential energy: Approximate methods | |
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Ritz's method | |
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Approximation errors | |
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Types of error | |
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Estimating error in Ritz's method | |
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Selecting functions for Ritz's method | |
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Chapter summary | |
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Exercises | |
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Geometric Instability | |
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Point-mass pendulum: Stability | |
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Instability: Rigid links | |
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Potential energy: Stability | |
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Small deformation assumption | |
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Euler buckling of beam-columns | |
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Equilibrium | |
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Applications | |
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Limitations to the buckling formulae | |
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Eccentric loads | |
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Rigid links | |
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Euler columns | |
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Approximate solutions | |
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Buckling with distributed loads | |
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Deflection behavior for beam-columns with combined axial and transverse loads | |
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Chapter summary | |
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Exercises | |
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Virtual Work Methods: Virtual Displacements | |
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The virtual work theorem: Virtual displacement version | |
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The virtual work expressions | |
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External work expressions | |
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Axial rods | |
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Torsion rods | |
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Bending of beams | |
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Principle of virtual displacements: Proof | |
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Axial bar: Proof | |
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Beam bending: Proof | |
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Approximate methods | |
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Chapter summary | |
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Exercises | |
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Additional Reading | |
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Units, Constants, and Symbols | |
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Representative Material Properties | |
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Parallel-Axis Theorem | |
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Integration Facts | |
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Integration is addition in the limit | |
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Additivity | |
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Fundamental theorem of calculus | |
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Mean value | |
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The product rule and integration by parts | |
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Integral theorems | |
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Mean value theorem | |
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Localization theorem | |
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Divergence theorem | |
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Bending without Twisting: Shear Center | |
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Shear center | |
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Index | |