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Body and Surface Forces (b) Sectioned Axially Loaded Beam Surface Forces: T(x) S (a) Cantilever Beam Under Self-Weight Loading Body Forces: F(x) Elasticity Theory, Applications and Numerics M.H. Sadd, University of Rhode Island

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Traction Vector P1P1 P2P2 P3P3 p (Externally Loaded Body) FF n AA (Sectioned Body) Elasticity Theory, Applications and Numerics M.H. Sadd, University of Rhode Island

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Stress Tensor Traction on an Oblique Plane x z y n TnTn Elasticity Theory, Applications and Numerics M.H. Sadd, University of Rhode Island

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Stress Transformation Elasticity Theory, Applications and Numerics M.H. Sadd, University of Rhode Island

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Two-Dimensional Stress Transformation Elasticity Theory, Applications and Numerics M.H. Sadd, University of Rhode Island

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Principal Stresses & Directions (General Coordinate System) (Principal Coordinate System) Elasticity Theory, Applications and Numerics M.H. Sadd, University of Rhode Island

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Traction Vector Components Mohr’s Circles of Stress Admissible N and S values lie in the shaded area T nT n n AA S N Elasticity Theory, Applications and Numerics M.H. Sadd, University of Rhode Island

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Example 3-1 Stress Transformation Elasticity Theory, Applications and Numerics M.H. Sadd, University of Rhode Island

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Spherical, Deviatoric, Octahedral and von Mises Stresses... Spherical Stress Tensor... Deviatoric Stress Tensor Elasticity Theory, Applications and Numerics M.H. Sadd, University of Rhode Island... Octahedral Normal and Shear Stresses... von Mises Stress

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Stress Distribution Visualization Using 2-D or 3-D Plots of Particular Contour Lines Particular Stress Components Principal Stress Components Maximum Shear Stress von Mises Stress Isochromatics (lines of principal stress difference = constant; same as max shear stress) Isoclinics (lines along which principal stresses have constant orientation) Isopachic lines (sum of principal stresses = constant) Isostatic lines (tangent oriented along a particular principal stress; sometimes called stress trajectories) Elasticity Theory, Applications and Numerics M.H. Sadd, University of Rhode Island

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Example Stress Contour Distribution Plots Disk Under Diametrical Compression Elasticity Theory, Applications and Numerics M.H. Sadd, University of Rhode Island P P (a) Disk Problem (b) Max Shear Stress Contours (Isochromatic Lines) (c) Max Principal Stress Contours (d) Sum of Principal Stress Contours (Isopachic Lines) (e) von Mises Stress Contours (f) Stress Trajectories (Isostatic Lines)

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Equilibrium Equations F T n V S Elasticity Theory, Applications and Numerics M.H. Sadd, University of Rhode Island

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Stress & Traction Components in Cylindrical Coordinates Equilibrium Equations x3x3 x1x1 x2x2 r z dr zz rr rr rz zz dd Elasticity Theory, Applications and Numerics M.H. Sadd, University of Rhode Island

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Stress & Traction Components in Spherical Coordinates Equilibrium Equations RR x3x3 x1x1 x2x2 R RR RR Elasticity Theory, Applications and Numerics M.H. Sadd, University of Rhode Island

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