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Forces, Tractions and Stresses |
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The concept of Stress: Stresses can act either on physical points or across surfaces. A stress acting across a surface corresponds to a couple of traction acting on the opposite sides of the surface. A stress acting on a surface can be decomposed into a shear component (shear stress, τ), and a normal component (normal stress, σn). A stress is therefore represented by a couple of vector having similar magnitudes but opposite directions. |
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The stress acting on a small surface changes in magnitude and orientation with the normal n to the surface. As the surface changes orientation, the stress acting on it changes in magnitude and orientation. The stress vectors define an ellipsoid characterized by three principal orthogonal axes: σ1, σ2, σ3. It can be shown that there is only three positions of the surface for which the stress is perpendicular to it. |
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The state of stress acting on a material point is characterized by an ellipsoid called the stress ellipsoid. It is defined by three perpendicular axes called the principal stress axes: σ1, σ2, σ3. |
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