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Transformation of Stress

The general stress state at a given point may be represented by six components. They are sx, sy, and sz which define the normal stresses exerted on the faces of a small cubic element of the same orientation as the coordinate axes. The other three are txy, tyz, and tzx which represent the shearing stresses on the same element. Sometimes it is useful to use a different set of coordinate axes when analyzing, for example, the failure plane of a brittle shaft under torsion. This is because the failure plane is often at a 45° angle with respect to the shaft's axis and the stress state will be represented by a different set of components if the coordinate axes are rotated.


Plane Stress:

Principal Stress:
 

Max Shear Stress:



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