Stress transformation theory describes how the normal and shear stress components acting on a plane through a point change as the orientation of that plane is rotated, expressed via transformation equations derived from equilibrium of a stressed wedge in terms of the reference-plane stresses (normal stresses and shear stress) and the rotation angle. From these equations one derives the principal stresses (the extremal normal stresses, occurring on planes of zero shear) and the maximum shear stress (occurring on planes oriented 45° from the principal planes), and Mohr's circle provides a graphical construction that represents the full state of plane stress and all its rotated equivalents as points on a circle in normal-stress/shear-stress space. This belongs to the theory of stress analysis within mechanics of materials (strength of materials), extending the concept of stress invariance and principal stress evaluation from three dimensions to the two-dimensional (plane stress) case.
Stress transformation theory describes how the normal and shear stress components acting on a plane through a point change as the orientation of that plane is rotated, expressed via transformation eq…