We will assume that the stresses σx, σy, and τxy at a point are known. We need to compute the normal and shear stresses acting on an arbitrarily oriented face.

 

Derivation of stress transform equations

Note: τyx = τxy


The normal to this face will be called the n axis, the direction parallel to the face will be called the t axis,

and the z axis will extend out-of-plane.

The ntz reference axes form a right handed coordinate system similar to the xyz system. The +z axis in the new ntz coordinate frame must point in the same direction as the +z axis in the xyz coordinate system.