Simple graphical constructions for the direction of shear

The determination of the direction and sense of the resolved shear stress on a generally-oriented plane is greatly simplified by the use of a graphical technique based on the geometry of the representation quadric of a ‘reduced stress tensor’. This tensor is obtained by subtracting a constant equal to σ3 from each of the principal stress values. The calculation requires knowledge of the orientations of the principal stress axes and the ratio of the principal stress differences. A construction for finding the direction and sense of finite shear strain on a given plane is derived in an analogous fashion.