Case - 5 :Member subjected to only shear stress(q) with out normal stresses

The element ABCD is subjected only shear stress on all faces.
Given values for shear stresses is q on all faces and normal stresses are zero on all faces.

Normal stress on inclined plane

We know that,
$\sigma _{n}=\left( \frac{\sigma _{x} + \sigma _{y}}{2} \right) + \left( \frac{\sigma _{x} - \sigma _{y} }{2} \right) \cdot cos2\theta + q\cdot sin2\theta$
here Normal stress in Y direction is zero,
$\therefore \sigma _{n}=q\cdot sin2\theta$

Tangential stress on inclined plane