After torque $\mathrm{T}$ is applied, the shaft twists. The right-hand end of element $\mathrm{jkmn}$rotates with respect to the left-hand end by a small angle of twist $\mathrm{d\varphi }$. Points $\mathrm{k}$ and $\mathrm{m}$ move to new positions $\mathrm{k}\text{'}$ and $\mathrm{m}\text{'}$, respectively.

Notice that the element sides do not elongate or contract. However, the corners of the element are no longer equal to ${90}^{\circ }$. The element is in a state of pure shear.

Recall that shear strain is an angle. Assuming very small deformations, observe that the angle formed is:

${\mathrm{\gamma }}_{\max }=\frac{\mathrm{kk}\text{'}}{\mathrm{jk}}$

where ${\mathrm{\gamma }}_{\max }$ refers to the strain on the outside surface of the shaft.