MecMovies 4.0 : M6.2: Torsion Theory for Circular Sections

After torque $T$ is applied, the shaft twists. The right-hand end of element $jkmn$ rotates with respect to the left-hand end by a small angle of twist $dϕ$ . Points $k$ and $m$ move to new positions $k'$ and $m'$ , 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:

$γ_{\max} = \frac{kk'}{jk}$

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