HW$3$: Show that the stress function $=k(r^2-4a^2)$ is applicable to the solution of a solid circular section bar of

radius $2$a under pure shear. Determine the stress distribution in the bar in terms of the applied torque.

Hint: $$

Second moment of inertia: $$

${}_A{x}^{2}dxdy=I_y$

${}_A{y}^{2}dxdy=I_x$