Hooke's Law for shear is $\mathrm{\tau }=\mathrm{G\gamma }$. Multiply the preceding relationship by $\mathrm{G}$...

$\mathrm{G\gamma }=\frac{\mathrm{\rho }}{\mathrm{c}}{\mathrm{G\gamma }}_{\max }$

and apply Hooke's Law to produce the relationship that describes the variation of shear stress $\mathrm{\tau }$ over the cross section.

$\mathrm{\tau }=\frac{\mathrm{\rho }}{\mathrm{c}}{\mathrm{\tau }}_{\max }$

As with the shear strain, shear stress in a circular shaft varies linearly with the radial distance $\mathrm{\rho }$ from the centerline. The shear stress is zero at the centerline and increases linearly until it reaches a maximum value on the outermost surface of the shaft.