i$)$ A solid shaft, shown below, is $2\mathrm{.}5$m long and has a radius of $25$mm$.$ The shaft has a

tangential force of $225$N applied to it$.$ If the Modulus of rigidity $($G$)$ is $80$GPa

determine,

a$)$ The angle of twist, in radians.

b$)$ The maximum shear stress in the shaft $().$

c$)$ The distribution of shear stress in the shaft by hand sketching the diameter of

the bar, showing the stress in the end that is twisted. ii$)$ Your supervisor would now like you to compare the maximum shear stress in a$)$ above with a hollow shaft with similar dimensions. The hollow shaft is $2\mathrm{.}5m$ long

and has an outer radius of $25mm$ and an inner radius of $20mm.$ The hollow shaft

has the same torque applied as the solid shaft above. If the Modulus of rigidity $($G$)$

for the material used is $80$GPa determine,

a$)$ The angle of twist of the hollow shaft, in radians.

b$)$ The maximum shear stress in the tube $().$

c$)$ The distribution of shear stress in the hollow shaft by hand sketching the end of

the tube that is twisted and showing the stress distribution for the hollow shaft

material.