$(15$ points$)$ Two round torsion bars are used on a Dodge Dakota for the frontend suspension. Each torsion bar undergoes torsional deflection to support a portion of the weight of the truck under various road terrain. This downward force is placed on two torsion levers arms that are $10$ inches in length, which are attached to the torsion bars. The torsion bars are fixed to the truck body at the other end, and the total force on each front$-$end lever is $500$ lbs $.$ The torsion bars are made of steel $(G=11\mathrm{.}5E\frac{6}{P}SI,$ and are $30"$ long.

a$)$ If the torsion bars are hollow, with an OD of ${1\mathrm{.}25}^{\text{'}\text{'}}$ and an ID of ${1\mathrm{.}0}^{\text{'}\text{'}},$ what is the angular deflection in radians?

b$)$ What is the deflection in degrees?

c$)$ What is the maximum shear stress in the hollow bar?

Equations which may be needed:

Shear Stress in Torsion: $=T\frac{r}{J}$

Shear deformation: $=$ TL$/$GJ

J solid shaft $=\frac{}{32}(O{D}^4)$

J hollow shaft $($:$=\frac{}{32}(O{D}^4-I{D}^4)\}$