$(25$ points$)$ The shaft is made from Type $301$ cold rolled steel, with a cold rolled finish. The expected operating temperature is $900F,$ and a reliability of $99\mathrm{.}99\%$ is desired. A factor of safety of $2\mathrm{.}00$ for infinite life is desired. Additionally, the shaft is subjected to a constant torque of magnitude $T=800in-lbf,$ and cyclic loading as shown below.

Use the following assumptions and hints in your problem solving:

Think about the implications of a constant Torque on your values of Tm and Ta$.$ You can still use Eq$.10-8.$

For stress concentrations in the keyway, assume that the keyway will be constructed such that the $\frac{r}{d}$ ratio is always $\mathrm{.}021$; see Figure $10-16($ p $615)$ to find $K_t$ and $K_{ts}.$

Assume that shafts cannot be manufactured more precisely than $\mathrm{.}005$ inches. Thus, a delta of less than $\mathrm{.}005$ inches is sufficient to stop iterating.

Assume no stress concentrations at the bearings.

Assume that the bearing provides enough stiffness that deflection is not an issue.

a$.$ Complete Shear and Moment Diagrams for the Shaft.

b$.$ Explain why points $B$ and $C$ are considered critical.

c$.$ For Point B$,$ use the Shaft Equation $($Eq $10\mathrm{.}8)$ to determine the minimum required shaft diameter. Assume an initial diameter of $1$ in$,$ and do not iterate more than twice. Make all calculations by hand.