$1-(10$pts$)$ The rotating shaft shown below is carrying a load that produces a maximum moment of $750$ inlb.

a$)$ Estimate the fatigue stress concentration factors, $K_f,$ at the $\mathrm{.}1$ inch fillet and at the transverse $\frac{1}{16}$ inch hole in the shaft.

b$)$ Use the result of part $($a$)$ and determine the safety factor guarding against fatigue failure. The shaft is made of $1020$ hot$-$rolled steel. Use infinite life $({10}^6$ cycle$)$ and reliability of $90\%.$