$(30$pts$)$ A $1$ in$-$diameter $(D)$ solid round bar has a circular groove with a $r=0\mathrm{.}1-$in radius machined into it$,$ as shown in the figure. The bar is made with cold drawn steel $(S_{ut}=80$ksi, and $S_y=60$ksi $).$ This bar is subject to fluctuating load $(F)$ of $15$ kip to $-15$ kip $.$

a$.(5$ pts$)$ Compute the fatigue stress concentration factor.

b$.(5$ pts$)$ Compute the completely reversed stress.

c$.(5$ pts$)$ Compute the fully corrected endurance limit$.$

d$.(5$ pts$)$ Compute the fatigue safety factor.

e$.(10$ pts$)$ Compute the number of cycles to failure.