$5-(10$ pts$)$ The figure shows an automobile wheel with a single$-$ended wrench. The distance between A and $B$ is $12$ in $.$ and the handle diameter is $\mathrm{.}625$ in $.$ The handle is made of forged steel with $S_{ut}=60,000.$ The average tightening torque is $1200in-lb.$ Use reliability of $50\%.$ The outside diameter of the socket part of the wrench $($the part that fits over the lug nut$)$ is $1\mathrm{.}25$ and the fillet radius between the socket section and the solid section $(3$ in$.$ section$)$ is $\mathrm{.}25$ inch. Use $K_{fm}=1\mathrm{.}0($stress concentration factor applied to the mean stress$).$

a$)$ Estimate the value of the fatigue stress concentration factors $($bending and torsion$)$ at the fillet.

b$)$ Determine the number of cycles to failure, use ${10}^6$ as infinte life.