P$1.$ A $1-$in$,$ constant diameter shaft, is loaded with forces at A and B as shown, with ground reaction forces at O and C $.$ The shaft also transmits a torque of $1500$ lbf $*$ in throughout the length of the shaft. The shaft has a tensile yield strength of $50$ kpsi $.$

$($a$)$ Draw shear force and moment diagrams, find reaction forces

$($b$)$ Determine the minimum static factor of safety using the maximum$-$shear$-$stress failure theory.

$($c$)$ Determine the minimum static factor of safety using the distortion$-$energy failure theory.