A countershaft carrying static loads is shown in the figure. There are two support bearings located at O and C$.$

$($a$)$ Find the magnitudes of the bearing reaction forces, assuming the bearings act as simple supports

$($b$)$ Draw shear$-$force and bending moment diagi airs for the shaft

$($c$)$ If the shaft diameter is $30$ mm$,$ find the factor of safety according to the von Misses Theory assuming no step $1$ throughout the shaft for AISI $1020$ Steel $($S$=380$ MPa E$=205$ MPa, S$=210$ MPa. density$=7800$ kg$/$m$^3).$