P$3.$ The shaft ABD $($diameter $12$ mm $)$ in figure below is made from AISI $1040$ CD steel. Based on failure possibility at the wall at A $,$ determine the factor of safety using

$($a$)$ the Tresca failure theory.

$($b$)$ the von Misses failure theory.

$($Hint: There is effective bending moments My and Mz$,$ Torque Tx and axial load Fx at the wall at A$.)$