Problem $(2)$: A mild steel shaft is subjected to $3500$ Nm of bending moment at it critical point and transmits a torque of $2500$ Nm $.$ The shaft is made of steel having yield strength of $231$ MPa $.$ Take the factor of safety of $2.$ Estimate the size of the shaft based on $($a$)$ Maximum shear stress theory, and $($b$)$ Maximum distortion energy theory.

$[$Ans$.$: $($a$)d=72\mathrm{.}38mm,($b$)d=71\mathrm{.}33mm]$