Example $10\mathrm{.}4$

A semi$-$circular groove of radius $3$ mm is machined in a $50$ mm diameter shaft which is

then subjected to the following combined loading system:

$($a$)$ a direct tensile load of $50$ kN $,$

$($b$)$ a bending moment of $150$ Nm $,$

$($c$)$ a torque of $320$ Nm $.$

Determine the maximum value of the stress produced by each loading separately and hence

estimate the likely maximum stress value under the combined loading.