Question $5[15$ Marks$]$

A shaft with a diameter $\backslash (($d$)\backslash )$ of $50$ mm is made of a material with a shear yield stress $\backslash (\backslash$left$(\backslash$tau$\_\{$Y$\}\backslash$right$)\backslash )$ of $80$ MPa $.$ Use the Tresca Criterion to determine the maximum pure bending moment $\backslash (($M$)\backslash )$ that can be carried by the shaft if it carries a torque $(\backslash ($ T $\backslash ))$ of $500$ Nm and a direct compressive load $\backslash (($F$)\backslash )$ of $8$ kN $,$