Question $4$: $(20$ points$)$ A hollow circular steel shaft is subjected to a torsional moment of $0\mathrm{.}8$ kN$.$m and a bending moment of $1\mathrm{.}2$ kN$.$m$,$ as shown in Figure $4.$ The inside diameter of the shaft is $60\%$ of the outside diameter. Assume a safety factor of $2$ and the yield strength of the steel is $265$ MPa. Determine the outside diameter of the shaft according to the following failure criteria: a$)$ Maximum shear stress theory $($Tresca criterion$)$ b$)$ Maximum distortion energy theory $($von Mises criteria$)$ Note: $($the second moment of inertia is given as: $1=$ J$/2)102$