An axial force $P=50kN,$ a bending moment $M=5kN*m,$ and a torsion moment $T=8kN*m$ act simultaneously on a circular rod with a diameter $D=100mm.$ If the yield stress $Sy=260$MPa on the circular rod, apply the following failure $($surrender$)$ theory to find the safety factor n $.$

a$)$ Maximum shear stress theory $($Tresca$)$

b$)$ maximum shear strain energy theory $($von Mises$)$

Answer $(a)=2\mathrm{.}61,(b)=2\mathrm{.}86$