Problem $1(25$ points$).$ A shaft is loaded in bending and torsion such that $M_a=70Nm,T_a=45Nm,M_m=55$ Nm $,$ and $T_m=35Nm.$ For the shaft, $S_u=700$MPa and $S_y=560$MPa, and a fully corrected endurance limit$,S_e=210$MPa is assumed. Let $K_f=2\mathrm{.}2$ and $K_{fs}=1\mathrm{.}8.$ With a design factor of $2\mathrm{.}0$ determine the minimum acceptable diameter of the shaft using the $($a$)$ DE$-$Gerber criterion. $($b$)$ DE$-$elliptic criterion. $($c$)$ DESoderberg criterion. $($d$)$ DE$-$Goodman criterion. Discuss and compare the results.