Problem $3.$

A shaft is loaded in bending and torsion such that $M_a=70N*m,T_a=45N*m,M_m=55N*m,$ and $T_m=35N*m.$ For the shaft, $S_u=700$MPa and $S_y=560$MPa, and a fully corrected endurance limit of $S_e=210$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$-$ASME Elliptic criterion.

$($c$)$ DE$-$Soderberg criterion.

$($d$)$ DE$-$Goodman criterion.