The shaft from problem $2$ is now unchanged with one exception: a constant axial torque of $T_x=1000$

in$-$lb at the bearings has been added. $($a$)$ Sketch maximum$-$stress, alternating$-$stress, and mean$-$stress

stress elements for the critical section$/$point on the shaft $($show the stresses symbolically$).$ Calculate the

static factor of safety using $($b$)$ the MSSTF and $($c$)$ the DETF. Calculate the infinite life fatigue factor

of safety at the critical section using $($d$)$ the Soderberg criterion and $($e$)$ the Goodman criterion.

$($a$)$