Problem I:

The shaft shown in the figure is driven by a gear at the right keyway, drives a fan at the left keyway, and is supported by two deep$-$groove ball bearings. The shaft is made from AISI $1020$ cold$-$drawn steel. At steady$-$state speed, the gear transmits a radial load of $230$ lbf and a tangential load of $633$ lof at a pitch diameter of $8$ in$.$

$($a$)$ Determine fatigue factors of safety at any potentially critical locations using the DE$-$Goodman failure criterion.