$(5)$ The shaft shown below is machined from AISI $1040$ CD steel. The shaft rotates at $1600$ rpm and is supported in rolling bearings at A and $B.$ The applied forces are $F_1=2xYZlbf$ and $F_2=1xYZ$ lbf$.($Where $xYZ$ are the last three digits of your rocket number. For example, a rocket number $140613$ will have $x=6,Y=1,$ and $Z=3$ and $F_1=2613$ and $F_2=1613).$ Determine the minimum fatigue factor of safety based on achieving infinite life. If infinite life is not predicted, estimate the number of cycles to failure. Also check for yielding. $(5$ points$)$