Problem $5(30$ Marks$)$

The shaft shown in the figure is machined from AISI $\backslash (\backslash$mathbf$\{1040\}\backslash )$ CD steel. The shaft rotates at $\backslash (\backslash$mathbf$\{1600\}\backslash$mathbf$\{$~ r p m$\}\backslash )$ and is supported in rolling bearings at A and B $.$ The applied forces are F$1=\backslash (\backslash$mathbf$\{2500\}\backslash$mathbf$\{$~ l b f$\}\backslash )$ and F$2=1000$ lbf$.$ 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.