A system is loaded as shown in the figure below. Points A and $C$ are bearing locations. Shaft is made of a steel having Sy: $5$ABMP and Sut: $6$BA MPa. $($All dimensions are in mm$,$ D$/$d is $1\mathrm{.}1$ and fillet radius are $3$ mm$.)$

a$)$ Evaluate the total forces, moments and torques acting onto the system.

b$)$ Design the shaft based on a factor of safety of A$,$B for $90$ percent reliability and infinite life. The shaft is machined surface.

$($In the question A and B is the last two digits of your student number, respectively. If A and$/$or B is equal to zero assume them $1.$ A and B $=49$