A system $is$ located $as$ shown $in$ the figure below. Points A and $C$ ate bearing lolcations. Shaft $is$ made $of$ a steel having $Sy$: $5AB$ MPa and sut: $6BA$ MPa.$(Alldmentions$ are $inmm,\frac{D}{d}is1\mathrm{.}1$ and fillet radius are $3mm)$ a$)$ Evaluate the total forces, moments,torques acting on to 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. The value of A is $3$ and B is $9.$