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: $5$AB MPa 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.

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