Consider a solid circular shaft to which two pulleys are keyed, as shown in the figure. In this configuration, pulley A receives power from a motor through a belt, and the forces relative to the belt tensions are shown in the figure. The power is transmitted through shaft OC and delivered to the belt at pulley B$.$ Assume that at pulley B the belt tension on the loose side $($T$\_(2))$ corresponds to $15\%$ of the tension on the tight side $($T$\_(1)),$ i$.$e$.$ T$\_(2)=0\mathrm{.}15$T$\_(1).$ Based on this information, answer the following: $($a$)$ Determine the tensions in the belt at pulley B$,$ assuming that shaft OC rotates at constant speed; that is$,$ the problem can be treated as being in static equilibrium. $($b$)$ Determine the reaction forces of the bearings at points O and C$,$ which in practice can be assumed to act as simple supports. $($c$)$ Draw the shear force $($V$)$ and bending moment $($M$)$ diagrams for shaft OC$.($d$)$ For the point of maximum bending moment $($calculated in $($c$)),$ determine the normal stress due to bending and the shear stress due to torsion. $($e$)$ Still at the point of maximum bending moment $($calculated in $($c$)),$ determine the principal stresses and the maximum shear stress.