Problem $2.$ Consider a solid circular shaft to which two pulleys are keyed, as shown in Figure $2.$ In this configuration, pulley A receives power from a motor through a belt, and these forces are relative to the belt tensions shown in Figure $2.$ The power is transmitted through the shaft 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 questions: $($a$)$ Determine the tensions in the belt at pulley B$,$ assuming that the shaft 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 $($V$)$ and bending moment $($M$)$ diagrams for the shaft.

$($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.

Figure $2.$