The figure below shows a countershaft $(20$ cm diameter$)$ with $2$ V$-$belt pulleys with all elements

separated equidistant at a spacing of $1000\mathrm{.}5$Z cm$.$ A motor powers pulley C $(200$ cm diameter$)$

through a belt, with the tension at the tighter side being $3+($Z$/20)$ kN while the loose side is $2$ kN$.$

The power is transmitted through the shaft and delivered to the belt on pulley B $(100$ cm diameter$).$

For pulley B$,$ assume that the belt tension on the loose side at B is $30$ percent of the tension on the

tight side. Assume the shaft runs at a constant speed and the bearings act as simple supports.

$!!!!!!$ Z $=70.!!!!!!!!!$

a$)$ Determine the unknown tensions in the belt on pulley B$.$

b$)$ Find the reaction forces at the bearings.

c$)$ Draw shear force and bending moment diagrams on the x$-$y plane.

d$)$ Where is the maximum bending moment located? Determine the bending stress and the

torsional shear stress at the location of maximum bending.

e$)$ At the point of maximum bending moment, determine the principal stresses and the maximum

shear stress.