$3\mathrm{.}81.$

A countershaft carrying two V$-$belt pulleys is shown in the figure. Pulley A receives power from

a motor through a belt with the belt tensions shown. The power is transmitted through the

shaft and delivered to the belt on pulley B$.$ Assume the belt tension on the loose side at B is $15$

percent of the tension on the tight side.

a$.$ Determine the tensions in the belt on pulley $B,$ assuming the shaft is running at a

constant speed.

b$.$ Find the magnitudes of the bearing reaction forces, assuming the bearings act as

simple supports.

c$.$ Draw shear$-$force and bending$-$moment diagrams for the shaft. If needed, make one

set for the horizontal plane and another set for the vertical plane.

d$.$ At the point of maximum bending moment, determine the bending stress and the

torsional shear stress.

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

maximum shear stress.

Problem $3-81*$

Dimensions in inches.