Problem $04\mathrm{.}035-$ Use superposition to determine the minimum diameter to meet design criteria

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. For the steel countershaft shown below, assume the bearings have a maximum slope specification of $0\mathrm{.}064$ for good bearing life. Determine the$$shaft diameter needed to keep the bearings within the maximum slope specification.$($Round the final answer to three decimal places.$)$

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The minimum shaft diameter is in$.$

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