MIDTERM $-$ ME $323$ MACHINE DESIGN I

A countershaft carrying two $v-$belt pulleys is shown in the figure. Pulley A recelves 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 $8.$ Assume the belt tension on the loose side at $8$ is $25$ percent of the tension on the tight side $(T_2=0\mathrm{.}25T).$ The material is $1018$ CD steel $($For steel $S_1=60k,S_4=78kpsl,$ Marin factors; Surface condition modification factor $k_0=0\mathrm{.}8,$ Size modification factor k $=0\mathrm{.}9)(45$ points$)($a$)$ Draw free body, sheamforce and bending$-$moment diagrams for the shaft $($boty $x-y$ and $x-2$ planes$).$

$($Hint:$-$Determine the tensions in the belt on pulley $8,$ ossuming the shaft is running at a constant speed.$)$

$($b$)$ At the point of maximum bending moment, determine the bending stress and the torsional shearstress.

$($c$)$ Calculate the minimum safety factor $(n)$ for vielding. Use both the Distortion Energy Theory. $($DE$)$ and Maximum Shear Stress $($MSS$)$ Theory and compare the results.

$($d$)$ Calculate the minimum safety factor for fatigue. $)$ based on infinite life. $($Use Modified Goodman Fallure Theory$)$ The shaft rotates at a constant speed $($The bending is completely reversed due to rotation and the torsion is steady$).$ Shaft has a constant diameter.