MIOTERM $-$ ME $323$ MACHINE DESIGNI

$2)$ A countershaft carrying two $\backslash ($ v $\backslash )-$belt pulleys is shown in the figure. Pullev $\backslash ($ A $\backslash )$ recelves power from a motor through a beft with the belt tensions shown. The power is transmited through the shaft and detivered to the belt on pulley B$.$ Assume the belt tension on the loose side at $8$ is $25$ percent of the

$($a$)$ Oraw free body, shearforce and bendinemoment diagrams for the shaft $($boty $\backslash ($ x$-$y $\backslash )$ and $\backslash (\backslash$times $\backslash )-2$ planes$).$

$($Hint:Defermine the censions in the beft on pulley $0,$ ussuming the shaft is running at a constont speed.$)$

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

$($c$)$ Calculate the mintmum safety factor $\backslash (($n$)\backslash )$ for yletding. Use both the Diftortion Energy Theory $($DE$)$ and Maximum. Shear Stress $($MSS$)$ Theory and compare the results.

$($d$)$ Calculate the minimum safoty fackor for fatlgue ina$)$ based on infinite life. Use Modinied Goodman Fallure Theon$)$ The shafic rotates at a constant speed $($The bending is completely reversed due to rotation and the torsion is steady$).$ Shaft has a constant diameter.