The shaft mounted on two bearings $\backslash ($ A $\backslash )$ and $\backslash ($ C $\backslash )$ as shown transmits power from a helical gear $\backslash ($ B $\backslash )$ to the overhung bevel gear $\backslash ($ D $\backslash ).$ The pitch circle diameter of the helical gear is $500$ mm and the diameter of the bevel gear at the point of application of the force $\backslash ($ Q $\backslash )$ is $375$ mm $.$ The gears are keyed to the shaft. The shaft is made of hardened steel, $\backslash ($ S$\_\{$u$\}=1069\backslash$mathrm$\{$MPa$\},$ S$\_\{$y$\}=896\backslash$mathrm$\{$MPa$\}\backslash ).$

$($a$)$ Draw load, shear force, axial force, bending moment, and toque diagrams for the shaft in the $\backslash ($ x K $\backslash )$ and zz planes.

$($b$)$ Calculate the effective stresses at points $\backslash ($ B$,$ C $\backslash ),$ and $\backslash ($ E $\backslash )$ of the shaft and estimate the safety factor at those points, analytically and graphically. leniency

$4..$