$11-39.$ The end gear connected to the shaft is subjected to the loading shown. If the bearings at $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ exert only $\backslash ($ y $\backslash )$ and $\backslash ($ z $\backslash )$ components of force on the shaft, determine the equilibrium torque $\backslash ($ T $\backslash )$ at gear $\backslash ($ C $\backslash )$ and then determine the smallest diameter of the shaft to the nearest millimeter that will support the loading. Use the maximum shear stress theory of failure with $\backslash (\backslash$tau$\_\{\backslash$text $\{$allow $\}\}=60\backslash$mathrm$\{$MPa$\}\backslash ).$ Problems $11-39/40$