Required information

Use the general shaft layout given and determine the critical diameters of the shaft based on infinite fatigue life with a design factor of $1\mathrm{.}5.$ Check for yielding. Check the slopes at the bearings for satisfaction of the recommended limits in Table $7-2.$ Assume that the deflections for the pulleys are not likely to be critical. The material selected is $1050$ Q and $T.$ Given: $S_{ut}=163k$ and $S_y=117k.$

Use the following shaft layout assuming a gear transmits torque through a key and keyseat at location $A$ to another gear at location $B.$

Using the DE$-$Goodman criteria and a design factor of $1\mathrm{.}5,$ calculate the diameter based on the shaft's loadings and your guess for the shaff's diameter at the critical location, what is the shaft diameter and what is the factor of safety against yielding? Assume the notch radius to be $0\mathrm{.}02$ in $.($Round the final answers to three decimal places.$)$

The shaft diameter is $$ inches.

The factor of safety against yielding is