${?}^{*10-1\text{A}\text{s}\text{i}\text{m}\text{p}\text{l}\text{y}\text{s}\text{u}\text{p}\text{p}\text{o}\text{r}\text{t}\text{e}\text{d}\text{s}\text{h}\text{a}\text{f}\text{t}\text{i}\text{s}\text{s}\text{h}\text{o}\text{w}\text{n}\text{i}\text{n}\text{F}\text{i}\text{g}\text{u}\text{r}\text{e}\text{P}10-1.Aconstant-\text{m}\text{a}\text{g}\text{n}\text{i}\text{t}\text{u}\text{d}\text{e}\text{t}\text{r}\text{a}\text{n}\text{s}\text{v}\text{e}\text{r}\text{s}\text{e}}$ load $P$ is applied as the shaft rotates subject to a time$-$varying torque that varies from $T_{\text{m}\text{i}\text{n}}$ to $T_{\text{m}\text{a}\text{x}}.$ For the data in the row$($s$)$ assigned from Table P$10-1,$ find the diameter of shaft required to obtain a safety factor of $2$ in fatigue loading if the shaft is steel of $S_{ut}=108k$ and $S_y=62k.$ The dimensions are in inches, the force in pounds, and the torque in lb$-$in$.$ Assume no stress concentrations are present.

bearings are self$-$aligning so act as simple supports