$7-121$ A $3-$in$--$diameter $0\mathrm{.}4\%,C$ hot$-$rolled steel $($see Appendix B$)$ shaft has a reduced diameter of $2\mathrm{.}73$ in $.$ for $12$ in $.$ of its length, as shown in Fig. P$7-121.$ If the tool used to turn down the section has a radius of $0\mathrm{.}25$ in$.,$ determine the maximum allowable bending load $P$ that can be applied to the end of the shaft if a factor of safety of $3$ with respect to failure by yielding is specified. Neglect stress concentration at the wall.

Figure P$7-121$