A $4$ inch diameter $12$ foot long solid steel $(E=29,000$ ksi$)$ shaft having a circular cross section is used as a simply supported beam. A concentrated load $P$ is applied at the midspan. Calculate the maximum allowable load $P$ if the allowable deflection is $0\mathrm{.}5$ inches. Please include the weight of the beam in your calculation. The beam weighs $w=3\mathrm{.}56\frac{lb}{in}=42\mathrm{.}7\frac{lb}{ft}.$ Plesae answer in kips.