$14\mathrm{.}4$ Combining Chapter $11($Bending Stress$)$ AND Chapter $12($Transverse Shear Stress$)$

The $10$ foot simply supported beam is under the point forces shown. The crosssection of the beam is $\backslash (3\mathrm{.}5-\backslash$mathrm$\{$in$\}\backslash ).$ wide and $\backslash ($ d $\backslash )$ inches high. Given that the allowable shear stress is $120$ psi, and the allowable normal stress is $1800$ psi $($for both compression and tension$),$ determine the minimum height of the beam $\backslash ($ d $\backslash ),$ in inches, required to be meet all allowable internal stresses.