$5\mathrm{.}8-11$ A wood beam $\backslash ($ A B $\backslash )$ on simple supports with span length equal to $10$ ft is subjected to a uniform load of intensity $\backslash (125\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}\backslash )$ acting along the entire length of the beam, a concentrated load of magnitude $7500$ lb acting at a point $3$ ft from the right$-$hand support, and a moment at A of $18,500$ ft$-$lb $($see figure$).$ The allowable stresses in bending and shear, respectively, are $2250$ psi and $160$ psi.

a$.$ From the table in Appendix G$,$ select the lightest beam that will support the loads $($disregard the weight of the beam$).$

b$.$ Taking into account the weight of the beam $($weight density $\backslash (=35\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}^\{3\}\backslash )),$ verify that the selected beam is satisfactory, or if it is not, select a new beam.