$5\mathrm{.}8-11).$ A wood beam $AB$ on simple supports with span length equal to $10$ft is subjected to a uniform load of intensity $125l\frac{b}{ft}$ acting along the Entire length of the beam, a concentrated load of magnitude $75001b$ acting at a point $3ft$ from the right$-$hand support, and a moment at $A$ of $18,500ft-$lb$.$ The allowable stresses in bending And shesr, respectivily, are $2250$ psi and $160$ psi,

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

b$)$ Taking into account the weight $($weight density$=351\frac{b}{f}{t}^3),$ verify that the sefected beam is satisfadory, if not, select a new beam.