Problem $5\mathrm{.}8-9$ A wood beam $AB$ on simple supports with span length

equal to $10ft$ is subjected to a uniform load of intensity $125l\frac{b}{f}t$ acting

along the entire length of the beam, a concentrated load of magnitude

$7500lb$ acting at a point $3ft$ 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 $2250$ and $160.$

$($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 $=35l\frac{b}{f}{t}^3),$

verify that the selected beam is satisfactory, or if it is not, select a new beam.