A simple span beam with a uniformly distributed

dead load of $1\mathrm{.}0\frac{k}{f}t,$ plus its self$-$weight, and

concentrated dead loads of $2\mathrm{.}5$ kips and live loads of

$8\mathrm{.}0$ kips at the quarter points of a $20-ft$ span, is to be

designed with lateral supports at the supports and

mid$-$span. The live load deflection must be limited to

$\frac{1}{240}$ of the span. Use the correct $C_b$ and be sure to

check shear. Determine the least$-$weight W$-$shape to

carry the loads. Use A$992$ steel. Design by $($a$)$ LRFD

and $($b$)$ ASD.