Determine the least$-$weight W$-$shape to support a concentrated dead load of $24$ kips plus the beam selfweight and a concentrated live load of $15$kips on a $30ft$ span. The concentrated loads are located at the midpoint of the span. Lateral supports are provided at the supports

and at the load point. Use A$992$ steel and $C_b=1\mathrm{.}0.$ Design for flexure by $($a$)$ LRFD and $($b$)$ ASD.

Redesign the beam of Problem $33$ using the correct value of $C_b.$