C$.$ Beams, laterally unbraced $($Ch$\mathrm{.}9,10)$:

The W $30$ x $99$ beam with a $40$ ft span has lateral support supplied at its centerline, as

well as at its ends. If $F_y=50$ksi, determine the maximum permissible service live

load, $P_L.$ Neglect beam self$-$weight. Calculate $C_b$ by hand, then check using Steel

Construction Manual. Check adequacy of deflection limit state.

Solution: $C_b=1\mathrm{.}67,P_L=73\mathrm{.}1k$