Problem $1$

Design the most economical W$12,$ A$992,$ steel beam with the following parameters and loads.

$20ft$ long

Simply supported, i$.$e$.$ pinned boundary conditions

$Lb={24}^{\text{'}\text{'}}$

Uniform service dead load of $0\mathrm{.}25klf(w=0\mathrm{.}25\frac{k}{f}t$ dead load$)$

Uniform service live load of $2\mathrm{.}1klf,(w=2\mathrm{.}1\frac{k}{f}t$ live load$)$