Problem $2$:

Design a rectangular beam for a $20$ ft $.$ simply supported span.

Given: $w_{DL}=0\mathrm{.}8\frac{k}{f}t,w_{LL}=1\mathrm{.}5\frac{k}{f}t,w_{\text{s}\text{u}\text{p}\text{p}\text{e}\text{r}\text{i}\text{m}\text{p}\text{o}\text{s}\text{e}\text{d}\text{l}\text{o}\text{a}\text{d}}=0\mathrm{.}15\frac{k}{f}t$

$W_{\text{s}\text{e}\text{l}\text{f}}$ of the beam needs to be calculated and added to $w_{\text{t}\text{o}\text{t}\text{a}\text{l}}.$

Use load combination of $w_{\text{t}\text{o}\text{t}\text{a}\text{l}}=1\mathrm{.}2DL+1\mathrm{.}6LL$

From the architect, width and depth of the beam is specified as $h=25$ in$.,d=24$ in$.,$ b$=12$ in$.$

Use $f^{\text{'}}c=4,000$ psi and $fy=60,000,Es=29,000$ksi

It is required to check your design.