$(2)$

$f_c^{\text{'}}=4$ksi

Grade $60$ steel

NWC

$W_{DL}=2\mathrm{.}2kLf.$ including self$-$weignt.

$W_{LL}=1\mathrm{.}4KLf$

$I_g=\frac{1}{12}14{27}^3=22,964$

$f_r=7\mathrm{.}5\sqrt[\phantom{2}]{f_c^{\text{'}}}=474$

$I_{tr}=10,553i{n}^4$

The immediate deffection due to$.$ Live load $=\frac{l}{500}.$

Cheok if ${}_{LL}$ meets the criteria above.