Design a wood beam using $4"$ dimensional lumber $($the nominal size of the section is set

as $b=4",$ you need to determine the depth $d$ of the section$)$ to carry a uniform distributed

load of $300$ plf over a $12\text{'}$ span. The lumber is No$.2$ southern yellow pine $($SYP$)$ where $F_b$

$=1,100,F_v=80,$ and $E=1\mathrm{.}6{10}^6,$ adequately glued, screwed, and bolted to

provide composite action. The deflection requirement is $=2ptsD.$ You should consider

the beam's self$-$weight. $(Full$ credit $=2pts).$

Hints: $1$