A simple beam $AB$ is loaded as shown in the figure.

$($a$)$ Calculate the required section modulus $S($in in$.{?}^3)$ if ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=18,000,L=37ft,P=3,300lb,$ and $q=450l\frac{b}{f}t.($At this point, disregard the weight of the beam.$)$

in$.3$

your calculations.$)$

$in.{?}^{(}()()3)$

What is the suitable beam size?

$S1025\mathrm{.}4$

$S1250$

$S823$

$S1035$

$S1235$

$($b$)$ What is the maximum load $P$ that can be applied to your final beam selection in part $($a$)?($Enter the magnitude in lb$.)$