A single$-$span steel beam with simple supports is uniformly loaded as

shown in Figure $1.$

A$)$ Determine if the Wide Flange W$18$x$76$ is adequate for bending $($due

to DL$+$LL$)$ and deflections $($due to LL and $DL+LL).$

B$)$ Determine if the HSS$2012\frac{1}{2}$ is adequate for bending $($due to

$DL+LL)$ and deflections $($due to LL and $DL+LL).$

Given:

Distributed dead load, $q_{DL}=400lb\frac{f}{f}t$

Distributed live load, $q_{LL}=800lb\frac{f}{f}t$

Yield stress, $F_y=50$ksi

Allowable bending stress, $F_b=30$ksi

Modulus of Elasticity $($Young$\text{'}$s modulus$),E=29,000$ksi

Deflection limits:

DL $+$ LL: L$/240$

LL: L$/360$

Assume the section profile is compact and the beam is adequately

braced.

Parameters:

$L=50ft($span$)$

Figure $1-$ Beam Diagram

Figure $2-$ Wide Flange profile

HSS $2012\frac{1}{2}$

$A=28\mathrm{.}3i{n}^2$

$I=1550i{n}^4$

$Z=188i{n}^3$

Figure $3-$ HSS Profile