$4\mathrm{.}3$ While inspection a fa$$ade and opening the area above a window, you noticed a profile as shown

below $($a U$-$section$)$ is used as a lintel. The measurements shown were done at the site.

$($a$)$ Compute the location of the centroid of this section $(hat(y)).$

$($b$)$ Compute the moment of inertia $I_x.$

$($c$)$ Compute the section modulus $S_x.$

$($d$)$ It appears that this section was built by bending a flat plate of about $16$ inches wide and $\frac{3}{8}$

inches thick. If we used that flat plate laid horizontally, what would its $I_x$ be$?$

$($e$)$ Steel weighs about $490lb\frac{s}{f}{t}^3($or $0\mathrm{.}28lb\frac{s}{i}{n}^3).$ Compute the weight of the section shown

above per linear foot $($which is nearly the same as the weight of the flat plate per linear foot$).$

Then compute the ratio of the $I_x$ to weight for both the U$-$section and the flat plate and decide

which section is more efficient.