$3.$ For a rectangular Hollow Structural Sections $($HSS$)$ HSS Column from the Gateway Building structure, answer the following questions:

The geometry of the HSS column is as follows: outside of the HSS: $4"$x$4",$ inside: $\backslash (3\mathrm{.}5^\{\backslash$prime $\backslash$prime$\}\backslash$mathrm$\{$x$\}3\mathrm{.}5^\{\backslash$prime $\backslash$prime$\}\backslash ),$ the height of the column is $14$ ft $.$ Modulus of Elasticity $\backslash (=30,000\backslash$mathrm$\{$ksi$\}\backslash )$

$-$ Find the cross$-$sectional area and the least moment of inertia for the column. $(15$ points$)$

$-$ Find the Euler buckling load and Euler buckling stress for the column. $(15$ points$)$

$-$ With the column braced at the midpoint, what are the effective length of the column $($KL$)$ and the slenderness ratio of the column $(\backslash (\backslash$mathrm$\{$KL$\}/\backslash$mathrm$\{$r$\})\backslash )?(10$ points $\backslash ()\backslash )$

Hints:

You will need the Moment of Inertia Equation for a Hollow Rectangular Shape $($or section$)$

Be careful about the unit $($remember to convert ft to in$).$