Problem

$[$Points: $1/4].$ For the the com$-$

posite cross section shown in the figure,

$($a$)[$Points $0\mathrm{.}4/3]$ Compute the Moment of Inertia $I_x=I_y$ by hand via the Parallel$-$Axis Theorem. Tip: Exploit the symmetry that exists in one direction.

$($b$)[$Points $0\mathrm{.}5/3]$ Compute the Elastic Moment Capacity $M_E$ as a function of the yield stress ${}_y.$

$($c$)[$Points $0\mathrm{.}1/3]$ How much is the value of the Elastic Section Modulus $S$ given the outcome of $M_E?$

Problem

$[$Points: $1/4].$ For the column with the cross section of problem MEX$-01$ shown in the figure, compute the design compressive resistance capacity $P_u$ when it is $($a$)$ fixed at the bottom, no restriction at the top $($free rotation, free translation$)$ along the $x-$axis direction; $($b$)$ fixed at the botton, braced at the top $($free rotation, fixed traslation$)$ along the $y$ axis. Employ A$36$ steel $29,000,000l\frac{b}{i}{n}^2).$ Properties of the cross section: centroid $Y=2in,$ centroid $x=1\mathrm{.}7in,A=106i{n}^2,I_x=47\mathrm{.}33i{n}^2,I_y=43\mathrm{.}33i{n}^2,r_x=2\mathrm{.}17in,r_y=2\mathrm{.}08in,L=10in.$