Problem Hu$1-01($Points: $1/2)$

For the the L profile shown in the figure, compute the following cross$-$seciton properties around the global horizontal axis $x$ that crosses the global centroid:

$($a$)[$Points $\frac{0\mathrm{.}15}{2}]$ the Moment of Inertia, $I_{xg}$;

$($b$)[$Points $\frac{0\mathrm{.}05}{2}$ the Radius of Gyration, $r_x^x$;

$($c$)[$Points $\frac{0\mathrm{.}35}{2}$ the Elastic Moment Capacity $M_E$ as a function of the yeld stress ${}_y($take ${}_y$ as constant$).$

$($d$)[$Points $\frac{0\mathrm{.}05}{2}$ the Elastic Section Modulus $S_x$;

$($e$)[$Points $\frac{0\mathrm{.}35}{2}]$ the Plastic Moment Capacity $M_P$ as a function of the yeld stress ${}_y($take ${}_y$ as constant$).$

$($f$)[$Points $\frac{0\mathrm{.}05}{2}]$ the Plastic Section Modulus $Z_x.$