QUESTION $1[30$ MARKS$]$

A built$-$up section is shown in Figure $1.$ Calculate the following sectional properties of

the section with respect to $x-x$ and $Y-Y$ axis.

$1\mathrm{.}1$ The position of centroid.

$1\mathrm{.}2$ The second moment of area about $x-x,I_{}$

$1\mathrm{.}3$ The second moment of area about about $y-y,l_{yy}$

$1\mathrm{.}4$ The radius of gyration, $r_x$ and $r_y$

$1\mathrm{.}5$ The elastic section modulus, $Z_e$

$1\mathrm{.}6$ The plastic section modulus, $Z_p$

All dimensions are in millimetres.