A precast concrete beam has a cross$-$section as shown in the Figure $1,$ with respect

to $x-x$ and $Y-Y$ axis. $($all dimensions are in millimetres$).$

$2\mathrm{.}1$ Calculate the point of centroid

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

$2\mathrm{.}3$ Calculate the second moment of area about $y-y,l_{yy}$

$2\mathrm{.}4$ Calculate radius of gyration, $r_x$ and $r_y$

$2\mathrm{.}5$ Calculate the elastic section modulus

$2\mathrm{.}6$ Calculate the plastic modulus

Figure $1$