Find $I_{x^{\text{'}}{x}^{\text{'}}},I_{y^{\text{'}}{y}^{\text{'}}}$ and $I_{x^{\text{'}}{y}^{\text{'}}}$ for the cross section of teh beam shown in Fig. $1($a$),$ when the

origin of the coordinate frame $x^{\text{'}}-y^{\text{'}}$ lies at the centroid of the cross$-$section.

Ans: $I_{x^{\text{'}}{x}^{\text{'}}}=1\mathrm{.}141{10}^6,I_{y^{\text{'}}{y}^{\text{'}}}=6\mathrm{.}76{10}^5$ and $I_{x^{\text{'}}{y}^{\text{'}}}=4\mathrm{.}03{10}^5,$ all in $m{m}^4.$

$($a$)$

$($b$)$

$($c$)$