$*10-80.$ Determine the directions of the principal axes with origin located at point $O,$ and the principal moments of inertia for the area about these axes.

Probs. $10-80$

Ans:

${}_p=-27\mathrm{.}3$

$I_{\text{m}\text{a}\text{x}}=24\mathrm{.}6(10{)}^{6}m{m}^4$

$I_{\text{m}\text{i}\text{n}}=2\mathrm{.}56(10{)}^{6}m{m}^4$