Question $1(10$ marks$)$

a$)$ Determine the minimum and maximum moment of inertia of a profile around the axis through its centroid.

b$)$ Determine the angle between the positive $x$ axis and the major principle axis.

c$)$ If the profile is placed on a roof with a slope of $30($anti$-$clockwise from the positive $x-$axis$),$ what is the

second moment of area around the horizontal axis through the centroid?

Ixx $=12{10}^{6}m{m}^4$

$lyy=2\mathrm{.}02{10}^{6}m{m}^4$

$|xy=-1\mathrm{.}12{10}^{6}m{m}^4$

a$)\{$:$\frac{1}{5}b)$