Question $2(20$ marks$)$

The beam section shown in Figure Q$2$ has second moments of area I$\_($y$)=317,600$mm$^(4),$ I$\_($z$)=791,700$mm$^(4),$I$\_($yz$)=-298,500$mm$^(4).$ The beam is subjected to a bending moment M$\_(0)=1000$Nm about the y$1-$axis as shown. Determine:

$($a$)$ The principal moments of inertia of the beam section and the orientation of the principal axes;

$(10$ marks$)$

$($b$)$ The bending stress at point P $.$

$(10$ marks$)$

rigure all amensions in mm