Question $4$

$($a$)$ Determine the distance $\frac{?}{\text{b}\text{a}\text{r}}(y)$ to the centroid of the beam's cross$-$sectional area; then determine the moment of inertia of area about the $x^{\text{'}}$ axis which shows in Figure Q$4($a$).$

$(20$ marks$)$

$($b$)$ Determine the location $y_c$ of the centroidal axis $x_c-x_c$ of the beam's cross$-$sectional area as shown in Figure Q$4($b$).$ Neglect the size of the corner welds at A and $B$ for the calculation. Given $r=50mm,t=15mm,a=150mm,b=15mm$ and $c=150mm.$

$(5$ marks$)$