A thin$-$walled hollow quadratic $($HQ$)$ closed section beam shown in Figure Q$.3$ below

experiences a vertical shear force, $S_y,$ of $90kN$ passing through the point $1$ of the upper

side. The side length, $b,$ is $350mm$ and the wall thickness is $3mm.$

a$)$ Calculate the location of the centroid, $C,$ from the first moments of area.

marks$]$

b$)$ Calculate the second moments of area, $I_x$ and $I_y$ of the thin$-$walled HR$-$section.

marks$]$

c$)$ Assume to "cut" the closed section at point $1.$ Calculate the shear flow at the cut,

$q_{s,0}.$ Explain why it is a good idea to cut the at point $1.$

$[6$ marks$]$

d$)$ Calculate the total shear flow, $q_s,$ at points $1,2,3,4,5$ and $6.$

marks$]$

e$)$ Calculate the location and value of the maximum positive shear flow, $q_{s,\text{m}\text{a}\text{x}},$ and

sketch the shear flow distribution through the entire section.

$[3$ marks$]$

f$)$ Calculate the shear stress, $,$ at points $1,2,3,4,5$ and $6.$

$[3$ marks$]$