An I$-$section is cut at mid$-$height of the web to allow for mechanical pipes to pass through the bottom half of the section. The resulting T$-$section in the segment of the member that is cut is shown below. The sections $($before and after cutting$)$ are subject to a shear, $\backslash (+$V$\_\{$y$\}\backslash ).$ Show all work in sufficient detail and all work shall be in $\backslash ($ N $\backslash )$ and mm$.$ Use symmetry. Use centerline dimensions. Note the coordinate system used in the figure. All calculations shall be in terms of $\backslash ($ V $/$ I $\backslash ).$

a$)$ Determine the shear flow distribution, $\backslash ($ q $\backslash ),$ in the I$-$Section $($top and bottom T$-$sections$).$ Plot a diagram of the flow distribution at the centerline of each element$-$choose enough points to get a clear diagram.

b$)$ Determine the shear flow distribution, $\backslash ($ q $\backslash ),$ in the T$-$Section. Plot a diagram of the flow distribution at the centerline of each element$-$choose enough points to get a clear diagram.

c$)$ What is the ratio $($cut section $/$ full section$)$ of the maximum shear stresses, $\backslash (\backslash$tau $\backslash ),$ in the web to underside of flanges? You will need to compute $\backslash ($ I$\_\{$z$\}\backslash )$ for both sections.

d$)$ What can be concluded about cutting the section?