Problem $\backslash$#$3$: $(30$ points$)$ A thin$-$walled, closed, two$-$celled cross$-$section with one rectangular and one triangular cell is shown in Figure $3.$ The lengths of the midlines of the walls and the thicknesses of the walls are shown on the figure. The cross section is subjected to an overall counterclockwise torque $\backslash ($ T$=20\backslash$mathrm$\{$kN$\}-\backslash$mathrm$\{$m$\}\backslash )($not shown on the figure$).$ The shear modulus of the entire cross section is a constant $\backslash ($ G$=25\backslash$mathrm$\{$GPa$\}\backslash ).$

a$)$ Find the shear flows everywhere $($i$.$e$.$ on each wall$)$ on the cross$-$section. Draw a clear picture of the cross section to describe where and in what direction the shear flows act.

b$)$ Calculate the corresponding shear stresses everywhere on the cross section, as well.

c$)$ Find the angle of twist$/$length $\backslash (\backslash$theta $\backslash ),$ and find the torsional rigidity T$.$R$.$ of the cross section. Figure $3$