Problem $4)$

Find and draw the flexural shear flow $\backslash (\backslash$mathbf$\{$q$\}\backslash )$ in the legs of the thin C$-$Beam shown in the figure below $($note use the coordinate S$1,$ S$2,$ S$3,$ S$4$ so express your results, and draw the shear flow diagram identifying key points. The beam is subjected to a shear force equal to $\backslash (\backslash$mathrm$\{$Vz$\}=1000\backslash$mathrm$\{$~N$\}\backslash ).$ The dimensions of the beam are $\backslash (2\backslash$mathrm$\{$~h$\}=100\backslash$mathrm$\{$~mm$\}\backslash )$ and $\backslash (2\backslash$mathrm$\{$~L$\}=50\backslash$mathrm$\{$~mm$\}\backslash ),$ thickness for all webs is $3$ mm $.$ The force is applied along the center line of the vertical web $($as shown$).$