$5\mathrm{.}10-1$ through $5\mathrm{.}10-6$ A wide$-$flange beam $($see figure$)$ is subjected to a shear force $V.$ Using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantities:

$($a$)$ The maximum shear stress ${}_{\text{m}\text{a}\text{x}}$ in the web.

$($b$)$ The minimum shear stress ${}_{\text{m}\text{i}\text{n}}$ in the web.

$($c$)$ The average shear stress ${}_{\text{a}\text{v}\text{e}\text{r}}($obtained by dividing the shear force by the area of the web$)$ and the ratio $\frac{{}_{\text{m}\text{a}\text{x}}}{{}_{\text{a}\text{v}\text{e}\text{r}\text{.}}}.$

$($d$)$ The shear force $V$ web carried in the web and the ratio $V$ web $\frac{?}{V}.$

Note: Disregard the fillets at the junctions of the web and flanges and determine all quantities, including the moment of inertia, by considering the cross section to consist of three rectangles.

$5\mathrm{.}10-4$ Dimensions of cross section: $b=220mm,t=12mm,h=600mm,h_1=570mm,$ and $V=200kN.$