Problem $3(40$ pts$)-$ The beam below has the cross section given in Problem $2.$ Please answer the following questions:

$1.$ Draw the V$\backslash$&M diagrams.

$2.$ Calculate the normal stress, $\backslash (\backslash$sigma $\backslash ),$ at $\backslash ($ x$=5\mathrm{.}5\backslash$mathrm$\{$~m$\}\backslash )$ and draw its distribution. Is this where the normal stresses are max or min for the beam? Justify your answer with math.

$3.$ Calculate the shear stress, $\backslash (\backslash$tau $\backslash ),$ at $\backslash ($ x$=1\backslash$mathrm$\{$~m$\}\backslash )$ at locations $(1),(2),(3),$ and $(4)$ defined in Problem $2($location $(2)$ is at the neutral axis$)$ and draw its distribution.