Problem $1.$ Consider the cross$-$section shown in Figure $1,$ which corresponds to the profile of a beam$-$type element that is subjected to a bending moment of $\backslash ($ M$\_\{2\}=1\mathrm{.}13\backslash$mathrm$\{$kN$\}.\backslash$mathrm$\{$m$\}\backslash ).$ Based on the dimensions illustrated in the figure, answer the following questions:

$($a$)$ Determine the second moment of area of the profile $\backslash ((\backslash$mathrm$\{$Iz$\})\backslash ),$ the location of the neutral axis, and the distances of the top and bottom surfaces of the profile relative to the neutral axis.

$($b$)$ Calculate the stresses generated by bending at the points where the profile cross$-$section changes, namely, points A$,$ B$,$ C and D$.$