Problem $1$

The answer should be $480$ but idk how to get the solution. Given the following beam with the following cross$-$section and with the moment $($M$)$ shear $($S$)$ and axial $($N$)$ diagram.

Figure $1$: Schematics for problem $4.$

The expressions for the Moment $($M$),$ Shear $($S$),$ and Axial $($N$)$ are as follows $($units in $P$ and $Pmm)$:

$N(z)=-2$

$S(z)=\{\begin{array}{ccc}-1& if& z500\end{array}$

$0ifz500$

$M(z)=\{\begin{array}{ccc}-500-z& if& z500\end{array}$

$-1000ifz500$

If the centroid of the given cross$-$section is at $y=23\mathrm{.}5mm,$ the area is $A=162m{m}^2$ and the moment of inertia at the centroid is $I_{}=38290m{m}^4$ :

Calculate expressions that represent how the direct stress $({}_{zz})$ varies with $z$ at points $A,B,C,D,E,F$ and G$.$

Plot the expressions you found in the previous problem to see how the direct stress $({}_{zz})$ varies with $z$ at those points.