Given the following beam with the following cross$-$section and with the moment $(M)$ shear $(S)$ and axial $($N$)$

diagram.

Figure $2$: 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 the area is $A=70\mathrm{.}5m{m}^2$ and the moment of inertia at the centroid are $I_{}=4473m{m}^4,$

$I_{yy}=2899m{m}^4,I_{xy}=2810m{m}^4$ :

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

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

those points.

Compute the direct stress $({}_{})$ at points A$,$ B$,$ C and D when $z=500mm.$

What can you tell us if you compare the stress at points A and $B?$ Would it change if there was a moment

$M_y$ applied?

If the allowable stress is $300$MPa, what should be the value of $P?$