Problem $4$: Use the slope$-$deflection method to analyze the structure.

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E$=$I U $\backslash$text $\{$ Ura $\}$ I$=\backslash$delta U U$\backslash$left$($I U$^\{\backslash$circ$\}\backslash$right$)\backslash$mathrm$\{$mm$\}^\{\backslash$circ$\}$

$\backslash ]$

$4\mathrm{.}1)$ Determine the magnitude and direction of the support reactions.

$4\mathrm{.}2)$ Draw the shear and bending moment diagrams for the beam. Identify points where the shear crosses zero $($don$\text{'}$t do this for the moment$).$ Identify local maximums and minimums in the moment diagram.

$4\mathrm{.}3)$ Over time, the soil supporting the structure experiences some differential settlement. This causes the support at $\backslash ($ C $\backslash )$ to experience a settlement of $25$ mm $.$ Recalculate the magnitude and direction of the support reactions taking this into account.

$4\mathrm{.}4)$ If the supports at $\backslash ($ A $\backslash )$ and $\backslash ($ E $\backslash )$ was designed with a maximum moment capacity of $\backslash (120\backslash$mathrm$\{$kN$\}-\backslash$mathrm$\{$m$\}\backslash ),$ will the support settlement create issues with the design of the fixed supports? If so$,$ will the structure become unstable and collapse? Provide a brief discussion.