$($b$)$ For the beam shown in Fig. Q$\mathrm{.}2$b below, using the moment area method, determine the deflection of the beam at $E.$ The moment of inertia, I, of the section is $550{10}^{6}m{m}^4$ and the modulus of elasticity, E $,$ of the material is $200{10}^3$MPa.

$(50\%)$

Fig. Q$.2$ b $($not to scale$)$