QUESTION $4(20$ Marks$)$

Figure $4$ shows beam A$-$B$-$C with constant cross$-$section properties throughout and loaded as shown. Using the method of Direct Integration $($also known as double integration$)$ and given that the maximum deflection occurs at point B:

$($i$)$ Formulate the slope and deflection equations.

$[15]$

$($ii$)$ Compute the slope at A and deflection at B$.$ Take $E=200$GPa,$I=5\mathrm{.}53{10}^{-4}{m}^4$

$[5]$

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