Example$\mathrm{.}2.$ A horizontal beam of length $4\mathrm{.}0$ m and uniform cross$-$section, is simply supported at each end. The beam is subject to a point load of $45$ kN which acts $1\mathrm{.}0$ m from the left hand support and a uniformly disturbed load of $65k\frac{N}{m}$ over half its length.

Calculate the deflection at the middle of span.

$E=200,I=17**10-6$