A cantilever beam $($length $L=3m)$ with a uniform self$-$weight distribution $w_0,$ is used to support a series of equal loads $P=27kN,$ spaced a distance $b=0\mathrm{.}7m,$ apart along its length. Additionally, a force, $F_e$ and a bending moment $M_e,$ are applied at the free end of the beam, as shown in the figure. Calculate Fe and a bending moment Me $,$ such that slope and deflection at free end are both zero.

Assume $a=0\mathrm{.}1m.$