A cantilever beam $($length $L=3m)$ with a uniform self$-$weight distribution $w_o,$ is used to support a series of equal loads $P=49kN,$ spaced a distance $b$

$=1\mathrm{.}1m,$ 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.

The beam is made from standard ASTM A$6$ steel $(E=200$GPa,$=7820k\frac{g}{m}3)$ with designation W$200$x$200$x$52.$ The distributed load can be taken as $510$ Nm$.$ The I of the beam is $5\mathrm{.}268*10^-6$ m$^4.$Calculate force,

Fe and a bending moment Me $,$ such that slope and deflection at free end are both zero.

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