A cantilever beam $($length L$=4$m$)$ with a uniform self$-$weight distribution ${}_0,$ is used to support a series of equal loads $P=26$ kN$,$ spaced a distance $b=1\mathrm{.}1$ m$,$ apart along its length. Additionally, a force, $)$and a bending moment $M_e,$ are applied at the free end of the beam, as shown in the figure.

$($a$)$ Given that the beam is made from standard ASTM A$6$ steel $($E$=200$GPa, $\backslash$rho $=7820$ kg$/m^3$with designation W$200$x$200$x$52($matric$)$ accesed here, calculate the self$-$weight distribution ${}_{0,}($per unit length$).$

$($b$)$ If the loads, P are placed a distance a $=2\mathrm{.}32$m$,$ and both loads at the free$-$end $(F_e$ and $M_e)$ are removed, calculate the deflection at the free$-$end. Give the answer as negative to indicate deflection down, or positive to indicate deflection up$.$

$($c$)$ For the load condition in question $($b$),$ determine the reaction force if $F_e=2$P$+{}_{0*}L,$ and $M_e=0.$d$)$ In question $($c$),$ the position of the load, P has no influence on the reaction force. $(trueor$ false$)$