A central beam $\backslash ($ B D $\backslash )$ is joined at hinges to two cantilever beams $\backslash ($ A B $\backslash )$ and $\backslash ($ D E $\backslash ).$ All beams have the cross section shown. For the loading shown, determine the largest $\backslash ($ w $\backslash )$ so that the deflection at $\backslash ($ C $\backslash )$ does not exceed $4\mathrm{.}5$ mm $.$ Use $\backslash ($ E$=200\backslash )$ GPa. $($Round the final answer to one decimal place.$)$