Select the lightest H section $(600$ mm deep series$)$ for the situations shown in the accompanying figure. The concentrated loads P$1,$ P$2$ and P$3$ are functions P$3=1\mathrm{.}8$W$.$ Assume lateral support is provided only at the two supports and at the concentrated loads. Using both LRFD & ASD $($version after $2005)$ methods and SN$490$B steel, Fy$=3\mathrm{.}3$tf$/$cm$^2.$ Always consider the presence of the live load in the entire beam. $,$L$1=4$m$,$L$2=10$m$,$L$3=3$m$,$x$=5$m