$(2)$ A simply supported steel beam, span length $l=6m,$ span middle without lateral support. The upper flange is subject to full$-$span uniform load: permanent load standard value $q_{Gk}=80k\frac{N}{m}($including beam dead weight$),$ variable value $q_{Qk}=180k\frac{N}{m},$ they are all static loads. The steel is Q$345$ steel, $f_y=345\frac{N}{m}{m}^2.$ The selected section and size are shown in the following figure. Please check the bending strength and global stability of the beam. $($Full score is $20)$