A $6\mathrm{.}0$ m W$12$x$50$ is used as a compression nember. Assume the member is hinged at the top and fixed at the bottom for buckling in either principal direction. Use A$992$ steel $($Fy $=345$MPa $).$ Determine the critical slenderness ratio.

Properties of w$12$x$5$e:

$A=9420m^2$

$d=310m{m}^2$

$bf=205mm$

$tf=16\mathrm{.}3mm$

$tw=9\mathrm{.}49mm$

$cx=132mm$

$ry=49\mathrm{.}8mm$