$2\mathrm{.}8$ Two $180-$ mm $*70-$ mm channels are welded together to form a hollow square section. This section is used as a column $3$ m long, having the lower end built$-$ in and the upper end completely free. Calculate $($a$)$ the effective slenderness ratio; $($b$)$ the buckling load using the Rankine formula. Rankine's constant for pinned ends is $17500$ and the yield stress is $300$ MPa.

$[109,8$; $643,66$ kN$]$

$12\mathrm{.}9$