Consider a universal column 200mm x 200mm with a flange thickness of 10mm and web thickness of 7mm. The height of the column, which is fixed in concrete at its base, is 10m and the load is applied on top (free joint). Calculate the load necessary to induce the column to buckle.
Moment of inertia: I2 = 2× (b3×tf/12) + (tw3×d/12) = 2× (2003×10/12) + (73×180/12) = 13338478mm4
Buckling load: P = Kπ2ΕΙ2/ L2 = 0.25 × π2 × 210×106 ×13338478×10-12/ 102 = 69.11kN
The calculated buckling load is 69.11kN
Note that: K=0.25 for one end fixed and other end free, K=1 for pinned ends, K=2 for one end fixed and other end pinned and K=4 for fixed ends.