Column in buckling

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. ​

GIVEN:

1. Flange length (b): 200mm

2. Flange thickness (t_f): 10mm

3. Web length (d): 180mm (210mm-10mm-10mm)

4. Web thickness (t_w): 7mm

5. Length of column (L): 10m

6. Young’s Modulus for steel structures (E): 210GPa

SOLUTION:

Moment of inertia: I₂ = 2× (b³×t_f/12) + (t_w³×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.