Flexural buckling of an IPE 330 column

How much axial force can an IPE 330 column carry if it buckles about its weak axis? A short worked example with the numbers shown.

The section

Figure 1: IPE 330 with its dimensions. The y-axis is the strong axis.

The area is \(A = 62.6\) cm² and the radii of gyration are \(i_y = 137\) mm and \(i_z = 35.5\) mm. The steel is S235 (\(f_y = 235\) N/mm²) and \(\gamma_{M1} = 1.0\).

Relative slenderness

With the squash load \(N_{pl} = A f_y = 1471.1\) kN and \(\lambda_1 = 93.91\):

\[ \bar{\lambda}_y = \frac{6000/137}{93.91} = 0.466 \qquad \bar{\lambda}_z = \frac{3000/35.5}{93.91} = 0.900 \]

Reduction factor and resistance

Figure 2: Buckling curves a and b. The two points are the result of this example.

Axis	Curve	\(\bar{\lambda}\)	\(\chi\)	\(N_{b,Rd}\) [kN]
y (6 m)	a	0.466	0.934	1374.6
z (3 m)	b	0.900	0.661	972.8

Result

The weak axis governs. The column can carry \(N_{b,Rd} = 972.8\) kN, which is 66 % of the squash load.

Take-away

A short buckling length about the weak axis matters more than the strong-axis length: here half the length about z still gives the lower resistance.

The full derivation is in the chapter Flexural buckling.