Lateral buckling of beams - The Behaviour and Design of Steel Structures to EC3 - page 228

Figure 6.1 Lateral buckling of a cantilever.

6.2 Elastic beams

6.2.1 Buckling of straight beams

6.2.1.1 Simply supported beams with equal end moments

A perfectly straight elastic I-beam which is loaded by equal and opposite end
moments is shown in Figure 6.3. The beam is simply supported at its ends so
that lateral deflection and twist rotation are prevented, while the flange ends are
free to rotate in horizontal planes so that the beam ends are free to warp (see
Section 10.8.3). The beam will buckle at a moment M cr when a deflected and
twisted equilibrium position, such as that shown in Figure 6.3, is possible. It is
shown in Section 6.12.1.1 that this position is given by

π 2 EI z / L 2 φ = δ sin π x

M cr

v =

L ,

(6.1)