Lateral buckling of beams - The Behaviour and Design of Steel Structures to EC3 - page 229

1.4

Elastic buckling

Strain-hardening

1.2 Full plasticity M = M p

1.0

Beams without
residual stresses

0.8

Welded beams with
residual stresses

0.6

0.4

M

M Hot-rolled beams with

residual stresses
(see Fig. 3.9)

0.2

L

0

0 50 100 150 200 250 300

Slenderness ratio L/i z

Figure 6.2 Lateral buckling strengths of simply supported I-beams.

v

M cr

M cr

y

f

L z

(a) Elevation

(c) Section

Pins prevent end twist rotation ( f =0)
and allow end warping ( f = 0)

(b) Part plan

x

d v
d x

v

(d) Plan on longitudinal axis

Figure 6.3 Buckling of a simply supported beam.

where δ istheundeterminedmagnitudeofthecentraldeflection,andthattheelastic
buckling moment is given by

M cr = M zx , (6.2)