Lateral buckling of beams - The Behaviour and Design of Steel Structures to EC3 - page 240

Moment

Elastic buckling

M cr

Inelastic
buckling

Elastic bending
and twisting

M L

Curve A - equivalent initial
crookedness and twist

M I

M ult

Elastic limit Curve B - equivalent

residual stresses

Curve C - real beams

Lateral deflection and twist

Figure 6.11 Behaviour of real beams.

properties cause the beam to behave as shown by curve B in Figure 6.11. The
behaviourofrealbeamshavingbothtypesofimperfectionisindicatedbycurveC
inFigure6.11,whichshowsatransitionfromtheelasticbehaviourofabeamwith
curvatureandtwisttotheinelasticpost-bucklingbehaviourofabeamwithresidual
stresses.

6.5 Design against lateral buckling

6.5.1 General

It is possible to develop a refined analysis of the behaviour of real beams which
includes the effects of all types of imperfection. However, the use of such an
analysis is not warranted because the magnitudes of the imperfections are uncer-
tain. Instead, design rules are often based on a simple analysis for one type of
equivalent imperfection which allows approximately for all imperfections, or on
approximations of experimental results such as those shown in Figure 6.12.
FortheEC3methodofdesigningagainstlateralbuckling,themaximummoment
in the beam at elastic lateral buckling M cr and the beam section resistance W y f y
are used to define a generalised slenderness

λ LT = ( W y f y / M cr ) (6.25)