Lateral buckling of beams - The Behaviour and Design of Steel Structures to EC3 - page 241

1.5

Full plasticity M p

159 hot-rolled beams

Elastic buckling M cr

M

M

1.0

Q

Q Q

EC3 welded
I-sections ( h / b f >2)

0.5

L
4

L
4

L

EC3 rolled
I-sections ( h / b f >2)

0

0 0.5 1.0 1.5 2.0 2.5

Generalised slenderness

( M / M )

=

p cr

LT

Figure 6.12 Moment resistances of beams in near-uniform bending.

andthisisusedinamodificationofthefirstyieldequation6.18whichapproximates
theexperimentalresistancesofmanybeamsinnear-uniformbending,suchasthose
shown in Figure 6.12.

6.5.2 Elastic buckling moment

The EC3 method for designing against lateral buckling is an example of a more
general approach to the analysis and the design of structures whose strengths are
governed by the interaction between yielding and buckling. Another example of
thisapproachwasdevelopedinSection3.7,inwhichtherelationshipbetweenthe
ultimatestrengthofasimplysupporteduniformmemberinuniformcompression
and its squash and elastic buckling loads was used to determine the in-plane ulti-
mate strengths of other compression members. This method has been called the
method of design by buckling analysis, because the maximum moment at elastic
buckling M cr must be used, rather than the approximations of somewhat variable
accuracy which have been used in the past.
The first step in the method of design by buckling analysis is to determine the
load at which the elastic lateral buckling takes place, so that the elastic buckling
moment M cr can be calculated. This varies with the beam geometry, its loading,
anditsrestraints,butunfortunatelythereisnosimplegeneralmethodoffindingit.
However, thereareanumberofgeneralcomputerprogramswhichcanbeused
for finding M cr [6, 8, 10, 21-23], including the user-friendly computer program
PRFELB [18] which can calculate the elastic buckling moment for any beam or
cantilever under any loading or restraint conditions. While such programs have