Lateral buckling of beams - The Behaviour and Design of Steel Structures to EC3 - page 243

The EC3 uniform bending design buckling resistances M b , Rd for β = 0.75,
λ LT ,0 = 0.4, and α LT = 0.49 (rolled I-sections with h / b > 2) are compared with
experimental results for beams in near-uniform bending in Figure 6.12. For very
slenderbeamswithhighvaluesofthemodifiedslenderness λ LT ,thedesignbuck-
lingmomentresistance M b , Rd showninFigure6.12approachestheelasticbuckling
moment M cr , while for stocky beams the moment resistance M b , Rd reaches the
section resistance W y f y , and so is governed by yielding or local buckling, as
discussedinSection4.7.2.Forbeamsofintermediateslenderness,equations6.25-
6.27 provide a transition between these limits, which is close to the lower bound
of the experimental results shown in Figure 6.12. Also shown in Figure 6.12 are
the EC3 design buckling moment resistances for α LT = 0.76 (welded I-sections
with h / b > 2).
The EC3 provides two methods of design, a simple but conservative method
whichmaybeappliedtoanytypeofbeamsection,andalessconservativelimited
method.
For the simple general method, β = 1.0, λ LT ,0 = 0.2, and the imperfection
factor α LT dependsonthetypeofbeamsection,assetoutinTables6.4and6.3of
EC3. This method is conservative because it uses a very low threshold modified
slendernessof λ LT ,0 = 0.2,abovewhichthebucklingresistanceisreducedbelow
thesectionresistance W y f y ,andbecauseitignorestheincreasedinelasticbuckling
resistances of beams in non-uniform bending shown for example in Figure 6.10.
ForthelessconservativelimitedmethodforuniformbeamsofrolledI-section,
β = 0.75 and λ LT ,0 = 0.4, and a modified design buckling moment resistance

M b , Rd , mod = M b , Rd / f ≤ M b , Rd (6.28)

is determined using

f = 1 − 0.5 ( 1 − k c ) { 1 − 2 (λ LT − 0.8 ) 2 }

(6.29)

in which the values of the correction factor k c depend on the bending moment
distribution, and are given by
k c = 1 / √ C 1 = 1 / √ α m (6.30)

in which α m is the moment modification factor obtained from Figure 6.7 or
equation6.5,6.6,or6.13.TheEC3designbucklingmomentresistances M b , Rd , mod
for β = 0.75, λ LT ,0 = 0.4, and α LT = 0.49 (rolled I-sections with h / b > 2) are
comparedwiththeinelasticbucklingmomentapproximationsofequation6.23in
Figure 6.14.

6.5.4 Lateral buckling design procedures

FortheEC3strengthdesignofabeamagainstlateralbuckling,thedistributionof
the bending moment and the value of the maximum moment M Ed are determined