Beam-columns - The Behaviour and Design of Steel Structures to EC3 - page 311

for minor axis buckling, in which k yy and k zz are interaction factors whose values
may be obtained from Annex A or Annex B of EC3 and M c , y , Rd and M c , z , Rd are
thein-planebendingresistancesaboutthemajorandminoraxesrespectively.The
former is based on enhancing the elastically determined resistance to allow for
partialplastificationofthecross-section(i.e.followingSection7.2.3.3),whilstthe
latter reduced the plastically determined resistance to allow for instability effects
(i.e. following Section 7.2.3.2). Lengthy formulae to calculate the interaction
factors are provided in both cases.

7.3 Flexural-torsional buckling of isolated
beam-columns
When an unrestrained beam-column is bent about its major axis, it may buckle
by deflecting laterally and twisting at a load which is significantly less than the
maximumloadpredictedbyanin-planeanalysis.Thisflexural-torsionalbuckling
mayoccurwhilethememberisstillelastic,oraftersomeyieldingduetoin-plane
bending and compression has occurred, as indicated in Figure 7.13.

7.3.1 Elastic beam-columns

7.3.1.1 Beam-columns with equal end moments

Consider a perfectly straight elastic beam-column bent about its major axis (see
Figure7.1b)byequalandoppositeendmoments M (sothat β m =− 1),andloaded
by an axial force N . The ends of the beam-column are assumed to be simply

Load Load

1 Elastic buckling

1 Elastic buckling

3

Elastic-plastic
bending

3

Inelastic buckling

2

2 Inelastic buckling

First yield

Out-of-plane deformation In-plane deflection

(a) Out-of-plane behaviour (b) In-plane behaviour

Figure 7.13 Flexural-torsional buckling of beam-columns.