Beam-columns - The Behaviour and Design of Steel Structures to EC3 - page 319

Formemberswiththeintermediatelateralrestraintsagainstminoraxisbuckling,
failurebymajoraxisbucklingwithlateraltorsionalbucklingbetweentherestraints
becomes a possibility.This leads to requirement
N Ed

N b , y , Rd + k yy M y , Ed M b , Rd ≤ 1

(7.61)

which incorporates the major axis flexural buckling resistance N b , y , Rd and the
lateraltorsionalbucklingresistance M b , Rd . Formemberswithnolateralrestraints
along the span, equation 7.60 will always govern over equation 7.61.
The design of members subjected to bending and tension is discussed in
Section 2.4.
Aworkedexampleofcheckingtheout-of-planeresistanceofabeam-columnis
given in Section 7.7.4.

7.4 Biaxial bending of isolated beam-columns

7.4.1 Behaviour

The geometry and loading of most framed structures are three-dimensional, and
the typical member of such a structure is compressed, bent about both principal
axes and twisted by the other members connected to it, as shown in Figure 7.1c.
The structure is usually arranged so as to produce significant bending about the
major axis of the member, but the minor axis deflections and twists are often
significant as well, because the minor axis bending and torsional stiffnesses are
small. In addition, these deformations are amplified by the components of the
axial load and the major axis moment which are induced by the deformations of
the member.
The elastic biaxial bending of isolated beam-columns with equal and opposite
end moments acting about each principal axis has been analysed [16-22], but
the solutions obtained cannot be simplified without approximation. These anal-
yses have shown that the elastic biaxial bending of a beam-column is similar to
its in-plane behaviour (see curve 3 of Figure 7.2), in that the major and minor
axis deflections and the twist all begin at the commencement of loading, and
increase rapidly as the elastic buckling load (which is the load which causes elas-
ticflexural-torsionalbucklingwhentherearenominoraxismomentsandtorques
acting) is approached. First yield predictions based on these analyses have given
conservative estimates of the member resistances. The elastic biaxial bending of
beam-columns with unequal end moments has also been investigated. In one of
these investigations [16], approximate solutions were obtained by changing both
sets of unequal end moments into equivalent equal end moments by multiply-

ing them by the conversion factor 1 / √ F (see Figure 7.15) for flexural-torsional
buckling.
Althoughthefirstyieldpredictionsfortheresistancesofslenderbeam-columns
are of reasonable accuracy, they are rather conservative for stocky members in