Compression members - The Behaviour and Design of Steel Structures to EC3 - page 75

1.2

1

Elastic buckling
N cr / N y

0.8

0.6

0.4

Design buckling
resistance N b,Rd / N y

0.2

0

0 0.5 1 1.5 2 2.5

Generalised slenderness = N / y N cr

Figure 3.23 Compression resistance of structures designed by buckling analysis.

method for simply supported compression members. For this extrapolation, it
is assumed that the resistance N b , Rd of a compression member in a frame is
related to its squash load N y and to the axial force N cr carried by it when
the frame buckles elastically, and that this relationship (Figure 3.23) is the
same as that used for simply supported compression members of the same type
(Figure 3.13).
Thismethodofdesignbybucklinganalysisisvirtuallythesameastheeffective
length method which uses the design charts of Figure 3.21, because these charts
wereobtainedfromtheelasticbucklinganalysesofrestrainedmembers.Theonly
difference is that the elastic buckling load N cr may be calculated directly for the
methodofdesignbybucklinganalysis,aswellasbydeterminingtheapproximate
effective length from the design charts.
Theelasticbucklingloadofthemembermayoftenbedeterminedapproximately
bytheeffectivelengthmethoddiscussedinSection3.6. Incaseswherethisisnot
satisfactory,amoreaccuratemethodmustbeused.Manysuchmethodshavebeen
developed, and some of these are discussed in Sections 8.3.5.3 and 8.3.5.4 and in
[4-13],whileothermethodsarereferredtointheliterature[14-16].Thebuckling
loadsofmanyframeshavealreadybeendetermined, andextensivetabulationsof
approximations for some of these are available [14, 16-20].
While the method of design by buckling analysis might also be applied to
rigid frames whose loads act between joints, the bending actions present in those
frames make this less rational. Because of this, consideration of the effects of
buckling on the design of frames with bending actions will be deferred until
Chapter 8.