Frames - The Behaviour and Design of Steel Structures to EC3 - page 365

Ideally, the member stress resultants should be determined by a method of
frameanalysiswhichaccountsforbothsecond-ordereffects(P- δ andP- ),inelas-
tic behaviour, residual stresses, and geometrical imperfections, and any local or
out-of-plane buckling effects. Such a method has been described as an advanced
analysis.Notonlycananadvancedanalysisbeexpectedtoleadtopredictionsthat
are of high accuracy, it has the further advantage that the design process can be
greatly simplified, since the structure can be considered to be satisfactory if the
advanced analysis can show that it can reach an equilibrium position under the
design loads.
Past research on advanced analysis and the prediction of the strengths of real
structures has concentrated on frames for which local and lateral buckling are
prevented (by using Class 1 sections and full lateral bracing). One of the earliest,
andperhapsthesimplest,methodsofapproximatingthestrengthsofrigid-jointed
frames was suggested in [32] where it was proposed that the ultimate load factor
α ult ofaframeshouldbecalculatedfromtheloadfactor α p atwhichplasticcollapse
occurs (all stability effects being ignored) and the load factor α cr at which elastic
in-plane buckling takes place (all plasticity effects being ignored) by using

α ult = 1

1

α p + 1

(8.26)

α cr

or

α ult /α p = 1 − α ult /α cr (8.27)

However,itcanbesaidthatthismethodrepresentsaconsiderablesimplification
of a complex relationship between the ultimate strength and the plastic collapse
and elastic buckling strengths of a frame.
Moreaccuratepredictionsofthestrengthsoftwo-dimensionalrigidframescan
be made using a sub-assemblage method of analysis. In this method, the braced
or unbraced frame is considered as a number of subassemblies [33-35] such as
those shown in Figure 8.10.The conditions at the ends of the sub-assemblage are
approximated according to the structural experience and intuition of the designer
(itisbelievedthattheseapproximationsarenotcritical),andthesub-assemblageis
analysedbyaddingtogethertheload-deformationcharacteristics([36]andcurve5
inFigure7.2)oftheindividualmembers.Althoughtheapplicationofthismanual
technique to the analysis of braced frames was developed to an advanced stage
[37, 38], it does not appear to have achieved widespread popularity.
Furtherimprovementsinthepredictionofframestrengthareprovidedbycom-
puter methods of second-order plastic analysis, such as the deteriorated stiffness
methodofanalysis,inwhichprogressivemodificationsaremadetoasecond-order
elasticanalysistoaccountfortheformationofplastichinges[16,39,40].Theuse
of such an analysis is limited to structures with appropriate material properties,
andforwhichlocalandout-of-planebucklingeffectsareprevented.However,the
use of such an analysis has in the past been largely limited to research studies.