Frames - The Behaviour and Design of Steel Structures to EC3 - page 352

then be used with the design rules of EC3 to determine if the members and joints
are adequate.
Such an analysis must allow for any significant second-order moments arising
from the finite deflections of the frame. Two methods may be used to allow for
these second-order moments. In the first of these, the moments determined by a
first-order elastic analysis areamplifiedbyusingtheresultsofan elastic buckling
analysis . In the second and more accurate method, a full second-order elastic
analysis is made of the frame.
Alesscommonreasonforanalysingarigid-jointedframeistodeterminewhether
theframecanreachanequilibriumpositionunderthefactoredloads,inwhichcase
the frame is adequate.A first-order plastic analysis may be used for a frame with
negligible second-order effects. When there are significant second-order effects,
thenan advanced analysis maybemadeinwhichaccountistakenofsecond-order
effects, inelastic behaviour, and residual stresses and geometrical imperfections,
although this is rarely done in practice.
Thesevariousmethodsofanalysisarediscussedinmoredetailinthefollowing
sub-sections.
8.3.5.2 First-order elastic analysis
A first-order (linear) elastic analysis of a rigid-jointed frame is based on the
assumptions that:
(a) the material behaves linearly, so that all yielding effects are ignored,
(b) themembersbehavelinearly,withnomemberinstabilityeffectssuchasthose
causedbyaxialcompressionswhichreducethemembers'flexuralstiffnesses
(these are often called the P- δ effects), and
(c) the frame behaves linearly, with no frame instability effects such as those
caused by the moments of the vertical forces and the horizontal frame
deflections (these are often called the P- effects).
Forexample,fortheportalframeofFigure8.2,afirst-orderelasticanalysisignores
allsecond-ordermomentssuchas R R (δ + z / h ) intheright-handcolumn,sothat
thebendingmomentdistributionislinearinthiscase.First-orderanalysespredict
linear behaviour in elastic frames, as shown in Figure 1.15.
Rigid-jointed frames are invariably statically indeterminate, and while there
are many manual methods of first-order elastic analysis available [11-13], these
are labour-intensive and error-prone for all but the simplest frames. In the past,
designerswereoftenforcedtorelyonapproximatemethodsoravailablesolutions
for specific frames [14, 15]. However, computer methods of first-order elastic
analysis [16, 17] have formed the basis of computer programs such as [18-20]
whicharenowusedextensively.Thesefirst-orderelasticanalysisprogramsrequire
the geometry of the frame and its members to have been established (usually by