Technical
28 NSC
Jun 20
27 that this annex is limited to columns in rectilinear multi-storey
frames. The annex describes columns in multi-storey beam-andcolumn
framed buildings with …. concrete or composite floor
and roof slabs. Hardly the description of a portal frame!
Eurocode rules
One would not expect the fundamental physics to change simply
because the Eurocode was introduced. On that basis alone, one
should be confident that the same rules apply to orthodox portal
frames – that in-plane, the stability of the entire frame as one unit
is critical, followed by checks of the cross section and only out-ofplane
buckling checks.
The key clause is 5.2.2(7)a in BS EN 1993-1-1:
If second order effects in individual members and relevant
member imperfections are totally accounted for in the global
analysis of the structure, no individual stability check for the
members according to 6.3 is necessary.
In-plane second order effects are allowed for by determining
αcr (directly equivalent to λcr in BS 5950), and using an amplifier in
the global analysis if necessary. Frame imperfections are allowed
for by always including the equivalent horizontal forces (EHF) in
every combination. The only in-plane effects that are not
included in the global analysis are the individual member
imperfections, such as an initial lack of straightness. To consider
the impact of in-plane member imperfections, colleagues at the
SCI spent (very) many hours analysing a wide range of frames
with and without in-plane member imperfections. Imperfections
were modelled in both directions, in each member, to produce
the most onerous effect. The study concluded that the value of αcr
changed less than 0.3%. Two conclusions can be made. Firstly
that the effect of in-plane member imperfections on the stability
of the frame is small enough to be ignored – or presented
another way, we can say that all relevant in-plane effects have
been allowed for in the global analysis. We therefore do not need
an in-plane stability check of individual members. The second
conclusion is that as expected, BS 5950 was correct – “The inplane
stability of the members in a continuous frame …. should be
established by checking the in-plane stability of the frame itself”
The global analysis has not verified the out-of-plane
resistance – members still must be verified between restraints,
using section 6.3 of the Eurocode, aided perhaps by the guidance
in Annex BB, which is simply the guidance from BS 5950
‘translated’ into Eurocode nomenclature.
Member verification in section 6.3 of BS EN 1993-1-1
If (and only if ) the interaction factors in expressions 6.61 and 6.62
are taken from Annex B of the Eurocode (very strongly
recommended by SCI), it can be concluded that expression 6.61
deals with in-plane effects and expression 6.62 deals with out-ofplane
effects. Since we have concluded that no in-plane member
checks are needed (other than the possible internal columns
mentioned earlier), we can dispense with expression 6.61
altogether.
As there is no minor axis moment in a portal frame,
expression 6.62 reduces to a rather simpler form:
NEd
Nb,z,Rd
+ kzy
My,Ed
Mb,Rd
The numerators are the design force and major axis moment.
The denominators are the minor axis flexural resistance and the
lateral torsional buckling resistance, which with some judicious
interpolation can generally be obtained from look-up tables if
required. In all cases, the lateral torsional buckling resistance
depends on the shape of the bending moment diagram over the
length being considered, reflected in the value of the factor C1.
Resources are readily available to determine the C1 factor for
different shapes of bending moment diagram. The interaction
factor kzy is painful to compute, but in portal frames is generally
around 0.97 – there is not much loss in manual calculations if kzy
is assumed to be 1.0.
Conclusions
Portal frames are special in many ways, despite their frequent use
in the UK. They are slender, have significant axial forces in the
members, generally are sensitive to second-order effects,
experience reversing bending moments and demand very careful
restraints to otherwise unrestrained flanges. The objective of this
article was to confirm one special design feature – that in-plane
buckling is an concern for the frame as a whole, not for individual
members.
1 King, C, M.
In-plane stability of portal frames to BS 5950-1-2000 (P292)
SCI, 2001
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