Civil Engineering Reference
In-Depth Information
Lateral restraint
Q
1
L
2
Q
2
Rigid joint
Q
1
L
1
Column built-in at base
Figure 8.11
Flexural-torsional buckling of a portal frame.
load
Q
2
, then the beam remains straight and does not induce moments in the
columns, which buckle elastically out of the plane of the frame at a load given
by
Q
1
≈
π
2
EI
z
/(
0.7
L
1
)
2
(see Figure 3.15c). On the other hand, if the effects
of the compressive forces in the columns are small enough to be neglected, then
the elastic stiffnesses and restraining effects of the columns on the beam can be
estimated, and the elastic flexural-torsional buckling load
Q
2
of the beam can be
evaluated.The solution of a related problem is discussed in Section 6.9.
In general, however, both the columns and the beams of a rigid frame buckle,
and there is an interaction between them during out-of-plane buckling. This
interaction is related to that which occurs during the in-plane buckling of rigid
frames (see Sections 8.3.5.3 and 8.3.5.4 and Figures 8.6 and 8.7), and also to
that which occurs during the elastic flexural-torsional buckling of continuous
beams(seeSection6.8.2andFigure6.21).Becauseofthesimilaritiesbetweenthe
elastic flexural-torsional buckling of restrained beam-columns (Section 7.3.1.3)
and restrained columns (Section 3.6.4), it may prove possible to extend further
the approximate method given in Section 8.3.5.3 for estimating the in-plane
elastic buckling loads of rigid frames (which was applied to the elastic
flexural-torsional buckling of some beams in Section 6.8.2). Thus, the elas-
tic flexural-torsional buckling loads of some rigid frames might be calculated
approximately by using the column effective length chart of Figure 3.21a.
However, this development has not yet been investigated.
Ontheotherhand,therehavebeendevelopments[45-47]intheanalyticaltech-
niques used to determine the elastic flexural-torsional buckling loads of general
rigidplaneframeswithgeneralin-planeloadingsystems,andacomputerprogram
[48] has been prepared which requires only simple data specifying the geometry
oftheframe,itssupportsandrestraints,andthearrangementoftheloads.Theuse
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