Civil Engineering Reference
In-Depth Information
Cubic equation (3.22) can be used for taking into account the coupling of the basic
modes. It is interesting to note that cubic equation (3.22) can be considered as a
generalization of equation (5.5) in Eurocode 3, Part 1.3 [1992] for the flexural-torsional
buckling analysis of thin-walled columns subjected to concentrated end forces. The
generalization is twofold. First, while the corresponding equation in Eurocode 3 is only
valid for monosymmetrical cross-sections, cubic equation (3.22) can be used for cross-
sections of any shape with no restriction at all, as far as symmetry is concerned.
Second, apart from the concentrated load case, cubic equation (3.22) is also applicable
to columns subjected to uniformly distributed axial load.
(b)
Stability of storey-height columns in multistorey buildings
The storey-height columns of a multistorey building can lose stability in two
ways: they can develop sway buckling (when the joints develop relative
translation) or non-sway buckling. Of the critical loads of the two types, the
smaller one is of practical importance. Clearly, the column must have the
necessary stiffness against non-sway buckling. As for sway buckling,
engineering common sense suggests that if the bracing system is adequate, i.e.
if it has the necessary stiffness against the full-height buckling of the building
(cf.
Chapter 7
), then it is also ensured that the columns do not develop sway
buckling or, to be more precise, the sway buckling critical load is always greater
than that of the non-sway buckling. Detailed discussion of this phenomenon is
available elsewhere [Kollár and Zalka, 1999] and only the findings are summarized
here.
The aszsumption that the storey-height columns of a building with adequate
bracing system develop non-sway buckling is
•
conservative when the columns have the same type of joints at both ends, i.e.
fixed joints at both ends, or pinned joints at both ends and
•
unconservative when the columns have a fixed lower end and a pinned upper end.
The unconservative error can be eliminated by assuming that in the mixed case (fixed
lower end and pinned upper end) the columns are pinned at both ends.
