Civil Engineering Reference
In-Depth Information
The evaluation of the formulae of the basic critical loads (3.11) and (3.16) shows that
the most important characteristics that influence the values of the basic critical loads
are:
•
the height of the building,
•
the bending stiffnesses of the bracing system,
•
the warping stiffness of the bracing system,
•
the radius of gyration.
The sway critical loads are in direct proportion to the bending stiffnesses of the
bracing system and in inverse proportion to the square of the height of the building.
In a similar manner, the pure torsional critical load is in direct proportion to the
warping stiffness of the bracing system and in inverse proportion to the square of
the height. The Saint-Venant torsional stiffness affects the value of the critical load
through the critical load parameter
(k
s
)
but its effect is normally small as in most
practical cases
k
s
<1 holds. There is, however, a significant difference between the
sway-and pure torsional critical loads. The value of the pure torsional critical load
also depends on the radius of gyration. The effect of the radius of gyration is best
shown by formula (2.11). According to the formula which assumes uniformly
distributed floor load, the greater the size of the building (and the distance between
the shear centre and the centre of vertical load), the greater the radius of gyration
and consequently the smaller the pure torsional critical load. This is in sharp contrast
to sway buckling where the geometrical characteristics of the layout of the building
do not influence the critical load.
Formula (3.17) shows another interesting fact. When a structure is braced by
a bracing element of zero warping stiffness (e.g. a core of thinwalled, closed
cross-section), the value of the critical load for pure torsional buckling does not
depend on the height of the building nor on the distribution of the load.
α
3.1.2
Coupling of the basic modes; combined sway-torsional buckling
As the simultaneous differential equations (3.1) to (3.3) show, the basic modes
combine in the general case. The coupling of the basic modes can be taken into
account in two ways: approximately or exactly. If the main aim of the investigation
is to show whether or not the building is in a stable state, then the approximate
method can be used (first). It is very quick and simple, albeit conservative. If it
indicates an unstable building or a building with an insufficient safety margin,
then, as a second step, the exact method may still prove that the building is in a
stable state. (
Chapter 7
deals with the necessary level of safety against buckling.)
