Civil Engineering Reference
In-Depth Information
and a cantilever subjected to uniformly distributed vertical load, both with Saint-
Venant and warping torsional stiffnesses. Certain similarities emerge in the stress
analysis of the former case and the stability analysis of the latter case as the value
of torsion parameter
k
increases. The torsional buckling analysis of the cantilever
shows that the axis of the cantilever does not develop rotation in the upper regions
but a sudden twist develops near the bottom (Fig. 5.14). In the former case, the
load and the shear force, due to the rotation of the bracing system, tend to decrease
significantly in the upper section of the bracing element, with the 'centroid' of the
load shifting downwards. In both cases, 'activities' on the column (load, shear
force, rotation) are limited to the bottom section of the column as the value of the
Saint-Venant torsional stiffness increases.
Fig. 5.14
Pure torsional buckling of a cantilever with dominant
GJ
.
The fact that this analogy is only one in a series of analogies makes the situation even
more interesting. The same phenomenon can be observed with cantilevers developing
both bending and shear deformations. Furthermore, as far as bending and shear
deformations are concerned, similar phenomenon develops during the full-height
buckling of frameworks [Zalka and Armer, 1992].
5.4.2
Torsional moments
According to equations (5.5) and (5.11), unless the external load passes through the
shear centre of the bracing system, the equivalent column and the whole building it
represents undergo rotation. The floor slabs make the individual bracing elements
rotate and consequently they develop torsional moments.
The torsional resistance of the bracing system is provided by two sources: the
Saint-Venant torsional stiffness and the warping (bending torsional) stiffness.
