Civil Engineering Reference
In-Depth Information
In the boundary conditions,
H
is the height of the building.
The simultaneous differential equations (3.1) to (3.3) can be used to
demonstrate the spatial behaviour of the equivalent column. The nature of the
behaviour depends on the relative position of the shear centre of the bracing
system and the centroid of the vertical load—as described in section 2.3. Rotation
ϕ
appears in all three equations, showing that the resulting deformation is
composed of both sway and torsion, as a rule. Possibilities for the combination
are shown in
Fig. 2.4
where the whole bracing system is represented by the
equivalent column of open, thinwalled cross-section.
The solution of the simultaneous differential equations (3.1) to (3.3) in the
normal way would result in the eigenvalue of the problem, i.e. the critical load
of the building. There is, however, a much simpler way of producing the critical
load. It has been proved that the systems of differential equations (3.1) to (3.3)
can be solved in two steps: the basic critical loads which belong to the basic
modes have to be calculated first, then the coupling of the basic modes has to be
considered [Zalka, 1994c].
3.1.1
Doubly symmetrical systems—basic critical loads
The basic critical loads are those which belong to the basic (uncoupled) critical
modes: sway buckling in the principal planes and pure torsional buckling. This
is the case with doubly symmetrical arrangements when the shear centre of the
bracing system and the centre of the vertical load coincide and the three basic
