Civil Engineering Reference
In-Depth Information
critical load is obtained by the combination of the part critical loads. The methods are
described in detail in this section in relation to frameworks on fixed supports, and then
in the following sections they will be applied to frameworks on pinned supports,
frameworks with cross-bracing, infilled frameworks and coupled shear walls.
Fig. 9.3
Frameworks on fixed supports.
9.3.1
The application of summation theorems
Once the part critical loads are available, for example for frameworks under uniformly
distributed load, the repeated application of the Föppl-Papkovich theorem and the
Southwell theorem [Tarnai, 1999] results in a very simple formula for the critical load. In
considering the full-height bending of the structure as a whole unit and its shear
deformation, it is first assumed that the structure is stiffened against full-height bending
as a whole, then against developing shear deformation. The reciprocal summation of the
corresponding critical loads leads to the critical load of a framework with both full-height
bending and shear stiffnesses. However, the individual columns of the framework may
also develop full-height bending. The effect of this phenomenon can be taken into
account by applying the Southwell theorem: the critical load which belongs to the full-
