Abstract:
The research theme has reference to obtaining of the instantaneous image of a multi-bays
multi-storeys structure after the accidental damage of a lower column. This instantaneous
image, in fact, is represented by the bending moments diagram just after the accidental
collapse. Obtaining of this bending moments diagram is not an easy matter to achieve; it
requires the use of the concepts of the plastic analysis of the structures that cannot be ignored
and a series of retro-analyses. Indeed the bending moment diagram of any structure depends to
the nature of the loading and the conditions of supports with the assumption that the behaviour
is elastic everywhere through the structure. Actually, after the damage of a column, this
diagram of the bending moments will emphasize ineluctably sections or whole zones where the
moments are higher than the respective plastic moments. This is being right for a mathematical
point of view but impossible for a physical point of view.
Three storeys-three bays basic frame was selected in order to study the case of the damage
of a central column and an edge column. The results obtained after the series of retro-analyses
were encouraging. In addition, two other frames one with a storey in more and the other with
an additional bay were analyzed. The study in a first time related to the determination of truths
collapse mechanisms for the three frames retained by using the method “pushover”. These
same frames were reanalyzes after the damage of a central column and an edge column by
using the same method and with a series of retro-analyses until obtaining the instantaneous
image after the damage. The study was also relates to the study of the effects of some
influential parameters such as the variation of the ratio α = V/H, the variation of the ratio
Geometrical-mechanic l/M
pb, the form of rise in the frame, the position of the damaged
column.
The results obtained were presented in graphic form by the construction of interaction
diagrams, whereas these diagrams are recommended in the literature only for simple frames
"single bay – single storey".
The instantaneous images of the damaged frames revealed that, to in no case, it could be
have a total collapse, however partial collapses (elementary mechanisms) were observed with
some localised disorders
