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The details of the failure process after the decisive initial triggerthat sets the upper part in motion are of course very complicated
and their clarification would require large computer simulations.
For example, the upper part of one tower is tilting as it begins to
fall ~Appendix II!; the distribution of impact forces among the
underlying columns of the framed tube and the core, and between
the columns and the floor-supporting trusses, is highly nonuniform;
etc. However, a computer is not necessary to conclude that
the collapse of the majority of columns of one floor must have
caused the whole tower to collapse. This may be demonstrated by
the following elementary calculations, in which simplifying assumptions
most optimistic in regard to survival are made.
For a short time after the vertical impact of the upper part, but
after the elastic wave generated by the vertical impact has propagated
to the ground, the lower part of the structure can be approximately
considered to act as an elastic spring @Fig. 2~a!#.
What is its stiffness C
? It can vary greatly with the distribution of
the impact forces among the framed tube columns, between these
columns and those in the core, and between the columns and the
trusses supporting concrete floor slabs.
For our purpose, we may assume that all the impact forces go
into the columns and are distributed among them equally. Unlikely
though such a distribution may be, it is nevertheless the
most optimistic hypothesis to make because the resistance of the
building to the impact is, for such a distribution, the highest
. If the
building is found to fail under a uniform distribution of the impact
forces, it would fail under any other distribution.