Torres

Why Did the World Trade Center Collapse?—Simple Analysis1
Zdeneˇk P. Bazˇant, F.ASCE,2 and Yong Zhou3
Abstract: This paper presents a simplified approximate analysis of the overall collapse of the towers ofWorld Trade Center in New York
on September 11, 2001. The analysis shows that if prolonged heating caused the majority of columns of a single floor to lose their load
carrying capacity, thewhole tower was doomed.
DOI: 10.1061/~ASCE!0733-9399~2002!128:1~2!
CE Database keywords: New York; New York City; Disasters; Buildings; High-rise; Collapse; Analysis; Terrorism.
Introduction and Failure Scenario
The 110-story towers of the World Trade Center were designed to
withstand as a whole the forces caused by a horizontal impact of
a large commercial aircraft ~Appendix I!. So why dida total collapse
occur? The cause was the dynamic consequence of the prolonged
heating of the steel columns to very high temperature. The
heating lowered the yield strength and caused viscoplastic ~creep!
buckling of the columns of the framed tube along the perimeter of
the tower and of the columns in the building core. The likely
scenario of failure is approximately as follows.
In stage 1~Fig. 1!, the conflagration, caused by the aircraft fuel
spilled into the structure, causes the steel of the columns to be
exposed to sustained temperatures apparently exceeding 800°C.
The heating is probably accelerated by a loss of the protective
thermal insulation of steel during the initial blast. At such temperatures,
structural steel suffers a decrease of yield strength and
exhibitssignificant viscoplastic deformation ~i.e., creep—an increase
of deformation under sustained load!. This leads to creep
buckling of columns ~Bazˇant and Cedolin 1991, Sec. 9!, which
consequently lose their load carrying capacity ~stage 2!. Once
more than half of the columns in the critical floor that is heated
most suffer buckling ~stage 3!, the weight of the upper part of the
structure abovethis floor can no longer be supported, and so the
upper part starts falling down onto the lower part below the critical
floor, gathering speed until it impacts the lower part. At that
moment, the upper part has acquired an enormous kinetic energy
and a significant downward velocity. The vertical impact of the
mass of the upper part onto the lower part ~stage 4! applies enormous
verticaldynamic load on the underlying structure, far exceeding
its load capacity, even though it is not heated. This causes
failure of an underlying multifloor segment of the tower ~stage 4!,
in which the failure of the connections of the floor-carrying
trusses to the columns is either accompanied or quickly followed
by buckling of the core columns and overall buckling of the
framed tube, with thebuckles probably spanning the height of
many floors ~stage 5, at right!, and the upper part possibly getting
wedged inside an emptied lower part of the framed tube ~stage 5,
at left!. The buckling is initially plastic but quickly leads to fracture
in the plastic hinges. The part of building lying beneath is
then impacted again by an even larger mass falling with a greater
velocity, and theseries of impacts and failures then proceeds all
the way down ~stage 5!.
Elastic Dynamic Analysis
The details of the failure process after the decisive initial trigger
that 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!; thedistribution 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,...