The main paper proposing the PCF mode [2] had several discussers involved. The closure
of the discussion [15] pointed out a few flaws that crept into the competing analysis [3],
although these flaws had no adverse effects on the results. The defense of the analysis
presented in [2], on the other hand, was essentially relying on ignoring the arguments to the
contrary. The gross underestimate of the energy absorption capacity of the squashed column
that resulted is named here as the fatal mistake No.1.
From the above assumption Bazant concluded that after the initiation of failure of the
critical story, the columns in that squashed story offered only negligible resistance. That led
to the assumption that the upper part of the building, above that story, would be in a free fall
until a complete flattening of that story. At the end of the critical story squash the free-drop
velocity is over 8.5 m/s, resulting in a destructive impact. This in turn culminated in [2] as a
conclusion of a quick collapse of the entire edifice. We call this a “vanishing story
assumption” and refer to it as the fatal mistake No.2. (This free-fall assumption was not
openly stated, but there are numerous hints in [1, 2, 6] and [12] implying that it was used in
computational procedure.)
Conclusion:
A number of simple, transparent calculations of the North Tower collapse were presented in
[5] and the conclusion was that assuming even a modest resistance of columns during their
destruction would cause an unacceptably long collapse time. It is only when perfectly
frangible columns were adopted that the fall time was as low as 15.3 s. This removes the PCF
mode, as defined here, as a viable hypothesis of collapse.
Yet, the PCF achieved significant popularity, as based on [1] and [2], while the next work
[12] did not contribute anything new to the core of the subject. These papers, purporting to
explain the collapse, suffered from three fatal errors, as detailed above. Also, the whole
methodology was not justified. Some incredibly short fall times were quoted by the authors,
while all solutions were of a black-box type. The presentations in these papers are not a valid
description of what happened. The reasons for a smooth motion history and promptness of
collapse of the North Tower remain yet to be determined.
REFERENCES
[1] Bazant, Z.P. and Zhou, Y, “Why Did the World Trade Center Collapse?—Simple Analysis”. Journal of
Engineering Mechanics, Vol.128, No.1, pp.2–6, January 2002.
[2] Bazant, Z.P. and Verdure, M., “Mechanics of Progressive Collapse: Learning from World Trade Center and
Building Demolitions”. Journal of Engineering Mechanics, Vol.133, No.3, pp.308–319, March 2007.
[3] Szuladzinski, G. Discussion of “Mechanics of Progressive Collapse: Learning from World Trade Center and
Building Demolitions” by Z.P. Bazant and M. Verdure. Journal of Engineering Mechanics, ASCE, Vol.134,
No.10, Oct.2008, pp.913–915.
[5] Szuladzinski, G. “Temporal Considerations in Collapse of WTC Towers”.Int. J. Structural Engineering, Vol.
3, No. 3, Feb 2012, pp.189–207.
[6] Ja-Liang Le and Bazant, Z.P., “Why the Observed Motion History of World Trade Center Towers is Smooth”.
Journal of Engineering Mechanics, Vol. 137, No. 1, January 1, 2011, pg. 82–84.
[12] Bazant, Z.P., Le, J.-L., Greening, F.R., and Benson, D.B. (2008). “What did and did not cause collapse of
World Trade Center twin towers in New York?”. J. of Engrg. Mechanics ASCE 134 (10) 892–906.
[15] Bazant, Z.P. and Jia-Liang Le. Closure to “Mechanics of Progressive Collapse: Learning from World Trade
Center and Building Demolitions” by Bazˇant, Z.P. and Verdure, M., Journal of Engineering Mechanics,
Vol.133, No.3, pp.308–319, October 2008.