| Seffenrevpub.pdf | 50 KB | galendenzen | Sep 12, 2008 | ||||||||
Crockett Grabbe Debunks Keith Seffen
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Discussion of ”Progressive Collapse of the World Trade Center:
A Simple Analysis” by K.A. Seffen
February, 2008, Vol. 134, No. 2, pp. 125-132
DOI: 10.1061/(ASCE)0733-9399(2008)134:2(125)
Crockett Grabbe1
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Research Scientist, Dept. of Physics and Astronomy, Univ. of Iowa, Iowa City, IA
52242 and SeaLane Consulting, Iowa City, IA 52245-3314. E-mail: sealane@mchsi.com
Seffen’s paper presents what it calls a simple analysis for the dynamics of the
World Trade Center (WTC, implicitly just the South and North Towers) collapses. He
claims the ”factors responsible for the onset of collapse are now well established”, that:
(1) intense fires created by the aircraft compromised the remaining intact columns
near the impact [those undamaged by the plane collision] to sustain the weight of the
building above them.
(2) The subsequent ”near free fall” of these upper parts over just 1 story resulted in
dynamical overloading of the undamaged columns below by a ”factor of over 30”.
Seffen then goes on to develop a propagating instability model for how the fire brought
the Towers down. But these claimed factors are factually inaccurate. Furthermore,
in analyzing the model built on these factors, ideal assumptions are made that are in
disagreement with physical principles inherent in the collapses of the Towers, and yield
solutions that cannot provide answers or much insight into how the Towers fell.
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While the theory of these factors responsible for the onset of collapse have been
”well-proposed” as the cause of the collapse, they have not been well-established as
factors that explain well the observations of the collapse. The theory that Seffen is
improving on is the ”crush-down, crush-up” theory proposed initially by Bazant and
Zhou (2002). Yet this theory does not agree very well with observations on how the
Towers fell. For example, as film documentation of the South Tower collapse shows,
the top part of the South Tower does not even come close to ”crushing up” after the
bottom part of the Tower ”crushes down” to the ground.(NBC films, 2001) In fact,
the top part started toppling and fully disintegrated into gray clouds (produced from
pulverizing concrete from areas on fire) in mid-air, above the lower part of the Tower
(producing only white clouds from pulverizing concrete below where the fires were),
and it did so well before the lower part came down. In addition, both of the Towers
show major horizontal forces in their collapses, forces which are fully ignored in the
”crush-down, crush-up” theory, which treats the downward gravitational force as the
only force acting in 1D analyses of the collapses and neglects all horizontal motion. The
factors responsible for the onset of collapse assumed in this ”crush-down, crush-up”
theory are clearly not well-established.
Furthermore, it has been ”well-established” that the factors that caused the onset
of collapse in the South Tower appear definitely to not have been the fires. The fires
created from the plane impacts were not that intense just before the collapse initiation
for either Tower, and for the South Tower the fires seemed close to being contained and
put out by the firemen when suddenly rapidly horizontally-moving masses of material
violently broke through walls of the floors below where the fires had been burning
from the plane hit. As the film documentation shows, the collapse of the South Tower
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initiated 1-2 stories below the lowest floor where the fires had been burning, with very
dynamic (roughly 40 mph) hurtling of white material (broken and pulverized concrete)
in the horizontal direction away from the building — material with absolutely no fire
associated with it.(NBC films, 2001) This ejection and a subsequent horizontal ejec-
tion of rapidly-moving white material at floors just near this formed the white clouds
around the lower segment.
As presented by Grabbe (2008a), the force that ripped the South Tower apart at
one edge in the collapse was a force an order of magnitude larger in strength than
that of the force of gravity (the only force acting in Seffen’s model for the collapse).
There is similar evidence that the fires were not the cause of the North Tower collapse,
such as the energy analysis in Hoffman (2003) that calculates the amount of energy
expended in the collapse of the North Tower to be about an order of magnitude larger
than the energy that is available for gravitation collapse, the sole force in the model of
Seffen. These analyses effectively disprove what Seffen refers to as a ”well-established”
assumption – that gravitation was the only force involved in the collapses of the Tow-
ers.
Seffen builds on Bazant and Zhou’s 2002 paper (hereinafter called BZ), referring
to their work as establishing the virtually ”free-falling” upper parts that initiated the
collapse, even though BZ provided no physical mechanism that can possibly allow such
free-fall. Seffen states that then the subsequent gravitational ”near free-fall” of the
upper parts over the height of just one story resulted in dynamical overloading of the
undamaged lower columns by 30 times their static load. But there is no evidence to
support this incredible inference that as a result of the claimed gravitational initiation
the upper parts were suddenly virtually free-falling, nor are there means by which grav-
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itational collapse can produce such a ”near free-falling” state. For ”near free-falling”
to happen, the contiguous solid material making up the building below these sections
where the collapse initiates would suddenly massively lose its cohesion, an action the
fire above this solid material cannot possibly cause. That stationary momentum of
that lower contiguous material counters the momentum of falling parts from above,
and conservation of momentum keeps the free-fall state from being approached.
The only thing this author knows of that could create a virtual free-falling state
is massive explosions well below the fires, which could effectively ”liquefy” the lower
structure. Direct evidence for explosions, which were created by forces other than grav-
ity (such as the horizontal forces in the South Tower collapse initiation), was presented
in Grabbe (2007). Those forces are, of course, not present in Seffen’s model.
Seffen completely ignores conservation of momentum in all his uses of the word
”free-fall”. He has mathematically converted the problem from one of analyzing New-
ton’s equations of motion to an instability analysis of the column as a whole, in order to
improve on the the story-coupling limitations of the BZ analysis. However, one cannot
ignore conservation of energy and momentum, and the implications of these conserva-
tion laws is that the free-fall cavalierly referred to cannot happen in the gravitational
collapse of the Towers analyzed in Seffen’s model.(Grabbe, 2008b) He effectively avoids
the problems of the conservation laws in his analysis, but they not gone away, and pre-
vent achievement of the virtual free fall he asserts.
Seffen correctly identifies one of the several inadequacies of the BZ analysis, saying
”However, the link to progressive collapse is improperly asserted by claiming that, be-
cause each story locally collapses in an unstable manner, successive stories are bound to
fail sequentially.” In fact, there is no reason a gravitational collapse could not stop, at
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least temporarily, upon hitting adequately-sturdy structure in the story below. Seffen
tries to correct that inadequacy in BZ analysis by analyzing whether this is a prop-
agating instability. However, like BZ, he uses a grossly inadequate 1D model of the
Towers. The Towers cannot be analyzed as 1D sticks (i.e. 1500 f t ”telephone poles”).
This grossly ignores the horizontal extensions of the Towers, and completely misses
the internal structure that would be a major resistance to such instabilities – indeed,
also a major resistance to anything anything approaching free-fall. The Towers were
well-constructed over 44,000 f t2 horizontally for this stability, and all of that is ignored
in the simple 1D model that Seffen analyzes.
Seffen states that ”Each story is assumed to compress homogeneously such that the
overall ’wake’ above the crush-front and below the initiation site has a larger, uniform
density.” On the contrary, the early stages of the fall of the South Tower were very
non-uniform over these other 2 dimensions, making this 1D model fully inaccurate.
Using this oversimplied 1D model of the Towers, Seffen calculates the conditions for
the instability in Eq (21) as the maximum value the variable he defines as p∗ (non-
dimensionalized variable proportional to what he calls the ”steady-state propagation
pressure” P ∗ ) can be to still ”assure collapse” of the building. Furthermore, if p∗ is
sufficiently smaller than unity in his model it can apparently achieve the speedy col-
lapse observed for the Towers. Clearly his determination of what p∗ is for the Towers
is no good because of invalid assumptions used, including in particular the major over-
simplifications from his 1D model.
His statement on that ”More realistically, if there is a column fracture, p∗ is much
less than unity” shows this 1D assumption is clearly wrong because it ignores impor-
tant aspects of the 3D behavior of the Towers. There are actually about 286 columns,
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and they are designed to deal with fractures in individual columns by redistributing
the load to unfractured columns. Yet a 1D model must assume it is only 1 column.
One could try to translate his 1D analysis into the assumed uniform behavior of all
286 columns, but in fact these 286 columns are engineered not to act uniformly? Fur-
thermore, Seffen models the columns as being damaged by fire, but fire damage itself
definitely cannot be uniform over these other 2 dimensions. There is no sensible way
to make this translation, and the model is grossly unrealistic for the real WTC Towers.
Seffen ends the calculation correctly pointing out some of the limits of his model.
Stating ”Many simplifications have been made in this analysis for the sake of trans-
parency,” he mention some of these simplifications. However, he fails to describe one
of the most crucial oversimplifications of his model: the analysis of the Towers as 1D
objects. Such a treatment grossly oversimplified the very inhomogeneous nature of
fire throughout the 286 columns spread over 44,000 f t2 in those 3D Towers, leading
to erroneous conclusions. One cannot correctly analyze the stability of a complex 3D
structure in a simplified 1D analysis. Horizontal forces, complex building structure over
the other 2 dimensions, and inhomogeneities of the forces of destruction over these 2
dimensions are essential considerations in any correct analysis.
On the positive side, Seffen’s analysis of the 1D model might be viewed as a useful
initial analysis for building collapses from fire that to lowest order fit the model he
uses, possibly helping to identify important questions that need to be addressed in a
more complex 3D followup (e.g. why has no other high-rise in any industrial nation
ever collapsed from fire?). However, when this model and its analysis are applied as
an effort to explain the WTC collapses, claiming this is what caused the collapses,
it is decidely wrong, offering little in answers or insight how the WTC buildings fell.
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His 1D model and analysis is inadequate because it ignores fundamental 3D aspects
of the stability of the Towers, it disagrees with known physical principles such as the
conservation of energy, momentum, and mass – conservation laws that show that the
collapsing WTC Towers could not reach the virtual free-fall states observed by the
gravitational force as claimed, and it substantially disagrees with several observations
of how the Towers collapsed.
References
Bazant, Z.P. and Zhou, Y. (2002), ”Why did the World Trade Center collapse?–Simple
analyis,” J. Eng. Mech., 128(1), 2-6.
Grabbe, C.L. (2007), ”Direct Evidence for Explosions: Flying Projectiles and Widespread
Impact Damage,” J. 911 Stud., 14(8), 1-7, online at:
http://www.journalof911studies.com/volume/200704/GrabbeExplosionsEvidence.pdf
Grabbe, C.L. (2008a) ”Analysis of the Collapse of the South Tower of the World Trade
Center” American Physical Society’s April Meeting, online at:
http://meetings.aps.org/Meeting/APR08/Event/84051
http://www.sealane.org/writings/PhysSTFall.html
Grabbe, C.L. (2008b), ”Response to NIST on Energy and Momentum,” J. 911 Stud.
Jan. 29 Letter, online at:
http://www.journalof911studies.com/letters/g/GrabbeToNISTenergyMomentum.pdf
Hoffman, J., ”The North Tower’s Dust Cloud: Analysis of Energy Requirements for
the Expansion of the Dust Cloud Following the Collapse of 1 World Trade Center,”
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October 16, 2003, online at:
http://911research.wtc7.net/papers/dustvolume/volume.html
NBC film of South Tower collapse on 9/11/01, online at:
http://911research.wtc7.net/wtc/evidence/videos/index.html
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