A response to Bazant and Zhou.
Did the World Trade Center Collapse?—Simple Analysis"
by Zdenek P. Bazant and Yong Zhou appeared in the on-line version
of Journal of Engineering Mechanics ASCE, with the first version dated
9/13/01 and revisions dated 9/22/01 and 9/28/01. With such rapid
publication after 9/11, it is evident that the paper must have been rushed, with no time
for full peer review. Let's take a critical look at this paper. The
basic theory of Bazant & Zhou is explained as follows, and sketched in their
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
exhibits significant viscoplastic deformation (i.e., creep—an increase of
deformation under sustained load). This leads to creep buckling of columns
(e.g., Bazant and Cedolin 1991, Sec. 9), which consequently lose their load
carrying capacity (stage 2). Once more than about a 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 above this 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 vertical dynamic load on
the underlying structure, far exceeding its load capacity, even if it is not
heated. This causes failure of an underlying multi-floor 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 the buckles 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 the series of impacts and failures then
proceeds all the way down (stage 5).
The first problem with
the model proposed by Bazant and Zhou is that there is no evidence that the
columns were ever heated uniformly to anywhere near this temperature. An
article "Collapse of the World Trade Centre Towers" by engineer G
Charles Clifton of New Zealand argues that temperatures must have been less than
700 Deg. C, well less than the 800 degree threshold noted by Bazant and Zhou.
my opinion the fires had a less important role to play in the collapse of
than the damage from the initial impact. It took both to cause the collapse,
however the fire was in no way severe enough to have caused the collapse
on its own. The reasons for this opinion are as follows:
If the temperatures inside large regions of the building were in the order
of 700+ deg C, then these regions would have been glowing red hot
and there would have been visible signs of this from the outside. Also
there would have been visible signs of flames. If one looks at the photos
of the Cardington fire tests, the flames and glowing of the steelwork
is clearly visible even in the large enclosure test where the maximum
fire temperature was only 700 Deg C. In contrast, the pictures
of the towers after the impacts and prior to the collapses show sign
of severe burning over only relatively small regions of the tops of the
towers, even pictures taken from the air looking horizontally into the
of the First Interstate Bank fire in Los Angeles in the early 1990s
show what appears to be greater heating effects and over larger
regions than were apparent in either tower.
When fully developed fire conditions ( temperatures of over 700 deg C)
reached within a region of a building, this results in the breaking of
in any external windows within that region. This continuous breakage
of glass as the fully developed fire spread through the floor of the
First Interstate Bank, for example, was the most hazardous feature of
the fire to those at ground level around the building.
contrast, once the blast and fireball effects of the impacts had subsided,
there appeared to be little ongoing window breakage from either
tower, either as evidenced from pictures/video footage or as reported
from the ground. Significant areas of window even remained intact
within the impact region .... This is further evidence that
fully developed fire conditions did not spread much through and beyond
the initial devastated region, following the impacts.
So the basic premise of Bazant and Zhou is seriously flawed. But
let's move on to their next analysis:
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. According to
this hypothesis, one may estimate that C
71 GN/m (due to unavailability of precise data, an approximate design of
column cross sections had to be carried out for this purpose).
Why would all the
impact forces go into the columns as compression? In a tube structure, the
columns would bend outwards, placing stress on the perimeter frame and the floor
trusses. The entire tube and core system is a complex box which is much
stronger than the columns alone. Therefore, the number 71 GN/m is probably
a very serious underestimate of the strength of the underlying
As if to recognize the
problems with Bazant and Zhou, Clifton proposes a buckling theory for the South
Tower which is similar, but is based on locally focal structural defects rather
than any uniform distribution of stresses, and which does not require uniformly
after the impact the perimeter frame in the South East corner would have been
severely weakened, being reduced to an unknown number of intact box
columns in towards that corner on each of the two sides.
columns would have lost the lateral support from the floor slabs over many
levels and would have had to function as isolated columns spanning
multiple storey heights. They would likely have suffered blast damage and loss
of alignment, however immediately following the impact they still retained
sufficient compression capacity to resist their share of the loads from the 30 or
so floors above the impact region.
started by the impact would have then progressively weakened the vertical load
carrying capacity of the remaining core, causing progressively more load to
have to be carried by the perimeter frame system. In my opinion, based on the
footage taken of the building over that time, the fire would have had little
impact on the strength and stiffness of the perimeter frames, even in
corner. The stiffness of this system above the impact region would have
distributed this load approximately uniformly around the perimeter frames,
increasing the loading on these frames through the impact region, including on the
residual columns in the damaged corner.
combination of increasing compression load on these damaged columns, with
second order effects from this load acting on the buckled shape of these columns
over their unsupported length, would have caused their
collapse would have initiated in the damaged corner and spread rapidly
over the impact region, causing the tower above to fail by toppling
sideways with the floors above the impact region momentarily in an intact
seems almost reasonable, from a structural engineering point of view. But
is it correct?
Videos of the South
Tower collapse show the upper portion of the building appearing to slide
downwards, possibly disappearing behind the standing lower portions of the
building for a few moments as explosions emerge from the windows. I have spoken to an eyewitness of the
collapse, and his statement was that shards of glass flew out from the sides of
the building, and then the face of the building appeared to bow out for a
moment either before or during the collapse of the upper portion.
A recent Nova
television program ("Why The Towers Fell") suggests that the core of
the South Tower may have remained intact momentarily as the tube wall collapsed.
If the initial phase of
the collapse involved primarily sliding and shearing effects, it would account
for the low friction and high speed of this phase.
How it might have been done.
The World Trade Center was leased by
Westfield America and Larry Silverstein, on April 26th, 2001. Zim
Israeli Shipping moved out of the buildings around that time. With a
certain amount of shuffling of tenants from floor to floor, it should have been
possible for the owners to gain access to various parts of the building.
Critics of the demolition theory have often remarked on the difficulty and
expense of explosive demolition, requiring tens of thousands of pounds of
explosives, drilling into structural members, and months of time. However,
a particularly diabolical structural engineer with a clear understanding of the
unique flaws of the WTC architecture, might have hatched on the plan of
exploding the trusses supporting a single floor. This would have been
sufficient to bring about the sequence of events which destroyed the towers,
with the added benefit that if an airplane strike had occurred, the upper
stories would appear to fail at the location of the strike.
Have we been lied to?
At the very least, there has been plenty of confusion and
The first question was that the role of the load of fuel from the aircraft.
Early reports were that the hot fire was responsible for the collapse, but other
observers pointed out that no kerosene fire can burn hot enough to melt
steel. In point of fact, most of the fuel in the jets was contained in
their wing tanks. The thin aluminum of the tanks was pierced or stripped
as the airplanes penetrated the walls of the towers, and the result was the huge
fireball which was seen on national TV, where most of this fuel was burned.
A hot, vigorous fire would have blown out many windows in
the building and would have burned a red or white color. This was not what
happened. The fire in the World Trade Center was an ordinary smoldering
But let's suppose that the fire was hot enough to melt
steel. What would have happened in that case? Before it breaks, hot
steel begins to bend. This redistributes the forces in the structure and
puts elastic stress on those parts that are still cool. The process is
asymmetric, so that the structure should visibly bend before breaking.
Let's suppose the structure were sufficiently weakened
that it did fail catastrophically near the point of the airplane strike.
In this case, the intact structure below would exert an upward force on the base
of the upper story portion of the building (the part that has been broken
loose), while any asymmetry would allow the force of gravity to work uninhibited
on the tip of the skyscraper. Thus, the top section of the skyscraper
would tip and fall sideways. This seems like common sense, and the
analysis of Bazant & Zhou may not be sufficient to disprove it.
A thorough forensic examination of the wreckage, might
have provided a confident answer to the questions of why the WTC towers
collapsed. Have we had such an investigation? Bill Manning in Fire
Fire Engineering has good reason to believe that the
"official investigation" blessed by FEMA and run by the American
Society of Civil Engineers is a half-baked farce that may already have been
commandeered by political forces whose primary interests, to put it mildly,
lie far afield of full disclosure. Except for the marginal benefit obtained
from a three-day, visual walk-through of evidence sites conducted by ASCE
investigation committee members- described by one close source as a
"tourist trip"-no one's checking the evidence for anything.
Here are links and supporting
Bazant & Zhou
G. Charles Clifton
G. Charles Clifton
articles -- now back on the Web.
on wind sway stabilization
New York Times
New York Times
Justin Raimondo http://www.antiwar.com
Michael Rivero http://www.whatreallyhappened.com
Eric Hufschmid http://geocities.com/erichufschmid/index.html
Jared Israel http://emperors-clothes.com/news/albu.htm
Bill Manning Fire
King on WTC collapse
Posted 3/28/2002 by Jerry Russell; Updated 3/31/2002 and
Updated 4/6/2002: reference to WWII airplane strike to
Empire State Building deleted, documentation added.
Updated 5/1/2002: Video labelled as "South Tower
Collapse" was actually a video of the North Tower!! This error led to
the mistaken argument that the South Tower floors must have pancaked before the
tube walls collapsed.
Updated 2/14/2003: removed redundant arguments to
sharpen focus of article.
The author has a master's degree in Electrical Engineering from
Stanford University, and a Ph.D. in Psychology from the University of Oregon.