6 examples from Bazant and Verdure where Bazant’s derived 1-D stick model is taken to accurately reflect the behavior of real buildings, including the WTC towers:
Link to the paper:
Mechanics of Progressive Collapse: Learning from World
Trade Center and Building Demolitions
Zdenfk P. Bažant, F.ASCE; and Mathieu Verdure
http://www.civil.northwestern.edu/pe...Papers/466.pdf
BV abstract pg 308: “It is argued that, using inverse analysis, one could identify these parameters from a precise record of the motion of floors of a collapsing building. Due to a shroud of dust and smoke, the videos of the World Trade Center are only of limited use. It is proposed to obtain such records by monitoring _with millisecond accuracy_ the precise time history of displacements in different modes of building demolitions. The monitoring could be accomplished by real-time telemetry from sacrificial accelerometers, or by high-speed optical camera. The resulting information on energy absorption capability would be valuable for the rating of various structural systems and for inferring their collapse mode under extreme fire, internal explosion, external blast, impact or other kinds of terrorist attack, as well as earthquake and foundation movements.”
He is obviously suggesting that the 1-D stick model presented in this paper can be applied to real buildings. He is clearly arguing that the crush up and crush down equations (eqs 12 and 17) and the concept of crush down, then crush up can be applied to real 3-D buildings.
BV introduction pg 308, column 2: “A simplified one-dimensional analytical
solution of the collapse front propagation will be presented. It
will be shown how this solution can be used to determine the
energy absorption capability of individual stories if the motion
history is precisely recorded. Because of the shroud of dust and
smoke, these histories can be identified from the videos of the
collapsing WTC towers only for the first few seconds of collapse,
and so little can be learned in this regard from that collapse.
However, monitoring of tall building demolitions, which represent
one kind of progressive collapse, could provide such
histories. Development of a simple theory amenable to inverse
analysis of these histories is the key. It would permit extracting
valuable information on the energy absorption capability of various
types of structural systems in various collapse modes, and is,
therefore, the main objective of this paper.”
There is no doubt that he beleives these equations and the concept of crush down, then crush up represent the behavior of real buildings. He suggests the equations can be used to extract valuable information for real buildings. He states that application to real buildings is the main objective of the paper.
Not surprisingly, he applies the model to determine specific behavior of WTC1 and 2 in his later papers (BL and BLGB).
BV, What Can We Learn?—Proposal for Monitoring
Demolitions, pg 315-316: “We have seen that the main unknown in predicting cohesive
collapse is the mean energy dissipation Wf per story. The variable
mew(z) is known from the design, and the contraction ratio gamma(z)
can be reasonably estimated from Eq. (1) based on observing
the rubble heap after collapse. But a theoretical or computational
prediction of Fc is extremely difficult and fraught with
uncertainty. Eqs. (12) and (17) show that Fc(z) can be evaluated from
precise monitoring of motion history z(t) and y(t), provided
that mewz) and gamma(z) are known. A millisecond accuracy for
z(t) or y(t) would be required. Such information can, in theory,
be extracted from a high-speed camera record of the collapse.
Approximate information could be extracted from a
regular video of collapse, but only for the first few seconds
of collapse because later all of the moving part of the WTC
towers became shrouded in a cloud of dust and smoke (the visible
lower edge of the cloud of dust and debris expelled from
the tower was surely not the collapse front but was moving
ahead of it, by some unknown distance). Analysis of the record of
the first few seconds of collapse (NIST 2005) is planned, but
despite thousands of videos, not much can be learned from the
WTC.
(Major_Tom note: “mew” and “gamma” represent greek letters.)
He clearly thinks his 1-D model and his concept of crush down, then crush up can be used to extract real information from real, 3-d buildings.
BV, Implications and conclusions, pg 318 column 2:
4. The mode and duration of collapse of WTC towers are consistent
with the present model, but not much could be learned
because, after the first few seconds, the motion became obstructed
from view by a shroud of dust and smoke.
He states that to his knowledge the 1-D stick model and the concept of crush down, then crush up fits WTC1 and 2 behavior. The confirms this believe many times by applying the model to WTC1 and 2 in his following papers BL and BLGB.
5. The present idealized model allows simple inverse analysis
which can yield the crushing energy per story and other
properties of the structure from a precisely recorded history
of motion during collapse. From the crushing energy, one can
infer the collapse mode, e.g., single-story or multistory buckling
of columns.
Yes, he really believes crush down equations 12 and crush up equations 17 and the concept of crush down, then crush up represent the behavior of real buildings.
6. It is proposed to monitor the precise time history of displacements
in building demolitions—for example, by radio telemetry
from sacrificial accelerometers, or high-speed optical
camera—and to engineer different modes of collapse to be
monitored. This should provide invaluable information on
the energy absorption capability of various structural systems,
needed for assessing the effects of explosions, impacts,
earthquake, and terrorist acts.
He believes that valuable information appliable to the real world can be extracted from these equations. He believes that crush down, then crush up occurs in real buildings and that this is what happened to the WTC towers. In his following papers (BL and BLGB) he claims specific collapse properties of the WTC towers can be known by applying the conclusions of this 1-D stick model.
