some time ago I have posted a research paper on collapse of world trade center 2 from the perspective of an avalanche propagating in an one-dimensional structure of known mass density.
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The title of the paper is "Cherry Tree vs. Crêpes Suzette: Global Model of Collapse of WTC 2," and it was published in subject class Popular Physics; Physics and Society.
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Comments and critiques are welcome - no rants please. In particular, I am looking for comments that would improve the quality of the paper.
Please drop me a note at beck.charles_m@yahoo.com.
Charles M. Beck
I've skimmed over your paper. Unfortunately, I'm so rusty at physics that, while I understand it isn't unduly complicated, I've not digested it, fully.
Have you studied the Calladine & English paper? I've posted the reference at physorg, as well as on the stj911 forum. Unlike the Bazant Zhou paper, it has experimental evidence to back up the theory. In a nutshell, by considering inertial effects, it seems clear that buckling is not sufficiently constrained to the topmost floor being impacted (as in the Bazant Zhou scenario) such that a collapse of, say, more than a floor or two is possible.
In this case, well, the avalanche won't be very avalanche-y! :-)
The purpose of the Calladine and English paper is to help develop scaling rules such that engineers can make more accurate extrapolations from small models to full-scale ones. While I haven't worked out the specifics for the BZ scenario, it seems clear that if one did work out the relevant scaling, a global collapse would be impossible.
In terms of your paper, you may be able to modify it to model the behavior noted by Calladine and English as an energy sink term which is a function of height
and time. (And
time, to reflect the transient nature of compression waves propagating downwards ).
The complaints about ignoring inter-connectedness - which I made regarding Bazant/Zhou, NIST, and the Bazant/Verdure/Greening/Benson 'structureless rubble' approaches - are less of a concern for you as interconnectedness should favor arresting collapse. If you ignore a factor favoring arresting collapse, and yet still determine that collapse is still occurring too rapidly, you will still be able to make logical claims regarding - ahem - "missing" sources of destruction.
It is Bazant, et. al., that draw conclusions regarding the collapse of a structure, while ignoring factors that would tend to
contradict those conclusions were they to be included, that have a responsibility to improve their works in this fashion.
Even so, not being a structural engineer, there may be failure modes such that this is not true, and I am simply clueless regarding them. It'd be best to consult with some structural/civil engineers.
Lon Waters of stj911 is spearheading an attempt at the simulation that NIST wouldn't do. You should drop him a line. Also, recall (if you have read this thread prior to your first post), that structural engineering Professor Korol has looked over the Calladine and English paper, and pronounced it "very well done". I believe he'll agree with me that it's quite relevant to the BZ collapse scenario, more incisive, and contradicts it's conclusion. Even if I'm wrong on these points, I certainly recommend you contact him for input on improving your paper. He is definitely interested in the subject.
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Would you comment on NEU-FONZE's comment re your paper:
QUOTE
While the paper is full of fancy math and offers an interesting approach to the physics of the collapse, it is fundamentally flawed even before the math begins!
Why?
In the second sentence on page 1 of the paper we read:
" Approximately 56 minutes after being hit, WTC 2 collapsed to the ground in what appears to be a single-front avalanche, which started in the upper half of the building and reached the ground in time Tc = 11 seconds."
The author offers this time of precisely 11 seconds without further explanation or proof.
Now if this was a passing comment, as in the Kean Report's famous "The Towers collapsed in 9 seconds", I would not quibble. But the truth is Charles Beck's ASSUMPTION that WTC 2 collapsed in 11 seconds becomes central to his calculations. It artificially constrains the building to collapse in this time!
Greening, Bazant, Benson, etc, make no such assumption. In fact Greening's model is primarily intended to calculate the collapse time of WTC 1 and 2 so that Tc is treated as a variable.
I believe that most videos of the collapse of WTC 2 suggest that Tc was over 12 seconds. Now since collapse calculations are very sensitive to the time above and beyond the free fall time of 9.2 seconds, 12 seconds is 2.8/1.8 x 100 or 150 % higher than Charles Beck's assumed value of 11 seconds.
By FORCING WTC 2 to collapse faster than it actually did, Charles Beck's calculation gives totally UNREALISTIC results. He needs to repeat everything with Tc set at say 12, 13 and 14 seconds. I am quite sure an entirely different picture would emerge if he did!
NF
You can see wtc7.net for Hoffman's discussions of collapse times.
BTW, I sent an email to Professor Calladine requesting his view on relevance to Bazant Zhou, but didn't get an answer.
