Bazant's progressive collapse math is bogus.

[eomer]

I'm rescuing this subthread from a parent thread that got locked for reasons having nothing to do with this content.

The topic is Dr. Bazant's conclusion in a Journal of Engineering Mechanics article, http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/466.pdf">Mechanics of Progressive Collapse: Learning from World Trade Center and Building Demolitions that claims to demonstrate that progressive collapse was inevitable once collapse was initiated.

Here is the discussion we were having in that subthread:

eomer
Bazant's math is bogus. Anybody can learn to construct equations that don't conform to reality.

Discussion of “Mechanics of ProgressiveCollapse: Learning from World TradeCenter and Building Demolitions” byZdene˘k P. Bažant and Mathieu VerdureMarch 2007, Vol. 133, No. 3, pp. 308–319.DOI: 10.1061/(ASCE)0733-9399(2007)133:3(308)James R. Gourley11B.S. Chemical Engineering; Attorney, Carstens & Cahoon, LLP, Dallas,TX 75240. E-mail: [e-mail] -snip- The first problem with the original paper is that throughout it,the collapse is assumed to occur in two phases. As a result, allequations that purport to model the collapse are developed separatelyfor the first phase and for the second phase. In the firstphase, which the paper calls crush-down phase, the section of thetower above the aircraft impact zone (called Part C in the originalpaper; see Fig. 2 of the original paper) remains essentially intactas it progressively crushes down through the entire section of thetower structure below the impact zone called Part A in the originalpaper; see Fig. 2. The second phase, called the crush-up phase,starts when the entire lower structure of each tower (Part A) hasbeen completely destroyed by the upper part (Part C), and Part Callegedly impacts the dense pile of debris created during thecrush-down phase at high speed, thereby destroying Part C fromthe bottom up. Initially, this two-phase collapse mode may seemplausible, but after careful examination, it is clear that this twophasecollapse scenario is scientifically implausible, which callsinto question the veracity of all equations developed in the originalpaper. The paper appears to justify this collapse mode by making akey assumption that the authors do not support with any explanationor analysis. This key assumption, which is one of what theauthors call “reasonable . . . simplifying hypotheses” is that, duringthe building collapse, “(e)nergy is dissipated only at thecrushing front (this implies that the blocks in Fig. 2 may betreated as rigid, i.e., the deformations of the blocks away from thecrushing front may be neglected . . .)” In other words, the paperassumes that Part C of each tower is treated as a rigid block whileit crushes down through and destroys the lower structure. Althoughthis assumption may have had the intended effect of simplifyingthe paper’s collapse analysis, it also rendered the collapseanalysis at odds with the reality of the physics at work during thecollapse. It should be noted here that no lateral forces are consideredin this discussion in accordance with another simplifyingassumption made by the paper, namely, that the “only displacementsare vertical” (p. 312 of the paper). This simplifying assumptionis flawed (e.g., steel members and dust were spreadacross a wide area surrounding the location where the towersstood) but is beyond the scope of this discussion.

http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/D25%20WTC%20Discussions%20Replies.pdf

Once you realize that Bazant's math is based on gross simplifications, all persuasive power is sucked out of it (if you're paying attention). I don't claim that progressive collapse would not have occurred. I do claim that Bazant has not proved that it would.

Bolo Boffin
That's amusing - quoting Gourley's paper to refute Bazant.

You should know that Gourley's paper was only published so Bazant could demonstrate the gross simplifications presented by Gourley and other 9/11 CD advocates. Bazant ends his response with a recommendation that the writer take a class in basic structural engineering before trying to contribute to the subject further. JEM printed that. OUCH.

Please stop failing all over the place.

eomer
Here is visual proof that Bazant and his equations are wrong.

The top Part C of the tower (as Bazant refers to it) did not remain intact as a rigid block. The frames in this video are the proof:

http://911research.wtc7.net/wtc/evidence/videos/st_nbc1.html

1. First look at frame 6:03:00 and note the height of the intact Part C by measuring the height of the corner that is toward us. The distance you are looking for is from the very top of the corner of Part C down to the apparent bottom of Part C at the collapse zone.¹ This is the height of the top Part C that has started to move as an intact unit at collapse initiation.
   
2. Now look at frame 13:06:15 and note the distance from the top of Part C down that same corner. See if you can fit an intact Part C that is the same size as it was at collapse initiation before you run out of space at the intact lower Part A. You cannot.

The original Part C that we saw moving together as a unit at initiation cannot fit in the remaining space 7 seconds later. Crush-up has clearly occurred, causing the top Part C to be crushed to a size significantly smaller than it was at initiation. Bazant claimed that his equations demonstrate that the top Part C would remain intact as a rigid block and that crush-up would not occur. He and his equations are clearly wrong.


¹ The collapse zone can be determined in frame 6:03:00 by the point at which the corner has an obtuse angle due to the lean of the top Part C. I copied the frame into a photo editor and drew a straight line that I could line up with the lower part of the corner to determine where the angle occurs and therefore where both the collapse zone and the bottom of Part C are. I concluded that it occurs just above the point where the corner of the bottom intact building (Part A) becomes obscured by smoke. You may also need to alternate between watching the video in motion a number of times and watching it frame by frame to interpret where the top Part C is at each point and where the collapse initiation zone is.

eomer
More visual proof that Bazant's equations are wrong.

Bazant's equations assume that all the mass of Part A is incrementally added to that of Part C as the collapse works its way down.

Clearly from the video you can see, if it weren't already obvious, that some of the mass of Part A and/or Part C is ejected horizontally out of play and cannot be part of the mass that is crushing Part A. In addition, the horizontal momentum represents energy that Bazant erroneously counted in the downward force in his equations.

Further, you can see that portions of Part A remain standing after the collapse zone has passed well below them. In frame 17:08:15 you can see columns still standing when the collapse zone has moved quite a ways below them. There is also a significant chunk of structure that remains well above the collapse zone in frames 21:10:15 through 24:12:00 and then drops out of view.

All of the mass that was ejected horizontally out of play and all of the mass that remained standing above the progressing collapse zone represent undeniable error in Bazant's equations. This mass cannot be part of the mass that is (allegedly) crushing Part A as Bazant's formulas assume. All of the horizontal momentum represents energy that Bazant erroneously counted as part of the crushing force.

Rather than taking a conservative position on each of these points in order to demonstrate his assertion, Bazant does the opposite: he errs obviously in a direction that overstates his case. He goes so far as to assume that all the mass and all the momentum will count in his favor, a grossly false assumption. He therefore leaves us (and him) not knowing whether his assertion is true or not. Is the sum of his errors, a sum that obviously subtracts from his case, enough to have flipped the result he was going to get from collapse=false (if he had properly accounted for the mass and momentum) to collapse=true? No one knows, including Bazant. But what we do know for sure is that his equations are wrong.