New preprint from Beck

[Doctor Evil]

While looking for interesting physics papers I have found this preprint from C. Beck. It is titled "Role of Compaction Ratio in the Mathematical Model of Progressive Collapse".

Abstract:

We derive a mathematical model of progressive collapse and examine role of compaction. Contrary to a previous result by Ba\v{z}ant and Verdure, J. Engr. Mech. ASCE 133 (2006) 308, we find that compaction slows down the avalanche by effectively increasing the resistive force. We compare currently available estimates of the resistive force, that of Ba\v{z}ant and Verdure (2006) corrected for compaction for World Trade Center (WTC) 2, and of Beck, www.arxiv.org:physics/0609105, for WTC 1 and 2. We concentrate on a damage wave propagating through the building before the avalanche that figures in both models: an implicit heat wave that reduces the resistive force of the building by 60% in Ba\v{z}ant and Verdure (2006), or a wave of massive destruction that reduces the resistive force by 75% in Beck (2006). We show that the avalanche cannot supply the energy to the heat wave as this increases the resistive force by two orders of magnitude. We thus reaffirm the conclusion of Beck (2006) that the avalanche is initiated in the wake of the damage wave.

I am extremely busy now, and wont have the time to go through it carefully. However, I will be interested in any comments that some of our more engineering oriented members have.

One more personal comment: This paper has NOT been reviewed yet. In fact, this archive is meant for theoretical physics papers, and this paper does not really fit in. I hope this is not the start of a new trend of using this useful resource for purposes which are not entirely scientific.

 

[Dave Rogers]

The maths is a little too involved for me to follow in the time I have available, but I think the main point to note is that Beck is misrepresenting Bazant and Verdure. Beck says B&V are reducing the structural resistance to collapse by a factor of two from their initial estimate, then claiming that this is due to heating. He then interprets this as a claim by B&V that a heat wave is propagating down the towers during collapse.

Considering the total mass of the building to be M = 3.2 · 108 kg, this yields for the resistive force R/(M g) = r = 0.2, as their initial estimate. They noted that in order for the avalanche to reach the ground level in 2T ≃ 10.8 s [6] they had to use R/2 instead of R. The 50% reduction, they argued, came from heat (p.15, top paragraph of the on-line edition of [1]). That is, an assumption built in their model is that the avalanche pushes a heat wave in front of itself which reduces the strength of the building by 50%.

However, Bazant and Verdure don't say anything of the sort.

Since the first story to collapse was heated, the value of Fc within the interval of z corresponding to the height of that story was reduced to one half.​

My bolding.

In other words, B&V assume that only the first storey to collapse was heated; for the rest of the structure they use their original estimate for resistance to collapse. Beck's heat wave is purely his own interpretation of his own misunderstanding (I'm being charitable here) of Bazant and Verdure.

Having conjured up a non-existent energy loss term in the collapses, Beck then shows that this energy loss term would slow the collapse time for WTC2 to greater than the 10.8 seconds estimated by B&V. All the evidence, however, suggests that the collapse time was longer than 10.8s anyway.

In summary, then, Beck is reasoning from two invalid premises to reach an invalid conclusion.

Dave​

​

 

[Doctor Evil]

Thank you for the reply.

I wish I had the time to go over the papers myself, but I am extremely busy at the moment. Anyway, misrepresenting cited papers is a big nono. It is much worse when you do it to a paper you are trying to refute. I wish I could see the referee reports, and/or, Bazant's response.