Resistance of a Buckling Column -- some analysis and a question

Hi. This is my first post to this forum, although I've been reading it for some months. My name is Richard Johns, and I'm a philosopher of science, teaching in the philosophy department at the University of British Columbia. My doctoral thesis was a study of the kind of probability that physicists deal with, now published as a monograph *A Theory of Physical Probability* with the University of Toronto Press. My other main research interests are in logic, and the physics of self organisation.

I became aware of the anomalous failures of the WTC towers through a friend who is a civil engineer. I have done some reading about these "collapses", and am especially interested in Bazant's work. It is fascinating to see (apparently) absurd views published by such an able scholar in a reputable academic journal. I'm determined to get to the bottom of this.

I am planning to put my thoughts on this issue on my new personal bog:

So far there is just one, rather provisional, posting, which is pasted below.


There has been some recent discussion on 911Blogger about one of David Chandler's videos on his YouTube channel.

I have some points to make here.

1. Chandler's argument, while correct as far as it goes, establishes only an upper bound on the column resistance. A better empirical estimate is roughly 0 - 0.1mg. This can be seen as follows.

The video measures the downward acceleration of the roofline of WTC1, during the first few seconds of collapse, and measures a downward acceleration of around 0.64g. Chandler argues, correctly, that this implies that the block is resisted by an upward force of (1-0.64)mg = 0.36mg, where m is the mass of the block. Yet this is puzzling, since the columns were (just a moment before) supporting the full weight (mg) of this block. (Moreover, assuming a safety factor of 3, they the columns were capable of supporting at least 3mg, almost 10 times their measured resistance.)

Chandler's video is, in my opinion, a useful device to attract attention to this important puzzle. However, while the reasoning is correct as far as it goes, the true situation is actually far more disturbing than even his argument suggests. (I assume that he is aware of this, but wants to keep the argument as simple as possible.) Let me explain why.

Chandler's argument is usefully seen as being based on an idealised model of the tower, where the floors below the airplane impacts have zero mass, and hence no inertia. Also, in his model there is no energy consumed in the pulverisation of the concrete to a fine powder. The only force resisting the descent of the upper floors (above the plane impacts) therefore is due to the steel columns. In reality, of course, the lower floors have inertia, and concrete requires force to crush it. Hence Chandler's quick argument greatly over-estimates the column resistance, and so should be regarded as an upper bound rather than an estimate. The true situation is even more worrying than his argument suggests. But what really was the column resistance?

The best way to measure this from the video evidence, I think, is to use a different idealised model, based on what Kenneth Kuttler has called a "floating floor" model. In this model, the floors have inertia, which resists the acceleration of the falling block. One also includes an energy drain for the crushing of concrete, as well as a variable drain for the deformation of the columns. (For convenience, it's best to calculate using energies rather than forces, although of course the work done by a given force is simply the integral of that force with respect to displacement.) In such a model one easily calculates the downward acceleration of the top block, for a given value of the column resistance. One then adjusts that resistance value to bring the model's behaviour into line with reality, as seen in the videos. This is then a reasonably accurate empirical estimate of the mean column resistance.

What value is obtained by such a procedure? I haven't yet finished my analysis, but it is certainly very low -- much less than Chandler's upper bound of 0.36mg. I believe it is in the range 0 to 0.1mg -- somewhere around that.

2. The papers by Zdenek Bazant on the WTC collapses provide an alleged theoretical estimate that roughly agrees with this empirical estimate. Bazant compares the potential energy released as the "top block" descends one story with the energy absorbed by the plastic deformation of the columns over the same distance. He concludes (without, unfortunately, showing much of his calculation) that the energy released is at least 8.4 times the energy absorbed, so that the collapse will inevitably progress. In other words, the columns absorb about 12%, at most, of the energy released. Now, this energy fraction is easily converted to a force, using the fact that the work done to the columns must equal the integral of the force applied to them, with respect to the distance fallen. In other words, the average resistance of the columns is at most 12% of the weight of the block. This is at the upper end of what is allowed by the empirical data.

3. We see therefore that Chandler's argument will not disturb Bazant in any way, who has already accepted a much lower value for the column resistance. On the other hand, if Chandler's empirical upper bound for the column resistance is worryingly low, then Bazant's theoretical estimate is far more so! One may even wonder whether Bazant's estimate is genuine, given that he doesn't explain how he obtained it.

These darker suspicions are supported by the fact that Bazant's figure lies at the upper end of what is empirically possible. If one were to invent a figure, say to reassure the engineering community, then this would be the perfect value to choose. One would choose the highest, i.e. most plausible, value that was consistent with the data.

4. How is a non-specialist like me to evaluate the reasonableness of Bazant's upper bound? One obvious way is to compare it with the estimates of other experts. I am aware of two of these, one due to Gregory Szuladzinski in Journal of Engineering Mechanics and the other from Tony Szamboti in "The Missing Jolt", Journal of 9/11 Studies.

The estimates are similar in approach. They calculate the energy absorbed from the elastic compression, then plastic shortening, then plastic buckling of the columns. The resistive force of a column drops sharply after it begins to buckle, but it seems to remain above about 25% of the yield stress until the thing breaks ("fractures").

The outcomes of the two calculations are also similar, giving average resistances above mg, certainly far in excess of Bazant's alleged upper bound of 0.12mg. Szuladzinski and Szamboti both predict collapse arrest.

5. In JEM, Bazant replies to Szuladzinski, finding some ten or so errors in his calculation. (Although there seems to be some padding here, as correcting some of these "errors" would increase, rather than decrease, the resistance.) It is hard for me, as a non-specialist, to judge the validity of these objections, although I suspect that they are minor quibbles. It is telling, I think, that Bazant does not correct the calculation, showing what it ought to be. This indicates to me that the outcome would not be too different.

To avoid such trifling objections, if that's what they are, it would be useful to calculate a robust lower bound for the column resistance. Can we have that, please? By "robust" I mean that all reasonable allowances for lowering the column resistance have already been made, so that it is the lowest possible value. It is quibble-proof, so to speak.

I repeat (to all relevant experts): Can we have that, please?


Great work, and a great line of inquiry.

Thanks you for posting and welcome to ...

the hunt for truth.


Sounds like a good candidate for Scholars for 9/11 Truth & Justice

Thanks for your contributions to the movement.

You might also be interested in this blog post


I somehow missed that paper, but I will certainly read it now. It looks very interesting...

Good God...your paper needs to be published!

I'll defer to the experts here, but shouldn't no_body's paper be peer-reviewed and (widely) published?

It's very detailed and persuasive. Unless Im overlooking something, it's one of the best papers I've seen on the WTC "collapse."

Yes, it does

This paper should be It does an excellent job of bringing in the mass aspects and putting everything together.

I did encourage No_Body to get it published so it stays available and easy to find.

It was sent to the Journal of 911 Studies recently. If the editors are reading this I would hope they act swiftly on this paper.

Darker suspicions / fascinating puzzle

Thanks Richard. As a non-scientist, I am prone to mistakes about these kinds of things, but it seems you are saying that:

1) Bazant's estimate of 0.12mg for mean column resistance (in lower section of building) is suspiciously high. This is because--proportionately--it stands at the upper end of what is possible for the columns themselves, since other resistance factors such as inertia of concrete, pulverization of concrete, etc. will collectively provide a substantial part of the total 0.36mg.

2) Bazant's estimate is, on the other hand, extremely low, because the lower columns ought to be able to, and have demonstrated themselves to be able to, withstand much more than the 0.12mg. (This purposely repeats, and strengthens, the general idea from Chandler.)
In other words, Bazant appears to have chosen as high a number as he felt he could get away with (there's got to be at least a little resistance in the columns of the lower section), but this force (0.12mg) appears to be completely absurd--unless something removed the strength of the lower columns.

Thanks for furthering the search; there may be several Rosetta Stones for deciphering 9/11.

The values used in the Missing Jolt paper are a minimum


The values used in the Missing Jolt paper were calculated by myself and a retired civil engineering professor. We did the calculations with the intent of being conservative in the direction of providing the least resistance, so they are very likely to be the minimum. If you notice on pages 25 and 26 we explain that we use the column classifications which define their ability to sustain a full or partial plastic moment before local plate buckling occurs. At the 97th and 99th stories in question, we deemed all of the exterior columns and 14 of the 47 core columns to have the lowest rating of class 4. For the class 4 columns we considered them to not be able to sustain plastic shortening before buckling and this reduced the average plastic strain to 1.5% for all columns. During the buckling phase we then only used 0.5Mp for the class 4 columns.

If Gregory Szuladzinski came up with similar values I would assume he took a similar approach.

Since doing these calculations, and seeing just how much energy absorptive capability the columns actually did have, I asked Dr. Frank Greening to relay a request to Dr. Bazant that he provide his calculations for the energy absorption due to column deformation. I am also curious as to how he came up with only 0.12mg, and I am glad you also noticed that he doesn't provide any calculations to show how he obtained it in his paper. I made this request a couple of months ago and haven't heard anything back yet.

I don't believe Dr. Bazant considered the first floor on the bottom of the upper block (the 99th floor) in his calculations but that would only cause the energy he came up with to be about 0.55mg. I would also be willing to bet he only considered the resistance during buckling and did not calculate the elastic compression and plastic shortening energy drains by the columns before buckling. Using our figures and leaving out the above, he would have gotten 0.17mg, so it is a good bet he only considered the resistance during buckling of the lower block's top floor columns. He also considered the upper block to be in full freefall, whereas we used an actual measurement which was 71% of freefall when the first collision between floor slabs would have occurred after a fall of 11.44 feet. So Bazant's energy was 1.41 times higher than reality and dividing the 0.17mg, found with the Missing Jolt figures, by 1.41 gives Bazant's 0.12mg. I hope this gives you some insight on just what Dr. Bazant did and didn't do here.

Reprehensor has my e-mail address if you would like to contact me and discuss this further.

Great to see you posting here!

I know that I haven't been a lot of help lately, since I have been overwhelmed with other work demands right now (as you now), so I think this is a good forum to get some feedback from others.

From my quick read through your proposal, your suggested empirical method of establishing column resistance seems a worthwhile line of pursuit. I suspect though (without having tested any numbers), that developing a "robust" column resistance limit may be subject to a considerable amount of variability depending in particular upon the estimated energy loss through concrete pulverization. To a lesser extent there is also the potential for variability in the inertial and deformation energy losses. I presume that you will post your results on your new blog once you have finalized your calcs. Your work should include a sensitivity analysis that considers the range of estimates for these components. Though, if you still achieve results in the sub-unity range, then these may not be significant after all.

Clearly, if Bazant is not able to respond with analytical substantiation for his column resistances, as Tony has requested, then at the very least, we need to regard his proposal as non-conforming to the scientific method, or even the grade school method, e.g. "show your work." The peer-review process was clearly not as rigorous as it should be.


Another JEM Paper

I've also just come across this paper that I'd not seen before.

Seffen "ignores" the buckling phase in his analysis. His analysis is about 'progressive' collapse caused by column buckling and yet he ignores the buckling phase in his analysis. Unbelievable! and peer reviewed too!