Exodus 2006 : Keith Seffen's paper

Thursday, December 20, 2007

Dr Keith Seffen's paper - "Progressive Collapse of the World Trade Centre: a Simple Analysis"

Dr Keith Seffen's paper is now available here -

"Progressive Collapse of the World Trade Centre: a Simple Analysis"


Having now read it, a few comments, focussing mainly on the applicability of the model developed in this paper.

The applicability problems are mainly the result of assumptions developed in the introduction. To quote from page one -

"Those factors responsible for the onset of collapse are now well established. Despite localised and substantial horizontal impacts by fuel-laden aircraft, both towers survived until the intense fire compromised the ability of the remaining, in-tact columns close to the aircraft impact zones to sustain the weight of the buildings above them. The subsequent near free-falling of these upper parts over the height of just one storey resulted in dynamical “over-loading” of the relatively undamaged lower columns by a factor of 30 compared to their static load capacity, according to Bazant and Zhou (2002).

We can also argue, I think, that it is not "well established", and is speculative and not evidence based. The same might be said about the "intense fires" and of the nature of the failure of the "in-tact columns". Even so, it is a big leap from there to the next sentence, "the subsequent near free-falling of these upper parts" - thus going from "compromised" to a presumed simultaneous disappearance of all the columns, just like that.

As often elsewhere in this paper, he then cites Bazant and Zhou, as the authority to cover an otherwise surprising conjecture. This fire-generated "freefall" is important though, because that is all they have available to provide the initial collapse energy.

Seffen goes on to say this of Bazant and Zhou -

"They argue that the storey immediately below bears the brunt in terms of a localised, plastic buckling of its columns, and they show that the commensurate dissipation cannot arrest the motion of the falling part, leading to a sustained collapse."

Gordon Ross has done the best debunking of Bazant and Zhou that I have seen so far. -


Bazant and Zhou ignore the elastic deformations, and they only looked at the "storey immediately below", as if it was stood on the ground in isolation. Elastic deformations are the "springiness", which famously allowed the towers to sway in the wind, and which is characteristic of steel. Gordon Ross' analysis shows that this giant spring would have made a huge difference; and therefore the collapse would have been arrested with only minor buckling.

Seffen then gets on to his "propagating instabilities", page 2, saying, "damage accrues in a prescribed fashion following an initiation phase. Depending on the local collapse behaviour inveigled by the instability sweeping through the initially undamaged structure". Usually, it is normal in such cases to be able to point to some physical details, about the materials and the geometry, that allows this "instability" to propagate; but in this paper it is not developed beyond a series of floors being squashed.

Next, a rare comment that indicates the actual details of the collapses were ever studied. -

"It is also clear that both collapse modes were progressive, as indicated by film footage: there was the sound of each successive impact of floor upon floor and a matching sequence of lateral ejection of debris."

It is clear that he didn't notice that the top sections of the towers disintegrated first, into plumes of debris, before the collapse wave moved down the towers, thus totally invalidating their "freefall impact" idea as the power source to propagate the instability through the undamaged structure below.

See this photostudy of the collapses -


and also Gordon Ross -


I am also surprised he is saying "there was the sound of each successive impact of floor upon floor" since it doesn't seem that clear-cut, to me, particularly since some are heard just before the collapse. The video "911 Eyewitness" has a good study of this subject.

In the section titled "Progressive Instabilities", page 5, Dr Seffen gives another account of the collapse initiation -

"For both WTC towers, the distributed nature of the aircraft impact sites resulted in a reduced but uneven cross-sectional stiffness over several floors due to differing degrees of missing and deteriorating material.

As the most severely affected columns gave way at one level within the impact site, the upper parts fell onto an already weakened cross-section compared to the rest of the building further below.

The resulting impingement produced peak forces correctly identified by Bazant and Zhou (2002) to be far in excess of the design capacity of these columns and hence, above the expected value of “Pmax ” (Fig. 1) that could be reasonably carried by them, even if perfect and undamaged. These columns began to deform plastically, thereby seeding failure of this, next part of the structure."

This sounds almost reasonable, if you believe in the "intense fires", and sudden weakness in hot steel, and it sounds like the collapse would be strongly asymmetric. With a few more cites of Bazant and Zhou, in the next few paragraphs, this problem is avoided by having all columns, in the model, buckle in unison and in a one-dimensional and linear way.

Using this simplification, the mathematical model is then constructed, and by the end of page 7 we have a result from the model indicating that it only has a quarter of the usual static strength when hit by a progressive instability.

Interestingly, on page 8, he considers some other factors that might make the model seem unrealistic; including elastic buckling -

"The magnitude of this ratio can be very large, but elastic buckling of the relatively stocky WTC box columns is unlikely. Instead, Bazant and Zhou (2002) suggest that, more realistically, the columns fracture under very little bending immediately beyond the squash load, thereby removing the softening phase altogether in Fig.2. "

The only reason that the WTC columns can be regarded as "stocky" is because they are only looking at one floor at a time. In reality the columns were going from top to bottom, and this is where taking each floor in isolation is a false approximation. The extensive cross-bracing, within the structure is, another issue that is completely ignored by the model.

In the next section, titled Dynamical Model of Collapse, we have this -

"Lateral stability is not considered in view of the near vertical collapse of both WTC towers."

In other words, since both the towers collapsed completely vertically, there is no reason to consider why they might have gone asymmetric.

Also, we have -

"The building everywhere above this floor begins to accelerate downwards as a rigid undamaged body when, at time t = 0, it impinges on the floor and columns beneath, which are assumed to fail in the manner proposed in the previous section. The instability is formed as a level “crushing front”, its propagation is compatible with the uniform compression of successive storeys,"

A "rigid undamaged body" acts as a hammer and destroys the rest of the building, except as pointed out earlier, far from being rigid and undamaged, it can be seen to disintegrate into a plume of debris first. Therefore we know this mechanism being described did not happen, and the model takes no regard of the obvious loss of mass as the debris falls away. The way the model relies on the top section, the most lightly-built part, to behave as a rigid body while destroying the larger and most strongly-built section, is also worth considering.
On page 13, he says -

"Thus, it is entirely appropriate to move the study forward within the spirit of using Eqn 10 directly, for it is assumed primarily that dissipation is confined to quasi-static deformation in the columns and that the progressive nature of collapse demands a continuous mass entrainment."

It demands a "continuous mass entrainment" - unlike what was actually observed.

Then on page 14 -

"As argued in Bazant and Zhou (2002), it is likely that the uppermost parts of the WTC towers were falling freely due to an absence of column resistance in the first weakest storey"

I wonder if Dr Seffen considers it "likely" himself, or if he just modestly prefers the credit to go to Bazant and Zhou once again.

The model is then further developed, to finally produce graphs representing possible collapse times for the towers, had they suffered this type of collapse, against varying levels of resistance, from zero up to a point where the resistance would have arrested the collapse. This then allows the strength of the towers, against this type of progressive instability collapse, to be read off the graph by using the observed collapse times. There is no discussion about the variation of this figure between the two towers.

It would be interesting to see a computer simulation of the collapse described for the towers by this model - I am sure it would look most unlike what was actually seen.
I did wonder what real situation this model would in fact model. Two ideas have come to mind. A vertical stack of empty Coke-cans crushed by dropping a brick - provided those lateral instabilities were dealt with somehow. You can then calculate the downward speed of the brick crushing the tins.

Another is the Kung Fu exhibition stunt where somebody punches down through a stack of roof tiles. You can probably estimate the maximum number broken for various amounts of available continuous punch-force. Maybe not the most useful idea…

Dr Seffen's acknowledgements -

"The author is extremely grateful to two anonymous referees for insightful and supporting comments."