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'Some Misunderstandings Related to WTC Collapse Analysis'

Gregory Szuladzinski, Anthony Szamboti and Richard Johns

"Some Misunderstandings Related to WTC Collapse Analysis"

International Journal of Protective Structures.

Mod note:
Original direct link to pdf was replaced with a link to the abstract, the publisher will release the paper for free use on Jan. 1, 2014. There is currently an 18 GBP ($27.00 USD) copy fee charged for those without a subscription to the journal. However, copies can be sent to individuals for personal use by the authors and anyone they send it to. If you would like a copy, please send a request via:

Errors in Progressive Column Failure (PCF) Collapse Hypothesis

Following (perhaps substantially oversimplified) is my take on the key errors identified in the PCF hypothesis by the authors of this paper:

1. Adherents to the PCF hypothesis (Bazant's theory) underestimated the energy absorption capacity of the buildings' columns as they begin to deform. PCF doesn't take into account the stoutness of the World Trade Center columns.
2. PCF's underestimate of the strength of the deformed columns leads to an assumed free fall for most of the crushing of the first story. Measurements of the actual collapse of that floor demonstrate a constant speed consistent with significant resistance from deformed columns. The building did not approach free fall acceleration in that first story as assumed by the PCF model.
3. Evidence in the model and from statements within the papers of the PCF adherents demonstrate that the PCF hypothesis ignored the fact that the collapse began as a static event.

Other errors identified in the PCF theory of World Trade Center (WTC) towers collapses:

1. The mass of the upper portion of the building above the crash site was significantly overstated as used in the PCF model.
2. Other papers have demonstrated that even when making the PCF erroneous assumption that columns quickly lose strength after they begin to deform, the total collapse time couldn't be less than 15.3 seconds. Since the collapse was much faster and since the starting assumption of columns giving way to free fall (giving the upper part of the building more speed as it comes to the end of the collapse of the first story) are demonstrably wrong (based on measurement of the buildings collapse speed), the PCF theory is not a viable hypothesis of the collapse.


In order for PCF to work one must substantially over estimate the weight of the upper collapsing portion of the building, substantially underestimate the strength of deforming columns, and model the collapse as a continuous (non-static) event in a set of black box differential equations rather than a floor-by-floor explanation of the event. These errors in the PCF approach mean that the smooth and fast collapse of the WTC towers have not been shown to be a "natural gravitational collapse."

Awesome summary

Thanks, PR.

Is this correct though? "Measurements of the actual collapse of that floor demonstrate a constant speed consistent with significant resistance from deformed columns. " I would think it's more like "constant resistance from deformed columns." Perhaps one of the authors can comment.

The fall through the first story was measured at 5.11 m/s^2

acceleration, producing a velocity at the end of the first story of the fall of 6.13 m/s. This is far greater than what the resistance of the columns in a heat weakening situation would have allowed. The paper comments (at the top of page 7) that this is yet another indication that PCF does not explain the collapse.

Thanks, Tony

Did I miss anything serious, or misstate the case you made?

No, just the point picked up by jnelson

Otherwise you show you understood what the paper says fairly well.

The bottom line is a natural fall through heat weakened buckling columns would have been slow and the collapse would have easily arrested after one story. However, even giving the actual kinetic energy of the fall (no matter what the reason) using the actual fall velocity and actual mass, the fall should have been arrested in one to two stories if it was a natural event.

Bravo, Tony

Thank you again!

The paper calls out 3 fatal

The paper calls out 3 fatal mistakes in Bazant's PCF approach:
1. The gross underestimate of the energy absorption capacity of the squashed columns
2. After the initiation of failure of the critical story, the columns in that squashed story were assumed to offer only negligible resistance
3. A visible confusion between statics and dynamics: the initiation of motion took place in a static environment but Bazant ignored this, saying that what matters is energy, not the strength, nor stiffness

Thoughts and questions re collapse

Thanks to those who wrote this paper.
Wish I had the expertise to better understand it, but it seems a solid critique.

Wondered about this portion..
" ..320.45 × 106 kg for the whole tower. When this mass is divided by 117 floor levels (for 110 above-ground stories, 6 sub-levels, and the
roof) it gives a single floor mass of 2.74 × 106 kg. "

Does this take into account the difference in mass from the top to the bottom of the tower?
As I understand, the core (box) columns at the top are approx 1/2" thick vs those at the bottom being nearly 5" thick. Since the number of core columns is the same from top to bottom, then wouldn't this approx 10x thickness difference result in significant mass difference from top to bottom? -similar with the external columns/mass as well.

One result of the mass difference would seemingly be that it would thus be all the harder for the much thinner+lighter columns at the top to overcome the increasing thickness/mass/strength. Structurally, that would be akin to the upper section of a pyramid (such as at Giza) somehow smashing all the way down against the ever-larger/widening lower structure. Seems unlikely.

Also, considering how there would be a 'crush-up' as well as a 'crush-down' effect of the upper section of the tower moving downward would be all the more pronounced (crush-up effect, that is) as the upper section was increasingly mangled and encountering ever-thickening/stronger columns below.

So is this a valid consideration to collapse analysis? (that is, the apparent 10x difference in column thickness, thus difference in column mass & resistance, etc)

Also, how could random damage and fires result in what appears to be a mostly symmetrical collapse (in all 3 towers)? Wouldn't the initial deformations lead to rapid loss of integrity in those sections.. thus causing a highly Asymmetrical...topple-over style collapse? -assuming there was insufficient arresting of downward momentum.

Seems these 3 towers required at least some degree of controlled demolition to come down completely in the way they all did.. especially considering most known controlled demolitions of tall buildings do not appear very elegant..asymmetry, tilting, etc.

column mass per story vs. story mass


The 2.74 x 10e6 kg is an average mass per floor per se used in the description of the upper section and to derive it from the overall mass. But it is very close to what it actually would have been for all floors in the towers, as the structural steel is a small fraction of the mass of each floor and the difference in column size does not make that much of a difference. There were floors in the lower stories of the tower that were close in weight to those in upper stories.

If you are interested in estimated individual floor masses and structural steel mass per individual stories you should see Gregory Urich's mass analysis of the Twin Towers here

Gregory came up with an average floor mass of 2.46 x 10e6 kg and overall tower mass of 288.073 x 10e6 kg in his estimate, which was slightly lower than what we used in the paper. That was because we needed to stay with what the NIST had for actual loads. That was still a lot lower than the maximum design load mass used in Zdenek Bazant's analyses. The maximum design load was not what was actually on the building and should not have been used for failure analysis.

Column mass, etc

Thank you for responding and for providing the helpful mass-analysis link.
That makes sense when factoring in the other masses per floor (in addition to the columns, presumably incl external columns).

In this paper, were you considering/factoring the increasingly resistive strength of ever-thickening columns (core & exterior)?

Also, if there is at least an equivalent 'crush-up' effect (compared to crush-down), then the upper section--as any kind of unified block-mass--would seemingly be destroyed within approx a dozen floors (for North Tower). Thus, having very little unified mass to continue crushing down, right (esp with some of the mass going out over the sides)? -keeping in mind your analysis indicating the resistive forces should readily arrest the downward momentum Well before a dozen floors are destroyed.

Is it an apt analogy to consider, "I'd much rather stand under 200 lbs of sand (not unified) being dropped on me than under a 200 lb iron ingot.." ? -I'm trying to think of ways to characterize the physics so anyone can immediately/intuitively perceive the points.

Dave,The paper is really about

the failures of the first several stories of the collapse which is predominantly where the unnatural portion occurred.

As for the loose material argument it isn't all that strong in my opinion. While it is true from an impulsive load (impact) perspective, once there was enough rubble the floors would fail in a quasi-static way. Of course, that would take about ten stories worth of rubble, so this could not happen right away.

Scale model?

Thanks again, Tony--your responses are very helpful.

One last question.. would it be feasible to construct a scale model of a Twin Tower or WTC7--then test by applying damage/heat?

More to the point, if a decent scale-model could be fabricated, would it likely yield helpful information? -that is, does structural integrity scale up/down in predictable ways?

Scaled models for structural testing aren't that simple


To do an appropriate scaled model for a structural failure test would require much more than just scaling the size. The properties of the materials and the structural section need to be scaled properly also, and this would involve more than just being a size only scaling. There are things like moment of inertia, that affects bending stress, which is a function of the depth of the structural member cubed.

Moment of inertia of a rectangular prismatic section = 1/12 x width x depth^3

For example, the moment of inertia of a solid 14 inch square box column is 3,201.33 in^4. A 1/100 scaling of this property would have a moment of inertia of 3.21033 in^4.

If you were to simply scale it down by 1/100, due to size only, to a .140 inch square box column, you would have a moment of inertia of 0.0000321033 in^4. This would scale to 1/100,000,000 for that property. Since it is a function of the cube, the attempted scaling of 1/100 would be off by a factor of 100 x 100 x 100 = 1,000,000 or a million times for that property.

Buckling loads are a function of the length squared, so this is another non-linear property that would cause a problem with a size only scaled model.

Deflection of beams with vertical loads is a function of the length cubed (this is in addition to the moment of inertia issue with the cross section) and this would affect the test.

Although models scaled for size and shape can be useful for visual presentations, structures don't lend themselves to scaling for actual load testing very well. The best model would be an actual size section of the building and barring that an FEA computer model.


That's fascinating how the material/structural properties play out so differently with scale. Thanks so much for explaining.

Sounds like it would be extremely problematic to properly (physically) scale the structural aspects, so maybe with advances in computing (where performance doubles approx every 18 months), it will get easier to do computer modeling that could prove helpful.

Many of us greatly appreciate your expertise and time, Tony.

Summarizing this paper for people in general

Tony, how can we summarize your paper when providing an introductory discussion on peer-reviewed literature?
Is it correct to say that the latest developments in peer-reviewed civil engineering literature show that the WTC towers should not have failed?

Thanks for your hard work.



David Chandler posted a short summary of the paper on his site, part of which was taken from an explanation I had sent out with e-mails.

No reason you couldn't use what was already done, if it works for you. You can see it a third to halfway down the page here

I don't know that you can honestly say the latest developments in peer reviewed civil engineering literature show the towers shouldn't have failed. Of course, you should read Jonathan Cole and Timothy Eastman's survey of all of the peer reviewed literature on the towers here

It won't include the new paper by G. Szuladzinski, R. Johns, and myself, as it was not out when they wrote that paper, but it will give you an idea of what has been put out in the last few years prior to 2013.

Controlled demolition proven, why is there a debate?

It's just impossible to be anything other than a controlled demolition by basic physics. There is no debate.

FACT 1: An object falling under gravity cannot accelerate through resistance greater than the weight of the falling object.

The north tower  accelerated through the lower section at a uniform 64% freefall, which means that the lower section exerted resistance equal to 36% of the weight of the upper section, Newton's third law of equal and opposing forces states that the top block thus exerted 36% of it's weight, which means it’s exerting much less force than when supported at rest. This means a large portion of the resistance was removed by explosives.
Also the top section after collapsing the distance of 1 story did not slow at all upon encountering the intact lower section. This is impossible as a falling mass cannot crush MORE resistance and maintain the same speed, it slows. The mass continued to accelerate uniformly proving explosive demolition.

FACT 2: Newton's third law states that colliding objects exert equal force on each other, which means that for every floor destroyed in the lower section, a floor must be destroyed in the falling section, therefore after 15 floors there is no piledriver left, it would slow down before then anyway, as the mass of the falling object is reduced and energy is absorbed through disintegration and the superior upward resistance.

FACT3: The top section of the south tower topples to an angle of 22 degrees. Basic physics shows that the shift in center of mass due to the angle means that any torque imparted by gravitational pressure on the lower section accelerates the rotation of the top mass. The base of the top section acting as a fulcrum. The more gravitational pressure the top section provides, the more toppling would occur. discontinuation of toppling proves the removal of resistance, disproving gravity induced collapse and proving explosives.
An off centre, leaning mass CANNOT cause a symmetric collapse.

FACT 4: The symmetric, even collapse of WTC7 is IMPOSSIBLE without demolition as all structural supports must be removed simultaneously across each floor, and this repeated in sequence for each successive floor.this is impossible in a collapse resulting from structural or fire damage, as such causes result in organic uneven damage. even a slight integrity inequality ALWAYS leads to a messy uneven and in most cases partial collapse.

FACT 5: The 2.5 seconds of Freefall in WTC7 that NIST admits to is IMPOSSIBLE without Controlled demolition as all structural supports must be removed ahead of the collapse front, otherwise ANY intact structural resistance would slow the collapse to a rate less than freefall.