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Background Attack Aftermath Evidence Misinformation Analysis Memorial

Bazant and Zhou

Explaining the Collapses With Elastic Dynamic Analysis

Zdenek Bazant and Yong Zhou must be super-geniuses. They were able to understand how two skyscrapers could crush themselves to rubble, a newly observed behavior for steel structures, and write a paper about it in just two days. 1 Their "Why Did the World Trade Center Collapse?-Simple Analysis" uses "Elastic Dynamic Analysis" to confidently proclaim:

The structural resistance is found to be an order of magnitude less than necessary for survival.

The paper repeatedly claims to make the most optimistic assumptions about building survival with no discussion of what that means. It contains nonsensical engineering claims such as:

[... if the] majority of columns of a single floor to lose their load carrying capacity, the whole tower was doomed.

There are two major fallacies in this assertion:

  • It implies that the columns were capable of supporting only twice the gravity loads they were bearing above the impact zone. This ignores the fact that the upper floors, lacking standing-room-only crowds, were not carrying their design live loads, and it implies that reserve strength ratios (the extra strength designed into a structure beyond what is required to resist anticipated loads) are two-to-one instead of the five-to-one typical in engineered steel structures.
  • It implies that a failure of the columns to support the gravity loads above the impact zones would automatically lead to total collapse, despite the absence of a single example of a local collapse event leading to total collapse in any steel-framed building.

The paper mislabels phenomena, calling a fireball a blast. It is fond of vacuous qualifiers. It explains the buildings were doomed because after the first story collapsed, there was enormous kinetic energy and enormous vertical dynamic load, far exceeding [the columns'] load capacity. And with even larger mass falling with a greater velocity we get impacts and failures all the way down. It makes quantitative claims but doesn't back them up. Where did they find the following 12%?

(indeed, the energy dissipated in the columns during the fall is at most equal to 2X the yield moment of columns, X the number of columns, which is found to be only about 12% of the gravitational potential energy release if the columns were cold, and much less than that at 800 C).

The whole argument seems to be based on some (undisclosed) estimate of bending moments, in which case one of their simplifying assumptions seems to be that the columns are infinitely thin and have no compressional rigidity. The paper gives no argument that the model it is applying is applicable to the survivability of the Twin Towers. It makes sweeping claims that can't possibly be true. It's evasive, claiming to make only simplifying assumptions optimistic to building survival, without even bothering to list those assumptions.

One of the paper's assumptions it does disclose is that all of the columns of the first story to collapse were heated to 800 C. In that case they would have been glowing red-hot. Perhaps Bazant and Zhou can be forgiven for this oversight and for their wildly inaccurate engineering assumptions, given the short publication deadline they had to meet.


1. Why Did the World Trade Center Collapse?—Simple Analysis, Journal of Engineering Mechanics ASCE, 9/13/01

page last modified: 2007-01-17