# 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 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:

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

*and*

**enormous kinetic energy**

**enormous vertical dynamic load,***And with*

**far exceeding**[the columns']**load capacity.***we get*

**even larger mass falling with a greater velocity**

**impacts and failures***It makes quantitative claims but doesn't back them up. Where did they*

**all the way down.***find*the following 12%?

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 800º 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.

References

*Journal of Engineering Mechanics ASCE*, 9/13/01