(In a
previous post, I inadvertently reversed Bažant
et al's labelling of the sections. In their papers, section C is the upper block and section A the lower. If you substitute C for A and A for C throughout that previous post, it will make more sense.)
With respect to the model's assumption of vertical homogeneity, I see two possible problems with applying that assumption to the WTC towers:
- The mechanical floors might have been different enough to matter.
- Differential collapse rates between the core and the area outside the core, if combined with significant interactions between the two, could conceivably invalidate the assumption of vertical homogeneity.
If I understand you correctly, your objection to vertical homogeneity may be based upon the second of those problems. If so, that's really a problem with the one-dimensionality of the model.
If we dismiss the failure of the outer flooring system, do you think the model can be more reliably applied to what is left?
I'm not sure exactly what you mean by "dismiss"; in any case, you're asking me to speculate outside my competence. With those disclaimers...
As built, the WTC towers satisfied the assumption of vertical homogeneity pretty well, and that continued up through the beginning of the collapse, modulo the weakened state of impacted floors.
If (as
femr2 may
* be arguing) the downward progression of floor failures outstripped the downward progression of perimeter and/or core failures, then Bažant
et al's assumption of vertical homogeneity would begin to be violated, because sections in which the floors had failed but the perimeter and columns had not would be different from the lower section in which nothing had yet failed. That could make it more difficult or impossible to apply the model(s) to the later portion of the collapse, when the lag was greatest, although it might be possible to work around that problem by treating the frontier of floor failure as the lower crushing front.
I don't think I've seen anyone make that argument, possibly because few people believe that floor failures could have gotten very far ahead of perimeter and core failures.
If floor failure led perimeter and core failure, but not by much, then Bažant
et al's assumption of vertical homogeneity remained approximately true and their model(s) should remain approximately applicable (with appropriate parameters).
That said, I'm not an engineer.
†
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* I don't pretend to understand what (if anything) femr2 has been saying, and I no longer try.
† My areas of competence are not radically different from those of David B Benson, the fourth letter in BLGB.
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