...The homogeneity was their explicit simplifying hypothesis (4), which doesn't seem altogether unreasonable to unqualified lay folk like me....
..but on the face of it that assumption does not apply to WTC1 and 2. Threfore I questioned it. And the sequence of my recent posts will show that I have expressed no doubt that 'homogeneity' is valid for a conventional generic building. I have expressed doubt that it applies to WTC with two provisos as to how I could modify my opinion.
The model is one-dimensional, so the assumed homogeneity is vertical. Here is the assumption and its motivation as described by Bažant and Verdure:
Bažant and Verdure 2007 said:
(4) The stories are so numerous, and the collapse front traverses so many stories, that a continuum smearing (i.e., homogenization) gives a sufficiently accurate overall picture.
...As for your complaints about the columns,...
Sorry but it is not "complaints", discussion, investigation, questions, doubts but not "complaints". Complaints belongs with those who are prepared to defend what they think is Bazant et al at any cost to logic and courtesy of discussion.
So neither you nor I have any complaints about Bažant
et al.
I, however, have quite a few concrete criticisms of Bažant and Verdure's paper. Unfortunately, my concrete
complaints criticisms involve fairly insignificant errors, most of them easy to fix. I'd like to have stronger grounds for disliking the paper.
Witness the abusive posts littering the thread by those who would deny me and others the right to ask "How far is Bazant's work applicable in the real world?" I will not aquiesce to such bullying. Nor will I claim complete assurance in areas where I an not 100% certain.
Fine. Perhaps you can understand why I am not inclined to acquiesce to your incomplete assurances.
The source of Fc is the main difference between application to a generic model and application to WTC. and "Applicability...to the real world [including WTC]" is the topic under discussion.
No, the source of F
c is part of the
motivation for the model. If a model is reasonably accurate given its assumptions, then it should be possible to apply the model to any situation that comes sufficiently close to satisfying those assumptions, even if the situation to which the model is being applied bears no other resemblance to the motivating example.
....but the source of the resistance and its magnitude are the core issue of interest in determining how far Bazant is applicable to WTC.
The magnitude is relevant, but I don't see why its source should be. As explained above, the explanation you have given so far fails to convince.
...How is your scenario not modelled by reduced Fc?
...which is exactly what I have proposed myself but have had no response prior to your comments which do, at least, approach the issue.
To argue that a mathematical/scientific/engineering model does not apply to a real situation, you need to identify an error in the model's mathematics, science, or engineering, or you need to identify an assumption of the model that is violated by the real situation.
To identify an assumption of the model that's violated by the real situation, you have to identify the assumptions of the model. That can be difficult, especially when the model is described so poorly. It seems to me that you have been confusing the BV model's motivation with its assumptions.
You have also asserted that explicit assumption (4), quoted above, does not hold for the WTC towers. That would be relevant for collapse initiation, but my layperson's intuition says vertical homogeneity might be a reasonable approximation for the WTC towers when describing their collapse progression. If a qualified expert were to explain otherwise, I would listen.
Bažant and Verdure probably made some tacit assumptions. That usually happens, even in papers that are much better written. If a qualified expert were to identify tacit assumptions of their model that do not hold for the WTC towers, I would listen to that also.
I'm not denying your qualifications or expertise, and I know you think you've provided adequate explanations of your position. What I have written above may help you to understand why I am not fully convinced by your arguments.