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NIST, in essence, agrees with Major Tom. Shall we all just take note of that for a few moments.
From NIST FAQ.
http://www.nist.gov/el/disasterstudies/wtc/faqs_wtctowers.cfm
Since the dynamic amplification factor for a suddenly applied load is 2, an intact floor below the level of collapse initiation could not have supported more than six floors. Since the number of floors above the level where the collapse initiated exceeded six for both towers (12 for WTC 1 and 29 for WTC 2), neither tower could have arrested the progression of collapse once collapse initiated. In reality, the highest intact floor was about three (WTC 2) to six (WTC 1) floors below the level of collapse initiation. Thus, more than the 12 to 29 floors reported above actually loaded the intact floor suddenly.
This is a simplified model description of the collapse but NIST is saying that the floor to column connections were massively overloaded. That is not to say that an entire floor pan failed in one piece(so-called 'pancake' collapse). It standsa to reason that in a structure that was damaged more by impact in some regions, that those areas saw failure earlier. It stands to reason that a tilted upper , falling mass would impact lower regions on its lower edge first.
AFAIAC , MT's details as to what portion of the building went first is the only part that may be debated , and that's not really relevant to a characterization of how the collapse progressed.
Upper mass began coming down. Columns sections of upper falling mass CANNOT, at that time, be aligned with their original lower sections. THEREFORE the structures that will be hit by this falling mass is, by a vast margin, the floor pans. The only debate then would be what fails first, floor pan or truss connections to columns. (and it hardly matters, if either fails then collapse progresses further, mass increases, velocity increases, and collapse just keeps going. Columns are left there with nothing supporting them laterally)