The critical issue here is whether the upper block of floors would be able to crush each floor below it successively and, if so, how much its descent would be delayed by the loss of energy used up in the crushing. The paper at first appears to address this issue but on closer examination it really does not develop an answer to that question in any direct way.
First, the paper admits that the author does not know how to directly calculate the energy needed (E
1) and apparently from the wording believes that no one else knows how to calculate it directly:
Unfortunately there appears to be no simple way to calculate E1 from first
principles since the collapse of just one floor of a WTC tower is an extremely complex
process involving the bending and fracturing of numerous support structures.
Next, the paper cites someone else's estimate of E
1 but tells us that the methodology for that estimate is not disclosed:
In spite of these uncertainties, some estimates of the magnitude of E1, (the energy
needed to bring about the collapse of one floor), have been made. For example, Z. Bažant
et al. at Northwestern University, Illinois, have estimated that the maximum plastic
energy dissipated by the collapse of one floor, i.e. our quantity E1, is approximately equal
to 5.0 x 108 J. Unfortunately Bažant et al. do not give a detailed exposition on how this
value for E1 was derived, stating only that it is based on “approximate design
calculations” for one WTC tower /3/.
Next up is another citation to someone else's estimate, again with the methodology undisclosed. This estimate is not based on a direct calculation of the vertical impact of a block of floors but rather is based on a calculation of a sideways impact together with the assumption that you can equate the energy needed to crush the structure from the side with the energy needed to crush it from above:
Another calculation that may be used to estimate E1 was published by G.C. Lee et
al. in a MCEER Special Report /4/. Lee et al. assume that 36 exterior columns on WTC 1
were destroyed by the Boeing aircraft impact and conclude (without giving
computational details) that the energy absorbing capacity of these damaged columns
“does not exceed 7230 kips-ft” or about 107 J. Based on this estimate, and remembering
that one complete floor has 236 exterior columns, it follows that the exterior columns
comprising one floor of a WTC tower have an impact energy absorbing capacity of about
7 x 7 J. From the relative cross-sectional area of a core column (0.1236 m2) compared
to an exterior column (0.0184 m2), we estimate that the effective strength of the core
columns is about 6.7 times higher than the effective strength of the exterior columns. A
consideration of the collapse of the 47 core columns therefore adds about 9 x 107 J of
energy absorbing capacity. Thus, based on Lee’s calculations, the total energy absorbing
capacity of the structural supports of one floor of the WTC is estimated to be about 1.6 x
108 J, which we equate to our quantity E1 while noting that this estimate is significantly
lower than Bažant’s value of 5.0 x 108 J. However, it appears that Lee’s results are based
on very rough estimates of the energies involved so that the level of agreement with
Bažant’s estimates is as good as might be expected in view of the approximations
involved.
Finally, another citation to someone else's calculation that, like the previous one, depends on the assumption that a vertical impact needs the same energy as a sideways impact to crush the structure. It's not totally clear but let's give benefit of the doubt that the cited paper in this case does explain its methodology:
A much better estimate for E1, and one that is based on a very detailed analysis of
the aircraft impact events, may be derived from a paper published by T. Wierzbicki et al.
at MIT /5/. These authors have calculated the energy dissipated by the wing of a Boeing
767 cutting through the exterior columns of a WTC tower and report a value equal
to 1.139 x 106 J per column. On this basis, 2.69 x 108 J would be require to cut through all
236 exterior columns supporting one WTC floor. If we now assume, as previously
discussed, that the yield strength of the core columns is about 6.7 times higher than the
yield strength of the exterior columns, we estimate that an additional 3.60 x 108 J are
required to collapse the 47 core columns supporting each floor. Thus, based on T.
Wierzbicki et al. calculation, we estimate a total of 6.29 x 108 J of impact energy was
required to collapse one WTC floor, a value that is remarkably close to Bažant’s estimate
of 5.0 x 108 J for the plastic energy dissipated by the collapse of one floor.
So, keeping score, the author first admits that no one knows how to calculate the needed quantity directly, then cites one estimate of undisclosed methodology, followed by an estimate that is based on a sideways impact rather than a vertical one and does not disclose its methodology and then finally cites another estimate that is based on sideways impact but that apparently does disclose its methodology. The author finds some comfort in the fact that these three estimates, each one of dubious origin, are all in the same ballpark and then adopts the third one for the purposes of the rest of his paper (the estimate of 6.29 x 10
8 J that I bolded in the last excerpt).
I'm going to withhold judgement until structural engineers can do the math directly on a vertical impact. This sideways impact stuff isn't convincing to me since I have no way of knowing whether the assumption that vertical impact and sideways impact will be equivalent is valid or total bunk. It seems far fetched to say that we don't know how to calculate a vertical impact because it is too complex but still we somehow do know that a sideways impact would be the same and can be used as a surrogate.
Edit: minor wording