The upper section was continuously accelerating and velocity was continuously being gained but at the rate of about 0.7g, a slightly slower rate than freefall. The work done to continue the collapse through the remaining 0.3g resistance was not done by kinetic energy transfer but by the force of the static weight on a structure which could no longer support it. Which is amazing, as it was designed to provide 10 times that resistance to the upper section load and the aircraft impact damaged only about 15% of the columns and the columns were not affected enough by fire to justify it either. The NIST doesn't even have any columns which show they experienced enough temperature to weaken them. The structure obviously fell apart for some other reason.
The structure was designed to support a load -- that is, apply an upward force -- of up to some multiple of the actual load. (You say 5x the actual load, others say less, I'll accept your 5x figure for the sake of argument.)
What it was not designed to do was apply that force over a distance.
I did some quick calculations. After the top block had fallen 3 meters at 0.5 g acceleration, a velocity decrease of 1 m/s would have required the structure below to apply its maximum force of 5x the static load, for a period of about 0.1 second, while deflecting a distance of a third of a meter. This is getting very close to Heiwa's "rubber building" territory. (See his "Funny M" essay in which the building elastically compresses 3% of its height under its own static weight, and can compress 9% before reaching the elastic limit.)
So I went to see where your paper differs from my calculations, and found that you had not even attempted to calculate the forces acting over distances involved in creating the jolts you were looking for. Instead, you went over to the energy domain, which is where things went wrong.
In your energy calculations you have assumed that when the top structure reaches the next floor below, all of the following happen instantaneously and simultaneously across the entire acre-sized cross-section of the tower:
1.
every column undergoes its maximum elastic compression
2.
every column undergoes inelastic axial compression up to its axial strain limit
3.
every column then buckles on three hinges until squashed flat
4.
every column actually does this
twice, above and below the impact point!
I understand that these are analogous assumptions to Bazant's, but the difference is that Bazant was evaluating a limiting case for
least favorability for complete collapse, to show that collapse is expected even in such an unfavorable case. You are evaluating a limiting case
most favorable to produce a jolt.
If, after having done so, you observed a jolt larger than your most favorable case suggested was possible, then you might reasonably conclude that some other unknown factor was responsible for producing such a large jolt.
But from the fact that you did not observe a jolt as large as your most favorable case suggested was possible, you can conclude nothing at all. All it shows is that your most favorable case assumptions are too favorable and didn't happen.
This could be for any number of reasons, many of which have been discussed on this thread: the impacts were not column on column in perfect vertical alignment; the impacts were not uniformly timed across the area of the structure; the columns failed at welds prior to, and instead of, undergoing maximum axial plastic strain or 3-hinge bucking; the floors detached from the columns leaving the columns less braced against buckling. All of these possibilities are themselves supported by observation.
If you want to ascribe significance to a missing jolt, you will have to show that a jolt larger than those observed is to be expected under assumptions representing the
least favorable plausible case for producing a jolt. That is, redo your calculations with an initial tilt corresponding to the tilt observed in photographic recordings, and in which the only energy absorbed apart from momentum transfer is from breaking the bolts connecting the columns to the floors and then breaking the columns at their welds. If under those less-jolt-favorable conditions you still can show an expected jolt that exceeds observations, then you might have something.
Respectfully,
Myriad