Ergo,
In referring to a post by 'X', you said:
I'm not sure if your math is completely correct.
I just wanted to say (as someone with a PhD in math) that I am sure that his math is completely correct.
Also, regarding the video you posted, I would mention that experiments are useless unless you can show that your experiment is a valid test of the phenomenon you are investigating - that video did nothing but compare apples to oranges. Badly.
As I understand it, your hypothesis is that after the collapse was initiated (however it was initiated) and the upper block dropped through the height of 1 floor, the intact floors below the impact zone should have been able to arrest the collapse. Let's put this in a context that we can wrap some math around. In order for the collapse to arrest, the intact columns must retain the capacity to support the load of the upper block
AFTER they absorb all of the kinetic energy left after the upper block impacts the lower block (i.e. after they halt the motion of the upper block). Using conservation of momentum we can determine the velocity of the two floors that impacted each other and hence their kinetic energy. After impact the columns below the impact will be exerting force to slow the impact floors (now moving slower than the rest of the upper block) and the columns above the impact floors will be exerting force to slow the rest of the upper block (and transmitting that load to the impact floors). If we assume that the lower block can exert a force equal to the weight of the building times the safety factor (roughly accurate) then the lower block can at best decelerate the upper block by (safety factor) * g. In order to dissipate the kinetic energy of the upper block, the columns of the lower block must exert force over a distance (i.e. they must do work)
If we do the math (using the floor by floor masses given by Gregory Urich in the Journal of 9/11 studies and basic physics - I'll show my work upon request) for an impact between the 95
th floor and the 94
th floor we find that immediately after impact the combined floors are moving at about 4.24 m/s and the rest of the upper block is moving at 8.5 m/s - a total mass of about 40 kilotons with 1.36 gigaJoules of kinetic energy and that if the columns of the lower block can continuously exert the maximum amount of force possible they would have to compress at least 3.4m divided by the safety margin in order to dissipate this kinetic energy. Think about it - if the safety margin (the number of times its own weight the building can support) is 6, then the columns would still have to compress over half a meter in order to dissipate the kinetic energy and while they were doing this they would have to retain their full strength while heating up (that's how they dissipate the kinetic energy) significantly. It seems all but certain that in the case of the WTC the top of the lower block would be unable to exert its maximum force due to weakening by damage and fire and the fact that the weight would not be bearing where it was designed to (along the columns), but more generally spread out along the floor pan. There would be no rubble before this first impact, so you've got no missing mass and a damaged floor to try to catch a 40 kiloton mass with 1.36 gigaJoules of kinetic energy which at best (in a unphysically optimistic scenario) would require more than half a meter to do. Talk to a structural engineer and ask them if steel columns can perform this way. If the first floor impacted cannot survive, can the second fare any better? With a collapse speed of around 8.5m/s most of the newly created rubble will be unable to exit the footprint of the building (unless you can suggest a method that will impart greater lateral velocities to the rubble) and the mass will roughly double the kinetic energy that the next floor with have to deal with. It rapidly becomes totally inconceivable that a floor could survive. If you still think that the collapse should have arrested after one floor, please tell me how the kinetic energy of the upper block would have been dissipated.