Redistribute isn't really the right word concerning why an amplified load was needed to continue the collapse. The steel frame below was designed to take a significantly higher load than what was on it to provide a margin of safety.
But redistribute is the right word to describe how a structure handles the load that is sitting on it above. A properly designed building is redistributing load all the time due to wind, people moving around, furniture and other office furnishings being moved in and out. One floor in WTC 2 had to be reinforced because Cantor Fitzgerald (IIRC) put in a UPS room with huge lead batteries. The design as is wasn't enough to have properly dealt with that long-term mass.
When the jets tore through both buildings, both buildings had to suddenly redistribute a lot of weight from the upper sections because of damaged and/or missing columns. When the upper sections finally broke free, the structure below would have had to redistribute the sudden impact of the upper section immediately in order to arrest the falling mass. I'm quite happy with my use of the term.
I don't think the design parameters of the WTC building anticipated having ten of the top floors falling down into the rest of the building. I'll be happy to look at any documentation of this you might have.
The load is not amplified due to the acceleration of gravity. The load would only be amplified if it transferred a significant amount of it's momentum due to impact. This amplification is measureable using gravity units. If it decelerates at 96.6 ft/sec/sec on impact then it decelerated at a rate of three times that of 1 g and thus the static load was amplified by three times.
Obviously there's a more technical meaning here that I'm missing for the term
amplification. I simply take it to mean
making the force larger. A stationary mass has less force than an mass in motion. We've used the brick-on-head example many times. The brick stationary on your head is one level of load, one that's easily dealt with by your head. The brick dropped on your head from ten feet is a different level of load, one less easily dealt with by your head. That's a larger force, and gravity is indeed the factor that has made that force from the same mass larger.
But the more you talk, the more I understand what you are saying, and the more I understand how wrong you are.
I believe now that the load would only be amplified enough to overcome the structure below, and when I say "the structure below", I mean immediately below. It will only be amplified to the point of overwhelming the structure of the floor below. If the load is too great to be redistributed, the structure fails and the upper section continues down to the next floor.
Your mistake is taking the 31g figure that you imagine Bazant has claimed to happened, done calculations for what a 31g amplification would look like in the falling mass, and then demonstrated that WTC 1 didn't demonstrate that 31g amplification.
But Bazant only said that 31g was available, if I am reading him correctly. The upper section was bringing 31g to a 3g party (the estimated load capacity of the lower section). And even this case was of Bazant's best case scenario, something he does not claim actually happened on 9/11.
It seems to me that you should not be looking for a 31g amplification, but a 3g one.
If the amount of time for load application is lengthened then you are lowering the shock by absorbing the energy over a greater time frame. This works against an amplification occurring. It is the columns which are the issue not the floors.
You asked what would amplify a load. The formula for force is basically velocity and time. Manipulating either variable will make the end result larger.
Tony, it is indeed the floors that are the issue, because the floors are the weakest link in this chain. Most of the perimeter columns didn't buckle at all. Most of the core columns didn't buckle at all. But the floor trusses were doing their best impersonation of the Flying Spaghetti Monster. Tear the floor trusses loose from either the perimeter or the core, and the building is simply unzipping itself all the way down.
There can be no amplification while the impacting object is still accelerating.
I don't think this is right. When a mass could be accelerating at g, but is only accelerating at a drastically lower rate, then that mass is delivering a force to another body, a force greater than that which the mass could deliver at rest. Unless there is some technical reason why amplification could not mean this larger-than-static load, I think you're hung up here.
The reason for the lower than g acceleration was that the number of columns left intact during the demolition could not support the static load, but still provided some resistance to full acceleration at the rate of gravity.
I showed you, from your own data, that there are significant quantities of missing energy in the downward descent. Something is keeping that much mass from accelerating at g. There is some significant work being done somewhere in that collapse. You think it was crumpling columns left over from the demolition. I say it was the debris edge ripping apart the floor trusses.
The Balzac-Vitry was allowed to fall relatively unimpeded for two stories or about 25 feet with columns of those stories being pulled. At impact it was both crush up and crush down due to load amplification of the upper block. The impact occurrs at 1.5 seconds into the fall and the roofline shows a marked deceleration unlike WTC 1, which simply keeps accelerating.
The collapse does indeed last longer than the two seconds you measured. I withdraw the statement.