Golden Bear:
I would be the first to admit that the calculations I, David Benson and Prof. Bazant have done on the collapse of WTC 1 & 2 are crude approximations to what actually happened. However, I believe that finite element calculations for the entire 15 or so seconds of each collapse are simply not feasible. NIST's finite element calculations only covered the moments just before collapse initiation mainly because even this short time span required massive programs and processor times. It was not practical to do more. Hence, "simple" analytical modeling of the collapse is all that can realistically be done for the full 15 seconds of descent of the upper sections. However, the nice thing about this approach is that it is quite flexible so that mass shedding can be included as well as the increasing strength of the structure as you move from the upper floors to the lower floors. I have varied these parameters over a wide range of realistic values and found that there is a large window of conditions for which a collapse, once initiated, would be self-sustaining. I really urge you to write one of these programs and prove for yourself that what I am saying is true. Seeing is believing!
The destruction of the upper block during collapse is a very interesting question. Certainly there was some crush-up occurring during crush down of the lower section, but it's the mass of the upper section that counts. I also believe that the hat truss and mechanical floors near the top of the towers gave additional strength, mass and rigidity to the upper block compared to the lower section, creating a "pile-driver" effect. However, once crush down was completed, the upper block was moving so fast (~ 50 m/s) the total destruction of the upper section was assured.
First, I never said FEA would be feasible. I simply asked what you think one would show if it were performed.
Second, I do hope the revised version of your paper shows some calculations that prove the upper floors would remain a rigid block during the entire crush down phase. Anything short of this is just hand waving justification.
For example, you should at least try and quantify how much you think the hat truss strengthened the upper floors. You cannot simply say "well, the hat truss kept the upper block of floors together as a rigid block" without justifying that statement.
It's my understanding that the hat truss comprised only the top few floors and was meant to transfer loads between the exterior and core columns due to wind forces. You have to explain exactly how such a truss would prevent the buckling of the lowest floor of the upper block of floors when it impacts the lower structure. Bazant's theory seems to allege that only a single floor at a time in the lower structure is available to dissipate energy during crush down, therefore if you wish to keep your theory internally consistent, you have to allow the lowest floor of the upper structure to dissipate energy as well. The analysis might change once the crush up reached the floors comprising the hat truss, but again, under Bazant's theory you can't allow the hat truss to help keep the upper block of floors together unless you also allow the huge and in tact structural steel lattice below the highest floor of the lower structure to keep the lower block of floors together and rigid.
In other words, if the structural lattice below the highest floor of the lower structure is not available to help resist destruction of the lower structure, then the structural lattice above the lowest floor of the upper structure is not available to resist the destruction of the lowest floor of the upper block.
And again, I will keep coming back to the following salient point: the upper block of floors was very similar to the lower structure from a material, engineering and construction standpoint. It only stands to reason that whatever destruction occurs at impact between the upper and lower floors must be shared roughly equally between the upper and lower blocks of floors. There's simply no way around it. Bazant's theory doesn't take account of this fact, so it is incorrect.
Also, were the upper floors the only floors with mechanical floors, or did the lower structure include mechanical floors as well?