Then I imagine that much will depend on the geometric and mechanical properties of the structure (including non-structural elements). In particular: To the extent that the structural connections whose breaking suffices to let collapse continue are probably mostly not hit directly by the advancing front, but forces propagate (as some kind of wave?) through intermediate materials (concrete decks, the lengths of trusses, beams and girders...) and arrive at the connections split-seconds later, how do we estimate how much inelastic deformation has already occured until finally the connections break free?
Intuition, that bitch, tells me most structural connections are not the last to absorb energy from any one floor impact, and that means, intuitively, that most of the fail energy is included in the 2/3 inelastic deformation energy.
I have no idea how to model this.
One hint, that may be obvious to you but not the casual reader: a converges towards g/3, thus becomes constant; but the force involved, and thus kinetic energy (and with it all other energies involved), momentum, pressures etc. increase proportional to mass, which increases by the mass of one floor per floor.
Oh got another question, which may show I am not well-read on the issue, or maybe it is a good one: I think I read in passing on this board that posters agree that, according to observation, both collapses converged on a constant velocity, not constant acceleration. What's wrong here?
A last nitpick: Your post of Sat May 05, 2012 9:35 pm (not sure what time zone that us - UT? CET?), which you (largely?) copied from the older thread, starts off with
Uniform density ρ given total height H and mass M:
ρ = H/M
Should be M/H, not?
And perhaps needs pointing out that this is density in a 1D-world.
This actually had me fumbling with the entire math of that post for about 10 minutes.