First, let us review the basic argument (Baˇzant 2001; Baˇzant and Zhou 2002). After a drop
through at least the height h of one story heated by fire (stage 3 in Fig. 1 top), the mass
m of the upper part of each tower has lost enormous gravitational energy, equal to mgh (g
= gravity acceleration). Because the energy dissipation by buckling of the hot columns must
have been negligible by comparison, most of this energy must have been converted into kinetic
energy K = mv2/2 of the upper part of tower, moving at velocity v. Calculation of energy Wc
dissipated by the crushing of all columns of the underlying (cold and intact) story (Baˇzant and
Zhou 2002) showed that, approximately, the kinetic energy of impact K > 8.4 Wc.
In calculating Wc, it was noted that, in inelastic buckling, the inelastic deformation must
localize into inelastic hinges (Baˇzant and Cedolin 2003, sec. 7.10)). To obtain an upper bound
on Wc, the local buckling of flanges and webs, as well as possible steel fracture, was neglected
(which means that the ratio K/Wc was likely higher than 8.4). When the subsequent stories
are getting crushed, the loss mgh of gravitational energy per story exceeds Wc that by an ever
increasing margin, and so the velocity v of the upper part must increase from one story to the
next. This is the basic characteristic of progressive collapse, well known from many previous
disasters with causes other than fire (internal or external explosions, earthquake, lapses in
quality control; see, e.g., Levy and Salvadori 1992; Baˇzant and Verdure 2007).
Merely to get convinced of the inevitability of gravity driven progressive collapse, further
analysis is, for a structural engineer, superfluous.