Collapse, tower, WTC, mechanics, theory, evidence, observation, dust cloud, explosion, free fall, critical floor, fracture wave, progressive failure, the slowest mode, the fastest mode, intermediate mode, hybrid mode, analysis, calculations 

The purpose of this paper is to estimate the floors where the New York collapses started from based on the well-documented evidence that all collapses took time equal to free fall time. An earlier analysis of the government-supported, progressive failure version showed that all collapses started significantly lower than the floors subjected to fire as a result of impact of terrorist planes, see Cherepanov and Esparragoza (2007) in Int. J. Fracture, V. 143, pp 203-206. A new, more sophisticated analysis of the New York collapses called the hybrid theory is advanced below. It explores the possibility that collapses started on several floors simultaneously, not in one floor as suggested in all previous theories. According to the hybrid theory the collapses of World Trade Center towers ran in two phases: (i) in the first phase dynamic fracture waves disintegrated a part of the towers producing the dust cloud and explosion sound well-documented and well-evidenced, and (ii) in the second phase the progressive failure front disintegrated the lower part of the towers that remained intact in the first phase. To illustrate many possible modes of progressive failure the slowest mode, the fastest mode, and three intermediate modes were first studied below and then the hybrid mode was introduced. The hybrid theory allows one to get rid of evident defects of earlier theories and explain all basic facts and observations of the matter not understood before, in particular, why the time of all collapses was free fall time independent of the position of critical floors the collapses started from. It was shown that the floors disintegrated in the very beginning of the collapses were located considerably lower than the floors hit by terrorists and subjected to fire. And so, this most sophisticated analysis of the New York collapses confirms the earlier conclusion and suggests that fracture waves were produced by explosives and not arisen from thermal stresses of fire as hypotesised earlier. The numerical work in the present paper was done by Prof. I. E. Esparragoza from Pennsylvania State University.