The Collapse Times of Tall Multi-story buildings of Constant Cross-scection
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Howland, Bradford; Howland, Frank M.; Howland, Howard C.
We present a simple mathematical model of the collapse of tall multistory buildings in general and of the world trade center (WTC) towers in particular with the object of predicting the collapse times. In constructing the model we first considered two modes of demolition, one in which the supports of the bottom floor are destroyed and a second where the supports of the topmost level are destroyed. In both modes it is assumed that the retardation of the brittle structure of the building is insignificant. In the first model the entire building collapses in freefall, i.e. with one g acceleration. In the second mode of collapse we show that for very tall buildings the ratio of the time for collapse and the freefall time, as well as the reciprocal velocities of collapse, approach the square root of three as the number of floors is increased indefinitely. We then model the destruction of the WTC towers and the combination of the two modes of collapse. In this third mode of collapse the destruction of the building results in an agglomeration of floors impacted from the top by freefalling floors and impacting the lower floors below it. It may be shown that the agglomeration has an acceleration of 3/5 g. The model constructed along these lines for the collapse of the WTC towers, which had fractures originating at different floors, results collapse times that differ by 1.83 seconds. This difference accords well with the measured two second difference in collapse times derived from the video and seismic records.
building; collapse; mathematical model