A Contribution to Analysis of Collapse of High-Rise Building Inspired by the Collapses of WTC1 and WTC2: Derivation of Simple Formulas for Collapse Upper Speed and Acceleration

摘要

The paper is a contribution to the technical discussion concerning the collapses of the WTC buildings. It returns to the problem of the dynamics of the collapses;it does not concern the reason why the buildings started collapsing, but investigates the dynamics of the collapse itself. It works with the same assumptions as the official NIST report [1], i.e. that the falling mass hits the motionless mass beneath;the supporting columns loose stability and the mass of the pertinent floor starts to fall together with the falling mass. The aim was to derive the theoretical upper limit of the speed of the collapse, supposing that influence of the columns which resist the fall, is neglected. The differential equation of the fall was obtained using two independent laws of mechanics, with the identical result. Its solution can be found from a very simple explicit formula. The theoretical upper limit acceleration of the fall obtained by such formula is one third of the gravitational acceleration, which is faster than it was observed in the case of the collapses of WTC1 and WTC2. This leads to the conclusion that the mechanism of the collapse must be different from the assumed and the falling mass must not hit the motionless mass bellow it, but rather a mass which had started to fall before the impact of the falling mass occurred.