Equation of Motion Governing the Dynamics of Vertically Collapsing Buildings
Publication: Journal of Engineering Mechanics
Volume 138, Issue 12
Abstract
The present paper aims at contributing to a discussion, opened by several authors, on the proper equation of motion that governs the vertical collapse of buildings. The most striking and tragic example is that of the World Trade Center Twin Towers, in New York City, about 10 years ago. This is a very complex problem and, besides dynamics, the analysis involves several areas of knowledge in mechanics, such as structural engineering, materials sciences, and thermodynamics, among others. Therefore, the goal of this work is far from claiming to deal with the problem in its completeness, leaving aside discussions about the modeling of the resistive load to collapse, for example. However, the following analysis, restricted to the study of motion, shows that the problem in question holds great similarity to the classic falling-chain problem, very much addressed in a number of different versions as the pioneering one, by von Buquoy or the one by Cayley. Following previous works, a simple single-degree-of-freedom model was readdressed and conceptually discussed. The form of Lagrange’s equation, which leads to a proper equation of motion for the collapsing building, is a general and extended dissipative form, which is proper for systems with mass varying explicitly with position. The additional dissipative generalized force term, which was present in the extended form of the Lagrange equation, was shown to be derivable from a Rayleigh-like energy function.
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Acknowledgments
The first and second authors acknowledge CNPq, the Brazilian National Research Council, for the Research Grant number 303838/2008-6 and the Postdoctoral Grant number 150731/2011-6. The authors also acknowledge FAPESP, the State of São Paulo Research Foundation, for Ph.D. scholarships number 04/04611-5 (second author) and number 2010/07008-9 (third author).
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 138 • Issue 12 • December 2012
Pages: 1420 - 1431
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Jan 27, 2011
Accepted: Apr 12, 2012
Published online: Apr 14, 2012
Published in print: Dec 1, 2012
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