Equation of Motion Governing the Dynamics of Vertically Collapsing Buildings

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. DOI: 10.1061/(ASCE)EM.1943-7889.0000453. (C) 2012 American Society of Civil Engineers.

Climatic oscillations shape the phylogeographical structure of Atlantic Forest fire-eye antbirds (Aves: Thamnophilidae)

In the present study, mitochondrial (mt)DNA sequence data were used to examine the genetic structure of fire-eye antbirds (genus Pyriglena) along the Atlantic Forest and the predictions derived from the river hypothesis and from a Last Glacial Maximum Pleistocene refuge paleomodel were compared to explain the patterns of genetic variation observed in these populations. A total of 266 individuals from 45 populations were sampled over a latitudinal transect and a number of phylogeographical and population genetics analytical approaches were employed to address these questions. The pattern of mtDNA variation observed in fire-eye antbirds provides little support for the view that populations were isolated by the modern course of major Atlantic Forest rivers. Instead, the data provide stronger support for the predictions of the refuge model. These results add to the mounting evidence that climatic oscillations appear to have played a substantial role in shaping the phylogeographical structure and possibly the diversification of many taxa in this region. However, the results also illustrate the potential for more complex climatic history and historical changes in the geographical distribution of Atlantic Forest than envisioned by the refuge model. (c) 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, 105, 900824.