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.

Single intravitreal bevacizumab injection effects on contrast sensitivity in macular edema from branch retinal vein occlusion

Purpose: To evaluate the effect of a single intravitreal bevacizumab injection on visual acuity, contrast sensitivity and optical coherence tomography-measured central macular thickness in eyes with macular edema from branch retinal vein occlusion. Methods: Seventeen eyes of 17 patients with macular edema from unilateral branch retinal vein occlusion were treated with a single bevacizumab injection. Patients were submitted to a complete evaluation including best corrected visual acuity, contrast sensitivity and optical coherence tomography measurements before treatment and one and three months after injection. Visual acuity, contrast sensitivity and optical coherence tomography measurements were compared to baseline values. Results: Mean visual acuity measurement improved from 0.77 logMAR at baseline to 0.613 logMAR one month after injection (P=0.0001) but worsened to 0.75 logMAR after three months. Contrast sensitivity test demonstrated significant improvement at spatial frequencies of 3, 6, 12 and 18 cycles/degree one month after injection and at the spatial frequency of 12 cycles/degree three months after treatment. Mean +/- standard deviation baseline central macular thickness (552 +/- 150 mu m) reduced significantly one month (322 +/- 127 mu m, P=0.0001) and three months (439 perpendicular to 179 mu m, P=0.01) after treatment. Conclusions: Bevacizumab injection improves visual acuity and contrast sensitivity and reduces central macular thickness one month after treatment. Visual acuity returns to baseline levels at the 3-month follow-up, but some beneficial effect of the treatment is still present at that time, as evidenced by optical coherence tomography-measured central macular thickness and contrast sensitivity measurements.

Use of a Single L1 GPS Receiver for Monitoring Structures: First Results of the Detection of Millimetric Dynamic Oscillations

This paper presents preliminary results to determine small displacements of a global positioning system (GPS) antenna fastened to a structure using only one L1 GPS receiver. Vibrations, periodic or not, are common in large structures, such as bridges, footbridges, tall buildings, and towers under dynamic loads. The behavior in time and frequency leads to structural analysis studies. The hypothesis of this article is that any large structure that presents vibrations in the centimeter-to-millimeter range can be monitored by phase measurements of a single L1 receiver with a high data rate, as long as the direction of the displacement is pointing to a particular satellite. Within this scenario, the carrier phase will be modulated by antenna displacement. During a period of a few dozen seconds, the relative displacement to the satellite, the satellite clock, and the atmospheric phase delays can be assumed as a polynomial time function. The residuals from a polynomial adjustment contain the phase modulation owing to small displacements, random noise, receiver clock short time instabilities, and multipath. The results showed that it is possible to detect displacements of centimeters in the phase data of a single satellite and millimeters in the difference between the phases of two satellites. After applying a periodic nonsinusoidal displacement of 10 m to the antenna, it is clearly recovered in the difference of the residuals. The time domain spectrum obtained by the fast Fourier transform (FFT) exhibited a defined peak of the third harmonic much more than the random noise using the proposed third-degree polynomial model. DOI: 10.1061/(ASCE)SU.1943-5428.0000070. (C) 2012 American Society of Civil Engineers.