Anísio Andrade

AN ANALYTICAL STUDY ON THE LATERAL-TORSIONAL BUCKLING OF LINEARLY TAPERED CANTILEVER STRIP BEAMS

In this paper, the elastic lateral-torsional buckling of tapered cantilever strip beams acted by a tip load is investigated. Analytical solutions of the buckling problem are derived for cantilevers with a linearly varying depth. It is shown that the corresponding governing differential equation is a particular case of the general confluent equation, whose solution is given in terms of confluent hypergeometric functions. The buckling load corresponds to the lowest positive root of a 4×4 characteristic determinant arising from the introduction of the general solution of the differential equation into the boundary conditions. Finally, one discusses the optimization of the cantilever geometrical shape (for constant volume), as far as its resistance to lateral-torsional buckling is concerned.

Lateral-Torsional Stability Boundaries for Polygonally Depth-Tapered Strip Cantilevers Under Multi-Parameter Point Load Systems—An Analytical Approach

This paper reports an analytical study on the elastic lateral-torsional buckling behavior of strip cantilevers (i) whose depth is given by a monotonically decreasing polygonal function of the distance to the support and (ii) which are subjected to an arbitrary number of independent conservative point loads, all acting in the same “downward” direction. The study is conducted on the basis of a one-dimensional (beam) mathematical model. A specialized model problem, consisting of a two-segment cantilever acted by two loads, applied at the free end and at the junction between segments, is first considered in detail for it “contains all the germs of generality”. It is shown that the governing differential equations can be integrated in terms of confluent hypergeometric functions or Bessel functions (themselves special cases of confluent hypergeometric functions). This allows us to establish exactly the characteristic equation for this structural system, which implicitly defines its stability boundary. Moreover, it is shown that the methods used to solve the model problem also apply to the general problem. A couple of parametric illustrative examples are discussed. Some analytical solutions are compared with the results of shell finite element analyses—a good agreement is found.

Lateral-Torsional Buckling Analysis of Web-Tapered I-Beams Using Finite Element and Spline Collocation Methods

Tapered members are widely used in the steel construction industry, because of their structural efficiency, ability to meet architectural and functional requirements and competitive fabrication costs. According to the current design codes, the load-carrying capacity of laterally unsupported beams (either prismatic or tapered) bent in their stiffer principal plane is estimated on the basis of their cross-sectional and elastic lateral-torsional buckling resistances. Bearing this in mind, two of the authors have recently proposed and validated a one-dimensional model to characterise the elastic lateral-torsional buckling behaviour of tapered thin-walled open beams [1]. This model can be described as a kinematically constrained version of a nonlinear shell model and, from a mathematical viewpoint, it amounts to a self-adjoint eigenvalue problem for a system of ordinary differential equations and separated boundary conditions.

Acute renal failure and other complications induced by cocaine abuse

Cocaine is a social and medical problem. In the United States, 14.6% of a trialed population has already used cocaine. The physiopathology of the renal injury is multifactorial and largely remains unknown, and rhabdomyolysis is most frequently responsible for the renal injury.