https://hal.archives-ouvertes.fr/hal-00790779/document

Linear instability mechanisms for coupled translational galloping

In this paper, we present a novel analytic approach to solve the buckling instability of Euler-Bernoulli columns with arbitrarily axial nonhomogeneity and/or varying cross section. For various columns including pinned-pinned columns, clamped columns, and cantilevered columns, the governing differential equation for buckling of columns with varying flexural rigidity is reduced to a Fredholm integral equation. Critical buckling load can be exactly determined by requiring that the resulting integral equation has a nontrivial solution. The effectiveness of the method is confirmed by comparing our results with existing closed-form solutions and numerical results. Flexural rigidity may take a majority of functions including polynomials, trigonometric and exponential functions, etc. Examples are given to illustrate the enhancement of the load-carrying capacity of tapered columns for admissible shape profiles with constant volume or weight, and the proposed method is of benefit to optimum design of columns agains...

Buckling Analysis of Nonuniform and Axially Graded Columns with Varying Flexural Rigidity

A rationale for determining the natural period of RC building frames having infill

This paper gives an overview of wind-induced galloping phenomena, describing its manifold features and the many advances that have taken place in this field. Starting from a quasi-steady model of aeroelastic forces exerted by the wind on a rigid cylinder with three degree-of-freedom, two translations and a rotation in the plane of the model cross section, the fluid–structure interaction forces are described in simple terms, yet suitable with complexity of mechanical systems, both in the linear and in the nonlinear field, thus allowing investigation of a wide range of structural typologies and their dynamic behavior. The paper is driven by some key concerns. A great effort is made in underlying strengths and weaknesses of the classic quasi-steady theory as well as of the simplistic assumptions that are introduced in order to investigate such complex phenomena through simple engineering models. A second aspect, which is crucial to the authors’ approach, is to take into account and harmonize the engineering, physical and mathematical perspectives in an interdisciplinary way—something which does not happen often. The authors underline that the quasi-steady approach is an irreplaceable tool, tough approximate and simple, for performing engineering analyses; at the same time, the study of this phenomenon gives origin to numerous problems that make the application of high-level mathematical solutions particularly attractive. Finally, the paper discusses a wide range of features of the galloping theory and its practical use which deserve further attention and refinements, pointing to the great potential represented by new fields of application and advanced analysis tools.

Some research perspectives in galloping phenomena: critical conditions and post-critical behavior

In this paper, variational iteration method (VIM) is applied to the problem of determination of critical buckling loads for Euler columns with constant and variable cross-sections. VIM is a powerful method for the solution of nonlinear ordinary and partial differential equations and integral equations. Hence it is a suitable approach for the analysis of engineering problems where an exact solution is difficult to obtain. This study presents the application of VIM to various buckling cases and results are produced for columns with different support conditions and with different variation of cross-sections. The results obtained are accurate which show that variational iteration method is a very efficient technique in the analysis of elastic stability problems.

Determination of critical buckling load for elastic columns of constant and variable cross-sections using variational iteration method

An analysis of free vibrations of tall buildings, such as frame, shear-wall, and frame-shear-wall structures, is proposed and discussed in this paper. Frame buildings are treated as shear beams with varying cross sections, the solutions of mode shapes of such buildings are expressed in Bessel’s functions, and the parameter of determining the fundamental period can be found from a figure provided in the paper. Based on the fact that the shear deformation and bending deformation are all considered for shear wall and frame-shear-wall structures, the formulas for calculating free vibrations of such structures are presented. It is very simple and convenient to apply these formulas to dynamic analysis of tall buildings. The measurement results and statistical analysis of frame, shear-wall, and frame-shear-wall structures in sites, and three examples of determining free vibrations of structures are also given in this paper. The examples show that the effect of shear deformation on the first natural frequency is not significant, but the effect of that on higher natural frequencies may not be neglected.

Li Qiusheng

Papers

Analysis of Free Vibrations of Tall Buildings

Stability analysis of bars with varying cross-section

An evaluation of onset wind velocity for 2—D coupled galloping oscillations of tower buildings