Non Gaussian Response of Bridges Subjected to Turbulent Wind - Effect of the non Linearity of Aerodynamic Coefficients

Wind loads acting of bluff bodies like bridge decks are complex functions of the components of the turbulence and of the structural displacements and velocities. In order to simplify the representation of these loads, approached models are generally considered. Since a convenient linear approximation gives accurate results in many cases, such a model has been widely used during last decades. Some researchers have however showed that it is possible, and even necessary, to account for the non linearity of this kind of loading. Such a non linearity is likely to come either from the squared velocity or from the shape of the aerodynamic coefficients as functions of the wind angle of attack.

Non linear loading of the first kind (squared velocity) have already been studied in rather recent researches. Some of them are referenced at the end of this abstract. It has been showed that this so-called non linear quasi-steady aerodynamic loading leads to a non Gaussian response of the structure although the components of the turbulence are Gaussian. This has of course significant consequences on the structural design.

This paper aims at showing that the second origin of non linear loading terms, i.e. the non linearity of the aerodynamic coefficients, can also have significant consequences on the design of wind-loaded structures. Developments are carried out for bi- and tri-dimensional turbulence fields, and the main conclusions are that these effects are of prime importance of course when the non linearity of the aerodynamic coefficients is important, but also when the transverse component of the turbulence is important.

In a more detailed way, the proposed paper intends at presenting two main features. The first one consists in the determination of the statistical characteristics of the loading. In particular it is showed that the traditional linearization of the aerodynamic coefficients may lead to a significant inaccuracy of these statistical characteristics.

The second feature is the presentation of a simplified method to derive statistical characteristics of the response from those of the loading. This very simple method is compared with a heavy rigorous analysis. It is concluded that this simple approach can give good estimations of the response that could be used, for instance, for the pre-design of a structure.