Dynamic response of a bridge deck with one torsional degree of freedom under turbulent wind

Abstract

Abstract.Under special conditions of turbulent wind, suspension and cable-stayed bridges could reachinstability conditions. In various instances the bridge deck, as like a bluff body, could exhibit single-degree torsional instability. In the present study the turbulent component of flow has been considered as asolution of a differential stochastic linear equation. The input process is represented by a Gaussian zero-mean white noise. In this paper the analytical solution of the dynamic response of the bridge has beendetermined. The solution has been obtained with a technique of closing on the order of the moments.Key words:turbulent wind; stochastic analysis; Gaussian processes; bridges. 1. IntroductionThe aeroelastic behaviour of the deck in the suspension and cable-stayed bridges is one of themost complex and relevant aspects for the security of the structure. In fact the wind action couldcause the collapse of the bridge due to instability phenomena. Many mechanical models are adoptedto describe the dynamic behaviour of long-span decks. The most utilised one is the section modelwith two degrees of freedom. This model has visco-elastic restraints that reproduce, dynamically,the characteristics of the whole structural system. Most complex models consider the whole 3-Dstructure of the bridge under wind forces taking into account both the tridimensional behaviour of thestructure and the spatial distribution of the wind. Recently, a model with four degree of freedom has been proposed in substitution of the classicalsection model. It is a non-linear model able to analyse the global vibrational modes of the structureand the modes relative to the cables and the deck. The preliminary study of the dynamic behaviourof a long span bridge subjected to a turbulent wind action is usually developed with a section-modelof the deck. If the analysis is performed referring to the instantaneous velocity, the solution of theproblem is more complex. In fact the presence of time-depending excitations is described withstochastic models; moreover under special conditions of motion, these sections could reachinstability conditions. The classical flutter of bridge decks shows significant differences compared tothe one relative to the thin airfoil. The centre of the mass is on the symmetry axis of the section andit is very close to the torsion centre; in this way the inertial coupling is limited and the part of theaeroelastic moment due to the rotation velocity, always negative on the thin airfoil, could change thesign for a deck for a unstreamlined section. As a result a reduction and even the inversion of the total