A numerical model for wind loads simulation on long-span bridges

Abstract

A numerical model of the air flow problem around the girder of a long-span bridge is presented. The model is based on a finite volume formulation and it is able to simulate steady and non-steady wind loading conditions on the structure under the simplifying assumption, which is plausible for bridges with long spans, of a two-dimensional-like approaching flow. For a given bridge deck cross-section the proposed model allows the numerical evaluation of the flutter derivatives, which is useful to characterize in an analytical way the stability conditions of the overall wind-induced bridge response. In order to obtain satisfactory accuracy and stability of the numerical solution, a two-equation k–ϵ RNG turbulence model and special boundary conditions are employed. The accuracy and applicability of the model to wind engineering problems are successfully assessed by computing the aerodynamic behaviour of some simple cross-section shapes. Numerical results are also obtained for typical long-span bridge cross-sections and the comparison with the available wind tunnel measurements shows a good agreement.

Introduction

Long-span bridges are slender, light and flexible large-scale structures with deck dimensions very small compared to the main span length. Owing to their high flexibility, long-span bridges are often found very sensitive to wind effects and their major wind-related problems are associated with large deflections produced by oscillatory instabilities or by response to random wind gusts.

Pulsating aerodynamic forces come out from the non-steady wind–structure interaction and they act on the oscillating girder in addition to the steady wind loads. As a consequence, self-excited strong vibrations and the flutter of the bridge can occur at current wind speeds. Therefore, in long-span bridge design wind loading and the related aeroelastic stability problem must be considered together with the other classical loading conditions.

Beginning from the second part of the previous century, since the collapse of the first Tacoma Narrows Bridge, the bridge aerodynamic design has considerably progressed to a more and more analytical methodology, by which the mechanical aspects concerning bridge stability are deeply understood and characterized. During this process, the experimental data, which are needed by mathematical formulations to assess the response of long-span bridges, have been progressively identified with some degree of clarity.

A number of experimental approaches are usually adopted to characterize the bridge behaviour to wind excitation: section modelling, taut-strip modelling, full-bridge modelling and full-scale measurement [23]. Only the former three are normally applicable during the design phase and they need the use of wind tunnels. Instead, the fourth is adopted for calibrating the modelling parameters of the experimental approaches and it represents the only way to assess the real response of a prototype structure.

However, costs and realization time for these experimental approaches may be very large and then parametric analyses during the bridge design phase often result unacceptable. Hence, reduction of the turn-over time for the aerodynamic bridge characterization is highly desirable.

As a consequence of the fast growing computational power and of the improvements in the physical modelling, computational wind engineering is now being established to support or to replace some part of the expensive and time-consuming wind tunnel tests. These arguments, together with the capability to take into account turbulent high Reynolds’ number flows, which are involved in most bluff-body wind engineering applications, motivate the development of a numerical tool running on computational platforms with medium/high performances.

Starting from the basic aeroelastic aspects of long-span bridges, this paper addresses to the evaluation, through the numerical simulation, of the aerodynamic data which are useful during the design process. A relatively fast computer technique is employed. It is based on a two-dimensional finite volume formulation of the flow problem relating to an approaching cross-wind flow on a bridge deck.