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Responses of vortex-induced vibration (VIV) of long-span bridges are commonly measured at first via wind tunnel tests of sectional model and then converted to the prototype ones of the corresponding full bridges by some approximate formulae. In this paper, a time-domain full bridge analysis method was presented for predicting nonlinear VIV responses mode-by-mode based on a polynomial type of nonlinear mathematical model of vortex-induced force (VIF) on bridge deck cross section. In this method, the motion-dependant self-excited force (SEF) components of VIF were regarded as fully correlated span-wise in the case of smooth flow, while the motion-independent harmonic pure vortex-shedding force (PVSF) component of VIF was regarded as incompletely correlated along the bridge span. To take into account the incomplete span-wise correlation of PVSF, an equivalent generalized PVSF including the effect of the incomplete span-wise correlation of PVSF was defined by using a span-wise correlation coefficient of PVSF which could be obtained through a sectional model wind tunnel test of simultaneous pressure measurement. As an application example, the VIV responses of 12 vertical modes of a steel box deck cable stayed bridge with a main span of 688 m were analysed, and were compared with those converted with two approximate converting formulae, respectively, based on Scanlan’s linear and nonlinear mathematical model of VIF. It is found that the influence of the incomplete span-wise correlation of PVSF on the bridge VIV response is very small and can then be ignored.

To ensure the safety of bridges, the comfort of pedestrians and vehicles on bridges, the vortex-induced forces on flat-steel-box girders need to be investigated. The total vortex-induced forces integrated on the surfaces of girders have been studied extensively. This study will be mainly focused on the characteristics of surface distributed vortex-induced force, which can be beneficial to the vortex-induced vibration (VIV) reduction with local aerodynamic optimization. Computational Fluid Dynamics (CFD) method is employed for the simulation of the VIVof a flat-steel-box girder. The simulation results are verified through the comparison with the results of corresponding wind tunnel test. A self-adaptive nonlinear fitting method is proposed to determine the vortex-induced force model. A vortex-induced force contribution factor is defined to account the contribution of the components and the surface location. Based on the surface distributed vortex-induced force analysis, several conclusions are made. The vortex-induced force presents a fairly strong multiple-frequency characteristic, and the high-order terms should be carefully considered. Most energy of the VIV comes from the linear and third-order aerodynamic damping terms. In terms of location, the roof takes most of the aerodynamic damping and the total vortex-induced force. The flow separation around the underside upstream corner, the underside downstream corner and the middle downstream comer lead to large third-order aerodynamic damping term. The flow separation around the underside upstream corner has great contribution to the linear aerodynamic stiffness term.

Wind-tunnel tests of a large-scale sectional model with synchronous measurements of force and vibration responses were carried out to investigate the nonlinear behaviors of vertical vortex-induced forces (VIFs) on three typical box decks (i.e., fully closed box, centrally slotted box, and semi-closed box). The mechanisms of the onset, development, and self-limiting phenomenon of the vertical vortex-induced vibration (VIV) were also explored by analyzing the energy evolution of different vertical VIF components and their contributions to the vertical VIV responses. The results show that the nonlinear components of the vertical VIF often differ from deck to deck; the most important components of the vertical VIF, governing the stable amplitudes of the vertical VIV responses, are the linear and cubic components of velocity contained in the self-excited aerodynamic damping forces. The former provides a constant negative damping ratio to the vibration system and is thus the essential power driving the development of the VIV amplitude, while the latter provides a positive damping ratio proportional to the square of the vibration velocity and is actually the inherent factor making the VIV amplitude self-limiting. On these bases, a universal simplified nonlinear mathematical model of the vertical VIF on box decks of bridges is presented and verified in this paper; it can be used to predict the stable amplitudes of the vertical VIV of long-span bridges with satisfactory accuracy. Keywords: Box deck of bridge, Vertical vortex-induced vibration, Vertical vortex-induced force, Simplified nonlinear model, Wind-tunnel test, Large-scale sectional model, Synchronous measurement of force and vibration

Wind tunnel tests of synchronous measurements of the buffeting lifts and moments on six separated strips of a motionless 1:45 scale sectional model of a flat closed-box bridge deck were carried out...

A wind tunnel test of synchronized pressure measurement on a spring-suspended sectional model of a flat closed box deck at a large scale of 1/20 was carried out by taking Xiangshan Harbour Bridge in China as background. The chordwise correlation of the fluctuating aerodynamic pressures (FAP) on the surface of the box deck was then investigated at both stationary state and vortex-induced resonance (VIR) states of the deck model. Afterwards, an approximate approach was developed for estimating the spanwise correlation coefficients of pure vertical vortex-shedding force (VSF) on the deck under VIR state. On this basis, the spanwise correlation coefficients of both the integrated total vertical fluctuating aerodynamic force (FAF) and the pure vertical VSF on the flat box deck were then studied and compared to each other quantitatively at the stationary state as well as the VIR states at various wind speeds. Finally, the spanwise correlation coefficients of the surface FAP at some typical positions on the deck cross section were calculated and compared with that of the total vertical FAF and the vertical VSF. The results show that the chordwise correlation of the FAP on stationary deck is not strong at most part of the deck surface, however, can be enhanced with the increase of incident wind speed. The chordwise correlation of FAP can also be enhanced quite significantly by the deck oscillation under VIR states, but is still imperfect. Furthermore, the spanwise correlations of FAP at different positions on the deck cross section are clearly different from each other, and much weaker than that of the total vertical FAF, for both the stationary state and the VIR states of the deck. However, they are generally much stronger than that of the pure VSF in cases of notable VIR, and much weaker in the cases of slight VIR, such as near the onset of VIR. The spanwise correlation characteristics of both the pure vertical VSF and the total vertical FAF are hence very different from those of the surface pressures. Moreover, the spanwise correlation of the total vertical FAF on cross sections can be greatly intensified by the VIR because of the existence of a large portion of vortex-induced self-excited force (VISEF). On the other hand, the spanwise correlation of the vertical VSF under the VIR states is much weaker than that of total vertical FAF as well as that of the pure vertical VSF under the stationary state at same wind speeds. Finally, the variations of the spanwise correlation of both the total vertical FAF and the pure vertical VSF with the response displacement of VIR is quite complicated. The most violent VIR, the most correlated total FAF and the most correlated VSF occur generally at different wind speeds.

This paper was reviewed and accepted by the APCWE-IX Programme Committee for Presentation at the 9th Asia-Pacific Conference on Wind Engineering, University of Auckland, Auckland, New Zealand, held from 3-7 December 2017.

This paper was reviewed and accepted by the APCWE-IX Programme Committee for Presentation at the 9th Asia-Pacific Conference on Wind Engineering, University of Auckland, Auckland, New Zealand, held from 3-7 December 2017.

This paper was reviewed and accepted by the APCWE-IX Programme Committee for Presentation at the 9th Asia-Pacific Conference on Wind Engineering, University of Auckland, Auckland, New Zealand, held from 3-7 December 2017.