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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.

The safety of road vehicles on the ground in crosswind has been investigated for many years. One of the most important fundamentals in the safety analysis is aerodynamic characteristics of a vehicle in crosswind. The most common way to study the aerodynamic characteristics of a vehicle in crosswind is wind tunnel tests to measure the aerodynamic coefficients and/or pressure coefficients of the vehicle. Due to the complexity of wind tunnel test equipment and procedure, the features of flow field around the vehicle are seldom explored in a wind tunnel, particularly for the vehicle moving on the ground. As a complementary to wind tunnel tests, the numerical method using computational fluid dynamics (CFD) can be employed as an effective tool to explore the aerodynamic characteristics of as well as flow features around the vehicle. This study explores crosswind effects on a high-sided lorry on the ground with and without movement through CFD simulations together with wind tunnel tests. Firstly, the aerodynamic forces on a stationary lorry model are measured in a wind tunnel, and the results are compared with the previous measurement results. The CFD with unsteady RANS method is then employed to simulate wind flow around and wind pressures on the stationary lorry. The numerical aerodynamic forces are compared with the wind tunnel test results. Furthermore, the same CFD method is extended to investigate the moving vehicle on the ground in crosswind. The results show that the CFD results match with wind tunnel test results and the current way using aerodynamic coefficients from a stationary vehicle in crosswind is acceptable. The CFD simulation can provide more insights on flow field and pressure distribution which are difficult to be obtained by wind tunnel tests.

When a road vehicle moving on a bridge deck is passing by a bridge tower, the vehicle will be shielded briefly from the crosswind by the bridge tower. This study aimed to apply computational fluid dynamics to explore this special engineering problem for the first time. A stationary vehicle immerged in the wake of a bridge tower was first simulated and compared with wind tunnel test results. By using the dynamic mesh method, the moving of the vehicle passing by a bridge tower was then simulated. The results show that the computed aerodynamic coefficients of the stationary vehicle are generally larger than wind tunnel results. The side force and yawing moment coefficients of the moving vehicle are lower than those of the stationary vehicle. The results also show that the suddenly changing time of aerodynamic forces caused by the tower may be shorter than the average driver reaction time.

To investigate the safety of road vehicles running on a long-span bridge under high crosswinds, the aerodynamic forces of a moving vehicle-bridge deck system need to be determined. This paper reports the use of computational fluid dynamics (CFD) to simulate the aerodynamic forces on coupled vehicle-bridge deck systems under crosswinds in terms of aerodynamic coefficients. The aerodynamic coefficients of a stationary vehicle-deck system were simulated and then compared with wind tunnel results. A relative velocity method was then used to obtain the aerodynamic forces of a moving vehicle-deck system. The moving effects on the aerodynamic forces on the vehicle-deck system were evaluated. The results show that the movement of the vehicle on the first lane of the bridge deck does affect the aerodynamic coefficients of the bridge deck but has only slight effects on the aerodynamic coefficients of the vehicle if the relative yaw angle to the vehicle is taken into account.

With vibration amplitude increasing, the super high-rise building appears obvious pseudo-beat vibration under the combination of vortex-induced force and nonlinear damping force. Therefore, based on Scanlan nonlinear empirical model the first-order nonlinear pseudo-beat vibration responses of the super high-rise building are deduced with KBM method. And then the aerodynamic parameters and vortex-induced force can be identified with least square method. By using the aeroelastic model wind tunnel test of a certain super high-rise building, the wind-induced displacement vibration responses are gathered. By the least square method, each aerodynamic parameter is identified. It shows by analysis that the pseudo-beat vibration force is mainly offered by linear and nonlinear damping forces but secondary offered by linear stiffness force and periodic excitation force. The pseudo-beat vibration force calculated by KBM approximation has the predominant frequency like that of beat vibration response as well as high-order harmonic wave.

This paper presents a time domain approach for predicting buffeting response of long suspension bridges under skew winds. The buffeting forces on an oblique strip of the bridge deck in the mean wind direction are derived in terms of aerodynamic coefficients measured under skew winds and equivalent fluctuating wind velocities with aerodynamic impulse functions included. The time histories of equivalent fluctuating wind velocities and then buffeting forces along the bridge deck are simulated using the spectral representation method based on the Gaussian distribution assumption. The self-excited forces on an oblique strip of the bridge deck are represented by the convolution integrals involving aerodynamic impulse functions and structural motions. The aerodynamic impulse functions of self-excited forces are derived from experimentally measured flutter derivatives under skew winds using rational function approximations. The governing equation of motion of a long suspension bridge under skew winds is established using the finite element method and solved using the Newmark numerical method. The proposed time domain approach is finally applied to the Tsing Ma suspension bridge in Hong Kong. The computed buffeting responses of the bridge under skew winds during Typhoon Sam are compared with those obtained from the frequency domain approach and the field measurement. The comparisons are found satisfactory for the bridge response in the main span.

A long suspension bridge is often located within a unique wind environment, and strong winds at the site seldom attack the bridge at a right angle to its long axis. This paper thus investigates the buffeting response of long suspension bridges to skew winds. The conventional buffeting analysis in the frequency domain is first improved to take into account skew winds based on the quasi-steady theory andrnthe oblique strip theory in conjunction with the finite element method and the pseudo-excitation method. The aerodynamic coefficients and flutter derivatives of the Tsing Ma suspension bridge deck under skew winds, which are required in the improved buffeting analysis, are then measured in a wind tunnel using specially designed test rigs. The field measurement data, which were recorded during Typhoon Sam in 1999 by the Wind And Structural Health Monitoring System (WASHMS) installed on the Tsing Ma Bridge, are analyzed to obtain both wind characteristics and buffeting responses. Finally, the field measured buffeting responses of the Tsing Ma Bridge are compared with those from the computer simulation using the improved method and the aerodynamic coefficients and flutter derivatives measured under skew winds. The comparison is found satisfactory in general.

Tsing Ma Bridge in Hong Kong is the longest suspension bridge in the world carrying both highway and railway. It has two H-shape concrete towers, each of which is composed of two reinforced concrete legs and four deep transverse prestressed concrete beams. A series of wind tunnel tests have been performed to measure the aerodynamic coefficients of the tower legs and transverse beams in various arrangements. A 1:100 scaled 3D rigid model of the full bridge tower assembled from various tower components has been constructed for different test cases. The aerodynamic coefficients of the lower and upper segments of the windward and leeward tower legs and those of the transverse beams at different levels, with and without the dummy bridge deck model, were measured as a function of yaw wind angle. The effects of wind interference among the tower components and the influence of the bridge deck on the tower aerodynamicrncoefficients were also investigated. The results achieved can be used as the pertinent data for the comparison of the computed and field-measured fully coupled buffeting responses of the entire bridge under yaw winds.