Long-span Cable-supported Bridges Research Articles

Modal characteristics analysis and vibration control of long-span cable-stayed-suspension hybrid bridge based on strain energy method

The research on the modal characteristic analysis of long-span bridges is crucial for vibration analysis and control, yet literature regarding the modal characteristics of long-span bridges remains limited. This study thus aims to introduce a strain energy-based damping model to estimate the modal damping of long-span cable-supported bridges. Two different systems of cable-supported bridges are analyzed, and the strain energy proportions and modal damping ratios of various substructures for each mode are calculated. Based on the analysis of modal strain energy results, a strategy to control the vibration of long-span bridges is proposed and validated using the finite element methods. The results indicate that the main girder exhibits the highest strain energy proportion in low-order lateral bending modes, while it is the main cable in low-order vertical bending modes. Different substructures in higher-order modes contribute to the strain energy in varying proportions. For a specific mode, increasing the material damping of the substructure with the highest strain energy proportion effectively suppresses the vibration amplitude of the main girder in that mode. Additionally, installing V-shaped damping cables to control the vibration of substructures with higher strain energy proportions effectively suppresses the vibration of the main girder.

Cable-stayed bridge all-round morphology identification based on 3D point cloud model

Traditional inspection methods, that is, total station, can be labor-intensive, time-consuming, and efficiently challenging, especially for long-span cable-supported bridges. Recently, Terrestrial Laser Scanning (TLS) has been attractive in bridge digitization because of its non-contact and high-efficiency features. It can provide a comprehensive and all-round morphology assessment through establishing the bridge’s 3D point cloud model. Based on our previous research on point cloud registration of long-span bridges, this article focuses on spatial form identification using the registered point cloud model, specifically the identification of cable sag and girder spatial volume. In detail, precisely monitoring cable sag is critical for cable force identification, while accurate girder volume is essential bridge information, which should be tracked regularly and used for long-term performance evaluation and maintenance guidance. To evaluate the precision of the proposed TLS-based inspection solution, a case study is conducted on a 152 + 370 + 152 m cable-stayed bridge. Results show the identifying error of TLS-based solution remains at 2% for cable sag identification and 5% for girder volume recognition. The traffic-induced sag variance can also be captured by the point cloud data. Therefore, the TLS-based inspection method is thoroughly evaluated and demonstrated as a highly efficient and trustworthy solution.

Wind Resistance Performance Assessment of Long-Span Cable-Supported Bridges Based on Time-Varying Reliability Theory

Long-span cable-supported bridges constitute the most common type of bridge with a span of more than 400 m. They are generally designed as a double-tower long-span structure with good spanning capacity and economic performance. Wind resistance safety performance is the main index used to control the long-span cable-supported bridge structure. During the life of a long-span cable-supported bridge structure, because the service life of the cables is far shorter than the design life of the structure, the wind resistance performance of the structure will inevitably deteriorate significantly, which will seriously affect the structural service performance of symmetric cable-supported bridges. Under strong wind loads, the static wind stability and flutter stability of cable-stayed bridge structures are components of the limit state of bearing capacity, which directly affects the safety performance of the structure. We take the flutter and static wind stability of a long-span cable-supported bridge structure as the main design control index, use inverse reliability theory to calculate the reliability index of a symmetric cable-supported bridge structure, use inverse reliability theory to calculate the safety factor of a symmetric cable-supported bridge structure, and evaluate the time-varying wind resistance performance of a long-span cable-supported bridge structure by comprehensively considering the reliability index and safety factor. Taking a practical project concerning a long-span cable-supported bridge as a specific case, the time-varying wind resistance reliability of the bridge throughout its operation for more than 30 years is analyzed along with the parameter sensitivity. The results show that the wind resistance performance of the cable-supported bridge structure is obviously affected by its cables, and the degradation of cable performance will have a significant impact on the time-varying wind resistance performance of the structure, especially the critical wind speed of the structure, which has obvious time-varying characteristics. The safety factor and reliability index can be used to objectively evaluate the time-varying wind resistance performance of long-span cable-supported bridge structures.

Aerodynamic and Aerostatic Performance of a Long-Span Bridge with Wide Single Box Girder Installed with Vertical and Horizontal Stabilizers

The continuous increase in traffic volume requires wider single box girders for long-span cable-supported bridges. Flutter and aerostatic instability are challenging issues for these flexible bridges, especially when they are located in typhoon-prone regions. Aerodynamic countermeasures such as vertical and horizontal stabilizers, which are convenient in operation, saving in cost, and effective in the enhancement of flutter performance, are usually employed to withstand the wind environment requirement. This study investigates the aerodynamic and aerostatic effects of upper central vertical stabilizers (UCVS), lower central vertical stabilizers (BCVS), horizontal stabilizers (HS), and their combinations on two wide single box girders with an aspect ratio larger than 12 at various angles of attack (AOAs). The optimal layouts of stabilizers for the enhancement of flutter performance are studied using a series of wind tunnel tests. Their control mechanisms are examined and discussed using flutter derivatives and step-by-step (SBS) method. A new index of nominal torsional center (NTC) is proposed to intuitively describe the flutter modality. The correlations among different indexes of flutter modality, flutter derivatives, and Ucr are further analyzed. The static coefficients of the bridge girders and the aerostatic performance of the bridge with or without stabilizers are also analyzed. Experiment results show that the values of Ucr for 4- and 5-m-high single box girders increased by 13.9% and 46.3%, respectively, after the hybrid installation of UCVS, BCVS, and HS at their optimal conditions. The analytical solutions indicate that the installation of different stabilizers changes the variation trend of the aerodynamic damping ratio with the wind speed to increase or reduce the flutter boundary. Four flutter modality indexes including amplitude ratio (Ψ), phase difference (ψ), energy participation level (Ph), and NTC are all found that have no obvious correlations with Ucr. The static analysis on a three-dimensional bridge showed that the optimal stabilizer schemes for flutter have insignificant effects on aerostatic performance.

Predicting bridge longitudinal displacement from monitored operational loads with hierarchical CNN for condition assessment

Over the past few years, longitudinal displacement has gained popularity as a means of evaluating the condition of long-span cable-supported bridge components, such as bearings. However, accurately predicting bearing displacement under varying load conditions is challenging due to the exposure of bridges to environmental and traffic loads. To address this issue, a hierarchical convolutional neural network (HCNN) model was developed in this paper for predicting bearing displacement using comprehensive loads as predictors. Structural health monitoring (SHM) systems of a cable-stayed bridge are utilized to provide one-month datasets for training and testing of the proposed method. Temperature, wind, and vehicle loads are adopted as input variables, and bearing displacement is the output. Results demonstrated the effectiveness of the proposed approach in predicting bearing displacement with an accuracy of over 95.6%, surpassing other models like traditional CNN, encoder-decoder, and U-Net in both accuracy and efficiency. Additionally, the contributions of different loads in predicting displacement are investigated, demonstrating the importance of traffic loads. Cumulative displacement can consequently be calculated for condition assessment of components such as bearings and expansion joints. A comparison with another cable-stayed bridge showed that the expansion joints in the current bridge were in satisfactory condition. Overall, the proposed approach can facilitate predictive maintenance in long-span bridges, helping to prevent premature failures.

Experiment study on vortex-induced vibration of a twin-box girder with large cantilever plates

Due to their good aerodynamic stability performance, twin-box girders are frequently adopted in long-span cable-supported bridges. However, they are also susceptible to vortex-induced vibration (VIV) since the central slot changes the flow patterns around a bridge girder. In this paper, the VIV performance of a twin-box girder with large cantilever plates was investigated through wind tunnel tests of sectional models with 1:75 and 1:30 scale ratios. Furthermore, the effects of increasing the damping ratio and installing various conventional aerodynamic countermeasures such as guide vanes, grid plates, and central stabilizers on VIV suppression of the twin-box girder were investigated. A new type of aerodynamic countermeasure named the L-shaped windshield was proposed to suppress the VIV response of the twin-box girder to an acceptable level. The results indicated that significant vertical VIV occurred for the twin-box girder, and increasing the damping ratio and installing conventional aerodynamic countermeasures could not suppress the VIV response of the twin-box girder effectively. The attachments obviously worsened the vertical VIV performance of the twin-box girder, and the attachments on the upper surface showed a more significant effect. It was further demonstrated that the L-shaped windshield is an effective countermeasure that can completely suppress the vertical VIV of the twin-box girder by greatly reducing the motion-induced vortexes in the central slot with the help of low turbulence in the turbulent flow field.

Physics-Informed Neural Network for Flow Prediction Based on Flow Visualization in Bridge Engineering

Wind loads can endanger the safety and stability of bridges, especially long-span cable-supported bridges. Therefore, it is important to evaluate the potential wind loads during the bridge design stage. Traditionally, wind load evaluation is performed by wind tunnel testing, which is relatively expensive. With the development of computational fluid dynamics and high-performance computing, numerical simulations are becoming more accessible for designers. However, the costs required for accurate numerical results are still high, especially for high-fidelity simulations. Under this condition, searching for a more efficient method to evaluate the wind loads in bridge wind engineering has become a new goal. It seems that flow visualization is a good entry point. Although flow visualization techniques have been developed in recent years, it remains difficult to extract velocity and pressure fields from images. To address this problem, physics-informed neural networks (PINNs) have been developed and validated. This study establishes a PINN to investigate the two-dimensional viscous incompressible fluid flow passing a generic bridge deck section. Two cases with different Reynolds numbers are tested. After careful training, it is found that the PINN can accurately extract the velocity and pressure fields from the concentration field and predict the drag and lift coefficients. The results demonstrate that PINNs are a promising method for extracting useful flow information from flow visualization data in engineering applications.

Data-driven prediction of critical flutter velocity of long-span suspension bridges using a probabilistic machine learning approach

Among the consequences of wind-induced excitation on long-span cable-supported bridges, flutter instability is the most dangerous and can collapse bridge structures. Until now, the flutter velocity of long-span bridges can be computed after conducting an experimental wind tunnel test or by means of computational fluid dynamics (CFD). However, the approaches mentioned above are cost-prohibitive and time-consuming especially when there are many sampling designs to evaluate. Therefore, it is crucial to develop an alternative solution for evaluating the flutter performance of such structures while minimizing the associated cost and computation time without worsening the accuracy of the results. Scholars have proposed machine learning (ML) techniques to address this issue. Unfortunately, some ML techniques do not provide excellent generalization for small datasets and are prone to bias even when the accuracy is relatively high. Besides, conventional ML models do not consider the uncertainty in data. This study proposes a probabilistic machine learning approach to overcome the weaknesses of the conventional ML models. The dataset used to train the proposed model was generated from 73 sampling designs using a fully numerical approach that involved 2D URANS (Unsteady Reynolds-averaged Navier-Stokes) CFD simulations, quasi-steady flutter theory, finite element model, and multi-mode approach for critical flutter velocity computation. The deck cross-section's most influential parameters and the critical flutter velocity constitute the datasets used to build the proposed probabilistic machine learning model. Our finding substantiates that the probabilistic machine learning approach based on hierarchical Bayesian modeling (PML-HBM) overperformed the conventional machine learning models, including extreme gradient boosting regression (XGBR), random forest (RF), and the support vector regression(SVR). Therefore, PML-HBM can accurately predict the critical flutter velocity. This model is an interesting approach to circumvent the time and cost associated with wind tunnel tests and CFD simulations at the earlier design stage of long-span bridge aerodynamic study.

Cumulative displacement-based detection of damper malfunction in bridges using data-driven isolation forest algorithm

Long-span cable-supported bridges are flexible and prone to significant deformations under temperature, wind, and vehicle loads. Such large deformations induce frequent longitudinal movement at the end of the bridge girder, which can cause malfunction or failure in the components such as expansion joints, bearings, or longitudinal viscous dampers. This paper develops a condition assessment approach using the girder end displacement measurements, which primarily includes four steps, namely, data preprocessing, feature characterization, datasets preparation and splitting, and anomaly detection. The data preprocessing step considers the physics-based correlation between the temperature and displacement, which is used to pre-check noisy data issues in the displacement monitoring data. Subsequently, hourly cumulative displacement is calculated as the feature to feed into the machine learning model. The third step prepares the datasets and splits them into training and testing datasets. Then the isolation forest algorithm is implemented for anomaly detection with well-tuned parameters of the number of decision trees and the number of samples in each decision tree. Structural health monitoring data of a suspension bridge are collected to verify the proposed approach, and the detection targets are specified as viscous damper malfunction and a specific holiday period. The proposed approach demonstrates its ability to detect both events successfully, which can shed light on the predictive and preventive maintenance of the bridge.

Displacement response estimation of a cable-stayed bridge subjected to various loading conditions with one-dimensional residual convolutional autoencoder method

Displacement is an essential indicator of the functioning and safety of long-span cable-supported bridges under operational conditions. However, displacement estimation is challenging as these bridges are simultaneously subjected to various loading conditions such as temperature, wind, and vehicles. This article investigates an approach for estimating bridge displacement responses under multiple loads using a residual autoencoder model. Monitoring data of a cable-stayed bridge are collected to validate the proposed approach, including comprehensive measurements of the various loads and the displacement responses. Characteristics of temperature, wind, and vehicle loads are taken as the input, and the displacement responses at the mid-span of the main girder and top of the two pylons are taken as the output. The results showed the effectiveness of the proposed approach with an accuracy higher than 95%, which clearly outperformed other models such as long short-term memory networks in accuracy and efficiency. The effects of different types of loads are also investigated, and the wind load is found to be the most influential. Furthermore, multistep ahead prediction is carried out using the proposed approach, and good accuracy is achieved even 5 min ahead. The proposed approach can shed light on early warning of the malfunction of the bridge.

Probabilistic vortex-induced vibration occurrence prediction of the twin-box girder for long-span cable-stayed bridges based on wind tunnel tests

The twin-box girder is a recommendable structural style for long-span cable-supported bridges due to its excellent aeroelastic stability. Vortex-induced vibration (VIV) is a typical wind-induced vibration for this kind of girder with a high occurrence probability associated with wind characteristics, structural properties and aerodynamic configuration under uncertainty. Therefore, probabilistic approaches should be adopted to predict the occurrence of VIV under uncertainty. This paper presents such an approach to predict the VIV occurrence using the decision tree method. Wind tunnel tests on a large-scale section model are conducted to investigate the effects of structural damping ratio and wind speed on VIV performance. Uniform and turbulent wind flow fields under three attack angles of −3°, 0°, and −3° are tested. Moreover, wind direction at the bridge site is determined as a parameter affecting VIV occurrence. As a result, a decision tree considering the effects of structural damping ratio, wind direction and wind speed is formulated to estimate the probability of VIV occurrence. In order to suppress VIV, aerodynamic countermeasures (ACMs) with L-shaped windshields are applied. Furthermore, the probabilistic cost-benefit analysis of the application of ACMs is developed using a decision tree, and the probability of the positive cost-benefit from ACMs application is accordingly estimated. The application of the proposed probabilistic approach is investigated on a long-span cable-stayed bridge with two separated steel boxes.

Structural health monitoring on Yangluo Yangtze River Bridge: Implementation and demonstration

Long-span cable-supported bridge is one of crucial transportation infrastructures. Structural health monitoring (SHM) system that is used to assess structural service conditions and detect early damage has drawn a growing attention in engineering structural society. It provides a real-time monitoring of various structural changes under operational and extreme conditions. Yangluo Bridge over Yangtze River in Wuhan city of China is a 1280 m central span suspension bridge with an orthotropic steel box girder. Taking the SHM system of Yangluo Yangtze River Bridge as an example, this paper presents an implementation of SHM system on the bridge in terms of sensor layout, data acquisition strategy, data transmission, data processing, and abnormal alarm framework. With such an SHM system, the typical monitoring results are demonstrated such as operational environments, loadings, structural deformation, strains, dynamic properties, and structural responses. The SHM system of Yangluo Yangtze River Bridge is continuously gathering data and monitoring structural behavior. It is anticipated that it will provide either scientific or technological supports to the service comfort and safety of the bridge.

Experimental investigation on vortex-induced vibrations of a triple-box girder with web modification

Split type box girder is a recommendable structural style for long-span cable-supported bridges due to its excellent aeroelastic stability. A major issue of this kind of girder is its susceptibility to vortex-induced vibration (VIV), which has not been adequately investigated. This paper presents an experimental study on VIV of a triple-box girder with three different web modifications (namely curved web and linear-type webs with different slopes). Both small- and large-scale sectional models were employed for wind tunnel tests considering the Reynolds number effect. Results indicated that the triple-box girder showed poor VIV performances in both construction and completed phases. Generally, linear-type web was superior to curved web in terms of VIV performance. Increasing the structural damping and turbulence intensity of incoming flow were helpful for VIV mitigation. Geometric profiles and arrangement of appurtenant facilities on the girder have significant effects on the VIV performance. Aerodynamic optimal schemes were proposed for VIV mitigation both in construction and completed phases. Obvious discrepancies in VIV responses were observed between the small- and large-scale tests for several scenarios. Possible factors being responsible for the discrepancies were Reynolds number, turbulence intensity, nonlinearity of model structural damping, blockage ratio and geometric accuracy of the sectional models.

Short-term fatigue damage of tethers of long-span floating cable supported bridges under harsh waves

A floating bridge can be effectively used for sea-crossing in deep water. Because the superstructure of the bridge is supported by floating substructures with pontoons, the conventional fixed piers, towers, foundations, and piles are not required. Instead, a rational mooring system can be used to strictly maintain the target position of the floating substructures against environmental loads, including winds, waves, and currents. Recently, long-span cable-supported bridges with floating towers were investigated and found to overcome the limitations of conventional cable-supported bridges, when used as sea-crossing infrastructure. To design the moorings for very large floating structures, the structural safety should be carefully investigated. In addition to the maximum stress, fatigue damage should also be studied. This study aims to investigate the characteristics of the short-term fatigue damage accumulated at sections of the tethers in long-span cable-supported bridges under harsh wave conditions. To evaluate the accumulated fatigue damage due to waves, the Palmgren-Miner rule is used, wherein the time-series wave-induced stresses acting on sections of the tethers are analyzed using the rainflow counting method. The wave-induced stresses are obtained by conducting time-series hydrodynamic analyses for a floating-bridge model, using ABAQUS AQUA. An irregular wave with 100-year return period, modeled by JONSWAP wave spectrum, is applied to the structure. The effects of the floater type, draft, and initial tether inclination on the fatigue damage are summarized after intensive parametric studies.

Compressive strength equations for box-girder flanges stiffened with U-ribs in cable-supported bridges

When primary bending moments and axial forces are applied to a wide steel box girder in a long-span cable-supported bridge, top or bottom flanges are subjected to longitudinal in-plane compressional forces. In order to evaluate the ultimate compressive strength of such U-rib stiffened flanges, a total of 36 geometrically different numerical finite element models were carefully established taking into account the practical ranges of panel length and plate thickness of wide box girder flanges. Ultimate strength analyses were accordingly conducted on these hypothetical models incorporating local and global modes as possible initial geometric imperfections and different methods of imposing residual stresses. According to the resulting relationships between strengths and plate-like or column-like behavior, a set of functions is proposed to predict compressive strength and their coefficients are numerically determined by a regression analysis. The nominal strengths obtained from the proposed equations are then quantitatively compared to those of the FHWA (Federal Highway Administration) provisions, Eurocode 3, and KHBDC–CSB (Korea Highway Bridge Design Code–Cable-Supported Bridges) specifications. The strength equations developed in this study are expressed as simple equations and provide reliable strength predictions without any inherent subjectivity.

A gyroscopic stabilizer to improve flutter performance of long-span cable-supported bridges

Long-span cable-supported bridges are gaining considerable importance in the world. It is generally recognized that long-span cable-supported bridges can be very sensitive to wind effects due to their aerodynamic properties and deck flexibility. Flutter is usually a major concern because it can lead to structural deck failure. This communication introduces a prototype of gyroscopic device as an active stabilizer for improving flutter performance. A mathematical model of the gyroscopic device, installed at the bridge deck level, was studied and implemented to assess its effectiveness in increasing the critical wind speed. A preliminary study was conducted to evaluate the stabilizer’s performance on a benchmark long-span cable-supported bridge as a function of its gyricity. The results demonstrate that the gyroscopic stabilizer is very successful and bridge flutter threshold increases with the gyricity of the gyroscopic device, within a practical operational range.

Wind-Induced Phenomena in Long-Span Cable-Supported Bridges: A Comparative Review of Wind Tunnel Tests and Computational Fluid Dynamics Modelling

Engineers, architects, planners and designers must carefully consider the effects of wind in their work. Due to their slender and flexible nature, long-span bridges can often experience vibrations due to the wind, and so the careful analysis of wind effects is paramount. Traditionally, wind tunnel tests have been the preferred method of conducting bridge wind analysis. In recent times, owing to improved computational power, computational fluid dynamics simulations are coming to the fore as viable means of analysing wind effects on bridges. The focus of this paper is on long-span cable-supported bridges. Wind issues in long-span cable-supported bridges can include flutter, vortex-induced vibrations and rain–wind-induced vibrations. This paper presents a state-of-the-art review of research on the use of wind tunnel tests and computational fluid dynamics modelling of these wind issues on long-span bridges.

A comparative study of wind-induced dynamic response models of long-span bridges using artificial neural networks, support vector regression and buffeting theory

Long-span cable-supported bridges are structures susceptible to high dynamic responses due to the buffeting phenomenon. The current state-of-the-art method for buffeting response estimation is the buffeting theory. However, previous research has shown discrepancies between buffeting theory estimates and full-scale measured response, revealing a weakness in the theoretical models. In cases where wind and structural health monitoring data are available, machine learning algorithms may enhance the buffeting response estimation speed with less computational effort by bypassing the analytical model’s assumptions. In this paper, multilayer perceptron and support vector regression models were trained with synthetic and full-scale measured data from the Hardanger Bridge. The analytical response was also computed from buffeting theory applied to a finite element model of the bridge, and the estimates are compared. The prediction accuracy was evaluated with the normalized root mean square error, the mean absolute percent error and the coefficient of determination (R2). The machine learning models trained with synthetic datasets achieved very high accuracy with normalized root mean square errors ranging from 1.46E-04 to 7.21E-03 and are therefore suitable for efficient surrogate modeling. Further, the support vector regression model trained with the full-scale measured dataset achieved the best accuracy compared with the other methods.

Finite-Element Fatigue Analysis of a New Rib-to-Floor Beam Connection for Orthotropic Steel Decks

The potential fatigue performance of a new type of rib-to-floor beam (RFB) connection for orthotropic steel decks, the slit connection, was investigated via finite-element analysis. The slit RFB connection combines aspects of the previously used fitted RFB connection and extended cut-out RFB connection. Various slit geometries, floor beam restraint conditions, floor beam geometries, finite-element analysis meshes, and loading conditions were studied. The results show that the slit RFB connection is well suited for orthotropic steel decks in bridge deck replacement applications, where the orthotropic deck is supported by existing, stiff, transverse floor trusses (or floor beams) that are often present in existing long-span cable-supported bridges.

Effects of Wind-Barrier Layout and Wind Turbulence on Aerodynamic Stability of Cable-Supported Bridges

Wind barriers are nowadays commonly placed on bridges to protect vehicles from adverse cross-wind effects. In addition to this beneficial influence, wind barriers may adversely affect the bridge dynamic stability. This is particularly exhibited for long-span cable-supported bridges. It is therefore the scope of the present study to analyze the effects of wind barriers on aerodynamic and aeroelastic characteristics of bridge-deck sections of long-span cable-supported bridges together with the respective flow characteristics around bridge-deck sections. The focus is on various arrangements of wind barriers, i.e., (1) wind barriers placed at the windward bridge-deck edge only; (2) wind barriers placed at the leeward bridge-deck edge only; and (3) wind barriers placed at both windward and leeward bridge-deck edges. This was carried out experimentally on small-scale models in a boundary layer wind tunnel. Three typical bridge-deck section models were studied, i.e., Great Belt (Denmark), Kao-Pin Hsi (Taiwan), and Golden Gate (United States). The galloping susceptibility of the bridge-deck sections in all arrangements of wind barriers proved to be the same, as is the case for the empty bridge-deck sections without wind barriers; i.e., from this point of view, wind barriers do not adversely bridge dynamic stability. However, in configurations with the windward wind barrier only, as well as both windward and leeward wind barriers, the flutter susceptibility of the bridge-deck sections increases substantially; i.e., the critical flow velocity for the bridge flutter decreased significantly in comparison with the respective empty bridge-deck sections. For the leeward wind barrier only, the flutter susceptibility of the bridge-deck sections did not change and remained the same as it was for the empty bridge-deck sections. The empty bridge-deck sections do not exhibit any significant change concerning their susceptibility to flutter for various turbulence levels of the incoming freestream flow. The flutter susceptibility of cable-supported bridges equipped with wind barriers is lower in more turbulent incoming flows. The bridge decks with wind barriers are more resilient to flutter in more turbulent winds. Shear layers that separate from the top of the wind barrier may have an important role in the self-excited lift force and the pitch moment and, consequently, the dynamic behavior of bridge decks.