Stay Cables Research Articles

Infrared Thermography Inspection of Stay Cables

The injection of petroleum waxes into bridge stay cables is a proven method for protection against corrosion, primarily due to their sealing properties, adhesion to strands, and thermal stability. However, with a liquefaction point below 70°C, exceptional ambient conditions can lead to partial liquefaction of the injected waxes, especially for cables with a dark sheath, resulting in leaks and extrusions. Sections of stay cables may lose their corrosion protection without visible signs from the outside. This study explores the use of infrared thermography for identifying and mapping areas lacking wax. It involves acquiring high-resolution infrared thermal images of the stay cables and studying temperature variations. Since wax has a higher thermal inertia than air, a thermal gradient is expected between areas with wax and those without after the daily heating cycle. This paper presents a campaign conducted on a cable-stayed bridge in France. During this campaign, temporary instrumentation was deployed to identify the optimal intervention window. Multiple sessions of acquisitions using a high-precision thermal camera were then performed. The acquired images were subsequently rectified and assembled to create uniform and comprehensive panoramas of the stay cables. The results obtained for several characteristic cables are presented and discussed in this paper.

Algorithms for Computer-Based Calculation of Individual Strand Tensioning in the Stay Cables of Cable-Stayed Bridges

This paper introduces algorithms for computer-aided calculation, based on a proposed computational model for stay cables, decomposed from a bridge’s structural system. These algorithms determine the necessary tension forces and corresponding deformations in the cables for individual strand tensioning using lightweight hydraulic jacks. Two tensioning methods are discussed: the first involves single-cycle tensioning with varying force intensities, while the second employs multiple cycles by applying forces of constant intensity until achieving an equalization of forces in all strands of the cable. The efficiency of the proposed procedures is demonstrated through a numerical example.

Parameter Tuning and Positioning Strategy of VD and TMD Joint Control System for Multi-Modal Vibration of Stay Cables

Stay cables are becoming slender and their fundamental frequencies are becoming lower with the span of bridges increasing, thus leading to the occurrence of multi-modal vibration under various excitations. As a simple and effective strategy for cable vibration mitigation, the external damper is widely used in practice. However, one damper normally can target only fewer modes and poses limited effects on the control of multi-modal vibration. This paper proposed the use of a joint control system combining a viscous damper and a tuned mass damper for mitigating the multi-modal vibration of stay cables, followed by the optimization methodology of tuning and positioning. The control performance of the joint system was evaluated by numerical simulations. The feasibility of the joint control system was validated by analyzing the results of the comparative study, therefore providing a possible solution to multi-modal and high-modal vibration of stay cables.

Dynamical analysis of a stay cable with a nonlinear energy sink and time-delayed feedback control

Stay cables exist commonly in engineering and can exhibit sustainable and large vibrations under external excitations. The unexpected oscillations always lead to the fatigue and damage of structures, resulting in the economical loss. This paper studies the vibration control of a stay cable system with a nonlinear vibration absorber and time delay control. The governing equations of motion of the stay cable system under harmonic excitations are given. The stability and different bifurcations of the trivial equilibrium point of the system are analyzed. The bifurcation diagrams with respect to the control parameters are illustrated. The frequency responses of the forced system are obtained by using the harmonic balance method. Numerical simulations are performed to validate the obtained results and various dynamical phenomena are shown, such as the multi-period oscillations, quasi-periodic responses and chaotic motions. The effects of the time-delayed feedback control on the nonlinear dynamics and vibration reduction of the system are extracted. It is shown that the proper values of the time delay and feedback gain can improve the vibration reduction performance of the system, such as the suppression of the resonance peaks and elimination of the complex responses.

A Stay Cable Icing Identification Method Based on the Fusion of U-Net and ResNet50

A Stay Cable Icing Identification Method Based on the Fusion of U-Net and ResNet50

Vibration Mitigation via Tuned Mass Damper for Adjacent Stay Cables Interconnected with Rigid Cross-Tie

The characteristics of low damping and closely spaced natural frequencies make stay cables susceptible to wind-induced vibrations. This work proposed a novel damping device consisting of tuned mass damper (TMD) and rigid cross-tie (RCT) to mitigate the vibration of stay cables effectively. Two adjacent stay cables interconnected with RCTs can provide installation locations for TMDs, thus making the novel TMD-RCT control system feasible. Experimental control tests were carried out on a two-cable model of adjacent stay cables built in laboratory, where one TMD was designed based on the fundamental vibration mode of the stay cable. The effects of CT stiffness, number of RCTs, mass ratio, and installation position on the vibration reduction effect of the device were studied. To validate the efficacy of the proposed TMD-RCT device in vibration mitigation of stay cables under different loading cases, simulation tests and corresponding control performance evaluation were conducted.

Improved Deflection Prediction Model for PSC Box Girder with Stay Cable System during Tensioning Phase

To improve the accuracy of deflection prediction for prestressed concrete (PSC) box-girder bridges with a stay cable system (SCS) during tensioning, this study employs the Latin hypercube sampling (LHS) technique to sample random variables affecting long-term deflection of the main girder. A long-term deflection randomness analysis model is established, and the shear stiffness degradation factor is included to quantify the contribution of diagonal web cracking to the main girder deflection. Uncertainty and sensitivity analysis are conducted for the Dongming Huanghe River Highway Bridge. An objective function is applied to select the optimal combination of random variables, and a modified model is established and verified for accuracy. Results show that diagonal web-cracking accounts for 8.8% of total deflection and cannot be ignored, and the prestressed tension control stress, creep uncertainty coefficient, and concrete density significantly impact long-term deflection. The modified model predicts deflection with greater accuracy than the mean value model.

Stability in Parametric Resonance of a Controlled Stay Cable with Time Delay

The stability of the parametric resonance of a controlled stay cable with time delay is investigated. The in-plane nonlinear equations of motion are initially determined via the Hamilton principle. Then, utilizing the method of multiple scales, the modulation equations that govern the nonlinear dynamics are obtained. These equations are then utilized to investigate the effect of time delays on the amplitude and frequency-response behavior and, subsequently, on the stability of the parametric resonance of the controlled cable, that it is shown to depend on the excitation amplitude and the commensurability of the delayed-response frequency to the excitation frequency. The stability region of the parametric resonance is shifted, and the effects of control on the cable become worse by increasing time delay. The work plays a guiding role in the parametric design of the control system for stay cables.

Engineering Reliability-Based Condition Assessment for Stay Cables Using Non-Destructive Interferometric Radar

Structural health monitoring (SHM) of cable-stayed bridges requires periodic assessment for the deteriorating stay cables to ensure a long-term service life of the bridge. However, conducting the non-destructive SHM for operating cable-stayed bridges and analyzing the safety statuses of all the working cables are still challenging, due to the lack of in situ cable data for previously constructed bridges. This study developed an innovative framework of health condition assessment for stay cables based on cable vibration frequencies from an interferometric radar (IBIS-FS) using engineering reliability analysis (ERA). Taking a cable-stayed bridge in Victoria, Australia as a target structure for the case study, it shows that the presented framework can remotely monitor the accurate real-time load bearing conditions of stay cables by calculating tension forces, and effectively assess their health conditions. The results show that the natural frequency (up to the fifth mode) of a healthy cable remains constant under different external loadings but varies for damaged cables. The measured reliability index of all the stay cables is higher than the safety threshold factor at ultimate limit states, while one carries tension force higher than the maximum design load (lower than the minimum breaking load) and other three cables need to be monitored regularly due to their low reliability indices. This is attributed to an integrated effect of applied tension force, cable diameters, and minimum breaking loads.

Efficacy of SMA Wire in Vibration Suppression of a Stay Cable: An Experimental Investigation

Efficacy of SMA Wire in Vibration Suppression of a Stay Cable: An Experimental Investigation

Further Explanation on the Excitation Mechanism of Stay Cable Vibration in Dry Conditions

The present article outlines a research investigation carried out in a wind tunnel setting aimed at augmenting comprehension of the excitation mechanism of stay cable vibration in arid conditions. A multitude of wind tunnel experiments were thoroughly scrutinized. The study commenced by conducting measurements of the stay cable vibration in conditions of steady flow. The flow angle was set at 45 degrees, and the inclination was set at 25 degrees. The wind velocities varied during the experiment. Additionally, an investigation into the flow field surrounding the stay cable’s was conducted in both vertical and horizontal directions. By utilizing two hot wire anemometers in the cable wake, an extensive database of flow field measurements was obtained. The experimental results revealed that the vibration characteristics of the stay cable under the arid conditions considered in this study aligned with findings reported in existing literature. Notably, a deeper comprehension of the excitation mechanism of a stay cable in a dry state was attained. This mechanism is closely associated with the inhibition of Karman vortices and the development of low-frequency vortices. At low wind speeds, Karman vortices predominated, resulting in small-amplitude vibrations. However, as the wind speed increased, the influence of Karman vortices diminished progressively, while the low-frequency vortices grew stronger. These low-frequency vortices exhibited high energy and a significant correlation with shedding along the stay cable, thereby inducing cable vibration in a dry environment.

Anomaly diagnosis of stay cables based on vehicle-induced cable force sums

Stay cables are one of the most critical load-carrying components for cable-stayed bridges. Cable damage or performance degradation can affect the normal operation of bridges. Therefore, it is essential to evaluate the service performance of cables in real time to ensure bridge safety. In this paper, an anomaly diagnosis method for stay cables based on vehicle-induced cable force sums (VICFS) of cable pairs (defined as two symmetric cables upstream and downstream) is proposed. First, the theoretical relationship between the vehicle load and VICFS was derived through mechanical analysis. Second, a new anomaly-sensitive warning index was established based on the above derivation, and the anomaly diagnosis for stay cables was achieved by combining it with the X-bar control chart. Then, according to finite element simulation, the variations in VICFS in different cases were analyzed to verify the rationality of the theoretical derivation and the established warning index. Finally, an engineering application to an in-service cable-stayed bridge was carried out to validate the feasibility and effectiveness of the anomaly diagnosis method. The results show that the proposed method can accurately detect and locate damaged cables, which can be successfully applied to monitor the long-term performance of stay cables.

Damage Identification of Stay Cables Based on a Small Amount of Deflection Monitoring Data

For the problem of cable damage identification in cable-stayed bridges, we have presented a method for identifying cable damage based on deflection monitoring data from a small number of measurement points. We first describe the method to reduce the number of measurement points. We analyzed the distributional characteristics of the deflection difference before and after cable damage in cable-stayed bridges with optimized measurement points. The first derivative of the deflection difference is transformed by a wavelet transform to identify the location of the damaged cable. Then, the Kriging proxy model with exponential and deflection differences is established. The objective function is constructed from the residual deflection difference formed by the deflection difference and the measured deflection difference. With the particle swarm optimization algorithm, the damage parameters in the surrogate model are modified to minimize the objective function, and the damage to the cables is then identified. It is shown that the location of the damaged cable can be identified from the deflection data of a small number of measurement points with small error. The degree of damage can be accurately determined using the surrogate model.

Research on Algorithm of Corrosion Fatigue Damage Evolution of Stay Cables and Structural Mechanical Behavior with Cable Fracture

From the point of view of material multiscale analysis, the deterioration of the fatigue properties of the cable is due to the micro-damage inside the strand. To describe the damage failure process of the cable as accurately as possible, many micro damage details need to be implanted in the strand model. However, with the increase of the number of wires in the cable body, this modeling method will produce a large number of elements in the finite element model of the stay cable, which makes the calculation cannot be completed iteratively. Based on this, a time-step adaptive simulation method for corrosion fatigue damage evolution of stay cables was proposed in this paper. In this method, the corrosion fatigue damage evolution model was implanted in the local part of the strand model, and a damage variable was used to comprehensively consider the evolution behavior of distributed micro-damage in the strand, which satisfies the calculation accuracy and realizes the simulation of the whole process of fatigue deterioration of the stay cable, greatly improving the calculation accuracy and convenience. Then taking an in-service cable-stayed bridge as an example, the stress of the main beam and the local spatial stress of the main beam under the special condition of the cable damage failure were studied by combining the rod model with the local model, which provides data reference for the replacement of the cable of the cable-stayed bridge with a long construction life.

Effects of damping and helical fillets on galloping vibration of stay cable installed with a rectangular lamp

Lamps attached on the stay cable can change the stable circular cross-section of the stay cable, which is easy to cause galloping vibration. Stay cables of the Kuipu bridge in the Fuzhou City of China were equipped with damper and helical fillets. After the installation of rectangular lamps on this bridge, no obvious vibration of the stay cables was observed. This is totally different from another bridge, the Kuimen bridge in the Chongqing City of China, which has been recently reported by the authors. The purpose of this study is to clarify the effects of the helical fillets and the structural damping on galloping vibration. The features of galloping vibration of the stay cable attached to a rectangular lamp were carefully studied, and the effectiveness of damping and helical fillets in reducing the galloping vibration was evaluated. First, the force measurement wind tunnel tests on the segmental test model were carried out, and the lift and drag coefficients of the stay cable attached to the rectangular lamp were measured. The dangerous wind attack angle of galloping vibration was predicted by the galloping force coefficient. Second, 3-dimensional vibration measurement wind tunnel tests were carried out to measure the wind-induced response of the cable-lamp test models. The variation of wind-induced response of stay cable with yaw angle and wind velocity was measured for test models with and without helical fillets. In the test, the features of wind-induced vibration were studied at the damping level of 0.1%, 0.6%, 0.7%, 0.8%, and 1.0%. According to Den Hartog’s theory, the minimum coefficient of galloping force is about −9.8. The experimental results of 3-dimensional vibration measurement wind tunnel tests show that the helical fillets wrapped on the cable surface can enhance the critical wind velocity to a certain extent, but the critical wind velocity is still far lower than the design wind velocity. When the damping ratio of the stay cable is up to 1.0% ( SC = 35.1), the galloping vibration of the stay cable attached to a rectangular lamp on the Kuipu Bridge can be effectively mitigated.

Evaluation of Natural Frequency of a Cable Stayed Bridge Using System Identification Technique

Abstract: System Identification is an emerging area in the domain of structural engineering specially under structural health monitoring. For dynamic analysis or stimulation, the dynamic system parameters (i.e. natural frequency, mode shape, damping ratio etc.) are most important. Vibration data of actual structures are collected by different sensors. These data are analyzed with the help of different system identification technique to get inside view of the structure. This paper presents the synthetic vibration data generation of the model structure using Time History Analysis with the help of SAP2000 software. Time history analysis is performed on a cable stayed bridge. Joint acceleration, mode shapes, natural frequency etc. are found from this analysis. For system identification purpose the acceleration time history data of different locations are used to get the natural frequency of the cable stayed bridge which is a significant system identification parameter. This identification is done with the help of power spectral density (PSD) using MATLAB algorithm

Dynamic Formulation for Cable Stayed Bridge and It’s Validation

Cable stayed bridge is the most sensitive structure because of its higher flexibility. Exact bridge behavior can be obtained by proper dynamic bridge formulation. Cable stayed bridge deck and pylon can be modelled as abeam element. Researchers used to model cables with simple truss element and letter by parabolic cable element; although they are not presenting the exact cable performance under different lateral loads. In this study, a complete comprehensive study of modelling scheme for cable stayed bridge with improved catenary cable element is adopted by Equivalent modulus approach. The Modelling strategy involved finite element modelling with a dynamic stiffness method. A real CS Bridge is modelled in Midas-civil and results are compared. This improved innovative modelling approach agrees well with the bridge analysis results of the research article.

State of Art for Dynamic interaction of High Speed Bullet Train Load for Cable Stayed Bridge

Cable stayed bridge (CSB) is the center of attraction among all bridges due to aesthetic appearance and structural integrity. Earlier CSB used only for pedestrian and vehicular loads but with time passes it uses more intended towards mass transportation. When a bridge is designed to serve such heavy and rapid load; it should be analyzed for such load intensity. The question is how this high-speed rail load should be applied? The trainload is applied to bridge structure by different approaches by different researchers. In this article, a state of art for high-speed train load applications is discussed.

Stay cable vibration mitigation: A review

Stay cables in cable-stayed bridges are subjected to various types of dynamic excitation mechanisms under environmental loads. The excited vibrations can have a large amplitude because of low vibration frequencies and small inherent damping of cables. As cables become longer (the longest cables are around 600 m in cable-stayed bridges with a main span of 1000 m), more modes are vulnerable to wind and rain-wind induced vibrations, posing challenges to vibration mitigation. This paper presents a comprehensive review of recent advances in stay cable vibration mitigation, including theoretical modeling of cable damping system and techniques for enhancing multimode damping. Recent results on cable damping measurements, understanding of cable vibrations, and relevant aerodynamic countermeasures are also recalled. The reflections can provide guidance for cable vibration control design of cable-supported bridges and for the maintenance/upgrade of cable vibration mitigation system of existing bridges.

Optimization of Multiple Helical Fillets Surface to Suppress Rain-wind Vibration of Stay Cables: A Wind Tunnel Investigation

Aims: To develop a new cable surface for control rain wind induced cable vibration of stay cable. Background: Stay cables are light and vulnerable structures. Therefore, it can be easily excited by wind or rain wind interaction. Stay cables wrapped with a single helical fillet have been proposed so far. However, these countermeasures could prevent cable vibration well, especially in dry conditions. Objective: Therefore, the objective of this research is to develop a new cable surface to control not only RWIV but also dry galloping of stay cable. Methods: A wind tunnel test will be used to investigate the RWIV characteristics and its new countermeasure. Results: First, a rain wind-induced vibration of circular stay cable was reproduced in a wind tunnel environment. The effect of upper and lower water rivulets was examined to understand their role on RWIV better. A rainfall simulator was employed to generate artificial rainfall for two different wind tunnel experiments. Finally, to control the RWIV of stay cables, novel multiple helical surface fillets were used. The upper and lower rain rivulets can play a significant role in energizing the RWIV. It was also found that the multiple helical surface fillets can suppress the cable vibration well both in wet and dry conditions. Conclusion: Multiple helical fillets cable surface could successfully prevent both the RWIV and dry galloping. To fabricate helical fillet cable to control cable vibration, 04 to 12 fillets with sizes ranging from 3mmx7.5mm to 5mmx7.5mm and a pitch of 2.95D-4.78D (D: cable diameter) are the most influential parameters and suggested herewith for practical application.