Cables Of Cable-stayed Bridges Research Articles

Assessment of critical parameters affecting fretting fatigue life of bridge stay cables at saddle supports

Saddle systems are a popular solution for supporting cables in cable-stayed bridges. Fretting fatigue failure of cables at saddle supports is a primary design consideration for these systems. Critical parameters that affect the fretting fatigue life of the cables are the contact forces and the slip displacements at the contact points between the cables and the saddle. Determining these critical parameters is the first step in evaluating the fretting fatigue life of the cables. Wear in the contact points between the cables and the saddle can affect the load distribution in saddle systems and consequently affect these critical parameters. However, the effect of wear has not been studied in the previous works. This paper first discusses the methods proposed in the literature for evaluating contact forces and slip displacements in the contact points between a cable and a saddle. Then, a finite element model of the problem and a framework for modelling the wear are presented. Finally, fretting fatigue life is determined based on the different studied approaches. The main highlights of the current study are considering the effect of wear in the simulation and employing an enhanced FE model for slip displacement calculations. The results of the basic model without wear effects showed that the first contact point between the cable and the saddle is critical for fatigue failure. However, by incorporating wear in the model, the contact force at the first point dropped and the second contact point became critical; this is in line with the observations in large-scale fatigue tests of saddle systems.

Semiactive Control of Nonlinear Parametric Vibration of Super-Long Stay Cable in Cable-Stayed Bridge Installed with Magnetorheological Fluid Damper

As the stay cables of cable-stayed bridges become longer, parametric resonance with a large amplitude is more easily triggered, which becomes a vibration hazard of super-long stay cables. An increasing number of practical applications of vibration mitigation on stay cables demonstrate that vibration control strategies can effectively facilitate hazard mitigation and improve cable-stayed bridge reliability and service life. This study proposes a semiactive control approach to reduce the parametric vibration of super-long stay cables in cable-stayed bridges installed with magnetorheological fluid damper (MRFD). First, using the cable’s gravity sag curve equation, an equation governing the combined stay cable-bridge deck-damper control system was established to consider the effect of the chordwise force of cable gravity. Subsequently, a targeted LQR-based optimal active control law is proposed to provide the target control force in the semiactive control. The parametric influences on the performance of the LQR-based optimal active control were analysed to provide insight into the proposed control strategy. Since the semiactive control could achieve almost the same control efficacy of the targeted optimal active control, a semiactive control strategy employing MRFD is proposed to mitigate the parametric vibration of a super-long stay cable. Based on the proposed semiactive control strategy, the system was attached with the MRFD of the longest cable, S36, in the designed prototype long cable-stayed bridge. The efficacy of the established semiactive control system was also analysed. The analysis results confirm that the proposed semiactive control strategy and designed semiactive control system can perform similar to the LQR-based optimal active control. The semiactive control system attached to the MRFD can mitigate the parametric vibration of super-long stay cables in cable-stayed bridge engineering practice.

Enhancing vibration control in stay cables: a modified damping formulation with NS-HDR damper

Cables in cable-stayed bridges have low intrinsic damping, and dampers are often used as a countermeasure for cable vibration control. This paper presents an innovative asymptotic formula for calculating the additional damping in stay cables equipped with Negative Stiffness High Damping Rubber dampers (NS-HDR). The NS-HDR damper incorporates negative stiffness through a pre-compressed spring. The analysis employs models of flexural cables with fixed-fixed or hinged-hinged ends to derive the formulation of attainable damping ratio. The results of the study reveal that the NS-HDR damper, with its negative stiffness feature, exhibits a significantly higher added damping ratio in comparison to the conventional HDR damper configuration. To quantify this increased added damping resulting from negative stiffness, a modification factor is proposed. The accuracy and effectiveness of the proposed damping formula are successfully validated using the Finite Difference Method (FDM). Subsequently, the methodology is applied to design the damping of two existing stay cables (137.82m and 167.18m in length). Field measurements reveal that the damping in these cables falls below the required threshold of 0.5%. The proposed NS-HDR damper offers a viable solution to achieve the required damping ratio. These findings contribute significantly to the understanding and optimization of damping in stay cables employing HDR dampers, presenting potential applications in the field of bridge engineering. The research opens up new possibilities for enhancing vibration control and safety in cable-stayed bridges.

Influence of reduced drag load on stay cables on the construction cost of cable-stayed bridges: Two study cases

Rain–wind–induced vibrations (RWIVs) can cause the large-amplitude vibration of flexible cables in cable-stayed bridges; such vibration is one of the engineering safety problems that must be resolved. Currently, aerodynamic measures, such as dimples and spirals, are typically used as measures for suppressing vibration in stay cables. By calculating and comparing the equivalent static wind loads (ESWLs) of six typical cable-stayed bridges, the proportion of ESWL acting on the cable to that acting on the entire bridge increases approximately linearly with the bridge span. Hydrophobic coating can effectively suppress RWIVs and evidently relieve the ESWL. Hence, compared with the commonly used aerodynamic measures with surface roughness, this coating has a considerable potential as an alternative for suppressing vibration. Based on the foregoing, the wind resistance design optimization of two actual cable-stayed bridges with main spans of 420 and 1160 m is implemented to investigate the construction costs of cable wind load reduction. After optimization, the structural responses of the main towers are reduced by 4%–12%, and the optimized tower and foundation sizes are reduced by 5%–8%. The optimization for the two bridges exceed 5% and 7%, respectively. The construction investment savings are approximately 2.3 million and 7.2 million USD, respectively. These values further improve with increasing bridge span and design wind speed.

Fatigue of suspender anchorages under axial and bending loads of suspension bridges

Fatigue-induced damage is the primary failure mode observed in cables used in cable-supported bridges, such as suspenders in suspension bridges, stay cables in cable-stayed bridges, and hangers in arch bridges. Typically, cable failures occur at their anchorages in a combination of axial and bending fatigue. A computational framework to estimate axial and bending fatigue load spectrums caused by girder buffeting and train load is presented for suspenders of suspension bridges. The threaded rods of upper suspender anchorages were then accordingly evaluated. The results show that under girder buffeting of 15 m/s mean wind speed, short suspenders at the mid-span experience a maximum axial stress range of up to 35.00 MPa and a maximum rotation angle range of approximately 0.90°. Under train loads, the suspenders exhibit a maximum axial stress range of 26.88 MPa and a maximum rotation angle range of 1.42°. Threaded rods used in all suspenders generally do not experience damage under the axial fatigue load spectrum, but short suspenders in mid-span may experience significant cumulative damages under the bending fatigue load spectrum due to girder buffeting and train load. Girder buffeting tends to cause about 3 to 5 times more damage than train load. The predicted life for a failed suspender is generally consistent with actual observations (2.6 versus 2.0 years). Therefore, it is strongly recommended that the bending fatigue of short suspender anchorages due to girder buffeting should be carefully investigated in fatigue design, in addition to the bending fatigue of train load excitation.

Multiple Damaged Cables Identification in Cable-Stayed Bridges Using Basis Vector Matrix Method

A new damaged cable identification method using the basis vector matrix (BVM) is proposed to identify multiple damaged cables in cable-stayed bridges. The relationships between the cable tension stiffness and the girder bending strain of the cable-stayed bridge are established using a force method. The difference between the maximum bending strains of the bridges with intact and damaged cables is used to obtain the damage index vectors (DIXVs). Then, BVM is obtained by the normalized DIXV. Finally, the damage indicator vector (DIV) is obtained by DIXV and BVM to identify the damaged cables. The damage indicator is substituted into the damage severity function to identify the corresponding damage severity. A field cable-stayed bridge is used to verify the proposed method. The three-dimensional finite element model is established using ANSYS, and the model is validated using the field measurements. The validated model is used to simulate the strain response of the bridge with different damage scenarios subject to a moving vehicle load, including one, two, three, and four damaged cables with damage severity of 10%, 20%, and 30%, respectively. The noise effect is also discussed. The results show that the BVM method has good anti-noise capability and robustness.

Resonance analysis between deck and cables in cable-stayed bridges with coupling effect of adjacent cables considered

Resonance analysis between deck and cables in cable-stayed bridges with coupling effect of adjacent cables considered

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.

Theory of rain-wind-induced vibration of stay cables: A quasi-steady-state approximation

Rain-wind-induced vibration (RWIV) of stay cables in cable-stayed bridges is jointly induced by rainfall and incoming wind. It is a major concern to the bridge engineering community due to its very large vibration amplitude. Yet the characteristics and mechanism of RWIV have not been understood completely. In particular, a theoretical model that can well describe the RWIV is urgently needed for amplitude prediction in engineering applications. Following a recent experimental work, we propose a theoretical framework for the analytical analysis of RWIV in the present study. The moving upper rivulet, which plays a crucial role in the excitation of RWIV, is modeled with a quasi-steady-state approximation. The analytical and numerical results are first compared with the experimental data to validate the theory. Then, the effects of some key parameters, including cable mass, frequency, damping ratio, and dynamic upper rivulet, on RWIV are investigated in detail with the theoretical framework. The model in the present study provides quick and reliable evaluations of the vibration amplitude and influencing parameters of RWIV, without performing time-consuming experiments in wind tunnel or computational fluid dynamics simulations.

Damage detection of cables in cable-stayed bridges using vibration data measured from climbing robot

This paper presents a method for damage detection of bridge cables using the vibration signal coming from the sensor installed in the climbing robot. In this paper, the damage types are crack and local reduction in diameter. The climbing robot consisting of a body and three wheels connected to the body by three springs. The cable is considered as an axially loaded Euler beam. When there is no crack, the dynamic displacement of the robot is smooth and no distortion at the crack position can be inspected. However, when there is a damage in the cable, there is a distortion in the robot displacement at the damage location but this distortion is small and difficult to be observed visually. The distortion caused by the crack is presented as the significant peaks in the wavelet transform of the robot displacement. The proposed method is promising since it is efficient to detect cracks with depth as small as 1% of the cable diameter and to detect local changes in diameter with amplitude as small as 0.1%.

Inerter dampers with linear hysteretic damping for cable vibration control

Long stay cables in cable-stayed bridges have low and close-spaced modal frequencies and are subjected to multimode vibrations, e.g., rain–wind vibrations and vortex-induced vibrations. Many types of dampers used in practice for cable vibration control can be described using a linear hysteretic damping model, e.g., high-damping rubber dampers and viscous-shear dampers. Such dampers are able to provide frequency-independent damping effects while the maximal achievable damping is limited due to their intrinsic stiffness effect. Therefore, this study investigates dampers with linear hysteretic damping enhanced by inerters for cable vibration control. A general inerter damper, consisting of a spring with complex stiffness and an inerter in parallel which is then connected to another inerter in series, is attached to a cable for dynamic analyses. Complex modal analysis is performed to appreciate cable damping. The optimal damping effect is discussed with reference to dynamic properties of the damper with respect to frequency, with comparison to the system of a cable with an inerter damper with viscous damping. It is found that two inerters, respectively in parallel and in series with a damper of linear hysteretic damping, can achieve a large improvement on multimode damping of a cable. The inertance of the inerter in series with the damper needs to be large for optimal performance while a small inertance of the other inerter is preferable. Furthermore, a case study based on a cable attached with a viscous-shear damper on the Sutong Bridge is conducted to show the feasibility of the inerter dampers.

Modelling of stay cables with large earthquake-induced force variations in cable-stayed bridges

The present study proposes a practical yet reliable model for stay cables in cable-stayed bridges considering large force variation under seismic actions. The proposed model is capable of approximating the nonlinear equivalent stress-strain relationship of cables, taking into account the variation of equivalent modulus of cables during the earthquake as well as possible cable loosening. The cable performance based on the proposed method shows an overall good agreement with the actual response of cables. Then, the model is applied to a case cable-stayed bridge under seismic actions and the structural response is compared with the conventional method which models the cables with a constant equivalent modulus derived at dead load state. Comparing to the proposed model, the conventional method fails to accurately describe the cable force at the low stress level and shows discrepancies in time histories of the structural response in terms of amplitude and phase angle. Moreover, conventional method might lead to underestimation of the bending moment at the tower bottom and longitudinal displacement at deck end for most cases, resulting in unconservative seismic design. Such result highlights the importance of applying the proposed model in seismic design of cable-stayed bridges.

Damage Identification of Tie-Down Cables in Cable-Stayed Bridges Using Vehicle-Induced Displacement

Tie-down cables are critical components of uplift-restraint bearings in bridges. Damage of a tie-down cable substantially affects the safety of a bridge and driving conditions. In this study, a damage identification method for the tie-down cable in cable-stayed bridges is developed by using vehicle-induced displacement. First, a vehicle-induced displacement is derived through theoretical mechanical analysis. By introducing an area reduction factor for the tie-down cable, a displacement-based damage index is proposed, and the changing regularity of the proposed damage index is comprehensively illustrated in different damage cases. Then, the numerical simulation with the corresponding area reduction of the tie-down cable is implemented for a cable-stayed bridge to validate the rationality of the damage index. The results demonstrate that the proposed damage index is not affected by the weight of the vehicles and is effective in detecting the area reduction of tie-down cables without the information of vehicle weights. The changing regularity of the damage index can reflect the damage cases of tie-down cables. For the actual application of the proposed method, the damage index possessing a minimum initial value, which is obtained when vehicles pass in the outermost lane of a bridge, is optimum.

Optimal Design of Dampers for Multi-Mode Cable Vibration Control Based on Genetic Algorithm

Cables in cable-stayed bridges are subjected to the problem of multi-mode vibrations. Particularly, the first ten modes of long cables can have a frequency less than 3[Formula: see text]Hz and hence are vulnerable to wind-rain induced vibrations. In practice, mechanical dampers are widely used to mitigate such cable vibrations and thus they have to be designed to provide sufficient damping for all the concerned vibration modes. Meanwhile, the behaviors of practical dampers are complicated and better to be described by mechanical models with many parameters. Furthermore, additional mechanical components such as inerters and negative stiffness devices have been proposed to enhance the damper performance on cables. Therefore, it is increasingly difficult to optimize the damper parameters for suppressing multi-mode cable vibrations. To address this issue, this study proposes a novel damper design method based on the genetic algorithm (GA). The procedure of the method is first introduced where the damper performance optimization is formulated as a single-objective multi-parameter optimization problem. The effectiveness of the method is then verified by considering a viscous damper on a stay cable. Subsequently, the method is applied to optimize three typical dampers for cable vibration control, i.e. the positive stiffness damper, the negative stiffness damper, and the viscous inertial mass damper. The results show that the GA-based method is effective and efficient for cable damper design to achieve best multi-mode control effect and it is particularly useful for dampers with more parameters.

Deep Learning-Based Anomaly Detection to Classify Inaccurate Data and Damaged Condition of a Cable-Stayed Bridge

Cables of cable-stayed bridges are gradually damaged by weather conditions, vehicle loads, and corrosion of materials. Stayed cables are an essential factor closely related to the stability of a cable-stayed bridge. Damaged cables might lead to the bridge collapse due to tension capacity lost. Therefore, it is necessary to develop structural health monitoring (SHM) techniques that check the cable conditions. Besides, the sensor network system development has contributed to the state analysis, such as damage detection and structural deformation, by allowing us to collect large-scale SHM data. However, the collected SHM data might include abnormal data due to device malfunctioning or unexpected environmental inconstancies. Furthermore, since data anomalies interfere with accurate structural evaluation, we need to identify anomalies and treat them appropriately in the data preprocessing stage. However, the cause of anomalies may be either temporary errors or actual structural deformation. Anomalies caused by structural damage or sensor device failure are informative data that must not be replaced or deleted. In this paper, we distinguish between anomalies as inaccurate data and anomalies related to the state of structures or sensor devices and propose a framework to identify each of them. We train a Long Short Term Memory (LSTM) network based Encoder-Decoder architecture that processes multivariate time series and learn temporal correlation. The trained LSTM network discovers anomalies by calculating anomaly scores. We determine the anomalies emerging intermittently as errors and correct the erroneous data. If the anomalies persist, we recognize the data as generated by bridge damage or sensor device failure. We evaluate the proposed technique with cable tension data from an actual cable-stayed bridge.

Cable optimization of a cable-stayed bridge based on genetic algorithms and the influence matrix method

Structural optimization is an important tool for structural designers that helps them to find innovative design solutions and structural forms with a better exploitation of materials as well as decreased self-weight and minimum material costs. In this article, a design procedure coupling the influence matrix method and genetic algorithms to optimize stay cables in cable-stayed bridges is presented. Following that, the design procedure is utilized in the preliminary design of a twin towers double-cable planes cable-stayed bridge to be located in Ferrara, Italy. The cable cross-sectional areas and corresponding pre-tension forces are optimized simultaneously. The results demonstrate that the proposed procedure is a powerful tool for designing stay cables and predicting the optimum cross-sectional areas of stay cables under certain stress and displacement constraints.

Experimental study on high-mode vortex-induced vibration of stay cable and its aerodynamic countermeasures

In recent years, high-mode vortex-induced vibration (VIV) of stay cables has been observed in some cable-stayed bridges. It can cause undue stress and fatigue in the anchorages at the deck and/or pylons and in the cables themselves. In this study, experimental investigations were performed to characterise and control the high-mode VIV of stay cables by using horizontal- and inclined-rigid-stay-cable models. First, wind tunnel tests using the horizontal-rigid-dimpled-stay-cable model were performed to investigate the VIV characteristics of dimpled stay cables and effective VIV suppression measures. Wind tunnel tests were then conducted on an inclined rigid dimpled cylinder with and without helical fillets to investigate further the VIV characteristics of dimpled stay cables and effective suppression measures. Finally, stay-cable field measurements were made for comparison with the experimental results of the stay-cable model. The results show that stay-cable VIV can occur in cases of low damping, and the VIV of the stay cable can be effectively suppressed by increasing the damping ratio of the stay cable. Moreover, helical fillets with a diameter of d = 2.0 or 3.5 mm, which are usually used to control rain–wind induced vibration of stay cables in cable-stayed bridges, cannot effectively suppress the high-mode VIV responses of stay cables. The inclined-dimpled-stay-cable model with a damping ratio of 0.2 % at inclination angles of 25° and 40° exhibits significant VIV for the cases of wind yaw angles of 0°, 15°, -15°, and -30°. However, helical fillets with d = 10 mm (d = 0.07D, where D is the diameter of the stay cable) and pitch of 12D can effectively suppress the VIV responses of the stay cables.

A component mode synthesis method for reduced-order modeling of cable networks in cable-stayed bridges

Cables in cable-stayed bridges become increasingly long and interconnecting them using cross-ties to form a cable network is a promising method for suppressing their vibrations. Dynamics of such cable networks is complicated and not well-understood particularly for real networks consisting of many cables and cross-ties. This study proposes a general numerical model for free and forced vibration analyses of cable networks based on the component mode synthesis method. The model is developed by regarding each cable as a substructure and the dampers/cross-ties as massless interface elements. A coupling scheme is then presented to formulate the system model from the cable model and mechanical properties of the dampers/cross-ties. Model order reduction is realized for each cable using the modal truncation method in combination with generalized quasi-static correction modes to account for the damper/cross-tie induced discontinuity of cable responses at the connection points. Subsequently, free vibration analysis of typical cable networks has been conducted using the model, and the computed frequencies and mode shapes are found in excellent agreement with the close-form solutions, suggesting the effectiveness and accuracy of the method. Furthermore, the model is shown to be more efficient as compared to a finite difference model in forced vibration analysis of a three-cable network with an elastic cross-tie and near-anchorage dampers.

Structural health monitoring methods of cables in cable-stayed bridge: A review

Cables as the crucial components, its inspection is the key problem to ensure the safety of cable-stayed bridge. Study of the monitoring methods of cable tension has practical meaning to bridge stability. Firstly, this paper summarized static and dynamic theory of cables. Then, the traditional and innovative monitoring methods of cable force are analyzed, especially the recent emerging intelligent methods. At the end of the paper, a conclusion is provided for the future development of cable-stayed bridges.

Tension Force Estimation of Cables with Two Intermediate Supports

The presence of intermediate supports usually imposes difficulties in identifying the tension force of stayed cables in cable-stayed bridges or hanger cables in arch bridges. This paper establishes the partial differential equations of motion of the cable and derives two numerical models with (Model 1) and without (Model 2) considering the flexural rigidity. The effects of two intermediate supports on the identification accuracy of the cable tension force are further studied analytically and experimentally. The effects of several non-dimensional parameters (e.g. damper location, support stiffness, flexural rigidity, and mode order of the cable) on the identification accuracy of the models are also investigated. It is theoretically concluded that the simplified Model 2 provides acceptable accuracy on tension force identification when the non-dimensional parameter [Formula: see text] is greater than 90 (slender cables), whereas the accurate Model 1 can be applied for tension force identification at any scenarios. The feasibility of two models is further verified by three numerical examples and field tests on two real-world arch bridges.