Hanger Cables Research Articles

Parameter Study and Optimization of Static Performance for a Hybrid Cable-Stayed Suspension Bridge

The hybrid cable-stayed and suspension (HCSS) bridge is known for its stability and cost-effectiveness, with significant application potential. This study examined the static performance of an HCSS bridge with a 1440 m main span. A finite element model (FEM) was developed to assess key parameters, such as the span-to-rise ratio, cable-to-hanger ratio, pylon stiffness, steel–concrete interface, and cable stiffness. Through FEM analysis and parameter optimization using the zero-order and first-order optimization methods in an ANSYS module, key design variables were optimized. The results show that an inappropriate span-to-rise ratio negatively impacts mid-span girder forces, while increasing the cable-stayed area enhances the overall stiffness. Main cable stiffness plays a crucial role in load-bearing and deformation control. Significant force differences were observed between stay and hanger cables, with axial force in the main girder increasing from the side span to the pylon under dead load. Bending moments in the transition region varied widely under combined loads. Optimizing parameters, such as the span-to-rise and cable-to-hanger ratios, significantly improved the mechanical performance of HCSS bridges, offering valuable insights for future designs.

Experimental and numerical investigations on the tensile response of pin-loaded carbon fibre reinforced polymer straps

Carbon fibre reinforced polymer (CFRP) pin-loaded looped straps are increasingly being used in a range of structural load-bearing applications, notably for bridge hanger cables in network arch rail and highway bridges. The static performance of such CFRP straps is investigated through experimental and numerical analyses. Finite element (FE) models based on both one-eighth and half pin-strap assembly geometries were modelled. The resulting strains, stresses, and applied loads were compared against experimental data obtained using Digital Image Correlation, Distributed Fibre Optic Sensing (DFOS), and Fibre Bragg Grating (FBG) Sensing. The FE models effectively captured local strain distributions around the vertex area, close to the pin ends of the straps, as well as in the mid-shaft region, and aligned reasonably with experimental observations. The half FE model accurately predicted the overall strain distribution when compared to DFOS data; however, higher strain magnitudes (by 0.45–10.2 %) and larger strain reductions were observed in some locations. Regarding failure loads, the FE models agreed well with Schürmann's analytical solution and the maximum stress criterion, exhibiting less than 2.5 % deviations from the experimental data. Furthermore, the predicted onset of strap failure (by delamination) in the half model agreed with experimental values, with a maximum variance of 9.2 %.

Experimental study on vortex-induced vibrations of double-hanger cable: Upstream wake flow induces downstream vibrations

This study is inspired by an experimental observation for vortex-induced vibrations (VIVs) of a double-hanger cable system, in which a smaller vibration of the downwind hanger cable is re-excited over a narrow range of wind speeds beyond the “lock-in” range. This phenomenon is known as the wake vortex-induced vibrations (WVIVs), where the upstream wake flow induces downstream vibrations. To further investigate the characteristics and reasons for WVIVs, a refined wind tunnel test of double-hanger cable was conducted to consider the influence of aerodynamic interaction. The double-hanger cable was modeled by the tandem-arranged spring-mounted cylinders vibrating in two dimensions. The vibration responses of hanger cables were obtained under various wind speeds to reproduce the lock-in phenomenon. In addition, the vibration trajectory, phase relationship, damping ratio, inter-cable correlation, and the wind pressure on the surface of cables were analyzed. Finally, the Stockbridge dampers were designed to suppress the vibrations. The results show that under the aerodynamic interaction of the cables, the onset wind speed of VIVs in the double cables increases, and the downstream cable WVIVs closely follow the VIVs. During the WVIV phase, the downstream cable behavior is characterized by increased negative aerodynamic damping and an inverse displacement correlation between the cables. The phase relationships between the cables are time-varying due to the aerodynamic interaction. The first proper orthogonal decomposition mode of wind pressure dominates the cross-wind of motions and is crucial in vibrations. Stockbridge dampers can effectively reduce the amplitude of VIVs and eliminate WVIVs in cables.

Spacers combined with dampers for the wake-induced vibration mitigation of two parallel hanger cables

Cable wake-induced vibrations (CWIV) and tower column wake-induced vibrations (TWIV) are two types of detrimental vibrations for long hanger cables in suspension bridges. In this study, the hybrid control strategy that combines spacers with dampers is proposed as a potentially effective method for mitigating these vibrations. To validate this hypothesis, the control performance of spacers combined with dampers for both CWIV and TWIV is evaluated through aero-elastic wind tunnel tests. The universal characteristic equation of the hanger cable-spacers-damper system is derived. On this basis, modal behaviors of hanger cables with spacers and dampers are investigated to demonstrate the control principle of the hybrid strategy. The three-dimensional aero-elastic models of hanger cables, spacers, and the eddy current damper are designed and manufactured to evaluate the combined control performance of spacers and dampers for CWIV and TWIV by a series of wind tunnel tests. In addition, the effect of modal damping ratios on the control performance of TWIV is investigated by an oil damper installed at a high location on hanger cables. The results showed that spacers combined with dampers are more effective than spacers alone in mitigating CWIV and TWIV. The hybrid control strategy can suppress the vibration response of CWIV to an acceptable level, but a larger modal damping ratio in the first global mode (approximately 3%) is required to mitigate TWIV.

Dynamic modeling and analysis of hanger cables with spacers and dampers for vibration mitigation

Many suspension bridges are designed with hangers composed of pairs of cables. The hanger cables are featured by low fundamental frequencies and extremely low inherent damping, and thus subjected to various wind-induced vibrations, typically including wake-induced and vortex-induced vibrations. Spacers are required to connect the cables for suppressing wake-induced vibrations, which nevertheless provide nearly no additional damping. Damping devices are also required to suppress other types of vibrations, e.g., vortex-induced vibrations. A combination of spacers and dampers for vibration mitigation of hanger cables leads to a complex dynamic system. This paper focuses on modeling dynamic behaviors of such a system. A generalized and dimensionless numerical model is first established. Parametric analysis is then conducted to investigate the influences of spacers and dampers on system frequency and damping. It is found that equally distributed spacers with a dimensionless stiffness coefficient larger than 102 can be considered as rigid and further increasing stiffness cannot increase the system frequencies but leads to increased number of localized modes. A combination of near-anchorage dampers and viscoelastic spacers can provide adequate damping to both in-phase and out-of-phase cable vibrations. Variation in tension, mass and length ratios of the two cables is not effective in improving damping provided by viscoelastic spacers to in-phase vibrations.

Cable Force Determination Using Phase-Based Video Motion Magnification and Digital Image Correlation

The mode shape-aided method provides a simple and effective way for cable force determination, which, however, requires accurate parameter identification of the cable structure. This paper proposes a phase-based video motion magnification to process the image sequences of a cable. Digital image correlations were engaged to measure the dynamic displacement–time history, through tracking the surface characteristic features of the cable. Thereafter, a frequency–domain decomposition technique was applied to extract the natural frequency and mode shape of the cable from the displacement–time history measurements. The identified cable mode shapes, along with a tensioned pinned-pinned cable model, were used to estimate the cable force. The accuracy of the proposed methodology was subsequently verified through laboratory testing on an inclined cable model and field testing on a typical hanger cable of a real-world arch bridge. Overall, the study results indicated that the proposed methodology could expediently and cost-effectively estimate the tension forces of a cable with reasonably acceptable identification accuracy.

Wind Induced Hanger Vibrations – the Hålogaland Suspension Bridge

The hangers of the Hålogaland suspension bridge were recognised to vibrate during the final stages of construction, vibrations that persisted after the opening of the bridge to traffic. A preliminary survey indicated that the vibrations were due to vortex shedding excitation and thus could be mitigated by the addition of mechanical damper elements. The present paper gives an account of a measurement exercise launched to clarify the cause of the vibrations and to guide the placement of Stockbridge dampers on the individual hangers. Analysis of the measurements indicated that the structural damping of the hanger cables was significantly less than proposed by current engineering codes of practice and that vortex induced vibrations of the hangers occurred in a much wider wind speed range than proposed by guidelines in the field of electrical overhead conductors.

Fretting Fatigue Performance of Unidirectional, Laminated Carbon Fibre Reinforced Polymer Straps at Elevated Service Temperature.

The fretting fatigue performance of laminated, unidirectional (UD), pin-loaded, carbon fibre-reinforced polymer (CFRP) straps that can be used as bridge hanger cables was investigated at a sustained service temperature of 60 °C. The aim of this paper is to elucidate the influence of the slightly elevated service temperature on the tensile fatigue performance of CFRP straps. First, steady state thermal tests at ambient temperature and at 60 °C are presented, in order to establish the behaviour of the straps at these temperatures. These results indicated that the static tensile performance of the straps is not affected by the increase in temperature. Subsequently, nine upper stress levels (USLs) between 650 and 1400 MPa were chosen in order to establish the S–N curve at 60 °C (frequency 10 Hz; R = 0.1) and a comparison with an existing S–N curve at ambient temperature was made. In general, the straps fatigue limit was slightly decreased by temperature, up to 750 MPa USL, while, for the higher USLs, the straps performed slightly better as compared with the S–N curve at ambient temperature.

Cable structure design of suspension bridges through strand reduction method

AbstractCable structures hold a special place for the cost of suspension bridges. Considerable development of the structural cable material leads to design and construction of long‐span suspension bridges. Thus, designing cable structures that are cost‐effective and reliable is significant for these mega structures. The overall layout of a main cable is consistent with constant number of elements per span since the design of the first suspension bridge. However, the reduction of main cable area in regard to design loads could play an important role in saving cost of long span suspension bridges. This paper presents the strand reduction approach for the cable structure design of suspension bridges. The proposed approach has been implemented by releasing the required number of parallel wire strands in main cable of the suspension bridge at specific locations in accordance with axial loads on main and hanger cables where released strands are transformed into a hanger cable with special types of clamps. The strand reduction approach is named as “saddle‐clamp system” and has been compared with the current design of 1915 Canakkale Bridge. The results indicate that the strand reduction method provides 7.6% to 34.1% material quantity deduction for the cable structures of the suspension bridge.

Mode shape–aided cable force determination using digital image correlation

Assuming the distance between two nodal points of a specific cable vibration mode as the effective length of a pinned–pinned cable, mode shape–aided cable tension estimation methods are employed to estimate the cable force. This article proposes a framework based on digital image correlation technique for remote measurement of the dynamic displacement time history of cables in cable structures. Frequency domain decomposition technique is then used to extract the cable natural frequencies and mode shapes. Identified cable mode shapes are used along with a tensioned pinned–pinned cable model to estimate the cable force. Accuracy of the proposed methodology is investigated using the experimental data coming from a laboratory-scale test setup and hanger cables of a real-world arch bridge.

Natural Frequency of Tension Cable Based on Moment Inertia to Span Ratio: Determination Using Analytical, Numerical and Experimental Study

Health monitoring using vibration technique is usually conducted on cable structure. The hanger cable on the suspension bridge has a difference of span. To predict axial force of cable, the beam-string theory includes a parameter of bending stiffness. However, string theory has neglected the effect of bending stiffness. The shorter the span of the cable the greater the effect of the bending stiffness would be. This paper raises parameter moment of inertia to span ratio (I/L) to determine the apropriate analytical formula between string and beam-string. Experimental research was conducted using a vibration technique. The specimens use solid cylindrical steel beam, having length specimens of 2 m, hinge-hinge of boundary condition, and difference variations I/L of 0.024, 0.08, 0.58, 1.53 and 10.22. Numerical analysis was simulated by using Abaqus software v 6.13. The result shows that the ratio of I/L equally lowers than 0.082 has close to the analytical string theory. The ratio of I/L greather than 0.082 has close to the beam string theory.

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.

Image‐based back analysis for tension estimation of suspension bridge hanger cables

In suspension bridges, hanger cables are the main load-supporting members. The tension of the hanger cables of a suspension bridge is a very important parameter for assessing the integrity and safety of the bridge. In general, indirect methods are used to measure the tension of the hanger cables of a suspension bridge in use. A representative indirect method is the vibration method, which extracts modal frequencies from the cables' responses and then measures the cable tension using the cables' geometric conditions and the modal frequencies. In this study, ambient vibration tests were conducted on a suspension bridge in use to verify the validity of the image-based back analysis method, which can estimate the tension of remote hanger cables using the modal frequencies as a parameter. The tension estimated through back analysis, which was conducted to minimize the difference between the modal frequencies calculated using finite element analysis of the hanger cables and the measured modal frequencies, was compared with that measured using the vibration method. It was confirmed that reliable tension estimation is possible even with low-order modal frequencies when the image-based back analysis method is used.

Intelligent parameter identification for bridge cables based on characteristic frequency equation of transverse dynamic stiffness

Determining the cable force and other parameters of cables is important for condition assessment of cable-stayed structures. This study proposes a frequency characteristic equation of transverse dynamic stiffness for cables; this equation is suitable for measuring the vibrations to evaluate the primary factors that influence the accuracy of cable parameter identification. Further, a cable parameter identification method based on the particle swarm optimization algorithm is proposed. The method is suitable for a cable system of arbitrary length and with moderate sag especially when the measurement quality of the modal frequencies of cables is poor. Both numerical case studies and a cable vibration test proved that the proposed method can identify parameters with high accuracy for cables of any length and for cases requiring low-frequency measurement. Moreover, structural modal order information is not required. The extreme case is that only one order frequency can achieve highly accurate result in this way. The proposed method is suitable for parameter identification of short cables, hanger cables, and parallel strand cables, which are commonly applicable in engineering applications.

Model Order Identification for Cable Force Estimation Using a Markov Chain Monte Carlo-Based Bayesian Approach.

The tensile force on the hanger cables of a suspension bridge is an important indicator of the structural health of the bridge. Tensile force estimation methods based on the measured frequency of the hanger cable have been widely used. These methods empirically pre-determinate the corresponding model order of the measured frequency. However, because of the uncertain flexural rigidity, this empirical order determination method not only plays a limited role in high-order frequencies, but also hinders the online cable force estimation. Therefore, we propose a new method to automatically identify the corresponding model order of the measured frequency, which is based on a Markov chain Monte Carlo (MCMC)-based Bayesian approach. It solves the limitation of empirical determination in the case of large flexural rigidity. The tensile force and the flexural rigidity of cables can be calculated simultaneously using the proposed method. The feasibility of the proposed method is validated via a numerical study involving a finite element model that considers the flexural rigidity and via field application to a suspension bridge.

Numerical evaluation of multi-metric data fusion based structural health monitoring of long span bridge structures

This work focuses on structural health monitoring of long span bridges for damage detection. A feature extraction level data fusion based damage isolation strategy is presented using multi-metric sensing. The multi-metric sensing uses two types of sensors, namely strain sensors and accelerometers. The methodology combines the advantages offered by each type of sensors, while at the same time overcomes their limitations. The flexibility index method is applied and the flexibility matrices based on the strain and displacement data are combined after performing co-ordinate transformation. A study has been carried out on a simulated finite element model of the Great Belt East Bridge where realistic damage scenarios like damage in the girder, breaking of hanger cables, pier settlement, and loss of cable pretension were introduced on the structure. The study indicates that multi-metric sensing is indeed necessary as it reduces the possibility of false detections and increases the sensitivity and robustness of the methodology.

Multifunctional Robotic Crawler for Inspection of Suspension Bridge Hanger Cables: Mechanism Design and Performance Validation

This paper presents a robotic system, called multifunctional robotic crawler for cable INspection II, which is developed for inspection of hanger cables of suspension bridges. The robot can move over hanger cables and perform inspections with instruments such as cameras, nondestructive testing tools, etc. The novel mechanisms for the robotic system are proposed under the consideration of the environmental conditions of suspension bridges. Its driving mechanism adopts a crawler type one driven by brushless direct current motors, and the detachable adhesion tool ensures simple and quick installation procedures. The safe-landing mechanism for emergency situations guarantees the retrieval of the robot while preserving the safety of operators. This paper presents the robot system and its field test results under a super long-span suspension bridge, called Yeong-Jong Grand Bridge in South Korea. For practical applications, the real environmental conditions of a suspension bridge and the other fields where the robot can be applied are discussed.

Feasibility Study on Tension Estimation Technique for Hanger Cables Using the FE Model-Based System Identification Method

Hanger cables in suspension bridges are partly constrained by horizontal clamps. So, existing tension estimation methods based on a single cable model are prone to higher errors as the cable gets shorter, making it more sensitive to flexural rigidity. Therefore, inverse analysis and system identification methods based on finite element models are suggested recently. In this paper, the applicability of system identification methods is investigated using the hanger cables of Gwang-An bridge. The test results show that the inverse analysis and systemic identification methods based on finite element models are more reliable than the existing string theory and linear regression method for calculating the tension in terms of natural frequency errors. However, the estimation error of tension can be varied according to the accuracy of finite element model in model based methods. In particular, the boundary conditions affect the results more profoundly when the cable gets shorter. Therefore, it is important to identify the boundary conditions through experiment if it is possible. The FE model-based tension estimation method using system identification method can take various boundary conditions into account. Also, since it is not sensitive to the number of natural frequency inputs, the availability of this system is high.

Aeroelastic stability of a symmetric multi-body section model

The aeroelastic stability of a multi-body system is studied through a four-degree-of-freedom elastic model, which describes the linearized section dynamics of particular suspended bridges with doubly-symmetric cross-section, subject to a lateral stationary wind flow. A multi-parameter perturbation solution, applied to the modal problem in internal resonance conditions, allows a consistent reduction of the model dimensions. Focus is made on the particular parameter region corresponding to the triple internal resonance among a global torsional mode of the deck and two local modes of a pair of hanger cables. The bifurcation scenario described by a local stability analysis is featured by two dynamic instability boundaries, strongly interacting with each other. The parametric analysis of the critical wind velocity provides satisfying engineering results, pointing out how the presence of resonant light cables, as well as the addiction of dissipative couplings simulating passive viscous dampers acting on the cable-deck differential velocity, may have beneficial effects in preventing the aeroelastic instability of the full system.

Inspection Robot for Hanger Cable of Suspension Bridge: Mechanism Design and Analysis

Periodic maintenance of suspension bridge is critical to the safety of the bridge structure. Because most of the load on the bridge is supported by the cables, inspections on main cable or hanger are very important. In this paper, we propose a cable-climbing robot enabling convenient and safe visual inspection of the hanger cable. The robot is comprised of three identical modules assembled 120 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> apart circumferentially on a frame around the cable, and each module has three functional mechanisms, that is, driving, adhesion, and safe landing. The robot is controlled wirelessly by an operator on the ground, though ac power is supplied via a tether cable. In addition, the vision sensor consisting of three cameras provides images taken from three different directions covering the cable and the odometer made with a soft idler wheel locates the robot on the cable. The robot is able to transmit the visual images of the cable surfaces in realtime at a position, while climbing up and down. In this paper, the kinematic and force analysis of the robot is performed and its feasibility is experimentally demonstrated.