Main Cables Research Articles

Form-finding method for the target configuration under dead load of a new type of spatial self-anchored hybrid cable-stayed suspension bridges

General form-finding problems of cable-supported bridges are established based on a design scenario in which rigidly fixed starting control points must be given as necessary design constraints prior to independent analysis of any of its cable subsystems. This article presents a form-finding method to address a new case, in which the starting control point serves as an intermediate, flexibly variable connection, to couple two related cable subsystems in a multi-nonlinear environment for the target configuration under dead load (TCUD) of a novel type of spatial self-anchored hybrid cable-stayed suspension (HCSS) bridge. A two-layer framework is proposed by integrating finite element analysis (FEA) and analytical formulas with optimization algorithms to form a self-regulated interactive analysis among subsystems in an iterative manner. The outer layer seeks to achieve self-equilibrium of the global system under the control information of the TCUD, while the inner layer optimizes the subsystems in terms of the initial tensions in the main cables, stay-cables, branches and hangers to obtain a rational mechanical state of the bridge. Then, the TCUD and the intermediate starting control points are determined. To achieve computational stability, a high-performance accelerated Steffens-Newton (ASN) differential algorithm is developed for the shape finding of the cable-hanger subsystem, whereas the non-dominated sorting genetic algorithm (NSGA-II) is adopted as a multiobjective optimizer for TCUD optimization of the other subsystems. The proposed framework is applied to a real-scale self-anchored HCSS bridge, and its validity and performance are demonstrated by comparison studies with a non-optimal scheme and in-field test data.

Comparative analysis of calculation methods for Cable Curve of Landscape Suspension Bridges

The main cable curve control of landscape suspension bridge is not only the premise of achieving the ideal completed state, but also the key problem of suspension bridge construction control. By analysing the characteristics of the main cable of anchored double tower landscape suspension bridge, the analytical equations for calculating the main cable curve of suspension bridge are derived by parabolic method and segmented catenary method. Then combined with practical work, the main cable curve was calculation methods by using the two calculation methods. Results show that both the parabolic method and the catenary method can be used for the preliminary design of the main cable curve of the landscape suspension bridge, but the segmented catenary method with repeated revision iteration has higher accuracy.

Parametric analysis of the dynamic characteristics of a long-span three-tower self-anchored suspension bridge with a composite girder

Three-tower self-anchored suspension bridge (TSSB) is more and more favored because of its beautiful structure and strong adaptability to terrain and geological conditions. However, there are few engineering practices and related researches on super long-span three-tower self-anchored suspension bridges. A three-dimensional finite element model for the Fenghuang Yellow River Bridge, with the world’s longest span of its kind under construction, is established using the ANSYS finite element program, and the structural dynamic characteristics of the super long-span TSSB are studied and compared with those of several bridges of the same type or with similar spans. In addition, the influence of the key design parameters such as the stiffening girder stiffness, tower stiffness, main cable and suspender stiffness, central buckle, and longitudinal constraint system on the dynamic characteristics of the structure is analyzed. The results show that the first mode of the TSSB is longitudinal floating, the lower-order modes are dominated by vertical bending modes, while the higher-order modes are primarily vibration modes of the main cables, and the torsional modes exhibit strong coupling with the lateral sway of the towers and main cables. The frequency of the first antisymmetric vertical bending mode of the TSSB has an inversely proportional relationship with the main span length. Compared with a double-tower ground-anchored suspension bridge and cable-stayed bridge with similar spans, the TSSB has the lowest frequency for the first antisymmetric vertical bending mode and the highest frequency for the first symmetric vertical bending mode, with a more pronounced coupling with the towers and main cables in the torsional modes. Analysis of the structural parameters shows that the frequencies of the longitudinal floating mode, first antisymmetric vertical bending mode, first symmetric vertical bending mode, and first torsional mode are most sensitive to the longitudinal bending stiffness of the side tower, central buckle, vertical bending stiffness of the stiffening girder, and torsional stiffness of the stiffening girder, respectively. The research findings and relevant conclusions can provide basic data for response analysis of long-span TSSBs under dynamic loads and offer an engineering reference for the design of similar bridges around the world.

In-plane linear dynamic behavior and impact of key system parameters of low-sagged cable network

The use of a cross-tie is one of the effective countermeasures to suppress the undesired stay cable vibrations. It has been successfully applied on different cable-stayed bridges but the mechanics behind the cross-tie are not fully understood. Most of the studies dedicated to understand the dynamic behavior of the cable network assumed the main cables as taut cables. This assumption is acceptable on small to medium-sized cable-stayed bridges, however, in case of long span bridges, this assumption is unjustified. Therefore, in the current study, the in-plane modal behavior of a cable network is explored by considering the cable sag. An analytical approach is used to develop the characteristic equation of a basic sagged cable network. The in-plane modal behavior of the sagged cable network is compared with the taut cable network and also with the single sagged cable. The role of different system parameters, mainly the cross-tie stiffness and the cable sag, is explored to understand the in-plane modal behavior of a sagged cable network. During the parametric study, a comparison is also drawn with the conventional taut cable network and an in-depth discussion is made to discuss the role of different system parameters.

Analysis of a thermoelastic Timoshenko beam model

In this paper, we analyze a linear problem describing the vibrations of a coupled suspension bridge. The single-span roadbed is modeled as an extensible thermoelastic beam of Timoshenko type. The main cable is modeled as an elastic string and is connected to the roadbed by a distributed system of elastic springs. For this linear model, we obtain the existence and uniqueness of solutions by using the semigroup theory. The exponential decay property is also proved. Then, through a variational formulation, the model is numerically analyzed and some numerical experiments are performed to verify the behavior of the numerical method.

Exact dynamic analysis of multi-segment cable systems

Cable-supported structure is a common system widely used in engineering, with the rapid development of the infrastructure and transportation industry, its structural form has become more and more complicated. Multi-segment cable system, which consists of a suspension cable and several lateral supports, such as the cable-damper system, the main cable of a suspension bridge, etc., is one of the important cable support systems. Due to the low structural rigidity and damping, its dynamic problems have always been the focus of engineering. To obtain a more general conclusion, a unified dynamic model considering the effect of cable sag, additional cable force, flexural stiffness, and the support stiffness of lateral components are considered in this paper for the first time. However, the exact analysis of this model is difficult, in view of this, the dynamic stiffness method is employed in this paper to investigate the dynamic characteristic of the multi-segment cable system. The accuracy of the proposed method is verified by comparing with finite element solutions and experimental results. Results show that the position of lateral supports has a strong coupling effect and influence the lower-order mode more significantly than higher-order modes, and the maximum frequency value can be reached by installing the supports equidistantly.

Analysis of Stiffening Girder Erection Scheme of Single Tower and Single Span Asymmetric Suspension Bridge

The paper analyzes four different stiffening girder erection schemes of a single tower and single span asymmetric suspension bridge with the main span of 766m by using parameter analysis combined with finite element numerical simulation. Firstly, this paper proposes two methods to study the reasonable erection time of ground anchor suspender cables, and based on the Midas/Civil finite element software, the erection time of ground anchor suspender cables with four schemes is determined by using backward-calculation analysis method. Then the main cable deformation, cable saddle displacement, horizontal inclination of main cable, internal force of suspender cables and dynamic performance of different schemes are compared. The results show that for Scheme 3 adopted in the project, the deformation of main cable is the smallest, the change of the cable saddle displacement is more slowly, the horizontal inclination of the main cable is smaller, and the bending stiffness is larger. However, the torsional stiffness is small and the flutter stability is not as good as other schemes.

Consideration to Terminating Condition of Mains Cable for Radiated Emission Measurement Caused by Different Disturbance Sources

Very high frequency (VHF)-line impedance stabilization network (VHF-LISN), which is defined as the termination device for mains cable of equipment under test to specify the input impedance of each line at the mains power supply outlet, can improve correlation between test sites that perform radiated emission measurement. Balanced and unbalanced types of VHF-LISN are currently under proposal with International Special Committee on Radio Interference (CISPR) as a device for prescribing the terminating condition of the power supply cable. Simulation analysis with common mode (CM)/differential mode (DM) signal sources was performed to investigate the emission characteristics with the two types of termination devices under several measurement arrangements that used two-wire and three-wire mains cables. Furthermore, to confirm the validity of the simulation analysis, measurement of a versatile comb-generator-operated by ac mains was performed under the same test arrangement and two types of termination devices. Quasi CM/DM signal from an ac-operated comb generator was injected back into the mains cable of the same comb generator. This article explains how we ascertained the radiated emission characteristics with each termination device, and provides guidance for their appropriate usage.

Frictional Resistance between Main Cable and Saddle for Suspension Bridges. I: Friction Characteristic of Single Strand

Abstract The frictional resistance between main cable and saddle of a long-span, multispan suspension bridge is significant for the safety of the bridge. Typically, the main cable of a long-span, m...

Modified finite elements method to investigate vibrations of the main cables in suspended bridges

In this paper, a modified finite elements method is presented to study vibrations of a suspended bridge under moving vehicles. In this study, coupled lateral and torsional vibrations of the deck and lateral vibrations of the main cables are considered. The deck is considered as an Euler-Bernoulli beam. The suspended cable theory with the sag ratio less than 10% is used to study the vibrations of the main cables. In the finite elements method used in this study, the vibrational equations of the curved elements of the main cables are calculated in the Cartesian coordinates and change of tension is considered in the equations. Finally, the Newmark method is used to solve the vibrational equations in the time domain. To verify the finite elements method, it is compared with an analytical solution which is applied to a numerical example of the problem.

Circumferential Expansion Property of Composite Wrapping System for Main Cable Protection of Suspension Bridge

A composite wrapping system for main cable protection of suspension bridges was designed by using prepreg fiber-reinforced composites and nitrile rubber. The circumferential expansion performance of the system was tested, and the curves of circumferential bearing capacity and radial displacement of the components were obtained. Failure modes of each group of components were compared and analyzed. The results show that most of the components are vertically fractured at the lap transition. The increase of the number of prepreg layers contributed the most to the circumferential bearing capacity of components, with a growth rate of 65.31%~109.01%. The increase of rubber belt layers had the most significant effect on the radial displacement of the components, with a growth rate of 7.06%~23.5%. In the initial stage of the test, the strain of each part of the component was smaller due to the compaction by the loading device, and the strain value of the component was generally linearly increased during the loading process, during which the strain of the overlap was the smallest. The calculated cross-sectional temperature deformation of the main cable is in good agreement with the experimental data. The application of the rubber belt increases the deformation of the main cable; therefore, the protection system for the main cable could have more deformation redundancy and delay the arrival of the ultimate strain of the outer prepreg wrap.

Anomaly detection for large span bridges during operational phase using structural health monitoring data

In view of the limitation of damage detection in practical applications for large scale civil structures, a practical method for anomaly detection is developed. Within the anomaly detection framework, wavelet transform and generalized Pareto distribution (GPD) are adopted for data processing. In detail, to reduce the influence of thermal responses on signal fluctuations induced by anomaly events, wavelet transform is employed to separate thermal effects from raw signals based on the distinguished frequency bandwidths. Subsequently, a two-level anomaly detection method is proposed, i.e. threshold-based anomaly detection and anomaly trend detection. For the threshold-based anomaly detection, the threshold for anomaly detection is determined by GPD analytics, corresponding to a 95% guarantee rate within 100 years. Moreover, the threshold is periodically updated by incorporating the latest monitoring data to model the increase of traffic volumes and gradual degradations of structures. For the anomaly trend detection, the moving fast Fourier transform is adopted for discussion. Finally, the mid-span deflection of Xihoumen Suspension Bridge is selected as the index to validate the effectiveness of the proposed methodology. Two types of anomaly events are assumed in the case study, i.e. the overloading event and structural damage. The two-level anomaly detection is implemented. It is indicated through the case study that the proposed anomaly detection approach (without the influence of temperature) is able to detect three 100 ton overloaded vehicles and damages in main cables. However, the assumed cases subject to 100 ton vehicle and damages in stiffening girders are hardly detected by using the deflection index, owing to the sensitivity of the index to each anomaly event. In the future studies, a structural health monitoring-based multi-index anomaly detection system is promising to ensure the operational and structural safety of large span bridges.

Time simulation of aerodynamic response of long-span bridges to turbulent wind

An efficient computational procedure is developed for time simulation of buffeting and flutter response of suspension bridges. The structural model is reduced by quasi-static condensation leading to a typical 1:5 reduction of the number of dynamic degrees of freedom. The turbulent wind field is represented by a convected fully three-dimensional velocity field and simulated by an auto-regressive procedure in which the coefficients are determined explicitly from conditional mean values and variances in the convected field. This procedure permits free choice of the simulation points – typically the nodes of the structural model. The convection concept can include translation of a fully three-dimensional nodal lay-out, e.g. the double set of main cables and hangers. The wind field representation is a generalized orthotropic representation of the von Kàrmàn velocity spectrum. This implies that the coherence functions contain a length scale in addition to the traditional non-dimensional frequency, reducing the coherence at large separations and thereby the fluctuating response of long suspension bridges. The aerodynamic forces are represented by a compact rational representation which is included in a momentum based time integration procedure which allows a fairly detailed tailoring of structural and algorithmic damping. The procedure is sufficiently general to permit response analysis of the full bridge structure with two layers of cables, but examples demonstrate rather small effects on the lower modes from the wind load on the cables.

Probabilistic Fatigue Damage Analysis of Long Span Suspension Bridge Due to Wind Induced Buffeting

In order to consider the fluctuating wind load induced fatigue problem of long span suspension bridge, fatigue reliability formula is modified by assuming the fatigue life is accord with the weibull distribution. Based on the accurate bridge buffeting analysis of time history, the stress time history of components of a suspension bridge in east sea China is simulated, and then the fatigue damages and reliabilities are calculated. The results indicate that the main cables and hangers have enough fatigue reliability under the fluctuating wind load, the fatigue failure will not occur; the stiffening girder has larger fatigue damage, under 40 / (m.s-1) mean wind speed action, the girder of mid-support section’s average fatigue life is only 3.103 years, so the girder’s damage under strong wind action should be taken seriously.

Nizhou Bridge, China: an insight into deck erection gantries supported on main suspension cables

The Nizhou waterway bridge, part of the Second Humen Bridge over the Pearl River in China's Guangdong province, is the second longest suspension bridge in the world (1688 m main span). The reinforced concrete towers are 260 m tall and the main cable spacing is 42·1 m. The deck is an aerofoil-shaped orthotropic steel box 49·7 m wide and 4 m deep. Deck erection took place during the spring of 2018. Three 500 t safe working load deck erection gantries, supported on the main cables, lifted 175 deck segments into position in 10 weeks. Strand jacks were used for deck lifting and gantry relocation. This paper describes the deck erection gantries, from concept development, through detailed design and testing, to operation on site. It focuses on the innovative movement system specifically developed for this project to reduce operating cycle times and overcome the design constraints, particularly the large range of relative positions between the deck erection gantry and the cable bands. Cast nylon wheels and aluminium ramps were designed for the gantry to roll smoothly over cable bands. Insufficient industry guidance on the design of cast nylon wheels and their interaction with the main cables required a multidirectional approach, which involved hand calculations, finite-element analysis and testing.

Experimental investigation of wind-induced vibrations of main cables for suspension bridges in construction phases

The main cables of suspension bridges show a changing cross-sectional shape with the evolution of construction phases, and they may suffer from severe wind-induced vibrations at certain conditions. The primary objective of this research was to examine the aerodynamic performance of the main cable in construction phases and to develop appropriate countermeasures to eliminate the potential wind-induced vibrations. Two cross-sections with different shapes of a main cable were chosen, and a series of wind tunnel tests were performed in a reduced wind velocity range of 32–366 using elastically mounted sectional models. Galloping occurred for the two cross-sections under certain wind incidence angles when a critical velocity was reached. No obvious hysteresis phenomenon of galloping was observed in the tests. The steady amplitude of galloping increased linearly with wind velocity and the increasing rate almost kept constant for different structural damping ratios. The aerodynamic nonlinearity, rather than the structural damping nonlinearity, is the main source leading to the limited amplitude oscillation. An empirical expression of galloping amplitudes for the two cross-sections was derived based on the test data. Meanwhile, the critical wind velocity was studied in a Scruton (Sc) number range of 108–4196 (as varied by changing the initial structural damping ratio between 0.093% and 3.62%). Results showed that the Den Hartog criterion was applicable to forecast the possibility of galloping, but not able to estimate the critical wind velocity for the main cable. Linear fitting method can be used to predict the critical velocity based on the experimental data. Finally, three vibration mitigation measures were studied, and a combination of structural and aerodynamic measures was recommended for galloping mitigation of main cables.

Examination of corrosion evaluation criteria based on rust composition analysis in corrosion investigation of actual suspension bridge main cables

Examination of corrosion evaluation criteria based on rust composition analysis in corrosion investigation of actual suspension bridge main cables

Alternative active nonlinear total Lagrangian truss finite element applied to the analysis of cable nets and long span suspension bridges

An alternative geometrically nonlinear total Lagrangian finite element is presented and applied to solve cable, cable nets and a very long suspended bridge in both three and two-dimensional spaces from its setting-up through its response to earthquake. It includes dynamics, pseudo-dynamics regularization, elastic actuators and automatic stress calibration. Dynamics and pseudo-dynamics are used to perform transient structural analysis and the setting-up of very unstable structures. Elastic actuators allow pre-stressing structural members for the iterative structural design and cables natural length definition. Automatic stress calibration comprises continuous cables in complicated structures without sliding contact devices. The formulation is applied to model main cables of suspended bridges passing through saddle points. Inertial terms are introduced by an alternative mathematical way. Two simple examples are used to validate all aspects of the proposed formulation. Finally, a representative application is performed, i.e., the numerical design and analysis of a very long span suspension bridge by the proposed strategy.

Analytical methods for the assessment of hanger forces of a suspension bridge based on measured main cable configuration

The accurate measurement of the hanger tensile forces of suspension bridges is crucial for construction control and bridge maintenance. However, the commonly used vibration frequency method is not applicable to the short-hanger force assessment. The configuration of the main cable of a suspension bridge is closely related to hanger forces so that the main cable configuration can reflect the hanger forces. Based on the multi-segment catenary theory, this study proposed an analytical algorithm for the reverse assessment of hanger forces based on the measured configuration data of the main cable. First, the relationship between the hanger force and two critical parameters, that is, the horizontal force of the main cable and the catenary parameter, is established, in which the influence of the saddle arc on the main cable configuration is considered. Then, the horizontal force of the main cable is used as the breakthrough point, and a geometric condition (measuring the coordinates of a non-hanging point on the main cable) or a mechanical condition (measuring the tension of a long hanger by the vibration frequency method) is added. Using the nonlinear generalized reduced gradient method, the nonlinear equations are solved, and all hanger forces are identified. The proposed method feasibility and effectiveness are proved using a suspension bridge with a main span of 730 m as an example. The results show that the algorithm of adding a mechanical condition is lower in sensitivity, less affected by the accuracy of the additional condition, higher in precision, and easier to control, comparing to that of adding a geometric condition. Meanwhile, the horizontal force of the main cable and each hanger force exhibit a nearly perfect linear correlation.

Development of Hanger-Rope Inspection Robot for Suspension Bridges

This paper describes the development of a hanger-rope inspection robot for suspension bridges. The inspection robot inspects the hanger rope by going up and down the rope installed vertically downward from the main cable of a suspension bridge. The going-up-and-down mechanism of the robot consists of a drive roller driven by a motor and a non-excitation electromagnetic brake, and the robot can safely descend after climbing the rope at high speed. The developed robot is small in size and light in weight, and an inspection worker can easily install the robot on the rope. In addition, the robot can be wirelessly controlled with ease from the controller. First, this paper describes the hanger-rope inspection strategy of the suspension bridge. Then, the developed prototype 2 robot is introduced. Next, the result of the hanger-rope inspection in an actual suspension bridge and the problems are clearly revealed by experiment. Finally, the newly developed prototype 3 robot is introduced, and the result of the going-up-and-down experiment is described.