Suspension Bridge Cables Research Articles

Research on the Exchangeable Main Cable of Suspension bridge

Research on the Exchangeable Main Cable of Suspension bridge

Evaluation of load and resistance factors for the reliability-based design of the main cables of earth-anchored suspension bridges

This paper presents load and resistance factors for the reliability-based design of the main cables of earth-anchored suspension bridges for the Strength I Limit State defined in the AASHTO LRFD Bridge Design Specifications. Reliability analyses are performed for three suspension bridges in Korea with main span lengths ranging from 650 m to 1545 m, and the reliability indices and the Most Probable Failure Points (MPFP) of random variables are evaluated. The strength, load and stiffness parameters are taken into account as random variables. The advanced first-order second-moment method is employed to evaluate the reliability indices and the MPFP of the random variables. The elastic catenary cable element is utilized to discretize the main cables. Load factors are proposed based on the normalized MPFP of each load component considered in the Strength I Limit State. The resistance factor that yields the reference target reliability index for the main cable is found as 0.53. Two alternative resistance factors, which give lower and higher reliability indices than the reference value, are also proposed. The proposed load and resistance factors lead to a uniform reliability level for a main cable regardless of the length of the main span of a suspension bridge.

Analytical structural reliability analysis of a suspended cable

Suspended cables, including transmission lines, suspension bridge cables, and edge cables of roof structures, feature in high profile and large span projects for architectural reasons, for their functional efficiency, and for ease of construction, particularly over large spans. A suspended cable predominantly reacts external loads by means of axial tension, and is, therefore, able to make full use of the material strength. Because of the slenderness of the suspended cable, the structural response is nonlinear, even if the material property is within the elastic range. From a mechanics perspective, therefore, these types of structure exhibit high levels of geometric non-linearity. For this reason, the nonlinear relationships between tension force, normal displacement, and the external loads need to be considered. In aiming to determine the structural safety of a suspended cable, and to understand which uncertainty features have the greatest influence, these relationships are written within a probabilistic framework.This article briefly sets the analysis of suspended cables within the context of geometrically nonlinear elastic structures and corresponding finite element analysis methodologies. Analytical solutions to the tension and normal displacement of a suspended cable subjected to external loading are presented. Nonlinear performance functions, in the form of either the cable tension or normal displacement are stated. Analytical expressions for the required gradients of the performance function of a suspended cable with respect to the basic variables under static loads are developed. The structural reliability of a suspended cable is studied using a first-order reliability method (FOSM) and verified by comparison with Monte Carlo simulation (MCS) and Monte Carlo simulation based optimization principles (MCOP) for a number of examples. Load cases including, wind, snow, and temperature variation are included.

Structural health monitoring of suspension bridges with features affected by changing wind speed

Tools based on multivariate statistical analysis are becoming very popular for automatically revealing the existence of damage in structures using vibration data under changing environmental and operational conditions (typically temperature, humidity and traffic intensity). In this paper, methods of multivariate statistical analysis are newly applied for monitoring the structural health state of the main cables of suspension bridges, with the main contribution of removing non-linear aeroelastic correlations between dynamic features and wind speed.Considering natural frequencies as damage-sensitive features, an analytical parametric model of suspension bridge with damage in one main cable and subjected to wind loading is formulated, at first, as an extension of previous work. Model predictions demonstrate that apparent frequency variations caused by changes in incoming wind speed can likely be more significant than those produced by a small damage. A technique based on principal component analysis and novelty detection is adopted to cope with this issue and its application to long-term pseudo-experimental buffeting response data, generated by means of the analytical model, is presented. The results demonstrate the feasibility of permanent monitoring systems to reveal the existence of damages in wind-excited long-span bridges producing relative variations in the most sensitive natural frequency smaller than 0.1%.

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.

Use of Modal Flexibility Method to Detect Damage in Suspended Cables and the Effects of Cable Parameters

Modal flexibility is a widely accepted technique to detect structural damage using vibration characteristics. Its application to detect damage in long span large diameter cables such as those used in suspension bridge main cables has not received much attention. This paper uses the modal flexibility method incorporating two damage indices (DIs) based on lateral and vertical modes to localize damage in such cables. The competency of those DIs in damage detection is tested by the numerically obtained vibration characteristics of a suspended cable in both intact and damaged states. Three single damage cases and one multiple damage case are considered. The impact of random measurement noise in the modal data on the damage localization capability of these two DIs is next examined. Long span large diameter cables are characterized by the two critical cable parameters named bending stiffness and sag-extensibility. The influence of these parameters in the damage localization capability of the two DIs is evaluated by a parametric study with two single damage cases. Results confirm that the damage index based on lateral vibration modes has the ability to successfully detect and locate damage in suspended cables with 5% noise in modal data for a range of cable parameters. This simple approach therefore can be extended for timely damage detection in cables of suspension bridges and thereby enhance their service during their life spans.

Nonlinear Stability Analysis of Long-Span Suspension Bridge Cable Tower

The cable tower is the bearing component of long-span suspension bridges, and its structure is very high and bear large force, which determines the stability and is the key of safety control. As for the height of the main tower of a long-span suspension bridge up to 195.3 m, the finite element software ANSYS is used to establish a three-dimensional finite element model (FEM), and the effects of geometric nonlinearity and material nonlinearity on the stability of the main tower are analyzed. The calculation results show that geometrical nonlinearity and material defects have significant influence on the main tower stability, and the nonlinear stability should be considered under wind load in the design calculation.

Influential Parameter Study on the Main-Cable State of Self-Anchored Suspension Bridge

This paper made a thorough influencing parameter analysis on the unstressed state and completed state of main cable of self-anchored suspension bridge. The main cable curve, the amount and the action point of the resultant force of main cable on the main saddle were considered as the controlling objectives, the rational completed state of main cable was defined; Wusong bridge in Jilin city was taken as an example, the finite element mode of main cable was created. The unstressed state and the completed state of main cable under different parameters were calculated, and all the results were compared with the reference state, the influences of each parameter deviation on the state of main cable were studied: the self-weight and erection temperature of main cable had little effect on the state of main cable; the length of the mid-span main cable mainly influenced itself line-shape, while the length of the side-span main cable had significant effect on each controlling objective; made the unstressed line-shape of main cable as the controlling condition, the position deviation of the main saddle and back anchorage facet, happened before the main cable erection stage, had little effect on the completed state, but which will have great effect on the completed state when they happened after the main cable erection stage. Engineering example analysis results showed that, the tensile stiffness of main cable and the boom-completed force would have some effect on the completed state of main cable, and the tensile stiffness of main cable and the self-weight of the main beam should be tested before erecting the main cable, in the same time the deviation should be control within the rational limits; recommended that the unstressed shape of main cable should pre-lift, which could counteract the deformation of the main saddle and the back anchorage facet at the completed stage, this conclusion had a strong guiding significance and reference value on the work of constructing the main cable of self-anchored suspension bridge.

High-Strength Prefabricated Parallel Wire Strand for Ulsan Harbor Bridge and its Mass Production System in Korea

This research discusses recent developments and applications of a high-strength prefabricated parallel wire strand (PPWS) with a tensile strength of 1960 MPa. The cost efficiency of high-strength PPWS cables is briefly reviewed. Performance requirements of the newly developed wire and PPWS cable are proposed by referring to the existing specifications and building codes. Acceptance tests were performed on wire and PPWS cable specimens. The results confirmed that the PPWS cables have sufficient strength to be used as the main cables of the Ulsan Harbor Bridge, a long-span suspension bridge currently under construction in Korea. A mass production system for the PPWS cable, recently implemented in Korea, is outlined by describing notable aspects of the equipment and manufacturing process. We believe that the high-strength PPWS, combined with the efficient mass production system described in this study can provide a more economical solution for the aspects concerning the main cables of long-span suspension bridges.

Discussion on design of prestressed anchorage system for main cable of suspension bridge

Discussion on design of prestressed anchorage system for main cable of suspension bridge

Investigation on vortex-induced vibration of a suspension bridge using section and full aeroelastic wind tunnel tests

Obvious vortex induced vibration (VIV) was observed during section model wind tunnel tests for a single main cable suspension bridge. An optimized section configuration was found for mitigating excessive amplitude of vibration which is much larger than the one prescribed by Chinese code. In order to verify the maximum amplitude of VIV for optimized girder, a full bridge aeroelastic model wind tunnel test was carried out. The differences between section and full aeroelastic model testing results were discussed. The maximum amplitude derived from section model tests was first interpreted into prototype with a linear VIV approach by considering partial or imperfect correlation of vortex-induced aerodynamic force along span based on Scanlan\'s semi-empirical linear model. A good consistency between section model and full bridge model was found only by considering the correlation of vortex-induced force along span.

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.

Design research on dehumidification system for main cable of suspension bridge

Design research on dehumidification system for main cable of suspension bridge

마찰 접촉을 고려한 현수교 PPWS용 소켓의 거동 해석

현수교 주케이블용 평행강선 스트랜드(PPWS) 소켓의 엄밀한 수치해석을 위한 유한요소해석 모델을 제안하였고, 제안된 해석 모델을 이용하여 소켓의 거동을 분석하였다. 개별 강선과 소켓 내부 주입 합금재의 영향을 고려한 직교 이방성 재료 모델을 적용하였고, Coulomb 마찰 및 표면접촉 모델을 도입하여 소켓 내면과 주입 합금재 표면의 접촉 상태를 구현하였다. 인장 실험으로부터 측정된 소켓 외면의 변형율과 유한요소 해석 결과를 비교하여 제안된 유한요소 해석 모델의 타당성을 검증하였고, 마찰계수의 변화에 따른 소켓의 거동을 해석하였다. 해석 결과, 소켓 내면과 주입 합금재 표면의 마찰은 소켓과 주입 합금재에 발생하는 응력 집중을 크게 완화 시켰으며, 소켓 설계법에서 정의된 수직응력식은 소켓 내면과 주입 합금재 표면의 접촉응력 분포에서 상하부 사분위값의 평균을 대표하는 것으로 나타났다. A sophisticated finite element model is illustrated to analyze the behavior of Prefabricated Parallel Wire Strand(PPWS) sockets for main cables of suspension bridges. An orthotropic model is proposed for the casting material by considering both effects of individual wires and a casting alloy, and the contact between surfaces of a socket and a casting alloy is idealized by using the Coulomb friction and the surface-based contact model. The proposed FE model is verified by comparing the strain distributions obtained from the tensile test and FE analysis. The mechanical behavior of a socket is investigated with respect to the variation of the frictional coefficient. The result shows that the friction between surfaces significantly diminishes the stress concentration of a socket and a casting alloy, and the normal stress from the design equation represents the averaged value of the upper and lower quartiles in the distribution of contact stresses between a socket and a casting alloy.

현수교 PPWS용 소켓의 내벽 경사각이 소켓의 극한 하중계수에 미치는 영향

Ultimate load factors of PPWS(Prefabricated Parallel Wire Strand) sockets in main cables of suspension bridges are studied with respect to the tapered angles of the inner surface of sockets. After briefly reviewing the current design method, 15 numbers of finite element models of sockets are prepared by varying the number of wires in a strand and the tapered angles. The finite element models are updated by comparing experimental and numerical results, so that the models can reflect the real behavior of sockets. The stress distributions at the first yielding and ultimate states are analyzed by performing the incremental load analysis using ABAQUS. It is concluded that the optimized tapered angle of sockets should be determined at the specific angle between the results of verification equations of the required bonding length and stress resistance length.

Modeling of Very Large Interacting Multiple-Beam Systems with Application to Suspension Bridge Cables

Systems of parallel beams connected with springs appear often in engineering. Typical examples are bundles of wires, such as the ones appearing in suspension bridge cables. These connections result in coupling of the differential equations describing the problem. In this paper, two systems of parallel beams connected with springs perpendicular to the beams are examined: multiple beams connected with springs, and multiple beams of common stiffness connected with springs and subjected to a common tensile axial load. A method is proposed to decouple the system of coupled equations into uncoupled differential equations for which exact shape functions can be constructed, so that the computational effort associated with systems involving a very large number of beams can become manageable. Numerical examples are presented demonstrating the capabilities of the proposed method.

Contrastive Analysis on Limitation Span between Suspension Bridge Using Steel and CFRP Cable

Bridge constructions of crossing wider sea straits allowed the span of suspension bridge to move forward unceasingly, but the self-weight stress of the traditional high-strength steel as the material of main cable accounted for the ratio of allowable stress would be increasing with the growth of main span. That would limit the main span and load-carrying efficiency. Due to its high tensile strength，small mass density，excellent corrosion and fatigue resistant ability, the carbon fiber reinforced polymer(CFRP) was the ideal material for the main cable of suspension bridge. In this paper the limitation spans of two suspension bridge systems were studied by the static analysis and the theoretical formula derived from the ultimate strength of the main cable.

A mathematical model for assessment of material requirements for cable supported bridges: Implications for conceptual design

Recent technological developments have led to improvements in the strengths of materials, such as the steel and wire ropes used in the construction of cable supported bridges. This, combined with technological advancements in construction, has encouraged the design of structures with increasing spans, leaving the question of material and environmental costs behind. This paper presents a refined mathematical model for the assessment of relative material costs of the supporting structures for cable-stayed and cable suspension bridges. The proposed model is more accurate than the ones published to date in that it includes the self weight of the cables and the pylons. Comparisons of material requirements for each type of bridge are carried out across a range of span/dip ratios. The basis of comparison is the assumption that each structure is made of the same material (steel) and carries an identical design load, q, exerted by the deck. Calculations are confined to a centre span of a three-span bridge, with the size of the span ranging from 500m to 3000m. Results show that the optimum span/dip ratio, which minimises material usage, is 3 for a cable-stayed (harp type) bridge, and 5 for a suspension structure. The inclusion of the self weight of cable in the analysis imposes limits on either the span, or span/dip ratio. This effect is quantified and discussed with reference to the longest cable-supported bridges in the world completed to date and planned in the future.

Experimental Analysis of a Nondestructive Corrosion Monitoring System for Main Cables of Suspension Bridges

Corrosion of high-strength steel wires in a suspension bridge’s main cable has been attributed to the environment within the cable wrapping. A sensor network was developed to monitor and provide information in order to indirectly assess the environmental conditions and the deterioration of the interior of suspension bridge main cables. The overall functionality of both the individual sensors and the monitoring system was tested on a full-scale mock-up cable. The cable mock-up was covered in aluminum wrapping and an environmental chamber was built around it in order to subject the test specimen and sensor network to an aggressive corrosive environment created by cyclic temperature and humidity conditions. The temperature, relative humidity (RH), and corrosion rate levels were recorded by all sensors. The recorded data were analyzed in an attempt to determine general trends and correlations between the environmental variables themselves and their effects on corrosion rates. The recorded temperature fluctuations were highly dependent on the sensor depth within the cable; however, the RH levels were not. During cyclic testing, near-linear temperature increases and RH decreases were recorded close to the cable’s center. The baseline corrosion rate levels were affected by the RH levels, with significant increases in corrosion rates at RH levels greater than 50%. The temperature changes proved to impact the corrosion rates on a cyclic level, with high correlations between the temperature and corrosion rate readings recorded by linear polarization resistance corrosion rate sensors.

Structural health monitoring of cylindrical structures using guided ultrasonic waves

The research field of structural health monitoring (SHM) in the realm of civil engineering has emerged rapidly. SHM concepts are based on integrated sensors and actuators to evaluate the structural state. Beside common structural response methods and other nondestructive testing techniques, wave-based ultrasonic techniques are widely used especially because of their flexibility. Monitoring cable structures such as overhead transmission lines or stay cables in suspension bridges is one objective of those wave-based methods. These structures are subject to aging, corrosion and other static and dynamic loads (e.g., wind, temperature). The cylindrical structures act as waveguides whereby monitoring of large distances with a single ultrasonic transducer is possible. However, the wave propagation is multimodal and dispersive, which complicates analysis of the wave motion and development of monitoring applications. This work addresses several aspects of the propagation of guided waves in cylinders, especially the analysis of reflection and transmission at discontinuities using finite element and boundary element methods.