• Smart Structures and Systems
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• v.31 no.1
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• pp.57-68
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• 2023

Bridge hangers, such as those in suspension and cable-stayed bridges, suffer from cumulative fatigue damage caused by dynamic loads (e.g., cyclic traffic and wind loads) in their service condition. Thus, the identification of damage to hangers is important in preserving the service life of the bridge structure. This study develops a new method for condition assessment of bridge hangers. The tension force of the bridge and the damages in the element level can be identified using the Bayesian optimization method. To improve the number of observed data, the additional mass method is combined the Bayesian optimization method. Numerical studies are presented to verify the accuracy and efficiency of the proposed method. The influence of different acquisition functions, which include expected improvement (EI), probability-of-improvement (PI), lower confidence bound (LCB), and expected improvement per second (EIPC), on the identification of damage to the bridge hanger is studied. Results show that the errors identified by the EI acquisition function are smaller than those identified by the other acquisition functions. The identification of the damage to the bridge hanger with various types of boundary conditions and different levels of measurement noise are also studied. Results show that both the severity of the damage and the tension force can be identified via the proposed method, thereby verifying the robustness of the proposed method. Compared to the genetic algorithm (GA), particle swarm optimization (PSO), and nonlinear least-square method (NLS), the Bayesian optimization (BO) performs best in identifying the structural damage and tension force.

• Structural Engineering and Mechanics
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• v.71 no.6
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• pp.603-625
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• 2019

Main cable configurations under final dead load and in the unloaded state and critical construction parameters (e.g. unstrained cable length, unstrained hanger lengths, and pre-offsets for tower saddles and splay saddles) are the core considerations in the design and construction control of a suspension bridge. For the purpose of accurate calculations, it is necessary to take into account the effects of cable strands over the anchor spans, arc-shaped saddle top, and tower top pre-uplift. In this paper, a method for calculating the cable configuration under final dead load over a main span, two side spans, and two anchor spans, coordinates of tangent points, and unstrained cable length are firstly developed using conditions for mechanical equilibrium and geometric relationships. Hanger tensile forces and unstrained hanger lengths are calculated by iteratively solving the equations governing hanger tensile forces and the cable configuration, which gives careful consideration to the effect of hanger weight. Next, equations for calculating the cable configuration in the unloaded state and pre-offsets of saddles are derived from the cable configuration under final dead load and the conditions for unstrained cable length to be conserved. The equations for the main span, two side spans and two anchor spans are then solved simultaneously. In the proposed methods, coupled nonlinear equations are solved by turning them into an unconstrained optimization problem, making the procedure simplified. The feasibility and validity of the proposed methods are demonstrated through a numerical example.

• Smart Structures and Systems
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• v.2 no.2
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• pp.155-169
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• 2006

In this paper, the application of magnetoelasticity in static tension monitoring for large steel cables is discussed. Magnetoelastic (EM) stress sensors make contact-free tension monitoring possible for hanger cables and post-tensioned cables on suspension and cable-stayed bridges. By quantifying the correlation of magnetic relative permeability with tension and temperature, the EM sensors inspect the load levels in the steel cables. Cable tension monitoring on Qiangjiang (QJ) 4th Bridge demonstrates the reliability of the EM sensors.

• Journal of Korean Society of Steel Construction
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• v.21 no.2
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• pp.165-173
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• 2009

Hanger cables in suspension bridges are constrained by the horizontal clamp. So, the accuracy of estimated tension of hange cable using existing methods based on the simple mathematical model of singel cable decreases as the length of cable decreases because of the flexural rigidity. Therefore, back analysis and system identification techniques based on the finite element model are proposed recently. In this paper, the applicability of the back analysis and system identification techniques are compared using the hanger cable of Gang-An Bridge. The experimental results show that the back analysis and system identification techniques are more reliable than the existing string theory and linear regression method in the view point of the error of natural frequencies. However, the estimation error of tension can be varied according to the accuracy of finite element model in the model based methods. Especially, the boundary condition is more affective when the length of cable is short, so it is important to identify the boundary condition through experiment if it is possible. The tension estimation method using system identification technique is more attractive because it can easily consider the boundary condition and it is not sensitive to the number of input measured natural frequencies.

• Journal of Mechanical Science and Technology
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• v.17 no.6
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• pp.860-869
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• 2003

Dynamic characteristics of a catenary that supplies electrical power to high-speed railway is investigated. The catenary is a slender structure composed of repeating spans. Each span is in turn composed of the contact and messenger wires connected by the hangers in regular intervals. A finite element based dynamic model is developed, and numerical simulations are performed to determine the dynamic characteristics of the catenary The influence of the structural parameters on the response characteristics is investigated. The structural parameters considered include tension on the contact and messenger wires, stiffness of the hangers, and the hanger and span spacing. The hanger characteristics are found to be the dominant factors that influence the overall dynamic characteristics of the catenary.

• Journal of the Korea institute for structural maintenance and inspection
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• v.13 no.3 s.55
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• pp.135-144
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• 2009

The cable system of suspension bridges is a very important non-elastic element which caries an external load by a tension force of the cable, such that creates the integrity of a structure. It is not easy to find if cable system have been changed by the maintenance activities such as repairs or reinforcement. Sometimes the maintenance can cause structural deformations and changes of the tension force in cables. In most cases, the cable stayed bridges are managed by health monitering system, however, the main cable of suspension bridges need to develop more accurate and efficient monitoring system. The Namhee Bridge was constructed 35 years ago and it has been continually repaired and reinforced after then. This study describes the behavior of the cable system by analysing many of inspective reports and by using the results of hanger rope test and for the shape of main cables surveys.

• Structural Engineering and Mechanics
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• v.82 no.6
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• pp.735-745
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• 2022

The suspension thyristor valve can generate tremendous vertical acceleration responses in layers and large tension forces in hangers. A shaking table test of a scaled-down model of thyristor valves suspended on a hall building is performed to qualify the risk of vertical uplift of two representative types of valves, the chain valve and the rigid valve. Besides, an analytical model is established to investigate the source of the slackening of hangers. The test results show that the valves frequently experience a large vertical acceleration response. The soft spring joint can significantly reduce acceleration, but is still unable to prevent vertical uplift of the chain valve. The analytical model shows a stiffer roof and inter-story connection both contribute to a higher risk of vertical uplift for a rigid valve. In addition, the planar eccentricity and short hangers, which result in torsional motion of the valve, increase the possibility of vertical uplift for a chain valve. Therefore, spring joints with additional viscous dampers and symmetric layout in each layer are recommended for the rigid and chain valve, respectively, to prevent the uplift of valves.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.6
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• pp.1309-1317
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• 1994

Because the stiffening girders are constructed after the installation of hangers for typical suspension bridge, no additional tensioning to hangers in construction is necessary for this bridge type in which main cable is earth-anchored. However, for self-anchored suspension bridge, hangers are installed after temporarily supporting stiffening girders constructed in previous stage. Therefore, initial tension is required on installing hangers. Tension of hangers varies as the construction proceeds. Hence, it is necessary to determine the most efficient method of installing hangers among several methods. This study presents finite element procedures and the algorithms of construction stage analysis to simulate construction processes. Geometric nonlinear analysis scheme is also included. The most effective method regarding the installation of hangers is presented through the examples of actual bridge model.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.5A
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• pp.255-266
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• 2012

Main cable of a suspension bridge is the important member which shows the overall structure integrity at bridge completion. Configuration of main cable is a free hanging state at cable erection completion and is different from that at bridge completion supporting the dead loads such as hanger, girder, and so on. Accordingly, the configuration control under cable erection is considerably significant because the configuration at cable erection completion has direct influence on that at bridge completion. That is performed by sag adjustments at center, side span and tension adjustments at anchor span. The former needs the sag sensitivity which represents the control quantity of strand length corresponding to that of sag. The latter requires the tension sensitivity which shows the change of strand tension according to that of strand temperature. In this study, the fundamental equations of cable were derived with the assumption of either catenary or parabola shape, the differential-related equations using chain rule on horizontal tension were drawn from those and finally the estimation methods of the sag / tension sensitivity were proposed from both those. The nonlinear numerical analysis flow charts of sag sensitivity based on the catenary equations were proposed and the sag sensitivities grounded on the differential-related equations were compared with the results using them for various parameters of sag change. Also, considering the combinations of sag change parameters, the calculation method of the final variation for the cable sag was suggested. For the real suspension bridge under construction with PPWS method, the sag/tension sensitivity were estimated considering the construction conditions like the change of PPWS length, PPWS temperature, bridge span, etc.. We hope that this study will be a systematic guideline for the configuration control under main cable erection and improved highly by field verification in the real bridge site.

• Structural Engineering and Mechanics
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• v.51 no.5
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• pp.847-866
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• 2014

This paper describes a formulation to predict optimum post-tensioning forces and cable dimensioning for self-anchored cable-stayed suspension bridges. The analysis is developed with respect to both dead and live load configurations, taking into account design constrains concerning serviceability and ultimate limit states. In particular, under dead loads, the analysis is developed with the purpose to calculate the post-tensioning cable forces to achieve minimum deflections for both girder and pylons. Moreover, under live loads, for each cable elements, the lowest required cross-section area is determined, which verifies prescriptions, under ultimate or serviceability limit states, on maximum allowable stresses and bridge deflections. The final configuration is obtained by means of an iterative procedure, which leads to a progressive definition of the stay, hanger and main cable characteristics, concerning both post-tensioning cable stresses and cross-sections. The design procedure is developed in the framework of a FE modeling, by using a refined formulation of the bridge components, taking into account of geometric nonlinearities involved in the bridge components. The results demonstrate that the proposed method can be easily utilized to predict the cable dimensioning also in the framework of long span bridge structures, in which typically more complexities are expected in view of the large number of variables involved in the design analysis.