• Structural Engineering and Mechanics
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• v.43 no.5
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• pp.583-605
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• 2012

This paper presents a spatial catenary cable element for the nonlinear analysis of cable-supported structures. An incremental-iterative solution based on the Newton-Raphson method is adopted for solving the equilibrium equation. As a result, the element stiffness matrix and nodal forces are determined, wherein the effect of self-weight and pretension are taken into account. In the case of the initial cable tension is given, an algorithm for form-finding of cable-supported structures is proposed to determine precisely the unstressed length of the cables. Several classical numerical examples are solved and compared with the other available numerical methods or experiment tests showing the accuracy and efficiency of the present elements.

• Structural Engineering and Mechanics
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• v.15 no.1
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• pp.115-134
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• 2003

The Ting Kau Bridge in Hong Kong is a cable-stayed bridge comprising two main spans and two side spans. The bridge deck is supported by three towers, an end pier and an abutment. Each of the three towers consists of a single reinforced concrete mast which reduces its section in steps, and it is strengthened by transverse cables and struts in the transverse vertical plane. The bridge deck is supported by four inclined planes of cables emanating from anchorages at the tower tops. In view of the threat from typhoons, the dynamic behaviour of long-span cable-supported bridges in the region is always an important consideration in their design. This paper is devoted to the ambient vibration measurements of the bridge for evaluation of dynamic characteristics including the natural frequencies and mode shapes. It also describes the modelling of the bridge. A few finite element models are developed and calibrated to match with the field data and the results of subsequent structural health monitoring of the bridge.

• Structural Monitoring and Maintenance
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• v.1 no.4
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• pp.371-392
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• 2014

Long-span cable-supported bridges are flexible structures vulnerable to unsymmetric loadings such as railway traffic and strong wind. The torsional dynamic response of long-span cable-supported bridges under running trains and/or strong winds may deform the railway track laid on the bridge deck and affect the running safety of trains and the comfort of passengers, and even lead the bridge to collapse. Therefore, it is eager to figure out the torsional dynamic response of long-span cable-supported bridges under running trains and/or strong winds. The Tsing Ma Bridge (TMB) in Hong Kong is a suspension bridge with a main span of 1,377 m, and is currently the world's longest suspension bridge carrying both road and rail traffic. Moreover, this bridge is located in one of the most active typhoon-prone regions in the world. A wind and structural health monitoring system (WASHMS) was installed on the TMB in 1997, and after 17 years of successful operation it is still working well as desired. Making use of one-year monitoring data acquired by the WASHMS, the torsional dynamic responses of the bridge deck under rail traffic and strong winds are analyzed. The monitoring results demonstrate that the differences of vertical displacement at the opposite edges and the corresponding rotations of the bridge deck are less than 60 mm and $0.1^{\circ}$ respectively under weak winds, and less than 300 mm and $0.6^{\circ}$ respectively under typhoons, implying that the torsional dynamic response of the bridge deck under rail traffic and wind loading is not significant due to the rational design.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.265-272
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• 2005

For bridge-vehicle interaction analysis of cable-supported brides, the superposition method is applied based on the results of 3-dimensional free vibration analysis using General-purpose FEM Software. This study firstly performs the eigenvalue analysis for the free vertical and the torsional vibration of bridges using FEM analysis. Next the equations of motion considering interaction between bridges and vehicles/train are derived from mode superposition method. And then dynamic analysis is performed using the Newmark numericial method. Finally through the numerical examples, the dynamic responses of cable-supported bridges by this study are presented and discussed.

• Structural Engineering and Mechanics
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• v.21 no.4
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• pp.375-392
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• 2005

Cable supported structures offer an elegant and economical solution for bridging over long spans with resultant low material content and ease of construction. In this paper, a model of shallow cable supported footbridge with reverse profiled pre-tensioned cables is treated and its load deformation characteristics under different quasi-static loads are investigated. Effects of important parameters such as cable sag and pre-tension are also studied. Numerical results performed on a 3D model show that structural stiffness of this bridge (model) depends not only on the cable sag and cross sectional areas of the cables, but also on the pre-tension in the reverse profiled cables. The tension in the top supporting cables can be adjusted to a high level by the pre-tension in the reverse profiled bottom cables, with the total horizontal force in the bridge structure remaining reasonably constant. It is also evident that pre-tensioned horizontally profiled cables can greatly increase the lateral horizontal stiffness and suppress the lateral horizontal deflection induced by eccentric vertical loads.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.5
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• pp.313-322
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• 2019

Recently, there have been frequent occurrences of bridge fires. Fires in cable-supported bridges can damage and brake cables due to high temperatures. In this study, fire scenarios that can occur on cable-supported bridges were set up. In addition, based on the results of vehicle fire tests, a fire intensity model was proposed and cable heat transfer analyses were performed on a target bridge. The analyses results demonstrated that temperature rises were identified on cables with a smaller cross-sectional area. Furthermore, vehicles other than tankers did not exceed the fire resistance criteria. When the tanker fire occurred on a bridge shoulder, the minimum diameter cable exceeded the fire resistance criteria; the height of the cable exceeding the fire resistance criteria was approximately 14 m from the surface. Therefore, the necessity of countermeasures and reinforcements of fire resistance was established. The results of this study confirmed that indirect evaluation of the temperature changes of bridge cables under fire is possible, and it was deemed necessary to further study the heat transfer analysis considering wind effects and the serviceability of the bridge when the cable temperature rises due to fire.

• Wind and Structures
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• v.22 no.2
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• pp.253-272
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• 2016

The paper concerns with the method and results of wind tunnel investigations of the Strouhal number (St) of a stationary iced cable model of cable-supported bridges with respect to different angles of wind attack. The investigations were conducted in the Climatic Wind Tunnel Laboratory of the Czech Academy of Sciences in $Tel{\check{c}}$. The methodology leading to the experimental icing of the inclined cable model was prepared in a climatic section of the laboratory. The shape of the ice on the cable was registered by a photogrammetry method. A section of an iced cable model with a smaller scale was reproduced with a 3D printing procedure for subsequent aerodynamic investigations. The St values were determined within the range of the Reynolds number (Re) between $2.4{\cdot}10^4$ and $16.5{\cdot}10^4$, based on the dominant vortex shedding frequencies measured in the wake of the model. The model was oriented at three principal angles of wind attack for each of selected Re values. The flow regimes were distinguished for each model configuration. In order to recognize the tunnel blockage effect the St of a circular smooth cylinder was also tested. Good agreement with the reported values in the subcritical Re range of a circular cylinder was obtained. The knowledge of the flow regimes of the airflow around an iced cable and the associated St values could constitute a basis to formulate a mathematical description of the vortex-induced force acting on the iced cable of a cable-supported bridge and could allow predicting the cable response due to the vortex excitation phenomenon.

• Structural Engineering and Mechanics
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• v.54 no.2
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• pp.337-362
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• 2015

This paper presents a feasibility study on structural damage alarming and localization of long-span cable-supported bridges using multi-novelty indices formulated by monitoring-derived modal parameters. The proposed method which requires neither structural model nor damage model is applicable to structures of arbitrary complexity. With the intention to enhance the tolerance to measurement noise/uncertainty and the sensitivity to structural damage, an improved novelty index is formulated in terms of auto-associative neural networks (ANNs) where the output vector is designated to differ from the input vector while the training of the ANNs needs only the measured modal properties of the intact structure under in-service conditions. After validating the enhanced capability of the improved novelty index for structural damage alarming over the commonly configured novelty index, the performance of the improved novelty index for damage occurrence detection of large-scale bridges is examined through numerical simulation studies of the suspension Tsing Ma Bridge (TMB) and the cable-stayed Ting Kau Bridge (TKB) incurred with different types of structural damage. Then the improved novelty index is extended to formulate multi-novelty indices in terms of the measured modal frequencies and incomplete modeshape components for damage region identification. The capability of the formulated multi-novelty indices for damage region identification is also examined through numerical simulations of the TMB and TKB.

• Structural Engineering and Mechanics
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• v.56 no.6
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• pp.939-957
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• 2015

In this paper, a new approach based on the continuum model is proposed to estimate the main cable tension force of suspension bridges from measured natural frequencies. This approach considered the vertical vibration of a main cable hinged at both towers and supported by an elastic girder and hangers along its entire length. The equation reflected the relationship between vibration frequency and horizontal tension force of a main cable was derived. To avoid to generate the additional cable tension force by sag-extensibility, the analytical solution of characteristic equation for anti-symmetrical vibration mode of the main cable was calculated. Then, the estimation of main cable tension force was carried out by anti-symmetric characteristic frequency vector. The errors of estimation due to characteristic frequency deviations were investigated through numerical analysis of the main cable of Taizhou Bridge. A field experiment was conducted to verify the proposed approach. Through measuring and analyzing the responses of a main cable of Taizhou Bridge under ambient excitation, the horizontal tension force of the main cable was identified from the first three odd frequencies. It is shown that the estimated results agree well with the designed values. The proposed approach can be used to conduct the long-term health monitoring of suspension bridges.

• Journal of the Korea institute for structural maintenance and inspection
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• v.18 no.5
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• pp.87-95
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• 2014

Cable stayed bridge is supported by cables and the negative reaction occurs by cables at anchor pier. To solve this problem, the proper side span ratio and the negative reaction measure of anchor pier are needed. And structural system of cable stayed bridge is determined by solution of the negative reaction as installation of the intermediate pier, counterweight and so on. In feasibility study, Vam Cong bridge was planned as 5 span cable stayed bridge. However, it was changed to 3 span cable stayed bridge in detailed design because of constructability and economy. The intermediate pier was excluded in order to improve the constructability, and side span ratio increased to control the negative reaction. As a result, Vam Cong bridge secure constructability, structural safety, and efficiency.