• Structural Engineering and Mechanics
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• v.34 no.6
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• pp.719-738
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• 2010

The aim of this paper concerns with the nonlinear analysis of cable-stayed bridges including the vibration effect of cable stays. Two models for the cable stay system are built up in the study. One is the OECS (one element cable system) model in which one single element per cable stay is used and the other is MECS (multi-elements cable system) model, where multi-elements per cable stay are used. A finite element computation procedure has been set up for the nonlinear analysis of such kind of structures. For shape finding of the cable-stayed bridge with MECS model, an efficient computation procedure is presented by using the two-loop iteration method (equilibrium iteration and shape iteration) with help of the catenary function method to discretize each single cable stay. After the convergent initial shape of the bridge is found, further analysis can then be performed. The structural behaviors of cable-stayed bridges influenced by the cable lateral motion will be examined here detailedly, such as the static deflection, the natural frequencies and modes, and the dynamic responses induced by seismic loading. The results show that the MECS model offers the real shape of cable stays in the initial shape, and all the natural frequencies and modes of the bridge including global modes and local modes. The global mode of the bridge consists of coupled girder, tower and cable stays motion and is a coupled mode, while the local mode exhibits only the motion of cable stays and is uncoupled with girder and tower. The OECS model can only offers global mode of tower and girder without any motion of cable stays, because each cable stay is represented by a single straight cable (or truss) element. In the nonlinear seismic analysis, only the MECS model can offer the lateral displacement response of cable stays and the axial force variation in cable stays. The responses of towers and girders of the bridge determined by both OECS- and MECS-models have no great difference.

• Earthquakes and Structures
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• v.5 no.6
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• pp.657-678
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• 2013

For economical earthquake resistant design of cable-stayed bridge tower, the use of energy dissipation systems for the earthquake protection of steel structures represents an alternative seismic design method where the tower structure could be constructed to dissipate a large amount of earthquake input energy through inelastic deformations in certain positions, which could be easily retrofitted after damage. The design of energy dissipation systems for bridges could be achieved as the result of two conflicting requirements: no damage under serviceability limit state load condition and maximum dissipation under ultimate limit state load condition. A new concept for cable-stayed bridge tower seismic design that incorporates sacrificial link scheme of low yield point steel horizontal beam is introduced to enable the tower frame structure to remain elastic under large seismic excitation. A nonlinear dynamic analysis for the tower model with the proposed energy dissipation systems is carried out and compared to the response obtained for the tower with its original configuration. The improvement in seismic performance of the tower with supplemental passive energy dissipation system has been measured in terms of the reduction achieved in different response quantities. Obtained results show that the proposed energy dissipation system of low yield point steel seismic link could strongly enhance the seismic performance of the tower structure where the tower and the overall bridge demands are significantly reduced. Low yield point steel seismic link effectively reduces the damage of main structural members under earthquake loading as seismic link yield level decreases due their exceptional behavior as well as its ability to undergo early plastic deformations achieving the concentration of inelastic deformation at tower horizontal beam.

• Structural Engineering and Mechanics
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• v.52 no.1
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• pp.51-73
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• 2014

A three-dimensional finite element model for the Jiashao Bridge, the longest multi-span cable-stayed bridge in the world, is established using the commercial software package ANSYS. Dynamic characteristics of the bridge are analyzed and the effects of structural system measures including the rigid hinge, auxiliary piers and longitudinal constraints between the girders and side towers on the dynamic properties including modal frequency, mode shape and effective mass are studied by referring to the Jiashao Bridge. The analysis results reveal that: (i) the installation of the rigid hinge significantly reduces the modal frequency of the first symmetric lateral bending mode of bridge deck. Moreover, the rigid hinge significantly changes the mode shape and effective mass of the first symmetric torsional mode of bridge deck; (ii) the layout of the auxiliary piers in the side-spans has a limited effect on changing the modal frequencies, mode shapes and effective masses of global vibration modes; (iii) the employment of the longitudinal constraints significantly increases the modal frequencies of the vertical bending modes and lateral bending modes of bridge deck and have significant effects on changing the mode shapes of vertical bending modes and lateral bending modes of bridge deck. Moreover, the effective mass of the first anti-symmetric vertical bending of bridge deck in the longitudinal direction of the fully floating system is significantly larger than that of the partially constrained system and fully constrained system. The results obtained indicate that the structural system measures of the multi-span cable-stayed bridge have a great effect on the dynamic properties, which deserves special attention for seismic design and wind-resistant design of the multi-span cable-stayed bridge.

• Structural Engineering and Mechanics
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• v.30 no.1
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• pp.37-66
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• 2008

This paper focuses on the nonlinear vibrations of stay cables and evaluates the dynamic characteristics of stay cables by using the nonlinear enhanced MECS approach and the approximate approach. The nonlinear enhanced MECS approach is that both the girder-tower vibrations and the cable vibrations including parametric cable vibrations are simultaneously considered in the numerical analysis of cable-stayed bridges. Cable finite element method is used to simulate the responses including the parametric vibrations of stay cables. The approximate approach is based on the assumption that cable vibrations have a small effect on girder-tower vibrations, and analyzes the local cable vibrations after obtaining the girder-tower responses. Under the periodic excitations or the moderate ground motion, the differences of the responses of stay cables between these two approaches are evaluated in detail. The effect of cable vibrations on the girder and towers are also discussed. As a result, the dynamic characteristics of the parametric vibrations in stay cables can be evaluated by using the approximate approach or the nonlinear enhanced MECS approach. Since the different axial force fluctuant of stay cables in both ends of one girder causes the difference response values between two approach, it had better use the nonlinear enhanced MECS approach to perform the dynamic analyses of cable-stayed bridges.

• Structural Engineering and Mechanics
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• v.45 no.5
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• pp.703-722
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• 2013

In this paper a study about concrete arch bridges built by lattice cantilevers is presented. Lattice cantilevers are partial structures composed of deck, arch, piers and provisional steel diagonals, organized as reticular cantilever girders, in order to build arch bridges without the use of centrings, supports or temporary towers. Characteristics of this construction methodology with its variants are explained together with their implications in the erection sequence. Partial elastic scheme method is implemented in order to find initial forces of temporary cables and a forward analysis is carried out to follow the actual sequence of construction, by extending a procedure already applied to concrete cable-stayed bridges and to arches built by the classical suspended cantilever method. A numerical application on a case-study of a concrete arch bridge is performed together with a comparison between different methodologies followed for its construction sequence. Differences between erection by lattice cantilevers and cable-stayed cantilevers, are discussed. Results can be useful for designers in conceptual design of concrete arch bridges.

• Structural Engineering and Mechanics
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• v.40 no.4
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• pp.471-488
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• 2011

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 strengthened by transverse cables and struts. The bridge deck is supported by four inclined planes of cables emanating from anchorages at the tower tops. In view of the heavy traffic on the bridge, and threats from typhoons and earthquakes originated in areas nearby, the dynamic behaviour of long-span cable-supported bridges in the region is always an important consideration in their design. Baseline finite element models of various levels of sophistication have been built not only to match the bridge geometry and cable forces specified on the as-constructed drawings but also to be calibrated using the vibration measurement data captured by the Wind and Structural Health Monitoring System. This paper further describes the analysis of axle loading data, as well as the generation of random axle loads and simulation of vibrations of the bridge using the finite element models. Various factors affecting the vehicular loading on the bridge will also be examined.

• Journal of the Earthquake Engineering Society of Korea
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• v.8 no.4
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• pp.51-62
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• 2004

Fuzzy supervisory control technique for the seismic response control of cable-stayed bridges subject to earthquakes is studied. The proposed technique is a hybrid control method, which adopts a hierarchical structure consisting of several sub-controllers and a fuzzy supervisor. Sub-controllers are independently designed to reduced the responses to be controlled of a cable-stayed bridge, and a fuzzy supervisor achieves improved seismic control performance by tuning the pre-designed sub-controllers. It is realized by converting static gains of the sub-controllers into time-varying dynamic gains through the fuzzy inference mechanism. To evaluate the feasibility of the proposed technique, the benchmark control problem of cable-stayed bridge proposed by Dyke et al. is adopted. The control variables for the seismic response control of the cable-stayed bridge are determined to be t도 shear forces and bending moments at the base of the towers, the longitudinal displacements at the top of the towers, the relative displacements between the deck and the tower, and the tensions in the stay cables. Comparative results between the fuzzy supervisory controller and LQG controller demonstrate the effectiveness of the proposed control technique.

• Smart Structures and Systems
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• v.15 no.1
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• pp.99-117
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• 2015

The Stonecutters Bridge (SCB) in Hong Kong is the third-longest cable-stayed bridge in the world with a main span stretching 1,018 m between two 298 m high single-leg tapering composite towers. A Wind and Structural Health Monitoring System (WASHMS) is being implemented on SCB by the Highways Department of The Hong Kong SAR Government, and the SCB-WASHMS is composed of more than 1,300 sensors in 15 types. In order to establish a linkage between structural health monitoring and maintenance management, a Structural Health Rating System (SHRS) with relevant rating tools and indices is devised. On the basis of a 3D space frame finite element model (FEM) of SCB and model updating, this paper presents the development of an SHR-oriented 3D multi-scale FEM for the purpose of load-resistance analysis and damage evaluation in structural element level, including modeling, refinement and validation of the multi-scale FEM. The refined 3D structural segments at deck and towers are established in critical segment positions corresponding to maximum cable forces. The components in the critical segment region are modeled as a full 3D FEM and fitted into the 3D space frame FEM. The boundary conditions between beam and shell elements are performed conforming to equivalent stiffness, effective mass and compatibility of deformation. The 3D multi-scale FEM is verified by the in-situ measured dynamic characteristics and static response. A good agreement between the FEM and measurement results indicates that the 3D multi-scale FEM is precise and efficient for WASHMS and SHRS of SCB. In addition, stress distribution and concentration of the critical segments in the 3D multi-scale FEM under temperature loads, static wind loads and equivalent seismic loads are investigated. Stress concentration elements under equivalent seismic loads exist in the anchor zone in steel/concrete beam and the anchor plate edge in steel anchor box of the towers.

• Structural Engineering and Mechanics
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• v.90 no.2
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• pp.159-175
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• 2024

In order to solve the problem of calculating the reasonable completed bridge state of a self-anchored hybrid cable-stayed suspension bridge (SA-HCSB), this paper proposes an analytical method. This method simplifies the main beam into a continuous beam with multi-point rigid supports and solves the support reaction forces. According to the segmented catenary theory, it simultaneously solves the horizontal forces of the main span main cables and the stay cables and iteratively calculates the equilibrium force system on the main beam in the collaborative system bridge state while completing the shape finding of the main span main cable and stay cables. Then, the horizontal forces of the side span main cables and stay cables are obtained based on the balance of horizontal forces on the bridge towers, and the shape finding of the side spans are completed according to the segmented catenary theory. Next, the difference between the support reaction forces of the continuous beam with multiple rigid supports obtained from the initial and final iterations is used to calculate the load of ballast on the side span main beam. Finally, the axial forces and strains of each segment of the main beam and bridge tower are obtained based on the loads applied by the main cable and stay cables on the main beam and bridge tower, thereby obtaining analytical data for the bridge in the reasonable completed state. In this paper, the rationality and effectiveness of this analytical method are verified through a case study of a SA-HCSB with a main span of 720m in finite element analysis. At the same time, it is also verified that the equilibrium force of the main beam under the reasonably completed bridge state can be obtained through iterative calculation. The analytical algorithm in this paper has clear physical significance, strong applicability, and high accuracy of calculation results, enriching the shape-finding method of this bridge type.

• 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.