Response Of Cable-stayed Bridge Research Articles

Phase I Benchmark Control Problem for Seismic Response of Cable-Stayed Bridges

This paper presents the problem definition for the first generation of benchmark structural control problems for cable-stayed bridges. The benchmark problem is based on the Bill Emerson Memorial Bridge that is currently under construction in Cape Girardeau, Missouri. Construction of the bridge is expected to be completed in 2003. The goal of this study is to provide a testbed for the development of strategies for the control of cable-stayed bridges. Based on detailed drawings, a three-dimensional evaluation model has been developed to represent the complex behavior of the full scale benchmark bridge. The linear evaluation model is developed using the equations of motion generated around the deformed equilibrium position. Evaluation criteria are selected that are consistent with the goals of seismic response control of a cable-stayed bridge. Control constraints ensure that the results are representative of a control implementation on the physical structure. Each participant in this benchmark study is given...

Control of Seismically Excited Cable-Stayed Bridge Employing Magnetorheological Fluid Dampers

This paper examines the ASCE first generation benchmark problem for a seismically excited cable-stayed bridge, and proposes a new semiactive control strategy focusing on inclusion of effects of control-structure interaction. The subject of the ASCE benchmark problem is a cable-stayed bridge in Cape Girardeau, Missouri, for which construction is expected to be completed in 2003. The goal of the benchmark study is to provide a \Itestbed\N structure on which researchers can systematically compare and evaluate the relative merits of proposed structural protection for cable stayed-bridges. In this paper, magnetorheological (MR) fluid dampers, which belong to the class of controllable fluid dampers, are proposed for use in a control strategy for protecting the bridge. A clipped-optimal control algorithm, shown to perform well in previous studies involving MR fluid dampers, is employed. A comprehensive study of the adequacy of various types of dynamic models for MR fluid dampers, such as a Bingham model, a Bouc-Wen model, and a modified Bouc-Wen model, is provided. In contrast to previous studies, models considered in this study are based on experimental data for a full-scale MR fluid damper. Because the MR fluid damper is a controllable energy-dissipation device that cannot add mechanical energy to the structural system, the proposed control strategy is fail-safe in that bounded-input, bounded-output stability of the controlled structure is guaranteed. Numerical simulation results considering several historical earthquakes scaled to various magnitudes show that the proposed semiactive control strategy using MR fluid dampers is the promising one of the applicable control methods to reduce seismic responses of cable-stayed bridges.

Background component of buffeting response of cable-stayed bridges

For practical purpose, buffeting response of cable-stayed bridges to wind excitation is usually analytically determined by single-mode-based method, and the resultant response is written as the composition of the resonant component and the background component by the square root of sum squares (SRSS) method. The background component is sometimes neglected for simplifying computations. In the present paper, numerical computations on four representative cable-stayed bridges in China indicate that the background component usually has a significant contribution to the buffeting response of long-span cable-stayed bridges. Parametric studies on the effects of structural parameters on the buffeting background components for these four bridges are also performed. A simplified method introduced in literatures for estimation of the background component of buffeting response is then briefly discussed. Finally an approximate method for estimating the first vertical bending mode-buffeting response of cable-stayed bridges is proposed.

Modeling of cable vibration effects of cable-stayed bridges

The analysis of dynamic responses of cable-stayed bridges subjected to wind and earthquake loads generally considers only the motions of the bridge deck and pylons. The influence of the stay cable vibration on the responses of the bridge is either ignored or considered by approximate procedures. The transverse vibration of the stay cables, which can be significant in some cases, are usually neglected in previous research. In the present study, a new three-node cable element has been developed to model the transverse motions of the cables. The interactions between the cable behavior and the other parts of the bridge superstructure are considered by the concept of dynamic stiffness. The nonlinear effect of the cable caused by its self-weight is included in the formulation. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed model. The impact of cable vibration behavior on the dynamic characteristics of cable-stayed bridges is discussed.

Influence of Aerodynamical Feedbacks on Response of Cable-Stayed Bridges

Influence of Aerodynamical Feedbacks on Response of Cable-Stayed Bridges

Study on nonlinear analysis of a highly redundant cable-stayed bridge

A comparison on nonlinear analysis of a highly redundant cable-stayed bridge is performed in the study. The initial shapes including geometry and prestress distribution of the bridge are determined by using a two-loop iteration method, i.e., an equilibrium iteration loop and a shape iteration loop. For the initial shape analysis a linear and a nonlinear computation procedure are set up. In the former all nonlinearities of cable-stayed bridges are disregarded, and the shape iteration is carried out without considering equilibrium. In the latter all nonlinearities of the bridges are taken into consideration and both the equilibrium and the shape iteration are carried out. Based on the convergent initial shapes determined by the different procedures, the natural frequencies and vibration modes are then examined in details. Numerical results show that a convergent initial shape can be found rapidly by the two-loop iteration method, a reasonable initial shape can be determined by using the linear computation procedure, and a lot of computation efforts can thus be saved. There are only small differences in geometry and prestress distribution between the results determined by linear and nonlinear computation procedures. However, for the analysis of natural frequency and vibration modes, significant differences in the fundamental frequencies and vibration modes will occur, and the nonlinearities of the cable-stayed bridge response appear only in the modes determined on basis of the initial shape found by the nonlinear computation.

MULTI-MODE COUPLED BUFFETING ANALYSIS OF CABLE-STAYED BRIDGES

A procedure for the spectral analysis of buffeting response of long span bridges under unsteady wind loads is developed, with emphasis placed on inclusion of the multi-mode vibrations. The effect of mean wind velocity is considered through the aerodynamic stiffness and damping matrices using the flutter derivatives, while the effect of buffeting through the auto- and cross-power spectral densities. Compared with the conventional approach, the present approach is featured by the fact that no selection has to be made concerning the dominant modes. It can be reasonably used in analyzing cable-stayed bridges of complex geometry or of asymmetric shape, such as the Kao-Ping-Hsi Bridge, where the conventional approach has its limitations. The numerical studies indicate that using the conventional approach, by which the coupling effect is ignored, may significantly overestimate the critical wind velocity, while underestimating the buffeting responses of cable-stayed bridges.

Effect of support conditions on seismic response of cable-stayed bridges

The seismic response of a cable-stayed bridge is the result of the interaction between the input earthquake characteristics and the bridge properties like mass, stiffness, and support conditions. The support type used for the deck at the towers of cable-stayed bridges is one of the important parameters that greatly influences the seismic response of the bridge. This is demonstrated in the present paper by study of the change in modal characteristics and seismic response of two cable-stayed bridges for different types of the support conditions. The first bridge has concrete towers and a steel deck with a 371 m main span, and the second bridge also has concrete towers, but a composite deck with a 465 m main span. The study shows that elastic supports for the deck at the towers give very low deck displacements and deck bending moments compared to pinned or fixed connections. Roller supports produce low tower base shear and base moment but not necessarily a low response for the bridge as a whole. Roller supports also cause the bridge to have very low first longitudinal direction mode frequency; this indicates that the bridge is very flexible in the longitudinal direction. A study of the effect of variation of the longitudinal stiffness of the elastic deck supports shows that it strongly influences the first few longitudinal direction modes, but not the symmetric or higher modes. The study also shows that the seismic response of the bridge is highly influenced by the variation of the support stiffness for some earthquakes like 1940 El Centro earthquake, but to a lesser degree for others. Wave propagation effects were also studied for different support conditions of the bridge. It is observed that the seismic response shows a higher degree of variation with the changing wave velocities when the bridge deck has pinned or fixed supports, and that the change in the bridge response with the wave velocities is not very pronounced when the bridge deck has elastic or roller supports. For the first bridge, the critical responses were observed at very low wave velocities, and for the second bridge, the uniform motion case caused the critical response of the bridge at many locations.Key words: cable-stayed bridges, support conditions, seismic response, wave propagations.

Influence of Deck Material on Response of Cable-Stayed Bridges to Live Loads

During the last three decades, cable-stayed bridges have proven to be first-class structures providing vital transport links. Together with the construction process, erection procedure, and site conditions, the choice of material for the deck is a principal factor in the overall cost of construction. The effects of variable long-span bridge loads on the design of steel, composite, and concrete decks are investigated. Recent American and British long-span bridge loads have been used that are based on direct observations of modern traffic conditions. The three-dimensional finite-element models prepared for the study are based on the geometric and material properties of the Quincy Bayview cable-stayed bridge. Many cable arrangements are considered for the studied concrete, composite, and steel decks. A nonlinear analysis of the cable-stayed bridge models is carried out. The results of the different deck materials are compared. It is shown that the choice of material for the deck can be greatly affected by th...

Effect of support conditions on seismic response of cable-stayed bridges

The seismic response of a cable-stayed bridge is the result of the interaction between the input earthquake characteristics and the bridge properties like mass, stiffness, and support conditions. The support type used for the deck at the towers of cable-stayed bridges is one of the important parameters that greatly influences the seismic response of the bridge. This is demonstrated in the present paper by study of the change in modal characteristics and seismic response of two cable-stayed bridges for different types of the support conditions. The first bridge has concrete towers and a steel deck with a 371 m main span, and the second bridge also has concrete towers, but a composite deck with a 465 m main span. The study shows that elastic supports for the deck at the towers give very low deck displacements and deck bending moments compared to pinned or fixed connections. Roller supports produce low tower base shear and base moment but not necessarily a low response for the bridge as a whole. Roller supports also cause the bridge to have very low first longitudinal direction mode frequency; this indicates that the bridge is very flexible in the longitudinal direction. A study of the effect of variation of the longitudinal stiffness of the elastic deck supports shows that it strongly influences the first few longitudinal direction modes, but not the symmetric or higher modes. The study also shows that the seismic response of the bridge is highly influenced by the variation of the support stiffness for some earthquakes like 1940 El Centro earthquake, but to a lesser degree for others. Wave propagation effects were also studied for different support conditions of the bridge. It is observed that the seismic response shows a higher degree of variation with the changing wave velocities when the bridge deck has pinned or fixed supports, and that the change in the bridge response with the wave velocities is not very pronounced when the bridge deck has elastic or roller supports. For the first bridge, the critical responses were observed at very low wave velocities, and for the second bridge, the uniform motion case caused the critical response of the bridge at many locations.Key words: cable-stayed bridges, support conditions, seismic response, wave propagations.

Vibration control of cable-stayed bridges—part 1: modeling issues

The objective of the research presented here is to increase the understanding of how the complexities associated with modeling cable-stayed bridges, such as non-linear behaviour and the participation of highly coupled, high-order vibration modes in the overall dynamic response, affect the overall effectiveness of active control schemes. The 316-degree-of-freedom analytical model studied here is based on the Jindo Bridge located in South Korea. Computational considerations associated with control analyses require the size of the model to be significantly reduced, without loss of the important vibration characteristics and complexities. Three separate reduced-order modelling techniques for creating effective control models are studied here: the IRS method, the internal balancing method, and a modal reduction method. These methods are studied and compared on their ability to capture the complex dynamic response of cable-stayed bridges subjected to multiple-support excitation and their ability to create viable and computationally sound state-space models for control analyses. Results show that the modal reduction technique, because of the ability to select only those modes causing the largest force and displacement response, is most effective for control applications. © 1998 John Wiley & Sons, Ltd. Language: en

Dynamic Response of Cable-Stayed Bridges under Moving Loads

A modeling method for cable-stayed bridges with nonlinear cables that is used for the dynamic response under moving loads is discussed in this paper. Individual stay cables are modeled by short catenary cable elements in which the nonlinearity due to large displacements but small deformations and the nonlinearity due to the variations of tension are taken into account. A linear approximate bridge model is used to solve the dynamic response of cable-stayed bridges; the nonlinear contribution of the stay cables is added by means of an iterative procedure. Internal nodes of stay cables are not present in the linear approximate bridge model so that it contains a small number of degrees of freedom (DOF), whereas the nonlinear dynamic response of stay cables is computed at cable level, one at a time, by means of the finite-element method using many internal nodes for each stay cable. An illustrative example demonstrates that the proposed method is very efficient, inexpensive, and capable of exhibiting the resonance of stay cables excited by the bridge deck and towers.

Effect of material of deck on response of cable-stayed bridges to live loads

Effect of material of deck on response of cable-stayed bridges to live loads

Dynamic response of cable-stayed bridges to moving vehicles using the structural impedance method

The importance of dynamic interactions between cable-stayed bridges and heavy moving vehicles, such as trucks and locomotives, has been recognised by bridge engineers for a long time. A structural impedance algorithm is developed for analysing the dynamic response of cable-stayed bridges subjected to traversing vehicles. The bridge deck is modelled as an elastic plate, and the cables are idealised as springs for simplicity. The vehicles are modelled as a series of masses with suspension systems moving with different speeds and accelerations. A comprehensive computer program, CABLESIM, is developed for the static and dynamic analyses of a cable-stayed bridge. The accuracy of the numerical procedure and its computer implementation is verified with the available analytical and experimental results. A parametric study is conducted to investigate the effects of vehicle velocity, girder depth, different types of cable arrangements, and traffic load on the dynamic response of the deck. The numerical results are expected to be important in assessing the dynamics of cable-stayed bridge components and in determining the safety and allowable traffic conditions.

Influence of cable vibration on seismic response of cable-stayed bridges

In cable-stayed bridges, modelling the cables is of particular significance for the seismic behaviour of the structure. The common practice of modelling a cable by a single truss element is inadequate for seismic response calculations because it essentially precludes the lateral cable vibration modes. The present paper studies the influence of cable vibrations on the seismic response of cable-stayed bridges. Three bridge examples with different spans and properties were used. Cable vibrations are accounted for through the use of multiple links for each cable. Cable vibration effects are found to be significant for seismic response calculations, particularly when the cable fundamental frequencies are overlapping with the first few frequencies of the bridge. Parametric studies are conducted with regard to the number of links per cable, the effect of the modulus of elasticity of the cables, and different earthquakes on the bridge response. Modelling the cables by two links per cable such that at least the fundamental modes of the cable vibrations are represented can significantly account for the effect of cable vibrations. It is also observed that the equivalent modulus method cannot in any way account for the cable vibration effects. Key words: cable vibration, dynamic analysis, equivalent modulus, multiple links, seismic response, cable-stayed bridge.

Parametric study of cable-stayed bridge response due to traffic-induced vibration

The dynamic response of long-span cable-stayed bridges due to moving traffic loads is investigated utilizing three-dimensional models. Modal analysis is conducted using the deformed dead-load tangent stiffness matrix. A new concept, presented by discretization of cable into several elements, is used to study the effect of cable vibration on bridge dynamics. A computer algorithm is developed to simulate the applied traffic loads for both directions of the bridge deck. The algorithm is flexible in terms of handling different loading capacities, speeds and configurations. Parametric studies are conducted to investigate the effect of cable vibration, damping, vehicle-structure interaction, random roughness of the bridge deck, as well as span length and vehicle-speed. Cases of asymmetric traffic loading clustered in one direction are also considered in order to study the torsional response of the bridge. Results are discussed, summarized and plotted.