Seismic Response Of Cable-stayed Bridge Research Articles

Seismic response mitigation of girder displacement of cable-stayed bridge using inerter systems

Cable-stayed bridges have been widely utilized as transportation hubs in mountainous and coastal areas. Once these bridges are damaged during earthquakes, the routine for rescue operations will be interrupted, leading to enormous life and financial loss. Since damage of cable-stayed bridges are mainly caused by excessive displacement of main girders, this paper considers mitigating the displacement demands by implementing inerter systems between tower and main girder. Following brief introduction of inerter systems, a simplified three degree-of-freedom (DOF) dynamic model of a cable-stayed bridge prototype is established and verified by refined finite element (FE) model. Then the design parameters of inerter systems are optimized based on the dynamic amplification factor (DMF) method, while the influence of each parameter on the performance is discussed in detail. To further investigate the efficiency of these systems, the seismic responses of cable-stayed bridge with different inerter devices are computed and compared with the prototype, as well as system with conventional viscous dampers (VD). From the analytical results, the inerter systems are demonstrated effective in alleviating displacement demands of main girder of cable-stayed bridges and outperforming the commonly used VD. This study is believed able to provide basis for engineering application of inerter systems on cable-stayed bridges to improve the seismic performance and reliability against earthquakes.

Multi-angle and nonuniform ground motions on cable-stayed bridges

The definition of the spatial variability of the ground motion (SVGM) is a complex and multi-parametric problem. Its effect on the seismic response of cable-stayed bridges is important, yet not entirely understood to date. This work examines the effect of the SVGM on the seismic response of cable-stayed bridges by means of the time delay of the ground motion at different supports, the loss of coherency of the seismic waves, and the incidence angle of the seismic waves. The focus herein is the effect of the SVGM on cable-stayed bridges with various configurations in terms of their length and of design parameters such as the pylon shape and the pylon–cable system configuration. The aim of this article is to provide general conclusions that are applicable to a wide range of canonical cable-stayed bridges and to contribute to the ongoing effort to interpret and predict the effect of the SVGM in long structures. This work shows that the effect of the SVGM on the seismic response of cable-stayed bridges varies depending on the pylon shape, height, and section dimensions; on the cable-system configuration; and on the response quantity of interest. Furthermore, the earthquake incidence angle defines whether the SVGM is important to the seismic response of the cable-stayed bridges. It is also confirmed that the SVGM excites vibration modes of the bridges that do not contribute to their seismic response when identical support motion is considered.

Seismic Response of a Cable-Stayed Bridge considering Non-uniform Excitation Effect: Model Design and Shake Table Testing

In the absence of intensive tests on the cable-stayed bridges under non-uniform excitation, this study provides a practical and accurate approach to investigate the seismic response of cable-stayed bridges considering spatially varying earthquake inputs. The cable-stayed bridge model with a scale ratio of 1:120 was designed and tested on a newly-developed dual shake table system. Firstly, the modal test was conducted to evaluate the accuracy of the designed specimen. Secondly, both the same input cases and the different inputs cases were executed to study the wave passage effects on bridge specimen's dynamic response. Lastly, the effects of non-uniform excitation and site classification on the experimental bridge's seismic performance were studied with test results of various soil condition cases. The test results showed that the bending of the girder was magnified, while the swing of the tower was subdued when the effect of wave propagation was considered. Moreover, compared with the same input cases, the different inputs cases reported a larger response to the extent of 80%. Regarding the effects of site conditions, it was concluded that the site of soft soil had more influence on the dynamic responses of such bridge structures than that of the firm soil site.

PARAMETRIC STUDY OF CABLE STAYED BRIDGE USING DIFFERENT PYLON CONFIGUARTION

Cable stayed bridge are the most flexible bridge and getting popularity because of its economy for longer spans. Cable stayed bridges have good stability, optimum use of structural materials, aesthetic, low design and maintenance costs, and efficient structural characteristics. Therefore, this type of bridges are given preference for long span crossings compared to suspension bridges. A study is carried out to find the dynamic effect on different configuration of pylons of a cable stayed bridge. A pylon is inclined at 5o , 10o , 15o , 20o , 25o and 30o with vertical and horizontal axis both and compared with vertical pylon to study the dynamic response of bridge. The 3D bridge models are prepared on CSI BRIDGE software and bridge is analyzed seismically by Imperial Valley 1947, Earthquake. The bridge response in terms of Pylon, Girder and Cable axial force, moment and torsion is obtained. The study reveals that the different angle of the pylon has great influence in the seismic response of cable stayed bridge. We are getting minimum axial force at 10o in cable at main span, girder at main span and pylon.

Assessing time-dependent damage to a cable-stayed bridge through multi-directional ground motions based on material strain measures

Investigations into previous earthquakes indicated that the seismic damage to bridges was closely related to the length of their service lives. Based on this observation, finite-element time-dependent models of a cable-stayed bridge with a single pylon and wide deck were established by considering the effects of concrete carbonization on various structural components. Ground motion records were selected and matched with the design spectrum of site classification Ⅰ. Different combinations methods of ground motions inputs were compared with respect to the strain distributions of critical elements, and the representative method was then determined according to the maximum responses. The strain limits of reinforcing steel and concrete were defined based on previous studies, and were used to identify the time-dependent damage states of critical elements under earthquakes. The incremental dynamic analysis (IDA) method was applied to comparatively investigate the effect of concrete carbonization on the seismic response of cable-stayed bridge. Using the defined strain limits, the effect of concrete carbonization on the time-dependent seismic damage to the cable-stayed bridge was also discussed. The results show that the strength of steel and concrete can decrease as much as 23.30% and 12.66% respectively due to the concrete carbonization. The coupling damage to the bridge is found under multi-directional ground motions. The pylon is the most critical element during three-way seismic waves, in which the base suffers the most serious damage, the deck-level section follows and the cable anchorage portion remains in slight damage state. Taking the concrete carbonization into consideration, the damage level of the pylon base increases significantly, and brittle failure may occur to the pylon base when subjected to earthquakes with high peak ground accelerations (PGAs). However, the damage levels of other critical portions of the pylon decrease when the concrete carbonization is considered.

Influence of near-fault ground motion characteristics on the seismic response of cable-stayed bridges

Observations from several earthquakes indicate that near-fault (NF) ground motions have a significant influence on the seismic response of structures. However, existing studies have only discussed the influence of a certain NF characteristic on the seismic response, rather than systematically discussing and comparing the influence of different NF characteristics. Furthermore, current research is only suitable for a specific structure while the influence of NF characteristics on structures with different dynamic characteristics has not been revealed. As an important lifeline project, the safety of a cable-stayed bridge (CSB) during earthquakes is of great concern. Therefore, this paper investigates the influence of NF ground motions on the seismic response of CSB. Firstly, three major characteristics (i.e., the hanging wall effect, rupture directivity effect and high velocity pulse) of NF ground motions are analyzed using NF records of the Chi–Chi earthquake. Secondly, a finite element (FEM) model for modeling a prototype CSB is developed and benchmarked. Then, the seismic responses of the prototype CSB subjected to NF ground motions with different characteristics are analyzed using the benchmarked FEM model. The analyses show that hanging wall effect, rupture directivity effect, and high velocity pulse affect the seismic demand of the CSB to varying degrees. Furthermore, the influences of NF characteristics on the displacement response of CSBs with different fundamental periods are investigated using SDOF systems. The analysis results show that different NF characteristics have various influences on the displacement response of CSBs with different fundamental periods.

Effects of near-field ground motions and soil-structure interaction on dynamic response of a cable-stayed bridge

Seismic response of cable-stayed bridges is investigated with the main focus pertaining to the effects of near-field ground motions and soil-structure interaction on the dynamic response of the bridges. A 1/60 scale model of a typical cable-stayed bridge was designed and fabricated for the laboratory investigations. Three different types of ground motion records from the 1999 Chi-Chi earthquake, namely far-field, non-pulse near-field, and pulse-type near-field were employed in the experiments and the numerical analysis of the bridge. Laboratory simulation of the soil-structure interaction was accomplished by a box-spring system with interchangeable springs as foundations for the bridge towers. A three-dimensional numerical model of the bridge was developed, and its response was verified by the experimental results. Results from the numerical and experimental investigations indicated that the effects of foundation soil stiffness on the response of the bridge was influenced by the type of input ground motions. The bridge response was amplified when their foundation was in softer soils.

Seismic response of cable-stayed bridge subjected to single-support excitation on various soil condition

For cable-stayed bridge, pylon and girder are one of the most important factors in the design process. Because of the length this structure, it needs to consider the type of the soil because different soil type can be resulting a different earthquake loads. In this study, the behavior of superstructure was investigated using time history analysis subjected to excitation uniformly on the pylon and girder. The test model was a cable-stayed bridge which classified as a long-span bridge. For obtaining the effects of soil type condition, different response spectrums are considered for three soil types: firm, medium, and soft soil. The response spectrums were thus converted to become ground acceleration time history and displacement time history. The displacement was then applied longitudinally and transversally to the supports of the structure to determine the behavior of the bridge. The result shows that the maximum displacement on the pylon and girder due to longitudinal load was at the top of the pylon and in the middle of the main span. As for the transverse earthquake load, the maximum displacement was in the middle area of the pylon and the middle of the main span. The results also defines that the displacement caused by firm soil is smaller than medium soil and soft soil.

Longitudinal seismic responses of a cable-stayed bridge based on shaking table tests of a half-bridge scale model

This article studies the seismic response of a symmetric long-span cable-stayed bridge under longitudinal uniform excitations by finite element analysis and shaking table tests. The feasibility and method of performing shaking table tests are examined using a simplified half-bridge scale model. By taking advantage of the symmetry, it is possible to construct a scale model with a larger scale ratio than a full-bridge scale model. The main components of the scale model (i.e. tower, piers, girder, and cables) were fabricated using the same or similar materials as in the prototype. The design and construction of the scale model is presented. Longitudinal structural responses obtained from the finite element analysis and shaking table tests are compared. The seismic mitigation effects of viscous dampers are examined through shaking table tests.

Effect of spatial variability of earthquakes on cable-stayed bridges

This paper focuses on the effect of spatially variable ground motions on the towers of cable-stayed bridges with 200, 400 and 600 m main spans. Seismic analysis of the bridges is performed, taking account of different sources of the spatial variability, namely; incoherence and wave passage effects. To address these effects, the response of the towers is assessed under the effect of different propagation velocities of the seismic waves and different assumptions on the coherency of the ground motion, to conclude that the effect of spatially variable motions on the seismic response of cable-stayed bridges is dependent on the assumed wave propagation velocity and rate of coherency.

Deck–tower interaction in the transverse seismic response of cable-stayed bridges and optimum configurations

Modern design solutions in cable-stayed bridges give a significant importance to the seismic response in the transverse direction. This work is focused on the dynamic interaction between the deck and the towers, exploring the key role of different vibration modes. An extensive parametric analysis is proposed to address the influence of the main span length, the tower geometry, the cable-system arrangement, the width and height of the deck and the soil conditions. It is demonstrated that the vibration modes that govern the seismic response of cable-stayed bridges in the transverse direction involve the interaction between the tower and the deck, but the order of these modes and the parts of the deck that are affected change with the main span length. It is also observed that the interaction between the deck and the towers during the earthquake is maximised if their isolated vibration frequencies are close to each other, leading to a significantly large seismic demand. Analytical expressions are proposed to obtain the critical frequencies of the towers for which these interactions arise, and recommendations are given to define the tower geometry in order to avoid such problematic scenarios.

Intelligent active control of a benchmark cable-stayed bridge

A neural-fuzzy control strategy for cable-stayed bridge structures subjected to earthquake excitation is presented by employing electromagnet-driven active mass dampers (EMDs). The active EMD is an innovative control device for the earthquake response mitigation of structures. Ensuring fast selection of the control voltage in accordance with the characteristics of seismically excited bridge structures is one of the most important problems for EMD systems. In the proposed control strategy, a neural-network technique is used to solve the time-delay problem, and fuzzy logic algorithms are used to determine the control voltage from the response of the EMD. The control performance of the proposed neural-fuzzy control strategy was analysed for the benchmark control problem of a seismically excited cable-stayed bridge with an EMD system. The simulated results show that the proposed active neural–fuzzy control strategy can quickly determine an accurate voltage for the EMD system, and mitigate the seismic response of cable-stayed bridges.

Analysis for Influence of Structural System on Nonlinear Seismic Response of Cable-Stayed Bridge

For different structural system of cable-stayed bridge, the dynamic characteristics have obvious difference under seismic load. Dynamic time-history analysis of earthquake was applied, and the EI Centero seismic wave with modified peak acceleration was chose as the earthquake acceleration time-history input. As Jiangsu Siyang special-shaped single tower cable-stayed bridge for engineering background, considering geometric nonlinear of structure, the differences of dynamic characteristics of cable-stayed bridge structures were gained under two different situations. The single longitudinal seismic ground motion was chose under the first situation, while the longitudinal, lateral, and vertical seismic ground motion are introduced. For floating system, the displacements are the largest and the inner forces are the smallest. For rigid frame system, the displacements are the smallest and the inner forces are the largest. The others are not much difference. Comprehensively, semi-floating system has better performance under seismic load.

Seismic Response Analysis of Cable-Stayed Bridges

For floating system cable-stayed bridge, the longitudinal displacement of stiffening girder and moments of towers are very large when strong earthquake happens. Too large displacement of stiffening girder leads to collision between girders of the main bridge and the approaches. Using spatial finite element model and time history analysis method, the seismic responses of cable-stayed bridge are studied considering the elasto-plastic effects. The results show that the displacement of stiffening girder is very large when no seismic reduction measures are adopted. The viscous dampers installed between the stiffening girder and towers can efficiently reduce seismic responses of the cable-stayed bridge. Especially, the displacement of stiffening girder can be controlled well to meet the design requirement. Using the optimum parameters of damper, the height of pier under tower and intermediate supports in side span on seismic responses are studied in detail. The longitudinal displacement of stiffening girder increases with the pier height increasing. The intermediate supports in side span are benefit for seismic reduction.

Seismic Response Reduction of Cable-Stayed Bridge with Viscous Dampers

For floating system cable-stayed bridge, the longitudinal displacement of girder and moments of towers are very large when strong earthquake happens. The dampers installed between girder and towers in longitudinal direction can reduce efficiently displacement of the girder and moments of the towers induced by longitudinal seismic waves. Using spatial finite element model and time history analysis method, the influences of design parameters of viscous damper on seismic responses of cable-stayed bridge are studied in detail. The results of study show that, with the damping constant increasing, the longitudinal displacement of girder and moment of tower decrease, and the forces of damper increase. With velocity exponent increasing, the longitudinal displacement of girder and moment of tower increase, and the force of damper decrease. So, when determining the design parameters of damper, the cost of dampers, difficulty of construction and seismic reduction effects should be considered together.

Semi-active fuzzy control of cable-stayed bridges using magneto-rheological dampers

A semi-active fuzzy control technique to enhance the seismic performance of cable-stayed bridges using magneto-rheological (MR) dampers is presented. Conventional semi-active control techniques require a primary controller as a reference to determine the desired control force, and modulate the input voltage of the MR damper by comparing the desired control force and the actual damper force in a secondary controller. The proposed method, however, adopts fuzzy logic instead of primary and secondary controllers. The fuzzy logic directly determines the input voltage of an MR damper from the response of the MR damper. Thus, it provides a simple design procedure and can be easily implemented on a physical structure. The control performance of the proposed fuzzy control technique for the MR damper was evaluated for the benchmark control problem of a seismically-excited cable-stayed bridge. The simulated results show that the proposed semi-active fuzzy control technique can effectively mitigate the seismic response of cable-stayed bridges and successfully enhance the robust performance of the MR damper system.

Seismic response of a cable‐stayed bridge deck under multi‐component non‐stationary random ground motion

AbstractA Markov method of analysis is presented for obtaining the seismic response of cable‐stayed bridges to non‐stationary random ground motion. A uniformly modulated non‐stationary model of the random ground motion is assumed which is specified by the evolutionary r.m.s. ground acceleration. Both vertical and horizontal components of the motion are considered to act simultaneously at the bridge supports. The analysis duly takes into account the angle of incidence of the earthquake, the spatial correlation of ground motion and the quasi‐static excitation. A cable‐stayed bridge is analysed under a set of parametric variations in order to study the non‐stationary response of the bridge. The results of the numerical study indicate that (i) frequency domain spectral analysis with peak r.m.s. acceleration as input could provide more r.m.s. response than the peak r.m.s. response obtained by the non‐stationary analysis; (ii) the longitudinal component of the ground motion significantly influences the vertical vibration of the bridge; and (iii) the angle of incidence of the earthquake has considerable influence on the deck response. Copyright © 2003 John Wiley & Sons, Ltd.

Seismic isolation of cable‐stayed bridges for near‐field ground motions

AbstractThis study examines the efficacy of using seismic isolation to favorably influence the seismic response of cable‐stayed bridges subjected to near‐field earthquake ground motions. In near‐field earthquake ground motions, large amplitude spectral accelerations can occur at long periods where many cable‐stayed bridges have significant structural response modes. This combination of factors can result in large tower accelerations and base shears. In this study, lead–rubber bearing seismic isolators were modeled for three cable‐stayed bridges, and three cases of isolation were examined for each bridge. The nine isolated bridge configurations, plus three non‐isolated configurations as references, were subjected to near‐field earthquake ground motions using three‐dimensional time‐history analyses. Introduction of a small amount of isolation is shown to be very beneficial in reducing seismic accelerations and forces while at the same time producing only a modest increase in the structural displacements. There is a low marginal benefit to continue to increase the amount of isolation by further lengthening the period of the structure because structural forces and accelerations reduce at a diminishing rate whereas structural displacements increase substantially. In virtually all cases the base shears in the isolated bridges were reduced by at least 50several instances by up to 80individual near‐field records showed large variability from one record to the next, with coefficients of variation about the mean as large as 50assessing the characteristics of near‐field ground motion for use in isolation design of cable‐stayed bridges. Copyright © 2003 John Wiley & Sons, Ltd.

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...

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.