Seismic fragility analysis of three-tower cable-stayed bridges with different connection configurations

Seismic fragility analysis of three-tower cable-stayed bridges with three different structural systems,including rigid system(RS),floating system(FS),and passive energy dissipation system(PEDS),is conducted to study the effects of connection configurations on seismic responses and fragilities.Finite element models of bridges are established using OpenSees.A new ground motion screening method based on the statistical characteristic of the predominant period is proposed to avoid irregular behavior in the selection process of ground motions,and incremental dynamic analysis(IDA)is performed to develop components and systems fragility curves.The effects of damper failure on calculated results for PEDS are examined in terms of seismic response and fragility analysis.The results show that the bridge tower is the most affected component by different structural systems.For RS,the fragility of the middle tower is significantly higher than other components,and the bridge failure starts from the middle tower,exhibiting a characteristic of local failure.For FS and PEDS,the fragility of the edge tower is higher than the middle tower.The system fragility of RS is higher than FS and PEDS.Taking the failure of dampers into account is necessary to obtain reliable seismic capacity of cable-stayed bridges.

Dynamic Response of Sea-Crossing Rail-cum-Road Cable-Stayed Bridge Influenced by Random Wind–Wave–Undercurrent Coupling

Sea-crossing bridges are affected by random wind–wave–undercurrent coupling loads, due to the complex marine environment. The dynamic response of long-span Rail-cum-Road cable-stayed bridges is particularly severe under their influence, potentially leading to safety problems. In this paper, a fluid–structure separation solution method is implemented using Ansys–Midas co-simulation, in order to solve the above issues effectively while using less computational resources. The feasibility of the method is verified by comparing the tower top displacement response with relevant experimental data. From time and frequency domain perspectives, the displacement and acceleration responses of the sea-crossing Rail-cum-Road cable-stayed bridge influenced by wave-only, wind–wave, and wind–wave–undercurrent coupling are comparatively studied. The results indicate that the displacement and acceleration of the front bearing platform top are more significant than those of the rear bearing platform. The dominant frequency under wind–wave–undercurrent coupling is close to the natural vibration frequencies of several bridge modes,such that wind–wave–undercurrent coupling is more likely to cause a resonance effect in the bridge. Compared with the wave-only and wind–wave coupling, wind–wave–undercurrent coupling can excite bridges to produce larger displacement and acceleration responses: at the middle of the main girder span, compared with the wave-only case, the maximum displacement in the transverse bridge direction increases by 23.58% and 46.95% in the wind–wave and wind–wave–undercurrent coupling cases, respectively;at the tower top, the variation in the amplitude of the displacement and acceleration responses of wind–wave and wind–wave–undercurrent coupling are larger than those in the wave-only case, where the acceleration change amplitude of the tower top is from-0.93 to 0.86 m/s^(2) in the waveonly case, from-2.2 to 2.1 m/s^(2) under wind–wave coupling effect, and from-2.6 to 2.65 m/s^(2) under wind–wave–undercurrent coupling effect, indicating that the tower top is mainly affected by wind loads, but wave and undercurrent loads cannot be neglected.

Process Monitoring and Terminal Verification of Cable-Stayed Bridges with Corrugated Steel Webs under Contruction

In this paper,the construction process of a cable-stayed bridge with corrugated steel webs was monitored.Moreover,the end performance of the bridge was verified by load test.Owing to the consideration of the bridge structure safety,it is necessary to monitor the main girder deflection,stress,construction error and safety state during construction.Furthermore,to verify whether the bridge can meet the design requirements,the static and dynamic load tests are carried out after the completion of the bridge.The results of construction monitoring show that the stress state of the structure during construction is basically consistent with the theoretical calculation and design requirements,and both meet the design and specification requirements.The final measured stress state of the structure is within the allowable range of the cable-stayed bridge,and the stress state of the structure is normal and meets the specification requirements.The results of load tests show that the measured deflection values of the mid-span section of the main girder are less than the theoretical calculation values.The maximum deflection of the girder is−20.90 mm,which is less than−22.00 mm of the theoretical value,indicating that the girder has sufficient structural stiffness.The maximum impact coefficient under dynamic load test is 1.08,which is greater than 1.05 of theoretical value,indicating that the impact effect of heavy-duty truck on this type of bridge is larger.This study can provide important reference value for construction and maintenance of similar corrugated steel web cable-stayed bridges.

Probability evaluation method for cable safety of long-span cable-stayed bridges

A method of cable safety analysis is proposed for safety evaluation of long-span cable-stayed bridges. The Daniels＇ effect and the probability of broken wires in the cable are introduced to develop the cable strength model and the reliability assessment technique for long-span cable-stayed bridges based on the safety factors analysis of stay cables in service. As an application of the proposed model, the cable safety reliability of the cable No. 25 of Zhaobaoshan cable-stayed bridge in China is calculated. The effects of various parameters on the estimated cable safety reliability are investigated. The results indicate that the proposed method can be used to assess the safety level of stay cables in cable-stayed bridges effectively. The Daniels＇ effect should be taken into account for assessment, and the probability of broken wires can be used to simulate the deterioration of stay cables in service.

Mechanical performance evaluation of a new type of cable-stayed beam-arch combination bridge based on field tests

In order to study the mechanical performance of a new type of cable-stayed beam-arch combination bridge, the results of field static and dynamic load tests are comparatively analyzed with numerical results based on the Jingyi bridge straddling the Daxi River in Yixing. First, the test scheme, tasks, the corresponding measure method, as well as the relevant codes are described. Secondly, two sets of three- dimensional finite element models are established. One is Ansys which uses the solid element and the other is Midas which adopts the beam element. Finally, the experimental and analytical results are comparatively analyzed, and they show an agreement with each other. The results show that the bridge possesses adequate load-carrying capacity under all static load cases, but the capacity of dissipating external input energy is insufficient due to the relatively smaller damping ratio. The study results can provide a reference for further study and optimization of this type of bridge. Calibrated finite-element models that reflect the real conditions can be used as a baseline for future maintenance of the bridge.

Application of uncertain type of AHP to condition assessment of cable-stayed bridges

In order to guarantee the safety service and life-span of long-span cable-stayed bridges, the uncertain type of analytic hierarchy process （AHP） method is adopted to access the bridge condition. The correlative theory and applied objects of uncertain type of AHP are introduced, and then the optimal transitive matrix method is chosen to calculate the interval number judgment matrix, which makes the weights of indices more reliable and accurate. Finally, with Harbin Songhua River Cable-Stayed Bridge as an example, an index system and an assessment model are proposed for the condition assessment of this bridge, and by using uncertain type of AHP, the weights of assessment indices are fixed and the final assessment results of the bridge are calculated, which proves the feasibility and practicability of this method. The application of this assessment method can provide the scientific basis for maintenance and management of long-span cable-stayed bridges.

Longitudinal forces of continuously welded track on high-speed railway cable-stayed bridge considering impact of adjacent bridges

A proven beam-track contact model was used to analyze the track-structure interaction of CWR (continuously welded track) on bridge. Considering the impact of adjacent bridges, the tower-cable-track-beam-pier-pile finite element model of the cable-stayed bridge was established. Taking a bridge group including 40-32m simply-supported beam and (32+80+112)m single-tower cable-stayed bridge and 17-32m simply-supported beam on the Kunming-Shanghai high-speed railway as an example, the characteristics of CWR longitudinal force on the cable-stayed bridge were studied. It is shown that adjacent bridges must be considered in the calculation of the track expansion force and bending force on cable-stayed bridge. When the span amount of adjacent bridges is too numerous, it can be simplified as six spans; the fixed bearing of adjacent simply-supported beams should be placed on the side near the cable-stayed bridge; the track expansion device should be set at the bridge tower to reduce the track force near the bridge abutment.

Effects of fundamental factors on coupled vibration of wind-rail vehicle-bridge system for long-span cable-stayed bridge

In a wind-vehicle-bridge(WVB) system,there are various interactions among wind,vehicle and bridge.The mechanism for coupling vibration of wind-vehicle-bridge systems is explored to demonstrate the effects of fundamental factors,such as mean wind,fluctuating wind,buffeting,rail irregularities,light rail vehicle vibration and bridge stiffness.A long cable-stayed bridge which carries light rail traffic is regarded as a numerical example.Firstly,a finite element model is built for the long cable-stayed bridge.The deck can generally be idealized as three-dimensional spine beam while cables are modeled as truss elements.Vehicles are modeled as mass-spring-damper systems.Rail irregularities and wind fluctuation are simulated in time domain by spectrum representation method.Then,aerodynamic loads on vehicle and bridge deck are measured by section model wind tunnel tests.Eight vertical and torsional flutter derivatives of bridge deck are identified by weighting ensemble least-square method.Finally,dynamic responses of the WVB system are analyzed in a series of cases.The results show that the accelerations of the vehicle are excited by the fluctuating wind and the track irregularity to a great extent.The transverse forces of wheel axles mainly depend on the track irregularity.The displacements of the bridge are predominantly determined by the mean wind and restricted by its stiffness.And the accelerations of the bridge are enlarged after adding the fluctuating wind.

Semi-active control of a cable-stayed bridge under multiple-support excitations

This paper presents a semi-active strategy for seismic protection of a benchmark cable-stayed bridge with consideration of multiple-support excitations. In this control strategy, Magnetorheological (MR) dampers are proposed as control devices, a LQG-clipped-optimal control algorithm is employed. An active control strategy, shown in previous researches to perform well at controlling the benchmark bridge when uniform earthquake motion was assumed, is also used in this study to control this benchmark bridge with consideration of multiple-support excitations. The performance of active control system is compared to that of the presented semi-active control strategy. Because the MR fluid damper is a con-trollable 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. The numerical results demonstrated that the performance of the presented control design is nearly the same as that of the active control system; and that the MR dampers can effectively be used to control seismically excited cable-stayed bridges with multiple-support excitations.

Numerical simulation of dynamic characteristics of a cable-stayed aqueduct bridge

In this paper, a full-scale 3-D finite element model of the Jundushan cable-stayed aqueduct bridge is established with ANSYS Code. The shell, fluid, tension-only spar and beam elements are used for modeling the aqueduct deck, filled water, cables and support towers, respectively. A multi-element cable formulation is introduced to simulate the cable vibration. The dry （without water） and wet （with water） modes of the aqueduct bridge are both extracted and investigated in detail. The dry modes of the aqueduct bridge are basically similar to those of highway cable-stayed bridges. A dry mode may correspond to two types of wet modes, which are called the in-phase （with lower frequency） and out-of-phase （with higher frequency） modes. When the water-structure system vibrates in the in-phase/out-of-phase modes, the aqueduct deck moves and water sloshes in the same/opposite phase-angle, and the sloshing water may take different surface-wave modes. The wet modes of the system reflect the properties of interaction among the deck, towers, cables and water. The in-phase wet frequency generally decreases as the water depth increases, and the out-of-phase wet frequency may increase or decrease as the water depth increases.

Ground motion spatial variability effects on seismic response control of cable-stayed bridges

The spatial variability of input ground motion at supporting foundations plays a key role in the structural response of cable-stayed bridges （CSBs）; therefore, spatial variation effects should be included in the analysis and design of effective vibration control systems. The control of CSBs represents a challenging and unique problem, with many complexities in modeling, control design and implementation, since the control system should be designed not only to mitigate the dynamic component of the structural response but also to counteract the effects of the pseudo-static component of the response. The spatial variability effects on the feasibility and efficiency of seismic control systems for the vibration control of CSBs are investigated in this paper. The assumption of uniform earthquake motion along the entire bridge may result in quantitative and qualitative differences in seismic response as compared with those produced by uniform motion at all supports. A systematic comparison of passive and active system performance in reducing the structural responses is performed, focusing on the effect of the spatially varying earthquake ground motion on the seismic response of a benchmark CSB model with different control strategies, and demonstrates the importance of accounting for the spatial variability of excitations.

Optimization of Dead Load State in Earth-Anchored Cable-Stayed Bridges

In order to determine the reasonable completed dead load state in earth-anchored cable-stayed bridges,a practical method is proposed. The method is based on the rigidly supported continuous beam method and the feasible zone method,emphasizing on the mutual effect between the self-anchored structural parts and the earth-anchored ones. Three cable-stayed bridge models are designed with the main spans of 1 400 m,including a partially earth-anchored cable-stayed bridge,a cable-stayed-suspension bridge and a fully selfanchored cable-stayed bridge,in which the C50 concrete and Q345 steel are adopted. The partially earthanchored cable-stayed bridge and the cable-stayed-suspension bridge secure lower compressive force in the girder than the fully self-anchored cable-stayed bridge by 25 percent at least. The same is for the material consumption of the whole bridge. Furthermore,the anchor volume is more than 20% lower in the partially earthanchored cable-stayed bridge than that in the cable-stayed-suspension bridge. Consequently,the practical span of cable-stayed bridges can be accordingly extended.

Comparative Study on Structural Redundancy of Cable-Stayed and Extradosed Bridges Through Safety Assessment of Their Stay Cables

This study provides new insights into the comparison of cable-stayed and extradosed bridges based on the safety assessment of their stay cables.These bridges are often regarded as identical structures owing to the use of inclined cables;however,the international standards for bridge design stipulate different safety factors for stay cables of both types of bridges.To address this misconception,a comparative study was carried out on the safety factors of stay cables under fatigue and ultimate limit states by considering the effects of various untoward and damaging factors,such as overloading,cable loss,and corrosion.The primary goal of this study is to describe the structural disparities between both types of bridges and evaluate their structural redundancies by employing deterministic and nondeterministic methods.To achieve this goal,three-dimensional finite-element models of both bridges were developed based on the current design guidelines for stay cables in Japan.After the balanced states of the bridge models were achieved,static analyses were performed for different safety factors of stay cables in a parametric manner.Finally,the first-order reliability method and Monte Carlo method were applied to determine the reliability index of stay cables.The analysis results show that cable-stayed and extradosed bridges exhibit different structural redundancies for different safety factors under the same loading conditions.Moreover,a significant increase in structural redundancy occurs with an incremental increase in the safety factors of stay cables.

Dynamic effect of heavy-haul train on seismic response of railway cable-stayed bridge

This paper focuses on understanding and evaluating the dynamic effect of the heavy-haul train system on the seismic performance of a long-span railway bridge. A systematic study on the effect of heavy-haul trains on bridge seismic response has been conducted, considering the influence of vehicle modeling strategies and dynamic characteristics of the seismic waves. For this purpose, the performance of a long-span cable-stayed railway bridge is assessed with stationary trains atop it, where the heavy-haul vehicles are modeled in two different ways: the multi-rigid body model with suspension system and additional mass model. Comparison of the bridge response in the presence or absence of the train system has been conducted, and the vehicle loading situation, which includes full-load and no-load, is also discussed. The result shows that during the earthquake, the peak moment of the main girder and peak stress of stay cables increase by 80% and by 40% in the presence of fully loaded heavy-haul trains, respectively. At the same time, a considerable decrease appears in the peak acceleration of the main girder. This proves the existence of the damping effect of the heavy-haul train system, and this effect is more obvious for the fully loaded vehicles. Finally, this paper proposes an efficient vehicle modeling method with 2 degrees of freedom(DOF) for simplifying the treatment of the train system in bridge seismic checking.

Infl uence of structural parameters on dynamic characteristics and wind-induced buffeting responses of a super-long-span cable-stayed bridge

A 3D finite element （FE） model for the Sutong cable-stayed bridge （SCB） is established based on ANSYS. The dynamic characteristics of the bridge are analyzed using a subspace iteration method. Based on recorded wind data, the measured spectra expression is presented using the nonlinear least-squares regression method. Turbulent winds at the bridge site are simulated based on the spectral representation method and the FFT technique. The influence of some key structural parameters and measures on the dynamic characteristics of the bridge are investigated. These parameters include dead load intensity, as well as vertical, lateral and torsional stiffness of the steel box girder. In addition, the influence of elastic stiffness of the connection device employed between the towers and the girder on the vibration mode of the steel box girder is investigated. The analysis shows that all of the vertical, lateral and torsional buffeting displacement responses reduce gradually as the dead load intensity increases. The dynamic characteristics and the structural buffeting displacement response of the SCB are only slightly affected by the vertical and torsional stiffness of the steel box girder, and the lateral and torsional buffeting displacement responses reduce gradually as the lateral stiffness increases. These results provide a reference for dynamic analysis and design of super-long-span cable-stayed bridges.

Dynamic performance of cable-stayed bridge tower with multi-stage pendulum mass damper under wind excitations——I:Theory

In this paper, wind-induced vibration control of a single column tower of a cable-stayed bridge with a multi- stage pendulum mass damper （MSPMD） is investigated. Special attention is given to overcoming space limitations for installing the control device in the tower and the effect of varying natural frequency of the towers during construction. First, the finite element model of the bridge during its construction and the basic equation of motion of the MSPMD are introduced. The equation of motion of the bridge with the MSPMD under along-wind excitation is then established. Finally, a numerical simulation and parametric study are conducted to assess the effectiveness of the control system for reducing the wind-induced vibration of the bridge towers during construction. The numerical simulation results show that the MSPMD is practical and effective for reducing the along-wind response of the single column tower, can be installed in a small area of the tower, and complies with the time-variant characteristics of the bridge during its entire construction stage.

Numerical calculation on solar temperature field of a cable-stayed bridge with U-shaped section on high-speed railway

Based on transient temperature field theory of heat conduction, the solar temperature field calculation model of U-shape sectioned high-speed railway cable-stayed bridge under actions of concrete beams and ballast was established. Using parametric programming language, finite element calculation modules considering climate conditions, bridge site, structure dimension and material thermophysical properties were compiled. Six standard day cycles with the strongest yearly radiation among the bridge sites were selected for sectional solar temperature field calculation and temperature distributions under different temperature-sensitive parameters were compared. The results show that under the influence of sunshine, U-shape section of the beam shows obvious nonlinear distribution characteristics and the maximum cross-section temperature difference is more than 21℃; the ballast significantly reduces sunshine temperature difference of the beam and temperature peak of the bottom margin lags with the increase of ballast thickness; the maximum cross-section vertical temperature gradient appears in summer while large transverse temperature difference appears in winter.

Dynamic analysis and modal test of long-span cable-stayed bridge based on ambient excitation

To study the stiffness distribution of girder and the method to identify modal parameters of cable-stayed bridge, a simplified dynamical finite element method model named three beams model was established for the girder with double ribs. Based on the simplified model four stiffness formulae were deduced according to Hamilton principle. These formulae reflect well the contribution of the flexural, shearing, free torsion and restricted torsion deformation, respectively. An identification method about modal parameters was put forward by combining method of peak value and power spectral density according to modal test under ambient excitation. The dynamic finite element method analysis and modal test were carried out in a long-span concrete cable-stayed bridge. The results show that the errors of frequencies between theoretical analysis and test results are less than 10% mostly, and the most important modal parameters for cable-stayed bridge are determined to be the longitudinal floating mode, the first vertical flexural mode and the first torsional mode, which demonstrate that the method of stiffness distribution for three beams model is accurate and method to identify modal parameters is effective under ambient excitation modal test.

Analysis on Deflection Characteristics of Steel Cable-Stayed Bridge

Various kinds of deflection characteristics on the steel cable-stayed bridge(Nanjing No.3 Yangtze River Bridge)are investigated by different mathematical statistical methods.Firstly,via Pearson correlation coefficient calculation,it shows good consistency between the adjacent measuring point of side span or middle span.Secondly,taking mid-span deflection as an example,the correlation analysis of deflection and temperature is conducted.They are synchronous via cross correlation coefficient calculation but not completely linear and a"hysteresis loop"phenomenon of three stages is formed.The fitting result on the monitoring data at day time is consistent with the numerical value through the application of unit temperature difference between the cable and girder and the positive temperature gradient of girder in the finite element model.And the temperature effect is considerable.Vehicle loads effect is obtained from wavelet analysis.The extracted curve can indirectly reflect the change of traffic loads.Finally,the structural damage is analyzed through the trend fusion on the deflection,cable force and visual inspection from 2006 to 2015.Relevant conclusions can provide a basis for management departments to carry out special detection.

A simplified design method for metallic dampers used in the transverse direction of cable-stayed bridges

The aseismic design of cable-stayed bridges in the transverse direction with newly proposed metallic dampers that can accommodate both longitudinal and transverse movement of the deck has recently been considered.This work focuses on developing a simplified method to design an appropriate metallic damper.The seismic performance of cablestayed bridges with different damper stiffness,main span lengths,tower shapes and types of deck in the transverse direction are investigated.The transverse displacement of the deck of a cable-stayed bridge increases significantly with the increment of the damper stiffness,which proves that the design of the damper stiffness is crucial.A simplified model considering the damper stiffness,cable system and tower in the transverse direction is developed to evaluate the period and lateral displacement of a complicated cable-stayed bridge.Based on the simplified model,a design method is proposed and assessed using two cable-stayed bridges as examples.The results show that metallic dampers can be designed with high efficiency,and the optimal ductility of the damper can be selected.