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.

NONLINEAR TRANSIENT RESPONSE OF STAY CABLE WITH VISCOELASTICITY DAMPER IN CABLE-STAYED BRIDGE

Taking the bending stiffness, static sag, and geometric non-linearity into consideration, the space nonlinear vibration partial differential equations were derived. The partical differential equations were discretized in space by finite center difference approximation, then the nonlinear ordinal differential equations were obtained. A hybrid method involving the combination of the Newmark method and the pseudo-force strategy was proposed to analyze the nonlinear transient response of the inclined cable-dampers system subjected to arbitrary dynamic loading. As an example, two typical stay cables were calculated by the present method. The results reveal both the validity and the deficiency of the viscoelasticity damper for vibration control of stay cables. The efficiency and accuracy of the proposed method is also verified by comparing the results with those obtained by using Runge-Kutta direct integration technique. A new time history analysis method is provided for the research on the stay cable vibration control.

Hardware-in-the-Loop Simulation of Vibration Control of Stay Cables with Damper Based on dSPACE System

A simple and economical method based on dSPACE system is developed to measure the effect of cable vibration control.The experiments,numerical simulation and hardware-in-the-loop(HIL)simulation are carried out for the vibration control of stay cables with dampers.Firstly,the test results of solid cable vibration under harmonic excitation are compared with the numerical simulation results of cable vibration to ensure the correctness of the simulation of cable module.Then,the vibration test results of solid cable with damper under harmonic excitation are compared with the numerical simulation results of solid cable with damper to ensure the correctness of the relevant modules.Finally,the external load and the cable are imported into the real-time simulation system to simulate the control effect of the damper under the current excitation in real time.The results show that the simulation is correct and the HIL simulation is feasible in the bridge engineering.

Rain-Wind Induced Vibration Mitigation of Stay Cables by Aerodynamic Means

Stay cables with various surface profiles were tested in wind tunnel. Dimples and helical fillets were applied to mitigate the rain- wind induced vibration. The rain-wind excited responses of the cable with smooth surface were larger than those of the cables with dimples and helical fillets. At high Reynolds number, the drag coefficients of cables with dimples and helical fillets are much larger than those of smooth surface cable.

Study on Vibration Characteristics of Stay Cable-Nonlinear Viscous Damper System

Tension cables are easily prone to generating varied vibrations under the action of external loads, which adversely affects the safety of bridges. Therefore, it is necessary to take effective measures to suppress the vibrations of tension cables. Cable end dampers are widely used in vibration reduction for cable-stayed bridges due to their convenient installation and low costs. However, the previous studies on the tension cable-viscous damper systems mostly adopt the linear method, and the weakening effect of the flexibility of mounting brackets on the damper vibration reduction is not sufficiently taken into account. Therefore, this paper adopts the improved Kelvin model to conduct the derivation, solution, and parametric analysis of vibration equations for the stay cable-nonlinear viscous damper systems. The results of parametric analysis show that the maximum modal damping ratio that can be obtained by cables and the corresponding optimal damping coefficient of dampers are correlated with the damping nonlinear coefficient α, stiffness nonlinear coefficient β, vibration order n, installation position a/L, and stiffness coefficient μ, etc.;among them, n damping nonlinear coefficient α and stiffness nonlinear coefficient β are the key parameters that affect the parameter design of dampers, where damping nonlinear coefficient α mainly controls the optimal damping coefficient and stiffness nonlinear coefficient β mainly controls the maximum damping ratio. Based on the parametric analysis, the design principles of dampers and value requirements of key parameters under different vibration suppression objectives are presented.

A videogrammetric technique for measuring the vibration displacement of stay cables

Stay cables in cable-stayed bridges are prone to large amplitude oscillations under external excitations.The vibration of the cables is predominantly measured by using accelerometers to measure the acceleration.The dynamic displacement is then usually obtained indirectly from the double integration of the acceleration data.This paper reports an experimental method of measuring the displacement of stayed cables using a digital video camera.With the newly developed videogrammetric technique,the video clips are transferred into image frames,from which the shape and location of the target are identified.The displacement time history is then captured.The technique is applied to a cable-stayed bridge to measure the dynamic displacement of stay cables.The displacement is compared with the acceleration data in the frequency and time domains.The results show that the displacement measured by the digital video camera is comparable to the counterparts integrated from the acceleration data.The vibration frequencies identified from the acceleration are finally used to estimate the tension forces of the cables.The results show that the tension forces have insignificant changes after one year’s operation.

Vortex-induced vibration of stay cable under profile velocity using CFD numerical simulation method

Vortex-induced vibration(VIV)of a stay cablesubjected to a wind profile is numerically simulatedthrough combining computational fluid dynamics(CFD)code CFX 10.0 and computational structural dynamics(CSD)code ANSYS 10.0.A stay cable with the inclinedangle of 30°is used as the numerical model.Under aprofile of mean wind speed,unsteady aerodynamic liftcoefficients of the cable have been analyzed in both timedomain and frequency domain when VIV occurs.Theresults indicate that the lift coefficient wave response of thestay cable under a wind profile is different from that of aninfinitely long cable under a uniform flow in water(i.e.,without consideration of profile)obtained by directnumerical simulation.Cable oscillations can severelyaffect the unsteady aerodynamic frequencies,changeflow field distribution near the cable and affect the vortexshedding in the wake.

A simplified fragility analysis of fan type cable stayed bridges

A simplified fragility analysis of fan type cable stayed bridges usingProbabilistic Risk Analysis (PRA) procedure is presented for determining their failure probabilityunder random ground motion. Seismic input to the bridge support is considered to be a riskconsistent response spectrum which is obtained from a separate analysis. For the response analysis,the bridge deck is modeled as a beam supported on springs at different points. The stiffnesses ofthe springs are determined by a separate 2D static analysis of cable-tower-deck system. The analysisprovides a coupled stiffness matrix for the spring system. A continuum method of analysis usingdynamic stiffness is Used to determine the dynamic properties of the bridges .The response of thebridge deck is obtained by the response spectrum method of analysis as applied to multi-degree offreedom system which duly takes into account the quasi - static component of bridge deck vibration.The fragility analysis includes uncertainties arising due to the variation in ground motion,material property, modeling, method of analysis, ductility factor and damage concentration effect.Probability of failure of the bridge deck is determined by the First Order Second Moment (FOSM)method of reliability. A three span double plane symmetrical fan type cable stayed bridge of totalspan 689 m, is used as an illustrative example. The fragility curves for the bridge deck failure areobtained under a number of parametric variations. Some of the important conclusions of the studyindicate that (ⅰ) not only vertical component but also the horizontal component of ground motionhas considerable effect on the probability of failure; (ⅱ) ground motion with no time lag betweensupport excitations provides a smaller probability of failure as compared to ground motion with verylarge time lag between support excitation; and (ⅲ) probability of failure may considerablyincrease for soft soil condition.

Study on Fatigue Behavior of Anchorage of Cable and Girder of Long Span Cable-Stayed Bridge

A full scale model test is done and a FEM model is established to investigate the fatigue behavior of the Nancha cable stayed bridge of the Nanjing Second Yangtz River Bridge, a long span steel bridge with a main span of 628 m. The results of test and FEM are analyzed and compared. It is shown that they are in good agreement. It is verified that the fatigue characteristic of the anchorage structure of cable and girder of the bridge satisfies the requirements specified by Chinese, British and American codes.

Stochastic optimal control of cable vibration in plane by using axial support motion

A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is proposed. The nonlinear equation of cable motion in plane is derived and reduced to the equations for the first two modes of cable vibration by using the Galerkin method. The partially averaged Ito equation for controlled system energy is further derived by applying the stochastic averaging method for quasi-non-integrable Hamiltonian systems. The dynamical programming equation for the controlled system energy with a performance index is established by applying the stochastic dynamical programming principle and a stochastic optimal control law is obtained through solving the dynamical programming equation. A bilinear controller by using the direct method of Lyapunov is introduced. The comparison between the two controllers shows that the proposed stochastic optimal control strategy is superior to the bilinear control strategy in terms of higher control effectiveness and efficiency.

Key Technologies for Design of Changqing Yellow River Super-long Bridge of Zhengzhou Ji'nan HSR

Changqing Yellow River Super-long Bridge of Zhengzhou-Ji'nan HSR is a partial cable-stayed bridge with concrete main girder and a unit length of 1,080 m.Studies are carried out on the key technologies of bridge design,and the main conclusions are as follows:The whole unit adopts the supporting system of tower pier consolidation and tower-beam separation,and each pier is provided with seismic mitigation and isolation bearing;shaped-steel reinforced concrete bridge tower is adopted to bring into full play the tensile performance of steel and the compressive performance of concrete,and avoid the construction challenges of setting up multi-layer and multi-stirrup reinforcement while improving the bearing capacity of section;a new type of double-side and bi-directional anti-skid anchorage device is adopted for the cable saddle of wire divider pipe in order to withstand the unbalanced cable force,and verify the reliability of the anti-skid anchorage device by solid model test;and large-segment cantilever pouring design is adopted for the main girder with a maximum segment length of 8 m to effectively shorten the construction period of the bridge.

Vehicle-bridge coupled vibrations in different types of cable stayed bridges

Numerical analyses of the coupled vibrations of vehicle-bridge system and the effects of different types of cable stayed bridges on the coupled vibration responses have been presented in this paper using ANSYS. The bridge model and vehicle model were independently built which have no internal relationship in the ANSYS. The vehicle-bridge coupled vibration relationship was obtained by using the APDL program which subsequently imposed on the vehicle and bridge models during the numerical analysis. The proposed model was validated through a field measurements and literature data. The judging method, possibility, and criterion of the vehicle-bridge resonance （coupled vibrations） of cable stayed bridges （both the floating system and half floating system） under traffic flows were presented. The results indicated that the interval time between vehicles is the main influence factor on the resonance excitation frequency under the condition of equally spaced traffic flows. Compared to other types of cable stayed bridges, the floating bridge system has relatively high possibility to cause vehicle-bridge resonance.

Millau viaduct geotechnical studies and foundations

The Millau viaduct over the Tam River is an exceptional bridge considering the height under the deck and the 2.5 km total length. Each of the seven high piers is founded on a thick raft setting on four large piles of 5 m in diameter and 10-15 m deep. The ground schematically consists of limestone in the north and of marls in the south. As the bridge is very sensitive to foundation settlements, the concessionary company decided to use the observational method for controlling the displacements and if necessary stabilize the foundations. The measurements show that the movements have remained small and admissible, particularly in terms of the rotations. The settlements have not occurred continuously under the load, but by steps.