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.

Parametrically excited oscillation of stay cable and its control in cable-stayed bridges＂

This paper presents a nonlinear dynamic model for simulation and analysis of a kind of parametrically excited vibration of stay cable caused by support motion in cable-stayed bridges. The sag, inclination angle of the stay cable are considered in the model, based on which, the oscillation mechanism and dynamic response characteristics of this kind of vibration are analyzed through numerical calculation. It is noted that parametrically excited oscillation of a stay cable with certain sag, inclination angle and initial static tension force may occur in cable-stayed bridges due to deck vibration under the condition that the natural frequency of a cable approaches to about half of the first model frequency of the bridge deck system. A new vibration control system installed on the cable anchorage is proposed as a possible damping system to suppress the cable parametric oscillation. The numerical calculation results showed that with the use of this damping system, the cable oscillation due to the vibration of the deck and/or towers will be considerably reduced.

Nonlinear dynamic response of stay cables under axial harmonic excitation

This paper proposes a new numerical simulation method for analyzing the parametric vibration of stay cables based on the theory of nonlinear dynamic response of structures under the asynchronous support excitation. The effects of important pa- rameters related to parametric vibration of cables, i.e., characteristics of structure, excitation frequency, excitation amplitude, damping effect of the air and the viscous damping coefficient of the cables, were investigated by using the proposed method for the cables with significant length difference as examples. The analysis results show that nonlinear finite element method is a powerful technique in analyzing the parametric vibration of cables, the behavior of parametric vibration of the two cables with different Irvine parameters has similar properties, the amplitudes of parametric vibration of cables are related to the frequency and amplitude of harmonic support excitations and the effect of distributed viscous damping on parametric vibration of the cables is very small.

Anomaly Detection Algorithm for Stay Cable Monitoring Data Based on Data Fusion

In order to improve the accuracy and consistency of data in health monitoring system,an anomaly detection algorithm for stay cables based on data fusion is proposed.The monitoring data of Nanjing No.3 Yangtze River Bridge is used as the basis of study.Firstly,an adaptive processing framework with feedback control is established based on the concept of data fusion.The data processing contains four steps:data specification,data cleaning,data conversion and data fusion.Data processing information offers feedback to the original data system,which further gives guidance for the sensor maintenance or replacement.Subsequently,the algorithm steps based on the continuous data distortion is investigated,which integrates the inspection data and the distribution test method.Finally,a group of cable force data is utilized as an example to verify the established framework and algorithm.Experimental results show that the proposed algorithm can achieve high detection accuracy,providing a valuable reference for other monitoring data processing.

Dynamic Characteristics Evaluation of Innovative UHPC Pedestrian Cable Stayed Bridge

KICT (Korea Institute of Construction Technology) is conducting a project called “SUPER BRIDGE 200—Development of Low Cost and Long Life Hybrid Cable Stayed Bridge”. This project aims to reduce the construction and main- tenance costs of long-span bridges by 20% and double their lifetime through the exploitation of ultra-high performance concrete (UHPC). This paper presents the design and construction of the first pedestrian cable stayed bridge using UHPC developed by KICT. UHPC, compared to conventional concrete, has not only high compressive and tensile strengths but also high ductility. The UHPC developed at KICT is a steel fiber-reinforced cement compound presenting design compressive strength larger than 180 MPa and design tensile strength exceeding 10 MPa with water-to-binder ratio below 0.24 and admixing of 2 volume percentage of steel fiber. To show the applicability of UHPC to structures, a pedestrian cable stayed bridge (Super Bridge I) exploiting the characteristics of the developed UHPC has been planned, designed and erected at KICT. The dimension of UHPC deck is 2.7 m × 7 m as a precast segment with a typical thickness of deck of only 7 cm. However, harmful crack was observed in the deck at the time of the fabrication of the deck segments. Accordingly, new fabrication method was conceived and applied to prevent cracking of the UHPC slender deck. Four UHPC deck segments were fabricated successfully without any crack. After construction, the dynamic characteristics (natural frequencies and mode shapes) were evaluated through vibration tests since several users felt excess vibration. A vertical tuned mass damper (TMD) was proposed and installed on the parapet of the bridge. The TMD reduces the acceleration by about 30% from 0.0316 g to 0.0244 g when two pedestrians are crossing the bridge.

Study on longitudinal wind load calculation method of cables for cable-stayed bridge

Along with the expanding of span of cable-stayed bridge,wind load becomes a more and more important controlling factor for bridge the design.A very large proportion of the wind load acting on cables has exceeded that acting on deck.There was not any detailed prescript in Chinese code for calculation of longitudinal wind load on cables due to lack of theoretical research and experiment,and conservative simplified calculation was adopted during design,which leads to conservative and uneconomical design of structures.To resolve this problem,cable force experiment was carried out during the design of Sutong Bridge.By comparing with international research results,the calculation formula of longitudinal wind drag coefficient for cables was advanced to fill the blank of bridge wind resistant code of China,and has already been adopted in the Highway Bridge Wind Resistant Design Code(JTG/T D60-01-2004)with great significance for bridge engineering.

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.

Calculation model and mechanism analysis for rain-wind-induced vibration of stay cable

Rain-wind-induced vibration of cable was studied based on previous research achievements. According to the quasi-steady assumption, the governing equation of vertical motion of the cable was derived and the criterion for unstable motion and occurrence mechanism was studied. A comparison was performed between the oscillation responses of the stay cable obtained from calculated model and previous results. The results indicate that the analysis model can reflect the main characteristics of wind-rain-induced vibrationt of the cable which is amplitude- and velocity-restricted, and it is probably related with the periodic vortex shedding of wake flow. It is essential for the occurrence of rain-wind-induced or wind-induced vibration of cable that the derivative of lift coefficient with respect to transient angle of attack is less than zero. When rain-wind-induced vibration occurs, the aerodynamic force has a dual function for the vibration, and the maximum amplitude of stayed-cable is determined by the relative value of aerodynamic exciting force and aerodynamic damping force.

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.

Genetic Algorithms-based Optimization of Cable Stayed Bridges

Optimum design of cable stayed bridges depends on number of parameters. Design of Cable stayed bridge satisfying all practical constraints is challenging to the designers. Considering the huge number of design variables and practical constraints, Genetic Algorithms (GA) is most suitable for optimizing the cable stayed bridge. In the present work the optimum design is carried out by taking total material cost of bridge as objective function. During problem formulation most of the practical design variables and constraints are considered. Using genetic algorithms some parametric studies such as effect of geometric nonlinearity, effect of grouping of cables, effect of practical site constraints on tower height and side span, effect of bridge material, effect of cable layout, effect of extra-dosed bridges on optimum relative cost have been presented. Data base is prepared for new designers to estimate the relative cost of bridge.

Rolling Fatigue Test of Large-Sized UHPC Member for Cable Stayed Bridge

Recently, research strives to apply Ultra High Performance Concrete (UHPC) to large-sized structures owing to its remarkable mechanical performance and durability compared to normal concrete. The Korea Institute of Construction Technology proposed SuperBridge800, an edge girder type UHPC cable stayed bridge with central span of 800 m, through its detailed design. The bridge is designed to be erected through the connection of precast UHPC segments. The precast UHPC segment is monolithically composed of one ribbed deck slab and edge girders at each side. The connection between the precast segments is achieved by steel bars at the edge girders and by UHPC cast-in-place wet joint at the slab. Despite of the outstanding mechanical performance of UHPC, the fabrication of large-sized members is a difficult task since UHPC hardens faster than normal concrete and requires a special curing process. Therefore, the constructability of large-sized UHPC segment should be secured to achieve SuperBridge800. Besides, the performance of the connection between segments should also be guaranteed, especially in terms of the fatigue performance of the UHPC cast-in-place joint, which constitutes a weak point. To that goal, two half-scaled UHPC segments are manufactured and the constructability is examined by fabricating a large-sized UHPC member connected with respect to the design conditions. This study conducts rolling fatigue test on the so-fabricated large-sized UHPC member. Rolling fatigue test is carried out up to 2 million cycles considering actual vehicle load at each center and quarter points of the member. The test results confirm that the service limit state is satisfied.

Nonlinear Dynamic Reliability of Coupled Stay Cables and Bridge Tower

Nonlinear vibration can cause serious problems in long span cable-stayed bridges.When the internal resonance threshold is reached between the excitation frequency and natural frequency,large amplitudes occur in the cable.Based on the current situation of lacking corresponding constraint criteria,a model was presented for analyzing the dynamic reliability of coupling oscillation between the cable and tower in a cable-stayed bridge.First of all,in the case of cable sag,the d'Alembert principle is applied to studying the nonlinear dynamic behavior of the structure,and resonance failure interval of parametric oscillation is calculated accordingly.Then the dynamic reliability model is set up using the JC method.An application of this model has been developed for the preliminary design of one cable-stayed bridge located on Hai River in Tianjin,and time histories analysis as well as reliability indexes have been obtained.When frequency ratio between the cable and tower is approaching 1∶2,the reliability index is 0.98,indicating high failure probability.And this is consistent with theoretical derivation and experimental results in reference.This model,which is capable of computing the reliability index of resonance failure,provides theoretical basis for the establishment of corresponding rule.

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.

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.

Closure technique for the hybrid girder cable stayed bridge of Edong Bridge

Based on Edong Yangtze River Bridge, which is the second longest hybrid girder cable stayed bridge with 926 m long main span, the influencing factors and crucial techniques of the main span closure method for long span hybrid girder cable stayed bridge are studied. After theoretical analysis, numerical evaluation and practical test, the loading assistant closure method is employed in Edong Yangtze River Bridge. The loading assistant closure method, with better thermal adaptability and less influence on bridge line and the forced status, can meet the requirements of the unstressed state control method. Based on the mentioned advantages, the loading assistant closure method is applicable to long span hybrid girder cable stayed bridges. The conclusion can provide a reference for the further design of the similar brid^es.

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.

Wind-Tunnel Investigation of the Aerodynamic Performance of Surface-Modification Cables

The wind-induced vibration of stay cables of cable-stayed bridges, which includes rain-wind-induced vibration （RWIV） and dry galloping （DG）, has been studied for a considerable amount of time. In general, mechanical dampers or surface modification are applied to suppress the vibration. In particular, several types of surface-modification cable, including indentation, longitudinally parallel protuberance, helical fillet, and U-shaped grooving, have been developed. Recently, a new type of aerodynamically stable cable with spiral protuberances was developed. It was confirmed that the cable has a low drag force coefficient, like an indented cable, and that it prevented the formation of water rivulets on the cable surface. In this study, the stability for RWIV of this cable was investigated with various flow angles and protuberance dimensions in a wind-tunnel test. It was found that the spiral protuberance cable is aerodynamically stable against both RWIV and DG for all test wind angles. The effects of the protuberance dimensions were also clarified.

Modeling and Experiments of Spray System for Cable Painting Robot

Many cable-stayed bridges have been built in the world in the past decades,and cable-stayed structures have been adopted in many large constructions.The cable painting robot is safe and economically efficient for stay cable maintenance.In order to satisfy the need for spraying cables in high attitude,an automatic cable spray system for cable painting robots is presented in this paper.Using the β distribution,paint thickness distribution on a cylinder surface is modeled.The spray gun's number,angle and movement are analyzed to get coat evenness.Then a robotic spray system engineering prototype has been developed,which includes a cable electric running climbing base,a spray cover,four airless spray guns and a pressurized paint container.Experiments indicate that four airless spray guns can guarantee good coat quality for general stay cables.The field tests have been successfully conducted on Nanpu Bridge,Shanghai.

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.