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Title: Fatigue and reliability analyses of multiload suspension bridges with WASHMS
Authors: Chen, Zhiwei
Degree: Ph.D.
Issue Date: 2010
Abstract: Many long-span suspension bridges throughout the world are subject to very complicated loading, especially those that are located in wind-prone regions and that carry both trains and road vehicles. Given the multiple types of loading concerned and the complexity of the loading combinations, the fatigue analysis of long-span suspension bridges under railway, highway, and wind loading is a great challenge. To ensure the safety of such bridges and their users during their service life, several long-span bridges have been equipped with Wind and Structural Health Monitoring Systems (WASHMS), which measure the dynamic bridge responses and various loading types at the bridge site. The measured information provides an opportunity to carry out an accurate fatigue analysis of such bridges. This thesis focuses on the fatigue and reliability analyses of multiload suspension bridges by making use of the information provided by WASHMS. To undertake the fatigue analysis of multiload suspension bridges, a dynamic stress analysis of the bridge under multiple types of loading must first be conducted. In this thesis, a comprehensive framework is proposed for this analysis. In the framework, a complex finite element (FE) model of a suspension bridge is used for the stress analysis of the local bridge components, and the railway and road vehicles are also modeled using the FE method. The mode superposition method is adopted to make the dynamic stress analysis manageable. The connections between the bridge and trains and between the bridge and road vehicles are considered. All of the damping forces and nonlinear restoring forces of the suspension units are treated as pseudo forces in the train and road vehicle subsystems. The spatial distributions of both the buffeting forces and the self-excited forces over the bridge deck surface are considered in the dynamic stress analysis. The aerodynamic wind forces acting on the car body of a train or road vehicle are determined using a quasi-steady approach. A stepwise explicit integration method is adopted to find numerical solutions to the equations of motion of the wind-vehicle-bridge system. A set of computer programs coded in Fortran language and integrated with commercial FE software is developed to implement the functions of the dynamic stress analysis of a multiload suspension bridge. The computational accuracy of the proposed framework must be validated before it can be applied in fatigue assessment. The data measured by the WASHMS installed on the Tsing Ma suspension bridge provide an excellent validation opportunity. The main features of the bridge and its WASHMS are first introduced. The significant features of the FE model of the bridge are then outlined. To validate each step of the framework, three particular load cases are examined: under strong wind only, under strong wind and running trains, and under strong wind, running trains, and running road vehicles. The collection and pre-processing of the measurement data for the wind, trains, and road vehicles and the strain responses are presented, and selected data corresponding to the three load cases are analyzed to extract the most useful information. Finally, comparisons between the computed and measured dynamic stress responses are made for each load case in terms of time histories and amplitude spectra. The results indicate that to a certain extent, the proposed framework can accurately predict the dynamic stress responses of the local components of a suspension bridge under railway, highway, and wind loading. In addition to computational accuracy, computational efficiency is very important in calculating the dynamic stress responses of suspension bridges, because a great number of stress computations are required in fatigue analysis. It is thus necessary to develop an efficient engineering approach based on the framework mentioned above. Two major assumptions are adopted to simplify the coupled dynamic stress analysis approach for a suspension bridge subject to railway, highway, and wind loading. Trains and road vehicles are simplified as moving loads, and the stress responses induced by trains and road vehicles are calculated based on the stress influence lines. The stress responses induced by wind are computed based on the estimated buffeting and self-excited forces on the bridge deck. The three stress responses to the individual loading types are then superposed to obtain the combined response to multiple loading. The Tsing Ma Bridge is employed to verify the feasibility of the proposed method. The computational accuracy of the proposed method is validated by comparing the stress responses computed by the engineering approach and the coupled dynamic approach. The computational accuracy and efficiency of the proposed approach are further verified by comparing the computed daily stress time histories and the corresponding measured data. The results demonstrate that for a long suspension bridge carrying both railway and highway loading, the engineering approach has a high level of computational efficiency and an acceptable level of computational accuracy.
The deterministic approach based on the Miner's rule is widely applied in the fatigue analysis of bridge structures. Here, a general computational procedure based on this rule is proposed for the fatigue analysis of a multiload suspension bridge over its design life. The procedure is then applied to the Tsing Ma Bridge. The fatigue-critical locations for the fatigue analysis are first determined from the key bridge components. Databases of the dynamic stress responses at the critical locations induced by wind, railway, and highway loading are then established. 120 years of time histories of the dynamic stresses induced by railway, highway, and wind loading are generated based on the databases, and the multiple load-induced stress time histories are compiled. Finally, fatigue analysis of the time histories is performed to compute the cumulative fatigue damage over the bridge's design life. The cumulative fatigue damage induced by the three individual loading types and the damage magnification due to the multiple types of loading combined are also studied. The results indicate that it is necessary to consider the combined effect of loads in the fatigue analysis of multiload suspension bridges. Deterministic fatigue analysis is unable to consider the effects of uncertainties arising from load and structural properties, and thus a new framework for fatigue reliability analysis is proposed and applied to the Tsing Ma Bridge. A limit state function is defined to describe the relationship between the fatigue resistance and the fatigue loading. Based on loading data acquired from the WASHMS on the bridge, probabilistic models of railway, highway, and wind loading are established to describe the uncertainties inherent in the different loads. Using the probabilistic loading models, the dominant loading parameters are then generated using Monte Carlo Simulation (MCS), and the daily stochastic stress responses induced by the railway, highway, and wind loading are simulated at the fatigue-critical locations using FE stress analysis. The probability distribution of the daily sum of m-power stress ranges is estimated based on the daily stochastic stress responses. The probability distribution of the sum of m-power stress ranges over the period concerned is then estimated based on assumptions of future loading and traffic growth patterns. Finally, the fatigue failure probabilities for different time epochs are solved at fatigue-critical locations using the First-Order Reliability Method (FORM). The results demonstrate that the health condition of the bridge at the end of its design life will be satisfactory under current traffic conditions without growth, but that attention should be paid to future traffic growth because it may lead to a much greater failure probability. Miner's model is the most commonly used damage model as it is simple in expression, but being linear it cannot properly describe the nonlinear process of fatigue damage accumulation or take into account the loading sequence effect. The nonlinear continuum damage mechanics (CDM) model is thus applied to overcome these limitations. The basic theory and nonlinear properties of the CDM model are first introduced. To allow the model to be applied to fatigue analysis of a bridge over its design life, a simplification is adopted whereby an effective stress range and effective nonlinear accumulative parameter are employed to represent all of the stress ranges within a daily block of stress time history. This nonlinear model is then applied to compute the damage accumulation curves at fatigue-critical locations of the Tsing Ma Bridge, and the curves are compared with those estimated by the linear Miner's model. The results indicate that the damage estimated by the CDM model is much smaller than that calculated by the Miner's model at most of the fatigue-critical locations. Random variables are introduced into the nonlinear damage model, and a limit state function is defined for the reliability analysis. The MCS method is adopted to generate the random variables in this nonlinear process and to calculate the failure probability. Finally, the failure probabilities at the end of 120 years for the fatigue-critical locations are estimated using the CDM model, and compared with those estimated using the Miner's model. The results indicate that the failure probabilities estimated by the CDM model are slightly smaller than those estimated by the Miner's model for traffic growth occurring in certain typical patterns.
Subjects: Hong Kong Polytechnic University -- Dissertations
Suspension bridges -- Maintenance and repair
Bridges, Long-span -- Maintenance and repair
Pages: 1 v. (various pagings) : ill. (some col.) ; 30 cm.
Appears in Collections:Thesis

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