Z.X. Li

Finite element modelling for fatigue stress analysis of large suspension bridges

Fatigue is an important failure mode for large suspension bridges under traffic loadings. However, large suspension bridges have so many attributes that it is difficult to analyze their fatigue damage using experimental measurement methods. Numerical simulation is a feasible method of studying such fatigue damage. In British standards, the finite element method is recommended as a rigorous method for steel bridge fatigue analysis. This paper aims at developing a finite element (FE) model of a large suspension steel bridge for fatigue stress analysis. As a case study, a FE model of the Tsing Ma Bridge is presented. The verification of the model is carried out with the help of the measured bridge modal characteristics and the online data measured by the structural health monitoring system installed on the bridge. The results show that the constructed FE model is efficient for bridge dynamic analysis. Global structural analyses using the developed FE model are presented to determine the components of the nominal stress generated by railway loadings and some typical highway loadings. The critical locations in the bridge main span are also identified with the numerical results of the global FE stress analysis. Local stress analysis of a typical weld connection is carried out to obtain the hot-spot stresses in the region. These results provide a basis for evaluating fatigue damage and predicting the remaining life of the bridge.

Statistical analysis of online strain response and its application in fatigue assessment of a long-span steel bridge

This paper covers reliability assessment of the fatigue life of a bridge-deck section based on the statistical analysis of the strain-time histories measured by the structural health monitoring system permanently installed on the long-span steel bridge under study. Through statistical analysis of online strain responses in the frequency domain using multiple linear regression, a representative block of daily cycles of strain history is obtained. It is further assumed that all cycles of online strain response during bridge service are repetitions of the representative block. The rain-flow counting method is then used to determine the stress spectrum of the representative block of daily cycles. The primary assessment of fatigue life at a given value of failure probability is undertaken for the sample component in a bridge-deck section by using the classification of details for welded bridge components and the associated statistical fatigue model provided by the British Standard BS5400. In order to evaluate bridge fatigue at any value of failure probability, a modified probability model is proposed based on BS5400. The fatigue life of the considered component in the bridge-deck section is then evaluated for some other values of probability of failure which are not included in BS5400 by use of the modified probability model. The analytical results show that the modified model is practical for reliable evaluation of the service life of existing bridges under random traffic loading.

Determination of effective stress range and its application on fatigue stress assessment of existing bridges

This paper presents a unified approach on determination of the effective stress range based on equivalent law of strain energy and fatigue damage model, so as to provide an efficient approach for accurately assessing effective fatigue stress of existing bridge under traffic loading. A new theoretical framework to relate variable- and constant-amplitude fatigue is proposed in this paper. Different formulation for calculating effective stress range can be derived by the proposed theory, which include the effective stress range by the root mean square, by Miners law and a new effective stress range based on the nonlinear fatigue damage model. Comparison of the theoretical results of fatigue damage under the effective stress range of the variable-amplitude stress spectrum and experimental data of fatigue damage under realistic traffic loading has confirmed the validity of the proposed theory. As a way to relate variable-amplitude fatigue data with constant-amplitude data, the effective stress range provides the most convenient way for evaluating fatigue damage under variable-amplitude loading. The proposed theory is then applied to provide an efficient approach for accurately assessing fatigue damage of existing bridges under traffic loading, in which online strain history data measured from bridge structural health monitoring system is available. The proposed approach is applied to evaluate the effective stress range for the purpose of the fatigue analysis of a deck section of a long-span steel bridge-the Tsing Ma Bridge in Hong Kong.

Mixed-Dimensional Consistent Coupling by Multi-Point Constraint Equations for Efficient Multi-Scale Modeling

Finding an appropriate linking method to connect different dimensional element types in a single finite element model is a key issue in the multi-scale modeling. This paper presents a mixed dimensional coupling method using multi-point constraint equations derived by equating the work done on either side of interface connecting beam elements and shell elements for constructing a finite element multi-scale model. A typical steel truss frame structure is selected as case example and the reduced scale specimen of this truss section is then studied in the laboratory to measure its dynamic and static behavior in global truss and local welded details while the different analytical models are developed for numerical simulation. Comparison of dynamic and static response of the calculated results among different numerical models as well as the good agreement with those from experimental results indicates that the proposed multi-scale model is efficient and accurate.

Viscoplastic damage model applied to cracking of gravity dam

Abstract Assuming that material damages with a viscoplastic behavior, a finite element formulation is developed to analyze the evolution of damage by cracking in a gravity dam. An effective damage matrix is constructed to predict the possible sites of cracking based on the maximum normal stress criterion. The parameter λ is introduced such that the closure of those cracks that were already initiated could be accounted for as new ones are being developed. Numerical results are obtained to illustrate the spreading of cracks as the load is increased.

EVALUATIONS OF TYPHOON INDUCED FATIGUE DAMAGE USING HEALTH MONITORING DATA

This paper aims to evaluate the effect of a typhoon on IhtigllC damage in steel decks of long-span suspension bridges. The strain-time histories at critical locations of deck sections of long-span bridges during a typhoon passing the bridge area me investigated by using on-line strain data acquired fron1 the structural health monitoring system installed on the bridge. The fatigue damage models based on Miners law and the continuum damage mechanics are applied to calculate the increment of fatigue damage due to the action of a typhoon. It is found that for the case of Tsing Ma Bridge the stress spectrum generated by a typhoon is mllch different than that by the nonnul traffic and its histogram shapes can be described approximately as a Rayleigh distribution. The influence of typhoon londing on accumulative fatigue damage is more significant than that due to normal traffic loading. The increment of fatigue damage generated by hourly stress specttrum tor the maximum typhoon loading may be much greater than those for normal traffic loading. It concludes that it is necessary to evaluate typhoon induced fatigue damage for the purpose of accurately evaluating accumulative fatigue damage for the long-span bridge located at the typhoon prone region.

FATIGUE STRESS ANALYSIS OF SUSPENSION BRIDGES USING FEM

Fatigue is an important fallurc mode for large suspension bridges under traffic loadings. However, large suspension bridges have so many attributes tbat it is difficult to analyze their fatigue damage using experimental measurement methods. Numerical simulation is a feasible method of studying such fatigue damage. In British standards, the finite element method (FEM) is recommended as a rigorous method for steel bridge fatigue analysis. This paper aims at developing a model of a large slispension steel bridge using finite element methods (FEM) for fatigue stress analysis. The Tsing Ma Bridge (TMB) is selected for a case study and the corresponding finite element model is presented. The verification of the model is carried out with the help of the measured bridge modal characteristics and the online dala measured by the structural health moniloring system installed on the bridge. The results show that the constructed FE model is efficient for bridge dynamic analysis. Global structural analyses using the developed FE model are presented to determine the components of the nominal stress generated by railway loadings and some typical highway loadings. The critical locations in the bridge main span are also identified with the numerical results of the global FE stress analysis. It could be seen that the FE model could be served as a basis for evaluating fatigue damage and the remaining life of the bridge could then be evaluated.

Fatigue evaluation for Tsing Ma Bridge using structural health monitoring data

Fatigue assessment for the Tsing Ma Bridge (TMB) are presented based on the British standard BS5400 and the real-time structural health monitoring data under railway loading. TMB, as an essential portion of transport network for the Hong Kong airport, is the longest suspension bridge in the world carrying both highway and railway traffic. The bridge design has been mainly based on BS5400. A structural health monitoring system - Wind and Structural Health Monitoring System (WASHMS) for TMB has been operated since the bridge commissioning in May 1997. In order to assess the fatigue behavior of TMB under railway loading, strain gauges were installed on the bridge deck to measure the strain-time histories as soon as the bridge is loaded by a standard railway loading due to the service of an actual train. The strain-time history data at the critical members are then used to determine the stress spectrum, of which the rainflow method recommended for railway bridges by BS5400 is applied to count cycles of stress range. Miners law is employed to evaluate fatigue damage and remaining service life of the bridge. The evaluated results of fatigue damage and remaining service life would help us to well understand about the fatigue design of the bridge and status in fatigue accumulation.