Probabilistic approach for fatigue evaluation of welded connections with application to road steel bridges

Fatigue analysis of steel bridges asks for consideration of welded joints. Traditional fatigue analysis of welded joints under variable amplitude loadings is based on the nominal stress approach, wherein constant amplitude (CA) S-N curves are used in combination with modified Miner's linear damage accumulation rule. In current standards CA S-N curves are estimated by fitting a linear regression to experimental failure points, by neglecting run-outs and by somewhat arbitrarily fixing the constant amplitude fatigue limit (CAFL). Moreover, the scatter of fatigue life in high cycle fatigue (HCF) region is not modeled properly. Use of modified Miner's rule is also affected by two limitations: 1) The S-N curve reduced slope, m2, used for stress range cycles below the CAFL, has not been sufficiently justified by mean of variable amplitude (VA) fatigue test results; 2) Assuming the critical value of damage sum, Dc, equal to unity could lead to inaccurate consideration of load sequence effects. Many authors proposed to overcome the limitations related to the CA S-N curves by using Maximum Likelihood (ML) method to fit a random CAFL non-linear model to experimental data points. Nevertheless, this approach does not give explicit method to compute p-quantile S-N curve from ML estimate of model parameters. Furthermore, since the fitted model is not linear, the direct comparison with current standards is not straightforward. Concerning the limitations related to use of modified Miner's rule, many research works were carried out to investigate on the damage effect of stress range cycles below the CAFL as well as on the choice of the critical value of damage sum. However, these works only provide general trends and do not present a rigorous statistical approach which allows to overcome shortcomings of modified Miner's rule. This thesis work provides a rigorous probabilistic approach for estimation of: 1) Characteristic S-N curves for CA and VA fatigue loadings; and 2) Critical damage sum parameter, used in Miner's rule. New scheme combining ML and Monte-Carlo Simulations (MCS) methods is used. The new probabilistic approach also includes: 1) A new framework for fatigue reliability assessment of existing bridges; and 2) A new framework for re-calibration of partial safety factors for fatigue design. The application of ML-MCS approach for estimation of CA S-N curves to three study cases and the comparison with current standards, allowed for identifying inaccurate definition of fatigue strength in current standards, especially in high cycle fatigue (HCF) region. Moreover, the application to two study cases of ML-MCS approach for estimation of m2 and Dc parameters and the comparison with current standards, revealed an inadequate definition of damage accumulation mechanism in application of Miner's rule using current standards. The application of reliability analysis framework to the Venoge bridge study case showed the inaccuracy of Eurocode approach in reliability index assessment, during the 100 year-design life of the bridge. The issue related to the importance of the choice of target reliability index was also addressed for this study case. The revision of the Eurocode formats for fatigue design of structures, with application to two fatigue sensitive details, explained the inexactness of hypothesis of considering the same partial resistance factors for all verification formats and showed that Eurocode design format based on CAFL is highly unsafe.