A new formulation of a Logistic deterministic S-N curve is applied to fatigue data of metallic materials from ancient Portuguese riveted steel bridges. This formulation is based on a modified logistic relation that uses three parameters to fit the low-cycle- (LCF), finite-life- and high-cycle-fatigue (HCF) regions. This model is compared to the Kohout-Věchet fatigue model, which has a refined adjustment from very low-cycle fatigue (VLCF) to very high-cycle fatigue (VHCF). These models are also compared with other models, such as, Power law and fatigue-life curve from the ASTM E739 standard. The modelling performance of the S-N curves was made using the fatigue data considering the stress fatigue damage parameter for the materials from the Eiffel, Luiz I, Fão and Trezói riveted steel bridges. Using a qualitative methodology of graphical adjustment analysis and another quantitative using the mean square error, it was possible to evaluate the performance of the mean S-N curve formulation. The results showed that the formulation of the S-N curve using the Logistic equation applied to the metallic materials from the old bridges obtained superior performance to the analysed models, both in the estimation of fatigue behaviour in the low-cycle fatigue (LCF) region and in the lowest mean square error.
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