Approximated performance curve for steel bridges under joint state of probability of collapse, following the Weibull reliability model of cumulative damage

Steel bridges under fluctuating loads are under constant risk of reaching fatigue states that will lead to partial or complete collapse, as reported in the past (National Highway Institute, 2016). In the present research, a function that estimates the punctual probability of failure for a structural element, bases its capacity on the available fatigue capacity S-N curves for various previously studied structural elements (Munse, 1978). Said function estimates the probability of failure accounting the current approximated number of fatigue cycles the structure has been under. An additional modification to that methodology allows to account for corrosion effects if necessary, by a modification factor on the available S-N fatigue curves (Adasooriya et al., 2020). A joint probability of failure model based on said reliability function, using the Weibull model proposed by Munse (Munse, 1981) allows the researchers to construct a performance curve that allows to observe the effects of redundancy, fatigue and current age for a steel bridge under study as a function of number of fatigued elements. This methodology helped in studying a total of five steel bridges that currently are under service for Colombian highways. Results match the available information and evidence of advance deterioration becoming a powerful tool to decide on the theoretical probability of failure for a bridge, and future decision-making prioritization activities.