Improvement of the Nonlinear Damage Mathematical Model for Steel Components in Bridge Under Complex Stress

To investigate the relationship between load, damage, and fatigue life of complex engineering components under stress, this paper modifies the existing continuous nonlinear damage model based on the distortion energy density theory to reflect the usage and stress characteristics of Q345 steel components in bridges. A nonlinear damage model that accounts for actual complex stress conditions is proposed, and the model parameters are calculated using twist–bending fatigue test data. The cumulative damage predicted by the modified model under varying fatigue stress levels is analyzed as a function of the number of fatigue cycles. Furthermore, the modified model is microscopically validated through scanning electron microscopy (SEM) observation and analysis of twist–bending fatigue unloading specimens. Finally, according to the engineering application of the modified model in the complex load environments of steel bridges, a comparative analysis is conducted between the general nonlinear damage model, the modified nonlinear damage model, and the actual damage observed in bridge components. The actual component damage, calculated based on the component’s natural frequency, closely matches the damage predicted by the nonlinear damage correction model using bridge monitoring data. In contrast, a significant discrepancy exists between the damage values predicted by the nonlinear damage correction model and those from the general nonlinear damage model. The observed discrepancy confirms the improvement effect and engineering significance of the modified nonlinear damage theory. Furthermore, the study reveals that under the same equivalent stress amplitude, reliability decreases nonlinearly as the expected service life increases. Conversely, for a fixed expected service life, reliability declines more rapidly with higher equivalent stress amplitudes.