The fatigue behaviors of metals are different under different in-service environment and loading conditions. This study was devoted to investigating the combined effects of high and low cycle fatigue loads on the performance of the low alloy steel Q345. Three kinds of experiments were carried out, including the pure high cycle fatigue (HCF) tests, the pure low cycle fatigue (LCF) tests, and the combined high and low cycle fatigue (HLCF) tests. The prediction formulae were proposed for the combined high and low cycle fatigue failure. Scanning electron microscopy (SEM) and stereo microscope were used to analyze the microstructure and fracture morphology due to different fatigue loads. Case study on the combined high and low cycle fatigue damage of a steel arch bridge was carried out based on the FE method and the proposed formula. The results show that the LCF life decreases evidently due to the prior HCF damages. The HLCF fracture surface is relatively flat near the crack initiation side, and rugged at the other half part. The fatigue damages at the bridge joints increase significantly with consideration of the pre-fatigue damages caused by traffic load. In the 100th anniversary of service, the fatigue damage index without considering the HCF pre-damage is only about 50% of the coupled damage value.

The local instability of steel plates is the predominant seismic failure mode for steel bridge piers. However, the application of shell-based finite-element (FE) models in an engineering design presents significant difficulties, and existing simplified calculation methods have their own insufficiency. In this paper, single-column square-section steel bridge piers were studied to propose an equivalent hysteretic model for the fiber elements of steel piers that can consider the local instability behavior of steel plates. Using the length of the half-buckling wave at the bottom of pier as the length of effective damaged zone ($L_d$ ), average stress–strain curves of the cross-section points over the $L_d$ were extracted from the calculation results of a fiber-shell hybrid model. The two-surface constitutive model of material was modified by introducing the equivalent elastic modulus and skeleton curve and reducing the bounding surface radius to make the hysteresis and average stress–strain curves coincide. An equivalent hysteresis model for the fiber elements in the effective damaged zone was proposed, and the process for identifying model parameters was introduced. Using Q345qC structural steel as an example, regression formulae for equivalent hysteresis model parameters were established. Based on the comparison with calculation results of a hybrid element model, the improved fiber model can accurately calculate the seismic response of a structure under horizontal unidirectional or bidirectional earthquakes and significantly save calculation cost. The proposed equivalent hysteresis model can provide a method for calculating the elastoplastic seismic response with a high accuracy and good availability for the seismic design of steel piers under horizontal bidirectional earthquake actions.