Seismic fragility assessment of self-centering braced steel frames with cyclic degradation under mainshock-aftershock sequences

This paper investigates the seismic performance of steel frames with shape memory alloy (SMA) braces, with particular emphasis on the effects of cyclic degradation under mainshock-aftershock (MS-AS) sequences. An incremental dynamic analysis (IDA) framework for MS-AS sequences is first introduced. To account for the initial stiffness degradation, strength degradation, and residual strain accumulation of SMA, a self-centering model with cyclic degradation (SMCD) model was developed to analyze cumulative damage under mainshock-aftershock conditions. The self-centering frame with cyclic degradation (SCF-CD) was established based on the cyclic degradation model. For comparison, the cyclic degradation function of the SMCD mechanical model was removed, creating a simplified mechanical model applied to the traditional self-centering frame (SCF). A total of 200 recorded natural MS-AS ground motion pairs are selected to perform IDA on the SMA-braced steel frames. The results confirm that MS-AS sequences have significant effects on structural responses. Compared with the SCF frame, the SCF-CD frame exhibited larger peak interstory drift ratios (PIDR) and residual interstory drift ratios (RIDR), with the maximum RIDR being up to 7.2 times higher. In addition, the SCF-CD frame experienced more severe plastic hinge damage than the SCF frame. Under aftershock IDA, the SCF-CD frame required on average 14.49 % lower spectral acceleration ( S a ) to reach the same damage states, indicating that neglecting SMA brace cyclic degradation may lead to an overestimation of seismic performance. This finding is further supported by the fragility analysis, where the exceedance probabilities of the SCF frame were generally lower than those of the SCF-CD frame. Overall, the results demonstrate that disregarding the cyclic degradation of SMA braces can significantly overestimate the seismic performance of structures, especially under MS-AS conditions.