Shape memory alloys (SMA) are utilized in various engineering fields, owing to their unique properties. In this study, the collapse behavior of steel structures designed with a self-centering damper under seismic sequences was investigated. The proposed damper was made of SMA plates, friction devices, and polyurethane springs called axial polyurethane friction (APF) -SMA dampers to provide desirable damping capabilities and good self-centering behavior. Concentrically braced 14-story steel frames using four types of bracing systems (split X, chevron V, inverted chevron IV, and diagonal) were modeled in OpenSees with and without the APF-SMA damper to evaluate their seismic resistance performance. An incremental dynamic analysis (IDA) was performed for the frames, and the maximum inter-story drift IDA curves of the frames were developed and compared. The analysis results indicated that the APF-SMA damper limited the maximum inter-story drifts of the conventional steel frames and effectively reduced the residual inter-story drifts of the braced frames. Finally, the advantages of the proposed APF-SMA over the conventional braced frames were demonstrated through probabilistic analyses of the results based on the nonlinear response history analyses.