An increasing dynamic analysis is a parametric method used in various forms in recent years to estimate the performance of structures under seismic loads. In this research, the seismic behavior of steel moment frame with Buckling Restrained Braces equipped with shape memory alloy has been evaluated through increasing dynamical analysis. A form Shape memory alloy has been used as a concrete shell and a buckling restraind braces steel sheath. For this purpose, seismic behavior with non-buckling braces has been compared to the 10 records of the near field of the proposed FEMA P695 fault, in order to have a direct understanding of the behavior of this bracing and its dynamic response to earthquakes with different intensities. The results showed that steel frames with a buckling restrain brace equipped with a Shape memory alloy tended to collapse in the direction of the buckling frame and had a higher level of performance