This study evaluates the damping coefficient, the effective damping and the energy dissipated of a structure with and without buckling-restrained braces (BRB), subjected to 30 seismic records with different characteristics. These results are compared with the damping coefficient given by an international standard. The structure was modelled with a commercial software. The study is carried out on a symmetric 4-story steel moment-resisting frame that was tested without BRB at the E-Defense laboratory in Japan. The dynamic response of such unbraced bare frame was numerically simulated, obtaining a satisfactory agreement. The same numerical model was used to describe the dynamic behavior of the steel frame equipped with BRB. The seismic were three types of seismic records: Far-Field (inter and intra plate), and Near-Field (ten ground motion records in each series). These records were considered with and without scaling. Scaling was performed according to one of the Argentiniancodès spectrum. The results of the numerical modeling (damping coefficient, effective damping and energy dissipated) were discussed. In the conclusion, the main results of the study are highlighted.