Buckling braces are considered as highly efficient passive energy dissipation systems in seismic protection of buildings. This study compared three different steel core geometries (I, L, and cross-section (+)) and analyzed their interaction with the number of stories (1, 3, and 5) to identify the most optimal configuration for maximum energy dissipation while considering concrete deterioration. Comprehensive nonlinear numerical models were developed in Abaqus software using the concrete plasticity damage model. After validation with laboratory data, the models were subjected to nonlinear and cyclic static analyses. The structural response was evaluated through pushover curves, hysteresis loops, and Mises stress contours. Quantitative results showed that the cross-section core dissipated 15 and 35 percent more hysteresis energy than the I and L sections, respectively. The examination of the plastic equivalent stress and strain (PEEQ) contours confirmed that in the cross section, due to the geometric symmetry and the non-concentration of destructive stress, more than 85% of the volume of the yield zone uniformly entered the plastic phase and the full capacity of the damper was activated. In contrast, the I and L sections, due to the local buckling phenomenon and stress concentration at the edges, suffered a capacity loss before the average stress reached the full yield limit and only utilized 31.1% and 29.2% of their potential energy dissipation capacity, respectively. Also, increasing the number of stories from 1 to 5 improved the total energy dissipation by 40%, indicating the positive scalability of the BRB performance with increasing height. These findings constituted the main innovations of this research. Finally, this study recommended the use of cross sections in concrete frames to improve seismic damping and resilience.