This study presents an innovative energy-based approach for the design and probabilistic seismic assessment of non-symmetric reinforced concrete buildings subjected to bidirectional loading. The methodology integrates normalized hysteretic energy and absorbed power, providing a unified indicator to describe damage progression and collapse capacity in dynamic scenarios with multiple signals. Through energy-based damage indices, critical failure thresholds are identified, taking into account both maximum deformations and low-cycle fatigue effects. Numerical simulations, performed on a frame model derived from experimental shake table tests, confirm the effectiveness of this approach in identifying different damage states, from initial cracking to global collapse, in response to a wide range of seismic inputs. The study also includes probabilistic fragility curves to estimate the achievement of various damage levels, providing a comprehensive tool for performance-based seismic design. The results show the limitations of traditional displacement-based methods and underline the validity of energy-oriented criteria, proposing a possible adjustment of the damage status classification for a greater reliability in risk reduction. The comparison with previous studies and experimental tests on the same case has highlighted how the proposed method is able to overcome the limitations of procedures that do not adequately consider cumulative effects. Furthermore, it has highlighted the limitations of nonlinear static analyses, which often provide a partial view of the structural behavior, and the possible discrepancies between numerical modeling and experimental tests, potential sources of misinterpretations of the building behavior.