Asymmetrical designs have been demonstrated to be extremely hazardous in previous earthquakes. One possible cause of the susceptibility might be a disparity of mass or stiffness. The majority of the investigation was devoted to examining the eccentricity that results from an inconsistent distribution of stiffness. Conversely, the systems exhibiting mass eccentricity as a consequence of the unequal mass distribution at the floor level receive comparatively less awareness. Therefore, stiffness along with mass eccentric systems are jointly thoroughly examined in the current research owing to bidirectional components of ground motion that expose more accurately simulating the actual scenario. In order to provide a relatively precise forecast regarding column elements, the explanation of hysteresis behavior takes into account the impact of biaxial interaction caused by synchronous bidirectional movement. The vulnerability of asymmetric structures to stiffness or mass eccentricity has mostly been studied in idealized single-story systems with different levels of eccentricity. In addition, the subject matter of the research has expanded to cover three-story asymmetric systems in order to examine the impact of higher modes. This study investigates a three-story system with larger eccentricity in the first story for functional reasons and lower eccentricities in the upper stories for a more realistic scenario. The current study demonstrates that stiffness eccentric systems and mass eccentric systems are both susceptible to earthquakes. In addition, three-story systems have a significantly higher reaction than their single-story equivalents. This research could enhance design recommendations by providing a greater comprehension of the behavior of plan asymmetric systems.