The combination of replaceable and repairable properties in structures has introduced new approach called “Low Damage Design Structures”. These structural systems are designed in such a way that through self-centering, primary members and specific connections neither suffer damage nor experience permanent deformations after being exposed to severe earthquakes. The purpose of this study is the seismic assessment of steel moment resisting frames with the aid of rigid rocking cores. To this end, three steel moment resisting frames of 4-, 8-, and 12-story buildings with and without rocking cores were developed. The nonlinear static analysis and incremental dynamic analysis were performed by considering the effects of the vertical and horizontal components of 16 strong ground motions, including far-fault and near-fault arrays. The results reveal that rocking systems benefit from better seismic performance and energy dissipation compared to moment resisting frames and thus structures experience a lower level of damage under higher intensity measures. The analyses show that the interstory drift in structures equipped with stiff rocking cores is more uniform in static and dynamic analyses. A uniform interstory drift distribution leads to a uniform distribution of the bending moment and a reduction in the structure’s total weight and future maintenance costs.