Infrastructures could be designed and constructed to resist seismic lateral loads without experiencing a significant amount of damage concentrations in specific area. Having sufficient strength and stiffness to reduce the structural vulnerabilities against serious damages under seismic loading, requires structural elements to have adequate ductility and energy dissipating capability, which could be provided with the use structural dampers. These elements are typically replaceable, and designed to yield and protect the surrounding members from damages, and then be accessible after a major event. In this study, butterfly-shaped links with linearly varying width between larger ends and a smaller middle section are used for redesigning the prototype structures due to substantial ductility and stable energy dissipation capability. The effect of implementation of innovative seismic dampers in multi-story structures is investigated by analyzing multi-story prototype structures with structural seismic shear dampers, and subsequently compared with simple conventional linking beams. The results of the nonlinear response history analysis are summarized for 44 ground motions under maximum considered earthquake (MCE) and designed based earthquake (DBE) hazard levels. It is shown that implementation of the butterfly-shaped dampers in buildings with similar stiffness and strength leads to higher dissipated energy and less pinched curves compared to typical eccentrically braced frame systems. It is determined that the general stiffness and strength of the system with the butterfly-shaped link is close to conventional models; however, the demands on the surrounding boundary elements are lower than the corresponding conventional model, which could be beneficent for improving the seismic performance of the structural systems.