After yielding in frames with buckling restrained braces subjected to intense earthquakes, The insignificance of their post-yielding stiffness causes the structure's inability to return to its original state. There are various solutions to reduce permanent displacement in structures. In this research, the seismic response of the structure  with a vertically elastic truss in a frame with buckling restrained braces is studied. The responses of this system subjected to earthquake effects are compared with the frame responses with buckling restrained braces without elastic trusses. The existence of a strong vertical truss, which is essentially elastic, can lead to identical interstory drift ratio in all stories. In such a system, the base of the the elastic truss is connected to the ground with pinned connection, so that it is possible for the entire truss to be rotated. All members of the vertical truss, including the diagonal members, remain under the seismic force in the elastic range. While other braces that are buckling restrained come into the plastic zone in severe earthquakes, they provide a ductility and energy dissipation for the system. Designed structures are initially designed according to conventional design rules and then the systems are analyzed by nonlinear time history under the influence of earthquake and static nonlinear analysis. On average, for the structures under study, using a truss in the frame with buckling restrained braces reduces the amount of residual inter-story drift changed from 1.33 percent to 0. 58 percent.