Concentrically braced frame (CBF) systems are susceptible to buckling (which causes a decrease in energy absorption), although this system has considerable lateral stiffness and strength. To over this shortcoming, researchers have suggested the use of I-shaped steel dampers as a practical idea that prevents buckling and increases the energy absorption but reduces the stiffness of the system. To increase the stiffness of the damper, the thickness of the web or the thickness of the flange can be increased, but by increasing their thickness the shear capacity of the damper also increases. Nevertheless, with the increase in the capacity of the damper, the forces created in the elements outside the damper will also increase, which is usually not a suitable solution. Therefore, in this paper, the use of the low yield point for the web plate of an I-shaped damper is proposed to compensate for it. Accordingly, its behavior is investigated parametrically and numerically and also requires equations to design the system proposed. Results indicated that utilizing an LYP damper improves the behavior of the system in the case of energy absorption, stiffness, and strength. Comparing the LYP damper and the conventional I-shaped damper (made of A36 steel) reveals that both dampers pertain to stable hysteresis loops without any degradation, which confirms the capability of the I-shaped damper to dissipate seismic energy. Although the flange plate properties contribute to the load-bearing of the damper, the A36 damper is more affected by the flange plate than the LYP damper that is concluded for LYP dampers the flange plate contribution in the shear strength of the damper is ignorable at the beginning of imposed loading.