Almost all of seismic design codes for building systems accept heavy damages to buildings, in case of large earthquakes, although they don't accept the building's collapse. Nevertheless, past earthquakes have shown that level of the accepted damage may be so high that demolishing and reconstruction of the building becomes inevitable. This, in turn, results in some unacceptable consequences in large populated cities, such as thousands of homeless and/or jobless people for a very long time, very time consuming, difficult, and costly demolishing and debris removal processes, and finally very massive, and therefore, costly and time consuming required reconstruction works. Regarding these facts, any idea which can lead to creation of repairable buildings is greatly acknowledgeable. One such idea is 'Directed-Damage Design' (DDD) idea, which means guiding the damage to some pre-decided parts of the structural system, so that other parts do not experience any major plastic deformation, and therefore, making the building easily repairable only by replacing the damaged elements. Design of repairable buildings, have been paid great attention by some researchers in recent decade. Use of rocking mechanism of the building's structure (Azuhata et al. 2004) and employing telescopic columns in buildings with rocking/seesaw motion (Hosseini and Noroozinejad Farsangi 2012, Hosseini and Alavi 2014) are some samples of these researches. In previous researches, yielding base plates, yielding bolts, conventional and adaptive viscous dampers, friction dampers and some other devices have been used for energy dissipation. To use the DDD idea for creation of repairable steel buildings with square plan, in this study, a structural system having the capability of seesaw motion with respect to a central massive support has been considered in which the bottom ends of the all circumferential columns at the lowest story have been equipped with Double-ADAS (DADAS) dampers, which dissipate a great portion of the seismic input energy. The hysteretic behavior of DADAS dampers has been investigated by using finite element analysis. Seesaw motion of the structural system can make it possible to concentrate the damages in DADAS dampers at the base level of the building. At first a set of regular steel multistory buildings with 5, 8, 11 and 14 stories have been designed based on the conventional code provisions. Then, the structures of the designed buildings have been changed into the structure with seesaw motion by using, at the base level of the building, a massive central column, eliminating other middle columns, and equipping circumferential columns with DADAS dampers. To show the efficiency of the proposed structural system and dampers, a series of nonlinear time history analysis (NLTHA) have been performed by using a set of 3-component accelerograms of some selected earthquakes. Numerical results of NLTHA show that the proposed seesaw structures can efficiently decrease the seismic damage in the building, so that plastic deformation happens only ...