Apparent-weakening by adaptive passive stiffness shaping along the height of multistory building using negative stiffness devices and dampers for seismic protection

•Apparent weakening by adaptive stiffness shaping of structures using a negative stiffness device (NSD) for earthquake protection.•In this numerical study, we propose and verify the concept of adaptive stiffness shaping of a nine-story yielding structure.•Results presented confirm that the addition of NSD + NDs protects the structure from strong ground motion and improves performance.•Based on the performance for eight strong ground motions, we conclude that NSDs in conjunction with nonlinear dampers provide the significant response reductions.•We show that in addition to reduction of peak responses, the NSD systems in some cases also reduce the number of cycles of large base shears and deformations of the structure, hence aiding reducing fatigue damage to structures.•Results show, that if the distribution of apparent yield is properly designed for a structure, NSDs with nonlinear dampers results in a superior performance compared to the other cases considered in this paper.