The aim of this paper is based on the simple nonlinear procedure founded on the Park-Ang damage index model at different constant damage levels to evaluate the target displacement and performance point (P.P.). The mentioned procedure represents the intersection of the pushover capacity curve with the seismic hazard demand curve according to the equivalent period of vibration and damping in ADRS format. Hence, the damage-based response acceleration ratio is determined at different damage levels and periods for developing inelastic spectra from elastic ones. Then, the relation between the strength reduction factor (R-factor) and damage was extended at different damage levels and periods of vibration to predict the target displacement at the desired damage level, known as the performance point. It is worth mentioning that the cited procedure is represented for four hysteresis models, including Elastic-Perfectly-Plastic (EPP), Modified Clough (MC), moderate stiffness-strength deterioration (MSD), and severe stiffness-strength deterioration (SSD) models, to consider the theory for well-design and not well-designed systems in both steel and concrete structures. The mentioned procedure is the N₂ theory development based on the damage model called the DN₂ method in this investigation. Two experimental reinforced concrete bridge piers and three steel moment resisting frame structures with different periods, from low to high duration, are considered to verify the suggested procedure. Statistical results show that the target displacement and P.P. are evaluated appropriately regarding presented equations and proposed methodology compared to previous studies.