Optimum definition of equivalent non-linear SDF system in pushover procedure of multistory r/c frames

In the present paper, the optimum definition of an equivalent non-linear single-degree-of-freedom (SDF) system, which substitutes for a multistory plane reinforced concrete (r/c) frame, is presented. This optimum non-linear SDF system is suitable for use in approximative non-linear procedures, such as static (and modal) pushover analysis, in order to estimate the seismic demands of multistory plane r/c frames. This optimum definition of a non-linear SDF system is derived mathematically, for the special case of dynamic loading on masses of the multistory frame, using suitable simplified assumptions. The non-linear SDF system is suitable in the case of ground motion (seismic excitation) at the base of multistory plane frames, as the results of the system by applying this non-linear SDF system in a series of multistory plane r/c frames are verified by non-linear inelastic dynamic time-history analysis using the Drain-2D program. Finally, a numerical example of a nine-story plane r/c frame is given.