A simplified method to estimate nonlinear response with an approximate linear analysis for reinforced concrete structures

A background on simple methods to estimate nonlinear response of multi-degree-of-freedom (MDOF) systems currently in use is presented as an introduction to development of a new method. A series of nonlinear analyses of 105 concrete building structures with varying number of stories and structural configurations evaluated to determine the maximum drift demands imposed by a suite of 10 ground motions. The ground motions were selected and scaled to represent a smooth displacement spectrum. The combination of damping and effective stiffness of equivalent single-degree-of-freedom (SDOF) linear systems that resulted in the most accurate estimates of the maximum nonlinear drift for high and moderate seismic demands is presented. The location and magnitude of the story drift ratio (SDR) for linear SDOF and nonlinear MDOF models of the building systems was also examined and compared. A primary conclusion of the study was that an equivalent SDOF system evaluated with an effective period of 2.3 and 2.0 times initial period in regions of high and moderate seismicity, respectively, and a 10% damped response spectrum produced the most consistent and accurate estimate of nonlinear building displacement for the frames and earthquakes considered. In general, the magnitude of SDR for the nonlinear MDOF systems were 1.5 time the SDR for linear SDOF systems.