On frequency‐domain estimation of increase in design yield force levels of SDOF structures due to multiplicity of earthquake events

Abstract

The current earthquake design philosophy based on only the most critical earthquake may prove inadequate when the smaller events occurring before this event cause significant damage to the structure and repairs become infeasible. The design force levels may therefore be raised using the modified design force ratio, defined as the ratio of the yield force level for a specified damage level under all the seismic events to the yield force level for the same damage level under only the most critical event. This study considers the updating of the existing frequency‐based approach, using the power spectral density function (PSDF)‐based characterization of design ground motion, for the estimation of modified design force ratio spectrum. First, an empirical expression developed in the companion paper for modifying the damping of the equivalent linear oscillator is used such that the use of the PSDF compatible with 5%‐damping response spectrum leads to correct peak response, even when the equivalent damping ratio exceeds 5%. Next, the frequency‐domain design force ratio estimates are benchmarked in the case of steel and reinforced concrete oscillators by comparing those with the time‐domain estimates of equivalent Bouc–Wen oscillators over various sequences of events and by suitably adjusting the stiffness degradation parameter. It is shown in the case of a hypothetical seismic scenario that the optimal values of this parameter as 2.0 and 1.7 work well for the steel structures and reinforced concrete structures with high stiffness degradation respectively. Also, the proposed approach needs to be improved further for applicability in the case of reinforced concrete structures exhibiting significant pinching behavior.