Using pulse R-factors to estimate structural response to earthquake ground motions

A new method is developed for estimating inelastic response to strong ground motions. The method applies strength reduction (R) factors determined for a simple pulse to the elastic spectrum of the ground motions to estimate inelastic response spectra. Optimal pulse shapes and durations are identified among the 24 pulses considered for 15 strong ground motion records. The ground motions consist of short and long duration records at varied distances from the epicenter and near-fault records that contain forward directivity factors. The recommended pulse shapes and pulse durations result in better estimates of inelastic response spectra than those obtained using conventional R − μ − T relations. The recommended pulse durations indicate that the conventional relations should instead be in terms of T/T_g (rather than T), where T_g is the characteristic period of the ground motion. The response of bilinear systems to simple pulses was examined, and simple analytical expressions for the R-factors of short period systems having positive post-yield stiffness and long period elasto-plastic systems are reported. The equal energy rule is found to be applicable to only a limited set of pulse shapes. The response of 4- and 12-story moment-resistant frame buildings subjected to the 15 ground motions is evaluated. Estimates of the peak roof displacement are made using “equivalent” SDOF systems in conjunction with nonlinear static (pushover) analyses. Estimates of interstory drifts are made based on combinations of the first two modes, assuming their responses to be independent. It is found that reasonably good estimates of peak roof displacement can be made assuming all nonlinearity is captured by the response of a SDOF system to a simple pulse.