Dependence of Damping Correction Factors for Response Spectra on Duration and Numbers of Cycles

Many modern applications in earthquake engineering require the use of pseudoacceleration response spectra or relative displacement response spectra calculated for damping ratios other than the commonly assumed 5% of critical. The simplest way to obtain such spectra is to derive ratios of the spectral ordinates at the desired damping ratio to the 5% damped spectrum, which can then be applied as scaling factors. These scaling factors have previously been shown to be mildly dependent upon period as well as strongly dependent upon duration. In this paper, the dependence of the scaling factors with respect to both duration and the number of equivalent load cycles is quantified. Generic equations are derived that may be used to estimate the spectral response over a wide range of damping ratios as a function of significant duration (both $D_{5–75\%}$ and $D_{5–95\%}$ ), and number of cycles $\left[N_{rr}\right(2.0\left)\right]$ . While the dependence upon these predictor variables is clear, the derived relationships cannot be directly incorporated into design codes due to the fact that strong ground-motion duration and number of equivalent cycles are generally not specified as part of seismic design actions.