An Examination of the Reasons for, and Variability of, the Differences Between Response Spectra and Pseudo Response Spectra

For many decades, it has been common practice to overlook the differences between response spectra and pseudo response spectra. This practice stems from analyses indicating that the average difference between response spectra and pseudo response spectra is negligible for a viscous damping ratio of 5%, which is near‐universally adopted. As others have shown, the differences depend strongly on the damping ratio, earthquake magnitude, and oscillator period, with larger differences for larger damping, smaller magnitudes, and longer periods. To quantify the full statistical distribution of the ratio of the absolute acceleration response spectrum (SA) to the pseudo absolute acceleration response spectrum (PSA), we fit empirical ratios with the generalized gamma distribution. Data for magnitudes from 4.0 to 5.5 give 95% prediction intervals for the ratio of 1.00–1.02 at 1 s and 1.01–2.24 at 10 s for 5% damping. For 30% damping, these intervals increase to 1.14–2.01 at 1 s and 1.62–11.8 at 10 s, respectively. Further, we demonstrate how the shape of the ground‐motion Fourier amplitude spectrum interacts with the natural period of the oscillator to control the differences in the response spectra type. Routinely treating the two measures of acceleration response spectra as interchangeable may lead to unacceptable inconsistencies when the response spectra of individual records are important or when larger damping ratios are used, such as in direct displacement‐based design. If one must convert between them, the uncertainty of the conversion should be accounted for during analysis.