n-Spectra: A New IM for Improved Structural Response Assessment

In the context of performance-based earthquake engineering, we aim to better quantify the seismic demand on structures. This is usually done through the use of ground motion intensity measures (IM) such as PGA and elastic spectral acceleration (Sa). Unfortunately, these peak-valued IMs are often not sufficient to characterize the seismic demand or to predict the structural response. For stiffness-degrading and strength-degrading structural components and systems, the number of cycles of inelastic response determines the degree of degradation. In soil liquefaction, the number of cycles of loading above a strength threshold is critical. At present we have no simple and convenient way to estimate the number of response cycles that a given ground motion may induce above a given threshold. In this paper, we introduce a new ground motion IM we call "peak exceedance spectra" or "n-Spectra". For a given excitation motion, n-Spectra quantify how many times an elastic single-degree-of-freedom (SDOF) oscillator will exceed any given amplitude of response (e.g., Sa). The n=1 spectrum is the conventional elastic response spectrum. At any period, the n-Spectra plot serves as a cumulative histogram of spectral response peak amplitudes. By quantifying the number of demand peaks (and hence cycles) above a level of interest, n-Spectra provide a more complete estimator of the potential damage due to earthquake ground motions. n-Spectra are easy to compute, they complement conventional elastic response spectra, and have many practical applications. Because of this, n-Spectra have the potential to become a very useful tool in earthquake engineering. This paper presents an introduction to n-Spectra, their computation and interpretation and a list of potential applications for this new IM.