Empirical Response Spectra and the Response of Unmeasured Floors

A novel system identification method, called Mod-ξ (var), has been developed, implemented, and validated to analyze the seismic response of a three-dimensional reinforced concrete shear wall building during the 2010 mega-earthquake in central Chile (Mw = 8.8). This technique represents an advancement over conventional Least-Squares-based modal identification methods by estimating modal parameters within short time windows, allowing for a more accurate representation of seismic data in both the frequency and time domains. The Mod-ξ (var) method offers several significant advantages. It enables the tracking of time-varying dynamic properties throughout an earthquake, providing a detailed understanding of the building’s evolving structural response. Furthermore, it enables reliable estimation of continuous nonlinear modal responses. It facilitates the derivation of empirical response spectra for each seismic input, offering valuable insights into structural performance under varying seismic conditions. One key feature of this approach is its ability to estimate local responses on both instrumented and non-instrumented floors. This is achieved by combining the nonlinear modal responses with normalized seismic mode shapes for all floors, which can be obtained through ambient vibration testing. Additionally, the floor deformations derived from the Mod-ξ (var) method can be applied to a Finite Element Model to evaluate critical engineering quantities such as inter-story drift, internal forces, and local demands. This enables the estimation of essential structural parameters, including drift ratios, curvatures, internal forces, stresses, and strains—providing a comprehensive basis for advanced structural analysis and design.