Earthquake ground motion characterization using the Conditional Spectrum
A common goal of dynamic structural analysis is to predict the response of a structure subjected to ground motions having a specified spectral acceleration at a given period. This is important, for example, when coupling ground motion hazard curves from probabilistic seismic hazard analysis with results from dynamic structural analysis. The prediction is often obtained by selecting ground motions that match a target response spectrum, and using those ground motions as input to dynamic analysis. The commonly used Uniform Hazard Spectrum (UHS) conservatively implies that large-amplitude spectral values will occur at all periods within a single ground motion. An alternative, termed a Conditional Mean Spectrum (CMS), is presented here. The CMS provides the expected (i.e., mean) response spectrum, conditioned on occurrence of a target spectral acceleration value at the period of interest. The CMS may be a more appropriate target spectrum in some analysis situations, and is thus a useful tool for selecting ground motions as input to dynamic analysis.
At the below some codes for calculation of CMS is attached