Response Spectrum Superposition for Structures with Uncertain Properties

A response spectrum based stochastic approach is developed for analyzing the earthquake response of structures with uncertain properties. For this purpose, expressions for the variances of root-mean-square values of various response quantities at different levels of a multi-degree-of-freedom structure are derived in terms of the covariances of the modal parameters of the structure. The required covariances are defined as a function of the standard deviations of structural properties; i.e., mass, stiffness, and damping ratio. The validity of the proposed method has been established by computing a large number of example results and comparing them with the corresponding exact results obtained by the Monte Carlo simulation method. It is found that there may be significant variations in the response amplitudes for commonly associated uncertainties with the structural properties. The present study provides a simple, practical method to quantify such variations.