The complete SRSS modal combination rule

The complete Square-Root-of-Sum-of-Squares (c-SRSS) modal combination rule is presented. It expresses the structural response in terms of uncoupled SDOF modal responses, yet accounting fully for modal response variances and cross-covariances. Thus, it is an improvement over the classical SRSS rule which neglects contributions from modal cross-covariances. In the c-SRSS rule the spectral moments of the structural response are expressed rigorously in terms of the spectral moments of uncoupled modal responses and of some coefficients that can be computed straightforwardly as a function of modal frequencies and damping, without involving the computation of cross-correlation coefficients between modal responses. An example shows an application of the c-SRSS rule for structural systems with well separated and closely spaced modal frequencies, subjected to wide-band and narrow-band excitations. Comparisons with response calculations using the SRSS and the Complete Quadratic Combination rules are given and discussed in detail. Based on the c-SRSS rule a response spectrum formulation is introduced to estimate the maximum structural response. An example considering a narrow-band excitation from the great Mexico earthquake of September 19, 1985, is given and the accuracy of the response spectrum formulation is examined. Copyright © 2010 John Wiley & Sons, Ltd.