Alternate modal combination methods in response spectrum analysis

In piping analyses using the response spectrum method Square Root of the Sum of the Squares (SRSS) with clustering between closely spaced modes is the combination procedure most commonly used to combine between the modal response components. This procedure is simple to apply and normally yields conservative estimates of the time history results. The purpose of this study is to investigate alternate methods to combine between the modal response components. These methods are mathematically based to properly account for the combination between rigid and flexible modal responses as well as closely spaced modes. The methods are those advanced by Gupta, Hadjian and Lindley-Yow to address rigid response modes and the Double Sum Combination (DSC) method and the Complete Quadratic Combination (CQC) method to account for closely spaced modes. A direct comparison between these methods as well as the SRSS procedure is made by using them to predict the response of six piping systems. For two piping systems thirty-three earthquake records were considered to account for the impact of variations in the characteristics of the excitation. The results provided by each method are compared to the corresponding time history estimates of results as well as to each other. The degree of conservatism associated with each method is characterized. 7 refs., 4 figs., 2 tabs