Incremental dynamic analysis (IDA) requires the analysis of the non-linear response history of a structure for an ensemble of ground motions, each scaled to multiple levels of intensity and selected to cover the entire range of structural response. Recognizing that IDA of practical structures is computationally demanding, an approximate procedure based on the reduction of the number of ground motions is developed. A methodology based on data envelopment analysis (DEA), mathematical programming that can handle large numbers of variables and relations, is proposed to reduce the number of ground motions needed for the production of a reliable median IDA curve. The IDA curves computed by the exact and approximate procedures for two different sets of ground motions for the 9-storey SAC-Los Angeles building, are presented. The results demonstrate that the approximate procedure, which uses a limited number of input ground motions, is accurate enough for practical application in building evaluation and design.
