Incremental dynamic analysis (IDA)-a procedure developed for accurate estimation of seismic demand and capacity of structures-requires non-linear response history analysis of the structure for an ensemble of ground motions, each scaled to many intensity levels, selected to cover the entire range of structural response-all the way from elastic behaviour to global dynamic instability. Recognizing that IDA of practical structures is computationally extremely demanding, an approximate procedure based on the modal pushover analysis procedure is developed. Presented are the IDA curves and limit state capacities for the SAC-Los Angeles 3-, 9-, and 20-storey buildings computed by the exact and approximate procedures for an ensemble of 20 ground motions. These results demonstrate that the MPA-based approximate procedure reduces the computational effort by a factor of 30 (for the 9-storey building), at the same time providing results to a useful degree of accuracy over the entire range of responses-all the way from elastic behaviour to global dynamic instability-provided a proper hysteretic model is selected for modal SDF systems. The accuracy of the approximate procedure does not deteriorate for 9-and 20-storey buildings, although their dynamics is more complex, involving several 'modes' of vibration. For all three buildings, the accuracy of the MPA-based approximate procedure is also satisfactory for estimating the structural capacities for the limit states of immediate occupancy, collapse prevention, and global dynamic instability.

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This paper develops a modal pushover analysis-(MPA) based approximate procedure to quantify the collapse potential of structural systems. The computationally demanding incremental dynamic analysis (IDA) of the structural system is avoided by MPA of the structure in conjunction with empirical equations for the collapse strength ratio for the first-mode single-degree-of-freedom (SDF) system; higher modes of vibration play essentially no role in estimating the ground motion intensity required to cause collapse of the structure. Presented are collapse fragility curves for 6-, 9-, and 20-story regular special momentresisting teel frames computed by the exact and approximate procedures, demonstrating that the MPA-based approximate procedure requires only a small fraction (1% in one example) of the computational effort inherent in exact IDA and still achieves highly accurate results.(IDA) [15], which requires nonlinear response history analysis (RHA) of the structure for an ensemble of ground motions, each scaled to many intensity levels, selected to cover a wide range of structural response-all the way from elastic behavior to global dynamic instability.Recognizing that IDA of practical structures is computationally extremely demanding, the developers of IDA have devised the approximate method SPO2IDA [16]. Restricted to first-mode dominated structures, this procedure defines the force-deformation curve in initial loading of the SDF system to match the static pushover (SPO) curve of the structure, and determines the peak deformation of the nonlinear SDF system by Excel-based software [17]. Because the SPO curve depends on the choice of the height-wise distribution of forces, SPO curves are determined for several force distributions and the 'worst' SPO is chosen, but the choice is not unique. This procedure also requires estimating the elastic stiffness of the SDF system from the IDA curve, a task that is complicated because several vibration modes contribute to the responses plotted in the IDA curve.Modal pushover analysis (MPA) [18], an approximate analysis procedure rooted in structural dynamics theory [19], avoids the preceding issues concerning SPO2IDA. The MPA has been utilized to estimate seismic demands instead of nonlinear RHA. Encouraged by the accuracy of MPA in estimating IDA curves [20], this paper explores the potential of MPA in investigating the collapse of buildings. Collapse here is synonymous with dynamic sideway instability in one or several stories of the structural system. COLLAPSE FRAGILITY CURVESThe ground motion intensity that causes collapse of a building can be determined by IDA. This procedure requires a series of nonlinear RHA of the structure for an ensemble of ground motions, and each record is scaled to several levels of intensity to encompass the full range of structural behavior: from elastic to yielding that continues to spread, finally leading to global dynamic instability. The results of these analyses for one ground motion lead to one IDA curve. This is a plot of the ground motion i...