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While the two-parameter index reduces the overall dispersion, this reduction is most apparent atlarger drifts, where the structure behaves nonlinearly. In fact, comparing Figs. 4a and 4b, in theelastic range (at lower drifts), the two-parameter S index results in more variability thanSa(T 1 ). This follows from the fact that Sa(T 1 ) provides a nearly exact correlation with drift forthe linear case, whereas the period shift captured in S works best when the structurebehaves nonlinearly. This suggests that an improved index would be one where the α and T fparameters are devised to vary with the degree of inelastic action, similar in some ways to howthe period is shifted using the capacity spectrum method for calculating the target displacementfor nonlinear static pushover analyses.aR SaαaR SaαWhile the IDA’s provides useful information on the structural response, it is apparent from thecurves in Fig. 4 that the IDA’s do not reveal a definitive stability limit state. Some curves, suchas the one for the LP89-HCA record, asymptotically approach a bounding strength (in terms ofthe intensity measure), but others do not. For example, the CM92-RIO and Valparaiso plotsmaintain positive slopes at very large earthquake intensities and drifts. This reflects inherentlimitations of the inelastic time-history analysis to fully capture the strength and stiffnessdegradation at large inelastic deformations.Frame Stability Limit State DeterminationTo evaluate global instability, the authors have employed a procedure that integrates localdamage indices, computed during the time-history analysis, through a supplementary stabilityanalysis of the damaged structure. The basic procedure, described in detail by Mehanny andDeierlein (2001), entails a post-earthquake second-order inelastic stability analysis to assess theloss of gravity load capacity due to damage incurred during the earthquake. This procedure,which leads to the plot of an intensity measure versus gravity stability index λ u shown in Fig. 5,entails three basic steps. (1) Perform a nonlinear time-history analysis and calculate thecumulative damage indices. This provides the basis to quantify the localized (distributed)damage caused by a given earthquake ground motion. The damage indices are empiricalequations that track the structural damage as a function of cumulative plastic deformations. (2)Modify the analysis model based on the damage incurred during the time-history analysis. This9