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involves reducing element stiffness and strengths as a function of the cumulative damage indicesand incorporating the residual (permanent) building drift into the structural topology. (3)Reanalyze the modified structural model through a second-order inelastic static analysis undergravity loads up its inelastic stability limit. The resulting stability index, λ u in Fig. 5, is definedas the ratio of the vertical load capacity to the applied gravity loads, where the gravity loads areassumed as full dead load plus 25% of the live load.The stability index, λ u , provides a global failure criterion that integrates the effect of localdamage sustained under each earthquake record and intensity. Figure 5 shows the evolution ofthe stability index for the six-story RCS space frame, where there is a one-to-one correspondencebetween stability points in Fig. 5 and the maximum interstory drifts in Fig. 4. The initial valueof λ uo = 5.5 (on the horizontal axis in Fig. 5) is the index for the undamaged structure, implyingthat the undamaged frame has sufficient lateral strength/stiffness to maintain stability under 5.5times the gravity load. This large value reflects the fact that the structure has significant gravityloadoverstrength as a result of the high seismic loads. The point where the curves cross λ u =1.0is point at which the structure can no longer sustain stability under its self-weight due toextensive seismic damage. The stability index at this point is defined as λ f and the associatedmedian value of the seismic hazard value isµˆλ f. This level is defined as the ‘capacity’ – orcollapse limit state – of the structure. Between these limits, λ uo and λ f , a third limit point isidentified at λ u = 0.95λ uo , corresponding to the point at which the lateral stability begins to2.52.01.5α = 0.45T F = 1.65T 1S a (T 1 ,5%)1.51.0S a R S a α1.00.50.5λ u = 1.0λ u = 0.95λ uo0.00 2 4 6 8 10 12 140.00 2 4 6 8 10 12 14IDR MAXIDR MAX(a)(b)Figure 5 – Stability curves versus IM, (a) IM = S a , (b) IM = S a R saα10