Report - PEER - University of California, Berkeley

assess expected NSASS losses. For the case illustrated, these losses are relativelysmall. But the picture could change radically if the building were a museum, inwhich case the NSASS expected loss-EDP curve likely will be much steeper and maybe the dominant contributor to total losses. In this case, longer period structures andweaker structures (smaller base shear strength) become more attractive.This example serves to illustrate the evaluation of design options based onexpected losses, and the kinds of trade-offs that can be made between strength andstiffness based on the relative contributions of the subsystems to the total losses.3.2 Design Decisions Based on Collapse Performance TargetsProviding collapse safety implies adherence to capacity design concepts, and itimplies design for ductility. The latter is implicitly considered in present designapproaches with the judgmental response modification (R) factor or behavior (q)factor. These factors are tied to component detailing (ductility) requirements, and inthe design process they are used to reduce the strength design level to a fraction of theelastic demand associated with the spectral acceleration at the first mode period.Research has been performed recently on the “collapse capacity” of momentresisting frames, utilizing component hysteresis models that account for strengthdeterioration in the backbone curve (see Figure 4) and for cyclic deterioration instrength and stiffness (Ibarra 2003). The collapse capacity is defined as that value ofthe “relative intensity”, [S a (T 1 )/g]/γ, at which dynamic instability occurs in a sidewaysmode due to deterioration and P-∆ effects. It is noted that [S a (T 1 )/g]/γ is equivalent tothe ductility dependent strength reduction factor R µ . Collapse fragility curves of thetype shown in Figure 5 have been derived for regular frames subjected to a set of 40ground motions (Ibarra 2003). It has been concluded that the collapse capacitydepends primarily on the component ductility capacity δ c /δ y , the post capping stiffnessratio α c (see Figure 4), and the cyclic deterioration parameter γ s,c,k,a . Theseparameters, together with the fundamental period T 1 and the base shear strengthparameter γ = V y /W, control the design for collapse safety.ResidualStrengthElastic StiffnessPost-Capping StiffnessFcFyFr=λFyF Κs=αsKeKeδyδcHardening StiffnessCapping(Peak) PointKc=αcKeδrδProbability of Collapse10.80.60.40.2[Sa(T1)/g]/γ vs PROBABILITY OF COLLAPSEN=9, T1=0.9, BH, Peak Oriented Model, LMSR-N, ξ=5%,αs=0.03, δc/δy=Var, αc=Var, γs,c,k,a=Inf, λ=0δ c /δ y =6, α c =-0.10δ c /δ y =4, α c =-0.10δ c /δ y =2, α c =-0.10δ c /δ y =4, α c =-0.30δ c /δ y =2, α c =-0.3000 5 10 15[S a (T 1 )/g]/γFigure 4. Backbone curve fordeteriorating hysteretic models.Figure 5. Collapse fragility curves for 9-story frame structures with T 1 = 0.9 s.513