Report - PEER - University of California, Berkeley

2. The availability of cost-of-repair functions for each damage state.3. The ability to integrate fragility and cost-of-repair functions for each component.In the context of conceptual design it appears quite acceptable to use expectedcosts of repair for each damage state (E[L j │DM=dm i ]) and compute onlyexpected loss as a function of EDP, i.e.,mE [ L j | EDPj= edp ] = ∑ E[ L j | DM = dmi] P( DM = dmi| EDPj= edp ) (2)i=1The result is an expected loss-EDP relationship for the specific component.4. The summation of expected losses (as a function of EDP) over all thecomponents of the subsystem that is expected to govern the loss at the hazardlevels of interest. The result will be a single expected loss-EDP relationship forthis subsystem. The same process can be carried out for all three subsystems,which will provide information on the contribution of the individual subsystemsto the total loss, given a value of EDP.This process is straight forward, in concept, and is the most effective way toperform PBD. But at this time it is most difficult or impossible to implement, simplybecause of the lack of data. Expected loss-EDP relationship for the subsystem thatgoverns losses are not available at this time, but we have to raise the issue so that,hopefully, such relationships will be developed in the future. The added difficulty isthat these relationships do not yet account for downtime losses. Incorporation of suchlosses is an additional challenge for the future.Collapse also is a contributor to direct losses. In fact, it may be a majorcontributor for “non-conforming” structures (e.g., older RC frame structures, seeMiranda 2004). But for “conforming” structures (i.e., structures designed accordingto modern standards) most of the losses come from relatively moderate but frequentevents, rather than from complete or partial collapse. Thus, the cost of collapse is notconsidered in the expected loss-EDP relationships, and collapse is treated as aseparate performance level.2.2 Collapse Performance TargetsIn most codes and guidelines, it is assumed that adequate collapse safety (and lifesafety) is provided by limiting the maximum story drift at the design earthquake levelto a specific value (e.g., a drift limit of 0.02 at the 10/50 hazard level). The drift at thishazard level is estimated from either an elastic analysis or an inelastic time historyanalysis. But the latter usually is executed with the use of component hysteresismodels that do not account for strength and stiffness deterioration. Thus, these EDPpredictions cannot be used as indicators of actual collapse. With the advent ofdeterioration models that do account for important aspects of deterioration it isbecoming possible to trace the response of structures to collapse (e.g., Ibarra 2003)and to be specific about a collapse performance target. Such a target could beexpressed as a tolerable probability of collapse (say, 10%) at the 2/50 hazard level, or509