DRAFT: US-JAPAN PBEE PAPER BY CORDOVA ... - PEER

whereIM is the hazard intensity measure with the annual probability, Pacceptanc, of beingetanP accepceexceeded (i.e. P = H IM ) ). The term,acceptanceIM(P acceptanc ee122kδλ f, which reflects the variability ofthe median stability limitµˆλ f, can be moved to the left side of Eq. 16, resulting in the following:e− 1 2kδ2 λfˆ µλf≥ IMPacceptanceorφ ˆ µλf≥“seismic demand” (17)where φ = e2− 1 kδ2 λ f. This equation is similar to LRFD equations that are prevalent in codeprovisions where the “design strength” on the left side (the nominal strength reduced by a phifactor) is compared to the load effect or “seismic demand”. In this case there is no load factor onthe seismic demand since the recurrence interval of the demand is implicit in its definition.An important but perhaps misleading coincidence in Eq. 17 is that the probability associated withthe demand term (on the right side) turns out to be equal to the desired limit on the probability ofexceeding the median stability intensity,µˆλ f. This is different than saying that one is designingfor a given hazard with a specified probability of exceedance. From Eq. 15, the underlyingprobability statement implied in Eq. 17 is related to the likelihood of exceeding the stabilitycriterion,µˆλ ftaking into account both variability in the ground motion hazard and the record-torecordvariability in the stability index.Essentially, Eq. 17 enables one to establish whether a structure meets the collapse performanceobjective with a mean annual probability of exceedance, P acceptance . There are two basic inputrequirements for the procedure: (1) the “seismic demand” for the desired probability ofexceedance, IM P,acceptance , determined using either hazard maps or a probabilistic seismic hazardanalysis; and (2) the median stability limit,dispersion δλfor a representative set of ground motions.fµˆλ, of the structure and the correspondingf7. APPLICATION OF PROBABILISTIC COLLAPSE ASSESSMENTThis example will go through a collapse performance assessment for the 6-story RCS perimeterframe. The hazard analysis is based on a site at Yerba Buena Island (in San Francisco Bay)15