Report - PEER - University of California, Berkeley

where σ 2 ( L T |C ) is the variance of the total loss in the building given that collapse has2occurred and σ ( L T | NC,IM ) is the variance of the total loss in the building given thatcollapse has not occurred at intensity level im which can be computed as a function ofthe dispersion in the losses of individual components as followsN N[ ]∑∑2 LT| NC,IM = ai⋅ aj⋅L L NC IM⋅i , j|,σ σLi| NC,IM L j|NC , IMi= 1 j=1σ ρ (6)where σ is the dispersion of the loss in the ith component when collapse hasL i | NC,IMnot occurred at intensity level im, and ρ is the correlation coefficient betweenLi , L j|NC,IMthe losses in the ith and jth components conditioned on IM when collapse has notoccurred.The correlation between the losses in two individual components conditioned onthe ground motion intensity level, ρ , can be computed asρ =Li, L j | NC,IMσσLiL j | NC,IMLi| NC,IMσL j | NC,IMLi,L j|NC , IMwhere σ L i L j | NC,IM is the covariance of the loss between the ith and jth componentsconditioned on IM , when collapse has not occurred. As will be explained later, thiscorrelation is a function of three correlations: (1) the correlation of the engineeringdemand parameters EDP (i.e., response parameters) that have an influence on thecomponents; (2) the correlation of the damages in the components conditioned on theEDP; and (3) the correlation between the repair/replacement costs of the componentsassociated with a given damage state. The proposed approach not only takes intoaccount the correlation between losses in individual components but also the variationof this correlation with changes in the ground motion intensity level.3.1 Structural Response Estimation3. BUILDING-SPECIFIC LOSSIn the proposed approach the mean annual frequency of exceedance of the intensitymeasure, IM, (i.e., the seismic hazard curve) is from a conventional probabilisticseismic hazard analysis. For the United States this information is readily available atclosely spaced grid points, that permit to obtain seismic hazard curves for any zipcode or any geographical coordinates in the country.The selection of the parameter to be used to characterize the ground motionintensity for the structure (i.e., the intensity measure IM) depends on a number ofaspects such as the fundamental period of vibration of the structure, the responseparameters of interest, location of interest within the structure, level of nonlinearity,etc.(7)152