Report - PEER - University of California, Berkeley

Figure 3a, shows an example of fragility function for the first damage state of areinforced concrete column in the building. It is observed that the EDP, which in thiscase corresponds to the interstory drift ratio, associated to certain damage states ofstructural components exhibits a very large scatter. In order to reduce the uncertaintyin damage estimation for these damage states fragility surfaces were developed(Aslani and Miranda 2004a). In a fragility surface the mean and standard deviation ofEDP corresponding to a damage state are evaluated as a function of a new parameter,α, which allows the incorporation of additional information. The parameter α canincorporate information on the element (e.g., geometry, detailing, etc.), its loadingand or a combination of the two. The probability of exceeding the damage state isthen estimated as a function of the level of EDP in the component but also as afunction of the parameter α. Figures 3b and 3c present examples of the fragilitysurfaces developed to estimate the probability of experiencing a shear failure and orthe loss of vertical load carrying capacity in non-ductile reinforced concrete columnsFor more details on the fragility curves and fragility surfaces of structural componentsthe reader is referred to Aslani and Miranda 2004a.Consistent with parameters used in FEMA 356, fragility functions for nonstructuralcomponents were developed as a function of either IDR and PFA. Nonstructuralcomponents were assumed to be sensitive to only one of these parameters.Figure 4a presents an example of fragility functions developed for gypsum boardpartitions as a function of the level of the IDR imposed to the partition. Figure 4bpresents an example of fragility functions developed for suspended ceilings as afunction of the level of the PFA in the component. More details on the fragility ofnonstructural components are presented in Taghavi and Miranda (2003a).3.3 Estimation of the Probability of CollapseAs shown in Eqs (2) and (5) both the expected value of the losses and the dispersionof the losses for a given ground motion intensity require an estimate of the probabilityof collapse. Two different approaches were used to estimate the probability ofcollapse. In one approach collapse was produced by the occurrence of lateral dis-P(DM 1 |EDP i )Column1.00.80.60.40.20.00.000 0.010 0.020EDP [IDR]P (DM 2 | EDP i )1.00.50.00.080.04EDP [ IDR]0.000.300.150.00α shearP (DM 3 |EDP i )1.00.50.00.100.05EDP [ IDR]0.0020.010.00.0α AxialFigure 3. Fragility assessment of non-ductile reinforced concrete columns.155