Report - PEER - University of California, Berkeley
Report - PEER - University of California, Berkeley Report - PEER - University of California, Berkeley
P(C LVCC i |IM )1.00.80.60.40.20.00 20 40 60 80 100IM [ S d (cm) ]P(C LVCCi |IM )1.00.80.60.40.20.00 20 40 60 80 100IM [ S d (cm) ]P(C|IM)1.00.80.60.40.20.00 20 40 60 80 100IM [ S d (cm) ]Figure 5. Different steps of estimation of the probability of collapse of thesystem conditioned on IM .3.4 Repair or Replacement Costs EstimationFor each component loss functions are developed to estimate the cost of repair or costto replace each component. Loss functions are functions that provide information onthe probability of exceeding a certain level of repair or replacement cost given that thecomponent is in the damage measure, DM. Examples of these functions are given inAslani and Miranda (2004a).3.5 Modeling Correlation between Losses in Individual ComponentsEstimation of the correlation between losses in individual components requiresinformation on the correlation at three different levels; EDP | IM level, DM | EDPlevel and DV | DM level. The correlation at the response level, EDP | IM is estimatedbased on the results from nonlinear response history analyses. The correlation at thedamage level, DM | EDP, is mathematically modeled by categorizing componentsinto certain groups in terms of their damageability and estimating the joint probabilityof two components being at different damage states conditioned on the level ofdeformation each of them is subjected to. The correlation at the repair cost level, DV |DM, is estimated from the information on the correlation between different tasksrequired to repair the component.PFA 3, PFA roofρ EDPi,EDPj | IM, NC1.000.801.00.60 IDR 1, PFA 30.400.50.20IDR 1, IDR 30.00.000 10 20 30 40 50IM [S d (cm)]P(DM ki,DMkj|EDPi,EDP j)0.35Component iDM3| EDP iDM2| EDPi0.00.050.200.3DM1| EDP iComponentj0.0DM 1| EDPjDM 2| EDPjDM 3| EDPj0.00.100.0ρ (Li,Lj|DMki,DMkj,NC)1.00.50.0ColumnL | | DM 30.29L | | DM21.000.291.00L | | DM1Beam-column1.000.29L | DM 1 1Figure 6. Variations of the required parameters to estimate the correlation oflosses in individual components.L | DM2157
E [ L T| IM ]$10 M$8 M$6 M$4 Mσ [ L T| IM ]$10 M$8 M$6 M$4 MCorrelat edNon-correlat edν ( L T > $ )$2 M$2 M0.001(a) (b) (c)$0 M$0 M0.00010 20 40 60 80 100 0 20 40 60 80 100 $ 0 $ 4 $ 8 $ 12 $ 16IM [ S d(cm) ]IM [ S d(cm) ]L T [ million $ ]Figure 7. (a) Expected loss at different levels of intensity, (b) dispersion ofloss at different levels of intensity, (c) building loss curve.Figure 6 presents examples of each of the correlation at each of the above threelevel. Figure 6a shows how the correlation between different types of EDP varies asthe ground motion intensity increase. Shown in Figure 6b is an example of the jointprobability distribution of two components being at different damage states. Figure 6cshows the correlation between repair costs for a column and a beam-columnconnection.3.6 Building Loss EstimationFigure 7a presents the variations of the expected loss at different levels of intensity,E[L T |IM], estimated for the case study building. It can be seen that for this buildinglosses rapidly increase at small levels of ground motion intensity. Figure 7b presentsthe variations of the dispersion of the loss of the building with increasing level ofground motion intensity for two cases: when losses in individual components areassumed to be correlated and when they are assumed non-correlated. It can be seenthat correlation has significant effects on the uncertainty of the loss. For example, atS d =20 cm assuming that the losses are uncorrelated leads to an underestimation of25% of the dispersion of the loss.The loss curve for the case study building is shown in Figure 7c where it can beseen that losses smaller than $1,000,000 have relatively high mean annual frequenciesof exceedance.4. LOSS DEAGGREGATIONSimilarly to seismic hazard deaggregation (McGuire, 1995) building losses can alsobe disaggregated. In particular, it is interesting to investigate the ground motionintensities that most contribute to expected annual losses in a building. Figure 8provides three examples of loss deaggregation. Figure 8a presents the contribution ofcollapse and non-collapse expected loss to the total loss at different levels of intensity.It can be seen in the figure that at small levels of intensity, (S d
- Page 124 and 125: The future techniques will improve
- Page 126 and 127: Benefit-cost ratio(BCR) 2.5UC Berke
- Page 128 and 129: motivation to change the way they w
- Page 130 and 131: CHANGING THE PARADIGM FOR PERFORMAN
- Page 132 and 133: Ideally, the preliminary design of
- Page 134 and 135: ModelM1M2M3Table 1. Description of
- Page 136 and 137: Sample results from the response-hi
- Page 138 and 139: In FEMA 273/356, the intersection o
- Page 140 and 141: (M8 and M9) and the isolated frames
- Page 142 and 143: THE ATC-58 PROJECT PLAN FOR NONSTRU
- Page 144 and 145: The development of next-generation
- Page 146 and 147: for these flexible nonstructural co
- Page 148 and 149: spectra is several times larger tha
- Page 150 and 151: The variability is associated with
- Page 152 and 153: functions for a wide variety of non
- Page 154 and 155: SIMPLIFIED PBEE TO ESTIMATE ECONOMI
- Page 156 and 157: One can show (Porter et al. 2004) t
- Page 158 and 159: ( )FDM| EDP= xdm = 1 −FRdm , + 1,
- Page 160 and 161: 1. Facility definition. Same as in
- Page 162 and 163: Table 1. Approximation of seismic r
- Page 164 and 165: The EAL values shown in Figure 3 mi
- Page 166 and 167: ASSESSMENT OF SEISMIC PERFORMANCE I
- Page 168 and 169: where e -λτ is the discounted fac
- Page 170 and 171: IDR 3[rad]σPFAIDR34(g)σ PFA4media
- Page 172 and 173: Figure 3a, shows an example of frag
- Page 176 and 177: E [ L T | IM ]$ 10 M$ 8 M$ 6 M$ 4 M
- Page 178 and 179: SEISMIC RESILIENCE OF COMMUNITIES
- Page 180 and 181: 2. RESILIENCE CONCEPTSResilience fo
- Page 182 and 183: quantification tools could be used
- Page 184 and 185: structure remains elastic. This is
- Page 186 and 187: of Figure 7a will be used. It is as
- Page 188 and 189: Nigg, J. M. (1998). Empirical findi
- Page 190 and 191: acceleration with a 475-year return
- Page 192 and 193: limit states, the suggestions given
- Page 194 and 195: ∆NSLsi= SϑH(5)iTFor column-sway
- Page 196 and 197: Pinto et al., 2004). The probabilit
- Page 198 and 199: The main difficulty in assigning a
- Page 200 and 201: Crowley, H., R. Pinho, and J. J. Bo
- Page 202 and 203: analytical models generally have si
- Page 204 and 205: Figure 2. Structure of the response
- Page 206 and 207: can be used as a random variable of
- Page 208 and 209: 4. DERIVATION OF THE VULNERABILITY
- Page 210 and 211: 5. CONCLUSIONSDerivation of vulnera
- Page 212 and 213: REFERENCESAbrams, D. P., A. S. Elna
- Page 214 and 215: In general, these types of bench-mo
- Page 216 and 217: where & x&(t ) = acceleration at th
- Page 218 and 219: science building. The lateral load-
- Page 220 and 221: emain the same, the magnitude of sl
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P(C LVCC i |IM )1.00.80.60.40.20.00 20 40 60 80 100IM [ S d (cm) ]P(C LVCCi |IM )1.00.80.60.40.20.00 20 40 60 80 100IM [ S d (cm) ]P(C|IM)1.00.80.60.40.20.00 20 40 60 80 100IM [ S d (cm) ]Figure 5. Different steps <strong>of</strong> estimation <strong>of</strong> the probability <strong>of</strong> collapse <strong>of</strong> thesystem conditioned on IM .3.4 Repair or Replacement Costs EstimationFor each component loss functions are developed to estimate the cost <strong>of</strong> repair or costto replace each component. Loss functions are functions that provide information onthe probability <strong>of</strong> exceeding a certain level <strong>of</strong> repair or replacement cost given that thecomponent is in the damage measure, DM. Examples <strong>of</strong> these functions are given inAslani and Miranda (2004a).3.5 Modeling Correlation between Losses in Individual ComponentsEstimation <strong>of</strong> the correlation between losses in individual components requiresinformation on the correlation at three different levels; EDP | IM level, DM | EDPlevel and DV | DM level. The correlation at the response level, EDP | IM is estimatedbased on the results from nonlinear response history analyses. The correlation at thedamage level, DM | EDP, is mathematically modeled by categorizing componentsinto certain groups in terms <strong>of</strong> their damageability and estimating the joint probability<strong>of</strong> two components being at different damage states conditioned on the level <strong>of</strong>deformation each <strong>of</strong> them is subjected to. The correlation at the repair cost level, DV |DM, is estimated from the information on the correlation between different tasksrequired to repair the component.PFA 3, PFA ro<strong>of</strong>ρ EDPi,EDPj | IM, NC1.000.801.00.60 IDR 1, PFA 30.400.50.20IDR 1, IDR 30.00.000 10 20 30 40 50IM [S d (cm)]P(DM ki,DMkj|EDPi,EDP j)0.35Component iDM3| EDP iDM2| EDPi0.00.050.200.3DM1| EDP iComponentj0.0DM 1| EDPjDM 2| EDPjDM 3| EDPj0.00.100.0ρ (Li,Lj|DMki,DMkj,NC)1.00.50.0ColumnL | | DM 30.29L | | DM21.000.291.00L | | DM1Beam-column1.000.29L | DM 1 1Figure 6. Variations <strong>of</strong> the required parameters to estimate the correlation <strong>of</strong>losses in individual components.L | DM2157
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