Report - PEER - University of California, Berkeley
Report - PEER - University of California, Berkeley Report - PEER - University of California, Berkeley
acceleration with a 475-year return period for the life-safety limit state of non-criticalbuildings). The rationale underlying the current endeavour is that the definition ofsuch pairs of design and performance levels should instead be based on cost-benefitconsiderations derived from reliable and computationally efficient loss models,which, at their core, feature sound deformation-based principles and procedures thatlead to an explicit and accurate account of structural performance.This paper describes the first efforts in developing such a loss model, where thedistribution of damage states across a particular class of buildings at a specificlocation and for any given earthquake ground motion can be readily estimatedthrough a set of analytically derived relationships that correlate building displacementcapacity and height, which in turn can be related to displacement demand.1.2 Proposed MethodologyA new approach to displacement-based assessment of structural vulnerability ofreinforced concrete moment resisting frames has been proposed by Pinho et al. (2002)and subsequently developed in a deterministic framework by Glaister and Pinho(2003). Crowley et al. (2004) refined the approach and extended it into a fullyprobabilistic framework that incorporates the variability in the parameters that defineboth the demand and the capacity.The procedure uses mechanically-derived formulae to describe the displacementcapacity of classes of buildings at three different limit states. These equations aregiven in terms of material and geometrical properties, including the average height ofbuildings in the class. By substitution of this height through a formula relating heightto the limit state period, displacement capacity functions in terms of period areattained; the advantage being that a direct comparison can now be made at any periodbetween the displacement capacity of a building class and the displacement demandpredicted from a response spectrum.displacementLS3LS2LS1η LS1η LS2P LS1cumulativefrequencyPLSi – percentage ofbuildings failing LSiη LS3PLS2DemandSpectraP LS3T LS3T LS2T LS1effectiveperiod0H LS3H LS2H LS1HeightH LSi = f (T Lsi , LSi)Figure 1. A deformation-based seismic vulnerability assessment procedure.174
The original concept is illustrated in Figure 1, above, whereby the range of periodswith displacement capacity below the displacement demand is obtained andtransformed into a range of heights using the aforementioned relationship betweenlimit state period and height. This range of heights is then superimposed on to thecumulative distribution function of building stock to find the proportion of buildingsfailing the given limit state. The inclusion of a probabilistic framework into themethod, however, has meant that the simple graphical procedure outlined in Figure 1that treated the beam- or column-sway RC building stock as single building classescan no longer be directly implemented, but instead, separate building classes based onthe number of storeys need to be defined, as noted in subsequent sections.2.1 Classification of Buildings2. DETERMINISTIC IMPLEMENTATIONThe initial step required in this method is the division of the building population intoseparate building classes. A building class is to be considered as a group of buildingsthat share the same construction material, failure mechanism and number of storeys;e.g., reinforced concrete moment resisting frames of 3 to 5 storeys, exhibiting a beamswayfailure mode. A decision regarding whether a moment resisting frame willexhibit a beam-sway or a column-sway mechanism may be made considering theconstruction type, construction year and presence of a weak ground floor storey.2.2 Structural and Non-Structural Limit StatesDamage to the structural (load-bearing) system of the building class is estimatedusing three limit states of the displacement capacity. The building class may thus fallwithin one of four discrete bands of structural damage: none to slight, moderate,extensive or complete. A qualitative description of each damage band for reinforcedconcrete frames is given in the work by Crowley et al. (2004) along with quantitativesuggestions for the definition of the mechanical material properties for each limitstate, taken from the work of Priestley (1997) and Calvi (1999).Damage to non-structural components within a building can be considered to beeither drift- or acceleration-sensitive (Freeman et al., 1985; Kircher et al., 1997).Drift-sensitive non-structural components such as partition walls can becomehazardous through tiles and plaster spalling off the walls, doors becoming jammedand windows breaking. Acceleration-sensitive non-structural components includesuspended ceilings and building contents. At present, only drift-sensitive nonstructuraldamage is considered within this methodology, using three limit states ofdrift capacity. Interstorey drift can be used to predict drift-sensitive non-structuraldamage. Freeman et al. (1985) report that studies on dry wall partitions indicate aninitial damage threshold at a drift ratio of 0.25%, and a threshold for significantdamage at drift ratios between 0.5 to 1.0%. However, to ensure three non-structural175
- 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 174 and 175: P(C LVCC i |IM )1.00.80.60.40.20.00
- 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 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
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- 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
- Page 222 and 223: of sliding thresholds, are desirabl
- Page 224 and 225: Retrofit of Nonstructural Component
- Page 226 and 227: was developed to accommodate these
- Page 228 and 229: tested by Meinheit and Jirsa are us
- Page 230 and 231: where D is the maximum drift and N
- Page 232 and 233: in predicting damage as well as rep
- Page 234 and 235: 4.2.2 Modeling the Data Using Stand
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acceleration with a 475-year return period for the life-safety limit state <strong>of</strong> non-criticalbuildings). The rationale underlying the current endeavour is that the definition <strong>of</strong>such pairs <strong>of</strong> design and performance levels should instead be based on cost-benefitconsiderations derived from reliable and computationally efficient loss models,which, at their core, feature sound deformation-based principles and procedures thatlead to an explicit and accurate account <strong>of</strong> structural performance.This paper describes the first efforts in developing such a loss model, where thedistribution <strong>of</strong> damage states across a particular class <strong>of</strong> buildings at a specificlocation and for any given earthquake ground motion can be readily estimatedthrough a set <strong>of</strong> analytically derived relationships that correlate building displacementcapacity and height, which in turn can be related to displacement demand.1.2 Proposed MethodologyA new approach to displacement-based assessment <strong>of</strong> structural vulnerability <strong>of</strong>reinforced concrete moment resisting frames has been proposed by Pinho et al. (2002)and subsequently developed in a deterministic framework by Glaister and Pinho(2003). Crowley et al. (2004) refined the approach and extended it into a fullyprobabilistic framework that incorporates the variability in the parameters that defineboth the demand and the capacity.The procedure uses mechanically-derived formulae to describe the displacementcapacity <strong>of</strong> classes <strong>of</strong> buildings at three different limit states. These equations aregiven in terms <strong>of</strong> material and geometrical properties, including the average height <strong>of</strong>buildings in the class. By substitution <strong>of</strong> this height through a formula relating heightto the limit state period, displacement capacity functions in terms <strong>of</strong> period areattained; the advantage being that a direct comparison can now be made at any periodbetween the displacement capacity <strong>of</strong> a building class and the displacement demandpredicted from a response spectrum.displacementLS3LS2LS1η LS1η LS2P LS1cumulativefrequencyPLSi – percentage <strong>of</strong>buildings failing LSiη LS3PLS2DemandSpectraP LS3T LS3T LS2T LS1effectiveperiod0H LS3H LS2H LS1HeightH LSi = f (T Lsi , LSi)Figure 1. A deformation-based seismic vulnerability assessment procedure.174
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