Report - PEER - University of California, Berkeley
Report - PEER - University of California, Berkeley Report - PEER - University of California, Berkeley
The main difficulty in assigning a probability distribution to the yield strength ofthe steel used in a group of buildings, however, is the possibility that different gradeshave been used, which would lead to a distribution with multiple peaks and troughs(see Crowley et al., 2004). One approach to solve this problem could be to calculatethe probability of failure for the building class given each possible steel grade, usingthe normal distribution to model the dispersion for each grade, and then to compute aweighted average of failure, knowing or judging the use of each steel grade within thebuilding class. The validity of such an approach would become questionable,however, if different steel grades were often used within individual buildings.3.2.3 Probabilistic Modelling of Limit States Threshold ParametersDymiotis et al. (1999) have studied the seismic reliability of RC frames usinginterstorey drift to define the serviceability and ultimate structural limit states. Theyhave found that a lognormal distribution may be used to describe the variability ininterstorey drift for both limit states. Therefore, the variability in non-structural limitstates, defined in this work as a function of interstorey drift limiting values, will berepresented by means of lognormal distributions, using the mean drift ratios that havebeen suggested by Crowley et al. (2004).Kappos et al. (1999), on the other hand, report the ultimate concrete strainreached in 48 tests of very well-confined RC members. A simple statistical analysis ofthis data shows that it would appear that in the case of limit state sectional strains alognormal distribution is also able to describe the variability of these parameters.Hence, and since for the structural limit states it is the sectional steel and concretestrains that define respective boundaries, it would appear that a lognormal distributionmay also be applied to describe the variability in these limit state parameters. Again,the mean values suggested by Crowley et al. (2004) are employed, in tandem withassumed coefficients of variation.3.2.4 Probabilistic Modelling of Scatter in Empirical RelationshipsA number of empirical relationships have been used to derive the functions ofdisplacement capacity and period that have been presented in Section 2. Theseinclude empirical expressions for the plastic hinge length members and the yieldcurvature of RC members, all of which are discussed in Glaister and Pinho (2003),and an additional empirical parameter employed in the formula derived by Crowleyand Pinho (2004) to relate the height of a building to its yield period. All of theaforementioned relationships rely on empirical coefficients to relate one set ofstructural properties to another, as for example the coefficient of 0.1 in the yieldperiod vs. height equation, T y = 0.1H T . The mean value and standard deviation ofthese coefficients have been taken from the studies carried out to derive thoseformulae, with a normal distribution being used to model the respective dispersion.182
4. CONCLUSIONSOwing to its transparency, theoretical accuracy and computational efficiency, theprocedure presented herein is particularly suitable for loss estimation studies. Thedefinition of the displacement capacity is transparent as one may use any chosennumber of storeys, geometrical, material or limit state threshold properties in theequations and adapt these easily for use in any part of the world. The conceptualsoundness of the methodology has been preliminarily examined by Crowley et al.(2004) through a comparison of vulnerability curves derived using this procedure andthose provided in HAZUS; the curves derived using the proposed method led to morerealistic vulnerability models which appear to be consistent with field observationsfollowing destructive earthquakes. Finally, the large decrease in computational effortrequired for earthquake loss estimations for scenario events due to the directconsideration of the ground motion uncertainty is also a significant advantage of theproposed methodology.The above effectively means that the method does cater for rigorous, scenariobasedapproaches that can be applied to large areas within a reasonable timescale. Inthis manner, it will be possible for iterative loss assessment studies to be carried outfor a given urban area under events with varying return periods and assumingdifferent levels of building stock vulnerability, considering the effects, along withrespective costs, of different design code requirements and/or structural upgradingpolicies. The above could provide politicians, planners and code drafters withquantitative information to inform and guide their decisions, thus allowing thecalibration of local regulations for optimum balance between societal investment andpublic risk, rather than being based on pre-selected return periods whose basis issomewhat arbitrary.REFERENCESBommer, J. J. (2004). Earthquake actions in seismic codes: can current approachesmeet the needs of PBSD? This volume.Bommer, J. J., A. S. Elnashai, and A. G. Weir. (2000). Compatible acceleration anddisplacement spectra for seismic design codes. Proceedings 12 th WorldConference on Earthquake Engineering, Auckland, New Zealand, Paper no. 207.Calvi, G. M. (1999). A displacement-based approach for vulnerability evaluation ofclasses of buildings. Jrnl Earthqu. Eng. 3(3), 411-438.Comité Européen de Normalisation (2003) Eurocode 8, Design of Structures forEarthquake Resistance – Part 1: General rules, seismic actions and rules forbuildings, Pr-EN 1998-1. Final Draft. December 2003.Crowley, H., and R. Pinho. (2004). Period-height relationship for existing Europeanreinforced concrete buildings. Jrnl Earthqu. Eng. 8(SP1).183
- 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
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- 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
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- 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 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 212 and 213: REFERENCESAbrams, D. P., A. S. Elna
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- Page 220 and 221: emain the same, the magnitude of sl
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- Page 224 and 225: Retrofit of Nonstructural Component
- Page 226 and 227: was developed to accommodate these
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4. CONCLUSIONSOwing to its transparency, theoretical accuracy and computational efficiency, theprocedure presented herein is particularly suitable for loss estimation studies. Thedefinition <strong>of</strong> the displacement capacity is transparent as one may use any chosennumber <strong>of</strong> storeys, geometrical, material or limit state threshold properties in theequations and adapt these easily for use in any part <strong>of</strong> the world. The conceptualsoundness <strong>of</strong> the methodology has been preliminarily examined by Crowley et al.(2004) through a comparison <strong>of</strong> vulnerability curves derived using this procedure andthose provided in HAZUS; the curves derived using the proposed method led to morerealistic vulnerability models which appear to be consistent with field observationsfollowing destructive earthquakes. Finally, the large decrease in computational effortrequired for earthquake loss estimations for scenario events due to the directconsideration <strong>of</strong> the ground motion uncertainty is also a significant advantage <strong>of</strong> theproposed methodology.The above effectively means that the method does cater for rigorous, scenariobasedapproaches that can be applied to large areas within a reasonable timescale. Inthis manner, it will be possible for iterative loss assessment studies to be carried outfor a given urban area under events with varying return periods and assumingdifferent levels <strong>of</strong> building stock vulnerability, considering the effects, along withrespective costs, <strong>of</strong> different design code requirements and/or structural upgradingpolicies. The above could provide politicians, planners and code drafters withquantitative information to inform and guide their decisions, thus allowing thecalibration <strong>of</strong> local regulations for optimum balance between societal investment andpublic risk, rather than being based on pre-selected return periods whose basis issomewhat arbitrary.REFERENCESBommer, J. J. (2004). Earthquake actions in seismic codes: can current approachesmeet the needs <strong>of</strong> PBSD? This volume.Bommer, J. J., A. S. Elnashai, and A. G. Weir. (2000). Compatible acceleration anddisplacement spectra for seismic design codes. Proceedings 12 th WorldConference on Earthquake Engineering, Auckland, New Zealand, Paper no. 207.Calvi, G. M. (1999). A displacement-based approach for vulnerability evaluation <strong>of</strong>classes <strong>of</strong> buildings. Jrnl Earthqu. Eng. 3(3), 411-438.Comité Européen de Normalisation (2003) Eurocode 8, Design <strong>of</strong> Structures forEarthquake Resistance – Part 1: General rules, seismic actions and rules forbuildings, Pr-EN 1998-1. Final Draft. December 2003.Crowley, H., and R. Pinho. (2004). Period-height relationship for existing Europeanreinforced concrete buildings. Jrnl Earthqu. Eng. 8(SP1).183
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