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years. Using theSaR Sa0.5index the probability roughly doubles to a mean annual value of0.00009 or roughly a 0.5% in 50-year level. Since these probabilities are less than one-forth ofthe 2% in 50-year seismic hazard probability commonly used as the target for collapseprevention performance, these data suggest that current code provisions result in a conservativedesign for this case. Moreover, the failure probabilities are less by about a factor of five usingthe PSHA intensity data, implying an additional degree of conservatism in the design.Another interesting question raised by the results in Table 3 concerns the different resultsobtained using the S aT ) versus( 1aR Sa0.5S index. The fact that the two-parameter index resultsin higher failure probabilities suggests that for predicting collapse performance, simple scalingbased on S aT ) may be unconservative. This follows from the logic that the two-parameter( 1index more accurately represents the damaging effects of earthquakes in the hazard curve. Note,however, that the difference between the two indices is not too large for the Yerba Buena siteanalysis (PSHA) where the correlation between S a (T 1 ) and S a (T f ) is modeled more accuratelythan in the code-based technique.Table 3 – Failure probability and capacity factor design factorsYerba Buena Site Code Based TechniqueProbability of P f (S a (T 1 )) 1.19 x 10 -5 5.37 x 10 -5Failure P f (S a R 0.5 Sa ) 1.24 x 10 -5 9.29 x 10 -5IM = T )IM =S a( 1SaR Sa0.5φ 0.78 0.82φµ λf 1.13g 1.19g10%in50year 0.41g 0.48g2%in50year 0.56g 0.72gφ 0.94 0.96φµ λf 0.72g 0.73g10%in50year 0.30g 0.34g2%in50year 0.40g 0.51gFactored Capacity versus Nominal DemandAn alternate way of assessing the analysis results is through the LRFD-like approach describedby Eq. 17. Data for this method are summarized in the lower half of Table 3, where limitingvalues are reported for 2% in 50-year (0.0004) and 10% in 50-year (0.002) probability levels.Referring to Table 3, the φ factor ranges from φ = 0.78 to 0.82 for the S aT ) index and from( 1φ = 0.94 to 0.96 for theSaR Sa0.5index. The large difference between these ranges is directly18
elated to the reduced dispersion achieved using the two-parameter Sthe S aT ) index.( 1aR Sa0.5index as compared toAccording to the criteria, φ ˆ ≥ IM , the frame collapse performance limit passes the 2%µ λf P acceptanc ein 50-year and 10% in 50-year probability checks in all cases. These comparisons do reflect therelative difference in results between the S aT ) and( 1SaR Sa0.5indices that is similar to thedifference observed in the failure probabilities described previously. For example, consider theˆ λratio φ µ / IM between the factored capacity and the hazard intensity. Using data fromf P acceptanc ethe Yerba-Buena PSHA at the 2% in 50-year level, the ratios are φ ˆ / Sa2%in50= 1.13/0.56 =µ λ f2.0 for the S a( T 1) index and φ ˆ / SaR Sa 2% in50µ λ f= 0.72/0.4 = 1.8 for theaR Sa0.5S index.8. SUMMARY AND CONCL<strong>US</strong>IONSA method to assess seismic response and probabilistic collapse performance of structures ispresented and demonstrated by application to a composite moment frame building. Included is aproposal for a new two-parameter earthquake hazard intensity measureaR Sa0.5S that reflectsboth spectral intensity and spectral shape, thus accounting for inelastic strength and stiffnessdegradation (period elongation). Data are presented which show that this proposed indexsignificantly reduces the record-to-record variability in predicted response obtained frominelastic time history analyses. This has practical implications on improving the accuracy ofseismic assessment methods and reducing the number of records necessary to obtain a givenconfidence in the results.Equations are developed to interpret the probability of collapse using data from incrementeddynamic analyses. The equations are presented in two formats, one that directly computes theprobability of failure for a structure, and another, which mimics an LRFD format by applying a“phi-factor” to the capacity of the structure and comparing it to a specified hazard.19
Page 1 and 2: DEVELOPMENT OF A TWO-PARAMETER SEIS
Page 3 and 4: development of seismic hazard maps
Page 5 and 6: S a( T f) . Inoue (1990) provides t
Page 7 and 8: 6 @ 4m = 24mW530x92W610x101W610x101
Page 9 and 10: While the two-parameter index reduc
Page 11 and 12: significantly degrade. This point,
Page 13 and 14: already low when scaled by spectral
Page 15 and 16: whereIM is the hazard intensity mea
Page 17: 1e-1IBC CodeY-B PSHA1e-1IBC CodeY-B

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