Report - PEER - University of California, Berkeley

9Floor DisplacementsStory Drifts6Floor3NL−RHAMPACQCABSSUMG0 1 2 3 4 5Displacement/Height (%)0 1 2 3 4 5Story Drift Ratio (%)Figure 9. Responses at the right frame of unsymmetric-plan system U2determined by MPA using CQC and ABSSUM rules and nonlinear RHA.which the CQC modal combination rule is not valid. For such a case, the absolutesum (ABSSUM) rule may be more appropriate. Figure 9 shows that the “exact”demand is generally bounded by the two estimates determined by the MPA procedureusing two different modal combination rules, CQC and ABSSUM.The preceding scenario points to the need for evaluating the MPA procedureconsidering an ensemble of ground motions and documenting the bias and dispersionin this procedure applied to unsymmetric buildings, as has been accomplished forsymmetric buildings (Chopra and Goel, 2004a). Such a statistical investigation isnecessary for two reasons: First, the SRSS and CQC modal combination rules arebased on random vibration theory and are intended for use when the excitation ischaracterized by a smooth response (or design) spectrum. Second, accurate estimationof roof displacement is necessary for the success of any pushover procedure and thisusually is not assured for individual ground motions, as has been observed for the sixSAC buildings (Chopra et al., 2003). For the Los Angeles 9-story building, the ratioof roof displacement values determined by MPA and nonlinear RHA varied from 0.66to 1.70, with a median value of 1.21, over the 20 SAC ground motions.6. CONCLUDING COMMENTSBased on structural dynamics theory, the MPA procedure retains the conceptualsimplicity and computational attractiveness of the standard pushover procedures withinvariant lateral force distribution. Because higher-mode pushover analyses aresimilar to the first-mode analysis, MPA is conceptually no more difficult thanprocedures now standard in structural engineering practice. Because pushoveranalyses for the first two or three modal force distributions are typically sufficient inMPA, it requires computational effort that is comparable to the FEMA-356procedure, which requires pushover analysis for at least two force distributions.342