Report - PEER - University of California, Berkeley

5. EVALUATION OF MPA: UNSYMMETRIC-PLAN BUILDINGSComputed were the seismic demands resulting from one of the SAC ground motionsfor the SAC-Los Angeles 9-story building, a symmetric-plan system, and three masseccentricsystems, U1, U2, and U3, with different degrees of coupling between lateraland torsional motions as characterized by different values of the ratio of uncoupledlateral and torsional vibration periods. Figure 8 shows the story drifts at the right edgeof the building plan including a variable number of “modal” pairs (or “modes” forsymmetric building) in MPA superimposed with the “exact” result from nonlinearRHA. The first “modal” pair (“mode” for symmetric systems) alone is inadequate inestimating the story drifts, especially in the upper stories of the building, but with two“modal” pairs included, story drifts estimated by MPA are quite accurate.For the excitation considered, the MPA results are accurate for two unsymmetricsystems, U1 and U3, to a similar degree as they were for the symmetric building,which is apparent by comparing Figs. 8b and d with Fig. 8a; however, the results areless accurate for system U2 (Fig. 8c). Chopra and Goel (2004) demonstrated that thisloss of accuracy is not because the system has very close natural periods and strongcoupling of the lateral and torsional motions in each mode of vibration but becausethe roof displacement of system U2 due to the selected ground motion is considerablyunderestimated in the MPA procedure. This discrepancy occurs because theindividual “modal” responses attain their peaks almost simultaneously, a situation for9(a)(b)6Floor3NL−RHAMPA1 "Mode"2 "Modes"3 "Modes"G0 1 2 3 4 5NL−RHAMPA1 "Pair"2 "Pairs"3 "Pairs"0 1 2 3 4 5Floor963(c)NL−RHAMPA1 "Pair"2 "Pairs"3 "Pairs"G0 1 2 3 4 5Story Drift Ratio (%)NL−RHAMPA1 "Pair"2 "Pairs"3 "Pairs"(d)0 1 2 3 4 5Story Drift Ratio (%)Figure 8. Story drifts determined by MPA with variable number of “modal”pairs (or modes) and nonlinear RHA: (a) symmetric building; (b), (c), and(d) unsymmetric-plan systems U1, U2, and U3.341