Report - PEER - University of California, Berkeley

9BostonSeattleLos AngelesFloor63RSAMPA, P−∆ effectsExcludedIncluded9−StoryG0 0.5 1 1.5 220160 0.5 1 1.5 20 0.5 1 1.5 2Floor128420−StoryG0 0.5 1 1.5 20 0.5 1 1.5 2∆ * MPA or ∆* RSA0 0.5 1 1.5 2Figure 5. Median story drift ratios ∆ for two cases: P-∆ effects due togravity loads excluded or included and ∆ *RSAfor SAC buildings.4.2 Accuracy of MPAFor each of the six SAC buildings, Fig. 5 shows the median of r * MPA , the ratio ofresponse r computed by MPA and nonlinear RHA, for story drifts for two cases:gravity loads (and P-∆ effects) excluded or included; median values of r * RSA fromelastic analyses are also shown. The median value of r * RSA being less than oneimplies that the standard RSA procedure underestimates the median response ofelastic systems. Because the approximation in the RSA procedure for elastic systemsis entirely due to modal combination rules, the resulting bias serves as a baseline forevaluating additional approximations in MPA for inelastic systems. The additionalbias introduced by neglecting “modal” coupling in the MPA procedure depends onhow far the building is deformed in the inelastic range. The increase in bias isnegligible for both Boston buildings because they remain essentially elastic, slight forSeattle buildings because they are deformed moderately into the inelastic range, andsignificant for Los Angeles buildings, especially for the Los Angeles 20-storybuilding because it is deformed into the region of rapid deterioration of lateralcapacity, leading to collapse of its first-“mode” SDF system during six excitations.Because beam plastic rotations are directly related to story drifts, the MPA procedureis similarly accurate in estimating both demand quantities (Goel and Chopra, 2004a).The MPA procedure estimates member forces to similar or better accuracycompared to story drifts. Such comparative results are presented for bending moments*MPA339