Seismic response of vertically irregular frames: Response history and modal pushover analyses

This study compares the seismic demands for vertically irregular and "regular" frames determined by rigorous nonlinear response history analysis (RHA), due to an ensemble of 20 ground motions. Forty-eight irregular frames, all 12-story high with strong columns and weak beams, were designed with three types of irregularities-stiffness, strength, and combined stiffness and strength-introduced in eight different locations along the height using two modification factors. The effects of vertical irregularity on the median values of story drifts and floor displacements are documented. Next, the median and dispersion values of the ratio of story drift demands determined by modal pushover analysis (MPA) and nonlinear RHA were computed to measure the bias and dispersion of MPA estimates leading to the following results: (1) the bias in the MPA procedure does not increase, i.e., its accuracy does not deteriorate, in spite of irregularity in stiffness, strength, or stiffness and strength provided the irregularity is in the middle or upper story, (2) the MPA procedure is less accurate relative to the regular frame in estimating the seismic demands of frames with strong or stiff-and-strong first story; soft, weak, or soft-and-weak lower half; stiff, strong, or stiff-and-strong lower half, (3) in spite of the larger bias in estimating drift demands for some of the stories in particular cases, the MPA procedure identifies stories with largest drift demands and estimates them to a sufficient degree of accuracy, detecting critical stories in such frames, and (4) the bias in the MPA procedure for frames with a soft, weak, or soft-and-weak first story is about the same as for the regular frame.