Response To: B. Maison's Discussion of “Evaluation of Modal and FEMA Pushover Analyses: SAC Buildings”

Abstract

The authors agree with the discusser that even improved pushover analysis procedures can be inaccurate for buildings deforming far into the inelastic range—in the region of negative post-yield stiffness with significant degradation of lateral capacity. However, estimates of seismic demands obtained by MPA were much better than from FEMA force distribution over a wide range of responses—from essentially elastic response of Boston buildings to strongly inelastic response of Los Angeles buildings. For a wide range of buildings and ground motions, MPA estimates of seismic demands were accurate enough relative to the results of nonlinear RHA to be useful in the seismic evaluation of buildings. The potential and limitations of every approximate analysis procedure, including the NSP used in current practice and MPA, should be documented so that the procedure is not used outside its range of applicability. This was one of the objectives of our paper. Because MPA is based on structural dynamics theory, it offers three theoretical advantages. First, when applied to elastic systems it is equivalent to standard response spectrum analysis (RSA) (Chopra and Goel 2002, 2004) available in commercial software used by the profession. Second, although modal pushover analysis theory is strictly not valid for inelastic systems, the fact that elastic modes are coupled only weakly in the response of inelastic systems to modal inertia forces (Chopra and Goel 2002, 2004) permitted development of MPA, an approximate procedure. Third, the theory and concepts underlying MPA are extendable to unsymmetric-plan buildings (Chopra and Goel 2004). Contrary to the discusser’s interpretation of MPA as ‘‘an intricate ten-step procedure,’’ MPA retains the conceptual simplicity of current NSP with invariant force distribution, now common in structural engineering practice. Because higher-mode pushover analyses are similar to the first-mode analysis, MPA is conceptually no more difficult than procedures now standard in structural engineering practice. Because pushover analyses for the first two or three modal force distributions are typically sufficient in MPA, it requires computational effort that is comparable to the FEMA-356 procedure,