Statistics of Single-Degree-of-Freedom Estimate of Displacement for Pushover Analysis of Buildings

Investigated is the basic premise that the roof displacement of a multistory building can be determined from the deformation of a single-degree-of-freedom (SDF) system. The responses of both systems are determined rigorously by nonlinear response history analysis, without introducing any of the approximations underlying the simplified methods for estimating the deformation of a SDF system (see, e.g., FEMA-273 or ATC-40 guidelines). The statistics of the SDF system estimate of roof displacement are presented for a variety of generic frames and six SAC buildings subjected to ground motion ensembles. Data obtained for generic frames indicate that the first “mode” SDF system overestimates the median roof displacement for systems subjected to large ductility demand μ, but underestimates for small μ. The bias and dispersion tend to increase for longer period system for every value of μ. Similar data for SAC buildings demonstrate that the bias and dispersion on the SDF estimate of roof displacement increases when P-delta effects (due to gravity loads) are included. The modal pushover analysis procedure has the advantage of reducing the dispersion in the roof displacement and the underestimation of the median roof displacement for elastic or nearly elastic cases at the expense of increasing slightly the overestimate of roof displacement of buildings responding far into the inelastic range.