Improving static pushover analysis by optimal bilinear fitting of capacity curves

Abstract

An improvement of codes’ bilinear fit for static pushover (SPO) curves is put forward aimed at decreasing the error introduced in the conventional SPO analysis by the piecewise linear fitting of the capacity curve. In the approach proposed herein, the error introduced by the bilinear fit of the force-deformation relationship is quantified by studying it at the single degree of freedom (SDOF) system level, away from any interference from multiple degree of freedom (MDOF) effects. Incremental Dynamic Analysis (IDA) is employed to enable a direct comparison of the actual curved backbones versus their piecewise linear approximations in terms of the spectral acceleration capacity for a continuum of limit-states, allowing an accurate interpretation of the results in terms of performance. A near-optimal elasticplastic bilinear fit can be an enhanced solution to decrease systematically the error introduced in the SPO analysis if compared to the fit approaches provided by most codes. The main differences are (a) closely fitting the initial stiffness of the capacity curve and (b) matching the maximum strength value, rather than disregarding them in favor of balancing areas or energies. Employed together with selective area discrepancy minimization, this approach reduces the conservative bias observed for systems with highly curved force-deformation backbones.