Abstract
In this paper, a simplified method is proposed to estimate the peak inter-story drift ratios of steel frames with hysteretic dampers. The simplified method involved the following: (1) the inelastic spectral displacement is estimated using a single-degree-of-freedom (SDOF) system with multi-springs, which is equivalent to a steel frame with dampers and in which multi-springs represent the hysteretic behavior of dampers; (2) the first inelastic mode vector is estimated using a pattern of story drifts obtained from nonlinear static pushover analysis; and (3) the effects of modes higher than the first mode are estimated by using the jth modal period, jth mode vector, and jth modal damping ratio obtained from eigenvalue analysis. The accuracy of the simplified method is estimated using the results of nonlinear time history analysis (NTHA) on a series of three-story, six-story, and twelve-story steel moment resisting frames with steel hysteretic dampers. Based on the results of a comparison of the peak inter-story drift ratios estimated by the simplified method and that computed via NTHA using an elaborate analytical model, the accuracy of the simplified method is sufficient for evaluating seismic demands.
Highlights
Previous studies conducted over the past two decades have proposed energy dissipation systems that use displacement-dependent dampers and/or velocity-dependent dampers [1]
The accuracy of the simplified method is expressed by the following: (i) its bias denoted as a that is calculated by the median of the ratio of the peak inter-story drift ratio θiP, which is estimated by the simplified method, with respect to the corresponding peak inter-story drift ratio θi, which is computed via nonlinear time history analysis (NTHA) using the elaborate analytical model; and (ii) its dispersion denoted as σ that is calculated by the standard deviation of the natural logarithms of θiP /θi
With respect to the first mode, the inelastic spectral displacement of a steel frame with dampers is estimated by using an equivalent inelastic SDOF system that includes multi-springs in order to consider the hysteretic behavior of dampers, and the inelastic mode vector is estimated by using a pattern of story drifts that is obtained from nonlinear static pushover analysis (NSPA) of a steel frame with dampers with a lateral load pattern based on the first mode vector
Summary
Previous studies conducted over the past two decades have proposed energy dissipation systems that use displacement-dependent dampers and/or velocity-dependent dampers [1]. An energy-based design procedure based on achieving a balance between the mean energy dissipated per cycle by a structure and that dissipated by dampers was developed for the seismic retrofitting of existing buildings [3]. To determine the optimal damper volume related to seismic performance, extant studies have used a performance curve (called as performance spectra) for an elastic system [9,10] and an inelastic system [2,11,12,13] in the design process of buildings with dampers These studies have not considered the turn from an elastic mode vector to an inelastic mode vector caused by the yielding of a main structure.
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