Damping‐adjusted combination rule for the response spectrum analysis of base‐isolated buildings

Abstract

SUMMARY The classical response spectrum method continues to be the most popular approach for designing base‐isolated buildings, therefore avoiding computationally expensive nonlinear time‐history analyses. In this framework, a new method for the seismic analysis and design of building structures with base isolation system (BIS) is formulated and numerically validated, which enables one to overcome the main shortcomings of existing techniques based on the response spectrum method. The main advantages are the following: first, reduced computational effort with respect to an exact complex‐valued modal analysis, which is obtained through a transformation of coordinates in two stages, both involving real‐valued eigenproblems; second, effective representation of the damping, which is pursued by consistently defining different viscous damping ratios for the modes of vibration of the coupled BIS‐superstructure dynamic system; and third, ease of use, because a convenient reinterpretation of the combination coefficients leads to a novel damping‐adjusted combination rule, in which just a single response spectrum is required for the reference value of the viscous damping ratio. The proposed approach is specifically intended for design situations where (i) the dynamic behaviour of seismic isolators can be linearised and (ii) effects of nonproportional damping, as measured by modal coupling indexes, are negligible in the BIS‐superstructure assembly. Copyright © 2012 John Wiley & Sons, Ltd.

Closed-form stochastic response of linear building structures to spectrum-consistent seismic excitations

“…In this section, for demonstration purposes, a base-isolated building taken from Ref. [42] is analyzed as case study.…”

“…Detailed information on the spatial distribution of mass and stiffness can be found in Ref. [42] and, as much as possible, a notation consistent with Ref. [42] has been adopted in what follows.…”

“…SMs are first derived as functions of the parameters defining both the SDOF (single-degree-of-freedom) oscillators and the RS; then, direct and cross SMs of order up to two are obtained in closed-form for MDOF systems. Finally, these expressions are applied to the case of multi-story base-isolated buildings by applying a convenient double modal transformation of coordinates [42]. The proposed formulae are validated against MCS.…”

Base Isolation for Seismic Retrofitting of a Multiple Building Structure: Design, Construction, and Assessment

“…The complex mode superposition can give several advantages for the evaluation of seismic response, and it was found to be competitive in terms of computational effort with direct integration methods [41]. As an alternative, Muscolino et al [42] proposed an improved response spectrum method (RSM) for the seismic analysis and design of building structures with base isolation system. This method consists of a two-stage transformation of coordinates in parallel with a Damping-Adjusted Combination (DAC) rule.…”

Base Isolation for Seismic Retrofitting of a Multiple Building Structure: Evaluation of Equivalent Linearization Method

“…Thus, it may lead to unacceptable inaccuracies when the modal frequencies of the structure are close to each other (e.g., in the first three rigid-body modes for base-isolated buildings). In order to overcome these problems, Muscolino et al [21] proposed an improved Response Spectrum Method based on a two-stage transformation of coordinates in parallel with a Damping-Adjusted Combination (DAC) rule. As far as the response history analysis is concerned, it must be observed that the baseisolated structures are typically nonlinear and nonclassically damped systems.…”