New equivalent damping for the ATC nonlinear static procedure

• Published in: Nuclear engineering and design Vol. 374; p. 111044
• Main Authors: Nguyen, Thuong Anh, Labbé, Pierre, Hervé-Secourgeon, Guillaume
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2021; Elsevier BV
• Subjects: Concrete; Concrete construction; Constitutive relationships; Damping; Degrees of freedom; Ductility; Elastoplastic oscillator; Equivalence; Equivalent linear concept; Frequency dependence; Maximum displacement; Non-dimensional frequency dependence; Oscillators; Resonant frequencies; Retrofitting; Secant stiffness; Seismic analysis; Seismic engineering; Seismic response; Stiffness; Technology assessment; Transient analysis; White noise; Elastoplastic oscillator; Equivalent linear concept; Non-dimensional frequency dependence; Secant stiffness; Maximum displacement
• ISSN: 0029-5493; 1872-759X
• DOI: 10.1016/j.nucengdes.2020.111044

•Combination of two equivalence criteria: secant stiffness and maximum displacement.•New equivalent damping derived from a systematic numerical analysis.•Key parameter of equivalent damping: non-dimensional frequency of oscillator f0fc.•Wide range of considered oscillator stiffness from f0fc = 0.1 to f0fc = 2.•Validation of new equivalent damping with real signals from the database RESORCE.•Ductile range of validation is up to 20. The Nonlinear Static Procedure, also known in the literature as Pushover Analysis procedure or Capacity Spectrum Method (CSM), is mainly developed in the report of Applied Technology Council entitled “Seismic evaluation and retrofit of concrete buildings” ATC (1996). This is a widely practical engineering method to calculate the seismically induced ductility demand of a System, Structure or Component (SSC) without performing nonlinear transient analyses. Many authors have improved this method by introducing different equivalent linear concepts. However, discrepancy between predictive results by CSM and references obtained by transient nonlinear analyses remains quite important. In this paper, we present a new equivalent linear concept, in which the conventional equivalent frequency corresponding to the secant stiffness is adopted, and new equivalent damping value is calibrated so that the maximum displacement of equivalent linear oscillator is the same as the one of nonlinear oscillator. The new proposed damping values are derived from systematic analysis of the response of a series of nonlinear single degree of freedom (SDOF) oscillators to seismic type input motions. Oscillators have a bilinear elastic–plastic constitutive relationship with a hardening slope equal to 10% or 20% of the initial stiffness. Their natural frequency (f0) is such that f0/fc varies between 0.1 and 2.0, where fc is the central frequency of the input signal and their damping in elastic regime remained at 5%. Input motion is a set of one thousand synthetic filtered white noise signals. The novelty of the proposed approach is that new equivalent damping values exhibit strong frequency dependence on the f0/fc ratio, which has not been discussed so far. In order to validate the proposed equivalent linear concept, predictive results for nonlinear SDOF oscillators undergoing one hundred natural signals are performed by CSM with the new equivalent damping values and compared to reference results obtained from nonlinear transient analyses. It is concluded that the CSM using the new proposed equivalent damping values can determine the seismically induced ductility demand of SDOF oscillators with a better accuracy than methods used at the moment as a routine.