An Approximate Approach for Efficient Stochastic Incremental Dynamic Analysis

Abstract eng:
Incremental dynamic analysis (IDA) has been a well-established methodology in earthquake engineering for assessing the performance of structural systems under a suite of ground motion records, each scaled to several levels of seismic intensity. Nevertheless, the need for performing nonlinear dynamic analyses both for various excitation magnitudes and for a large number of seismic records renders the IDA methodology potentially a computationally highly demanding task. In this paper, an efficient stochastic IDA methodology for nonlinear/hysteretic oscillators is developed by resorting to nonlinear stochastic dynamics concepts and tools such as stochastic averaging and statistical linearization. Specifically, modeling the excitation as a non-stationary stochastic process possessing an evolutionary power spectrum (EPS), an approximate closedform expression is derived for the parameterized oscillator response amplitude probability density function (PDF) as a function of the excitation EPS intensity magnitude. In this regard, an IDA surface is determined providing the PDF of the engineering demand parameter (EDP) for a given intensity measure (IM) value. In contrast to an alternative Monte Carlo simulation (MCS) based determination of the IDA surface, the herein developed methodology determines the EDP PDF at minimal computational cost. Note that the technique can account for physically realistic excitation models possessing not only time-varying intensities but time-varying frequency contents as well. Numerical examples include a bilinear/hysteretic single-degree-of-freedom (SDOF) oscillator, whereas comparisons with pertinent MCS data demonstrate the reliability of the developed stochastic IDA methodology.

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