Stochastic Finite Element Analysis of Frame Structures Subjected to Seismic Actions

Abstract eng:
The majority of existing methods for the assessment of the dynamic response variability of structures with uncertain system properties are usually limited to linear elastic analysis considering only monotonic loading. In the framework of the stochastic finite element method [1], an efficient approach has been recently introduced by the authors for the analysis of frame structures subjected to transient seismic actions [2]. This approach is used here to assess the nonlinear stochastic response and reliability of a steel moment-resisting frame. The frame is modeled with a mixed fiber-based, beam-column element, whose kinematics is based on the natural mode method [3]. The uncertain parameters of the problem are the stiffness and strength, both described by homogeneous nonGaussian translation stochastic fields [4]. The frame is subjected to natural ground motion records corresponding to three levels of increasing seismic intensity as well as to power spectrum-compatible stochastic accelerograms. The response variability of the frame is computed using Monte Carlo simulation. Probabilities of the demand, expressed in terms of various engineering demand parameters-EDPs (displacements, forces) exceeding given thresholds, are calculated. Moreover, the effect of the correlation structure of the stochastic fields (describing the two uncertain parameters) on the response variability is investigated using two spectral density functions with spectral power concentrated at zero wave number and also shifted away from it. Finally, useful conclusions are provided regarding the influence of the correlation length (correlation scale) of the stochastic fields on the response variability and reliability. The COV of the EDPs and the reliability are found to vary significantly not only with the correlation length but also in many different ways among the records of the same intensity level. These observations underline the importance of realistic uncertainty quantification and can serve as guidelines in structural analysis and design. References [1] G. Stefanou, The stochastic finite element method: past, present and future. Computer Methods in Applied Mechanics and Engineering, 198, 1031-1051, 2009. [2] G. Stefanou, M. Fragiadakis, Nonlinear dynamic analysis of frames with stochastic nonGaussian material properties. Engineering Structures, 31, 1841-1850, 2009. [3] A. Papachristidis, M. Fragiadakis, M. Papadrakakis, A 3D fiber beam-column element with shear modeling for the inelastic analysis of steel structures. Computational Mechanics, 45, 553-572, 2010. [4] M. Grigoriu, Simulation of stationary non-Gaussian translation processes. J. of Engineering Mechanics (ASCE), 124, 121-126, 1998.

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