Probabilistic Evaluation of Seismic Demand for Inelastic Multi-Story Regular Frames Using Multivariate Non-Linear Regressions

Abstract eng:
The prediction of structural demand is of great importance for seismic performance based design. The evaluation of the building’s structural performance includes parameters which characterize the intensity of the ground motion (IMs) correlated with engineering demand parameters (EDPs). The paper presents a study on the variability reduction of the EDPs that are expressed as a function of a vector of IMs. The multivariate nonlinear regression is used for estimation of the correlation between IMs and EDPs. Because a single IM parameter proved not to be enough to estimate different EDPs with sufficient accuracy, a set of two IM parameters were considered: the spectral acceleration at the fundamental period of vibration, SA(T1), and the ratio between the spectral acceleration at the second period of vibration and the spectral acceleration at the fundamental period of vibration, SA(T2)/SA(T1). The second parameter was introduced in order to capture the influence of the second vibration mode. The considered EDPs are: Maximum Interstory Drift Ratio, Roof Drift Ratio, Average Interstory Drift Ratio and Peak Inter-story Drift Ratio. The study was conducted on a family of 2D one-bay regular multi-story frame structures having some main characteristics: (i) the mass is constant at all floor levels; (ii) the bay is two times larger than the story height; (iii) the moment of inertia is the same for the columns in a story and the beam above them; (iv) the first mode shape is a straight line; (v) the fundamental period is equal with 0.1N and/or 0.2N; (vi) frames are designed so that simultaneous yielding is attained under a parabolic, linear and uniform load pattern; (vii) hysteretic behavior at the component level is modeled using a bi-linear model with 3% strain hardening in the moment-rotation relationship; (viii) for the non-linear time history analysis, 5% Rayleigh damping is assigned for the first 2 modes of vibration. The efficiency of using a vector of IMs to evaluate the EDPs for regular structures having a significant influence of the higher modes on their total response is shown.

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