Probabilistic Hazard Model of Inelastic Oscillator based on Equivalent Linearization Technique

Abstract eng:
Predictors of seismic structural demands that are less time consuming than nonlinear dynamic analysis (NDA) are useful for structural performance assessment and design. Several techniques for realizing such predictors have been proposed using the results of a nonlinear static pushover analysis. These techniques often use the maximum response of an inelastic oscillator that is "equivalent" to the original frame. In reliability-based seismic design, it is necessary to express the maximum response of the inelastic oscillator probabilistically. Such information could be obtained via NDA, which requires hundreds of samples. In practice, the use of simpler methods such as an equivalent linearization technique¹ (EqLT) using an elastic response spectrum seems more reasonable. Using Capacity spectrum (CS) method², the inelastic displacement can be estimated graphically as the intersection of capacity spectrum and demand spectrum (DS), and DS's are being developed on the basis of probabilistic approaches such as a uniform hazard spectrum (UHS) and a conditional mean spectrum (CMS). We investigated the accuracy and applicability of the use of either a UHS or a CMS along with the CS method to estimate the exceedance probability (EProb) of the maximum displacement of an inelastic oscillator in 50 years, S^I_D50 . The results can be summarized as follows: • EProb’s of S^I_D50 can be estimated fairly accurately by a CS method that uses a UHS when the natural period is longer than or equal to 1.0 s. The accuracy increases with increase in the second stiffness ratio and with decrease in the yield base shear coefficient. • The CS method that uses CMS could provide fairly optimistic estimates when EProb is 20% or less in 50 years. This could be due to the ignorance of many other possible events of e.g.10% in 50 years. • The accuracy of CS method with UHS is investigated in standard normal stochastic process, and the slopes and locations of CS with which the CS method provides an accurate estimate are identified.

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