Probabilistic estimation of maximum inelastic displacement demands for performance‐based design

Abstract

A probabilistic approach to estimate maximum inelastic displacement demands of single-degree-of-freedom (SDOF) systems is presented. By making use of the probability of exceedance of maximum inelastic displacement demands for given maximum elastic spectral displacement and the mean annual frequency of exceedance of elastic spectral ordinates, a simplified procedure is proposed to estimate mean annual frequencies of exceedance of maximum inelastic displacement demands. Simplifying assumptions are thoroughly examined and discussed. Using readily available elastic seismic hazard curves the procedure can be used to compute maximum inelastic displacement seismic hazard curves and uniform hazard spectra of maximum inelastic displacement demands. The resulting maximum inelastic displacement demand spectra provide a more rational way of establishing seismic demands for new and existing structures when performance-based approaches are used. The proposed procedure is illustrated for elastoplastic SDOF systems having known-lateral strength located in a region of high seismicity in California. a site [1][2][3][4]. Using the geometry and location with respect to the site of all possible seismic sources, the probability distribution of earthquake magnitudes at each source and attenuation relationships, a conventional PSHA permits the estimations of the mean annual frequency (MAF) of exceedance of a certain peak ground motion parameter (e.g. peak ground acceleration, etc.) or a linear elastic response spectral ordinate (e.g. pseudo-acceleration, S a ) by integration over all possible sources, earthquake magnitudes and distances. However, conventional PSHA only provides probabilistic estimates of demands on linear elastic systems while most structures are likely to undergo significant inelastic deformations in the event of strong, or even moderate, earthquake ground motions. Therefore, it is of utmost importance to develop rational methods to estimate lateral displacement demands on inelastic systems.Although most structures do not behave like single-degree-of-freedom (SDOF) systems, various studies have shown that inelastic SDOF systems may provide the basis for estimating global deformation demands of buildings [5][6][7][8][9][10][11]. Based on this observation, non-linear static procedures have been introduced in recent seismic recommendations for design of new structures as well as for assessment and rehabilitation of existing structures [12][13][14][15][16][17] in which roof displacements are estimated from maximum displacements of SDOF inelastic systems. In these design provisions the estimation of maximum inelastic SDOF displacements is done through simplified procedures by either applying modification factors on maximum SDOF elastic displacement demands or by considering equivalent SDOF systems with elongated fundamental period and increased damping ratio [18]. However, the inherent uncertainty introduced by approximating maximum inelastic displacements from maximum elastic displacements is neglected.The objective of thi...

Deaggregation of seismic loss of spatially distributed buildings

“…There are several applicable models and methods in the literature: FEMA and NIBS (2003), ATC (2005), and Ruiz-Garcia and Miranda (2007) considered the use of an equivalent SDOF system with the capacity spectrum method and/or the displacement coefficient method to estimate the maximum inelastic displacement demand, whereas Vamvatsikos and Cornell (2005) considered the multi-degree-of-freedom system with incremental dynamic analysis and linked to the nonlinear static push-over curve to circumvent considerable computation. The advantages of simplified approaches include that the effects of record-to-record variability on structural responses can be assessed in detail, whereas their disadvantages are that accurate prediction of structural responses becomes difficult, especially if higher mode effects are significant and forces/moments over a height of a structure are of interest.…”

Bridge Seismic Retrofit Measures Considering Subduction Zone Earthquakes

“…This has also been used as a means of estimating maximum inelastic displacement demand as a part of performance-based design (Ruiz-Garcia and Miranda 2007). A constant strength approach was further used as mechanism for determining the sensitivity of inelastic SDOF systems to the orientation of input ground motions (Goda 2012).…”

“…Several studies involving analysis of inelastic structural demands of earthquakes have been conducted utilizing primarily crustal earthquakes , (Ibarra et al 2005a), (Ruiz-Garcia and Miranda 2003), (Ruiz-Garcia and Miranda 2007). Extending this research to large magnitude long duration subduction zone earthquakes has been limited by the availability of recorded ground motions as such earthquakes occur with less frequency than crustal earthquakes.…”

The effect of hysteresis behaviour models on maximum displacement demand of SDOF systems

“…Bazzurro ve Luco [8], farklı yatay dayanım oranı (yatay yük taşıma kapasitesinin deprem hesabına esas ağırlığa oranı) ve titreşim periyoduna sahip TSD sistemlerin doğrusal olmayan zaman tanım alanında analizleri için ölçeklendirilmemiş ve hedef spektrumla uyumlu olacak şekilde ölçeklendirilmiş gerçek ivme kaydı setlerini ayrı ayrı kullanmıştır. D'Ambrisi ve Mezzi [9] ile Ruiz-Garcia ve Miranda [10] TSD sistemlerin maksimum ötelenme talebinin tahmini amacıyla zaman tanım alanında analiz sonuçlarını kullanarak geliştirdikleri olasılıksal bir yaklaşım önermiştir. İnel ve diğ.…”