Inelastic displacement ratios for evaluation of existing structures

Abstract

SUMMARYResults of a detailed statistical study of constant relative strength inelastic displacement ratios to estimate maximum lateral inelastic displacement demands on existing structures from maximum lateral elastic displacement demands are presented. These ratios were computed for single-degree-of-freedom systems with di erent levels of lateral strength normalized to the strength required to remain elastic when subjected to a relatively large ensemble of recorded earthquake ground motions. Three groups of soil conditions with shear wave velocities higher than 180 m=s are considered. The in uence of period of vibration, level of lateral yielding strength, site conditions, earthquake magnitude, distance to the source, and strain-hardening ratio are evaluated and discussed. Mean inelastic displacement ratios and those associated with various percentiles are presented. A special emphasis is given to the dispersion of these ratios. It is concluded that distance to the source has a negligible in uence on constant relative strength inelastic displacement ratios. However, for periods smaller than 1 s earthquake magnitude and soil conditions have a moderate in uence on these ratios. Strain hardening decreases maximum inelastic displacement at a fairly constant rate depending on the level of relative strength for periods of vibration longer than about 1:0 s while it decreases maximum inelastic displacement non-linearly as the period of vibration shortens and as the relative-strength ratio increases for periods of vibration shorter than 1:0 s. Finally, results from non-linear regression analyses are presented that provide a simpliÿed expression to be used to approximate mean inelastic displacement ratios during the evaluation of existing structures built on ÿrm sites.

Inelastic Displacement Ratios of Degrading Systems

“…The third equation used to estimate the inelastic ratios of degrading systems is based on the expression proposed by Ruiz-Garcia and Miranda (2003) as follow:…”

“…The expression results in general in accurate estimates, although an error of up to 15% was observed for a few modified Clough degrading systems. The expressions by Chopra and Chintanapakdee (2004) and Ruiz-Garcia and Miranda (2003) in general provide conservative estimates for inelastic ratios, and can be therefore used for design purposes. New coefficients for both expressions were developed for degrading modified Clough models.…”

Fuzzy-logic based inelastic displacement ratios of degrading RC structures

“…where T c is the period separating the acceleration and velocity sensitive regions and equal to 0.33 for NEHRP soil type C and α is the strain hardening ratio of the degrading SDOF The third equation is proposed by Ruiz-Garcia and Miranda [15]: (6) where Ts is the characteristic period at the site which is assumed to equal 0.85 for NEHRP soil type C. Constants of the equations, a, b and d are also site dependent and equal to 48, 1.8 and 50 respectively. The constant b was recalibrated later by Chenouda and Ayoub [23] to fit modified Clough systems and was found to be equal to 2.2.…”

“…They also studied the effects of period of vibration, lateral yielding strength level, site conditions with shear wave velocity higher than 180 m/s (600 ft/s), earthquake magnitude, epicenter distance and strain hardening ratio on inelastic displacement ratio [15]. They derived an equation to predict the inelastic displacement ratios of existing structures on firm sites restricted to elasto-plastic systems.…”

Bridge Seismic Retrofit Measures Considering Subduction Zone Earthquakes

“…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.…”