Normalized Residual Displacements for Bilinear and Pinching Oscillators
Publication: Journal of Structural Engineering
Volume 146, Issue 11
Abstract
A correct estimation of residual displacements due to an earthquake event is crucial in satisfying the limit state of repairability after the event and for assessing the safety of structures against future earthquake events. An attempt is made in this study to obtain the statistical estimates of constant-ductility residual displacement spectra, for bilinear and pinching oscillators with 5% initial damping, in terms of the 5%-damping elastic displacement spectrum. The normalized residual displacement spectra (at the mean level and 0.1- and 0.9-fractile levels) are described as three-coefficient and four-coefficient mathematical functions for pinching and bilinear models, respectively. The coefficients of these functions are proposed to be estimated through scaling equations in terms of three model parameters for a given set of the ductility ratio and hysteretic energy capacity coefficient in the case of a bilinear model and for a given set of the pinching parameters, ductility ratio, and hysteretic energy capacity coefficient in the case of a pinching model.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request. These include all the simulated records.
References
Baber, T. T., and M. N. Noori. 1985. “Random vibration of degrading, pinching systems.” J. Eng. Mech. 111 (8): 1010–1026. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:8(1010).
Borzi, B., G. M. Calvi, A. S. Elnashai, E. Faccioli, and J. J. Bommer. 2001. “Inelastic spectra for displacement-based seismic design.” Soil Dyn. Earthquake Eng. 21 (1): 47–61. https://doi.org/10.1016/S0267-7261(00)00075-0.
Christopoulos, C., S. Pampanin, and M. J. N. Priestley. 2003. “Performance-based seismic response of frame structures including residual deformations. Part I: Single-degree-of-freedom systems.” J. Earthquake Eng. 7 (1): 97–118. https://doi.org/10.1080/13632460309350443.
Guerrero, H., J. Ruiz-Garcia, and T. Ji. 2017. “Residual displacement demands of conventional and dual oscillators subjected to earthquake ground motions characteristic of the soft soils of Mexico City.” Soil Dyn. Earthquake Eng. 98 (Jul): 206–221. https://doi.org/10.1016/j.soildyn.2017.04.014.
Harikrishnan, M. G. 2009. “Estimation of residual displacement for horizontal ground motions.” M.Tech thesis, Dept. of Civil Engineering, Indian Institute of Technology Kanpur.
Ibarra, L. F., R. A. Medina, and H. Krawinkler. 2005. “Hysteretic models that incorporate strength and stiffness deterioration.” Earthquake Eng. Struct. Dyn. 34 (12): 1489–1511. https://doi.org/10.1002/eqe.495.
Ji, D., W. Wen, C. Zhai, and E. I. Katsanos. 2018. “Residual displacement ratios of SDOF systems subjected to ground motions recorded on soft soils.” Soil Dyn. Earthquake Eng. 115 (Dec): 331–335. https://doi.org/10.1016/j.soildyn.2018.09.001.
Kawashima, K. 2000. “Seismic design and retrofit of bridges.” In Proc., 12th World Conf. on Earthquake Engineering. Wellington, New Zealand: New Zealand Society for Earthquake Engineering.
Kawashima, K., G. A. MacRae, J. Hoshikuma, and K. Nagaya. 1998. “Residual displacement response spectrum.” J. Struct. Eng. 124 (5): 523–530. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:5(523).
Kumari, R., and V. K. Gupta. 2007. “A modal combination rule for peak floor accelerations in multistoried buildings.” ISET J. Earthquake Technol. 44 (1): 213–231.
Lee, V. W., and M. D. Trifunac. 1987. Strong earthquake ground motion data in EQINFOS: Part 1. Los Angeles: Dept. of Civil Engineering, Univ. of Southern California.
Liossatou, E., and M. N. Fardis. 2015. “Residual displacements of RC structures as SDOF systems.” Earthquake Eng. Struct. Dyn. 44 (5): 713–734. https://doi.org/10.1002/eqe.2483.
Liossatou, E., and M. N. Fardis. 2016. “Near-fault effects on residual displacements of RC structures.” Earthquake Eng. Struct. Dyn. 45 (9): 1391–1409. https://doi.org/10.1002/eqe.2712.
MacRae, G. A., and K. Kawashima. 1997. “Post-earthquake residual displacements of bilinear oscillators.” Earthquake Eng. Struct. Dyn. 26 (7): 701–716. https://doi.org/10.1002/(SICI)1096-9845(199707)26:7%3C701::AID-EQE671%3E3.0.CO;2-I.
Mahin, S. A., and V. V. Bertero. 1981. “An evaluation of inelastic seismic design spectra.” J. Struct. Div. 107 (9): 1777–1795.
Mukherjee, S., and V. K. Gupta. 2002. “Wavelet-based generation of spectrum-compatible time-histories.” Soil Dyn. Earthquake Eng. 22 (9–12): 799–804. https://doi.org/10.1016/S0267-7261(02)00101-X.
Rahnama, M., and H. Krawinkler. 1993. Effects of soft soil and hysteresis model on seismic demands. Stanford, CA: John A. Blume Earthquake Engineering Center, Dept. of Civil and Environmental Engineering, Stanford Univ.
Ruiz-Garcia, J. 2010. “On the influence of strong-ground motion duration on residual displacement demands.” Earthquakes Struct. 1 (4): 327–344. https://doi.org/10.12989/eas.2010.1.4.327.
Ruiz-Garcia, J., and H. Guerrero. 2017. “Estimation of residual displacement ratios for simple structures built on soft-soil sites.” Soil Dyn. Earthquake Eng. 100 (Sep): 555–558. https://doi.org/10.1016/j.soildyn.2017.07.008.
Ruiz-Garcia, J., and E. Miranda. 2006. “Residual displacement ratios for assessment of existing structures.” Earthquake Eng. Struct. Dyn. 35 (3): 315–336. https://doi.org/10.1002/eqe.523.
Saifullah, M. 2018. “Scaling of ductility-based residual displacements for bilinear and pinching oscillators.” M.Tech thesis, Dept. of Civil Engineering, Indian Institute of Technology Kanpur.
Sengupta, P., and B. Li. 2017. “Hysteresis modeling of reinforced concrete structures: State of the art.” ACI Struct. J. 114 (1): 25–38. https://doi.org/10.14359/51689422.
Trifunac, M. D., and A. G. Brady. 1975. “A study on the duration of strong earthquake ground motion.” Bull. Seismol. Soc. Am. 65 (3): 581–626.
Trifunac, M. D., and V. W. Lee. 1985. Preliminary empirical model for scaling pseudo relative velocity spectra of strong earthquake acceleration, in terms of magnitude, distance, site intensity and recording site conditions. Los Angeles: Dept. of Civil Engineering, Univ. of Southern California.
Information & Authors
Information
Published In
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Oct 7, 2019
Accepted: May 29, 2020
Published online: Aug 22, 2020
Published in print: Nov 1, 2020
Discussion open until: Jan 22, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.