Practical Equations for Predicting Maximum Displacement of Single Friction Pendulum Isolation Systems
Publication: Practice Periodical on Structural Design and Construction
Volume 27, Issue 3
Abstract
Predicting maximum displacement is an important task in designing any isolation system, including isolation systems using single friction pendulum (SFP) bearings. Many design codes allow an equivalent linear force (ELF) procedure to be used to predict this engineering demand, providing that the system satisfies some specific conditions. An ELF procedure is much simpler than a dynamic time-history analysis procedure because it does not require time-history inputs. However, this procedure is still time-consuming because it requires an iteration process. This study aimed to develop simple equations to directly calculate the maximum displacement without iterating. The database for developing these equations was obtained by performing the ELF procedure in a current standard on a wide range of isolation systems subjected to a wide range of ground-shaking strengths. As a result, a simple equation that can directly predict the maximum displacement of any isolation system using SFP bearings was proposed. The inputs to the equation include friction coefficient and concave radius of the bearings in the system and the 1-s spectral acceleration of the site. The proposed equation confidently predicts the maximum displacement calculated by the ELF procedure with an average displacement ratio, which is the ratio between the predicted and computed values, of 1.015. The minimum and maximum ratios in the investigated database were 0.975 and 1.092, respectively.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available in a repository or online in accordance with funder data retention policies.
Link to the repository: https://github.com/nhanddao/StaticProcedure_SFB_ML.
References
ASCE. 2017. Minimum design loads and associated criteria for buildings and other structures. ASCE/SEI 7-16. Reston, VA: ASCE.
CEN (European Committee for Standardization). 2004. Design of structures for earthquake resistance. Eurocode 8. Brussels, Belgium: CEN.
Chopra, A. K. 2015. Dynamics of structures: Theory and applications to earthquake engineering. Upper Saddle River, NJ: Prentice Hall.
Chopra, A. K., and R. K. Goel. 2000. “Evaluation of NSP to estimate seismic deformation: SDF systems.” J. Struct. Eng. 126 (4): 482–490. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:4(482).
Dao, N. D., H. Nguyen-Van, T. H. A. Nguyen, and A. B. Chung. 2020. “A new statistical equation for predicting nonlinear time history displacement of seismic isolation systems.” Structures 24 (Apr): 177–190. https://doi.org/10.1016/j.istruc.2020.01.019.
Dicleli, M., and S. Buddaram. 2007. “Comprehensive evaluation of equivalent linear analysis method for seismic-isolated structures represented by SDOF systems.” Eng. Struct. 29 (8): 1653–1663. https://doi.org/10.1016/j.engstruct.2006.09.013.
Dwairi, H. M., M. J. Kowalsky, and J. M. Nau. 2007. “Equivalent damping in support of direct displacement-based design.” J. Earthquake Eng. 11 (4): 512–530. https://doi.org/10.1080/13632460601033884.
Fadi, F., and M. C. Constantinou. 2010. “Evaluation of simplified methods of analysis for structures with triple friction pendulum isolators.” Earthquake Eng. Struct. Dyn. 39 (1): 5–22. https://doi.org/10.1002/eqe.930.
Franchin, P., G. Monti, and P. E. Pinto. 2001. “On the accuracy of simplified methods for the analysis of isolated bridges.” Earthquake Eng. Struct. Dyn. 30 (3): 363–382. https://doi.org/10.1002/eqe.12.
Gulkan, P., and M. A. Sozen. 1974. “Inelastic responses of reinforced concrete structures to earthquake motions.” ACI J. 71 (12): 604–610.
Guyader, A., and W. Iwan. 2004. “An improved capacity spectrum method employing statistically optimized linearization parameters.” In Proc., 13th World Conf. on Earthquake Engineering. Vancouver, BC, Canada: Canadian Association for Earthquake Engineering.
Hwang, J. S. 1996. “Evaluation of equivalent linear analysis methods of bridge isolation.” J. Struct. Eng. 122 (8): 972–976. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:8(972).
Hwang, J. S., and J. M. Chiou. 1996. “An equivalent linear model of lead-rubber seismic isolation bearings.” Eng. Struct. 18 (7): 528–536. https://doi.org/10.1016/0141-0296(95)00132-8.
Hwang, J. S., and L. H. Sheng. 1993. “Effective stiffness and equivalent damping of base-isolated bridges.” J. Struct. Eng. 119 (10): 3094–3101. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:10(3094).
Iwan, W. 1980. “Estimating inelastic response spectra from elastic spectra.” Earthquake Eng. Struct. Dyn. 8 (4): 375–388. https://doi.org/10.1002/eqe.4290080407.
Iwan, W., and N. Gates. 1979. “Estimating earthquake response of simple hysteretic structures.” J. Eng. Mech. Div. 105 (3): 391–405. https://doi.org/10.1061/JMCEA3.0002481.
Jara, J. M., G. Raya, B. A. Olmos, and G. Martinez. 2017. “Applicability of equivalent linearization methods to irregular isolated bridges.” Eng. Struct. 141 (Jun): 495–511. https://doi.org/10.1016/j.engstruct.2017.03.052.
Jara, M., and J. Casas. 2006. “A direct displacement-based method for the seismic design of bridges on bilinear devices.” Eng. Struct. 28 (6): 869–879. https://doi.org/10.1016/j.engstruct.2005.10.016.
Jara, M., J. Jara, B. Olmos, and J. Casas. 2012. “Improved procedure for equivalent linearization of bridges supported on hysteretic isolators.” Eng. Struct. 35 (Feb): 99–106. https://doi.org/10.1016/j.engstruct.2011.10.028.
Kowalsky, M. J., M. J. N. Priestley, and G. A. Macrae. 1995. “Displacement-based design of RC bridge columns in seismic regions.” Earthquake Eng. Struct. Dyn. 24 (12): 1623–1643. https://doi.org/10.1002/eqe.4290241206.
Kwan, W., and S. Billington. 2003. “Influence of hysteretic behavior on equivalent period and damping of structural systems.” J. Struct. Eng. 129 (5): 576–585. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:5(576).
Lin, Y. Y., and E. Miranda. 2009. “Evaluation of equivalent linear methods for estimating target displacements of existing structures.” Eng. Struct. 31 (12): 3080–3089. https://doi.org/10.1016/j.engstruct.2009.08.009.
Liu, T., T. Zordan, B. Briseghella, and Q. Zhang. 2014. “Evaluation of equivalent linearization analysis methods for seismically isolated buildings characterized by SDOF systems.” Eng. Struct. 59 (2): 619–634. https://doi.org/10.1016/j.engstruct.2013.11.028.
Makris, N., and G. Kampas. 2013. “Estimating the ‘effective period’ of bilinear systems with linearization methods, wavelet and time-domain analyses: From inelastic displacements to modal identification.” Soil Dyn. Earthquake Eng. 45 (Feb): 80–88. https://doi.org/10.1016/j.soildyn.2012.11.007.
Mavronicola, E., and P. Komodromos. 2011. “Assessing the suitability of equivalent linear elastic analysis of seismically isolated multi-storey buildings.” Comput. Struct. 89 (21–22): 1920–1931. https://doi.org/10.1016/j.compstruc.2011.05.010.
Miranda, E., and J. Ruiz-Garcia. 2002. “Evaluation of approximate methods to estimate maximum inelastic displacement demands.” Earthquake Eng. Struct. Dyn. 31 (3): 539–560. https://doi.org/10.1002/eqe.143.
Nguyen, T. T., and N. D. Dao. 2022. “Evaluating the accuracy of an equivalent linear model in predicting peak displacement of seismic isolation systems using single friction pendulum bearings.” Period. Polytech. Civ. Eng. 66 (1): 63–74. https://doi.org/10.3311/PPci.17687.
Ozdemir, G., and M. C. Constantinou. 2016. “Evaluation of equivalent lateral force procedure in estimating seismic isolator displacements.” Soil Dyn. Earthquake Eng. 30 (10): 1036–1042. https://doi.org/10.1016/j.soildyn.2010.04.015.
Papagiannopoulos, G. A. 2018. “Jacobsen’s equivalent damping concept revisited.” Soil Dyn. Earthquake Eng. 115 (Dec): 82–89. https://doi.org/10.1016/j.soildyn.2018.08.001.
Pavlou, E. A., and M. C. Constantinou. 2004. “Response of elastic and inelastic structures with damping systems to near-field and soft-soil ground motions.” Eng. Struct. 26 (9): 1217–1230. https://doi.org/10.1016/j.engstruct.2004.04.001.
Quaranta, G., and F. Mollaioli. 2018. “On the use of the equivalent linearization for bilinear oscillators under pulse-like ground motion.” Eng. Struct. 160 (Apr): 395–407. https://doi.org/10.1016/j.engstruct.2018.01.055.
Rahgozar, N., N. Rahgozar, and A. S. Moghadam. 2019. “Equivalent linear model for fully self-centering earthquake-resisting systems.” Struct. Des. Tall Special Build. 28 (1): e1565. https://doi.org/10.1002/tal.1565.
Ramirez, O. M., M. C. Constantinou, J. D. Gomez, and A. S. Whittaker. 2002. “Evaluation of simplified methods of analysis of yielding structures with damping systems.” Earthquake Spectra 18 (3): 501–530. https://doi.org/10.1193/1.1509763.
Rosenblueth, E., and I. Herrera. 1964. “On a kind of hysteretic damping.” J. Eng. Mech. Div. 90 (4): 37–48. https://doi.org/10.1061/JMCEA3.0000510.
Ryan, K. L., and A. K. Chopra. 2004. “Estimating the seismic displacement of friction pendulum isolators based on non-linear response history analysis.” Earthquake Eng. Struct. Dyn. 33 (3): 359–373. https://doi.org/10.1002/eqe.355.
Theodossiou, D., and M. Constantinou. 1991. Evaluation of SEAOC design requirements for sliding isolated structures. Buffalo, NY: Univ. of Buffalo (SUNY).
Tsopelas, P., M. C. Constantinou, C. A. Kircher, and A. S. Whittaker. 1997. Evaluation of simplified methods of analysis for yielding structures. Buffalo, NY: Univ. of Buffalo (SUNY).
Virtanen, P., et al. 2020. “SciPy 1.0: Fundamental algorithms for scientific computing in python.” Nat. Methods 17 (3): 261–272. https://doi.org/10.1038/s41592-019-0686-2.
Warn, G. P., and A. S. Whittaker. 2004. “Performance estimates in seismically isolated bridge structures.” Eng. Struct. 26 (9): 1261–1278. https://doi.org/10.1016/j.engstruct.2004.04.006.
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Published In
Practice Periodical on Structural Design and Construction
Volume 27 • Issue 3 • August 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Oct 25, 2021
Accepted: Feb 20, 2022
Published online: Apr 21, 2022
Published in print: Aug 1, 2022
Discussion open until: Sep 21, 2022
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