Approximate Method for Transverse Response Analysis of Partially Isolated Bridges
Publication: Journal of Bridge Engineering
Volume 18, Issue 11
Abstract
Current analysis procedures for seismically isolated bridges frequently use an equivalent (approximate) linearization approach to represent the response of nonlinear isolation/energy dissipation devices. Linearization allows standard linear elastic analysis methods, e.g., the response spectrum method, to be conveniently used for design purposes. The linearization approach is by nature an iterative method implying the need to repeatedly correct and analyze a numerical finite-element model. A further simplification could be achieved using closed form equations to represent (1) the structure displacement patterns and (2) the restoring forces from structural elements. The paper explores such a possibility with reference to partially isolated continuous bridges, i.e., bridges with isolation devices at piers and pinned supports at abutments. The role and effect of higher modes of vibration on the system response are discussed, and an approximate method is proposed to account for such effects. An improvement of the classical Jacobsen’s approximation for the effective viscous damping ratio is also proposed using the results of response history analyses. The latter are carried out on two-dimensional numerical models of five case studies, generated from a real existing bridge supposed to be isolated with friction pendulum devices. Comparison of approximate predictions with response history analysis results is presented and discussed. Nonlinear dynamic analyses of a three-dimensional numerical model of the existing bridge were also carried out for comparison purposes.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was partially supported by the European Community, through the Project “Assessment of the seismic vulnerability of an old RC viaduct with frame piers and study of the effectiveness of different isolation systems through pseudo-dynamic test on a large scale model (RETRO),” funded within the 7th Framework Program by the Seismic Engineering Research Infrastructures for European Synergies (SERIES). Comments received by two anonymous reviewers are gratefully acknowledged. The authors also acknowledge stimulating discussions with Iunio Iervolino for the statistical assessment of the study results. The comments of the reviewers and the personal communications were very useful to significantly improve the paper quality.
References
AASHTO. (2010). Guide specifications for seismic isolation design, 3rd Ed., Washington, DC.
Applied Technology Council (ATC). (2005). “Improvement of nonlinear static seismic analysis procedures.” FEMA 440, Final Rep. from ATC-55 Project, Redwood City, CA.
Benjamin, J. R., and Cornell, C. A. (1970). Probability, statistics and decision for civil engineers, McGraw Hill, New York.
Blandon, C. A., and Priestley, M. J. N. (2005). “Equivalent viscous damping equations for direct displacement based design.” J. Earthquake Eng., 9(Suppl. 2), 257–278.
Charney, F. A. (2008). “Unintended consequences of modeling damping in structures.” J. Struct. Eng., 134(4), 581–592.
Chopra, A. K., and Goel, R. K. (2002). “A modal pushover analysis procedure for estimating seismic demands for buildings.” Earthquake Eng. Struct. Dynam., 31(3), 561–582.
Christopoulos, C., and Filiatrault, A. (2006). Principles of passive supplemental damping and seismic isolation, IUSS Press, Pavia, Italy.
Della Corte, G., and De Risi, R. (2012). “Abutment reactions and higher modes of vibration of continuous bridges.” Proc., 15th World Conf. on Earthquake Engineering, International Association for Earthquake Engineering (IAEE), Tokyo.
Der Kiureghian, A. (1981). “A response spectrum method for random vibration analysis of MDF systems.” Earthquake Eng. Struct. Dynam., 9(5), 419–435.
Dicleli, M., and Buddaram, S. (2006). “Improved effective damping equation for equivalent linear analysis of seismic-isolated bridges.” Earthquake Spectra, 22(1), 29–46.
Dicleli, M., and Mansour, M. Y. (2003). “Seismic retrofitting of highway bridges in Illinois using friction pendulum seismic isolation bearings and modelling procedures.” Eng. Struct., 25(9), 1139–1156.
Dwairi, H. M., and Kowalsky, M. J. (2004). “Investigation of the Jacobsen’s equivalent viscous damping approach as applied to displacement-based seismic design.” Proc., 13th World Conf. on Earthquake Engineering, International Association for Earthquake Engineering (IAEE), Tokyo.
European Committee for Standardization (CEN). (2005). “Design of structures for earthquake resistance—Part 2: Bridges.” EN 1998-2 2005, Eurocode 8, Brussels, Belgium.
Hetényi, M. (1964). Beams on elastic foundation, University of Michigan Press, Ann Arbor, MI.
Makris, N., Kampas, G., and Angelopoulou, D. (2010). “The eigenvalues of isolated bridges with transverse restraints at the end abutments.” Earthquake Eng. Struct. Dynam., 39(8), 869–886.
Mander, J. B., Priestley, M. J. N., and Park, R. (1988). “Theoretical stress-strain model for confined concrete.” J. Struct. Eng., 114(8), 1804–1825.
McKenna, F., Mazzoni, S., Scott, M. H., and Fenves, G. L. (2004). Open system for earthquake engineering simulation (OpenSEES) (version 1.7.4). Pacific Earthquake Engineering Research Center, Univ. of California at Berkeley, Berkeley, CA.
Mosqueda, G., Whittaker, A. S., and Fenves, G. L. (2004). “Characterization and modelling of friction pendulum bearings subjected to multiple components of excitation.” J. Struct. Eng., 130(3), 433–442.
Paolacci, F., and Giannini, R. (2012). “An experimental and numerical investigation on the cyclic response of a portal frame pier belonging to an old reinforced concrete viaduct.” Earthquake Eng. Struct. Dynam., 41(6), 1109–1127.
Pennucci, D., Sullivan, T. J., and Calvi, G. M. (2011). “Displacement reduction factors for the design of medium and long-period structures.” J. Earthquake Eng., 15(Suppl. 1), 1–29.
Priestley, M. J. N., Calvi, G. M., and Kowalsky, M. J. (2007). Displacement based seismic design of structures, IUSS Press, Pavia, Italy.
Sullivan, T. J., Priestley, M. J. N., and Calvi, G. M. (2012). A model code for the displacement-based seismic design of structures, IUSS Press, Pavia, Italy.
Tsai, M.-H. (2008). “Transverse earthquake response analysis of a seismically isolated regular bridge with partial restraint.” Eng. Struct., 30(2), 393–403.
Tubaldi, E., and Dall’Asta, A. (2011). “A design method for seismically isolated bridges with abutment restraint.” Eng. Struct., 33(3), 786–795.
Information & Authors
Information
Published In
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jul 25, 2012
Accepted: Jan 30, 2013
Published online: Feb 1, 2013
Published in print: Nov 1, 2013
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.