Identification of the Controlling Mechanism for Predicting Critical Loads in Elastomeric Bearings
Publication: Journal of Structural Engineering
Volume 139, Issue 12
Abstract
Assessing the stability of individual isolators is an important consideration for the design of seismic isolation systems composed of elastomeric bearings. A key component for the stability assessment is the prediction of the critical load capacity of the individual bearings in the laterally undeformed (service) configuration and at a given lateral displacement (seismic). The current procedure for estimating the critical load capacity of an elastomeric bearing at a given lateral displacement, with a bolted connection detail, uses a ratio of areas to reduce the critical load capacity from that in the laterally undeformed configuration, referred to as the reduced area method. Although the reduced area method provides a simple means for the estimate, it lacks a rigorous theoretical basis and is unable to capture the trends observed from experimental data. In this study, the capability of two analytical models for predicting critical loads and displacements in elastomeric bearings is evaluated by comparison with data from past experimental studies. A global variance-based sensitivity analysis is performed on the analytical model showing the best predictive capability to identify the model parameters to which the model prediction is most sensitive. The results of the sensitivity analysis demonstrate that the model prediction is most sensitive to the properties that control the nonlinear behavior of the rotational spring for lateral displacements greater than approximately 0.6 times bearing diameter/width. This finding suggests that the stability of elastomeric bearings at large lateral displacements is controlled by the transition from the yield moment to the ultimate moment in an individual rubber layers. A modified analytical model is proposed based on the results of this sensitivity analysis. The predictive capability of the more parsimonious modified model is shown to be similar, if not improved, by comparison to the original model.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Support for the first and third author was provided by the National Science Foundation through award number CMMI-1031362. Support for the second author was provided by a Science to Achieve Results Graduate Fellowship from the Environmental Protection Agency. Any opinions, findings, and recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the funding institutions.
References
Arwade, S. R., Moradi, M., and Louhghalam, A. (2010). “Variance decomposition and global sensitivity for structural systems.” Eng. Struct., 32(1), 1–10.
Buckle, I. G., and Liu, H. (1993). “Stability of elastomeric seismic isolation systems.” Proc., Seminar on Seismic Isolation, Passive Energy Dissipation, and Control, Applied Technology Council, Redwood City, CA, 293–305.
Buckle, I. G., and Liu, H. (1994). “Experimental determination of critical loads of elastomeric isolators at high shear strain.” NCEER Bull., 8(3), 1–5.
Buckle, I. G., Nagarajaiah, S., and Ferrell, K. (2002). “Stability of elastomeric isolation bearings: Experimental study.” J. Struct. Eng., 128(1), 3–11.
Gent, A. N. (1964). “Elastic stability of rubber compression springs.” J. Mech. Eng. Sci., 6(4), 318–326.
Gent, A. N. (2001). Engineering with rubber: How to design rubber components, 2nd Ed., Hanser, Munich, Germany.
Haringx, J. A. (1948). “On highly compressible helical springs and rubber rods and their application for vibration-free mountings. I.” Philips Res. Rep., 3, 401–449.
Haringx, J. A. (1949a). “On highly compressible helical springs and rubber rods and their application for vibration-free mountings. II.” Philips Res. Rep., 4, 49–80.
Haringx, J. A. (1949b). “On highly compressible helical springs and rubber rods and their application for vibration-free mountings. III.” Philips Res. Rep., 4, 206–220.
Iizuka, M. (2000). “A macroscopic model for predicting large-deformation behaviors of laminated rubber bearings.” Eng. Struct., 22(4), 323–334.
Kala, Z. (2011). “Sensitivity analysis of steel plane frames with initial imperfections.” Eng. Struct., 33(8), 2342–2349.
Kelly, J. M. (1991). “Dynamic and failure characteristics of bridgestone isolation bearings.”, Earthquake Engineering Research Center, College of Engineering, Univ. of California, Berkeley, CA.
Kelly, J. M. (1997). Earthquake resistant design with rubber, 2nd Ed., Springer, London.
Kikuchi, M., Nakamura, T., and Aiken, I. D. (2010). “Three-dimensional analysis for square seismic isolation bearings under large shear deformations and high axial loads.” Earthquake Eng. Struct. Dyn., 39(13), 1513–1531.
Koh, C. G., and Kelly, J. M. (1988). “A simple mechanical model for elastomeric bearings used in base isolation.” Int. J. Mech. Sci., 30(12), 933–943.
Ledolter, J., and Hogg, R. V. (2010). Applied statistics for engineers and physical scientists, 3rd Ed., Pearson, Upper Saddle River, NJ.
Matlab version 7.11.0584 [Computer software]. MathWorks, Inc., Natick, MA.
Saltelli, A., Tarantola, S., Campolongo, F., and Ratto, M. (2004). Sensitivity analysis in practice: A guide to assessing scientific models, Wiley, Hoboken, NJ.
Nagarajaiah, S., and Ferrell, K. (1999). “Stability of elastomeric seismic isolation bearings.” J. Struct. Eng., 946–954.
Saltelli, A., et al. (2008). Global sensitivity analysis: The primer, Wiley, Hoboken, NJ.
Sanchez, J., Masroor, A., Mosqueda, G., and Ryan, K. (2013). “Static and dynamic stability of elastomeric bearings for seismic protection of structures.” J. Struct. Eng., 139(7), 1149–1159.
Sobol’, I. M. (1993). “Sensitivity analysis for non-linear mathematical models.” Math. Model. Comput. Exp., 1(4), 407–414.
Sobol’, I. M. (2001). “Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates.” Math. Comput. Sim., 55(1–3), 271–280.
Stanton, J. F., Scroggins, G., Taylor, A. W., and Roeder, C. W. (1990). “Stability of laminated elastomeric bearings.” J. Eng. Mech., 116(6), 1351–1371.
Tang, Y., Reed, P., Wagener, T., and van Werkhoven, K. (2007). “Comparing sensitivity analysis methods to advance lumped watershed model identification and evaluation.” Hydrol. Earth Syst. Sci., 11(2), 793–817.
Tauchert, T. (1974). Energy principles in structural mechanics, McGraw-Hill, New York.
Wagener, T., and Kollat, J. (2007). “Visual and numerical evaluation of hydrologic and environmental models using the Monte Carlo Analysis Toolbox (MCAT).” Environ. Modell. Software, 22(7), 1021–1033.
Weisman, J., and Warn, G. P. (2012). “Stability of elastomeric and lead-rubber seismic isolation bearings.” J. Struct. Eng., 138(2), 215–223.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 139 • Issue 12 • December 2013
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jul 2, 2012
Accepted: Jan 29, 2013
Published online: Jan 31, 2013
Published in print: Dec 1, 2013
Discussion open until: Feb 11, 2014
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.