Are Some Top-Heavy Structures More Stable?
Publication: Journal of Structural Engineering
Volume 140, Issue 5
Abstract
This technical note investigates the dynamic response and stability of a rocking frame that consists of two identical free-standing slender columns capped with a freely supported rigid beam. Part of the motivation for this study is the emerging seismic design concept of allowing framing systems to uplift and rock along their plane in order to limit bending moments and shear forces— together with the need to stress that the rocking frame is more stable the more heavy is its cap-beam, a finding that may have significant implications in the prefabricated bridge technology. In this technical note, a direct approach is followed after taking dynamic force and moment equilibrium of the components of the rocking frame, and the remarkable results obtained in the past with a variational formulation (by the same authors) is confirmed—that the dynamics response of the rocking frame is identical to the rocking response of a solitary, free-standing column with the same slenderness, yet with larger size, which produces a more stable configuration. The motivation for reworking this problem by following a direct approach is to show, in the simplest possible way, that the heavier the freely supported cap beam, the more stable is the rocking frame, regardless of the rise of the center of gravity of the cap beam. The conclusion is that top-heavy rocking frames are more stable that when they are top-light.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Financial Support for this study has been provided by the action Aristeia of the Operational Programme Education and Lifelong Learning, and is cofunded by the European Social Fund (ESF) and the National Resources of Greece.
References
Acikgoz, S., and DeJong, M. J. (2012). “The interaction of elasticity and rocking in flexible structures allowed to uplift.” Earthquake Eng. Struct. Dyn., 41(15), 2177–2194.
Allen, R. H., Oppenheim, I. J., Parker, A. R., and Bielak, J. (1986). “On the dynamic response of rigid body assemblies.” Earthquake Eng. Struct. Dyn., 14(6), 861–876.
Apostolou, M., Gazetas, G., and Garini, E. (2007). “Seismic response of slender rigid structures with foundation uplift.” Soil Dyn. Earthquake Eng., 27(7), 642–654.
Aslam, M., Scalise, D. T., and Godden, W. G. (1980). “Earthquake rocking response of rigid bodies.” J. Struct. Div., 106(2), 377–392.
Beck, J. L., and Skinner, R. I. (1974). “The seismic response of a reinforced concrete bridge pier designed to step.” Earthquake Eng. Struct. Dyn., 2(4), 343–358.
Cheng, C.-T. (2008). “Shaking table tests a self-centering designed bridge substructure.” Eng. Struct., 30(12), 3426–3433.
Cohagen, L., Pang, J. B. K., Stanton, J. F., and Eberhard, M. O. (2008). “A precast concrete bridge bent designed to recenter after an earthquake.” Research Rep., Federal Highway Administration, Washington, DC.
Dimitrakopoulos, E. G., and DeJong, M. J. (2012). “Revisiting the rocking block: Closed-form solutions and similarity laws.” Proc. R. Soc. London Ser. A, 468(2144), 2294–2318.
Hogan, S. J. (1989). “On the dynamics of rigid-block motion under harmonic forcing.” Proc. R. Soc. London Ser. A, 425(1869), 441–476.
Housner, G. W. (1963). “The behaviour of inverted pendulum structures during earthquakes.” Bull. Seismological Soc. Amer., 53(2), 404–417.
Kelly, J. M. (1997). Earthquake-resistant design with rubber, 2nd Ed., Springer, London.
Konstantinidis, D., and Makris, N. (2005). “Seismic response analysis of multidrum classical columns.” Earthquake Eng. Struct. Dyn., 34, 1243–1270.
Konstantinidis, D., and Makris, N. (2009). “Experimental and analytical studies on the response of freestanding laboratory equipment to earthquake shaking.” Earthquake Eng. Struct. Dyn., 38(6), 827–848.
Konstantinidis, D., and Makris, N. (2010). “Experimental and analytical studies on the response of 1/4-scale models of freestanding laboratory equipment subjected to strong earthquake shaking.” Bull. Earthquake Eng., 8(6), 1457–1477.
Makris, N., and Konstantinidis, D. (2003). “The rocking spectrum and the limitations of practical design methodologies.” Earthquake Eng. Struct. Dyn., 32(2), 265–289.
Makris, N., and Roussos, Y. (2000). “Rocking response of rigid blocks under near-source ground motions.” Geotechnique, 50(3), 243–262.
Makris, N., and Vassiliou, M. F. (2013). “Planar rocking response and stability analysis of an array of free-standing columns capped with a freely supported rigid beam.” Earthquake Eng. Struct. Dyn., 42(3), 431–449.
Mander, J. B., and Cheng, C.-T. (1997). ‘‘Seismic resistance of bridge piers based on damage avoidance design.’’, National Center for Earthquake Engineering Research, Dept. of Civil and Environmental Engineering, State Univ. of New York, Buffalo, NY.
Papaloizou, L., and Komodromos, K. (2009). “Planar investigation of the seismic response of ancient columns and colonnades with epistyles using a custom-made software.” Soil Dyn. Earthquake Eng., 29(11–12), 1437–1454.
Peña, F., Lourenço, P. B., and Campos-Costa, A. (2008). “Experimental dynamic behavior of free-standing multi-block structures under seismic loadings.” J. Earthquake Eng., 12(6), 953–979.
Resemini, S., Lagomarsino, S., and Cauzzi, C. (2008). “Dynamic response of rocking masonry elements to long period strong ground motion.” Proc., 14th World Conf. on Earthquake Engineering, Beijing, China.
Sakai, J., and Mahin, S. (2004). “Analytical investigations of new methods for reducing residual displacements of reinforced concrete bridge columns.”, Pacific Earthquake Engineering Research Center, Univ. of California, Berkeley, CA.
Shenton, H. W., III. (1996). “Criteria for initiation of slide, rock, and slide-rock rigid-body modes.” J. Eng. Mech., 690–693.
Skinner, R. I., Robinson, W. H., and McVerry, G. H. (1993). An introduction to seismic isolation, Wiley, New York.
Spanos, P. D., and Koh, A. S. (1984). “Rocking of rigid blocks due to harmonic shaking.” J. Eng. Mech., 1627–1642.
Tso, W. K., and Wong, C. M. (1989). “Steady state rocking response of rigid blocks part 1: Analysis.” Earthquake Eng. Struct. Dyn., 18(1), 89–106.
Wacker, J. M., Hieber, D. G., Stanton, J. F., and Eberhard, M. O. (2005). “Design of precast concrete piers for rapid bridge construction in seismic regions.”, Federal Highway Administration, Washington, DC.
Yim, C. S., Chopra, A. K., and Penzien, J. (1980). “Rocking response of rigid blocks to earthquakes.” Earthquake Eng. Struct. Dyn., 8(6), 565–587.
Zhang, J., and Makris, N. (2001). “Rocking response of free-standing blocks under cycloidal pulses.” J. Eng. Mech., 473–483.
Information & Authors
Information
Published In
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Dec 20, 2012
Accepted: Aug 29, 2013
Published online: Feb 3, 2014
Published in print: May 1, 2014
Discussion open until: Jul 3, 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.