Effect of Supplemental Hysteretic and Viscous Damping on Rocking Response of Free-Standing Columns
Publication: Journal of Engineering Mechanics
Volume 145, Issue 5
Abstract
This paper investigated the nonlinear, rocking seismic response of slender, free-standing columns when equipped along their sides (or at their pivoting points) with vertical energy dissipation devices which offer either hysteretic or viscous (linear or nonlinear) dissipation. The paper derived the nonlinear equations of motion and then revisited the transverse response of the South Rangitikei Rail Bridge. The analysis showed that the 72-m-tall stepping bridge piers exhibit remarkable seismic performance even when excited with recorded ground motions that are much stronger than the known strong motions at the time of the design of the bridge. Subsequently, the paper showed that there are isolated examples of earthquake excitations in which the response of the rocking bridge pier when damped with either hysteretic or viscous dampers is more aggravated than the undamped response. This phenomenon may also manifest when idealized mathematical pulses are used. The paper concluded that the effectiveness of supplemental hysteretic or viscous damping in suppressing rocking response depends strongly on the local kinematic characteristics of the ground motion. Whenever the damped response exceeds the undamped response the exceedance is marginal, and in most cases the damped response is lower than the undamped response.
Get full access to this article
View all available purchase options and get full access to this article.
References
Alavi, B., and H. Krawinkler. 2001. Effects of near-fault ground motions on frame structures. Stanford, CA: John A. Blume Earthquake Engineering Center, Stanford Univ.
Aslam, M., D. T. Scalise, and W. G. Godden. 1980. “Earthquake rocking response of rigid bodies.” J. Struct. Div. 106 (2): 377–392.
Baber, T., and Y.-K. Wen. 1981. “Random vibration of hysteretic degrading systems.” J. Eng. Mech. Div. 107 (EM6): 1069–1087.
Beck, J. L., and R. Skinner. 1972. The seismic response of a proposed reinforced concrete railway viaduct. New Zealand: Physics and Engineering Laboratory, Dept. of Scientific and Industrial Research.
Beck, J. L., and R. Skinner. 1973. “The seismic response of a reinforced concrete bridge pier designed to step.” Earthquake Eng. Struct. Dyn. 2 (4): 343–358. https://doi.org/10.1002/eqe.4290020405.
Bertero, V. V., R. Herrera, and S. Mahin. 1976. “Establishment of design earthquakes—Evaluation of present methods.” In Proc., Int. Symp. on Earthquake Structural Engineering. St. Louis.
Bertero, V. V., S. A. Mahin, and R. A. Herrera. 1978. “Aseismic design implications of near-fault san fernando earthquake records.” Earthquake Eng. Struct. Dyn. 6 (1): 31–42. https://doi.org/10.1002/eqe.4290060105.
Black, C. J., I. D. Aiken, and N. Makris. 2002. Component testing, stability analysis, and characterization of buckling-restrained unbonded braces (tm). Berkeley, CA: Pacific Earthquake Engineering Research Center.
Black, C. J., N. Makris, and I. Aiken. 2003. “Component testing and modeling of buckling restrained unbonded braces.” In Proc., Conf. on Behaviour of Steel Structures in Seismic Areas–Stessa, 141–145. Naples, Italy.
Black, C. J., N. Makris, and I. D. Aiken. 2004. “Component testing, seismic evaluation and characterization of buckling-restrained braces.” J. Struct. Eng. 130 (6): 880–894. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:6(880).
Bolt, B. A. 1971. “The San Fernando Valley, California, earthquake of February 9 1971: Data on seismic hazards.” Bull. Seismol. Soc. Am. 61 (2): 501–510.
Bolt, B. A. 1975. “The San Fernando earthquake, 1971.” Chap. 21 in Magnitudes, aftershocks, and fault dynamics: Bulletin 196. Sacramento, CA: California Division of Mines and Geology.
Bouc, R. 1967. “Forced vibration of mechanical systems with hysteresis.” In Proc., 4th Conf. on Non-Linear Oscillation. Prague, Czechoslovakia.
Bradley, B. A., and M. Cubrinovski. 2011. “Near-source strong ground motions observed in the 22 February 2011 Christchurch earthquake.” Seismol. Res. Lett. 82 (6): 853–865. https://doi.org/10.1785/gssrl.82.6.853.
Chang, S., and N. Makris. 2000. “Effect of various energy dissipation mechanisms in suppressing structural response.” In Proc., 12th World Conf. on Earthquake Engineering Tokyo: International Association for Earthquake Engineering.
Chatzis, M., M. García Espinosa, C. Needham, and M. Williams. 2018. “Energy loss in systems of stacked rocking bodies.” J. Eng. Mech. 144 (7): 04018044. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001443.
Chatzis, M., and A. Smyth. 2012. “Robust modeling of the rocking problem.” J. Eng. Mech. 138 (3): 247–262. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000329.
Constantinou, M. C., T. T. Soong, and G. F. Dargush. 1998. Passive energy dissipation systems for structural design and retrofit. Buffalo, NY: Multidisciplinary Center for Earthquake Engineering Research.
Dimitrakopoulos, E. G., and M. J. DeJong. 2012. “Overturning of retrofitted rocking structures under pulse-type excitations.” J. Eng. Mech. 138 (8): 963–972. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000410.
Garini, E., G. Gazetas, and I. Anastasopoulos. 2015. “3-dimensional rocking and sliding case histories in the 2014 Cephalonia, Greece earthquakes.” In Proc., Int. Conf. on Earthquake Geotechnical Engineering, 1–4. Christchurch, New Zealand.
Hall, J. F., T. H. Heaton, M. W. Halling, and D. J. Wald. 1995. “Near-source ground motion and its effects on flexible buildings.” Earthquake Spectra 11 (4): 569–605. https://doi.org/10.1193/1.1585828.
Hogan, S. 1989. “On the dynamics of rigid-block motion under harmonic forcing.” Proc. R. Soc. Lond. A 425 (1869): 441–476. https://doi.org/10.1098/rspa.1989.0114.
Hogan, S. 1990. “The many steady state responses of a rigid block under harmonic forcing.” Earthquake Eng. Struct. Dyn. 19 (7): 1057–1071. https://doi.org/10.1002/eqe.4290190709.
Housner, G. W. 1963. “The behavior of inverted pendulum structures during earthquakes.” Bull. Seismol. Soc. Am. 53 (2): 403–417.
Ikegami, R., and F. Kishinouye. 1947. “A study on the overturning of rectangular columns in the case of the Nankai earthquake on December 21, 1946.” Bull. Earthquake Res. Ins. 25 (1): 49–55.
Ikegami, R., and F. Kishinouye. 1950. “The acceleration of earthquake motion deduced from overturning of the gravestones in case of the Imaichi earthquake on Dec. 26, 1949.” Bull. Earthq. Res. Inst. Tokyo Univ. 28 (1): 121–128.
Ishiyama, Y. 1982. “Motions of rigid bodies and criteria for overturning by earthquake excitations.” Earthquake Eng. Struct. Dyn. 10 (5): 635–650. https://doi.org/10.1002/eqe.4290100502.
Kampas, G., and N. Makris. 2012. “Time and frequency domain identification of seismically isolated structures: Advantages and limitations.” Earthquake Struct. 3 (3–4): 249–270. https://doi.org/10.12989/eas.2012.3.3_4.249.
Kelly, J. M. 1993. Earthquake-resistant design with rubber. London: Springer.
Kelly, J. M., R. Skinner, and A. Heine. 1972. “Mechanisms of energy absorption in special devices for use in earthquake resistant structures.” Bull. NZ Soc. Earthquake Eng. 5 (3): 63–88.
Kimura, K., K. Yoshioka, T. Takeda, Z. Fukuya, and K. Takemoto. 1976. “Tests on braces encased by mortar in-filled steel tubes.” In Vol. 1041 of Proc., Summaries of Technical Papers of Annual Meeting, 1–42. Tokyo: Architectural Institute of Japan.
Kirkpatrick, P. 1927. “Seismic measurements by the overthrow of columns.” Bull. Seismol. Soc. Am. 17 (2): 95–109.
Konstantinidis, D., and N. Makris. 2007. “The dynamics of a rocking block in three dimensions.” In Proc., 8th Hellenic Society of Theoretical and Applied Mechanics Int. Congress on Mechanics. Athens, Greece: Hellenic Society of Theoretical and Applied Mechanics.
Kounadis, A. N., G. J. Papadopoulos, and D. M. Cotsovos. 2012. “Overturning instability of a two-rigid block system under ground excitation.” ZAMM-J. Appl. Math. Mech. 92 (7): 536–557. https://doi.org/10.1002/zamm.201100095.
Makris, N. 1997. “Rigidity-plasticity-viscosity: Can electrorheological dampers protect base-isolated structures from near-source ground motions?” Earthq. Eng. Struct. Dyn. 26 (5): 571–591. https://doi.org/10.1002/(SICI)1096-9845(199705)26:5%3C571::AID-EQE658%3E3.0.CO;2-6.
Makris, N. 2014a. “A half-century of rocking isolation.” Earthq. Struct. 7 (6): 1187–1221. https://doi.org/10.12989/eas.2014.7.6.1187.
Makris, N. 2014b. “The role of the rotational inertia on the seismic resistance of free-standing rocking columns and articulated frames.” Bull. Seismol. Soc. Am. 104 (5): 2226–2239. https://doi.org/10.1785/0120130064.
Makris, N., and C. J. Black. 2002. “Uplifting and overturning of equipment anchored to a base foundation.” Earthquake Spectra 18 (4): 631–661. https://doi.org/10.1193/1.1515730.
Makris, N., and S.-P. Chang. 2000. “Response of damped oscillators to cycloidal pulses.” J. Eng. Mech. 126 (2): 123–131. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:2(123).
Makris, N., and M. F. Vassiliou. 2012. “Sizing the slenderness of free-standing rocking columns to withstand earthquake shaking.” Arch. Appl. Mech. 82 (10–11): 1497–1511. https://doi.org/10.1007/s00419-012-0681-x.
Makris, N., and J. Zhang. 2001. “Rocking response of anchored blocks under pulse-type motions.” J. Eng. Mech. 127 (5): 484–493. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:5(484).
Mavroeidis, G. P., and A. S. Papageorgiou. 2003. “A mathematical representation of near-fault ground motions.” Bull. Seismol. Soc. Am. 93 (3): 1099–1131. https://doi.org/10.1785/0120020100.
Muto, K., H. Umemura, and Y. Sonobe. 1960. “Study of the overturning vibrations of slender structures.” In Vol. 2 of Proc., 2nd World Conf. on Earthquake Engineering, 1239–1261. Tokyo: Association for Science Documents Information.
Ricker, N. 1943. “Further developments in the wavelet theory of seismogram structure.” Bull. Seismol. Soc. Am. 33 (3): 197–228.
Ricker, N. 1944. “Wavelet functions and their polynomials.” Geophysics 9 (3): 314–323. https://doi.org/10.1190/1.1445082.
Skinner, R., J. Kelly, and A. Heine. 1974. “Hysteretic dampers for earthquake-resistant structures.” Earthquake Eng. Struct. Dyn. 3 (3): 287–296. https://doi.org/10.1002/eqe.4290030307.
Skinner, R., W. Robinson, and G. McVerry. 1993. An introduction to seismic isolation. New York: Wiley.
Skinner, R., R. Tyler, A. Heine, and W. Robinson. 1980. “Hysteretic dampers for the protection of structures from earthquakes.” Bull. New Zealand Nat. Soc. Earthquake Eng. 13 (1): 22–36.
Soong, T., and G. Dargush. 1999. “Passive energy dissipation and active control.” In Structural engineering handbook. Boca Raton, FL: CRC Press.
Spanos, P. D., and A.-S. Koh. 1984. “Rocking of rigid blocks due to harmonic shaking.” J. Eng. Mech. 110 (11): 1627–1642. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:11(1627).
Symans, M., F. Charney, A. Whittaker, M. Constantinou, C. Kircher, M. Johnson, and R. McNamara. 2008. “Energy dissipation systems for seismic applications: Current practice and recent developments.” J. Struct. Eng. 134 (1): 3–21. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:1(3).
Tso, W., and C. Wong. 1989. “Steady state rocking response of rigid blocks part 1: Analysis.” Earthquake Eng. Struct. Dyn. 18 (1): 89–106. https://doi.org/10.1002/eqe.4290180109.
Vassiliou, M. F., S. Burger, M. Egger, J. A. Bachmann, M. Broccardo, and B. Stojadinovic. 2017. “The three-dimensional behavior of inverted pendulum cylindrical structures during earthquakes.” Earthq. Eng. Struct. Dyn. 46 (14): 2261–2280. https://doi.org/10.1002/eqe.2903.
Vassiliou, M. F., and N. Makris. 2011. “Estimating time scales and length scales in pulselike earthquake acceleration records with wavelet analysis.” Bull. Seismol. Soc. Am. 101 (2): 596–618. https://doi.org/10.1785/0120090387.
Veletsos, A., N. Newmark, and C. Chelapati. 1965. “Deformation spectra for elastic and elastoplastic systems subjected to ground shock and earthquake motions.” In Vol. 2 of Proc., 3rd World Conf. on Earthquake Engineering, 663–682. Tokyo: International Association for Earthquake Engineering.
Wada, A., E. Saeki, T. Takeuchi, and A. Watanabe. 1989. Development of unbonded brace. Tokyo: Nippon Steel.
Wen, Y.-K. 1976. “Method for random vibration of hysteretic systems.” J. Eng. Mech. Div 102 (2): 249–263.
Wong, C., and W. Tso. 1989. “Steady state rocking response of rigid blocks part 2: Experiment.” Earthquake Eng. Struct. Dyn. 18 (1): 107–120. https://doi.org/10.1002/eqe.4290180110.
Yim, C., A. K. Chopra, and J. Penzien. 1980. “Rocking response of rigid blocks to earthquakes.” Earthquake Eng. Struct. Dyn. 8 (6): 565–587. https://doi.org/10.1002/eqe.4290080606.
Zhang, J., and N. Makris. 2001. “Rocking response of free-standing blocks under cycloidal pulses.” J. Eng. Mech. 127 (5): 473–483. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:5(473).
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 145 • Issue 5 • May 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Jun 12, 2018
Accepted: Oct 8, 2018
Published online: Feb 26, 2019
Published in print: May 1, 2019
Discussion open until: Jul 26, 2019
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.