Simplified expressions for modelling rigid rocking structures on two-spring foundations
DOI:
https://doi.org/10.5459/bnzsee.45.1.31-39Abstract
This paper presents a new technique for modelling the dynamic response of uplifting rigid structures subjected to base excitation. The proposed technique exploits the use of a two spring foundation, and subsequently an equivalent single-degree-of-freedom procedure is established to model the dynamics of the system. A set of simplified closed-form expressions have been developed to estimate the system’s restoring force-displacement characteristics. The simplified expressions only require details of the system geometry and are shown to predict the nonlinear force-displacement characteristics of a rocking structure as closely as those determined from a complicated pushover analysis.
This paper presents two additional numerical examples to demonstrate the use of the proposed technique to simulate the displacement time-histories of a prototype structure under free-vibration-decay or when subjected to earthquake excitations.
References
Anderson, D. L. (2003). "Effect of foundation rocking on the seismic response of shear walls". Canadian Journal of Civil Engineering, 30 (2), 360-365. DOI: https://doi.org/10.1139/l02-053
Arze, E. (1993). "Seismic design of industrial facilities". Tectonophysics, 218 (1-3), 23-41. DOI: https://doi.org/10.1016/0040-1951(93)90257-K
Beck, J. L. and Skinner, R. I. (1974). "Seismic Response of a Reinforced Concrete Bridge Pier Designed to Step". Earthquake Engineering & Structural Dynamics, 2 (4), 343-358.
Chopra, A. K. and Yim, S. C. S. (1985). "Simplified Earthquake Analysis of Structures with Foundation Uplift". Journal of Structural Engineering, 111 (4), 906-930. DOI: https://doi.org/10.1061/(ASCE)0733-9445(1985)111:4(906)
Design Simulation Technologies, Inc. (2003). Working Model 2D (6.0.0). Available Distributor: Design Simulation Technologies, Inc., Canton, MI 48187 <http://www.workingmodel.com>
Housner, G. W. (1963). "The behaviour of Inverted pendulum structures during earthquakes". Bulletin of the Seismological Society of America, 53 (2), 403-417.
Huckelbridge, A. A. and Clough, R. W. (1978). "Seismic Response of Uplifting Building Frame". ASCE J Struct Div, 104 (8), 1211-1229.
Ichinose, T. (1986). "Rocking Motion of Slender Elastic Body on Rigid Floor". Bulletin of the New Zealand National Society for Earthquake Engineering, 19 (1), 18-27. DOI: https://doi.org/10.5459/bnzsee.19.1.18-27
Jennings, P. C. and Bielak, K. (1973). "Dynamics of buildingsoil interaction". Bulletin of the Seismological Society of America, 63 (1), 9-48.
Kelly, T. E. (2009). "Tentative Seismic Design Guidelines for Rocking Structures". Bulletin of the New Zealand Society for Earthquake Engineering, 42 (4), 239-274. DOI: https://doi.org/10.5459/bnzsee.42.4.239-274
McManus, K. J. (1980). "The seismic response of bridge structures free to rock on their foundations," A report submitted in partial fulfilment of the requirements for the degree of Master of Engineering at the University of Canterbury, Christchurch, New Zealand, University of Canterbury, Christchurch, N.Z.
Meek, J. W. (1975). "Effects of Foundation Tipping on Dynamic Response". Journal of the Structural Division, ASCE, 101 (7), 1297-1311.
Palmeri, A. and Makris, N. (2008). "Response analysis of rigid structures rocking on viscoelastic foundation". Earthquake Engineering and Structural Dynamics, 37 (7), 1039-1063. DOI: https://doi.org/10.1002/eqe.800
Pampanin, S. (2006). "Controversial aspects in seismic assessment and retrofit of structures in modern times: Understanding and implementing lessons from ancient heritage". Bulletin of the New Zealand Society for Earthquake Engineering, 39 (2), 120-134. DOI: https://doi.org/10.5459/bnzsee.39.2.120-133
Psycharis, I. N. (1991). "Effect of base uplift on dynamic response of SDOF structure". Journal of Structural Engineering New York, N.Y., 117(3), 733-754. DOI: https://doi.org/10.1061/(ASCE)0733-9445(1991)117:3(733)
Psycharis, I. N. and Jennings, P. C. (1983). "Rocking of slender rigid bodies allowed to uplift". Earthquake Engineering & Structural Dynamics, 11 (1), 57-76. DOI: https://doi.org/10.1002/eqe.4290110106
Psycharis , I. N., Papastamatiou, D. Y. and Alexandris, A. P. (2000). "Parametric investigation of the stability of classical columns under harmonic and earthquake excitations". Earthquake Engineering & Structural Dynamics, 29, 1093-1109. DOI: https://doi.org/10.1002/1096-9845(200008)29:8<1093::AID-EQE953>3.0.CO;2-S
Sharpe, R. D. and Skinner, R. I. (1983). "The Seismic Design of an Industrial Chimney with Rocking Base". Bulletin of the New Zealand Society for Earthquake Engineering, 16 (2), 98-106.
Tse, J., Bryson, J. and Abrahams, M. J. (2002). "Reconstruction of the Lions Gate Bridge Construction Engineering and Methods". 19th annual International Bridge Conference, Pittsburgh, U.S.A.
Xu, C., and Spyrakos, C. C. (1996). "Seismic analysis of towers including foundation uplift". Engineering Structures, 18 (4), 271-278. DOI: https://doi.org/10.1016/0141-0296(95)00059-3
Yim, C. S. and Chopra, A. K. (1984a). "Earthquake Response of Structures with Partial Uplift on Winkler Foundation". Earthquake Engineering & Structural Dynamics, 12, 263-281. DOI: https://doi.org/10.1002/eqe.4290120209
Yim, S. C. S. and Chopra, A. K. (1984b). "Dynamics Of Structures On Two-Spring Foundation Allowed To Uplift". Journal of Engineering Mechanics, ASCE, 110 (7), 1124-1146. DOI: https://doi.org/10.1061/(ASCE)0733-9399(1984)110:7(1124)
Yim, S. C. S. and Chopra, A. K. (1985). "Simplified Earthquake Analysis Of Multistory Structures With Foundation Uplift". Journal of Structural Engineering New York, N.Y., 111 (12), 2708-2731. DOI: https://doi.org/10.1061/(ASCE)0733-9445(1985)111:12(2708)
