Toppling of Computer‐Type Equipment under Base Excitation
Publication: Journal of Engineering Mechanics
Volume 119, Issue 1
Abstract
An analysis is given of the statistical and probabilistic properties of the random time at which a piece of essential equipment, such as a computer, may topple under base excitations. The equipment is modeled as a rigid block, and the base accelerations are modeled as white noises in horizontal and vertical directions. The cases of a free‐standing block and an anchored block are both considered. The white‐noise idealization resembles the most intense portion of ground acceleration in a seismic event, which is an acceptable simplification provided that the correlation times of actual base excitations are short compared with the dominant quasi‐periods of the induced rocking motion. It is shown that the presence of vertical excitation about one‐half the level of horizontal excitation may increase the probability of toppling by 30–40%, and that larger blocks are more stable than the smaller ones of the same geometrical proportion. The analysis is also applicable to such objects as monuments, storage tanks, and certain types of tall buildings.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Aslam, M., Godden,W. G., and Scalise, D. T. (1980). “Earthquake rocking response of rigid bodies.” J. Struct. Div., ASCE, 106(2), 377–392.
2.
Bharucha‐Reid, A. T. (1960). Elements of Markov processes and their applications. McGraw‐Hill, New York, N.Y.
3.
Dimentberg, M. F., and Menyailov, A. I. (1979). “Response of a single‐mass vibroimpact system to white noise random excitation.” Zeitschift Für Angewandte, Mathematik und Mechanik, Berlin, West Germany, 59, 709–716.
4.
Gianini, R., and Masiani, R. (1991). “Random vibration of the rigid block.” Computational stochastic mechanics, P. D. Spanos, and C. A. Brebbia, eds., Computational Mech. Publications/Elsevier Appl. Sci., London, England, 741–752.
5.
Hasminsky, R. Z. (1964). “On the behavior of a conservative system with small friction and small random noise.” Prikladnaya Mathematika i Mecanica, 28(5), 1126–1130 (in Russian).
6.
Housner, G. W. (1963). “The behavior of inverted pendulum structures during earthquakes.” Bull. Seismological Soc. of Am., 53(2), 403–417.
7.
Ishiyama, Y. (1982). “Motion of rigid bodies and criteria for overturning by earthquake excitations.” Earthquake Engrg. and Struct. Dynamics, 10, 635–650.
8.
Itô, K. (1951). “On stochastic differential equations.” Memoirs, American Mathematical Society, 4, 51–89.
9.
Iyengar, R. N., and Manohar, C. S. (1991). “Rocking response of rectangular rigid blocks under random noise base excitations.” Int. J. Nonlinear Mech., 26(6), 885–892.
10.
Kirkpatrick, P. (1927). “Seismic measurements by the overthrow of columns.” Bull. Seismological Soc. of Am., 17(2), 95–109.
11.
Landa, P. S., and Stratonovich, R. L. (1962). “Theory of stochastic transitions of various systems between different states.” Proc., Moscow University, Moscow, U.S.S.R., Series III(1), 33–45 (in Russian).
12.
Priestley, M. J. N., Evison, R. J., and Carr, A. J. (1978). “Seismic response of structures free to rock on their foundations.”Bull. New Zealand Nat. Soc. of Earthquake Engrg., 11(3) 141–150.
13.
Psycharis, I. N., and Jennings, P. C. (1983). “Rocking of slender rigid bodies allowed to uplift.” Earthquake Engrg. and Struct. Dynamics, 11, 57–76.
14.
Spanos, P. D., and Koh, A. S. (1984). “Rocking of rigid blocks due to harmonic shaking.” J. Engrg. Mech., ASCE, 110(11), 1627–1642.
15.
Spanos, P. D., and Koh, A. S. (1986). “Analysis of block random rocking.” Soil Dynamics and Earthquake Engrg., 5(3), 178–183.
16.
Wong, E., and Zakai, M. (1965). “On the relation between ordinary and stochastic equations.” Int. J. Engrg. Sci., 3(3), 213–229.
17.
Yim, C. S., Chopra, K., and Penzien, J. (1980). “Rocking response of rigid blocks to earthquakes.” Earthquake Engrg. and Struct. Dynamics, 8, 565–587.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 119 • Issue 1 • January 1993
Pages: 145 - 160
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Feb 4, 1992
Published online: Jan 1, 1993
Published in print: Jan 1993
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.