Rocking Response of Free-Standing Blocks under Cycloidal Pulses
Publication: Journal of Engineering Mechanics
Volume 127, Issue 5
Abstract
This paper examines in depth the transient rocking response of free-standing rigid blocks subjected to physically realizable trigonometric pulses. First, the expressions for the dynamic horizontal and vertical reactions at the pivot point of a rocking block are derived and it is shown that the coefficient of friction needed to sustain pure rocking motion is, in general, an increasing function of the acceleration level of the pulse. Subsequently, this paper shows that under cycloidal pulses a free-standing block can overturn with two distinct modes: (1) by exhibiting one or more impacts; and (2) without exhibiting any impact. The existence of the second mode results in a safe region that is located on the acceleration-frequency plane above the minimum overturning acceleration spectrum. The shape of this region depends on the coefficient of restitution and is sensitive to the nonlinear nature of the problem. This paper concludes that the sensitive nonlinear nature of the problem, in association with the presence of the safe region that embraces the minimum overturning acceleration spectrum, complicates further the task of estimating peak ground acceleration by only examining the geometry of free-standing objects that either overturned or survived a ground shaking.
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References
1.
Anooshehpoor, A., Heaton, T. H., Shi, B., and Brune, J. N. ( 1999). “Estimates of the ground acceleration at Point Reyes station during the 1906 San Francisco earthquake.” Bull. Seismological Soc. of Am., 89(4), 843–853.
2.
Aslam, M., Scalise, D. T., and Godden, W. G. (1980). “Earthquake rocking response of rigid bodies.”J. Struct. Div., ASCE, 106(2), 377–392.
3.
Campillo, M., Gariel, J. C., Aki, K., and Sanchez-Sesma, F. J. ( 1989). “Destructive strong ground motion in Mexico City: Source, path and site effects during the great 1985 Michoagan earthquake.” Bull. Seismological Soc. of Am., 79(6), 1718–1735.
4.
High-performance numeric computation and visualization software. (1992). MathWorks, Natick, Mass.
5.
Hogan, S. J. ( 1989). “On the dynamics of rigid-block motion under harmonic forcing.” Proc., Royal Soc., London, A425, 441–476.
6.
Hogan, S. J. ( 1990). “The many steady state responses of a rigid block under harmonic forcing.” Earthquake Engrg. and Struct. Dyn., 19(7), 1057–1071.
7.
Housner, G. W. ( 1963). “The behaviour of inverted pendulum structures during earthquakes.” Bull. Seismological Soc. of Am., 53(2), 404–417.
8.
Iwan, W. D., and Chen, X. D. ( 1994). “Important near-field ground motion data from the Landers earthquake.” Proc., 10th Eur. Conf. Earthquake Engrg., Balkema, Rotterdam, The Netherlands.
9.
Jacobsen, L. S., and Ayre, R. S. ( 1958). Engineering vibrations, McGraw-Hill, New York.
10.
Makris, N., and Roussos, Y. ( 1998). “Rocking response and overturning of equipment under horizontal pulse-type motions.” Rep. No. PEER-98/05, Pacific Earthquake Engrg. Res. Ctr., University of California, Berkeley, Calif.
11.
Makris, N., and Roussos, Y. ( 2000). “Rocking response of rigid blocks under near-source ground motions.” Géotechnique, London, 50(3), 243–262.
12.
Pompei, A., Scalia, A., and Sumbatyan, M. A. (1998). “Dynamics of rigid block due to horizontal ground motion.”J. Engrg. Mech., ASCE, 124(7), 713–717.
13.
Scalia, A., and Sumbatyan, M. A. ( 1996). “Slide rotation of rigid bodies subjected to a horizontal ground motion.” Earthquake Engrg. and Struct. Dyn., 25, 1139–1149.
14.
Shenton, H. W., III. (1996). “Criteria for initiation of slide, rock, and slide-rock rigid-body modes.”J. Engrg. Mech., ASCE, 122(7), 690–693.
15.
Shi, B., Anooshehpoor, A., Zeng, Y., and Brune, J. N. ( 1996). “Rocking and overturning of precariously balanced rocks by earthquake.” Bull. Seismological Soc. of Amer., 86(5), 1364–1371.
16.
Spanos, P. D., and Koh, A. S. (1984). “Rocking of rigid blocks due to harmonic shaking.”J. Engrg. Mech., ASCE, 110(11), 1627–1642.
17.
Tso, W. K., and Wong, C. M. ( 1989a). “Steady state rocking response of rigid blocks Part 1: Analysis.” Earthquake Engrg. and Struct. Dyn., 18(1), 89–106.
18.
Tso, W. K., and Wong, C. M. ( 1989b). “Steady state rocking response of rigid blocks Part 2: Experiment.” Earthquake Engrg. and Struct. Dyn., 18(1), 107–120.
19.
Yim, C.-S., Chopra, A. K., and Penzien, J. ( 1980). “Rocking response of rigid blocks to earthquakes.” Earthquake Engrg. and Struct. Dyn., 8(6), 565–587.
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Received: Jan 14, 2000
Published online: May 1, 2001
Published in print: May 2001
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