Stochastic Earthquake Response of Tapered Column
Publication: Journal of Engineering Mechanics
Volume 110, Issue 8
Abstract
This paper presents a stochastic analysis of a tapered column subjected to gravity as well as horizontal and vertical earthquake accelerations. The normal mode approach is used. The approach considers the effect of both non‐uniformity in column configuration and axial loading on mode shapes and natural frequencies. The earthquake accelerations are modeled as non‐stationary Gaussian random processes with either white or non‐white power spectra. This allows the statistical moments of column responses to be solved from a set of first order ordinary differential equations derived from the theory of Markov process. Both time histories of responses and spatial distribution of maximum responses along the elevation of the column are presented. Exact analytical sequences can be applied to handle problems of nonuniform columns.
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References
1.
Abu‐Saba, E. G., “Vibration of Chimney Supported on Elevated Concrete Slab,” Journal of the Structural Division, ASCE, Vol. 97, No. ST2, Feb., 1971.
2.
Ariaratnam, S. T., “Dynamic Stability of a Column under Random Loading,” Dynamic Stability of Structures, G. Herrman, ed., Pergamon Press, Inc., New York, N.Y., 1967.
3.
Arya, A. S., and Paul, D. K., “Earthquake Response of Tall Chimneys,” Proc. Sixth World Conf. Earthq. Engrg., New Delhi, India, 1977.
4.
Bolotin, V. V., Statistical Methods in Structural Mechanics, Holden‐Day, San Francisco, 1969.
5.
Clough, R. W., and Penzien, J., Dynamics of Structures, McGraw‐Hill, New York, N.Y., 1975.
6.
Gasparini, D. A., “Response of MDOF Systems to Nonstationary Random Excitation,” Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM1, Feb., 1979.
7.
Housner, G. W., and Keightley, W. O., “Vibrations of Linearly Tapered Cantilever Beams,” Journal of the Engineering Mechanics Division, ASCE, Vol. 88, No. EM2, April, 1962.
8.
Iyengar, R. N., and Shinozuka, M., “Effect of Self‐Weight and Vertical Acceleration on the Behavior of Tall Structures during Earthquakes,” Earthq. Engrg. Struct. Dym., Vol. 1, 1972, pp. 69–78.
9.
Lin, Y. K., and Shih, T. Y., “Column Response to Horizontal‐Vertical Earthquakes,” Journal of the Engineering Mechanics Division, ASCE, Vol. 106, No. EM6, Dec., 1980.
10.
Lin, Y. K., and Shih, T. Y., “Vertical Seismic Load Effect on Building Response,” Journal of the Engineering Mechanics Division, ASCE, Vol. 107, No. EM2, April, 1982.
11.
Lin, Y. K., Probabilistic Theory of Structural Dynamics, McGraw‐Hill, New York, N.Y., 1967.
12.
Rosenfeld, H., “Consideration of the Rotation of the Foundation in the Analysis of a Steel Chimney 130 M. High, Subject to Seismic Movement,” Proc. Third World Conf. Earthq. Engrg., Auckland and Wellington, New Zealand, 1965.
13.
Rumman, W. S., “Earthquake Forces in Reinforced Concrete Chimneys,” Journal of the Structural Division, ASCE, Vol. 93, No. ST6, Dec., 1967.
14.
Shiau, L.‐C., and Yang, H. T. Y., “Elastic‐Plastic Seismic Response of Chimney,” Journal of the Structural Division, ASCE, Vol. 106, No. ST4, Apr., 1980.
15.
Shih, T. Y., and Lin, Y. K., “Vertical Seismic Load Effect on Hysteretic Columns,” Journal of the Engineering Mechanics Division, ASCE, Vol. 108, No. EM2, April, 1982.
16.
Shinozuka, M., and Henry, L., “Random Vibration of a Beam Column,” Journal of the Engineering Mechanics Division, ASCE, Vol. 91, No. EM5, 1965.
17.
Solodovnikov, V. V., Introduction to the Statistical Dynamics of Automatic Control Systems, Dover Publications, Inc., New York, N.Y., 1960.
18.
Spanos, P.‐T. D., “Non‐Stationary Random Vibration of a Linear Structure,” Int. J. Solids Structures, Vol. 14, 1978, pp. 861–867.
19.
Spanos, P.‐T. D., and Lutes, L. D., “Probability of Response to Evolutionary Process,” Journal of the Engineering Mechanics Division, ASCE, Vol. 106, No. EM2, April, 1980.
20.
Stratonovich, R. L., Topics in the Theory of Random Noise, Vol. I, Gordon and Breach, New York, N.Y., 1963.
21.
Tajimi, H., “A Statistical Method of Determining the Maximum Response of a Building Structure during an Earthquake,” Proc. Second World Conf. Earthq. Engrg., Tokyo and Kyoto, Japan, 1960.
22.
Timoshenko, S. P., and Gere, J. M., Theory of Elastic Stability, 2nd ed., McGraw‐Hill, New York, N.Y., 1961.
23.
Westermo, B. D., “Gravity and Dynamic Response of Vertical Beams,” Journal of the Engineering Mechanics Division, ASCE, Vol. 107, No. EM5, Oct., 1981.
24.
Wang, M. C., and Uhlenbeck, G. E., “On the Theory of the Brownian Motion II,” in Selected Papers on Noise and Stochastic Processes, ed. by N. Wax, Dover Publications, Inc., New York, N.Y., 1954.
25.
Wirsching, P. H., and Yao, J. T.‐P., “Random Behavior of Columns,” Journal of the Engineering Mechanics Division, ASCE, Vol. 97, No. EM3, 1971.
26.
Wong, E., Stochastic Processes in Information and Dynamical Systems, McGraw‐Hill, New York, N.Y., 1971.
27.
Yamamoto, S., and Suzuki, N., “Experimental and Theoretical Analysis of Response against Earthquakes of Tower Structures Having Non‐Uniform Sections Governed by Bending Vibrations,” Proc. Third World Conf. Earthq. Engrg., Auckland and Wellington, New Zealand, 1965.
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Copyright © 1984 ASCE.
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Published online: Aug 1, 1984
Published in print: Aug 1984
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