Envelopes for Seismic Response Vectors. I: Theory
Publication: Journal of Structural Engineering
Volume 126, Issue 4
Abstract
In the design or analysis of structures for seismic loads, the effects of forces acting simultaneously in a member must be considered. The most common example is in the interaction of bending moments and axial load in columns. The usual response spectrum method provides the maximum values of individual responses, but the critical combination of these responses may not involve any of these maxima. In this paper, a response-spectrum-based procedure for predicting the envelope that bounds two or more responses in a linear structure is developed. It is shown that, for an assumed orientation of the principal axes along which the ground motion components are uncorrelated, this envelope is an ellipsoid. For the case when the orientation of the principal axes is unknown, a “supreme” envelope is derived, which corresponds to the most critical orientation of the axes. The response envelope can be superimposed on a capacity curve to determine the adequacy of a given design. In a companion paper, the results of a numerical study are presented to illustrate the accuracy and significance of this method.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Anastassiadis, K. (1993). “Directions sismiques défavorables et combinaisons défavorables des efforts.” Annales de l'Institut Technique du Batiment et des Travaux Publics, 512, 83–97 (in French).
2.
Clough, R. W., and Penzien, J. (1993). Dynamics of structures. McGraw-Hill, New York.
3.
Der Kiureghian, A. (1981). “A response spectrum method for random vibration analysis of MDF systems.” Earthquake Engrg. and Struct. Dyn., 9(5), 419–435.
4.
Der Kiureghian, A., and Nakamura, Y. (1993). “CQC modal combination rule for high-frequency modes.” Earthquake Engrg. and Struct. Dyn., 22(11), 943–956.
5.
Gupta, A. K. (1990). Response spectrum method in seismic analysis and design of structures. Blackwell, Cambridge, Mass.
6.
Gupta, A. K., and Singh, M. P. (1977). “Design of column sections subjected to three components of earthquake.” Nuclear Engrg. and Des., 41(1), 129–133.
7.
Menum, C., and Der Kiureghian, A. (1998). “A replacement for the 30%, 40% and SRSS rules for multicomponent seismic analysis.” Earthquake Spectra, 14(1), 153–163.
8.
Menum, C., and Der Kiureghian, A. (2000). “Envelopes for seismic response vectors. II: Application.”J. Struct. Engrg., ASCE, 126(4), 474–481.
9.
Penzien, J., and Watabe, M. (1975). “Characteristics of 3-dimensional earthquake ground motions.” Earthquake Engrg. and Struct. Dyn., 3(4), 365–373.
10.
Recommended lateral force requirements and commentary “blue book.” (1996). 6th Ed., Seismology Committee, Structural Engineers Association of California, Sacramento, Calif.
11.
Singh, M. P., and Chu, S. L. (1976). “Stochastic considerations in seismic analysis of structures.” Earthquake Engrg. and Struct. Dyn., 4(3), 295–307.
12.
Singh, M. P., and Maldonado, G. O. (1991). “An improved response spectrum method for calculating seismic design response. Part 1: Classically damped structures.” Earthquake Engrg. and Struct. Dyn., 20(7), 621–635.
13.
Smeby, W., and Der Kiureghian, A. (1985). “Modal combination rules for multicomponent earthquake excitation.” Earthquake Engrg. and Struct. Dyn., 13(1), 1–12.
14.
Wilson, E. L., Der Kiureghian, A., and Bayo, E. P. (1981). “A replacement for the SRSS method in seismic analysis.” Earthquake Engrg. and Struct. Dyn., 9(2), 187–194.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 126 • Issue 4 • April 2000
Pages: 467 - 473
History
Received: Jun 30, 1998
Published online: Apr 1, 2000
Published in print: Apr 2000
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.