Inverse Damping Perturbation for Stiffness Design of Shear Buildings
Publication: Journal of Structural Engineering
Volume 122, Issue 6
Abstract
The problem in this paper is to find the set of story stiffnesses of an elastic shear building with added viscous dampers such that each mean maximum interstory drift due to spectrum-compatible design earthquakes would coincide with the specified value. Two simple stiffness formulas have been derived by means of the proposed inverse perturbation procedure of damping level, referred to as the “inverse damping perturbation.” The first formula enables one to evaluate the primary effect of heavy damping for stiffness design, and the second formula enables one to evaluate the effect of off-diagonal terms of the modal damping matrix that is neglected in the first formula. A storywise criterion is derived by use of the second formula as to whether the effect can be negligible or not.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bischof, C., and Griewank, A. (1992). “ADIFOR: A FORTRAN system for portable automatic differentiation.”Proc., 4th AIAA/USAF/ NASA/OAI Symp. on Multidisciplinary Anal. and Optimization, 433–441.
2.
Caughey, T. K.(1960). “Classical normal modes in damped linear dynamic systems.”J. Appl. Mech., 27, 269–271.
3.
Caughey, T. K., and O'Kelly, M. E. J.(1961). “Effect of damping on the natural frequencies of linear dynamic systems.”J. Acoustical Soc. of Am., 33(11), 1458–1461.
4.
Cronin, D. L. (1976). “Approximation for determining harmonically excited response of non-classically damped systems.”J. Engrg. Indust., 98B(2), 43–47.
5.
Der Kiureghian, A.(1981). “A response spectrum method for random vibration analysis of MDF systems.”Earthquake Engrg. and Struct. Dynamics, 9, 419–435.
6.
Foss, K. A.(1958). “Coordinates which uncouples the equations of motion of damped linear dynamic systems.”J. Appl. Mech., 25(9), 361–364.
7.
Gasparini, D. A., and Vanmarcke, E. H. (1976). “Simulated earthquake motions compatible with prescribed response spectra-SIMQKE.”NISEE/Computer Applications, Massachusetts Inst. of Technol. (MIT), Cambridge, Mass.
8.
Hahn, G. D., and Sathiavageeswaran, K. R.(1992). “Effects of added-damper distribution on the seismic response of buildings.”Comp. and Struct., 43(5), 941–950.
9.
Hearn, A. C. (1987). REDUCE user's manual, version 3.3, The Rand Corp., Santa Monica, Calif.
10.
Igusa, T., Der Kiureghian, A., and Sackman, J. L.(1984). “Modal decomposition method for stationary response of non-classically damped systems.”Earthquake Engrg. and Struct. Dynamics, 12, 121–136.
11.
Lin, R. C., Liang, Z., Soong, T. T., Zhang, R. H., and Mahmoodi, P.(1991). “An experimental study on seismic behavior of viscoelastically damped structures.”Engrg. Struct., 13(1), 75–84.
12.
Mahmoodi, P.(1969). “Structural dampers.”J. Struct. Div., ASCE, 95(8), 1661–1672.
13.
Miyazaki, M., and Mitsuyama, Y. (1992). “Design of a building with 20% or greater damping.”Proc., 10th World Conf. Earthquake Engrg., Asociación Española de Ingeniería Sísmica, Madrid, Spain, VII, 4143– 4148.
14.
Nakamura, T., and Ohsaki, M.(1988). “Sequential optimal truss generator for frequency ranges.”Comp. Methods in Appl. Mech. Engrg., 67(2), 189–209.
15.
Nakamura, T., and Yamane, T.(1986). “Optimal design and earthquake-response constrained design of elastic shear buildings.”Earthquake Engrg. and Struct. Dynamics, 14(5), 797–815.
16.
Newmark, N. M., and Hall, W. J. (1982). Earthquake spectra and design . Earthquake Engrg. Res. Inst., Berkeley, Calif.
17.
Sackman, J. L., Der Kiureghian, A., and Nour-Omid, B.(1983). “Dynamic analysis of light equipment in structures: modal properties of the combined system.”J. Engrg. Mech., ASCE, 109(1), 73–89.
18.
Scholl, R. E. (1984). “Brace dampers: An alternative structural system for improving the earthquake performance of buildings.”Proc., 8th World Conf. Earthquake Engrg., Earthquake Engrg. Res. Inst., San Francisco, Calif., V, 1015–1022.
19.
Suarez, L. E., and Singh, M. P.(1987). “Eigenproperties of nonclassically damped primary structure and oscillator systems.”J. Appl. Mech., 54(9), 668–673.
20.
Thomson, W. T., Calkins, T., and Caravani, P.(1974). “A numerical study of damping.”Earthquake Engrg. and Struct. Dynamics, 3(1), 97–103.
21.
Warburton, G. B., and Soni, S. R.(1977). “Errors in response calculations for non-classically damped structures.”Earthquake Engrg. and Struct. Dynamics, 5(4), 365–376.
22.
Wilson, E. L., and Penzien, J.(1972). “Evaluation of orthogonal damping matrices.”Int. J. Numerical Methods in Engrg., 4(1), 5–10.
23.
Wilson, E. L., Der Kiureghian, A., and Bayo, E. P.(1981). “A replacement for SRSS method in seismic analysis.”Earthquake Engrg. and Struct. Dynamics, 9(2), 187–194.
24.
Xu, K. M., and Igusa, T.(1991). “Dynamic characteristics of non-classically damped structures.”Earthquake Engrg. and Struct. Dynamics, 20(12), 1127–1144.
25.
Yang, J. N., Sarkani, S., and Long, F. X.(1990). “A response spectrum approach for seismic analysis of nonclassically damped structures.”Engrg. Struct., 12(7), 173–184.
26.
Zhang, R. H., Soong, T. T., and Mahmoodi, P.(1989). “Seismic response of steel frame structures with added viscoelastic dampers.”Earthquake Engrg. and Struct. Dynamics, 18(3), 389–396.
27.
Zhang, R. H., and Soong, T. T.(1992). “Seismic design of viscoelastic dampers for structural applications.”J. Struct. Engrg., ASCE, 118(5), 1375–1392.
Information & Authors
Information
Published In
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Jun 1, 1996
Published in print: Jun 1996
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.