Comparison of Methods for Computing Equivalent Viscous Damping Ratios of Structures with Added Viscous Damping
Publication: Journal of Structural Engineering
Volume 134, Issue 1
Abstract
Three analysis methods are compared for determining the equivalent viscous damping ratios in a simple one-story, one-bay system with three different added damping configurations. The analysis methods are modal strain energy using the undamped mode shapes, free vibration log decrement, and complex eigenvalue-eigenvector analysis. The damping configurations include a diagonal configuration, a horizontal configuration, and a toggle-braced system. For each of these systems, a variety of linkage stiffness and damper capacities are considered. In all cases the structure, exclusive of the dampers, is assumed to remain elastic. A brief discussion is provided for the behavior of systems with nonlinear viscous dampers. The results of the study show that significantly different values may be obtained for the effective viscous damping in the same system when different analysis approaches are used. For the toggle-braced system with relatively flexible linkages, it was shown that the modal strain energy approach consistently produced increasing effective damping with increased damper capacity, while the other two methods indicated the opposite results. Subsequent analysis of the toggle-braced structure using the complex eigenvalue-eigenvector approach showed that the effective system damping was indeed decreasing with an increased device damping constant, and that the behavior could be attributed to the axial flexibility of the toggle brace linkage. The analysis indicated that the greater the flexibility of the linkage relative to the damping constant of the device, the greater the phase difference between the deformational velocity in the device and the relative horizontal velocity of the story containing the device. While the phase shift is evident from response history analysis, the most efficient visualization tool is a plot of the damped mode shapes on a complex plane.
Get full access to this article
View all available purchase options and get full access to this article.
References
ASCE. (2005). Minimum design loads for buildings and other structures, ANSI/ASCE 7-05, American Society of Civil Engineers, Reston, Va.
Chopra, A. K. (2001). Dynamics of structures, 2nd Ed., Prentice-Hall, Upper Saddle River, N.J.
Clough, R. W., and Penzien, J. (2003). Dynamics of structures, 2nd Ed., (revised), Computers and Structures, Berkeley, Calif.
Constantinou, M. C., Soong, T. T., and Dargush, G. F. (1998). Passive energy dissipation systems for structural design and retrofit, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, N.Y.
Constantinou, M. C., and Symans, M. (1992). “Experimental and analytical investigation of seismic response of structures with supplemental fluid viscous dampers.” Technical Rep. No. NCEER-92-0032, National Center for Earthquake Engineering Research, State Univ. of New York, Buffalo, N.Y.
Constantinou, M. C., Tsopelas, P., Hammel, W., and Sigaher, A. N. (2001). “Toggle-brace-damper seismic energy dissipation systems.” J. Struct. Eng., 127(2), 105–112.
CSI. (2002). ETABS version 8 user reference manual, Computers and Structures, Berkeley, Calif.
CSI. (2004). SAP2000 version 9 basic analysis reference manual, Computers and Structures, Berkeley, Calif.
FEMA. (2004). “NEHRP recommended provisions for seismic regulations for new buildings and other structures.” FEMA Rep. No. 450-1, Federal Emergency Management Agency, Washington, D.C.
Filiatrault, A., Tremblay, R., and Wankitkorkul, A. (2001). “Performance of passive damping systems for the seismic retrofit of steel moment resisting frames subjected to near field ground motions.” Earthquake Spectra, 17(3), 427–456.
Goel, R. K. (2001). “Simplified analysis of asymmetric structures with supplemental damping.” Earthquake Eng. Struct. Dyn., 30(9), 1399–1416.
Hanson, R. D., and Soong, T. T. (2001). Seismic design with supplemental energy dissipation devices, Earthquake Engineering Research Institute, Oakland, Calif.
Humar, J. L. (1990). Dynamics of structures, Prentice-Hall, Englewood Cliffs, N.J.
Hurty, W. C., and Rubenstein, M. F. (1964). Dynamics of structures, Prentice-Hall, Englewood Cliffs, N.J.
Inman, D. J. (2001). Engineering vibration, 2nd Ed., Prentice-Hall, Upper Saddle River, N.J.
Lallement, G., and Inman, D. (1995). “A tutorial on complex eigenvalues.” Proc., 13th Int. Modal Analysis Conf., Nashville, Tenn.
Liang, Z., and Lee, G. C. (1991). “Damping of structures: Part 1—Theory of complex damping.” Rep. No. NCEER-91-0004, National Center for Earthquake Engineering Research, State Univ. of New York, Buffalo, N.Y.
Lin, W. H., and Chopra, A. K. (2002). “Earthquake response of elastic SDF systems with non-linear fluid viscous dampers.” Earthquake Eng. Struct. Dyn., 31(9), 1623–1642.
Mathsoft, Inc. (2002). Mathcad 11 user’s guide, Cambridge, Mass.
McNamara, R. J. (2001). “Practical solution to reduce the wind induced response of tall buildings.” Proc., 6th World Congress on Tall Buildings, Melbourne, Australia.
Prakash, V., Powell, G. P., and Campbell, S. (1993). Drain-2DX base program description and user guide, Dept. of Civil Engineering, Univ. of California, Berkeley, Calif.
Wilson, E. L. (2002). Three dimensional static and dynamic analysis of structures, Computers and Structures, Inc., Berkeley, Calif.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 134 • Issue 1 • January 2008
Pages: 32 - 44
Copyright
© 2008 ASCE.
History
Received: Feb 22, 2005
Accepted: Apr 13, 2006
Published online: Jan 1, 2008
Published in print: Jan 2008
Notes
Note. Associate Editor: Michael D. Symans
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.