Evaluating Accuracy of FEMA-356 Proposed Equation for Effective Damping Ratio for Viscous and Visco-elastic Dampers

Document Type : Research Article


Department if Civil and Environment Engineering, School of Engineering, Shiraz university, Shiraz, Iran


The use of dampers for retroftting and reducing seismic induced vibrations of structures is rising. Among all types of dampers, viscous and visco-elastic dampers are extensively used for buildings. Adding dampers increases equivalent damping ratio of structure which decreases displacement and member stresses. FEMA-356 has proposed an equation for calculating equivalent damping ratio of shear buildings with added dampers, based on the frst mode of vibration. In the present research, the goal was to study the accuracy of FEMA-356 formula for evaluating equivalent damping ratio with
dampers as compared with the theoretical one. For the latter, the calculation is based on the hysteresis force-displacement response of the dampers. For obtaining hysteresis response, dynamic equation of motion of 2 to 12 stories 2D shear buildings equipped with viscous and visco-elastic dampers subjected to harmonic base excitation were solved. Both regular and mass distributed in height irregular structures with added dampers at all levels were considered. In addition to that, dampers were considered at random stories of the buildings and accuracy of equivalent damping ratios of FEMA-356 were evaluated. This study has shown that for viscous dampers, error of FEMA-356 formula in comparison with theoretical
formula for viscous dampers would be in the range of 1 to 3 percent and for visco-elastic ones in which stiffness ratio of visco-elastic dampers to story shear stiffness is 10 percent, would be in the range of 1 to 17 percent. When the stiffness ratio is decreased to 5 percent, the error would decrease to 2, in the worst case. Also, it has been shown that mass irregularity in the height of the buildings increases the maximum error from 17% to 58% for viscoelastic dampers; no signifcant effect for viscous dampers. Moreover, addition of dampers in random stories of buildings up to six stories would increase error of FEMA-356 formula about 42 and 50 percent, respectively, for viscous and visco-elastic dampers.


Main Subjects

[1] Z. Liang, G. C. Lee, G. F. Dargush, J. Song, Structural damping-application in seismic response modifcation, CRC Press, 2006.
[2] R. D. Hanson, C. Xia, and Y. F. Su, Design of supplemental damping device for buildings, Earthquake engineering, Tenth world conference, Balkema, Rotterdam (1992).
[3] J. S. Hiwang, Seismic design of structures with viscous dampers, International training programs for seismic design of structures by National center for research on earthquake engineering, Taiwan,2002.
[4] F. Sadek, B. Mohraz, M. Riley, Linear procedure for structures with velocity-dependent dampers, Journal of Structural Engineering, 126 (2000) 87-895.
[5] Building Seismic Safety Council (BSSC), Prepared by the NEHRP guidelines for the seismic rehabilitation of buildings, FEMA 273 Report, Washington, D.C., U. S. A., 1997.
[6] S. A. Mousavi, A. Ghorbani-Tanha, Optimum placement and characteristics of velocity-dependent dampers under seismic excitation, Earthquake Engineering and Engineering Vibration, 11(3) (2012) 403-414.
[7] J. Scheller, U. Starossek, A versatile active mass damper for structural vibration control, Proceedings of the 8th International Conference on Structural Dynamics, Leuven, Belgium (2011).
[8] A. Yahyaabadi, S. M. Zahrai, Studying rooftop damper frame in braced structures under near and far feld earthquake excitations, Amirkabir Journal of Science & Research (Civil & Environmental Engineering), 41(1) ( 2008) 1- 11
[9] M. Mohebbi, H. Rasouli Dabbagh, S. Moradpour,Seismic
 vibration control of nonlinear structures using semiactive tuned mass dampers, Amirkabir Journal of Science
 & Research (Civil & Environmental Engineering), 46(2)
 ( 2014) 41- 43
[10] J. Kang, H.Tagawa, Seismic performance of steel structures with seesaw energy dissipation system using fluid viscous dampers, Journal of Engineering Structures, 56 (2013) 431–442.
[11] S. M. Zahrai, S. A. Mousavi, Suitable energy dissipation device for private typical buildings with poor seismic performance”, Journal of Seismology and Seismic Engineering, 14(2) (2012) 131-143.
[12] K. S. Kumar, C. A. Jeyasehar, K. Muthumania, A design methodology for supplemental damping for seismic performance enhancement of frame structures, Asian Journal of Civil Engineering, 13(5) (2012) 659-678.
[13] I. D. Aiken, D. K. Nims, A. S. Whittaker , J. M. Kelly, Testing of passive energy dissipation systems, Earthquake Spectra, 9(3) (1993) 335-370.
[14] ASCE, Pre-standard and Commentary for The Seismic Rehabilitation of Buildings, Prepared by the American Society of Civil Engineering, Published by the Federal Emergency Management Agency, FEMA 356 Report, Washington, DC., U. S. A., 2000.
[15] R. K. Goel: Seismic response study of asymmetric systems with linear and nonlinear fluid viscous dampers, Report No. CP/SEAM-2002/06, California Polytechnic State University, U.S.A. , 2002.
[16] ATC-55, Improvement of Nonlinear Static Analysis Procedures, Prepared by the Applied Technology Council for the Building Seismic Safety Council, Published by the Federal Emergency Management Agency, FEMA 440 Report, Washington, DC., U. S. A. , 2005.
[17] J. L. Hummar: Dynamic of Structures, Second Edition, A.A.Balkema, Publisher,Tokyo, Japan, 2001.[18] A. K. Chopra: Dynamics of Structures: Theory and Applications to Earthquake Engineering, Prentice Hall, New Jersey, U.S.A. 1995.
[19] Iranian code of practice for seismic resistant of buildings, standard No.2800-5 (Third edition), BHRC publication No. S-253, 2005.
[20] M. S. Williams, A. Blakeborough, B. Wu, Static and real-time dynamic testing of passive dissipation devices, 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada (2004).
[21] Y. C. Fung:Foundations of solid mechanics, PrenticeHall, Englewood cliffs, N. J., U.S.A. 1965.
[22] G. V. Berg: Elements of structural dynamics, PrenticHall, New Jersey, U.S.A., 1989.