New expressions to estimate damping in direct displacement baseddesign for special concentrically-braced frames

Document Type : Research


1 Associate Professor ,Civil Engineering Department, K. N. Toosi University of Technology, Tehran ,Iran

2 PhD Student ,Civil Engineering Department, K.N. Toosi University of Technology, Tehran, Iran


Different expressions have been developed to determine damping of structures based on various hysteretic models and ductility levels. Since Slenderness ratio is an important parameter on the hysteretic behavior of special concentrically- braced frames (SCBF), in this paper new expressions for determination of damping of such frames are developed based on slenderness ratio and ductility. Two types of SCBF are considered: Inverted V braced frame and X braced frame. Using Jacobsen method, damping is determined and then modified by means of nonlinear time history analysis for special inverted V and X braced frames. A simplified methodology is proposed by using revised effective mass to modify the hysteretic damping. Using the simplified methodology, expressions are proposed to estimate damping for special concentrically- braced frames.


1. Priestley, M. J. N., Calvi, G. M. and Kowalsky, M.J. Displacement-Based Design of Structures, 2007, IUSS Press, Pavia, Italy.
2. Gulkan, P. and Sozen, M.A. (1974). "Inelastic responses of reinforced concrete structures to earthquake motion.", ACI Journal, Vol. 17, No. 12, PP. 604-610.
3. Kowalsky, M.J., Priestley, M.J.N. and MacRae, G.A. (1994). "Displacement-based design: a methodology for seismic design applied to single degree of freedom reinforced concrete structures", Structural Systems Research Report 1994, University of California, San Diego.45
4. Judi, H. J., Davidson, B. J. and Fenwick, R. C. (2000). "Direct displacement based design-a damping perspective," Proceedings of the 12th world conference on earthquake engineering, September, Auckland, New Zealand
5. Iwan, W.D. (1980). "Estimating Inelastic Response Spectra from Elastic Spectra", Earthquake Eng. and Structural Dynamics, Vol. 8, 375-388. [DOI:10.1002/eqe.4290080407]
6. Kwan, W. P. and Billington, S. L. (2003). "Influence of hysteretic behavior on equivalent period and damping of structural systems," Journal of Structural Engineering ASCE, Vol. 129, No. 5, PP. 576- 585 [DOI:10.1061/(ASCE)0733-9445(2003)129:5(576)]
7. Priestley, M.J.N. (2003). "Myths and fallacies in earthquake engineering, Revisited", The 9th Mallet Milne Lecture, 2003, IUSS Press (Rose School), Pavia, Italy.
8. Dwairi, H. and Kowalsky, M.J. (2004). "Investigation of Jacobsen's equivalent viscous damping approach as applied to displacement-based seismic design", Proceeding of 13th World Conference on Earthquake Engineering, August 1-6 Vancouver, BC, Canada
9. Dwairi, H., Kowalsky, M.J. and Nau, J.M. (2007). "Equivalent damping in support of direct displacement-based design", Journal of Earthquake Engineering, Vol. 11, No. 4, PP. 512-530. [DOI:10.1080/13632460601033884]
10. Harris, J L. (2004). "Comparison of steel moment frames designed in accordance with force-based and direct displacement-based design", Proceedings SEAOC Convention, August, Monterey, Canada.
11. Blandon, C. A. and Priestley, M. J. N. (2005). "Equivalent viscous damping equations for direct displacement-based design", Journal of Earthquake Engineering, Vol. 9, No. 2, PP. 257-278 [DOI:10.1142/S1363246905002390]
12. Della Corte, G. and Mazzolani, F. M. (2008). "Theoretical developments and numerical verification of a displacement based design procedure for steel braced structures", In: Proceedings of the 14th world conference on earthquake engineering, Beijing, 12-17 Oct
13. Jacobsen, L. S. (1960). "Damping in composite structures.", In: Proceedings of 2nd world conference on earthquake engineering, vol. 2, Tokyo and Kyoto, Japan, PP. 1029-1044.
14. Iwan, W.D and Gates, N.C. (1979). "The effective period and damping of a class of hysteretic structures", Earthquake Engineering and Structural Dynamics, Vol. 7, No. 3, PP.199-211 [DOI:10.1002/eqe.4290070302]
15. Kowalsky, M.J. and Ayers, J.P. (2002). "Investigation of equivalent viscous damping for direct displacement based design", The 3rd Japan-US workshop on performance based earthquake engineering methodology for reinforced concrete building structures, Seattle, Washington.
16. Grant, D.N., Blandon, C.A. and Priestley, M.J.N. (2005). Modeling inelastic response in direct displacement-based design, Report 2005/03, IUSS Press, Pavia.
17. Priestley, M.J.N. and Grant, D.N. (2005). "Viscous damping in seismic design and analysis", Journal of Earthquake Engineering, Vol. 9, No. 2, PP. 229-255 [DOI:10.1142/S1363246905002365]
18. AISC (2010). Seismic provisions for structural steel buildings, An American National Standard, ANSI/AISC 341-10, American Society of Civil Engineers, Chicago
19. Wakabayashi, M., Nakamura, T. and Yoshida, N. (1977). "Experimental studies on the elastic-plastic behavior of braced frames under repeated horizontal loading (part1: experiments of braces with an H-shaped cross section in a frame)", Bulletin of the disaster prevention research institute, Vol. 27, No. 3, PP. 121-154
20. OpenSees (2010). Open system for earthquake engineering simulation, Pacific Earthquake Engineering Research Center, University of California, Berkeley.
21. Aguero, A., Izvernari, C. and Tremblay, R. (2006). "Modeling of the seismic response of concentrically braced steel frames using the OpenSees analysis environment", International Journal of Advanced Steel Construction, Vol. 2, No. 3, PP. 242-74. [DOI:10.18057/IJASC.2006.2.3.5]
22. Uriz, P., Filippou, F.C. and Mahin, S.A. (2008). "Model for Cyclic Inelastic Buckling of Steel Braces", Journal of Structural Engineering ASCE, Vol. 134, No. 4, PP. 619-28 [DOI:10.1061/(ASCE)0733-9445(2008)134:4(619)]
23. Yang, T.Y., Moehle, J.P. and Stojadinovic, B. (2009). Performance Evaluation of Innovative Steel Braced Frames, Pacific Earthquake Engineering Research center, PEER 2009/103, University of California,
24. Hsiao, P.C., Lehman, D.E. and Roeder, C.W. (2012). "Improved analytical model for special concentrically braced frame", Journal of Constructional Steel research, Vol. 73, PP. 80-94 [DOI:10.1016/j.jcsr.2012.01.010]
25. Archambault, M. H., Tremblay, R. and Filiatrault, A. (1995). Etude du comportementse'ismique des ontreventements ductiles en X avec profile's tubulaires en acier, Rapport no.EPM/GCS 1995-09, De'partement dege'nie civil, E'cole Polytechnique, Montreal.
26. Tremblay, R., Archambault, M.H. and Filiatrault, A. (2003). "Seismic response of concentrically braced steel frames made with rectangular hollow bracing members", Journal of Structural Engineering ASCE, Vol. 129, No. 12, PP. 1626-1636 [DOI:10.1061/(ASCE)0733-9445(2003)129:12(1626)]
27. ASCE (2010). Minimum design loads for buildings and other structures, An ASCE Standard, ASCE/SEI 7-10. American Society of Civil Engineers, Reston Berkeley.