Effect of the viscous damping on the seismic response of Low-rise RC frame building

Keywords: RC frame building, Damping approach, Nonlinear time history analysis, Engineering demand parameters


The equivalent viscous damping is a key parameter in the prediction of the maximum nonlinear response. Damping constitutes a major source of uncertainty in dynamic analysis. This paper studies the effect of using viscous damping, on the reduction of the seismic responses of reinforced concrete RC frame buildings modeled as three-dimensional multi degree of freedom (MDOF) systems, and the use of nonlinear time history analysis as a method of visualized behavior of buildings in the elastic and inelastic range. This study focuses on the implications of the available modeling options on analysis. This article illustrates the effect of using the initial or tangent stiffness in Rayleigh damping in analysis of structures.  Correspondingly, this work is also concerned with the estimation of Rayleigh, mass-proportional or stiffness-proportional damping on engineering demand parameters (EDPs). As a result of a series of considerations, a damping modeling solution for nonlinear time history analysis (NLTHA) was carried out to compute the damage index. The application example is a building designed according to reinforced concrete code BAEL 91 and Algerian seismic code RPA 99/Version 2003 under seven earthquake excitations. The simulations demonstrated the accuracy and effectiveness of the proposed method to account for all of the above effects.

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Author Biographies

Fatima Zohra Baba-Hamed, University of Sciences and Technology of Oran

Department of Civil Engineering.

Luc Davenne, University of Paris Ouest

Laboratory of Energetics Mechanics Electromagnetism.


J. Mazars, S. Grange, and C. Desprez, “Seismic risk: Structural response of constructions,” European Journal of Environmental and Civil Engineering, vol. 15, no. sup1, 2011. [Online]. Available: https://doi.org/10.1080/19648189.2011.9695309

R. Villaverde, “Methods to assess the seismic collapse capacity of building structures: State of the art,” Journal of Structural Engineering, vol. 133, no. 1, january 2007. [Online]. Available: https://doi.org/10.1061/(ASCE)0733-9445(2007)133:1(57)

T. Rossetto and A. Elnashai, “Derivation of vulnerability functions for european-type rc structures based on observational data,” Engineering Structures, vol. 25, no. 10, august 2003. [Online]. Available: https://doi.org/10.1016/S0141-0296(03)00060-9

A. Chopra and R. Goe, “Direct displacement-based design: Use of inelastic vs. elastic design spectra,” Earthquake Spectra, vol. 17, no. 1, february 2001. [Online]. Available: https://doi.org/10.1193/1.1586166

A. Chopra and R. Goe, “A modal pushover analysis procedure for estimating seismic demands for buildings,” Earthquake EngngStruct. Dyn., vol. 31, no. 3, march 2002. [Online]. Available: https://doi.org/10.1002/eqe.144

P. Fajfar, “A nonlinear analysis method for performance-based seismic design,” Earthquake Spectra, vol. 16, no. 3, august 2000. [Online]. Available: https://doi.org/10.1193/1.1586128

FEMA-273. (1997, Oct.) NEHRP guidelines for the seismic rehabilitation of buildings. Federal Emergency Management Agency. Washigton D.C., EE.UU. [Online]. Available: https://www.scinc.co.jp/nanken/pdf/fema273.pdf

A. Chopra and F. McKenna, “Modeling viscous damping in nonlinear response history analysis of buildings for earthquake excitation,” Earthquake Engng Struct. Dyn., vol. 45, no. 2, february 2016. [Online]. Available: https://doi.org/10.1002/eqe.2622

D. Pant, A. Wijeyewickrema, and M. ElGawady, “Appropriate viscous damping for nonlinear time-history analysis of base-isolated reinforced concrete buildings,” Earthquake Engineering & Structural Dynamics, vol. 42, no. 4, december 2013. [Online]. Available: https://doi.org/10.1002/eqe.2328

S. Chang, “Nonlinear performance of classical damping,” Earthquake Engineering and Engineering Vibration, vol. 12, no. 2, june 2013. [Online]. Available: https://doi.org/10.1007/s11803-013-0171-3

P. Jehel, P. Léger, and A. Ibrahimbegovic, “Initial versus tangent stiffness-based rayleigh damping in inelastic time history seismic analyses,” Earthquake Engineering and Engineering Vibration, vol. 43, march 2014. [Online]. Available: https://doi.org/10.1002/eqe.2357

A. Chopra, Dynamics of structures: theory and applications to earthquake engineering. New Jersey, EE.UU.: Prentice Hall, 1995.

T. Heitz, C. Giry, B. Richard, and F. Ragueneau, “How are the equivalent damping ratios modified by nonlinear engineering demand parameters?” presented at 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN), Rhodes Island, GR, 2017.

D. Pan, G. Chen, and Z. Wang, “Suboptimal rayleigh damping coefficients in seismic analysis of viscously-damped structures,” Earthquake Engineering and Engineering Vibration, vol. 13, no. 4, december 2014. [Online]. Available: https://doi.org/10.1007/s11803-014-0270-9

D. Chrisp, “Damping models for inelastic structures,” M.S. thesis, University of Canterbury, Christchurch, NZ, 1980.

P. Shing and S. Mahin, “Elimination of spurious higher-mode response in pseudodynamic tests,” Earthquake Engineering Structural Dynamics, vol. 15, no. 4, may 1987. [Online]. Available: https://doi.org/10.1002/eqe.4290150403

F. Charney, “Consequences of using rayleigh damping in inelastic response history analysis,” presented at Congreso Chileno de Sismología e Ingeniería Antisísmica IX Jornadas, Concepción, CL, 2005.

P. Léger and S. Dussault, “Seismic-energy dissipation in MDOF structures,” Journal of Structural Engineering-asce, vol. 118, no. 5, may 1 1992. [Online]. Available: https://doi.org/10.1061/(ASCE)0733-9445(1992)118:5(1251)

J. Hall, “Problems encountered from the use (or misuse) of Rayleigh damping,” Earthquake Engineering & Structural Dynamics, vol. 35, no. 5, april 2006. [Online]. Available: https://doi.org/10.1002/eqe.541

F. Zareian and R. Medina, “A practical method for proper modeling of structural damping in inelastic plane structural systems,” Computers & Structures, vol. 88, no. 1-2, january 2010. [Online]. Available: https://doi.org/10.1016/j.compstruc.2009.08.001

E. Erduran, “Evaluation of rayleigh damping and its influence on engineering demand parameter estimates,” Earthquake Engineering & Structural Dynamics, vol. 41, no. 14, november 2012. [Online]. Available: https://doi.org/10.1002/eqe.2164

S. Salawdeh and J. Goggins, “Direct displacement based seismic design for single storey steel concentrically braced frames,” Earthquakes and Structures, vol. 10, no. 5, february 2016. [Online]. Available: https://doi.org/10.12989/eas.2016.10.5.1125

L. Sarno, A. Elnashai, and G. Manfredi, “Assessment of RC columns subjected to horizontal and vertical ground motions recorded during the 2009 L’Aquila (Italy) earthquake,” Engineering Structures, vol. 33, no. 5, may 2011. [Online]. Available: https://doi.org/10.1016/j.engstruct.2011.01.023

P. Jennings, “Equivalent viscous damping for yielding structures,” Journal of the Engineering Mechanics Division, vol. 94, no. 1, pp. 103– 116, 1968.

P. Gulkan and M. Sozen, “Inelastic responses of reinforced concrete structure to earthquake motions,” Journal of the American Concrete Institute, vol. 71, no. 12, pp. 604–610, Dec. 1974.

W. Iwan and N. Gates, “The effective period and damping of a class of hysteretic structures,” Earthquake Engineering & Structural Dynamics, vol. 7, no. 3, may/june 1979. [Online]. Available: https://doi.org/10.1002/eqe.4290070302

E. Miranda and J. Ruiz, “Evaluation of approximate methods to estimate maximum inelastic displacement demands,” Earthquake Engineering & Structural Dynamics, vol. 31, no. 3, march 2002. [Online]. Available: https://doi.org/10.1002/eqe.143

W. Kwan and S. Billington, “Influence of hysteretic behavior on equivalent period and damping of structural systems,” Journal of Structural Engineering, vol. 129, no. 5, may 2003. [Online]. Available: https://doi.org/10.1061/(ASCE)0733-9445(2003)129:5(576)

M. Priestley and D. Grant, “Viscous damping in seismic design and analysis,” Journal of Earthquake Engineering, vol. 9, no. sup2, january 2005. [Online]. Available: https://doi.org/10.1142/S1363246905002365

H. Dwairi, M. Kowalsky, and J. Nau, “Equivalent damping in support of direct displacement-based design,” Journal of Earthquake Engineering, vol. 11, no. 4, 2007. [Online]. Available: https://doi.org/10.1080/13632460601033884

T. Heitz, C. Giry, B. Richard, and F. Ragueneau, “Identification of an equivalent viscous damping function depending on engineering demand parameters,” Engineering Structures, vol. 188, no. 4, june 1 2019. [Online]. Available: https://doi.org/10.1016/j.engstruct.2019.03.058

M. Abbasi and M. Moustafa, “Effect of damping modeling and characteristics on seismic vulnerability assessment of multi-frame bridges,” Journal of Earthquake Engineering, april 2019. [Online]. Available: https://doi.org/10.1080/13632469.2019.1592791

J. Smith, Vibration of Structures: Applications in civil engineering design. New York, EE.UU.: Broadview Press, 1988.

A. Alipour and F. Zareian, “Study rayleigh damping in structures; uncertainties and treatments,” presented at 14th World Conference on Earthquake Engineering, Beijing, CN, 2008.

T. Caughey and M. O’kelly, “Classical normal modes in damped linear dynamic systems,” Journal of Applied Mechanics, vol. 32, no. 3, 1965. [Online]. Available: https://doi.org/10.1115/1.3627262

L. Rayleigh and J. Strutt, The Theory Of Sound. New York, EE.UU.: Dover Publications, 1896.

P. Jehel, “A critical look into rayleigh damping forces for seismic performance assessment of inelastic structures,” Engineering Structures, vol. 78, november 1 2014. [Online]. Available: https://doi.org/10.1016/j.engstruct.2014.08.003

E. Smyrou, M. Priestley, and A. Carr, “Modelling of elastic damping in nonlinear time-history analyses of cantilever RC walls,” Bulletin of Earthquake Engineering, vol. 9, no. 5, october 2012. [Online]. Available: https://doi.org/10.1007/s10518-011-9286-y

M. Priestley, D. Grant, and C. Blandon, “Direct displacement-based seismic design,” presented at NZSEE Conference, New Zealand, 2005.

Regles Parasismiques Algeriennes RPA99/Version 2003, Algerian Earthquake Resistant Regulations «RP A 99»/Version 2003, Ministry of Housing and Urbanism, 2003.

(2019) Seismosoft. SeismoStruct v7.0.6. Seismosoft-Earthquake Engineering Software Solutions. Accessed. [Online]. Available: https://seismosoft.com/

J. Mander, M. Priestley, and R. Park, “Theoretical stress-strain model for confined concrete,” Journal of Structural Engineering, vol. 114, no. 8, september 1988. [Online]. Available: https://doi.org/10.1061/(ASCE)0733-9445(1988)114:8(1804)

J. Martínez and A. Elnashai, “Confined concrete model under cyclic load,” Materials and Structures, vol. 30, no. 3, pp. 139–147, Apr. 1997.

M. Menegotto and P. Pinto, “Method of analysis for cyclically loaded rc frames including changes in geometry and non-elastic behaviourof elements under combined normal force and bending,” presented at IABSE reports of the working commissions, Zurich, SUI, 1973.

F. Filippou, V. Bertero, and E. Popov, “Effects of bond deterioration on hysteretic behavior of reinforced concrete joints,” Earthquake Engineering Research Center, University of California, Los Angeles, CA, Tech. Rep. UCB/EERC-83/19, Aug. 1983.

S. Mitrović, J. Ožbolt, and V. Travaš, “Three-dimensional finite element formulation for nonlinear dynamic analysis of seismic site and structure response,” Journal European Journal of Environmental and Civil Engineering, vol. 19, no. 7, 2015. [Online]. Available: https://doi.org/10.1080/19648189.2014.973534

(2016) Seismomatch- a program for spectral matching of earthquake records. Seismosoft-Earthquake Engineering Software Solutions. Accessed. [Online]. Available: https://bit.ly/2knOV07

Eurocode 8: Design of structures for earthquake resistance-Part 1 : General rules, seismic actions and rules for buildings, European Standard Norme Europeenne Europaische Norm, en 1998-1, 2004.

How to Cite
Baba-Hamed F. Z., & Davenne L. (2020). Effect of the viscous damping on the seismic response of Low-rise RC frame building. Revista Facultad De Ingeniería Universidad De Antioquia, (96), 32-43. https://doi.org/10.17533/udea.redin.20191045