Influence of Viscous Damping Models on the Inelastic Response of Reinforced Concrete Columns and Bridges
Publication: Journal of Structural Engineering
Volume 149, Issue 2
Abstract
The appropriate estimation of displacements is crucial in performance-based design. Among the options to assess deformation demands, Nonlinear Time History Analysis (NLTHA) is the most sophisticated. However, previous research has shown that NLTHA is sensitive to the viscous damping model definition, and there is substantial disagreement in the engineering community regarding damping model choices. Thus, the goal of this paper is to show the impact of viscous damping model assumptions on the nonlinear response of bridges. A displacement sensitivity study was conducted on several multi-span bridges using various viscous damping models and earthquake records. The results indicate that the mean displacement varies as a function of the displacement ductility level and damping model. In order of ascending displacement demand, the Wilson-Penzien model had the lowest demands followed by the Rayleigh-Initial stiffness, Mass proportional, Rayleigh-Tangent stiffness, Tangent stiffness proportional damping, and Zero-damping. Also, this paper proposes a new viscous damping model. We expect these findings to help practitioners understand the implications of the choice of the damping model and guide the analyst when selecting damping parameters.
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Data Availability Statement
Inputs and output files from models and codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The first author is pleased to acknowledge MINCIENCIAS and the Fulbright Association in Colombia for a scholarship to pursue his Ph.D. studies in the United States. Financial support from NC State University and the Alaska Department of Transportation and Public Facilities is also gratefully appreciated.
References
Abbasi, M., and M. A. Moustafa. 2021. “Effect of damping modeling and characteristics on seismic vulnerability assessment of multi-frame bridges.” J. Earthquake Eng. 25 (8): 1616–1643. https://doi.org/10.1080/13632469.2019.1592791.
Bernal, D. 1994. “Viscous damping in inelastic structural response.” J. Struct. Eng. 120 (4): 1240–1254. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:4(1240).
Caltrans. 2019. Seismic design criteria 2.0. Sacramento, CA: Dept. of Transportation—State of California.
Carr, A. J. 2004. RUAUMOKO-3D—A program for inelastic time-history analysis. Christchurch, New Zealand: Univ. of Canterbury.
Charney, F. A. 2008. “Unintended consequences of modeling damping in structures.” J. Struct. Eng. 134 (4): 581–592. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:4(581).
Chopra, A. K., and F. McKenna. 2016. “Modeling viscous damping in nonlinear response history analysis of buildings for earthquake excitation.” Earthquake Eng. Struct. Dyn. 45 (2): 193–211. https://doi.org/10.1002/eqe.2622.
Chrisp, D. 1980. “Damping models for inelastic structures.” Master’s thesis, Dept. of Civil and Natural Resources Engineering, Univ. of Canterbury.
Cruz, C., and E. Miranda. 2017. “Evaluation of the Rayleigh damping model for buildings.” Eng. Struct. 138 (May): 324–336. https://doi.org/10.1016/j.engstruct.2017.02.001.
Hall, J. F. 2006. “Problems encountered from the use (or misuse) of Rayleigh damping.” Earthquake Eng. Struct. Dyn. 35 (5): 525–545. https://doi.org/10.1002/eqe.541.
Hasgul, U., and M. Kowalsky. 2014. “Impact of viscous damping models on nonlinear response of SDOF systems.” In Proc., 10th US National Conf. on Earthquake Engineering. Oakland, CA: Earthquake Engineering Research Institute. https://doi.org/10.4231/D37S7HS9R.
Johnson, N., M. S. Saiidi, and D. Sanders. 2009. “Nonlinear earthquake response modeling of a large-scale two-span concrete bridge.” J. Bridge Eng. 14 (6): 460–471. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000009.
Kong, C. 2017. “Rapid direct displacement-based assessment approach for bridge structures.” Ph.D. dissertation. Dept. of Civil, Construction and Environmental Engineering, North Carolina State Univ.
Martinez, D. 2021. “Impact of viscous damping model assumptions on the nonlinear response of bridge structures.” Ph.D. dissertation, Dept. of Civil, Construction and Environmental Engineering, North Carolina State Univ.
Martinez, D., and M. Kowalsky. 2020. “Impact of viscous damping model assumptions on the nonlinear response of multi-span bridges.” In Proc., 17th World Conf. on Earthquake Engineering. Tokyo: Japan Association of Earthquake Engineering.
Martinez, D., and M. Kowalsky. 2022a. “Comparison of seismic demands on RC bridge columns using the AASHTO guide specification, DDBA, and nonlinear analysis for shallow crustal and subduction tectonic regimes.” J. Bridge Eng. 949 (6): 1–14. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001868.
Martinez, D., and M. Kowalsky. 2022b. “Recommended parameters for the Takeda degrading stiffness hysteretic model for modern RC circular bridge columns.” ACI Struct. J. 119 (6). https://doi.org/10.14359/51736116.
Martinez, D., and M. Kowalsky. 2022c. “Trilinear modal damping for the inelastic analysis of reinforced concrete bridges.” In Proc., 12th National Conf. on Earthquake Engineering, 1–5. Oakland, CA: Earthquake Engineering Research Institute.
Montejo, L. A., and M. J. Kowalsky. 2007. CUMBIA set of codes for THA analysis of reinforced concrete members. Raleigh, NC: North Carolina State Univ.
Petrini, L., C. Maggi, M. J. N. Priestley, and G. M. Calvi. 2008. “Experimental verification of viscous damping modeling for inelastic time history analyses.” Supplement, J. Earthquake Eng. 12 (S1): 125–145. https://doi.org/10.1080/13632460801925822.
Priestley, M. J. N., G. M. Calvi, and M. J. Kowalsky. 2007. Displacement-based seismic design of structures. Pavia, Italy: IUSS Press.
Priestley, M. J. N., and D. N. Grant. 2005. “Viscous damping in seismic design and analysis.” Supplement, J. Earthquake Eng. 9 (S2): 229–255. https://doi.org/10.1142/S1363246905002365.
Qian, X., A. K. Chopra, and F. McKenna. 2021. “Modeling viscous damping in nonlinear response history analysis of steel moment-frame buildings: Design-plus ground motions.” Earthquake Eng. Struct. Dyn. 50 (3): 903–915. https://doi.org/10.1002/eqe.3358.
Sakai, J., and S. Unjoh. 2007. “Shake table experiment on circular reinforced concrete bridge column under multidirectional seismic excitation.” Struct. Eng. Res. Front. 1–12. https://doi.org/10.1061/40944(249)37.
Smyrou, E., M. J. N. Priestley, and A. J. Carr. 2011. “Modelling of elastic damping in nonlinear time-history analyses of cantilever RC walls.” Bull. Earthquake Eng. 9 (5): 1559–1578. https://doi.org/10.1007/s10518-011-9286-y.
Wilson, E. L., and J. Penzien. 1972. “Evaluation of orthogonal damping matrices.” Int. J. Numer. Methods Eng. 4 (1): 5–10. https://doi.org/10.1002/nme.1620040103.
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© 2022 American Society of Civil Engineers.
History
Received: Oct 28, 2021
Accepted: Oct 7, 2022
Published online: Dec 6, 2022
Published in print: Feb 1, 2023
Discussion open until: May 6, 2023
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Cited by
- Diego R Martinez, Mervyn J Kowalsky, Nonlinear seismic performance of RC bridges using the ESA, EDA, DDBA, and nonlinear analysis with various viscous damping models, Earthquake Spectra, 10.1177/87552930221145435, 39, 1, (242-268), (2023).