Abstract

A resilient dual frame-wall lateral force-resisting system, designed to mitigate frame-expansion challenges in self-centering structures, has been introduced. One notable obstacle encountered when applying direct displacement-based design (DDBD) to this dual frame-wall system is the ductility-damping relationship that can be used for estimating nonlinear structural responses. To address this issue, more than 3.5 million damping data points were generated through nonlinear time-history (NLTH) analyses by creating the linearized substitute system. These analyses span a broad range of parameters, including the fundamental period of the original system, ductility, normalized subsystem stiffness ratio, and post-yielding stiffness ratio of the subsystems. The results reveal that the equivalent viscous damping ratio (EVDR) exhibits significant period dependency for a wide range of periods. Both ductility and the subsystem stiffness ratio, which govern the hysteresis response area, exert a substantial influence on EVDR, except for the post-yielding stiffness ratio. Consequently, an EVDR model that takes into account the effective period, ductility, and normalized subsystem stiffness ratio was formulated and was validated using an additional data set of over 0.2 million data points. Ductility-period design displacement spectra were also proposed to illustrate the implementation of the proposed EVDR model and provide an easy way to understand the equivalent procedure.

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Data Availability Statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

The research described in this paper was financially supported by the National Natural Science Foundation of China (52278213) and the China Scholarship Council (202108610187). Chuandong Xie would like to express his gratitude to Ms. Yiqing Chen for reviewing and refining the work. Any options, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the sponsors.

References

ASCE. 2022. Minimum design loads and associated criteria for buildings and other structures. ASCE/SEI 7-22. Reston, VA: ASCE.
Blandon, C. A., and M. J. N. Priestley. 2005. “Equivalent viscous damping equations for direct displacement based design.” J. Earthquake Eng. 9 (sup2): 257–278. https://doi.org/10.1142/S1363246905002390.
CEN (European Committee for Standardization). 2013. Design of structures for earthquake resistance—Part 1: General rules, seismic actions and rules for buildings. Eurocode 8. Brussels: CEN.
Chan, N., A. Hashemi, P. Zarnani, and P. Quenneville. 2021. “Damping-ductility relationships for flag-shaped hysteresis.” J. Struct. Eng. 147 (7): 04021093. https://doi.org/10.1061/(ASCE)ST.1943-541X.0003055.
Chancellor, N., M. Eatherton, D. Roke, and T. Akbaş. 2014. “Self-centering seismic lateral force resisting systems: High performance structures for the city of tomorrow.” Buildings 4 (3): 520–548. https://doi.org/10.3390/buildings4030520.
Chou, C.-C., and J.-H. Chen. 2011. “Seismic tests of post-tensioned self-centering building frames with column and slab restraints.” Front. Archit. Civ. Eng. China 5 (3): 323. https://doi.org/10.1007/s11709-011-0119-5.
Clifton, C., M. Bruneau, G. Macrae, R. Leon, and A. Fussell. 2011. “Steel building damage from the Christchurch earthquake series of 2010-2011.” J. Struct. Eng. Soc. N. Z. 24 (2): 27–42.
Dong, W., M. Li, T. Sullivan, G. MacRae, C.-L. Lee, and T. Chang. 2023. “Direct displacement-based seismic design of glulam frames with buckling restrained braces.” J. Earthquake Eng. 27 (8): 2166–2197. https://doi.org/10.1080/13632469.2022.2110999.
Dowden, D. M., and M. Bruneau. 2016. “Kinematics of self-centering steel plate shear walls with NewZ-BREAKSS post-tensioned rocking connection.” Eng. J. 53 (3): 117–136. https://doi.org/10.62913/engj.v53i3.1103.
Dwairi, H. M., M. J. Kowalsky, and J. M. Nau. 2007. “Equivalent damping in support of direct displacement-based design.” J. Earthquake Eng. 11 (4): 512–530. https://doi.org/10.1080/13632460601033884.
Elattar, A., A. Zaghw, and A. Elansary. 2014. “Comparison between the direct displacement based design and the force based design methods in reinforced concrete framed structures.” In Proc., 2nd European Conf. on Earthquake Engineering. Istanbul, Turkey: European Association for Earthquake Engineering.
FEMA. 2009. Quantification of building seismic performance factors (FEMA P-695). Washington, DC: FEMA.
Garlock, M. M., R. Sause, and J. M. Ricles. 2007. “Behavior and design of posttensioned steel frame systems.” J. Struct. Eng. 133 (3): 389–399. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:3(389).
Gulkan, P., and M. A. Sozen. 1974. “Inelastic responses of reinforced concrete structure to earthquake motions.” J. Proc. 71 (12): 604–610. https://doi.org/10.14359/7110.
Heitz, T., C. Giry, B. Richard, and F. Ragueneau. 2019. “Identification of an equivalent viscous damping function depending on engineering demand parameters.” Eng. Struct. 188 (Jun): 637–649. https://doi.org/10.1016/j.engstruct.2019.03.058.
Hu, F., G. Shi, and Y. Shi. 2017. “Experimental study on seismic behavior of high strength steel frames: Global response.” Eng. Struct. 131 (Jan): 163–179. https://doi.org/10.1016/j.engstruct.2016.11.013.
Huang, X., Z. Zhou, Q. Xie, R. Xue, and D. Zhu. 2017. “Force distribution analysis of self-centering coupled-beams for moment-resisting-frames without floor elongation.” Eng. Struct. 147 (Sep): 328–344. https://doi.org/10.1016/j.engstruct.2017.05.055.
Jacobsen, L. S. 1930. “Steady forced vibration as influenced by damping.” Trans. ASME-APM 52 (15): 169–181. https://doi.org/10.1115/1.4057368.
Jayasooriya, E. M. S. D., D. W. U. Indika, K. K. Wijesundara, and P. Rajeev. 2021. “Equivalent viscous damping for steel eccentrically braced frame structures with buckling restraint braces.” Innovative Infrastruct. Solutions 6 (4): 216. https://doi.org/10.1007/s41062-021-00503-2.
Kalapodis, N. A., E. V. Muho, and D. E. Beskos. 2022. “Seismic design of plane steel MRFS, EBFS and BRBFS by improved direct displacement-based design method.” Soil Dyn. Earthquake Eng. 153 (Feb): 107111. https://doi.org/10.1016/j.soildyn.2021.107111.
Khan, E., M. J. Kowalsky, and J. M. Nau. 2016. “Equivalent viscous damping model for short-period reinforced concrete bridges.” J. Bridge Eng. 21 (2): 04015047. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000803.
Kim, H.-J., and C. Christopoulos. 2009. “Seismic design procedure and seismic response of post-tensioned self-centering steel frames.” Earthquake Eng. Struct. Dyn. 38 (3): 355–376. https://doi.org/10.1002/eqe.859.
Kowalsky, M. J., M. J. N. Priestley, and G. A. MacRae. 1995. “Displacement-based design of RC bridge columns in seismic regions.” Earthquake Eng. Struct. Dyn. 24 (12): 1623–1643. https://doi.org/10.1002/eqe.4290241206.
Li, Z., Z. Wang, M. He, and Z. Shu. 2023. “Direct displacement-based design of steel-timber hybrid structure with separated gravity and lateral resisting systems.” J. Build. Eng. 69 (Jun): 106216. https://doi.org/10.1016/j.jobe.2023.106216.
Lin, Y.-C., R. Sause, and J. M. Ricles. 2013. “Seismic performance of steel self-centering, moment-resisting frame: Hybrid simulations under design basis earthquake.” J. Struct. Eng. 139 (11): 1823–1832. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000745.
Liu, L., S. Li, and J. Zhao. 2018. “A novel non-iterative direct displacement-based seismic design procedure for self-centering buckling-restrained braced frame structures.” Bull. Earthquake Eng. 16 (11): 5591–5619. https://doi.org/10.1007/s10518-018-0408-7.
Lowes, L. N., N. Mitra, and A. Altoontash. 2003. A beam-column joint model for simulating the earthquake response of reinforced concrete frames. Berkeley, CA: Pacific Earthquake Engineering Research Center, Univ. of California.
Mazza, F., and A. Vulcano. 2014. “Equivalent viscous damping for displacement-based seismic design of hysteretic damped braces for retrofitting framed buildings.” Bull. Earthquake Eng. 12 (6): 2797–2819. https://doi.org/10.1007/s10518-014-9601-5.
McKenna, F., M. H. Scott, and G. L. Fenves. 2010. “Nonlinear finite-element analysis software architecture using object composition.” J. Comput. Civ. Eng. 24 (1): 95–107. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000002.
Medhekar, M. S., and D. J. L. Kennedy. 2000. “Displacement-based seismic design of buildings—Application.” Eng. Struct. 22 (3): 210–221. https://doi.org/10.1016/S0141-0296(98)00093-5.
Miranda, E., and J. Ruiz-García. 2002. “Evaluation of approximate methods to estimate maximum inelastic displacement demands.” Earthquake Eng. Struct. Dyn. 31 (3): 539–560. https://doi.org/10.1002/eqe.143.
Mohebkhah, A., and J. Tazarv. 2021. “Equivalent viscous damping for linked column steel frame structures.” J. Constr. Steel Res. 179 (Apr): 106506. https://doi.org/10.1016/j.jcsr.2020.106506.
MOHURD (Ministry of Housing and Urban-Rural Development of the People’s Republic of China). 2016. Code for seismic design of buildings. GB 50011-2010 (2016 version). Beijing: China Architecture & Building Press.
Petrini, L., C. Maggi, M. J. N. Priestley, and G. M. Calvi. 2008. “Experimental verification of viscous damping modeling for inelastic time history analyses.” J. Earthquake Eng. 12 (sup1): 125–145. https://doi.org/10.1080/13632460801925822.
Priestley, M. J. N., G. Calvi, and M. Kowalsky. 2018. Displacement-based seismic design of structures. 2nd ed. Pavia, Italy: Eucentre.
Priestley, M. J. N., and D. N. Grant. 2005. “Viscous damping in seismic design and analysis.” J. Earthquake Eng. 9 (sup2): 229–255. https://doi.org/10.1142/S1363246905002365.
Rosenblueth, E., and I. Herrera. 1964. “On a kind of hysteretic damping.” J. Eng. Mech. Div. 90 (4): 37–48. https://doi.org/10.1061/JMCEA3.0000510.
Salado Castillo, J. G., M. Bruneau, and N. Elhami-Khorasani. 2022. “Seismic resilience of building inventory towards resilient cities.” Resilient Cities Struct. 1 (1): 1–12. https://doi.org/10.1016/j.rcns.2022.03.002.
Shibata, A., and M. A. Sozen. 1976. “Substitute-structure method for seismic design in R/C.” J. Struct. Div. 102 (1): 1–18. https://doi.org/10.1061/JSDEAG.0004250.
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.
Tarawneh, A., S. Majdalaweyh, and H. Dwairi. 2021. “Equivalent viscous damping of steel members for direct displacement based design.” Structures 33 (Oct): 4781–4790. https://doi.org/10.1016/j.istruc.2021.07.056.
Wang, X., C. Xie, Z. Jia, and G. Vasdravellis. 2022. “Seismic behaviour of post-tensioned beam-to-column connection using slender energy-dissipating rectangles.” Eng. Struct. 250 (Jan): 113444. https://doi.org/10.1016/j.engstruct.2021.113444.
Wang, X.-T., C.-D. Xie, L.-H. Lin, and J. Li. 2019. “Seismic behavior of self-centering concrete-filled square steel tubular (CFST) column base.” J. Constr. Steel Res. 156 (May): 75–85. https://doi.org/10.1016/j.jcsr.2019.01.025.
Wijesundara, K. K., R. Nascimbene, and T. J. Sullivan. 2011. “Equivalent viscous damping for steel concentrically braced frame structures.” Bull. Earthquake Eng. 9 (5): 1535–1558. https://doi.org/10.1007/s10518-011-9272-4.
Wood, A., I. Noy, and M. Parker. 2016. “The Canterbury rebuild five years on from the Christchurch earthquake.” Reserve Bank N. Z. Bull. 79 (Feb): 1–16.
Xie, C., X. Wang, and G. Vasdravellis. 2023a. “Mechanical behaviour and experimental evaluation of self-centring steel plate shear walls considering frame-expansion effects.” J. Build. Eng. 72 (Aug): 106636. https://doi.org/10.1016/j.jobe.2023.106636.
Xie, C., X. Wang, and G. Vasdravellis. 2023b. “Steady-state dynamic response analysis of single-degree-of-freedom dual frame-wall resilient system.” Soil Dyn. Earthquake Eng. 172 (Sep): 108043. https://doi.org/10.1016/j.soildyn.2023.108043.
Xie, C., X. Wang, G. Vasdravellis, and W. Liang. 2024. “Displacement profile for direct-displacement based seismic design of dual frame-wall resilient system.” J. Constr. Steel Res. 214 (Mar): 108495. https://doi.org/10.1016/j.jcsr.2024.108495.
Yu, J., J. Huang, B. Li, and X. Feng. 2021. “Experimental study on steel plate shear walls with novel plate-frame connection.” J. Constr. Steel Res. 180 (May): 106601. https://doi.org/10.1016/j.jcsr.2021.106601.
Zhang, Y., Q. Li, Y. Zhuge, A. Liu, and W. Zhao. 2019. “Experimental study on spatial prefabricated self-centering steel frame with beam-column connections containing bolted web friction devices.” Eng. Struct. 195 (Sep): 1–21. https://doi.org/10.1016/j.engstruct.2019.05.085.
Zhao, G., L. Xu, X. Zhu, and L. Xie. 2023. “A displacement design spectral method adapted to the Chinese seismic design code.” J. Vibr. Shock 42 (8): 266–274.

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Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 150Issue 10October 2024

History

Received: Dec 4, 2023
Accepted: May 3, 2024
Published online: Aug 7, 2024
Published in print: Oct 1, 2024
Discussion open until: Jan 7, 2025

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School of Civil Engineering, Xi’an Univ. of Architecture and Technology, Xi’an 710055, PR China. ORCID: https://orcid.org/0000-0003-0331-1851. Email: [email protected]
Xiantie Wang [email protected]
Professor, School of Civil Engineering, Xi’an Univ. of Architecture and Technology, Xi’an 710055, PR China (corresponding author). Email: [email protected]
Associate Professor, School of Energy, Geoscience, Infrastructure and Society, Institute for Infrastructure & Environment, Heriot-Watt Univ., Edinburgh EH14 4AS, UK. ORCID: https://orcid.org/0000-0002-7910-8190. Email: [email protected]
Wanggeng Liang, Ph.D. [email protected]
School of Civil Engineering, Xi’an Univ. of Architecture and Technology, Xi’an 710055, PR China. Email: [email protected]

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