Equivalent Viscous Damping of Cross-Laminated Timber Structural Archetypes
Publication: Journal of Structural Engineering
Volume 147, Issue 4
Abstract
This paper attempts to formulate an expression for the estimation of equivalent viscous damping (EVD) for cross-laminated timber (CLT) structural archetypes as a function of ductility. The paper aims at contributing toward the direct displacement-based design procedure (DDBD) of CLT structures, which makes use of equivalent viscous damping and secant stiffness estimations as proxies for the estimation of the nonlinear behavior of structures. The available hysteretic models of CLT structures are very elaborate, and the inelastic time-domain simulations using hysteretic models are not easily manageable. Hence, the adoption of equivalent viscous damping is a crucial feature of any DDBD method. In this paper, the authors estimate the EVD of a set of 16 typologies of CLT buildings with an increasing slenderness ratio. The minimum of the squared error between the maximum drift of the elastic time-history and the hysteretic response gives the EVD. The extended energy-dependent generalized Bouc Wen (EEGBW) model, calibrated on experimental data, is used to predict the inelastic seismic response of the single CLT shear wall. The correlation between EVD and ductility is compared to existing EVD formulations referring to concrete and steel structures.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author upon reasonable request.
References
Aloisio, A., R. Alaggio, and M. Fragiacomo. 2019a. “Dynamic identification of a masonry façade from seismic response data based on an elementary ordinary least squares approach.” Eng. Struct. 197 (Oct): 109415. https://doi.org/10.1016/j.engstruct.2019.109415.
Aloisio, A., R. Alaggio, and M. Fragiacomo. 2020a. “Fragility functions and behaviour factors estimation of multi-storey CLT structures characterized by an energy-dependent hysteretic model.” Earthquake Spectra. https://doi.org/10.1177/8755293020936696.
Aloisio, A., R. Alaggio, J. Köhler, and M. Fragiacomo. 2020b. “Extension of generalized Bouc-Wen hysteresis modeling of wood joints and structural systems.” J. Eng. Mech. 146 (3): 04020001. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001722.
Aloisio, A., L. D. Battista, R. Alaggio, E. Antonacci, and M. Fragiacomo. 2020d. “Assessment of structural interventions using Bayesian updating and subspace-based fault detection methods: The case study of S. Maria di Collemaggio basilica, L’Aquila, Italy.” Struct. Infrastruct. Eng. 1–15. https://doi.org/10.1080/15732479.2020.1731559.
Aloisio, A., L. Di Battista, R. Alaggio, and M. Fragiacomo. 2019b. “Analysis of the forced dynamics of a masonry facade by means of input-output techniques and a linear regression model.” In Proc., COMPDYN, 2019, 7th Int. Conf. on Computational Methods in Structural Dynamics and Earthquake Engineering. Athens, Greece: National Technical Univ. of Athens Zografou Campus.
Aloisio, A., A. Di Pasquale, M. Fragiacomo, and R. Alaggio. 2020c. “Assessment of seismic retrofitting interventions of a masonry palace using operational modal analysis.” Int. J. Archit. Heritage. https://doi.org/10.1080/15583058.2020.1836531.
Aloisio, A., M. Fragiacomo, and G. D’Alò. 2019c. “Traditional T-F masonries in the city centre of L’Aquila—The Baraccato Aquilano.” Int. J. Archit. Heritage 1–18. https://doi.org/10.1080/15583058.2019.1624874.
Aloisio, A., M. Fragiacomo, and G. D’Alò. 2020f. “The 18th-century Baraccato of L’Aquila.” Int. J. Archit. Heritage 14 (6): 870–884. https://doi.org/10.1080/15583058.2019.1570390.
Aloisio, A., D. Pasca, R. Tomasi, and M. Fragiacomo. 2020e. “Dynamic identification and model updating of an eight-storey CLT building.” Eng. Struct. 213 (Jun): 110593. https://doi.org/10.1016/j.engstruct.2020.110593.
Antonacci, E., A. Aloisio, D. Galeota, and R. Alaggio. 2020. “The S. Maria di Collemaggio basilica: From vulnerability assessment to first results of SHM.” J. Archit. Eng. 26 (3): 05020007. https://doi.org/10.1061/(ASCE)AE.1943-5568.0000426.
Bezabeh, M., S. Tesfamariam, and S. Stiemer. 2016. “Equivalent viscous damping for steel moment-resisting frames with cross-laminated timber infill walls.” J. Struct. Eng. 142 (1): 04015080. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001316.
Biot, M. A. 1958. “Linear thermodynamics and the mechanics of solids.” In Proc., 3rd US National Congress of Applied Mechanics, American Society of Mechanical Engineers. New York: American Society of Mechanical Engineers.
Blandon, C. A., and M. Priestley. 2005. “Equivalent viscous damping equations for direct displacement based design.” Supplement, J. Earthquake Eng. 9 (S2): 257–278. https://doi.org/10.1142/S1363246905002390.
Calvi, G. M. 1999. “A displacement-based approach for vulnerability evaluation of classes of buildings.” J. Earthquake Eng. 3 (3): 411–438.
Calvi, G. M., M. J. N. Priestley, and M. J. Kowalsky. 2007. “Displacement based seismic design of structures.” In Proc., New Zealand Conf. on Earthquake Engineering, 2007, 1–24. New York: Citeseer.
Cao, J., H. Xiong, F.-L. Zhang, L. Chen, and C. R. Cazador. 2020. “Bayesian model selection for the nonlinear hysteretic model of CLT connections.” Eng. Struct. 223 (Nov): 111118. https://doi.org/10.1016/j.engstruct.2020.111118.
Casagrande, D., S. Bezzi, G. D’Arenzo, S. Schwendner, A. Polastri, W. Seim, and M. Piazza. 2020. “A methodology to determine the seismic low-cycle fatigue strength of timber connections.” Constr. Build. Mater. 231 (Jan): 117026. https://doi.org/10.1016/j.conbuildmat.2019.117026.
Casagrande, D., G. Doudak, L. Mauro, and A. Polastri. 2018. “Analytical approach to establishing the elastic behavior of multipanel CLT shear walls subjected to lateral loads.” J. Struct. Eng. 144 (2): 04017193. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001948.
Chen, Z., and M. Popovski. 2020. “Mechanics-based analytical models for balloon-type cross-laminated timber (CLT) shear walls under lateral loads.” Eng. Struct. 208 (Apr): 109916. https://doi.org/10.1016/j.engstruct.2019.109916.
Chopra, A. K. 1995. Dynamics of structures theory. London: Pearson.
Christensen, R. 2012. Theory of viscoelasticity: An introduction. Amsterdam, Netherlands: Elsevier.
Di Egidio, A., R. Alaggio, A. Aloisio, A. M. De Leo, A. Contento, and M. Tursini. 2019. “Analytical and experimental investigation into the effectiveness of a pendulum dynamic absorber to protect rigid blocks from overturning.” Int. J. Non Linear Mech. 115 (Oct): 1–10. https://doi.org/10.1016/j.ijnonlinmec.2019.04.011.
Di Gangi, G., C. Demartino, G. Quaranta, M. Vailati, G. Monti, and M. Liotta. 2018. “Timber shear walls: Numerical assessment of the equivalent viscous damping.” In Proc., 9th Int. Conf. on Computational Methods (ICCM2018). Roma: Sapienza Università di Roma.
Dormand, J. R., and P. J. Prince. 1980. “A family of embedded Runge-Kutta formulae.” J. Comput. Appl. Math. 6 (1): 19–26. https://doi.org/10.1016/0771-050X(80)90013-3.
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.
Ferry, J. D. 1980. Viscoelastic properties of polymers. New York: Wiley.
Filiatrault, A., M. Epperson, and B. Folz. 2004. “Equivalent elastic modeling for the direct-displacement-based seismic design of wood structures.” ISET J. Earthquake Technol. 41 (1): 75–99.
Fitzgerald, D., A. Sinha, T. H. Miller, and J. A. Nairn. 2020. “Toe-screwed cross-laminated timber connection design and nonlinear modeling.” J. Struct. Eng. 146 (6): 04020093. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002656.
Foliente, G. C. 1995. “Hysteresis modeling of wood joints and structural systems.” J. Struct. Eng. 121 (6): 1013–1022. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:6(1013).
Gavric, I., M. Fragiacomo, and A. Ceccotti. 2015. “Cyclic behavior of CLT wall systems: Experimental tests and analytical prediction models.” J. Struct. Eng. 141 (11): 04015034. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001246.
Gulkan, P., and M. A. Sozen. 1974. “Inelastic responses of reinforced concrete structure to earthquake motions.” J. Proc. 71 (12): 604–610.
Hashemi, A., H. Bagheri, S. M. M. Yousef-Beik, F. M. Darani, A. Valadbeigi, P. Zarnani, and P. Quenneville. 2020. “Enhanced seismic performance of timber structures using resilient connections: Full-scale testing and design procedure.” J. Struct. Eng. 146 (9): 04020180. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002749.
Hashemi, A., and P. Quenneville. 2020. “Large-scale testing of low damage rocking cross laminated timber (CLT) wall panels with friction dampers.” Eng. Struct. 206 (Mar): 110166. https://doi.org/10.1016/j.engstruct.2020.110166.
Iwan, W. D. 1973. “A generalization of the concept of equivalent linearization.” Int. J. Non Linear Mech. 8 (3): 279–287. https://doi.org/10.1016/0020-7462(73)90049-8.
Iwan, W. D. 1980. “Estimating inelastic response spectra from elastic spectra.” Earthquake Eng. Struct. Dyn. 8 (4): 375–388. https://doi.org/10.1002/eqe.4290080407.
Izzi, M., G. Rinaldin, A. Polastri, and M. Fragiacomo. 2018. “A hysteresis model for timber joints with dowel-type fasteners.” Eng. Struct. 157 (Feb): 170–178. https://doi.org/10.1016/j.engstruct.2017.12.011.
Jacobsen, L. S. 1930. “Steady forced vibration as influenced by damping.” Trans. ASME-APM 52 (15): 169–181.
Kowalsky, M. J. 2002. “A displacement-based approach for the seismic design of continuous concrete bridges.” Earthquake Eng. Struct. Dyn. 31 (3): 719–747. https://doi.org/10.1002/eqe.150.
Kowalsky, M. J., M. N. Priestley, and G. A. MacRae. 1994. Vol. 94 of Displacement-based design: A methodology for seismic design applied to single degree of freedom reinforced concrete structures. La Jolla, CA: Structural Systems Research, Univ. of California, San Diego.
Lancaster, P. 1960. “Free vibration and hysteretic damping.” Aeronaut. J. 64 (592): 229. https://doi.org/10.1017/S0368393100072515.
Liu, J., F. Lam, R. O. Foschi, and M. Li. 2020. “Modeling the coupling effect of CLT connections under biaxial loading.” J. Struct. Eng. 146 (4): 04020040. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002589.
Loo, W. Y., C. Kun, P. Quenneville, and N. Chouw. 2014. “Experimental testing of a rocking timber shear wall with slip-friction connectors.” Earthquake Eng. Struct. Dyn. 43 (11): 1621–1639. https://doi.org/10.1002/eqe.2413.
Loss, C., T. Tannert, and S. Tesfamariam. 2018. “State-of-the-art review of displacement-based seismic design of timber buildings.” Constr. Build. Mater. 191 (Dec): 481–497. https://doi.org/10.1016/j.conbuildmat.2018.09.205.
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.
Muñoz, W., M. Mohammad, A. Salenikovich, and P. Quenneville. 2008. Determination of yield point and ductility of timber assemblies: In search for a harmonised approach. Tacoma, WA: Engineered Wood Products Association.
Muravyov, A. 1998. “Forced vibration responses of a viscoelastic structure.” J. Sound Vib. 218 (5): 892–907. https://doi.org/10.1006/jsvi.1998.1819.
Priestley, M. 2003. Myths and fallacies in earthquake engineering, revisited: The ninth mallet Milne lecture, 2003. Pavia: Istituto Universitario di Studi Superiori di Pavia.
Priestley, M. N. 1993. “Myths and fallacies in earthquake engineering-conflicts between design and reality.” Bull. N.Z. Nat. Soc. Earthquake Eng. 26 (3): 329–341. https://doi.org/10.5459/bnzsee.26.3.329-341.
Rosenblueth, E., and I. Herrera. 1964. “On a kind of hysteretic damping.” J. Eng. Mech. Div. 90 (4): 37–48.
Roylance, D. 2001. Engineering viscoelasticity. Cambridge, MA: Massachusetts Institute of Technology.
Shahnewaz, M., Y. Pan, M. Shahria Alam, and T. Tannert. 2020a. “Seismic fragility estimates for cross-laminated timber platform building.” J. Struct. Eng. 146 (12): 04020256. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002834.
Shahnewaz, M., M. Popovski, and T. Tannert. 2020b. “Deflection of cross-laminated timber shear walls for platform-type construction.” Eng. Struct. 221 (Oct): 111091. https://doi.org/10.1016/j.engstruct.2020.111091.
Song, J., and A. Der Kiureghian. 2006. “Generalized Bouc–Wen model for highly asymmetric hysteresis.” J. Eng. Mech. 132 (6): 610–618. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:6(610).
Sotayo, A., et al. 2020. “Review of state of the art of dowel laminated timber members and densified wood materials as sustainable engineered wood products for construction and building applications.” Dev. Built Environ. 1 (Feb): 100004. https://doi.org/10.1016/j.dibe.2019.100004.
Sun, X., M. He, Z. Li, and F. Lam. 2020. “Seismic performance of energy-dissipating post-tensioned CLT shear wall structures. II: Dynamic analysis and dissipater comparison.” Soil Dyn. Earthquake Eng. 130 (Mar): 105980. https://doi.org/10.1016/j.soildyn.2019.105980.
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Published In
Journal of Structural Engineering
Volume 147 • Issue 4 • April 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Apr 14, 2020
Accepted: Oct 14, 2020
Published online: Jan 21, 2021
Published in print: Apr 1, 2021
Discussion open until: Jun 21, 2021
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