Abstract

Mass timber has gained increasing focus as a sustainable alternative to concrete structures, and recent innovations have allowed timber buildings as high as 25 stories. However, although critical factors such as fire safety have been studied thoroughly, other facets, such as long-term material performance, have been neglected. Thorough assessments of sustainability must consider the full service life of a building, including its time-dependent behavior. Deformations in timber elements undergoing these time-dependent effects, namely creep, will have notable implications for the serviceability of a building. This study proposes a comprehensive model for predicting moisture-dependent creep in timber, based on the theory of microprestress in partially saturated porous materials. The model is implemented numerically using a Kelvin-chain approximation for basic creep and midpoint integration for mechanosorptive effects, resulting in a computationally efficient approach. Results show the model is able to fully capture the effects of moisture cycling, including effects of hygrothermal gradients. Using both calibrated and estimated parameters the model also predicts with reasonable accuracy the long-term moisture-dependent creep in structural-scale mass timber elements.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

The user material subroutines used in this study are available from the corresponding author upon reasonable request.

Acknowledgments

Financial support from the US National Science Foundation (NSF) under Grant No. CMMI–1762757 is gratefully acknowledged.

References

Aira, J. R., F. Arriaga, and G. Íñiguez-González. 2014. “Determination of the elastic constants of scots pine (Pinus sylvestris l.) wood by means of compression tests.” Biosyst. Eng. 126 (Oct): 12–22. https://doi.org/10.1016/j.biosystemseng.2014.07.008.
Alnaggar, M., G. Di Luzio, and G. Cusatis. 2017. “Modeling time-dependent behavior of concrete affected by alkali silica reaction in variable environmental conditions.” Materials 10 (5): 471. https://doi.org/10.3390/ma10050471.
Bach, L. 1968. “Nonlinear mechanical behavior of wood in longitudinal tension.” For. Prod. J. 18 (3): 60–66. https://doi.org/10.5555/19680606361.
Barber, D., and R. Gerard. 2015. “Summary of the fire protection foundation report-fire safety challenges of tall wood buildings.” Fire Sci. Rev. 4 (1): 1–15. https://doi.org/10.1186/s40038-015-0009-3.
Bažant, Z. 1972. “Thermodynamics of interacting continua with surfaces and creep analysis of concrete structures.” Nucl. Eng. Des. 20 (2): 477–505. https://doi.org/10.1016/0029-5493(72)90124-0.
Bažant, Z. 1985. “Constitutive equation of wood at variable humidity and temperature.” Wood Sci. Technol. 19 (2): 159–177. https://doi.org/10.1007/BF00353077.
Bažant, Z., and Y. Xi. 1995. “Continuous retardation spectrum for solidification theory of concrete creep.” J. Eng. Mech. 121 (2): 281–288. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:2(281).
Bažant, Z. P., G. Cusatis, and L. Cedolin. 2004. “Temperature effect on concrete creep modeled by microprestress-solidification theory.” J. Eng. Mech. 130 (6): 691–699. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:6(691).
Bažant, Z. P., and M. Jirasek. 2018. “Creep and hygrothermal effects in concrete structures.” In Vol. 225 of Solid mechanics and its application. New York: Springer.
Bengtsson, R., R. Afshar, and E. K. Gamstedt. 2022. “An applicable orthotropic creep model for wood materials and composites.” Wood Sci. Technol. 56 (6): 1585–1604. https://doi.org/10.1007/s00226-022-01421-x.
Bond, B. H. 1993. “Development of tension and compression creep models for wood using the time-temperature superposition principle.” Ph.D. thesis, Dept. of Wood Science and Forest Products, Virginia Tech.
Breton, J. 1999. “Creep behavior of FPR-reinforced Douglas-fir and western hemlock glulam beams.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Univ. of Maine.
Cavalli, A., D. Cibecchini, M. Togni, and H. S. Sousa. 2016. “A review on the mechanical properties of aged wood and salvaged timber.” Constr. Build. Mater. 114 (Jul): 681–687. https://doi.org/10.1016/j.conbuildmat.2016.04.001.
Chassagne, P., E. B. Saïd, J.-F. Jullien, and P. Galimard. 2005. “Three dimensional creep model for wood under variable humidity-numerical analyses at different material scales.” Mech. Time-Depend. Mater. 9 (4): 1–21. https://doi.org/10.1007/s11043-005-9001-y.
Crawford, R. H., and X. Cadorel. 2017. “A framework for assessing the environmental benefits of mass timber construction.” Procedia Eng. 196: 838–846. https://doi.org/10.1016/j.proeng.2017.08.015.
DeSantis, A., M. Stoner, and W. Pang. 2023. “Investigation of cross laminated timber’s long-term performance (creep).” In Proc., World Conf. on Timber Engineering. Scotland, UK: Curran Associates.
Di Luzio, G., and G. Cusatis. 2013. “Solidification–microprestress–microplane (SMM) theory for concrete at early age: Theory, validation and application.” Int. J. Solids Struct. 50 (6): 957–975. https://doi.org/10.1016/j.ijsolstr.2012.11.022.
Dubois, F., J.-M. Husson, N. Sauvat, and N. Manfoumbi. 2012. “Modeling of the viscoelastic mechano-sorptive behavior in wood.” Mech. Time-Depend. Mater. 16 (4): 439–460. https://doi.org/10.1007/s11043-012-9171-3.
Dubois, F., H. Randriambololona, and C. Petit. 2005. “Creep in wood under variable climate conditions: Numerical modeling and experimental validation.” Mech. Time-Depend. Mater. 9 (2): 173–202. https://doi.org/10.1007/s11043-005-1083-z.
Florisson, S., L. Muszynski, and J. Vessby. 2021. “Analysis of hygro-mechanical behavior of wood in bending.” Wood Fiber Sci. 53 (1): 27–47. https://doi.org/10.22382/wfs-2021-04.
Fortino, S., F. Mirianon, and T. Toratti. 2009. “A 3D moisture-stress fem analysis for time dependent problems in timber structures.” Mech. Time-Depend. Mater. 13 (4): 333–356. https://doi.org/10.1007/s11043-009-9103-z.
Gowda, S., M. Kortesmaa, and A. Ranta-Maunus. 1996. Long term creep tests on timber beams in heated and non-heated environments. Espoo, Finland: Technical Research Centre of Finland.
Granello, G., and A. Palermo. 2019. “Creep in timber: Research overview and comparison between code provisions.” N. Z. Timber Des. J. 27: 6–22.
Grossman, P., and R. Kingston. 1954. “Creep and stress relaxation in wood during bending.” Aust. J. Appl. Sci. 5 (4): 403–417.
Hanhijärvi, A., and P. Mackenzie-Helnwein. 2003. “Computational analysis of quality reduction during drying of lumber due to irrecoverable deformation. I: Orthotropic viscoelastic-mechanosorptive-plastic material model for the transverse plane of wood.” J. Eng. Mech. 129 (9): 996–1005. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:9(996).
Hassani, M. M., F. K. Wittel, S. Hering, and H. J. Herrmann. 2015. “Rheological model for wood.” Comput. Methods Appl. Mech. Eng. 283 (Jan): 1032–1060. https://doi.org/10.1016/j.cma.2014.10.031.
Hering, S., and P. Niemz. 2012. “Moisture-dependent, viscoelastic creep of European beech wood in longitudinal direction.” Eur. J. Wood Wood Prod. 70 (5): 667–670. https://doi.org/10.1007/s00107-012-0600-4.
Hill, C. A. S., and J. Dibdiakova. 2016. “The environmental impact of wood compared to other building materials.” Int. Wood Prod. J. 7 (4): 215–219. https://doi.org/10.1080/20426445.2016.1190166.
Hofer, U., C. Pichler, R. Maderebner, and R. Lackner. 2019. “Lomnitz-type viscoelastic behavior of clear spruce wood as identified by creep and relaxation experiments: Influence of moisture content and elevated temperatures up to 80°C.” Wood Sci. Technol. 53 (4): 765–783. https://doi.org/10.1007/s00226-019-01099-8.
Holzer, S. M., J. R. Loferski, and D. A. Dillard. 1989. “A review of creep in wood: Concepts relevant to develop long-term behavior predictions for wood structures.” Wood Fiber Sci. 4: 376–392.
Hoyle, R. J., M. C. Griffith, and R. Y. Itani. 1985. “Primary creep in Douglas-fir beams of commercial size and quality.” Wood Fiber Sci. 17 (3): 300–314.
Huč, S., and S. Svensson. 2018. “Coupled two-dimensional modeling of viscoelastic creep of wood.” Wood Sci. Technol. 52: 29–43. https://doi.org/10.1007/s00226-017-0944-3.
Hunt, D. G. 1999. “A unified approach to creep of wood.” Proc. R. Soc. London, Ser. A: Math. Phys. Eng. Sci. 455 (1991): 4077–4095. https://doi.org/10.1098/rspa.1999.0491.
Kordziel, S., S. V. Glass, C. R. Boardman, R. A. Munson, S. L. Zelinka, S. Pei, and P. C. Tabares-Velasco. 2020. “Hygrothermal characterization and modeling of cross-laminated timber in the building envelope.” Build. Environ. 177 (Jun): 106866. https://doi.org/10.1016/j.buildenv.2020.106866.
Kordziel, S., S. Pei, S. V. Glass, S. Zelinka, and P. C. Tabares-Velasco. 2019. “Structure moisture monitoring of an 8-story mass timber building in the pacific northwest.” J. Archit. Eng. 25 (4): 04019019. https://doi.org/10.1061/(ASCE)AE.1943-5568.0000367.
Kristian, B. D. 2009. “Mechanical properties of clear wood from Norway spruce.” Ph.D. thesis, Dept. of Structural Engineering, Norwegian Univ. of Science and Technology.
Mårtensson, A. 1994. “Mechano-sorptive effects in wooden material.” Wood Sci. Technol. 28 (6): 437–449. https://doi.org/10.1007/bf00225463.
Masoero, E., and G. Di Luzio. 2020. “Nanoparticle simulations of logarithmic creep and microprestress relaxation in concrete and other disordered solids.” Cem. Concr. Res. 137 (Nov): 106181. https://doi.org/10.1016/j.cemconres.2020.106181.
Massaro, F. M., and K. A. Malo. 2019. “Long-term behaviour of norway spruce glulam loaded perpendicular to grain.” Eur. J. Wood Wood Prod. 77 (5): 821–832. https://doi.org/10.1007/s00107-019-01437-4.
Mirianon, F., S. Fortino, and T. Toratti. 2008. A method to model wood by using Abaqus finite element software. Helsinki, Finland: VTT Technical Research Centre of Finland.
Mohager, S., and T. Toratti. 1992. “Long term bending creep of wood in cyclic relative humidity.” Wood Sci. Technol. 27 (1): 49–59. https://doi.org/10.1007/BF00203409.
Morlier, P. 1994. Creep in timber structures. London: CRC Press.
Muszyński, L., R. Lagana, S. M. Shaler, and W. Davids. 2005. “Comments on the experimental methodology for determination of the hygro-mechanical properties of wood.” Holzforshung 59 (2): 232–239. https://doi.org/10.1515/HF.2005.037.
NDS (National Design Specification). 2017. National design specification for wood construction. Leesburg, VA: American Wood Council.
Ozyhar, T., S. Hering, and P. Niemz. 2013. “Viscoelastic characterization of wood: Time dependence of the orthotropic compliance in tension and compression.” J. Rheol. 57 (2): 699–717. https://doi.org/10.1122/1.4790170.
Ranta-Maunus, A., and M. Kortesmaa. 2000. “Creep of timber during eight years in natural environments.” In Vol. 31 of Proc., World Conf. on Timber Engineering. Vancouver, BC, Canada: Conference Secretariat.
Ross, R. J. 2010. Wood handbook: Wood as an engineering material. Madison, WI: USDA Forest Service, Forest Products Laboratory.
Sinko, R., Z. P. Bažant, and S. Keten. 2018. “A nanoscale perspective on the effects of transverse microprestress on drying creep of nanoporous solids.” Proc. R. Soc. A: Math. Phys. Eng. Sci. 474 (2209): 20170570. https://doi.org/10.1098/rspa.2017.0570.
Śliwa-Wieczorek, K., P. Szeptyński, T. Kozik, and M. Gubert. 2023. “Creep behavior of clt beams with finite thickness layers of flexible adhesives.” Materials 16 (12): 4484. https://doi.org/10.3390/ma16124484.
Thémelin, A. 1998. “Comportement en sorption de produits ligno-cellulosiques.” Bois Forets Des Tropiques 256: 55–67.
Tong, D., S. A. Brown, D. Corr, and G. Cusatis. 2020. “Wood creep data collection and unbiased parameter identification of compliance functions.” Holzforschung 74 (11): 1011–1020. https://doi.org/10.1515/hf-2019-0268.
Tong, D., S.-A. Brown, H. Yin, D. Corr, E. Landis, G. Di Luzio, and G. Cusatis. 2023. “Orthotropic hygroscopic behavior of mass timber: Theory, computation, and experimental validation.” Mater. Struct. 56 (6): 109. https://doi.org/10.1617/s11527-023-02196-8.
Toratti, T. 1991. Creep of wood in varying environment humidity part I: Simulation of creep. Helsinki, Finland: Laboratory of Structural Engineering and Building Physics, Helsinki Univ. of Technology.
Tschoegl, N. 1989. The phenomenological theory of linear viscoelastic behavior. Cham, Switzerland: Springer.
Van der Put, T. 2015. Exact failure criterion of wood: Theory extension and synthesis of all series a publications. Delft, Netherlands: Delft Wood Science Foundation Publication.
Wanninger, F., and A. Frangi. 2014. “Experimental and analytical analysis of a post-tensioned timber connection under gravity loads.” Eng. Struct. 70 (Jul): 117–129. https://doi.org/10.1016/j.engstruct.2014.03.042.
Yu, T., A. Khaloian, and J.-W. Van De Kuilen. 2022. “An improved model for the time-dependent material response of wood under mechanical loading and varying humidity conditions.” Eng. Struct. 259 (May): 114116. https://doi.org/10.1016/j.engstruct.2022.114116.

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 150Issue 7July 2024

History

Received: Oct 10, 2023
Accepted: Feb 9, 2024
Published online: Apr 30, 2024
Published in print: Jul 1, 2024
Discussion open until: Sep 30, 2024

Permissions

Request permissions for this article.

Authors

Affiliations

Dept. of Civil and Environmental Engineering, Northwestern Univ., 2145 N Sheridan Rd., Evanston, IL 60208 (corresponding author). ORCID: https://orcid.org/0000-0002-7467-3991. Email: [email protected]
Professor, Dept. of Civil and Environmental Engineering, Politecnico di Milano, Piazza Leonardo da Vinci, 32, Milano MI 20133, Italy. ORCID: https://orcid.org/0000-0003-1971-8445. Email: [email protected]
Professor, Dept. of Civil and Environmental Engineering, Northwestern Univ., 2145 N Sheridan Rd., Evanston, IL 60208. ORCID: https://orcid.org/0000-0001-7436-3910. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share