Simulation of the Localized Modulus of Elasticity of Hardwood Boards by Means of an Autoregressive Model
Publication: Journal of Materials in Civil Engineering
Volume 33, Issue 6
Abstract
An autoregressive (AR) model for the simulation of modulus of elasticity (MOE) fluctuations along hardwood boards without pronounced knot periodicity is presented. The model is calibrated based on contiguous, localized (100 mm gauge length) empirical MOEs from European white oak boards. The calibration involves the computation of the sample autocorrelation function (SACF). For this computation, the stationary data resulting from a two-step transformation method are used: (1) first, board-internal MOE normalization suppresses the interboard bias; and (2) the rather left-skewed normalized data are described by a log-gamma distribution, which is then mapped to to obtain the needed stationary data. A first-order AR process suffices to accurately describe the data and is thus used as a basis to simulate MOE profiles, followed by the sketched transformation procedure in reverse order. The quality of the simulated MOE profiles and of the methodological approach is shown by comparison with the experimental MOE profiles. It was found that the simulation model correctly reproduces the statistical information of the MOE variations while also producing very plausible profiles, with similar characteristics as the empirical MOE profiles. This model can be used to better study the size effect of glued-laminated timber by means of numerical simulations.
Formats available
You can view the full content in the following formats:
Data Availability Statement
Some or all data, models, or code generated or used during the study are available in a repository or online in accordance with funder data retention policies (Tapia and Aicher 2020).
Acknowledgments
The financial support of the work by the German foundation, Fachagentur Nachwachsende Rohstoffe e.V. (FNR), contract 2200414, within the European ERA-WoodWisdom project “European hardwoods for the building sector (EU Hardwoods)” is gratefully acknowledged.
References
Aicher, S., A. Christian, and G. Dill-Langer. 2014. “Hardwood glulams—Emerging timber products of superior mechanical properties.” In Proc., World Conf. Timber Engineering, CD-ROM PAP7-11, edited by A. Salenikovich. Quebec City: Université Laval.
Aicher, S., and G. Stapf. 2014. “Glulam from European white oak: Finger joint influence on bending size effect.” In Vol. 9 of RILEM bookseries, 641–656. New York: Springer.
Akaike, H. 1974. “A new look at the statistical model identification.” IEEE Trans. Autom. Control 19 (6): 716–723. https://doi.org/10.1109/TAC.1974.1100705.
Bechtel, F. K. 1985. “Beam stiffness as a function of pointwise E, with application to machine stress rating.” In Proc., Symp. on Forest Products Research International—Achievements and the Future. Pretoria, South Africa: National Timber Research Institute of the South African Council for Scientific and Industrial Research.
Blaß, H. J., M. Frese, P. Glos, P. Linsenmann, and J. Denzler. 2005. “Biegefestigkeit von brettschichtholz aus buche.” In Karlsruher Berichte zum Ingenieurholzbau No. 1. Karlsruhe, Germany: Karlsruhe Institute of Technology.
Briggert, A., A. Olsson, and J. Oscarsson. 2020. “Prediction of tensile strength of sawn timber: Definitions and performance of indicating properties based on surface laser scanning and dynamic excitation.” Mater. Struct. 53 (3): 54. https://doi.org/10.1617/s11527-020-01460-5.
Brockwell, P. J., and R. A. Davis. 2002. Introduction to time series and forecasting. New York: Springer.
Bulleit, W. M., and R. A. Chapman. 2004. “Characterization of the correlation structure of lumber strength properties.” Wood Sci. Technol. 38 (4): 285–296. https://doi.org/10.1007/s00226-004-0234-8.
CEN (European Committee for Standardization). 2009. Sawn timber—Appearance grading of hardwoods—Part 1: Oak and beech. EN 975-1. Brussels, Belgium: CEN.
CEN (European Committee for Standardization). 2012. Timber structures—Structural timber and glued laminated timber—Determination of some physical and mechanical properties. EN 408. Brussels, Belgium: CEN.
CEN (European Committee for Standardization). 2019. Statistical evaluation of test results MOR, MOE and density with structural sized spruce log specimens tested in axial compression at dry and wet (water saturated) state. EN 384. Brussels, Belgium: CEN.
Colling, F., and M. Scherberger. 1987. “Variation of MOE in longitudinal direction of boards.” Holz Roh- Werkstoff 45 (3): 95–99. https://doi.org/10.1007/BF02605978.
DIN (German Institute for Standardization). 2008. Strength grading of wood—Part 5: Sawn hard wood. DIN 4074-5. Berlin: DIN.
Ehlbeck, J., F. Colling, and R. Görlacher. 1984. Einfluß keilgezinkter lamellen auf die biegefestigkeit von brettschichtholzträgern. Karlsruhe, Germany: Versuchsanstalt für Stahl, Holz und Steine, Universität Fridericiana Karlsruhe.
ETA (European Technical Assessment). 2018. European technical assessment—VIGAM—Glued laminated timber of oak. ETA-13/0642. Vienna, Austria: Austrian Institute of Construction Engineering.
Fink, G. 2014. “Influence of varying material properties on the load-bearing capacity of glued laminated timber.” Ph.D. thesis, Institute of Structural Engineering, ETH Zurich.
Foschi, R. O. 1987. “A procedure for the determination of localized modulus of elasticity.” Holz Roh- Werkstoff 45 (6): 257–260.
Foschi, R. O., and J. D. Barrett. 1980. “Glued-laminated beam strength: A model.” ASCE J. Struct. Div. 106 (8): 1735–1754.
Frese, M. 2006. “Die biegefestigkeit von brettschichtholz aus buche—Experimentelle und numerische untersuchungen zum laminierungseffekt.” Ph.D. thesis, Holzbau und Baukonstruktionen, Universität Karlsruhe.
Isaksson, T. 1999. “Modelling the variability of bending strength in structural timber—Length and load configuration effects.” Ph.D. thesis, Division of Structural Engineering, Lund Institute of Technology.
Kandler, G., J. Füssl, E. Serrano, and J. Eberhardsteiner. 2015. “Effective stiffness prediction of GLT beams based on stiffness distributions of individual lamellas.” Wood Sci. Technol. 49 (6): 1101–1121. https://doi.org/10.1007/s00226-015-0745-5.
Kline, D., F. Woeste, and B. Bendtsen. 1986. “Stochastic model for modulus of elasticity of lumber.” Wood Fiber Sci. 18 (2): 228–238.
Lam, F., R. O. Foschi, J. D. Barrett, and Q. Y. He. 1993. “Modified algorithm to determine localized modulus of elasticity of lumber.” Wood Sci. Technol. 27 (2): 81–94. https://doi.org/10.1007/BF00206227.
Lam, F., and E. Varoglu. 1991. “Variation of tensile strength along the length of lumber—Part 2: Model development and verification.” Wood Sci. Technol. 25 (6): 449–458. https://doi.org/10.1007/BF00225237.
Lam, F., Y.-T. Wang, and J. D. Barrett. 1994. “Simulation of correlated nonstationary lumber properties.” J. Mater. Civ. Eng. 6 (1): 34–53. https://doi.org/10.1061/(ASCE)0899-1561(1994)6:1(34).
Olsson, A., and J. Oscarsson. 2017. “Strength grading on the basis of high resolution laser scanning and dynamic excitation: A full scale investigation of performance.” Eur. J. Wood Wood Prod. 75 (1): 17–31. https://doi.org/10.1007/s00107-016-1102-6.
Showalter, K., F. Woeste, and B. Bendtsen. 1987. “Effect of length on tensile strength in structural lumber.” In Research paper FPL-RP-482. Madison, WI: US Dept. of Agriculture, Forest Service, Forest Products Laboratory.
Tapia, C., and S. Aicher. 2018. “A stochastic finite element model for glulam beams of hardwoods.” In CD-ROM Proc., World Conf. on Timber Eng. (WCTE 2018). Seoul: National Institute of Forest Science.
Tapia, C., and S. Aicher. 2019. “Variation and serial correlation of modulus of elasticity between and within European oak boards (Quercus robur and Q. petraea).” Holzforschung 74 (1): 33–46. https://doi.org/10.1515/hf-2019-0038.
Tapia, C., and S. Aicher. 2020. Replication data for: Simulation of the localized modulus of elasticity of hardwood boards by means of an autoregressive model. Stuttgart, Germany: DaRUS. https://doi.org/10.18419/darus-863.
Taylor, S., and D. Bender. 1991. “Stochastic model for localized tensile strength and modulus of elasticity in lumber.” Wood Fiber Sci. 23 (4): 501–519.
Viguier, J., D. Bourreau, J.-F. Bocquet, G. Pot, L. Bléron, and J.-D. Lanvin. 2017. “Modelling mechanical properties of spruce and Douglas fir timber by means of X-ray and grain angle measurements for strength grading purpose.” Eur. J. Wood Wood Prod. 75 (4): 527–541. https://doi.org/10.1007/s00107-016-1149-4.
Information & Authors
Information
Published In
Journal of Materials in Civil Engineering
Volume 33 • Issue 6 • June 2021
Copyright
This work is made available under the terms of the Creative Commons Attribution 4.0 International license, https://creativecommons.org/licenses/by/4.0/.
History
Received: Jun 15, 2020
Accepted: Sep 28, 2020
Published online: Mar 31, 2021
Published in print: Jun 1, 2021
Discussion open until: Aug 31, 2021
Authors
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.