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Comparison of classical beam theory and finite element modelling of timber from fibre orientation data according to knot position and loading type

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Abstract

Timber mechanical properties assessment relies on grading methods that use non-destructive measurements in input, among which fibre orientation gives satisfactory outcomes. Several models exist in the literature to use fibre orientation data, based on either classical beam theory or finite element modelling. The present paper proposes to compare them for axial and bending loadings. To this end, the main approach was to use several artificial beams, for which fibre orientation was modelled around various knot positions in the tangential plane of wood. It is shown that beam theory modelling, despite considering the heterogeneity of moduli of elasticity in beam longitudinal direction, does not truly represent the actual deformations that can be depicted with finite element modelling. It results in significant differences in the accuracy of the assessment of the local modulus of elasticity, the finite element modelling being better. This finding was supported by experimental results obtained on laminated veneer lumber beams with a high knottiness. Additionally, this paper provides a comparison of different methods to compute localized moduli of elasticity that are typically used as strength predictors. The outcomes indicate that their behaviour depends on the loading type (axial or bending), the knot position in the beam, and the length of the sliding window across which they were computed. A localized bending modulus of elasticity (MoE) computed from the displacements, referred to as the 'apparent MoE', was defined in the objective to improve the accuracy of strength predictions.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request. 

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References

  • Baño V, Arriaga F, Soilán A, Guaita M (2011) Prediction of bending load capacity of timber beams using a finite element method simulation of knots and grain deviation. Biosyst Eng 109:241–249. https://doi.org/10.1016/j.biosystemseng.2011.05.008

    Article  Google Scholar 

  • Briggert A, Olsson A, Oscarsson J (2020) Prediction of tensile strength of sawn timber: definitions and performance of indicating properties based on surface laser scanning and dynamic excitation. Mater Struct 53:54. https://doi.org/10.1617/s11527-020-01460-5

    Article  Google Scholar 

  • Burger N, Glos P (1995) Relationship of moduli of elasticity in tension and in bending of solid timber. In: Proceedings of CIB-W18 Meeting, Copenhagen, Denmark, Paper 28–5–2

  • CEA (2018) Cast3M [Computer software], Finite element code developed by the CEA, (French atomic energy commission). https://www-cast3m.cea.fr/

  • Drewett TA (2015) The growth and quality of UK-grown Douglas-fir. Thèse, Edinburgh Napier University

  • Duriot R (2021) Développement de produits LVL de douglas aux propriétés mécaniques optimisées par l’exploitation de la mesure en ligne de l’orientation des fibres lors du déroulage. These de doctorat, HESAM

  • Duriot R, Pot G, Girardon S, Denaud L (2021a) New perspectives for LVL manufacturing wood of heterogeneous quality—Part. 2: modeling and manufacturing of bending-optimized beams. Forests 12:1275. https://doi.org/10.3390/f12091275

    Article  Google Scholar 

  • Duriot R, Pot G, Girardon S, Roux B, Marcon B, Denaud L (2021b) New perspectives for LVL manufacturing wood of heterogeneous quality—Part. 1: Veneer mechanical grading based on online local wood fiber orientation measurement. Forests 12:1264. https://doi.org/10.3390/f12091264

    Article  Google Scholar 

  • Ehrhart T, Palma P, Schubert M, Steiger R, Frangi A (2022) Predicting the strength of European beech (Fagus sylvatica L.) boards using image-based local fibre direction data. Wood Sci Technol 56:123–146. https://doi.org/10.1007/s00226-021-01347-w

    Article  CAS  Google Scholar 

  • EN 338 (2016) Structural timber—strength classes. CEN European Committee for Standardization, Brussels

    Google Scholar 

  • EN 408 (2012) Timber structures—structural timber and glued laminated timber—determination of some physical and mechanical properties. CEN European Committee for Standardization, Brussels

    Google Scholar 

  • Foley C (2001) A three-dimensional paradigm of fiber orientation in timber. Wood Sci Technol 35:453–465. https://doi.org/10.1007/s002260100112

    Article  CAS  Google Scholar 

  • Frayssinhes R, Girardon S, Denaud L, Collet R (2020) Modeling the influence of knots on Douglas-Fir Veneer fiber orientation. Fibers 8:54. https://doi.org/10.3390/fib8090054

    Article  Google Scholar 

  • Fuchs MB (2016) The unit-load method. Structures and their analysis. Springer, Cham, pp 85–110. https://doi.org/10.1007/978-3-319-31081-7_6

    Chapter  Google Scholar 

  • Gil-Moreno D, Ridley-Ellis D, O’Ceallaigh C, Harte AM (2022) The relationship between bending and tension strength of Irish and UK spruce and pine. Eur J Wood Prod 80:585–596. https://doi.org/10.1007/s00107-022-01787-6

    Article  CAS  Google Scholar 

  • Goodman JR, Bodig J (1980) Tension behavior of wood: an anisotropic, inhomogeneous material: final report to the National Science Foundation: grant ENG 76-84421. Colorado State University, Dept. of Civil Engineering, Fort Collins, Colorado

  • Grazide C, Coureau J-L, Cointe A, Morel S (2018) Mechanical performance curves for the strength grading of maritime pine. Eur J Wood Prod 76:877–888. https://doi.org/10.1007/s00107-017-1241-4

    Article  Google Scholar 

  • Hanhijärvi A, Ranta-Maunus A (2008) Development of strength grading of timber using combined measurement techniques. Technical Report VTT Publications 686, VTT Technical Research Centre of Finland

  • Hankinson (1921) Investigation of crushing strength of spruce at varying angles of grain. Air Serv Inf Circ 3:16

    Google Scholar 

  • Hu M, Olsson A, Johansson M, Oscarsson J (2018) Modelling local bending stiffness based on fibre orientation in sawn timber. Eur J Wood Prod 76:1605–1621. https://doi.org/10.1007/s00107-018-1348-2

    Article  Google Scholar 

  • Hu M, Olsson A, Hall S, Seifert T (2022) Fibre directions at a branch-stem junction in Norway spruce: a microscale investigation using X-ray computed tomography. Wood Sci Technol. https://doi.org/10.1007/s00226-021-01353-y

    Article  Google Scholar 

  • Huber JAJ, Broman O, Ekevad M, Oja J, Hansson L (2022) A method for generating finite element models of wood boards from X-ray computed tomography scans. Comput Struct 260:106702. https://doi.org/10.1016/j.compstruc.2021.106702

    Article  Google Scholar 

  • Kretschmann DE (2010) Wood handbook, chapter 05: mechanical properties of wood. For. Prod. Lab. Dep. Agric. For. Serv. Madison Wis. USA

  • Longuetaud F, Pot G, Mothe F, Barthelemy A, Decelle R, Delconte F, Ge X, Guillaume G, Mancini T, Ravoajanahary T, Butaud J-C, Collet R, Debled-Rennesson I, Marcon B, Ngo P, Roux B, Viguier J (2022) Traceability and quality assessment of Douglas fir (Pseudotsuga menziesii (Mirb.) Franco) logs: the TreeTrace_Douglas database. Ann For Sci. https://doi.org/10.1186/s13595-022-01163-7

    Article  Google Scholar 

  • Lukacevic M, Kandler G, Hu M, Olsson A, Füssl J (2019) A 3D model for knots and related fiber deviations in sawn timber for prediction of mechanical properties of boards. Mater Des 166:107617. https://doi.org/10.1016/j.matdes.2019.107617

    Article  Google Scholar 

  • Nyström J (2003) Automatic measurement of fiber orientation in softwoods by using the tracheid effect. Comput Electron Agric 41:91–99. https://doi.org/10.1016/S0168-1699(03)00045-0

    Article  Google Scholar 

  • Olsson A, Oscarsson J (2017) Strength grading on the basis of high resolution laser scanning and dynamic excitation: a full scale investigation of performance. Eur J Wood Prod 75:17–31. https://doi.org/10.1007/s00107-016-1102-6

    Article  Google Scholar 

  • Olsson A, Oscarsson J, Serrano E, Källsner B, Johansson M, Enquist B (2013) Prediction of timber bending strength and in-member cross-sectional stiffness variation on the basis of local wood fibre orientation. Eur J Wood Prod 71:319–333. https://doi.org/10.1007/s00107-013-0684-5

    Article  CAS  Google Scholar 

  • Olsson A, Pot G, Viguier J, Faydi Y, Oscarsson J (2018) Performance of strength grading methods based on fibre orientation and axial resonance frequency applied to Norway spruce (Picea abies L.), Douglas fir (Pseudotsuga menziesii (Mirb.) Franco) and European oak (Quercus petraea (Matt.) Liebl./Quercus robur L.). Ann For Sci 75:102. https://doi.org/10.1007/s13595-018-0781-z

    Article  Google Scholar 

  • Olsson A, Pot G, Viguier J, Hu M, Oscarsson J (2022) Performance of timber board models for prediction of local bending stiffness and strength—with application on douglas fir sawn timber. Wood Fiber Sci 54:226–245

    Article  CAS  Google Scholar 

  • Oscarsson J, Olsson A, Enquist B (2014) Localized modulus of elasticity in timber and its significance for the accuracy of machine strength grading. Wood Fiber Sci 46:489–501

    CAS  Google Scholar 

  • Pollet C, Henin J-M, Hébert J, Jourez B (2017) Effect of growth rate on the physical and mechanical properties of Douglas-fir in western Europe. Can J For Res 47:1056–1065. https://doi.org/10.1139/cjfr-2016-0290

    Article  Google Scholar 

  • Rais A, Bacher M, Khaloian-Sarnaghi A, Zeilhofer M, Kovryga A, Fontanini F, Hilmers T, Westermayr M, Jacobs M, Pretzsch H, van de Kuilen J-W (2021) Local 3D fibre orientation for tensile strength prediction of European beech timber. Constr Build Mater 279:122527. https://doi.org/10.1016/j.conbuildmat.2021.122527

    Article  Google Scholar 

  • Saad K, Lengyel A (2022) Accurate finite element modelling of knots and related fibre deviations in structural timber. J King Saud Univ Eng Sci. https://doi.org/10.1016/j.jksues.2022.01.005

    Article  Google Scholar 

  • Simonaho S-P, Tolonen Y, Rouvinen J, Silvennoinen R (2003) Laser light scattering from wood samples soaked in water or in benzyl benzoate. Optik-Int J Light Electron Opt 114:445–448. https://doi.org/10.1078/0030-4026-00293

    Article  Google Scholar 

  • Steiger R, Arnold M (2009) Strength grading of Norway spruce structural timber: revisiting property relationships used in EN 338 classification system. Wood Sci Technol 43:259–278. https://doi.org/10.1007/s00226-008-0221-6

    Article  CAS  Google Scholar 

  • Viguier J (2015) Classement mécanique des bois de structure. Prise en compte des singularités dans la modélisation du comportement mécanique. [Strength grading of structural timber. Consideration of local singularities to predict mechanical properties]. PhD thesis, Université de Lorraine

  • Viguier J, Bourreau D, Bocquet J-F, Pot G, Bléron L, Lanvin J-D (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 Prod 75:527–541. https://doi.org/10.1007/s00107-016-1149-4

    Article  CAS  Google Scholar 

  • Viguier J, Bourgeay C, Rohumaa A, Pot G, Denaud L (2018) An innovative method based on grain angle measurement to sort veneer and predict mechanical properties of beech laminated veneer lumber. Constr Build Mater 181:146–155. https://doi.org/10.1016/j.conbuildmat.2018.06.050

    Article  Google Scholar 

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Funding

This study was funded by the region of Burgundy Franche‐Comté and the French National Research Agency (EffiQuAss project ANR‐21‐CE10‐0002‐01).

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Authors and Affiliations

  1. Arts et Métiers Institute of Technology, LaBoMaP, UBFC, HESAM, Rue Porte de Paris, 71250, Cluny, France

    Guillaume Pot, Stéphane Girardon, Joffrey Viguier & Louis Denaud

  2. Université de Lorraine, LERMAB, 27 Rue Philippe Séguin, 88000, Epinal, France

    Robin Duriot

Authors
  1. Guillaume Pot
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  2. Robin Duriot
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  3. Stéphane Girardon
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  4. Joffrey Viguier
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  5. Louis Denaud
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Contributions

Conceptualization: GP, RD, SG, JV, LD; Methodology: GP, RD, SG, JV, LD; Data Curation: GP, RD; Software: GP, RD, SG, JV; Formal analysis and investigation: GP, RD, SG; Writing - original draft preparation: GP, RD; Writing - review and editing: SG, JV, LD; Funding acquisition: GP, LD; Supervision: GP, LD, SG

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Correspondence to Guillaume Pot.

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Pot, G., Duriot, R., Girardon, S. et al. Comparison of classical beam theory and finite element modelling of timber from fibre orientation data according to knot position and loading type. Eur. J. Wood Prod. 82, 597–617 (2024). https://doi.org/10.1007/s00107-024-02055-5

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