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

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.