Abstract
Finite element models (FEM) were used to simulate beam sections in bending with a knot. They aim at evaluating the mechanical behaviour of timber considering the effect of this singularity on resulting bending strength. By using linear elastic theory and an adapted failure criterion (Tsaï–Hill), an equivalent state can be deduced, giving information about the influence of knot on the load bearing capacity of the element. Several 2D-FEM were then developed using the free software Castem® by considering plane strain. The beam section was considered like a composite material with two materials; the wood and the knot. The slope of grain around the defect was implemented by using a simple exponential equation parameterized as a function of the radius of the singularity. The location and the size of the defect and the longitudinal modulus of elasticity of wood were investigated in this study. Results exhibit performance curves specific to bending strength. These numerical performance curves were not used to predict the bending strength but to identify some thresholds, function of the size and the location of a critical knot and the stiffness of structural beams. 188 beams with a length of 4.5 m and a cross-section of 200 × 100 mm² were tested to study the efficiency of numerical thresholds. This study shows that it is possible, by identifying only the geometrical properties of the critical defect and the stiffness of the structural beam, to improve the prediction of the bending strength of beams with a large cross-section in Maritime pine up to C40.
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Acknowledgements
The authors are grateful to the Regional Council of Aquitaine for funding of this study through the project “Morphomécanique du Pin Maritime”. The authors thank also the French National Research Agency (ANR) for supporting this study through the Xyloplate project, Equipex XYLOFOREST (ANR-10-EQPX-16).
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Grazide, C., Coureau, JL., Cointe, A. et al. Mechanical performance curves for the strength grading of maritime pine. Eur. J. Wood Prod. 76, 877–888 (2018). https://doi.org/10.1007/s00107-017-1241-4
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DOI: https://doi.org/10.1007/s00107-017-1241-4