Numerical Evaluation of Longitudinal Modulus of Elasticity of Eucalyptus grandis Timber Beams

Currently, the standard NBR 7190:1997 (Design of Wood Structures) makes no reference to any test aimed to determine the stiffness and strength of structural-sized lumber components, restricting this analysis to small and clear specimens. Methodologies proposed by international standard do not include optimum criteria in their calculation models. This study presents an alternative methodology to determine the longitudinal modulus of elasticity in Eucalyptus grandis timber beams, based on a combination between the Finite Element and the Least Square Methods. Besides the use of numerical methods, the modulus of elasticity was also analytically obtained by the equation presented in NBR 7190:1997, concerning the static three-point bending test, adapted to a non-destructive testing condition. Results found for the elastic modulus for the Eucalyptus grandis species showed statistical equivalence between the methodologies, which implies the reliability of using Brazilian standard for the characterization of structural components subjected to bending. However, these results cannot be extended for other woods from the same species or different species, justifying the use of the numerical calculation approach discussed in this paper.