Alternative methodology for calculating the modulus of elasticity of wooden beams of structural dimensions

Abstract

This study aims to present an alternative calculation methodology based on the Least Squares Method for determining the modulus of elasticity in bending wooden beams of structural dimensions. The equations developed require knowledge of three or five points measured in displacements along the piece, allowing greater reliability on the response variable, using the statistical bending test at three points and non-destructively, resulting from imposition of measures from small displacements L/300 and L/200, the largest being stipulated by the Brazilian norm NBR 7190:1997. The woods tested were Angico, Cumaru, Garapa and Jatoba. Besides obtaining the modulus of elasticity through the alternative methodology proposed, these were also obtained employing the Brazilian norm NBR 7190:1997, adapted to the condition of non-destructive testing (small displacements) and for pieces of structural dimensions. The results of the modulus of elasticity of the four species of wood according to both calculation approaches used proved to be equivalent, implying the good approximation provided by the methodology of calculation adapted from the Brazilian norm.KEYWORDS: wood, beam theory, modulus of elasticity, Least Squares Method. METODOLOGIA ALTERNATIVA PARA O CÁLCULO DO MÓDULO DE ELASTICIDADE EM VIGAS DE MADEIRA DE DIMENSÕES ESTRUTURAISRESUMO: Este trabalho objetiva apresentar uma metodologia alternativa de cálculo fundamentada no Método dos Mínimos Quadrados para a determinação do módulo de elasticidade na flexão, em vigas de madeira de dimensões estruturais. As equações desenvolvidas requerem o conhecimento de três ou cinco pontos medidos em deslocamentos ao longo da peça, permitindo maior confiabilidade sobre a variável resposta, utilizando-se do ensaio de flexão estática a três pontos e de forma não destrutiva, decorrente da imposição das medidas de pequenos deslocamentos L/300 e L/200, sendo a maior delas estipulada pela norma Brasileira NBR 7190:1997. As madeiras testadas foram Angico, Cumaru, Garapa e Jatobá. Além da obtenção dos módulos de elasticidade pela metodologia alternativa proposta, estes foram também obtidos do emprego da norma Brasileira NBR 7190:1997, adaptada para a condição de ensaio não destrutivo (pequenos deslocamentos) e para peças de dimensões estruturais. Os resultados dos módulos de elasticidade das quatro espécies de madeira, segundo ambas as abordagens de cálculo utilizadas, mostraram-se equivalentes, implicando na boa aproximação fornecida pela metodologia de cálculo adaptada da norma Brasileira.

PHYSICAL-MECHANICAL CHARACTERIZATION OF Eucalyptus urophylla WOOD

“…Despite the great potentiality, Eucalyptus urophylla wood still has low levels of use in civil construction (Christoforo et al, 2014), which is also justified by the lack of knowledge of its physical and mechanical properties, especially in the absence of characteristics such as age or region source. Due to the problem raised, this research aimed to present the main physical and mechanical properties of the Eucalyptus urophylla species as well as to investigate the effect of the moisture content (12%, 30% -saturated) in the properties evaluated, reinforcing the wide possibility of use timber as structural elements.…”

Evaluation of the Tensile Modulus of Elasticity in Parallel Direction to the Grain for <i>Eucalyptus grandis</i> Wood Specie

“…The characterization of wood, as well as other materials, follows the premise and methods of calculation of national and international standards. However, in the calculation of the elastic modulus in these standards methodologies of optimization criteria are not used, getting the stiffness determined by the inclination of the linear elastic portion of the stress×strain diagram or knowledge of two levels of successive deformation measured in the region of proportionality between stress and strain [1][2][3][4][5].…”

Evaluation of the Moisture Content in Stiffness Properties of Structural Glulam Beams

“…In cases of large structures with different geometric shapes, the use of glued laminated (glulam) members highlights in building construction, circumventing restrictions on the use of lumber, besides conferring convenient dimensional stability to manufactured pieces, limited only by production parameters and transport conditions [1][2][3].…”