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This paper focuses on the main characteristics of a tree-shaped timber structural system or simply tree-shaped. One of them is the complexity of its steel connections, responsible for the joint of bar elements, compounding a complex structural system, which requires the application of the CYPECAD software version 2007 to solve the calculations problems. Its efficiency was confirmed by a variety of laboratory tests carried out with the whole structure. The tree-shaped is a timber structure that can be used in a large number of destinations, including residences, malls, sheds, hangars, etc.. Originally, it was conceived based on the well-known masterpiece "Sagrada Família", whose author was Architect Antoni Gaudi I Cornet (1852-1926 in Barcelona/Spain. It was designed at the end of 19th century and its construction is still not finished. Gaudi inverted the logical order of the gothic concepts, i.e., light weights below and heavy weights above. Based on this concept, he always had in mind the figure of a tree in nature. The tree-shaped follows the same idea, using timber pieces connected by steel plates. Theoretical and numerical analyses have shown its efficiency and lightness for use in timber structures.

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.

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