Determination of the longitudinal modulus of elasticity in structural sawn wooden beams by the least squares method
DOI:
https://doi.org/10.5935/1809-2667.20120032Keywords:
Sawn wood, Modulus of elasticity, Least Squares MethodAbstract
This paper proposes an alternative method of calculation based on the Least Squares Method to determine the longitudinal modulus of elasticity in structural-sized wooden beams. The developed equations require knowledge of three points of displacements, allowing greater reliability on the dependent variable when using the static four-point bending test. Using the Jatobá (Hymenaea sp) wood in the study, the methodology proposed here was used in combination with a simplified one, requiring knowledge of displacement only at the midpoint of the beam in order to compare the results among them. Results show statistical equivalence between the models, indicating a good approximation of the simplified model for calculating the modulus of elasticity in wooden structural bending here evaluated.Downloads
References
AMERICAN SOCIETY FOR TESTING AND MATERIALS (ASTM). Standard methods of testing structural panels in flexure. ASTM D 3043-95. Annual book of ASTM standards. West Conshohocken, Philadelphia: ASTM, 1995.
AMERICAN SOCIETY FOR TESTING AND MATERIALS (ASTM). Standard specification for evaluation of structural composites lumber products. ASTM D 5456. Annual book of ASTM standards. West Conshohocken, PA: ASTM, 2006.
AMERICAN SOCIETY FOR TESTING AND MATERIALS (ASTM). Standard test method of static tests of lumber in structural sizes. ASTM D 198. Annual book of ASTM standards, v. 03.01. West Conshohocken, PA: ASTM, 1997.
AMERICAN SOCIETY FOR TESTING AND MATERIALS (ASTM). Standard test methods for mechanical properties of lumber and wood-base structural material. ASTM D 4761-96. Annual book of ASTM standards. West Conshohocken, PA: ASTM, 1996.
ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS (ABNT). Projeto de Estruturas de Madeira. NBR 7190, Rio de Janeiro, 1997.
BODIG, J.; JAYNE, B. A. Mechanics of wood and wood composites. Malabar, Florida: Krieger Publishing Company, 1992.
CALIL, C. JR.; LAHR, F. A. R.; DIAS, A. A. Dimensionamento de elementos estruturais de madeira. Barueri-São Paulo: Manole, 2003.
EUROPEAN STANDARD (EN). Estruturas de Madeira - Métodos de teste - Determinação das propriedades mecânicas de painéis derivados de madeira. EN 789. Bruxelas, 1995. (versão portuguesa)
FIORELLI, J. Estudo teórico e experimental de vigas de madeira laminada colada reforçadas com fibra de vidro. São Carlos, 2005. 108p. Tese (Doutorado em Ciência e Engenharia de Materiais) - Universidade de São Paulo, 2005.
GUITARD, D. Mécanique du matériau bois et composites. França: Cepadues-editions, 1987.
MINÁ, A. J. S.; OLIVEIRA, F. G. R.; CALIL JR, C.; DIAS, A. A.; SALES, A. Avaliação não destrutiva de postes de madeira por meio de ultra-som. Scientia Forestalis, n. 65, p. 188-196, 2004.
MIOTTO, J. L; DIAS, A. A. Produção e avaliação de vigas de madeira laminada colada confeccionadas com lâminas de eucalipto. Revista Tecnológica, Edição Especial ENTECA, p. 35-45, 2009.
OLIVEIRA, F. G. R.; SALES, A. Ultrassonic measurements in Brazilian hardwood. Materials Research, v. 5, n. 1, p. 51-55, 2002.
PALMA. H. A. L.; BALLARIN, A. W.; ABILIO, R. M. Propriedades mecânicas de painéis LVL de Pinus tropicais. In: ENCONTRO BRASILEIRO EM MADEIRA E ESTRUTURAS DE MADEIRAS, 11., 2008a, Londrina- PR.
PALMA. H. A. L.; BALLARIN, A. W.; ROCHA, C. D. Propriedades de flexão de vigas LVL de Eucalyptus grandis. In: ENCONTRO BRASILEIRO EM MADEIRA E ESTRUTURAS DE MADEIRAS, 11., 2008b, Londrina- PR.
PIGOZZO, J. C.; PLETZ, E.; LAHR, F. A. R. Aspectos da classificação mecânica de peças estruturais de madeira. In: ENCONTRO BRASILEIRO EM MADEIRAS E EM ESTRUTURAS DE MADEIRA, 7., 2000, São Carlos, SP.
ROCCO LAHR, F. A. Sobre a determinação de propriedades de elasticidade da madeira. São Carlos, SP, 1983, 216p. Tese (Doutorado em Engenharia de Estruturas) - Escola de Engenharia de São Carlos, Universidade de São Paulo, 1983.
ROSS, R. J.; BRASHAW, B. K.; PELLERIN, R. F. Nondestructive evaluation of wood. Forest Products Journal, v. 48, n. 1, p. 14-19, 1998.
WERKEMA, M. C. C.; AGUIAR S. Planejamento e análise de experimentos: como identificar e avaliar as principais variáveis influentes em um processo. Belo Horizonte: Fundação Christiano Ottoni, Escola de Engenharia da UFMG, 1996.
Downloads
Published
Issue
Section
License
The authors of the manuscript submitted to Vértices, hereby represented by the corresponding author, agree to the following terms:
The authors retain the copyright and grant Vértices the right of first publication.
At the same time the work is licensed under the Creative Commons Attribution 4.0 International License, allowing third parties to copy and redistribute the material in any medium or format and to remix, transform, and build upon its content for any legal purpose, even commercially, provided the original work is properly cited.
Authors will not receive any material reward for the manuscript and Essentia Editora will make it available online in Open Access mode, through its own system or other databases.
Authors are authorized to enter into additional contracts separately for non-exclusive distribution of the version of the work published in Vértices (eg, publish in institutional repository or as book chapter), with acknowledgment of authorship and initial publication in this journal.
Authors are permitted and encouraged to disseminate and distribute the post-print (ie final draft post-refereeing) or publisher's version/PDF at online information sources (eg, in institutional repositories or on their personal page) at any time after the first publication of the article by Vértices.
Essentia Editora may make normative, orthographic and grammatical changes in the originals in order to maintain the standard language, with the final consent of the authors.
The content and opinions expressed in the manuscript are the sole responsibility of the author (s).