Elasticity moduli in round wooden beams of Pinus caribaea

Abstract

This research aimed at estimating both longitudinal (E) and shear (G) elasticity moduli of round structural-sized beams made of Pinus caribaea timber, verifying thus the validity of the G = E/ 20 relationship established by the Brazilian standard ABNT NBR 7190: 1997 (Designing of Wooden Structures). We tested twenty pieces of green wood with average length, diameter and conicity of 750 cm, 30 cm and 4%, respectively. Two static bending tests were applied at three points of each piece, being nondestructive and using different distances between supports. In the first trial, the length and diameter relationship (L/ d) was set as being equal to 24; yet in the second test, it was set at 12. The elasticity moduli were estimated by a successive use of the Timoshenko beam theory equation, which take s into account the shearing stress effect on displacement calculations. The results of both longitudinal and shear moduli were related through the least square assessment method; thus, we could find a relationship of G = E/ 43. As a result, we observed that the tested wooden pieces are at odds with the Brazilian standards.KEY WORDS: Stiffness, bending, beam theory, least square. MÓDULOS DE ELASTICIDADE EM VIGAS ROLIÇAS DE MADEIRA Pinus caribaea RESUMO:Este trabalho objetivou avaliar os valores dos mód ulos de elasticidade longitudinal (E) e transversal (G) em peças roliças estruturais de madeira Pinus caribaea, de maneira a se verificar a validade da relação G=E/20 estabelecida pela norma brasileira ABNT NBR 7190:1997 (Projeto de Estruturas de Madeira). As vinte peças de madeira (verde) testadas apresentam comprimento médio de 750 cm, diâmetro médio de 30 cm e conicidade média de 4%. Foram realizados dois ensaios de flexão estática a três pontos por peça, conduzidos de forma não destrutiva, diferenciados apenas pelas distâncias entre os apoios. No primeiro ensaio, foi utilizada a relação (L/d) entre comprimento (L) e diâmetro (d) das peças igual a vinte e quatro; e, no segundo, realizado na sequência, com L/d igual a doze. Os módulos de elasticidade foram obtidos de acordo com o emprego sucessivo da equação da teoria de vigas de Timoshenko, que leva e m consideração a influência dos esforços cisalhantes no cálculo dos deslocamentos. Os resultados obtidos entre os módulos de elasticidade longitudinal e transversal foram relacionados pelo método dos mínimos quadrados, sendo encontrada a relação G=E/43, evidenciando, para as peças de madeira aqui investigadas, a divergência de resultados para com a norma brasileira. PALAVRAS-CHAVE:Rigidez, flexão, teoria de vigas, mínimos quadrados.

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