Abstract
This research aimed to present, with the aid of the three-points static bending, conducted nondestructively, analytical methodology to determine the longitudinal (<i>E</i>) and the shear modulus (<i>G</i>) of elasticity in round timber beams. The wood used was <i>Eucalyptus </i>clones. Were used three different values to the form factor coefficient of the circular cross section, allowing evaluating the differences between the shear stiffness values obtained. The results of the analysis of variance indicated no statistical equivalence between the shear modulus of elasticity, revealing be significant the influence of the form factors used to determine the shear modulus of elasticity. The coefficient (<i>λ</i>) of the relationship between the modulus of elasticity (<i>E=λÎG</i>) obtained from the least squares method were equal to 118, revealing 5.9 higher than the relationship (<i>E=20ÎG</i>) presented in the Brazilian standard ABNT NBR 7190:1997. It is emphasized that these results may be different for the same or different wood species, justifying the use of this methodology in each research developed.
Highlights
For the design of various structures in wood, such as silos, roofs, buildings, bridges, among others, engineers, architects and designers make use of normative documents, such as the Brazilian standard ABNT NBR 7190:1997 (Design of Structures Wood), which does not address the anisotropy of wood, with an emp irical relat ionship for obtaining the shear modulus of elasticity (G) known longitudinal modulus of elasticity (E) expressed as: G=E/20, which motivates development of new research on this topic, and highlight the work done by Rocco Lahr[4], Bu rd zik Nkwera[5], Zangiác omo Rocco Lahr[6] and Christoforo et al.[7]
Christoforo et al.[7] presented an analytical methodology for the calculation of the shear and longitudinal modulus of elasticity in pieces of lu mber, using the three-points static bending, adapted from the Brazilian standard ABNT NBR 7190[8], based on the methodology presented by Rocco Lahr[4]
The moduli of elasticity were obtained in the condition of geomet ric linearity, the largest displacements being limited to the experiments L/200 reason, as defined by the small d isplacements of Brazilian standard ABNT NBR 7190[8]
Summary
Rocco Lahr[4] study, among others, the influence of the dimensions of the test pieces of lumber for which the effect of shear fo rces beco me neg lig ib le in the calcu lat ion of displacements, reach ing the rat io L/h≥21, where L is the. Zangiácomo and Rocco Lahr[6] studied the relationship between the length and diameter (D) in round timber beams for which the effect of shear forces becomes negligible in the calculation of d isplacements, arriv ing at 24 and 15 relations for the Pinus elliottii and Pinus caribaea wood species, res p ectiv ely. Christoforo et al.[7] presented an analytical methodology for the calculation of the shear and longitudinal modulus of elasticity in pieces of lu mber, using the three-points static bending, adapted from the Brazilian standard ABNT NBR 7190[8], based on the methodology presented by Rocco Lahr[4]. Results of the coefficients (α) between the modules of elasticity (E=α·G)
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