Poisson’s Ratios for Wood Species for Structural Purposes

Abstract

The broader knowledge about physical and mechanical properties of wood allows reliable timber structures design. Even little addressed in the literature, in several situations Poisson's ratios are required for the evaluation of stresses acting on structural elements. This study aimed to obtain values of Poisson's ratios (ν), plans Longitudinal-Radial (νLR) and Longitudinal-Tangential (νLT), for species Peroba Rosa (Aspidosperma polyneuron) and Jatobá (Hymenaea courbarilL.). For this purpose, forty samples Peroba Rosa and eight samples of Jatobá were prepared for testing in compression parallel to the grain, following the recommendations of ABNT NBR 7190 standard. The results of means confidence intervals, considered at the level of 5% significance, revealed that the Poisson's ratios νLR e νLT to Peroba Rosa are 0.27 and 0.42, respectively, and 0.25 and 0.43 to Jatobá.

Full text

Poisson’s Ratios for Wood Species for Structural Purposes
Francisco A. Rocco Lahr 1,a, André L. Christoforo2,b, Eduardo Chahud3,c,
Luiz A. Melgaço N. Branco3,d, Rosane A. G. Battistelle4,e
and Ivaldo D. Valarelli4, f
1 Department of Structural Engineering, São Carlos Engineering School, University of São Paulo
(EESC/USP), São Carlos, 13566-590, Brazil.
2 Department of Civil Engineering, Federal University of São Carlos, São Carlos, 13565-905, Brazil.
3 Faculty of Engineering and Architecture, FUMEC University, Belo Horizonte, 30130-009, Brazil.
4 Department of Civil Engineering, State University of São Paulo “Júlio de Mesquita Filho”, Bauru,
17033-360, Brazil.
afrocco@sc.usp.br, balchristoforo@yahoo.com.br, cechahud@gmail.com, dluizmelg@fumec.br,
erosane@feb.unesp.br, fivaldo@feb.unesp.br
Keywords: Anisotropy, parallel compression, Poisson's ratio.
Abstract. The broader knowledge about physical and mechanical properties of wood allows
reliable timber structures design. Even little addressed in the literature, in several situations
Poisson's ratios are required for the evaluation of stresses acting on structural elements. This study
aimed to obtain values of Poisson's ratios (ν), plans Longitudinal-Radial (νLR) and Longitudinal-
Tangential (νLT), for species Peroba Rosa (Aspidosperma polyneuron) and Jatobá (Hymenaea
courbaril L.). For this purpose, forty samples Peroba Rosa and eight samples of Jatobá were
prepared for testing in compression parallel to the grain, following the recommendations of ABNT
NBR 7190 standard. The results of means confidence intervals, considered at the level of 5%
significance, revealed that the Poisson's ratios νLR e νLT to Peroba Rosa are 0.27 and 0.42,
respectively, and 0.25 and 0.43 to Jatobá.
Introduction
Wood is a material with complex anatomical composition and presents itself as orthotropic
material [1], with three axes of symmetry (longitudinal, radial and tangential).
The broader knowledge about physical and mechanical properties of the wood allows reliable
timber structures design but requires the full characterization of the species of interest [2].
Among the mechanical properties of wood, even little addressed in the literature the Poisson's
ratio is important in several situations, especially in cases including structural elements in plates
systems, among others, which motivates the development of research on this topic [3-5].
This study aimed to obtain values of Poisson's ratios (ν), plans Longitudinal-Radial (νLR) and
Longitudinal-Tangential (νLT), for species Peroba Rosa (Aspidosperma polyneuron) and Jatobá
(Hymenaea courbaril L.). This will enlarge knowledge about the mechanical properties of wood in
question, providing a more accurate and reliable structural design.
Material and Methods
Poisson’s ratios νLR e νLT for Peroba Rosa and Jatobá were obtained by considering results of
compression tests on specimens (5×5×10cm) in the parallel direction to the grain, following the
recommendations of the Brazilian standard ABNT NBR 7190: 1997 [6].
Compression parallel to grain tests were carried out within the Wood and Timber Structures
Laboratory (LaMEM), Department of Structural Engineering (SET), São Carlos Engineering School
(EESC), University of São Paulo (USP), with the aid of universal testing machine AMSLER, load
capacity 25 tons.
Advanced Materials Research Vol. 1088 (2015) pp 690-693 Submitted: 25.10.2014
© (2015) Trans Tech Publications, Switzerland Accepted: 07.11.2014
doi:10.4028/www.scientific.net/AMR.1088.690
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,
www.ttp.net. (ID: 177.34.172.13-27/01/15,15:58:21)

Deformation were calculated by measuring the displacements with deflectometers, accuracy
0.001 mm, positioned in the fiber direction and perpendicular to them (Figure 1). Forty specimens
were produced for Peroba Rosa (one of them presented defects and it was necessary not to ignore it
in statistical analysis) and eight for Jatobá wood species.
Figure 1. Position of deflectometers in compression paralles to grain tests.
The choice for using deflectometers instead of strain gages in the specimens is justified by more
representativeness of the area covered by deflectometers. Strain gages are useful for spot
deformation register. It is noteworthy that many attempts were made in order to improve the system
for setting the deflectometers, searching for an adequate performance in the compressive tests.
Related to the specimens, it is indispensable that the growth rings should be perfectly parallel to the
faces, improving the reliability of results.
From Hooke's law, the Poisson's ratios (ν) for Peroba Rosa and Jatobá species, in radial (νLR) and
tangential (νLT) directions were obtained by means of Equations 1 and 2. In them, εA is the specific
axial deformation; εR is the specific radial deformation and εT is the specific tangential deformation.
R
LR
A
ε
ν
ε
= (1)
T
LT
A
ε
ν
ε
= (2)
In statistical analysis, the confidence interval for the mean was employed, 5% level of
significance, expressed by Equation 3, enabling verify the extremes of variation of Poisson
regression coefficients (amplitudes) and the representativeness of the mean values.
x x
05 05
s s
x t x t
n n
µ
− ⋅ ≤ ≤ + ⋅
(3)
From Equation 3,
x
denotes the average value of the variable, t05 is the value of "t" test, Sx is
the standard deviation and n the number of samples evaluated. To validate the results of the
confidence interval, distribution normality was confirmed using Anderson-Darling test. For inherent
considerations of inherent test, P-value higher than 5% sets the normal distribution of Poisson's
ratios values, and no normality otherwise.
Results and Discussion
Table 1 shows the results of the Poisson's ratios and νLR e νLT for each of the test specimens,
Peroba Rosa species, with the mean values (
x
), coefficient of variation (Cv) and the smaller (Min)
and the higher (Max) values found, respectively.
Advanced Materials Research Vol. 1088 691

TABLE 1. POISSON’S RATIOS, PEROBA ROSA.
ν
LR
ν
LT
ν
LR
ν
LT
0.44
0.62
0.29
0.48
0.44
0.61
0.24
0.35
0.20
0.38
0.27
0.40
0.28
0.41
0.14
0.35
0.10
0.22
0.26
0.42
0.21
0.31
0.32
0.42
0.33
0.50
0.16
0.30
0.41
0.72
0.25
0.42
0.18
0.44
0.26
0.39
0.22
0.39
0.28
0.45
0.13
0.49
0.28
0.38
0.35
0.28
0.32
0.45
0.28
0.30
0.27
0.41
0.35
0.49
0.29
0.42
0.14
0.46
Statistics
0.35
0.53
0.18
0.19
x
0.27
0.43
0.49
0.65
Cv (%) 34 27
0.31
0.46
Min 0.10
0.19
0.20
0.31
Max 0.49
0.72
0.10
0.27
0.34
0.46
0.26
0.38
0.30
0.45
0.34
0.62
The results of the Poisson coefficient for both species of wood were close to those obtained by
[3], that worked with other wood species.
The P-values of the Anderson-Darling normality test for the coefficients of νLR e νLT, Peroba
Rosa wood specie, were equal to 0.546 and 0.149, respectively, validating the use of the confidence
interval.
Confidence intervals (µ) for the coefficients of Poisson νLR e νLT, Peroba Rosa species, are
0.24≤µ≤0.30 and 0.38≤µ≤0.46, respectively. With this, in a significance level of 5%, it can be
considered that νLR ranges between 0.24 and 0.30; and that νLT ranges between 0.38 and 0.46.
Moreover, it is accepted that the mean values of Poisson's ratios consist of good estimates on these
wood properties.
Table 2 shows the results of the Poisson's ratios and νLR e νLT for each of the test specimens,
Jatobá species, with the mean values (
x
), coefficient of variation (Cv) and the smaller (Min) and
the higher (Max) values found, respectively.
TABLE 2. POISSON’S RATIOS, JATOBÁ.
ν
LR
ν
LT
0.21
0.46
0.21
0.59
0.30
0.30
0.20
0.42
0.27
0.41
0.28
0.40
0.19
0.31
Statistics
0.36
0.52
x
0.25
0.52
Cv
24
23
Mín
0.19
0.30
Máx
0.36
0.59
692 Advances in Materials Science

The P-values of the Anderson-Darling normality test for the coefficients of νLR e νLT, Jatobá
wood specie, were equal to 0.254 and 0.721, respectively, validating the use of the confidence
interval.
Confidence intervals (µ) for the coefficients of Poisson νLR e νLT, Jatobá species, are
0.20≤µ≤0.30 and 0.35≤µ≤0.51, respectively. With this, in a significance level of 5%, it can be
considered that νLR ranges between 0.20 and 0.30; and that νLT ranges between 0.35 and 0.51.
Moreover, it is accepted that the mean values of Poisson's ratios consist of good estimates on these
wood properties.
Conclusions
Based on experiments conducted, it can be concluded:
- It is feasible to conduct tests for compression parallel to grain for determining νLR and νLT,
using deflectometers, 0.001 accuracy, to measure the longitudinal and transverse deformations;
- For Peroba Rosa wood species, average coefficients of Poisson νLR and νLT and are equal to
0:27 and 0:42, respectively;
- For Jatobá wood, average coefficients of Poisson νLR and νLT and are equal to 0:25 and 0:43,
respectively.
This information allows greater reliability and safety design of structures when employing the
Peroba Rosa and Jatobá wood species investigated in this research. Moreover, the results may be
excellent indicatives of Poisson’s ratios for structural timbers.
References
[1] F. A. Rocco Lahr. On the determination of elastic properties of wood. 216 p. 1983. Thesis
(Ph.D. in Structural Engineering). Brazil, EESC/USP Press (1983), 216 p.
[2] A. L. Christoforo, K. A. Blecha, A. L. C. Carvalho, L. F. S. Resende and F. A. L. Rocco.
Journal of Civil Engineering Research. Vol. 3 (2013), p. 103.
[3] N. T. Mascia and E. A. Nicolas. Construction & Building Materials. Vol. 41 (2013), p. 696.
[4] N. T. Mascia and R. O. Simoni. Engineering Failure Analysis. Vol. 35 (2013), p. 712.
[5] N. T. Mascia and L. Vanalli. Construction & Building Materials. Vol. 30 (2012) p. 528.
[6] Brazilian Association of Technical Standards (ABNT) NBR 7190. Design of Timber Structures.
Brazil, ABNT Press (1997), p. 107.
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