1. Introduction

Wood is a material with great variability in their mechanical and physical properties, being the study and knowledge of these properties essential to its best processing [1, 2], providing rational use, whether in industry or in civil construction [3, 4].

Studies with Paricá Wood specie (Schizolobiumamazonicum Herb.) and Cumaru Wood specie (Dipterixodorata) present different values for mechanical and physical properties, classifying it according Brazilian standard ABNT NBR 7190:1997 [5] at belonging to strength classes C20 and C60 of the dicotyledonous, respectively [6-8].

Researches with different positions, sizes and grain directions of the specimens were realizes to determine more information to mechanical and physical properties of the wood [9-12].

The density of wood is one of the main physical properties of wood, because with it is possible to estimate their mechanical properties [13, 14]. Classifying the Wood species according to their densities is also possible to plan programs for drying wood to minimize the problems of this process [15].

The anisotropy property of the wood is very important to studies of their characteristics and is related with their moisture content. The dimensions of the wood undergo variations according to the increase or decrease in moisture content. Below the fibers saturation point can determine the swelling and shrinkage of the wood only increasing or decreasing moisture content, respectively [14, 17]. The Brazilian standard ABNT BR 7190:1997 [5] recommended 25% for moisture content of reference for fiber saturation point.

The anisotropy coefficient (ratio between shrinkage or swelling in tangential and radial directions, respectively), is an important parameter that indicates the best application of wood specie relating it to their drying quality (Table 1).

Table 1. Anisotropy coefficient and wood quality [18]

The aim of this research is to get more information about wood anisotropy, using polynomial (linear; quadratic; cubic) and exponential regression models, estimate the full shrinkage, anisotropy coefficient and shrinkage coefficient by density of five Wood specie, classifieds in five strength classes for dicotyledonous according Brazilian standard ABNT NBR 7190:1997 [5].

2. Material and Methods

The research was carried outat Wood and Timber Structures Laboratory (LaMEM), São Carlos School of Engineering (EESC), University of SãoPaulo (USP), Brazil.

The density (ρ_12%), full shrinkage (radial [RS]; tangential [TS]; volumetric [VS]), inverse anisotropy coefficient (1/AC), anisotropy coefficient (AC) and shrinkage coefficient (radial [RSC]; tangential [TSC]; volumetric [VSC]) of Wood species were obtained according ABNT NBR 7190:1997 standard, using moisture content at the fiber saturation point (PS) for shrinkage coefficients calculation.

The Wood species used in this research were Cedro Doce (Cedrela sp.), Canafístula (Cassia ferrugínea), Angelim Araroba (Vataireopsisararoba), Mandioqueira (Qualeasp.) e Angelim Vermelho (Diniziaexcelsa). Were used 12 specimens for Wood species to obtain the above cited properties and plus 12 for testing of compression parallel to the grain to obtain the characteristic strength value (f_c0,k), responsible for defining the strength classes (Table 2).

Table 2. Strength classes of Wood species used according ABNT NBR 7190:1997 Standard

The regression models for fullshrinkages, anisotropy coefficients and shrinkage coefficients at function of density were exponential (Equation 1) and linear (Equation 2), quadratic (Equation 3) and cubic (Equation 4) polynomial. The aim of regression models find the values for coefficients of functions [a, b, c and d] presented in Equations 1, 2, 3 and 4 according methods of least square fundaments (lower residue). The adjusts were realized for each property and according obtained values by specimens for five Wood species, totaling 60 specimens for each answer.

(1)

(2)

(3)

(4)

The significance and quality of stipulated adjusts were evaluated by variance analysis (ANOVA) of regression, with level of significance of 5% (α), having as null hypothesis (H₀) the no-significance of regression by adjusted coefficients and significance of regression as alternative hypothesis (H₁). P-value less the level of significance implies reject the null hypothesis, otherwise accepted the answer.

3. Results and Discussion

Table 3 present the results of mean values for each property for five wood species studied in this research.

Table 3. Mean values of wood species properties

Cedro Doce Wood specie had the lowest density, shrinkage volumetric and radial, tangential and volumetric shrinkage coefficient. This result is consistent, therefore, Wood species with more density has more dimensional variation, because it has more wood per unit volume [19, 20].

According Tables 1 and 3, Cedro Doce Wood specie present excellent quality, because present shrinkage anisotropy coefficient less than 1.5 can be used in furnitures, miters, sports equipment and other uses. The other Wood species studied are classified as normal quality, because present shrinkage anisotropy coefficient greater than 1.5 and less than 2.0, can be used in shelves, tables and cupboard [17, 18].

The shrinkage anisotropy coefficient found to Mandioqueira Wood specie (1.990) is equal the value determined to Cedro Marinheiro Wood specie (Guareatrichilioides L. (Meliaceae)), satisfactory result, because the two species belong to the C50 dicotyledonous strength classes [17].

The mean value of volumetric shrinkage for Bracatinga Wood Specie (Mimosa scabrella Benthan) is 7.65%, less than the values found for the woods studied in this research [21].

The Eucalypt Wood specie (Eucalyptus benthamii Matenet Cambage) have radial shrinkage, tangential shrinkage and anisotropy coefficient equal to 5.91%, 13.87% and 2.36, respectively [22]. The anisotropy coefficients of the Wood species used in this research are betters, with greater opportunities for more refined uses. The mean value fiber saturation point found to all Wood species were equal to 23.17%, very close to the 25% recommended by Brazilian standard ABNT NBR 7190:1997 [5].

Table 4 to 10 presents the results of ANOVA regression models for seven studied properties. The label NS is no-significance of adjusted coefficient in the model (P-value > 0.05).

Table 4. Results of regression models for radial shrinkage (RS)

Table 5. Results of regression models for tangential shrinkage (TS)

Table 6. Results of regression models for volumetric shrinkage (VS)

Table 7. Results of regression models for inverse anisotropy coefficient (1/AC)

Table 8. Results of regression models for radial shrinkage coefficient (RSC)

Table 9. Results of regression models for tangential shrinkage coefficient (TSC)

Table 10. Results of regression models for volumetric shrinkage coefficient (VSC)

The results of determination coefficients adjusted R²(Adj.) showed the possibility of estimative of tangential and volumetric shrinkages by density.

For tangential and volumetric shrinkages, of linear adjusts for quadratics observed increases in R²(Adj.) value and reduction in variation coefficient of regression, and with cubic polynomial, ANOVA present no-significance in the results, equal occur for others properties. However, the variation coefficient of adjusts using exponential functions presents lower results of R²(Adj.) compared to variation coefficient of linear and quadratic polynomial functions, but presents variation coefficients well below derived of polynomials, showing be the exponentials models the betters among the evaluated, for the greater representation.

For exponential models, the determination coefficients adjusted were below to 70% according with Montgomery [23], the representation of adjusted model present R²(Adj.) upper to 70%. The results indicate the feasibility of estimate of tangential and volumetric shrinkages by density, however, need more researches with other Wood species.

4. Conclusions

The Cedro Doce Wood specie presented excellent quality in relation to anisotropy coefficient and others Wood species studies were classifieds at normal quality.

The results of determination coefficients adjusted R²(Adj.) showed the possibility of estimative of tangential and volumetric shrinkages by density.

Even considered significant to the regressions for the tangential and volumetric shrinkage by analysis of variance, but with adjusted coefficients of determination lower than 70%, news researches should realized with other Wood species, enabling find general expressions for estimating such properties using the knowledge of the density.