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Engenharia Agrícola

Print version ISSN 0100-6916On-line version ISSN 1809-4430

Eng. Agríc. vol.40 no.2 Jaboticabal Mar./Apr. 2020  Epub Apr 22, 2020 

Technical Paper

Agricultural Building and Environment


André L. Christoforo1  *

Diego H. de Almeida2 

Luciano D. Varanda3 

Tulio H. Panzera4 

Francisco A. R. Lahr5 

1Universidade Federal de São Carlos (UFSCar)/ São Carlos - SP, Brasil.

2Fundação Universidade Federal de Rondônia (UNIR)/ Porto Velho - RO, Brasil.

3Instituto SENAI de Inovação Biomassa / Três Lagoas - MS, Brasil.

4Universidade Federal de São João del-Rei (UFSJ)/ São João del-Rei - MG, Brasil.

5Escola de Engenharia de São Carlos (EESC) da Universidade de São Paulo (USP)/ São Carlos - SP, Brasil.


Wood has been used for several purposes such as in civil and rural construction. Knowing wood mechanical behavior under short-term loading is essential for safer structural designs. However, wood toughness is a mechanical property little investigated for this purpose. Thus, this study aimed to evaluate, using exponential and polynomial regression models (linear, quadratic, and cubic), the possibility of estimating toughness as a function of apparent density, compression parallel to grain strength, and modulus of rupture in static bending. Thirty-six Brazilian tropical wood species from south of Roraima, Mato Grosso do Sul, and north and northeast of Mato Grosso were tested. Our results showed the significance and representativeness of all investigated fits, among which a cubic polynomial function is the most indicated for wood toughness estimates.

KEYWORDS Apparent density; tropical wood species; modulus of elasticity; compression parallel to grain strength; toughness


Wood has been widely used by man throughout history. It has been directly related to problem solving such as housing, crossing of natural and/or artificial barriers, production of multiple-purpose vehicles, storage and transport of agricultural goods, manufacturing of furniture, utensils and sporting artifacts, among others uses (Toong et al., 2014; Araújo et al., 2016; Cademartori et al., 2016; Calil Neto et al., 2017).

Knowledge of wood physical and mechanical properties allows its better use (Fiorelli & Dias, 2011; Carreira et al. 2012; Molina et al., 2012. Because of the difficulty of characterizing wood species, they are often used without basic understanding of their properties, what leads to material waste (Andrade Jr. et al., 2014; Chen & Guo, 2017).

Special attention has been paid to the performance of wood species used in impacting practices, mainly in applications such as the above mentioned, thus motivating research in the area. For instance, there are the studies of Beltrame et al. (2010), Beltrame et al. (2012), Stolf et al. (2014), and Stolf et al. (2015), which investigated the influence of factors such as wood moisture content and growth ring orientation on total absorbed energy or toughness (W), impact resistance, resilience coefficient, and dynamic dimension. However, these studies did not estimate toughness as a function of other properties of wood characterization (Almeida et al., 2014).

To increase knowledge about wood behavior under impact load, this study aimed to evaluate the possibility of predicting wood toughness as a function of apparent density (12% moisture) and also flexural and compressive strength parallel to grain using regression models.


Apparent density (ρ), compression parallel to grain strength (fc,0), modulus of rupture in static bending (fm), and toughness (W) (using Charpy pendulum) were obtained according to the ABNT NBR 7190 (1997) standards.

Tests were carried out in the Laboratory of Wood and Timber Structures (LaMEM), São Carlos Engineering School/ University of São Paulo (EESC/USP). Twelve specimens were used for each Brazilian tropical wood species (Table 1) and each studied property.

TABLE 1 Brazilian tropical wood species and provenances. 

Popular name Scientific name Region of provenance
Angelim Amoroso Vatairea fusca South of Roraima
Angelim Araroba Vataireopsis araroba South of Roraima
Angelim Ferro Hymenolobium sp South of Roraima
Angelim Pedra Hymenolobium petraeum South of Roraima
Angelim Pedra Verdadeiro Dinizia excelsa South of Roraima
Angico Preto Piptadenia macrocarpa South of Roraima
Branquilho Terminalia sp Mato Grosso do Sul
Cafearana Andira sp South of Roraima
Cambará Rosa Erisma sp North of Mato Grosso
Casca Grossa Ocotea odorifera South of Roraima
Castelo Gossypiospermum praecox Northeast of Mato Grosso
Catanudo Calophyllum sp Northeast of Mato Grosso
Cedro Amargo Cedrela odorata South of Roraima
Cedro Doce Cedrela sp South of Roraima
Cedrona Cedrelinga catenaeformis South of Roraima
Copaíba Copaifera sp South of Roraima
Cupiúba Goupia glabra South of Roraima
Cutiúba Qualea paraensis South of Roraima
Garapa Apuleia leiocarpa North of Mato Grosso
Guaiçara Luetzelbburgia sp North of Mato Grosso
Guarucaia Peltophorum vogelianum North of Mato Grosso
Ipê Tabebuia serratifolia South of Roraima
Itaúba Mezilaurus itauba North of Mato Grosso
Jatobá Hymenea sp South of Roraima
Louro Preto Ocotea sp South of Roraima
Maçaranduba Manilkara sp South of Roraima
Mandioqueira Qualea sp South of Roraima
Oitica Amarela Clarisia racemosa North of Mato Grosso
Oiuchu Rapanea sp Northeast of Mato Grosso
Paul-óleo Copaifera sp Northeast of Mato Grosso
Piolho Tapirira guianesis South of Pará
Quarubarana Erisma uncinatum South of Roraima
Rabo de Arraia Vochysia sp South of Roraima
Sucupira Diplotropis sp South of Roraima
Tatajuba Bagassa guianensis South of Roraima
Umirana Qualea retusa South of Roraima

The regression models for estimating wood toughness as a function of apparent density (ρ), compression parallel to grain strength (fc,0), and modulus of rupture in static bending (fm) were as follows: exponential, linear, polynomial, quadratic, and cubic. Fits were based on average values for each wood property.

Table 1 shows the 36 wood species used for estimation of toughness as a function of apparent density. Guaiçara and Tatajuba were not used in regressions involving compression parallel to grain strength. Angelim Pedra Verdadeiro, Guaiçara, and Piolho were not considered in regressions involving modulus of rupture in static bending due to high coefficients of variation (above 46%).

Model significance was assessed by analysis of variance (ANOVA) at 5% significance. Null hypothesis (H0) was accepted when the model was not significant, while an alternative hypothesis (H1) was accepted when the model was significant. Values of p below the level of significance implies rejecting H0.


Table 2 shows the averages of toughness, apparent density, compression parallel to grain strength, and modulus of rupture in static bending for all studied Brazilian tropical wood species. The CVmin and CVmax are minimum and maximum values of coefficient of variation per property, respectively. Figures 1, 2, and 3 show the regression models for wood toughness estimation as a function of apparent density (ρ), compression parallel to grain strength (fc,0), and modulus of rupture in static bending (fm), respectively.

TABLE 2 Averages of wood properties for each Brazilian tropical species. 

Wood Species W (N·m) ρ (g/cm3) fc,0 (105 N/m2) fm (105 N/m2)
Angelim Amoroso 96 0.77 599 892
Angelim Araroba 69 0.67 508 754
Angelim Ferro 174 1.17 795 1320
Angelim Pedra 88 0.69 592 922
Angelim Pedra Verdadeiro 198 1.13 775 -
Angico Preto 146 0.89 725 1203
Branquilho 92 0.81 485 829
Cafearana 74 0.68 575 937
Cambará Rosa 33 0.67 345 632
Casca Grossa 122 0.79 585 1067
Castelo 140 0.76 548 1030
Catanudo 131 0.80 506 831
Cedro Amargo 46 0.51 391 669
Cedro Doce 53 0.50 315 566
Cedrona 45 0.57 413 605
Copaíba 59 0.70 502 799
Cupiúba 67 0.85 537 786
Cutiúba 162 1.15 790 1269
Garapa 144 0.92 734 1189
Guaiçara 228 1.09 - -
Guarucaia 127 0.92 624 956
Ipê 150 1.06 762 1226
Itaúba 145 0.91 690 1166
Jatobá 202 1.08 935 1613
Louro Preto 67 0.68 569 927
Maçaranduba 197 1.14 829 1363
Mandioqueira 119 0.85 708 1131
Oitica Amarela 134 0.76 699 1075
Oiuchu 174 0.93 774 1225
Paul-óleo 61 0.70 524 800
Piolho 145 0.83 619 -
Quarubarana 49 0.54 378 674
Rabo de Arraia 74 0.72 575 793
Sucupira 172 1.10 937 1465
Tatajuba 97 0.94 - 1106
Umirana 52 0.71 533 656
CVmin (%) 12 4 9 7
CVmax (%) 28 17 21 23

FIGURE 1 Graphs of regression models for toughness estimation as a function of apparent density: (a) exponential, (b) linear, (c) quadratic, and (d) cubic. 

FIGURE 2 Graphs of regression models for toughness estimation as a function of compression parallel to grain strength: (a) exponential, (b) linear, (c) quadratic, and (d) cubic. 

FIGURE 3 Graphs of regression models for toughness estimation as a function of modulus of rupture in static bending: (a) exponential, (b) linear, (c) quadratic, and (d) cubic. 

Table 3 presents the regression models for estimation of toughness for a set of tropical wood species and the adjusted coefficient of determination (R2Adj.). A cubic regression model showed better determination coefficients (above 77.77%) to estimate toughness as a function of apparent density (ρ), compression parallel to grain strength (fc, 0), and modulus of rupture in static bending (fm). Toughness as a function of modulus of rupture in static bending had the highest R2Adj., above 85%.

TABLE 3 Regression models for wood toughness estimation. 

Regression Model Equation R2Adj. (%) Fsig (ANOVA) P-value (ANOVA)
Toughness as a function of apparent density
Exponential W=152.06ρ1.93 74.70 104.54 0.000
Linear W=91.23+247.3ρ 77.20 119.64 0.000
Quadratic W=90.62+245.8ρ+0.9ρ2 76.50 58.06 0.000
Cubic W=489.01-2018ρ+2835ρ2-1139ρ3 77.77 41.62 0.000
Toughness as a function of compression parallel to grain strength
Exponential W=0.072fc,01.67 77.90 117.32 0.000
Linear W=64.26+0.2870fc,0 79.91 125.52 0.000
Quadratic W=51.58+0.2437fc,0++0.000035fc,02 78.40 60.95 0.000
Cubic W=258.5-1.413fc,0++0.002818fc,020.000001fc,03 80.30 45.88 0.000
Toughness as a function of modulus of rupture in static bending
Exponential W=0.046fm1.70 85.50 190.39 0.000
Linear W=61.65+0.1723fm 86.80 212.93 0.000
Quadratic W=81.84+0.2142fm0.000020fm2 86.60 103.99 0.000
Cubic W=93.90.3283fm++0.000509fm20.000007fm3 86.80 70.94 0.000

ANOVA p-values of regression models were lower than the 5% significance level, that is, all fits were significant.

The adjusted coefficients of determination (R2Adj.) for all approaches were higher than 70%, i.e., all fits were significant (Montgomery, 2005). The highest p-values (ANOVA) derived from proxies using linear polynomials, followed by exponentials. Conversely, the highest R2Adj. values, together with lower coefficients of variation (22% and 28%), derived from three-degree polynomials, showing a better toughness estimate by using cubic polynomial functions.

Almeida et al. (2014) used apparent density to estimate wood toughness of six wood species (Teca, Paricá, Pinus, Eucalipto, Jatobá and Angico) and obtained good regression models (R2 > 70%). These authors concluded that toughness can be explained by wood apparent density, as shown in our findings.

Adamopoulos & Passialis (2010) carried out a linear regression model to estimate toughness as a function of modulus of elasticity of Picea abies L. Karsten at different fiber orientations (radial and tangential). They observed coefficients of regression ranging from 54.6% to 92.3%, showing a correlation between such properties.


From all of the foregoing we may conclude:

    -. Regression models for estimation of wood toughness showed to be significant in all cases, that is, wood toughness can be estimated as a function of apparent density, compression parallel to grain, and modulus of rupture in static bending, as all these properties had R2Adj. above 70%;

    -. Regression model statistical results showed that a cubic polynomial model provided the best fit for the three investigated approaches; therefore, toughness can be estimated by apparent density, compression parallel to grain, or modulus of rupture in static bending. These results help estimate this property that is little explored in research on wood characterization but of great importance in structural projects, wherein woods are subjected to impacting actions.


The authors would like to thank the Brazilian Research Agency CNPq and the Wood and Woody Structures Laboratory (LaMEM – EESC/USP) for financial and technical support.


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Received: October 11, 2017; Accepted: December 10, 2019

*Corresponding author. Universidade Federal de São Carlos (UFSCar)/ São Carlos - SP, Brasil. E-mail:

Area Editor: Edilson Costa

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