Influence of loading face on the modulus of elasticity in static bending of tropical wood

Influência da face de carregamento no módulo de elasticidade na flexão estática em madeiras tropicais

Abstract

The modulus of elasticity is a fundamental parameter in the structural design of timber elements, as it directly controls displacement response and serviceability performance. The methodology established by NBR 7190-3:2022 and by other international standards for determining this property is based on static bending tests performed on small clear prismatic specimens. However, these standards do not explicitly define which longitudinal face of the specimen should be subjected to loading, which may introduce an additional source of variability in the measured results. Considering the anisotropic behavior and inherent heterogeneity of wood, this study evaluated the existence of significant variations in the modulus of elasticity obtained from the four longitudinal faces of specimens from twelve tropical hardwood species. Statistical analyses based on paired t-tests at a 95% confidence level confirmed significant differences, demonstrating that the loading face influences the estimated stiffness. The least squares method was applied to quantify the variability between the maximum and minimum modulus values obtained for each specimen. An average variation of approximately 4% was observed among the different loading face configurations. Based on these findings, a correction coefficient (γ = 0.96) is proposed to adjust modulus of elasticity values derived from bending tests, enhancing measurement representativeness and reliability for structural applications.

Keywords
Stiffness; Mechanical properties; Static bending test; Hardwood; Small clear specimens

Resumo

O módulo de elasticidade é um parâmetro fundamental para o dimensionamento estrutural de elementos de madeira, pois governa diretamente os deslocamentos e desempenhos gerais em serviço. A metodologia estabelecida pela NBR 7190-3:2022 e por normas internacionais baseia-se em ensaios de flexão estática realizados em corpos de prova prismáticos isentos de defeitos. Contudo, tais normas não especificam qual face longitudinal deve ser submetida ao carregamento, o que pode introduzir variabilidade adicional nos resultados. Considerando o comportamento anisotrópico e a heterogeneidade intrínseca da madeira, este estudo avaliou a existência de variações significativas no módulo de elasticidade obtido a partir das quatro faces longitudinais de corpos de prova de doze espécies tropicais. Testes-t pareados, com nível de confiança de 95%, indicaram diferenças estatisticamente significativas, evidenciando a influência da face de carregamento na rigidez estimada. O método dos mínimos quadrados foi utilizado para quantificar a diferença entre os valores máximo e mínimo obtidos por corpo de prova, sendo observada variação média de aproximadamente 4%. Propõe-se, assim, um coeficiente de correção (γ = 0,96) para ajuste dos valores obtidos, visando maior representatividade e confiabilidade para aplicações estruturais.

Palavras-chave
Rigidez; Propriedades mecânicas; Ensaio de flexão estática; Madeira tropical; Corpo de prova isento de defeito

1 Introduction

Due to its favorable strength-to-density ratio and workability, wood is a widely used material in various industrial sectors, including civil construction, furniture, packaging, paper, and decorative items. Its application can occur in different forms, such as roundwood in its natural state, sawn elements, or even as mass timber, enabling the production of components with dimensions and properties suitable for various structural designs (Forest Products Laboratory, 2021; Shigue, 2018).

Wood is a complex biological material, characterized by a tissue organization that integrates macroscopic, microscopic, and chemical components (Botosso, 2011; Wiedenhoeft; Eberhardt, 2021). Its structure presents three main orthotropic axes: longitudinal (parallel to the tree stem and fiber direction), radial (perpendicular to the growth rings), and tangential. This anatomical configuration confers anisotropic mechanical behavior to the material, with properties varying significantly according to the loading direction (Arriaga et al., 2023; Dias et al., 2019; Malaga-Toboła et al., 2019; Mascia, 1991; Pfeil; Pfeil, 2021).

Among the mechanical properties of wood elements, the modulus of elasticity governs deformability under bending actions and, consequently, controls the magnitude of structural displacements. This parameter plays a central role in overall stability and serviceability performance, particularly in flexural members. In structures composed of native forest wood species, the value adopted in structural analysis is commonly derived from mean results obtained in static bending tests performed on solid specimens. These experimentally determined values are incorporated into design calculations, influencing both ultimate limit state verifications and serviceability assessments, related to deflection control and instantaneous displacement prediction.

The significance of this parameter becomes even more evident in engineered timber systems, such as glued laminated timber elements (glulam) and other mass timber configurations. In these applications, individual lamellae are evaluated beforehand through standardized bending procedures for nondestructive mechanical grading, enabling their allocation into subgroups with compatible stiffness characteristics. The effective modulus attributed to the composite member is commonly established based on these preliminary measurements, creating a direct link between the reliability of experimental characterization and the structural performance of the assembled element.

The assessment of physical and mechanical properties of wood from native forests is standardized in Brazil by NBR 7190-3 (ABNT, 2022), which establishes the use of small clear specimens. Among the prescribed procedures, the three-point static bending test is used to determine the modulus of elasticity (E_M). The method requires nominal square cross-section specimens with longitudinal grain orientation, positioned over two supports with a concentrated force applied at midspan.

However, the standard does not specify which of the four possible specimen faces should be subjected to loading, nor does it establish criteria to guide the selection of the loading face. Furthermore, due to the way specimens are extracted from different regions of the log, the growth rings that could guide test standardization by indicating the wood's anatomical axes are not always visible or may present angular deviations.

Similar concerns may be raised with respect to other standards that also prescribe the determination of bending properties using three-point static bending tests on small clear specimens. The internationally adopted ISO 13061-4 specifies that specimens must be prepared with one face parallel to the radial direction of the wood, and the load should be applied to either the radial or tangential surface, allowing for the selection among four possible testing faces (ISO, 2014). Comparable guidelines are also found in GB/T 1936.2 (China) and JIS Z 2101 (Japan) (JIS, 2009; SAC, 2009).

In D143 (United States) (ASTM, 2025), more specific criteria are established, specifying that the load must be applied to a surface parallel to the growth rings (American Society for Testing and Materials, 2025). The same methodology is found in BS 373 (United Kingdom), as well as in standards from countries with tropical forest resources, including NTC 663 (Colombia) and IS 1708-5 (India) (BS, 1957; IS, 1986; ICNTC, 1973). Despite the more specific guidance regarding grain orientation, the selection between two testing faces is still permitted, introducing a potential source of variability in the results.

Beyond the challenges in achieving repeatable test conditions, it is important to consider wood's natural structural variations that occur during tree growth. These variations may lead to differences between specimen faces, particularly due to fiber orientation patterns, which can vary along the trunk as a result of species-specific genetic traits and environmental conditions (Campos, 1970; Costa; Souza, 2022; Silva; Venturin; Carvalho, 2024). Such variations may cause deviations from the ideal longitudinal axis, affecting stress distribution during testing and influencing the results depending on the selected loading face (Betts; Miller; Gupta, 2010; Reiterer; Stanzl-Tschegg, 2001; Sun et al., 2022).

At the microscopic scale, wood exhibits structural variability in its tissue components across the trunk cross-section. Juvenile wood, typically located in central regions, features larger cells with thinner walls, resulting in lower density and stiffness. In contrast, mature wood, predominant in outer layers, displays smaller cells with thicker walls, providing enhanced mechanical response (Coradin, 2002; Mayard et al., 2022; Vidaurre et al., 2011). Additionally, variations in wood chemical composition, especially cellulose crystallinity (the primary cell wall component), directly influence key properties such as stiffness and strength (Duarte et al., 2020; Thomas et al., 2021).

Previous studies have demonstrated that wood's mechanical properties vary according to loading orientation, directly reflecting the material's anisotropy and complex anatomical structure(Borůvka; Novák; Šedivka, 2020; Carrasco et al., 2018; Carrasco; Mantilla, 2016; Felipe Hideyoshi et al., 2013; Kurata, 2020; Logsdon; Zenésio Finger; Jesus, 2010; Malaga-Toboła et al., 2019; Mayard et al., 2022; Reiterer; Stanzl-Tschegg, 2001; Sun et al., 2022; Yoshihara; Tsunematsu, 2007). However, the variability in the modulus of elasticity obtained from bending tests remains underexplored in the technical literature, as highlighted by Icimoto et al. (2015) in their contribution to the subject. This gap demands further investigation to enhance the reliability of empirical data, particularly in the analysis of native tropical wood species.

Given the intrinsic heterogeneity of wood and the multiple sources of variability associated with its anatomical structure and orthotropic behavior, this study investigates whether statistically significant differences exist in the modulus of elasticity obtained from distinct loading faces in static bending tests. If confirmed, such differences would indicate that current experimental procedures may introduce systematic variability into stiffness characterization. In this context, a correction factor is proposed to account for the identified influence, thereby reducing uncertainty in stiffness determination. By improving the representativeness of the modulus of elasticity, the proposed approach contributes to more reliable structural analyses, enhances the consistency of serviceability predictions, and supports the structural and economic optimization of timber systems.

2 Materials and methods

Specimens were selected from batches of twelve tropical wood species, obtained from the native Amazon rainforest, as listed in Table 1. The mean density values, as well as their classification into strength classes according to NBR 7190 (ABNT, 2022), had been previously determined in accordance with the normative procedures established in Part 3 of the same standard.

Table 1
Studied species

Species	Scientific name	Density (g/cm³)	Strength class
Cedro	Cedrela sp.	0.54	D20
Caixeta	Simarouba amara	0.33	D30
Quarubarana	Erisma sp.	0.54	D30
Breu Sucuruba	Trattinickia burseraefolia	0.54	D40
Cupiúba	Goupia glabra	0.85	D40
Louro	Ocotea sp.	0.71	D40
Mirarema	Hymenolobium sp	0.72	D40
Catanudo	Micropholis sp.	0.80	D50
Quina Rosa	Cinchona sp.	0.96	D50
Tachi Branco	Sclerolobium paraensis	0.72	D50
Fava Amargosa	Vatairea paraensis	0.90	D60
Itaúba	Mezilaurus itauba	0.91	D60

• Note: Strength class = Classification according to NBR 7190-1 (ABNT, 2022), indicating dicotyledonous species (D) followed by the characteristic compressive strength parallel to grain adopted for design calculations (value in MPa).

The experimental tests were conducted at the Wood and Timber Structures Laboratory (LaMEM), affiliated with the Department of Structural Engineering (SET) of the São Carlos School of Engineering (EESC-USP).

2.1 Mechanical tests

The static bending tests were carried out in accordance with the procedures prescribed by NBR 7190-3 (ABNT, 2022) for small clear specimens from native forests. For each species, twelve specimens with nominal dimensions of 5 × 5 × 115 cm were prepared, each extracted from a different timber beam (Figure 1). Since the standard does not define the orientation of the cross-section with respect to the annual rings, the transverse sections of the specimens did not present a predefined relationship with the anatomical directions of the wood.

Figure 1
Static bending test specimen

The specimens were tested using an AMSLER universal testing machine, with a support span equal to 21h (where h corresponds to the nominal height of 5 cm), resulting in a clear span (L) of 105 cm (Figure 2). This span-to-depth ratio was adopted to minimize shear influence on displacement measurements.

Figure 2
Static bending test setup scheme

Mid-span displacements were measured using a displacement transducer, while the applied forces were monitored by a calibrated load cell (Figure 3). Data acquisition was performed using a dedicated digital system.

Figure 3
Static bending test procedure

Due to the need to test the same specimen on all four faces, the modulus of elasticity was determined using an adapted procedure based on mid-span displacement limits. The lower and upper limits of the loading-cycle procedure were defined directly from the displacements corresponding to L/300 and L/200, respectively, maintaining the specimens within the elastic range. For the adopted span (L) of 105 cm, these values corresponded to 3.5 mm and 5.25 mm. This approach ensured that the tests remained within the elastic range while preserving the integrity of the specimens during successive measurements on different faces.

The modulus of elasticity was calculated using Equation 1:

Eq. 1 $E_M=\frac{(F_{M,(L/200)}-F_{M,(L/300)})*L^3}{(V_{(L/200)}-V_{(L/300)})*4*b*h^3}$

Where:

E_M is the modulus of elasticity in static bending (MPa);

F_M,(L/200) and F_M,(L/300) is the forces recorded at the adopted mid-span displacement limits of L/200 and L/300 (N);

V_(L/200) and V_(L/300) is the midspan displacements for L/200 and L/300 (mm);

L is the Span length (mm);

b is the cross-sectional width (mm); and

h is the cross-sectional height (mm).

This procedure was repeated for each of the four faces of the specimen, with each face positioned upward during testing, enabling the determination of the modulus of elasticity (E_M).

2.2 Statistical analysis

For each specimen, the four modulus of elasticity values obtained from the different loading faces were arranged in ascending order. The lowest value within each set was designated as E_min, and the highest as E_max, while the remaining two intermediate values corresponded to the other loading faces (E_int1 and E_int2). For the purposes of statistical comparison, the E_min and E_max groups were selected, as they represent the extreme bounds of stiffness variation that may arise solely from the choice of loading face. This approach allows the assessment of whether the testing configuration can systematically influence the modulus determination.

A paired t-test was initially applied to evaluate whether statistically significant differences existed between the mean values of the E_min and E_max groups. The analysis employed a 95% confidence level, with differences considered statistically significant when the p-value was less than 0.05.

If a significant difference between faces was confirmed, the E_min/E_max ratio was analyzed to quantify the relationship between extreme modulus of elasticity values. The least squares method (Equation 2) was used to determine a correction factor γ to quantify this variation (Christoforo et al., 2011; Icimoto et al., 2015).

Eq. 2 $f\left(\gamma \right)=\frac{1}{2}{\sum }_{}^{}{(\frac{E_{\min }}{E_{\max }}ratio-\gamma Unit)}^2$

Where:

ƒ(γ) is the least squares function;

E_min/E_maxratio is the ratio of minimum to maximum elastic modulus (E_M) values in the sample;

γ is the correction factor representing the proportional relationship between faces E_min and E_max; and

Unit is the expected ratio (E_min/E_max = 1).

The γ value was determined by minimizing the sum of squared errors. As the adopted function is a convex parabola, the minimum point corresponds to the mean of observed E_min/E_max ratios.

3 Results and discussion

Using the data acquisition system, the force–displacement curves corresponding to the final loading cycle were obtained for each tested face (Figure 4).

Figure 4
Force–displacement curves obtained for the four loading faces

The graphical analysis demonstrated that, within the linear segment of the final loading cycle, the same displacement level corresponded to different force values depending on the loaded face, thereby revealing variations in the slope of the force–displacement curves. Since the slope of this relationship is directly associated with the flexural stiffness of the specimen, these differences indicated corresponding variations in the modulus of elasticity obtained for the same specimen. In light of this behavior, statistical analyses were conducted to determine whether the observed variations represented merely numerical fluctuations or whether they constituted significant differences attributable to the loading face.

The bending test procedure established by NBR 7190 (ABNT, 2022) does not prescribe a specific anatomical orientation for specimen positioning, nor does it establish any hierarchical distinction among the lateral faces. Therefore, in order to enable a consistent statistical comparison, the four modulus of elasticity values obtained for each specimen, one from each loading face, were reorganized according to their numerical values. For each specimen, the values were arranged in ascending order and designated as E_min, E_int1, E_int2 and E_max, corresponding, respectively, to the lowest, the two intermediates, and the highest recorded results. This strategy allowed the statistical evaluation of intra-specimen variability associated with the loading face, thereby ensuring methodological coherence in the comparative analysis.

The modulus of elasticity values obtained from the twelve bending specimens tested for each species, organized from lowest (E_min) to highest (E_max), are presented in Table 2.

Table 2
Modulus of elasticity results organized by face

Species	Statistic	EM (MPa)
		Emin	Eint1	Eint2	Emax
Cedro	x̄	8,841	8,873	8,904	8,932
	Min.	6,752	6,792	6,804	6,838
	Max.	11,064	11,083	11,126	11,136
Caixeta	x̄	8,668	8,827	8,931	9,088
	Min.	6,495	6,682	6,748	6,826
	Max.	10,393	10,586	10,749	10,816
Quarubarana	x̄	8,644	8,838	8,981	9,107
	Min.	6,959	7,012	7,328	7,438
	Max.	11,790	11,793	11,959	12,054
Breu Sucuruba	x̄	11,696	11,793	11,942	12,103
	Min.	8,783	9,052	9,272	9,696
	Max.	13,436	13,450	13,532	13,605
Cupiúba	x̄	13,313	13,501	13,609	13,799
	Min.	11,290	11,310	11,332	11,376
	Max.	16,602	16,777	16,793	16,836
Louro	x̄	14,491	14,684	14,851	15,040
	Min.	10,662	10,791	10,811	11,035
	Max.	17,329	17,572	17,726	17,938
Mirarema	x̄	13,823	13,957	14,108	14,260
	Min.	10,552	10,588	10,614	10,844
	Max.	17,777	17,848	18,155	18,235
Catanudo	x̄	14,444	14,680	14,854	15,074
	Min.	10,998	11,330	11,444	11,562
	Max.	16,931	17,320	17,436	17,559
Quina Rosa	x̄	19,897	20,041	20,218	20,400
	Min.	16,689	16,895	17,102	17,175
	Max.	23,896	24,104	24,382	24,424
Tachi Branco	x̄	14,887	15,092	15,535	15,712
	Min.	12,841	13,353	13,503	13,590
	Max.	16,105	16,248	17,319	17,458
Fava Amargosa	x̄	19,265	19,450	19,822	20,024
	Min.	18,118	18,313	18,494	18,608
	Max.	20,836	21,027	21,838	21,841
Itaúba	x̄	17,336	17,477	17,645	17,747
	Min.	15,690	15,787	15,920	16,042
	Max.	19,873	20,165	20,274	20,304

Comparative results between the mean values of the E_min and E_max groups revealed distinct variations among the analyzed species. Tachi Branco (Sclerolobium paraensis) showed the highest percentage difference, with the E_max group values being 5.5% higher than those of the E_min group, followed by Quarubarana (Erisma sp.), with a 5.4% variation. In contrast, Cedro (Cedrela sp.) and Itaúba (Mezilaurus itauba) exhibited the smallest differences between groups, with values of 1% and 2.4%, respectively.

To complement the comparison of mean values, Figure 5 presents the boxplot distribution of the intra-species amplitudes, defined as the difference between the highest (E_max) and lowest (E_min) modulus of elasticity values obtained for each specimen. This representation allows a broader assessment of the dispersion and consistency of the experimental results across species.

Figure 5
Distribution of the difference between E_max and E_min per specimen

The graphical analysis revealed that all species exhibited non-negligible amplitude values, indicating measurable intra-specimen variability in stiffness determination. However, the magnitude and dispersion of these amplitudes were not uniform among species. Consistent with the tendencies observed in the mean comparison, species such as Fava Amargosa and Tachi Branco presented higher median amplitudes and wider interquartile ranges, reflecting greater internal variability between the extreme modulus values obtained. Conversely, Cedro and Itaúba exhibited more concentrated distributions, characterized by reduced interquartile ranges and lower median amplitudes, suggesting comparatively greater consistency in the measured stiffness values.

Although differences in dispersion magnitude were observed among species, no clear systematic pattern or structured behavior could be visually identified. The amplitudes varied in scale and spread, yet without indicating a progressive or grouped trend. These observations suggested that the dispersion reflects intrinsic material variability, supporting the need for subsequent inferential analysis to determine the statistical relevance of the differences between groups.

To statistically analyze the observed numerical differences, the normality assumption required for the paired t-test was first assessed. For this purpose, the paired differences between E_max and E_min were calculated for each specimen, and their distribution was evaluated using the Anderson-Darling normality test at a 5% significance level. The p-values ranged from 0.058 for Fava Amargosa (Vatairea paraensis) to 0.980 for Caixeta (Simarouba amara), indicating that the normality assumption was satisfied for all species. Therefore, paired t-tests were applied to compare the E_min and E_max groups within each species, with the results presented in Table 3.

Table 3
Results of the paired t-test between groups E_min and E_max

Species	Paired t-test
	95% CI	T-value	p-value
Cedro	(-105.4; -77.1)	-14.23	0.000
Caixeta	(-491.0; -348.4)	-12.96	0.000
Quarubarana	(-516.0; -409.4)	-19.11	0.000
Breu Sucuruba	(-558.5; -255.4)	-5.91	0.000
Cupiúba	(-717.0; -256.0)	-4.65	0.001
Louro	(-634.2; -463.1)	-14.12	0.000
Mirarema	(-551.9; -322.0)	-8.37	0.000
Catanudo	(-699.5; -560.2)	-19.90	0.000
Quina rosa	(-620.4; -386.1)	-9.45	0.000
Tachi Branco	(-1010.9; -638.5)	-9.75	0.000
Fava Amargosa	(-1010.0; -508.0)	-6.65	0.000
Itaúba	(-495.7; -325.8)	-10.64	0.000

For the twelve batches studied, the tests resulted in p-values lower than 0.05, leading to rejection of the null hypothesis and confirming a statistically significant difference between the mean values of E_min and E_max.

This behavior may be associated with the orthotropic and non-homogeneous nature of wood, whose mechanical response is influenced by factors acting at different structural scales, including growth-ring orientation, grain angle, density, tissue arrangement, fiber wall thickness, ray and vessel distribution, parenchyma proportion, and microfibril angle (Arriaga et al., 2023; Borůvka; Novák; Šedivka, 2020; Mayard et al., 2022; Sun et al., 2022). Beyond the individual influence of these factors, their spatial arrangement within the material may lead to a non-uniform stiffness distribution across the cross-section, affecting the position of the neutral axis, which may shift relative to the geometric centroid (Betts; Miller; Gupta, 2010; Davis; Gupta; Sinha, 2012).

Consequently, depending on the face selected for loading, these structural patterns may be differently oriented with respect to the bending stress distribution, leading to differences in the force–displacement response and, therefore, in the modulus of elasticity obtained from each tested face. Nevertheless, this interpretation should be considered a possible micromechanical explanation, since its confirmation would require complementary anatomical characterization and assessment of the local stiffness distribution.

Thus, using Equation 2, the overall correction coefficient γ was determined as the mean of the E_min/E_max ratios calculated for all species treated as a single dataset. Since 12 specimens were evaluated for each of the 12 species, a total of 144 paired ratios were considered, resulting in a correction coefficient γ of 0.964.

To assess the adequacy of this coefficient, a one-sample t-test was applied, comparing the mean values of the E_min/E_max ratios for each species to the proposed γ (Figure 6).

Figure 6
Mean plot of E_min/E_max ratios for each species with 95% CI

For Breu Sucuruba (Trattinickia burseraefolia), Cupiúba (Goupia glabra), Louro (Ocotea sp.), Mirarema (Hymenolobium sp.), and Fava Amargosa (Vatairea paraensis), the γ coefficient of 0.964 adequately represents the mean E_min/E_max ratios. The obtained p-values exceeded the 5% significance level (ranging from 0.210 to 0.883), indicating no statistical difference from the proposed value. This adequacy is also evidenced by the proximity of the individual means to γ, particularly considering the agreement within the first two decimal places.

Cedro (Cedrela sp.), Quina Rosa (Cinchona sp.), and Itaúba (Mezilaurus itauba) showed smaller stiffness differences between faces, with correction factors ranging from 0.975 to 0.989. Although the confidence intervals of their means did not precisely include the proposed γ value, it is noteworthy that the adoption of a slightly lower coefficient contributes to safety in the application of the corrected results. Thus, the observed statistical difference does not compromise either the feasibility or reliability of the suggested coefficient.

For Caixeta (Simarouba amara), Quarubarana (Erisma sp.), Catanudo (Micropholis sp.), and Tachi Branco (Sclerolobium paraensis), the obtained p-values (ranging from 0.001 to 0.017) indicated statistically significant differences from the γ value, with confidence intervals deviating more substantially from the proposed coefficient. Nevertheless, the observed discrepancies remained relatively small, limited to the second decimal place. Considering the application of stiffness results in structural design, the adoption of a more conservative correction coefficient, on the order of 0.950, would be feasible. However, this choice requires careful consideration, balancing the principles of safety against the potentially excessive penalization of the other species that showed better agreement with the originally proposed value.

Applying a similar statistical methodology, Icimoto et al. (2015) also identified significant differences between tested faces in eight species, proposing a correction coefficient γ of 0.920, corresponding to an 8% difference between the E_min and E_max values obtained. However, it should be noted that, at the time of that study, the Brazilian standard used in the research, NBR 7190 (ABNT, 2022), did not yet distinguish between timber from native and planted forests, a distinction that was only incorporated in the 2022 revision due to the higher incidence of defects and greater variability in plantation-grown wood. Therefore, it is reasonable to assume that the greater deviation observed in their study may be associated with the inclusion of Pinus and Eucalyptus species in the analyzed dataset.

Based on the statistical analyses, the γ factor, estimated through the least squares method from the pooled E_min/E_max ratios, proved to be a viable correction parameter. To ensure operational simplicity and procedural standardization, it is recommended that γ be rounded to 0.960, corresponding to an estimated 4% difference in modulus of elasticity between tested faces. Alternatively, the adoption of γ equal to 0.950 is suggested as a conservative approach, aligned with the minimum values observed in the analyzed species, providing an increased safety margin in the application of the correction factor.

4 Conclusions

This study investigated whether the face of the prismatic specimen subjected to loading influences the results of static bending tests used to determine the modulus of elasticity. The motivation arose from the fact that the methodology suggested by the Brazilian standard (ABNT, 2022) and other international standards (e.g., ISO 13061-4 (ISO, 2014) and D143 (ASTM, 2025)), even when specifying preferred growth-ring alignment, allows different loading-face options, thereby potentially introducing variability in the results. The main findings are summarized below:

1. statistical analysis of static bending test results from twelve tropical hardwood species revealed significant differences in modulus of elasticity values between the loading faces, as confirmed by t-tests at the 95% confidence level. These results demonstrate that the loading face has a measurable influence on the mechanical response, contributing to variability in the results;

2. specific analysis for each species showed considerable variation in response to loading face influence. Tachi Branco (Sclerolobium paraensis) and Quarubarana (Erisma sp.) exhibited the largest differences between modulus of elasticity values (5.5% and 5.4%, respectively), while Cedro (Cedrela sp.) and Itaúba (Mezilaurus itauba) showed the smallest variations (1.0% and 2.4%);

3. a least squares analysis across all species revealed an average 4% difference between the values obtained from the four tested faces. Based on this, a correction factor γ = 0.960 is proposed to adjust bending test results, improving their accuracy, comparability, and applicability in engineering design; and

4. considering the wide diversity of native tropical species and the intrinsic variability of the material, this study reinforces the importance of expanding experimental databases to progressively calibrate the correction factor γ and refine testing procedures and normative guidelines related to the determination of the modulus of elasticity.

Given the fundamental role of the modulus of elasticity in the control of serviceability limit states, its accurate determination is essential for structural applications in the built environment. A reliable stiffness value enables consistent prediction and control of expected deflections, thereby contributing to structural durability, user comfort, and safety throughout the service life of wood elements.

In this context, implementing measures to improve testing standardization and result reliability becomes essential. The proposed correction factor is readily implementable, as it does not require significant changes to existing testing methodologies and may represent a practical step toward reducing uncertainty in the assessment of wood mechanical properties. As a possible practical application, the modulus of elasticity obtained from a standardized single-face bending test could be adjusted by multiplying it by the coefficient γ, resulting in a conservative estimate of stiffness that accounts for the variability associated with the random selection of the loading face. However, it should be emphasized that the purpose of this study is primarily to quantify this source of variability and to contribute scientific evidence to future discussions on testing procedures. Therefore, decisions regarding the incorporation of such a correction factor, as well as the way it would be implemented in practical applications, should remain the responsibility of the standardization committees.

Overall, the outcomes of this research provide valuable insights for advancing the structural use of wood, as greater consistency in experimental results enables more precise design, facilitating optimized material utilization, cost-effective construction, and broader adoption in engineering applications. Additional studies involving a larger number of species are recommended to assess the applicability of the proposed correction coefficient across a more diverse range of wood species, contributing to its refinement and technical robustness. Complementary anatomical analyses are also suggested to better understand the origin of the observed variations among the tested faces.

Declaration of Generative AI and AI-Assisted Technologies in the Writing Process

The authors declare that AI tools were not used to generate or write the content of the manuscript.

Financial Support

The authors acknowledge the financial support provided by the São Paulo Research Foundation (FAPESP-Brazil) grant number 2024/01522-5, by Brazilian National Council for Scientific and Technological Development (CNPq-Brazil) grant number 130898/2024-4 and by Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES-Brazil) grant number 88887.968336/2024-00.

CARDOSO, M. C.; OLIVEIRA, R. J. G. F. de; OLIVEIRA, V. V. de; CHRISTOFORO, A. L.; LAHR, F. A. R. Influence of loading face on the modulus of elasticity in static bending of tropical wood. Ambiente Construído, Porto Alegre, v. 26, e153971, jan./dez. 2026. ISSN 1678-8621 Associação Nacional de Tecnologia do Ambiente Construído. http://dx.doi.org/10.1590/s1678-86212026000101023

Data Availability Statement

The data that support the findings of this study are available, upon reasonable request, from the corresponding author Maria Clara Cardoso ([e-mail]).

References

• AMERICAN SOCIETY FOR TESTING AND MATERIALS. D143-25: test methods for small clear specimens of timber. West Conshohocken, 2025.
• ARRIAGA, F. et al Mechanical properties of wood: a review. Forests, v. 14, n. 6, p. 1202, 2023.
• ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS. NBR 7190: projeto de estruturas de madeira: parte 3: métodos de ensaio para corpos de prova isentos de defeitos para madeiras de florestas nativas. Rio de Janeiro, 2022.
• BETTS, S. C.; MILLER, T. H.; GUPTA, R. Location of the neutral axis in wood beams: A preliminary study. Wood Material Science and Engineering, v. 5, n. 3/4, p. 173–180, 2010.
• BORŮVKA, V.; NOVÁK, D.; ŠEDIVKA, P. Comparison and analysis of radial and tangential bending of softwood and hardwood at static and dynamic loading. Forests, v. 11, n. 8, p. 896, 2020.
• BOTOSSO, P. C. Identificação macroscópica de madeiras: guia prático e noções básicas para o seu reconhecimento. Brasília: Embrapa Florestas, 2011.
• BRITISH STANDARD. BS 373: methods of testing small clear specimens of timber. London, 1957.
• CAMPOS, J. C. C. Principais fatores do meio que afetam o crescimento das árvores. Floresta, v. 2, n. 3, 1970.
• CARRASCO, E. V. M. et al. Determinação do módulo de elasticidade da madeira em função da inclinação das fibras utilizando tomógrafo acústico. Matéria, Rio de Janeiro, v. 22, suppl. 1, 2018.
• CARRASCO, E. V. M.; MANTILLA, J. N. R. Influência da inclinação das fibras da madeira na sua resistência ao cisalhamento. Ciência Florestal, v. 26, n. 2, p. 535–543, 2016.
• CHRISTOFORO, A. L. et al Numerical evaluation of the modulus of longitudinal elasticity in structural round timber elements of the Eucalyptus genus. Engenharia Agrícola, v. 31, n. 5, p. 1007–1014, 2011.
• CORADIN, V. T. R. A estrutura anatômica da madeira e princípios para sua identificação Brasília: Ibama, 2002.
• COSTA, W. M. da; SOUZA, M. N. Fatores bióticos na recuperação de áreas degradadas: ação da flora e da fauna. In: SOUZA, Maurício Novaes (org.). Tópicos em recuperação de áreas degradadas Canoas: Mérida Publishers, 2022. v. 4.
• DAVIS, P. M.; GUPTA, R.; SINHA, A. Revisiting the neutral axis in wood beams. Holzforschung, v. 66, n. 4, p. 497–503, 2012.
• DIAS, A. A. et al Estruturas de madeira: projetos, dimensionamento e exemplos de cálculos. Rio de Janeiro: Elsevier, 2019.
• DUARTE, B. B. et al Influence of physical and chemical components on the physical-mechanical properties of ten brazilian wood species. Materials Research, v. 23, n. 2, 2020.
• FELIPE HIDEYOSHI, I. et al Influence of the wood specimen position on calculus of the bending modulus of elasticity. International Journal of Materials Engineering, v. 3, n. 3, p. 41–46, 2013.
• FOREST PRODUCTS LABORATORY. Wood handbook: wood as an engineering material. General Technical Report FPL-GTR-282. Edited by Robert J. Ross and James R. Anderson. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory, 2021. 543 p.
• ICIMOTO, F. H. et al Influence of specimen orientation on determination of elesticity in static bending. Maderas. Ciencia y Tecnología, v. 17, n. 2, p. 229–238, 2015.
• INDIAN STANDARDS INSTITUTION. IS 1708-1 to 18: methods of testing of small clear specimens of timber. New Delhi, 1986.
• INSTITUTO COLOMBIANO DE NORMAS TÉCNICAS Y CERTIFICACIÓN. NTC 663: maderas: determinacion de la resistencia a la flexion. Bogotá: ICONTEC, 1973.
• INTERNATIONAL ORGANIZATION FOR STANDARDIZATION. ISO 13061-4: physical and mechanical properties of wood: test methods for small clear wood specimens: part 4: determination of modulus of elasticity in static bending. Geneva, 2014.
• JAPANESE STANDARDS ASSOCIATION. JIS Z 2101: methods of test for woods. Tokyo, 2009.
• KURATA, Y. A Comparison of the loading direction for bending strength with different wood measurement surfaces using near-infrared spectroscopy. Forests, v. 11, n. 6, p. 644, 2020.
• LOGSDON, N. B.; ZENÉSIO FINGER, Z. F.; JESUS, J. M. H. de. Influência do ângulo entre o esforço aplicado e a direção das fibras da madeira sobre o módulo de elasticidade. Floresta, v. 40, n. 4, p. 837–848, 2010.
• MALAGA-TOBOŁA, U. et al. Influence of wood anisotropy on its mechanical properties in relation to the scale effect. International Agrophysics, v. 33, n. 3, p. 337–345, 2019.
• MASCIA, N. T. Considerações a respeito da anisotropia da madeira São Carlos, 1991. Tese (Doutorado em Engenharia de Estruturas) - Escola de Engenharia de São Carlos, Universidade de São Paulo, São Carlos, 1991.
• MAYARD, R. et al. Influência dos anéis de crescimento nas propriedades mecánicas da madeira de Pinus. Madera y Bosques, v. 28, n. 3, 2022.
• PFEIL, W.; PFEIL, M. Estruturas de madeira: dimensionamento segundo a norma brasileira NBR 7190/97 e critérios das normas norte-americana NDS e européia EUROCODE 5. 6. ed. Rio de Janeiro: LTC, 2021.
• REITERER, A.; STANZL-TSCHEGG, S. E. Compressive behaviour of softwood under uniaxial loading at different orientations to the grain. Mechanics of Materials, v. 33, n. 12, p. 705–715, 2001.
• SHIGUE, E. K. Difusão da construção em madeira no Brasil: agentes, ações e produtos. São Carlos, 2018. Dissertação (Mestrado em Arquitetura, Urbanismo e Tecnologia) - Instituto de Arquitetura e Urbanismo, Universidade de São Paulo, São Carlos, 2018.
• SILVA, K. G.; VENTURIN, N.; CARVALHO, W. A. C. Fatores bióticos e abióticos que interferem na dinâmica de florestas tropicais brasileiras. Revista Eletrônica Científica Ensino Interdisciplinar, v. 10, n. 32, 2024.
• STANDARDIZATION ADMINISTRATION OF CHINA. GB/T 1936.2: method for determination of the modulus of elasticity in static bending of wood. Beijing, 2009.
• SUN, J. et al Compressive mechanical properties of larch wood in different grain orientations. Polymers, v. 14, n. 18, p. 3771, 2022.
• THOMAS, L. H. et al. Nanostructural deformation of high-stiffness spruce wood under tension. Scientific Reports, v. 11, n. 1, p. 453, 2021.
• VIDAURRE, G. et al. Lenho juvenil e adulto e as propriedades da madeira. Floresta e Ambiente, v. 18, n. 4, p. 469–480, 2011.
• WIEDENHOEFT, A.; EBERHARDT, T. L. Structure and function of wood. In: FOREST PRODUCTS LABORATORY. Wood handbook: wood as an engineering material Edited by Robert J. Ross and James R. Anderson. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory, 2021. chap. 3, p. 3-1–3-20.
• YOSHIHARA, H.; TSUNEMATSU, S. Feasibility of estimation methods for measuring young’s modulus of wood by three-point bending test. Materials and Structures, v. 39, n. 1, p. 29–36, 2007.

Corresponding author:

[e-mail].

Editor:

Marcelo Henrique Farias de Medeiros

Conflict of Interest

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Publication Dates

• Publication in this collection
  07 Sept 2026
• Date of issue
  Jan-Dec 2026

History

• Received
  03 Mar 2026
• Reviewed
  05 July 2026
• Accepted
  08 July 2026