Evaluation of the characteristic values of mechanical properties in five tropical wood species using different statistical methods

ABSTRACT

Brazilian Code NBR 7190:2022 for timber structures design adopts a simplified approach for determining characteristic values from small samples, based on the Centered Estimator Method assuming data normality. However, there is a gap in literature regarding its accuracy compared to the widely used approach in interna-tional codes, which defines the characteristic value as the 5th percentile of a fitted statistical distribution. This study evaluated strength and stiffness properties in tension and compression parallel to grain of five Brazilian tropical species, comparing the characteristic values obtained by NBR 7190-3:2022 with those derived from the 5th percentile of normal, lognormal, two-parameter Weibull, three-parameter Weibull, Gamma, and Logistic distributions. Results indicated that the normal distribution was adequate in most cases, while three-parameter Weibull distribution demonstrated greater flexibility in fitting, in capturing skewness in strength/stiffness distributions but also resulted in less conservative characteristic values. Additionally, it was observed that NBR 7190-3:2022 method led to characteristic values of mechanical properties, on average, 7% to 29% higher than those obtained from the 5th percentile of the analyzed statistical distributions. These results suggest the need to revise the Centered Estimator Method in NBR 7190-3:2022, to improve estimating characteristic value reliability.

Keywords:
Statistical distributions; Centered Estimator Method; Compression and tension strength parallel to grain; Modulus of elasticity

1. INTRODUCTION

Present in the daily life of civil construction, in urban and rural projects, as well as playing a crucial role in industries such as paper, furniture, packaging, and musical instruments, wood stands out as the biological material with great recognition and application [¹, ²]. Mechanical properties characterization of a wood batch is an experimental process to understand its properties and applications, evaluating feasibility of its use in structural design. This process allows for determining strength capacity, that is, the maximum strength that can be admitted for the material, so safety conditions of a structural project are met. Numerical values associated with strength capacity are usually called characteristic value, and there are different approaches for its determination.

In Brazil, the normative document that provides guidelines regarding testing methods as well as timber structures design is NBR 7190 [³], recently updated and subdivided into seven parts. NBR 7190 [³] distinguishes two ways of determining characteristic values depending on the testing methods used. If tests are carried out on small clear specimens, as for tropical species, NBR 7190-3 [⁴] guides that the characteristic value should be determined based on the Centered Estimator Method. This method assumes that strength follows a normal (Gaussian) distribution, usually used when sample size is equal to or greater than 12. On the other hand, tests on structural size pieces, such as those performed for reforestation species, NBR 7190-4 [⁵] indicates a non-parametric procedure for determining the characteristic value, considered as an estimate corresponding to the lower limit of the 5th percentile value. Such code indicates this value be determined from the tail fitting procedure to a Weibull distribution.

International codes that adopt normal or lognormal distribution for timber strength include ISO 12122-1 [⁶]; European code EN 14358 [⁷], and USA code ASTM D2915 − 17 [⁸], with the latter also allowing Weibull distribution use. Although less common, Weibull, Gamma, and Logistic distributions can be considered in specific design and structural analysis contexts. Despite not being widely prescribed in international codes, these distributions can be viable alternatives depending on the data statistical characteristics and the criteria adopted for strength evaluation. Typically, in these cases, characteristic value is related to the 5th percentile of the distribution determination.

Some studies shown in literature have evaluated whether wood mechanical properties conform to the distributions specified in codes. CHRISTOFORO et al. [⁹] studied normal, lognormal, Weibull, and exponential probability distribution models and compared them with the characteristic value calculated using the Centered Estimator Method, considering five tropical species. The best fitting model found by authors was the normal distribution. Studies by SILVA et al. [¹⁰] showed that, through Shapiro-Wilk and Kolmogorov-Smirnov normality tests, the data for compression strength parallel to grain of seven tropical wood species conformed to the normal distribution. However, the authors did not make comparisons with other probability distributions. IWUOHA et al. [¹¹] conducted tests on Gmelina arborea wood to determine elastic properties in compression and tension parallel to grain, in compression perpendicular to grain, and static bending, in addition to strength values for these and other properties, including shear parallel to grain and density. Authors observed that the statistical distributions used to determine wood properties had little influence on the final values, except for modulus of elasticity, for which distribution choice significantly impacted the results. Furthermore, they found that, for a coefficient of variation of 28%, lognormal distribution overestimated the 5th percentile value by 18% and 20% compared to normal and Weibull distributions, respectively.

In this context, characteristic values estimation for properties of a wood batch is closely related to economic and safety aspects of a project, as improperly determined values can lead to over or under design of a structure. For this reason, it is essential to study the characteristic value estimation using different probability distributions. Thus, the aim of this study was to compare the method indicated by Brazilian code NBR 7190-3 [⁴], used as a guideline for characterizing batches of native wood species, with other statistical methods, based on the determination of the 5th percentile of statistical distributions.

2. THEORETICAL BASIS

2.1. Characteristic value estimating according to NBR 7190-3

Brazilian Code NBR 7190-3 [⁴] presents a simple method for estimating characteristic values of the mechanical properties of a wood batch, if data follow a normal probability distribution. The code recommends the application of this method for determining characteristic value of native wood batches, based on tests with at least 12 specimens. Moreover, this method involves evaluating three different numbers for defining characteristic values. The first analysis is proposed by Equation (1), known as the Centered Estimator Method. In this, X_w,k represents the characteristic value of a given mechanical property of wood. The subscript w refers to the type of loading condition, while indicates that the value is the characteristic value. Furthermore, in Equation (1), n is the sample size, and the test results should be organized in ascending order (X₁ ≤ X₂ ≤ ··· ≤ X_n), discarding the largest value if n is odd. Coefficient 1.1 is suggested by NBR 7190-3 [⁴] to ensure a reasonable estimator eccentricity, preventing 50% of the estimates from corresponding to values lower than the true characteristic strength [¹²].

(1) $$X_{w,k}=\left(2\frac{X_1+X_2+\mathrm{...}+X_{\frac{n}{2}-1}}{\frac{n}{2}-1}-X_{\frac{n}{2}}\right).1\cdot 1$$

The second value to be considered in selecting X_w,k is that it must be at least 70% of the full sample mean. This consideration comes from the equation for determining value corresponding to a specific lower percentile in normal distribution, shown in Equation (2), where μ is the sample mean, z is the standard normal statistic associated with the desired percentile, and CV is the coefficient of variation, defined as the ratio between the standard deviation and the mean. NBR 7190-3 [⁴] recommends considering a coefficient of variation 18% for strengths to normal stresses. For a 5% percentile value (z = 1.645) and a coefficient of variation 18%, the corresponding value is close to 70% of the sample mean.

(2) $$X=\mu \cdot \left(1-Z\cdot CV\right)$$

The third value considered is that X_w,k should be at least equal to or greater than the smallest test value obtained (X₁). This restriction is justified once the smallest value in sample is already a pessimistic estimate of characteristic value [¹²]. Finally, NBR 7190-3 [⁴] establishes that the highest of the three values should be chosen: that determined by the Centered Estimator Method, 70% of the sample mean, or X₁. However, for safety purposes, the code also stipulates that the adopted characteristic value should not exceed the full sample mean.

2.2. Characteristic value estimation based on statistical distributions

Another approach for determining characteristic values involves considering the value of the 5th percentile of a probability distribution, for which the analyzed data set has a significant fit, evaluated through goodness-of-fit tests. In timber structures, this method is widely applied in studies shown in literature [⁹, ¹¹] as well as outlined in international codes such as ISO 12122-1 [⁶] and EN 14358:2016 [⁷]. In this approach, the data set is fitted to a probability density function of a given statistical distribution, determining the parameters for shape, location, and scale. Then, the fit quality must be evaluated. For this, goodness-of-fit tests, such as Anderson-Darling and the Kolmogorov-Smirnov tests, are generally used. If the fit is statistically significant, characteristic value is determined based on the lower 5th percentile of the adjusted distribution, as schematically shown in Figure 1.

Figure 1
Lower 5th percentile of a statistical distribution.

3. MATERIALS AND METHODS

3.1. Wood species

For this study, some properties of five tropical wood species, listed in Chart 1, were evaluated. The five species selected for this study are hardwoods, and the batches used were sourced from certified areas of the Amazon Forest.

Chart 1
Tropical wood species used in the research.

COMMON NAME	SCIENTIFIC NAME
Caixeta	Simarouba amara
Cambará Rosa	Erisma sp.
Maçaranduba	Manilkara spp.
Casca Grossa	Pouteria pachycarpa
Ipê	Tabebuia serratifolia

This work assessed elastic and strength properties of wood under tension and compression parallel to grain. These properties were selected based on their relevance to structural applications and the availability of a sufficient number of specimens. The specimen nominal dimensions used in each test are presented in Figure 2, manufactured according to NBR 7190-3 [⁴] recommendations. For each test and each species, 32 specimens were produced. Since sample size exceeds 30, it is assumed that Central Limit Theorem holds, contributing to analysis greater robustness [¹³,¹⁴,¹⁵]. In addition, the sample size of 32 complies with the requirements of NBR 7190-3 [⁴], which recommends a minimum of 12 specimens per test. It is also consistent with similar studies in the literature on Brazilian hardwood species, in which 12 to 35 specimens were tested per species [⁹, ¹⁰]. All specimens were taken from clear pieces and were pre-dried to reach a moisture content of close to 12%. This conditioning process was carried out in a controlled-environment oven. To verify moisture content, additional specimens were fully oven-dried at the end of the process, and their moisture content was determined by the method specified in NBR 7190-3 [⁴].

Figure 2
Nominal dimensions (mm) of specimens recommended by NBR 7190-3 [⁴]: (a) Compression parallel to the grain and (b) Tensile parallel to the grain.

3.2. Methods

In this study, strength and stiffness properties in tension and compression parallel to grain were evaluated based on tests conducted according to NBR 7190-3 [⁴] recommendations. Both tests were performed on an AMSLER universal testing machine with 250 kN capacity, with the force applied monotonical and progressively at a rate of 10 MPa/min. The following properties were determined: strength in compression parallel to grain (f_c0), strength in tension parallel to grain (f_t0), longitudinal modulus of elasticity in compression parallel to grain (E_c0), and longitudinal modulus of elasticity in tension parallel to the grain (E_t0). The tests were conducted at ambient conditions, with temperature close to 25 °C and relative humidity around 70%. The specimens were removed from the controlled environment only moments before testing, to minimize the influence of moisture variation on their mechanical properties.

For this study, characteristic values were assessed both from the 5th percentile of the adjusted statistical distribution and from simplified method of NBR 7190-3 [⁴] for small samples. Distributions considered were: normal, lognormal, two-parameter Weibull, three-parameter Weibull, Gamma, and Logistic, whose probability density functions are presented in Equations (3), (4), (5), (6), (7) and (8) respectively.

(3) $$f(x)=\frac{1}{\sqrt{2\cdot \pi \cdot {\sigma }^2}}\cdot e-{\frac{1}{2}}^{{\left(\frac{x-\mu }{\sigma }\right)}^2},x\in \left(-\infty ,\infty \right)$$

(4) $$f(x)=\frac{1}{x\cdot \sigma \sqrt{2\cdot \pi }}\cdot e-\frac{1}{2}\cdot \frac{{\left(In(x-\mu )\right)}^2}{{\sigma }^2},x\succ 0$$

(5) $$f(x)=\frac{\delta }{{\alpha }^{\delta }}\cdot x^{\delta -1}\cdot e^{-{\left(\frac{x}{\alpha }\right)}^{\delta }},x\succ 0$$

(6) $$f(x)=\frac{\delta }{{\alpha }^{\delta }}\cdot {\left(x-\gamma \right)}^{\delta -1}\cdot e^{-{\left(\frac{x-\gamma }{\alpha }\right)}^{\delta }},x\succ \gamma$$

(7) $$f(x)=\frac{x^{k-1}\cdot e^{-\left(x/\theta \right)}}{{\theta }^k\cdot \text{Γ}(k)},x\succ 0$$

(8) $$f(x)=\frac{1}{4\cdot s}\cdot sec{h}^2\cdot \left(\frac{x-\mu }{2\cdot s}\right)$$

In Equation (3), σ and μ represent population mean and standard deviation, respectively. In Equation (4), σ is the standard deviation and μ is the mean of the logarithm. In Equation (5), the parameters δ and α refer to the shape and scale parameters, respectively. In Equation (6), in addition to the shape (δ) and scale (α) parameters, γ corresponds to the location parameter. In Equation (7), k and θ are the shape and scale parameters, respectively, with Γ(k) representing the Gamma function. Finally, in Equation (8), μ and s correspond to the location and scale parameters, respectively.

Furthermore, Anderson-Darling (AD) test with a 5% significance level was applied to assess the fit of each distribution to the mechanical properties. The 5th percentile value was considered significant only when the corresponding distribution showed adherence in the AD test, meaning the test returned a p-value greater than the 5% significance level.

4. RESULTS AND DISCUSSION

4.1. Mechanical properties

Table 1 presents the mean values and coefficients of variation (CV) for each property and species. In the case of f_c0, the coefficients of variation for Cambará and Casca Grossa species slightly exceeded the reference value 18% established by NBR 7190-3 [⁴], resulting in 19.25% and 19.51%, respectively, but still remained very close to this threshold. Regarding to f_t0, the coefficients of variation for Cambará, Casca Grossa, and Ipê species were above 21%. For Caixeta, the weakest wood among the evaluated species, the coefficient of variation found was 8.75% for f_t0. The greater variability in the tensile test is mainly due to the brittle nature of this property, causing the specimen to often fail at the grips before reaching its actual force capacity [¹⁶]. Nonetheless, no value was excluded from the analysis, since such removals could lead to an undue increase in the characteristic value. Even in cases of premature grip failure, it is not possible to determine whether the specimen would indeed support a higher load. The coefficients of variation for E_c0 and E_t0 were consistent with values reported in literature for tropical species [¹⁷,¹⁸,¹⁹].

Table 1
Mechanical properties.

SPECIE	INDEXES	fc0 (MPa)	ft0 (MPa)	Ec0 (MPa)	Et0 (MPa)
Caixeta	Mean	40.56	53.16	8717	10110
	CV (%)	7.41	8.75	24.86	9.30
Cambará	Mean	42.13	62.41	10502	10729
	CV (%)	19.25	31.96	27.01	28.70
Maçaranduba	Mean	84.72	139.94	22067	21761
	CV (%)	10.11	15.68	11.49	11.95
Casca Grossa	Mean	58.72	123.47	16692	17311
	CV (%)	19.51	21.29	22.63	17.90
Ipê	Mean	74.72	96.75	17321	17090
	CV (%)	15.58	29.30	12.76	14.83

4.2. Characteristic values

Table 2 presents the characteristic values determined based on the 5th percentile of different statistical distributions, as well as those obtained using the method established by NBR 7190-3 [⁴]. Additionally, characteristic values for which the Anderson-Darling goodness-of-fit test indicated no significant adherence to the respective distribution are highlighted. Furthermore, Figures 3, 4, 5, 6 and 7 present the histograms and the corresponding fitted probability distributions for Caixeta, Cambará, Maçaranduba, Casca Grossa, and Ipê, respectively. From Table 2 and the histograms, it is observed that data fit almost all distributions simultaneously, with some exceptions. Among the distributions studied, three-parameter Weibull showed significant adherence in all cases. In other words, this provides greater flexibility in capturing datasets asymmetries of wood mechanical properties, aligning with findings in literature [²⁰]. This flexibility is especially important in cases where positive skewness is present, which may result from species-specific anatomical characteristics or consistent defects in the tested specimens.

Table 2
Characteristic values determined based on statistical distributions and the centered estimator method.

PROPERTIES	SPECIES	NORMAL	LOGNORMAL	2P- WEIBULL	3P- WEIBULL	GAMA	LOGISTIC
fc0 (MPa)	Caixeta	35.62	35.89	34.23	36.03	35.82	35.43	38.50
	Cambará	28.78	29.55	27.98	28.84	29.53	28.56	31.09
	Maçaranduba	70.64	71.06	68.22	70.15	71.15	70.68	75.39
	Casca Grossa	39.88	42.37	35.9*	44.35	41.96	39.25	47.01
	Ipê	55.58	56.29*	53.79	55.04	56.37	56.23	58.45
ft0 (MPa)	Caixeta	45.51	45.77	43.99	45.54	45.8	45.32	49.94
	Cambará	29.60	34.03	29.32	33.27	33.49	28.37	43.68
	Maçaranduba	103.85	106.61	98.63	108.49	106.32	101.46	115.65
	Casca Grossa	80.22	85.48	73.46	87.92	84.68	78.32	89.91
	Ipê	50.13	58.09	47.33	59.31	56.81	47.91	67.73
Ec0 (MPa)	Caixeta	5153*	5816*	4643*	6387	5692*	4915*	6848
	Cambará	5837*	6695	5348*	7266	6542	5575*	7352
	Maçaranduba	17895	18176	16852	18471	18152	17617	19792
	Casca Grossa	10478	10952	10148	10789	10915	10385	11684
	Ipê	13684	13787	13242	13499	13812	13803	15051
Et0 (MPa)	Caixeta	8563	8637	8199	8684	8637	8482	9408
	Cambará	5664	6399	5257*	6002	6310	5629	7596
	Maçaranduba	17482	17591	16831	17217	17625	17618	19308
	Casca Grossa	12213	12629	11650	12834	12583	11859	13017
	Ipê	12922	13271	11994	13269	13231	12723	14582

• * non-significant percentile value (p-value < 0.05)

Figure 3
Histograms and fitted probability distributions for mechanical properties of Caixeta wood.

Figure 4
Histograms and fitted probability distributions for mechanical properties of Cambara wood.

Figure 5
Histograms and fitted probability distributions for mechanical properties of Maçaranduba wood.

Figure 6
Histograms and fitted probability distributions for mechanical properties of Casca Grossa wood.

Figure 7
Histograms and fitted probability distributions for mechanical properties of Ipê wood.

The normal and lognormal distributions, as considered by NBR 7190-3 [⁴], ISO 12122-1 [⁶]; EN 14358 [⁷] and ASTM D2915 − 17 [⁸] to represent the mechanical properties of wood, proved effective in almost all cases, as confirmed by the Anderson-Darling goodness-of-fit test results. For strength properties, only Ipê did not conform to the lognormal distribution for tension parallel to the grain. Additionally, only Caixeta and Cambará failed to conform to the normal or lognormal distribution (in the case of Caixeta, both) for the modulus of elasticity in compression parallel to the grain. Therefore, the results confirm that the assumptions adopted by these standards are largely consistent with the behavior of the data analyzed in this study.

Table 3 presents the ratio between the values determined using NBR 7190-3 [⁴] method and the characteristic values obtained from the 5th percentile of statistical distributions. The results indicate that criterion adopted by NBR 7190-3 [⁴] leads to a less conservative approach when evaluating characteristic value compared to direct determination using the fifth percentile of all assessed probability distributions. Among the statistical distributions analyzed, the three-parameter Weibull and Lognormal distributions resulted in the highest characteristic values. On the other hand, two-parameter Weibull distribution yielded the most conservative values, meaning the lowest characteristic values, since this version of the distribution does not include a location parameter, thereby fixing its lower bound at zero.

Table 3
Comparison of characteristic values of NBR 7190-3 method with values of the 5th percentiles of the adjusted statistical distributions.

PROPERTIES	SPECIES	NBR	NBR	NBR	NBR	NBR	NBR
		NORMAL	LOGNORMAL	2P- WEIBULL	3P- WEIBULL	GAMA	LOGISTIC
fc0 (MPa)	Caixeta	1.08	1.07	1.12	1.07	1.07	1.09
	Cambará	1.08	1.05	1.11	1.08	1.05	1.09
	Copaíba	1.07	1.06	1.11	1.07	1.06	1.07
	Casca Grossa	1.18	1.11	1.31	1.06	1.12	1.20
	Ipê	1.05	1.04	1.09	1.06	1.04	1.04
	Mean	1.09	1.07	1.15	1.07	1.07	1.10
ft0 (MPa)	Caixeta	1.10	1.09	1.14	1.10	1.09	1.10
	Cambará	1.48	1.28	1.49	1.31	1.30	1.54
	Copaíba	1.11	1.08	1.17	1.07	1.09	1.14
	Casca Grossa	1.12	1.05	1.22	1.02	1.06	1.15
	Ipê	1.35	1.17	1.43	1.14	1.19	1.41
	Mean	1.23	1.14	1.29	1.13	1.15	1.27
Ec0 (MPa)	Caixeta	1.33	1.18	1.47	1.07	1.20	1.39
	Cambará	1.26	1.10	1.37	1.01	1.12	1.32
	Copaíba	1.11	1.09	1.17	1.07	1.09	1.12
	Casca Grossa	1.12	1.07	1.15	1.08	1.07	1.13
	Ipê	1.10	1.09	1.14	1.11	1.09	1.09
	Mean	1.18	1.10	1.26	1.07	1.12	1.21
Et0 (MPa)	Caixeta	1.10	1.09	1.15	1.08	1.09	1.11
	Cambará	1.34	1.19	1.44	1.27	1.20	1.35
	Copaíba	1.10	1.10	1.15	1.12	1.10	1.10
	Casca Grossa	1.07	1.03	1.12	1.01	1.03	1.10
	Ipê	1.13	1.10	1.22	1.10	1.10	1.15
	Mean	1.15	1.10	1.21	1.12	1.11	1.16

From Table 3, it is observed that, considering the average of the five species evaluated, NBR 7190-3 [⁴] method overestimates characteristic values by 7% to 29%, depending on statistical distribution and mechanical property analyzed. For example, in the case of f_c0, characteristic values obtained using normative method were, on average, 9% and 7% higher than those determined by the 5th percentile of normal distribution and three-parameter Weibull distribution, respectively. For f_t0, overestimation was even more pronounced, reaching an average of 23% compared to normal distribution. Regarding the modulus of elasticity, the difference between the normative values and those determined by the 5th percentile ranged from 7% to 26% for E_c0 and from 10% to 21% for E_t0, based on the average across the five evaluated species. Such overestimation of characteristic values can pose safety risks in structural design, as it implies using design reference values that exceed the actual load-bearing capacity of a significant portion of the material.

4.3. Eccentricity coefficient analysis

Since the Centered Estimator Method led to characteristic values overestimating compared to those determined from the 5th percentile of statistical distributions, it is inferred that the 1.1 coefficient, which accounts for eccentricity, is not adequate in reliability terms. Figure 8 presents graphs of characteristic values determined using Centered Estimator Method, as described in Equation (1), but varying eccentricity coefficient between 0.50 and 1.50 in increments of 0.10, while imposing the other constraints of NBR 7190-3 [⁴]. Additionally, the dotted line indicates the characteristic values determined from the 5th percentile of the normal distribution, which serves as the basis for comparison, was adjusted for each property and species. It is worth noting that although NBR 7190-3 [⁴] assumes a normal distribution, this method also assumes a coefficient of variation of 18%, which does not accurately represent the reality of each property, as previously shown in Table 1.

Figure 8
Characteristic values versus eccentricity coefficient, comparing the NBR 7190-3 method with the 5th percentile of the normal distribution (error bars show 95% confidence intervals for the latter).

From Figure 8, it is observed that when coefficients lower than approximately 1.0 are adopted, most characteristic values are no longer limited by equation but rather by constraints that prevent values from being lower than the smallest value in the dataset or below 70% of the mean value. Furthermore, even when using coefficients lower than 1.10, as indicated by NBR 7190-3 [⁴], this does not guarantee that the characteristic values determined by the Centered Estimator Method will be equal to or lower than those directly obtained from the normal distribution, due to the imposed method limits, even when considering the 95% confidence intervals. In this context, based on the trends revealed by the graphs in Figure 8, adopting an eccentricity coefficient within the range of 0.95 to 1.05 could contribute to reducing the overestimation of characteristic values, without compromising the simplicity of the method proposed by the standard, ensuring that the characteristic value determined by the standardized method tends to fall within the confidence bounds of the 5th percentile from the normal distribution. On the other hand, there are exceptions where, even when the eccentricity coefficient is reduced to extremely low values, such as 0.5, the resulting characteristic value may still exceed that obtained from the 5th percentile of the normal distribution, precisely due to the additional constraints imposed by the standard. The Centered Estimator Method remains convenient for quick estimation with simple calculations, but it may be less reliable than determining the 5th percentile from a fitted probability distribution that adequately represents the data.

5. CONCLUSIONS

The study of elastic and strength properties of five Brazilian native species showed that the method proposed by NBR 7190-3 [⁴] for determining characteristic values leads to higher estimates than those obtained directly from the 5th percentile of statistical distributions. In other words, although NBR 7190-3 [⁴] provides a simplified method suitable for small samples, its application to larger datasets may compromise structural reliability by characteristic values overestimating. Depending on the distribution considered, overestimations ranged from 7% to 15% for f_c0 and from 13% to 29% for f_t0. For modulus of elasticity, normative values were between 7% and 26% higher in compression parallel to grain and between 10% and 21% higher in tension parallel to grain. Additionally, the present study showed that the data adhered to the normal distribution in almost all evaluated cases, indicating that assuming normality of wood properties in NBR 7190-3 [⁴] is valid in most contexts. Three-parameter Weibull distribution proved to be the most flexible, showing adherence in all cases. The study also revealed that if the eccentricity coefficient 1.1, as established by NBR 7190-3 [⁴] were replaced with a value within the range of 0.95 to 1.05, characteristic values would be closer to those determined directly from the 5th percentile of adjusted statistical distributions, although in some cases, they would still be slightly overestimated.

Future work will focus on evaluating additional mechanical properties, such as shear strength, bending strength, and compression perpendicular to the grain. In addition, complementary studies should be conducted with other wood species, including both Brazilian hardwoods and non-tropical species, to assess the generalizability of the findings. Further research is also recommended to evaluate how sample size affects the reliability of the characteristic value, particularly for datasets with fewer than 12 specimens. Regarding the proposed revision of the eccentricity coefficient, future studies could apply structural reliability models, such as Monte Carlo simulations, to assess more appropriate values.

6. ACKNOWLEDGMENTS

Authors would like to thank the team at Wood and Timber Structures Laboratory, Department of Structural Engineering, São Carlos Engineering School, University of São Paulo for their support in conducting tests; and the National Council for Scientific and Technological Development (CNPq - Brazil) for the financial support through processes nº 141049/2024-3 and nº 313198/2023-3 and the São Paulo Research Foundation (FAPESP) through process nº 2024/01589-2.

DATA AVAILABILITY

Data will be made available on request.

7. BIBLIOGRAPHY

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Publication Dates

• Publication in this collection
  03 Oct 2025
• Date of issue
  2025

History

• Received
  07 Apr 2025
• Accepted
  15 Aug 2025