CHARACTERISTIC STRENGTHS IN THE COMPRESSION AND IN THE STATIC BENDING AS PARAMETERS TO ESTIMATE CHARACTERISTIC SHEAR STRENGTH FOR TIMBER DESIGN

RESISTÊNCIAS CARACTERÍSTICAS NA COMPRESSÃO E FLEXÃO ESTÁTICA COMO PARÂMETROS PARA A ESTIMATIVA DA RESISTÊNCIA CARACTERÍSTICA AO CISALHAMENTO NO PROJETO DE MADEIRA

ABSTRACT

To simplify the characterization of wood species, the Brazilian standard document ABNT NBR 7190-1 (2022) establishes the determination of mechanical properties employing the characteristic strength in the compression parallel to grain (f_c0,k). This mechanical property is estimated using the linear relation given by the following expression f_v0,k = 0.12·f_c0,k Brazilian and European standard documents support the estimation of f_v0,k using relations among properties. However, the European guidelines in the EN 384 (2019) have used the conventional characteristic strength in the static bending test (f_M,k). Thus, this study aimed to investigate the efficiency of the ratio f_v0,k = 0.12·f_c0,k for adopting 30 hardwoods. The variance analysis results demonstrate the divergence among the experimental outcomes and those values estimated using the relation cited. Therefore, regression models at two parameters were considered to obtain more accurate estimates of f_v0,k by adopting f_c0,k, and f_M,k as independent variables. Regarding the results, the geometric (R² = 80.80%) and linear (R² = 74.19%) models were the most accurate for the estimates of f_v0,k in terms of f_c0,k, and f_M,k, respectively. This fact evinces the good accuracy of the models under consideration, which may provide a more rigorous structural design compared to the correlation currently prescribed by the ABNT NBR 7190-1 (2022).

Keywords:
Brazilian hardwood; characteristic strengths; Shear strength estimates

RESUMO

Para simplificar a caracterização de espécies de madeira, o documento normativo brasileiro ABNT NBR 7190-1 (2022) estabelece a determinação de propriedades mecânicas por meio da resistência característica na compressão paralela às fibras (f_c0,k). Essa propriedade mecânica é estimada utilizando-se da relação linear dada pela expressão a seguir f_v0,k = 0.12·f_c0,k. Ambos os documentos normativos europeu e brasileiro prescrevem a estimativa da f_v0,k empregando-se relações entre propriedades, embora as diretrizes da europeia contidas na EN 384 (2019) utilize a resistência característica convencional obtida no teste de flexão estática (f_M,k). Assim, esse estudo teve o objetivo de investigar a eficiência da relação f_v0,k = 0.12·f_c0,k para 30 espécies folhosas. Os resultados da análise de variância demonstram a divergência entre os resultados experimentais e aqueles estimados utilizando-se da relação citada. Portanto, modelos de regressão em função de dois parâmetros foram considerados para se obter estimativas mais precisas da f_v0,k através da adoção da f_c0,k e f_M,k como variáveis independentes. Com relação aos resultados, os modelos geométrico (R² = 80.80%) e linear (R² = 74.19%) foram os mais precisos para a estimativa da f_v0,k em termos da f_c0,k e f_M,k, respectivamente. Este fato evidencia a boa precisão dos modelos em questão, o que pode proporcionar um dimensionamento estrutural mais rigoroso quando comparado à correlação atualmente prescrita pela ABNT NBR 7190-1 (2022).

Palavras-Chave:
Madeiras folhosas brasileiras; resistências características; estimativas da resistência ao cisalhamento

1. INTRODUCTION

Due to the growing demand for efficient and sustainable buildings, wood is being considered as the forthcoming industrial resource due to greater recognitions and broader applications for the civil construction (Araujo et al., 2016; Kuzman and Sandberg, 2017; Wieruszewski and Mazela, 2017; Żmijewki and Wojtowicz-Jankowska, 2017; Nesheim et al., 2021, Niebuhr and Sieder, 2021).

In view of the excellent mechanical-strength and density relation, wood is basically a smart alternative for timber-based tall buildings, whose structure weights correspond to a high proportion of loads to be resisted (Pries and Mai, 2013; Ramage et al., 2017; Lima Jr. et al., 2018; Huber et al., 2018; Araujo, 2021). Buildings with wood-designed structures offer good performance to seismic events, as heavier structures are subjected to greater seismic forces (Ramage et al., 2017).

In addition to the efficiency of wood for structural buildings, this material is still natural, biodegradable, renewable and recyclable and therefore it is effectively an environmentally friendly solution (Wang et al., 2014; Araujo et al., 2016; Souza et al., 2018; Lima Jr. et al., 2018; Araujo, 2021). Due to efficiency of the wood as a structural element, timber construction has become the most popular, economic and practical housing solution in the Northern Hemisphere (Araujo et al., 2016). As a result, the construction of buildings with six or more floors has been observed in the last decade (Ramage et al., 2017). Expressive uses of wood are being confirmed. While wood is the main material in 80% of houses in Scotland and New Zealand, it is also applied for nearly 7% of the Brazilian residences (Mahapatra et al., 2012; Araujo et al., 2018, 2020).

Despite the evident potential for reforestation and the demand for new houses, the use of wood for housing in Brazil is practically insignificant when compared to traditional masonry buildings (Araujo et al., 2018). The lacks of qualified labor and knowledge of species and properties have contributed to the inadequate utilization of wood, resulting in the erroneous production of buildings with unexpected lifespans and misuse of material advantages (Pedreschi et al., 2005).

In this scenario, Almeida et al. (2020) argue about the importance of elaboration of studies to provide, for the Brazilian market, sufficient information about the benefits and features of timber construction and the physical and mechanical properties of lignocellulosic materials to enable the design of rational projects for timber-based structures.

In addition to prescribing procedures for dimensioning of timber structures [ABNT NBR 7190-1 (2022)], the Brazilian standard document ABNT NBR 7190-3 (2022) has established methods for the complete experimental characterization of the physical-mechanical properties of this biomaterial. In order to simplify the characterization of wood, this Brazilian normative allows the determination of mechanical properties as a function of the characteristic compression strength parallel to the grain (f_c0,k).

Among the prescribed estimates, there is the determination of characteristic shear strength parallel to the grain (f_v0,k) through the linear relation (Equation 1) between f_c0,k and f_v0,k values. Concerning hardwoods, the ABNT NBR 7190-1 (2022) implicitly adopts λ equal to 0.12, according to the standard calibration.

(Eq. 1) $f_{V0,k}=\lambda \cdot f_{c0,k}$

Due to expressive volume of native tree species cataloged in the Brazilian Amazon – around 7700 as raised by Steege et al. (2016) – every effective procedure for the characterization of wood species is highly desirable, since the economic resources can be allocated to the characterization of unfamiliar hardwoods as a strategy to promote their uses as well as reduce predatory utilization of the most usual species.

Some researchers have investigated the efficiency of relations between properties prescribed by the standard documents. In Brazil, they have considered the ABNT NBR 7190 (1997), which is the last version before the recent update to ABNT NBR 7190-1 (2022). Thus, there are studies from Lahr et al. (2017), Almeida et al. (2018) and Almeida et al. (2020) about the relations between properties of stiffness of hardwoods.

Regarding f_v0,k, Matos and Molina (2016) obtained, through tests for Eucalyptus saligna species, a λ equal to 0.13, whose value is close to the specifications of the ABNT NBR 7190-1 (2022). On the other hand, Christoforo et al. (2019) obtained a λ equal to 0.23 for a grouping of five hardwood species. This result is according to the experiment of Couto et al. (2020), which verified a λ equal to 0.22 for a set of 10 hardwoods, being a value approximately 80% higher than stated in ABNT NBR 7190-1 (2022). These aforementioned studies highlight the need for a review about the ratio mentioned that is still implicit in the updated Brazilian standard document through its calibration. This justification is motivated by the interest of the academic field on the correlation between mechanical properties. These studies from literature were designed making use of a reduced number of species, in which the aim was to determine only the coefficient λ for the best description of the linear relation between f_v0,k and f_c0,k. Besides, these studies did not investigate the different regression models such as exponential, geometric and logarithmic.

Both Brazilian ABNT NBR 7190-1 (2022) and European EN 384 (2019) standards allow the determination of f_v0,k through the correlation of properties. However, f_v0,k values are estimated by the conventional characteristic strength in the static bending test (f_M,k). In this context, making use of a significant number of hardwood species, this study aims to investigate the statistical equivalence among the experimental values of f_v0,k and the estimated values (Equation 1) as well as provide, in case of divergence, models of regression as a function of f_c0,k and f_M,k, respectively.

2. MATERIALS AND METHODS

2.1 Materials

Thirty hardwood species were adopted in this study (Table 1), which were bought as normally acquired in local markets through planks – this consideration reflected the way in which wood has been used/obtained for structural purposes in the Brazilian construction. Thus, age and origin of the tropical trees were not identified due to the lack of information.

Table 1
Scientific name and identification number (ID) of 30 tropical hardwood species.
Tabela 1
Nome científico e número de identificação (ID) de 30 espécies de folhosas tropicais.

ID	Brazilian Popular Name	Scientific Name	ID	BrazilianPopular Name	Scientific Name
1	Angelim amargoso	Vatairea fusca (Ducke) Ducke	16	Louro preto	Ocotea neesiana (Miq.) Kosterm.
2	Angelim ferro	Hymenolobium cf. heterocarpum Ducke	17	Louro verde	Sextonia cf. rubra (Mez) van der Werff
3	Angelim Saia	Vatairea cf. guianensis Aubl.	18	Maçaranduba	Manilkara cf. inundata (Ducke) Ducke
4	Angelim vermelho	Dinizia excelsa Ducke	19	Mandioqueira	Qualea paraensis Ducke
5	Castanheira	Bertholletia excelsa Bonpl.	20	Oiticica amarela	Clarisia racemosa Ruiz & Pav.
6	Castelo	Calycophyllum multiflorum Griseb.	21	Oiuchu	Pradosia sp. Liais
7	Canatudo	Calophyllum longifolium Willd.	22	Parinari	Parinari excelsa Sabine
8	Cedro amargo	Cedrela odorata L.	23	Pau-óleo	Copaifera langsdorffii Desf.
9	Cedro doce	Cedrela cf. fissilis Vell.	24	Piolho	Tapirira sp. Aubl.
10	Copaíba	Copaifera multijuga Hayne	25	Quarubarana	Erisma uncinatum Warm.
11	Cutiúba	Goupia paraensis Huber	26	Quina rosa	Geissospermum sericeum Miers
12	Garapa	Apuleia leiocarpa (Vog.) Macbr.	27	Rabo de arraia	Vochysia haenkeana Mart.
13	Goiabão	Planchonella pachycarpa Pires	28	Sucupira	Diplotropis sp. Benth.
14	Itaúba	Mezilaurus itauba (Meisn.) Taub. ex Mez	29	Tachi	Tachigali glauca Tul.
15	Jatobá	Hymenaea courbaril L.	30	Umirana	Ruizterania retusa (Spruce ex Warm.) Marc.-Berti

• Source: Flora of Brazil (2020).
• Fonte: Plantas do Brasil (2020).

2.2 Methods

Experimental tests were carried out in the dependences of the Laboratory of Wood and Timber Structures (LaMEM) of the University of São Paulo (USP), São Carlos, Brazil. For that, it was adopted twelve specimens per species and mechanical property under investigation, which resulted in 1080 experimental determinations. The extraction of specimens was executed with dimensions of specimens in millimeters for testing and obtainment of sampling values of bending (f_M), compression (f_c0) and shear (f_v0) strength along the direction parallel to the grain.

After testing, values of f_c0, f_v0 e f_m were determined (Equations 2, 3 and 4) for each specimen, according to ABNT NBR 7190-3 (2022).

(Eq. 2) $f_{c0}=\frac{F_{c0,max}}{A}$

(Eq. 3) $f_{v0}=\frac{F_{v0,max}}{A_{v0}}$

(Eq. 4) $f_M=\frac{M_{max}}{W_e}$

Where, F_c0,max , F_v0,max , A, A_v0, M_max and _W, represent, respectively, the maximum force in the compression, maximum shear force, initial area of transversal section of specimen for compression, initial area of critical section of specimen for shear stress, maximum bending moment from static test, and modulus of transversal section of static bending specimen. According to the prescriptions from the ABNT NBR 7190-3 (2022), the load was applied monotonically increasing at 10 MPa/min for static bending and compression tests and at 2.5 MPa/min for shear stress test.

Specimens were tested with moisture content (MC) at 12% since it is prescribed by the ABNT NBR 7190-3 (2022) as the equilibrium moisture content (EMC). However, for those that did not achieve the EMC, the strengths were corrected as recommended by the Brazilian standard (Equation 5).

(Eq. 5) $f_{12\%}=f_{MC}\cdot \left[1+\frac{3\cdot \left(\text{MC}-12\right)}{100}\right]$

In this equation, f_12% and f_MC% are the strength at 12% and at a certain moisture content, respectively.

To determine the characteristic strength (f_w,k - f_c0,k, f_v0,k and f_M,k ), all sampled values at 12% MC were sorted in ascending order $\left(f1\le f2\le f3\dots \le f_n=f12\right)$ . Then, according to ABNT NBR 7190-1 (2022), f_w,k was taken as the highest value among f1 and those values obtained through relations (Equations 6 and 7) given by the code.

(Eq. 6) $f_{w,k}=f_m\cdot \left[1-\mathrm{1.645.}\delta \right]\approx 0.70\cdot f_m$

(Eq. 7) $f_{w,k}=\left[2\cdot \frac{f_1+f_2+f_3+\dots +f_{\left(n/2\right)-1}}{\left(n/2\right)-1}-f_{n/2}\right]\cdot 1.10$

In which, f_m is the average value of sampled strengths and δ represents the coefficient of variation of samples. In favor of safety, the ABNT NBR 7190-1 (2022) admits that strengths have normal distributions and δ does not exceed 18%. Although the present study seeks to estimate f_v0,k through f_M,k as considered by the European standard document EN 384 (2019), the sample dimensions, laboratory procedures and equations to determine characteristic strengths were used in accordance to the Brazilian standard document ABNT NBR 7190-1 (2022) for purposes of comparing results.

In order to verify the effectiveness of the estimation of f_v0,k in terms of f_c0,k (Equation 1), the analysis of variance (ANOVA) at 5% significance was adopted. Null hypothesis (H₀) was featured by the equivalence among experimental and calculated values (f_v0,k and 0.12·f_c0,k) of the thirty species, while the alternative hypothesis (H₁) was based on the no equivalence situation. With P-value greater than or equal to the significance level adopted (P-value ≥ 0.05), the H₀ is accepted, then the estimate (Equation 1) offers good estimation for f_v0,k. In the P-valor < 0.05, H₁ is adopted otherwise and, therefore, equations that are more precise must be determined.

In case of H₁ is true, models of regression (Equations 8 9 10 11) were further adopted to estimate f_v0,k (dependent variable - y) of the thirty species in terms of f_c0,k and f_M,k (independent variables - x), respectively. Then, these equations were analyzed through analysis of variance at a 5% significance level with respect to the prediction of experimental results.

(Eq. 8) $y=a+b\cdot x\left[\text{Linear}\right]$

(Eq. 9) $y=a\cdot e^{bx}\left[\text{Exponential}\right]$

(Eq. 10) $y=a+b\cdot in\left(x\right)\left[\text{Logarithmic}\right]$

(Eq. 11) $y=a\cdot x^b\left[\text{Geometric}\right]$

In which, a and b are parameters of models, which are adjusted by the method of least squares. Thereby, two hypotheses were formulated: null (H₀) and alternative (H₁). H₀ is accepted if P-value is superior to the significance level (P-valor > 0.05), which implies that the model under test is not representative (variations of x are not able to explain the variations of y). For P-value ≤ 0.05, H₀ is accepted otherwise, that is, the tested model is representative.

In order to assess the quality of adjustments, the values of the coefficient of determination (R²) were determined for each model, which allows selecting those representative situations (P-value ≤ 0.05) with better estimates. Finally, normality test of Anderson-Darling was executed to validate the distribution of values.

3. RESULTS

Results for characteristic strengths (f_v0,k, f_c0,k and f_M,k ) [Table 2] were obtained in accordance with the ABNT NBR 7190-1 (2022) for thirty hardwoods studied (Table 1).

Table 2
Results of f_c0,k, f_v0,k and f_M,k of 30 hardwoods studied.
Tabela 2
Resultados da f_c0,k, f_v0,k and f_M,k das 30 espécies estudadas.

ID*	fc0,k(MPa)	fv0,k(MPa)	fM,k(MPa)	ID*	fc0,k(MPa)	fv0,k(MPa)	fM,k(MPa)
1	47.52	12.76	78.76	16	50.60	10.40	83.16
2	76.03	17.20	88.73	17	49.14	9.77	85.74
3	51.06	12.10	76.70	18	79.46	20.77	125.80
4	72.73	13.35	90.24	19	61.53	14.34	80.78
5	38.93	7.04	46.61	20	62.41	15.18	90.49
6	54.54	15.55	99.92	21	72.34	14.63	89.17
7	50.91	12.30	58.17	22	55.22	12.01	86.57
8	33.18	8.56	55.53	23	45.06	10.62	63.07
9	29.99	7.13	39.69	24	43.74	12.39	53.05
10	44.13	10.25	71.65	25	27.20	6.70	59.07
11	55.28	12.63	88.83	26	61.60	11.37	99.44
12	65.36	16.28	103.18	27	44.79	9.30	55.43
13	43.10	12.14	91.12	28	90.46	17.42	120.34
14	68.44	16.32	95.30	29	75.46	14.54	98.49
15	89.96	23.08	133.56	30	51.28	9.83	48.09

• * ID is the identification of each hardwood cataloged in the Table 1 for this representative research.
• Source: Author’s data.
• *ID é a identificação de cada espécie folhosa catalogada na Tabela 1 para a pesquisa de representatividade.
• Fonte: Dados do autor.

Hardwood species studied (Table 2) included all strength classes (C20, C30, C40, C50 and C60) prescribed by ABNT NBR 7190-1 (2022), which evinces the broad scope and relevance of the results. Thereby, two hardwoods were classified as C20 (cedro doce and quarubarana), two species as C30 (castanheira and cedro amargo), seven species as C40 (angelim amargoso, copaíba, goiabão, louro verde, pau-óleo, piolho and rabo de arraia), seven as C50 (angelim saia, castelo, canatudo, cutiúba, louro preto, parinari and umirana) and twelve species as C60 (angelim ferro, angelim vermelho, garapa, itaúba, jatobá, maçaranduba, mandioqueira, oiticica amarela, oiuchu, quina rosa, sucupira and tachi).

In the sequence, the results of ANOVA at 5% significance and the normality test of AndersonDarling to evaluate the f_v0,k in terms of f_c0,k (Equation 1) are also presented. It was possible to see that the groups of values – f_v0,k (experimental values) and f_v0,k (Equation 1) – are not equivalent (P-Value = 0.000), indicating an inaccuracy of f_v0,k (Equation 1) from the ABNT NBR 7190-1 (2022). Subsequently, results of Anderson-Darling test confirmed the assumption of normal distribution of data with P-value equal to 0.960.

As an alternative to the Brazilian ratio (Equation 1), the adjustments (Figure 1) were obtained through the regression models (Equations 8 9 10 11) for the estimate of f_v0,k in terms of f_c0,k considering the thirty hardwoods described (Table 1).

Figure 1
Regression models to estimate f_v0,k in terms of f_c0,k: (a) linear; (b) exponential; logarithmic (c); and (d) geometric.
Figura 1
Modelos de regressão para se estimar f_v0,k em termos da f_c0,k: (a) linear; (b) exponencial; logarítmico (c); e (d) geométrico.

As result, all adjustments (Figure 1) were significant (P-value < 0.05), which suggests that variations of f_c0,k are able to explain the variations of f_v0,k. Among the models under consideration, the geometric model (Figure 1D, Equation 12) is the most accurate option, with R² equal to 80.80%.

(Eq. 12) $f_{v0,k}=0.34\cdot {\left(f_{c0,k}\right)}^{0.90}$

In the sequence, results of adjustment (Figure 2) were obtained from the models of regression (Equations 8 9 10 11) in the estimation of f_v0,k through f_M,k.

Figure 2
Models of regression to estimate f_v0,k from f_M,k: (a) linear; (b) exponential; logarithmic (c); and (d) geometric.
Figura 2
Modelos de regressão para se estimar f_v0,k a partir da f_M,k: (a) linear; (b) exponencial; logarítmico (c); e (d) geométrico.

Analogously to the models of regression considering f_c0,k (Figure 1), all tested adjustments through the consideration of f_M,k for estimation of f_v0,k were significant (P-value < 0.05). Therefore, variations of f_M,k are able to explain those variations of f_v0,k. Concerning the models, the linear one (Figure 2A) is the more accurate, with (R² = 74.19%).

In order to measure any errors from the estimates of f_v0,k (Equations 1, 12 and 13), a calculation (Equation 14) was used, since this compared f_v0,k^{(experimental)} and f_v0,k^(estimated). Then, errors (Table 3) were identified for each wood species under consideration. From, the three estimates (1, 12 and 13) demonstrated, in percentage, average errors were of 46.90%, 10.80% e 12.77%, respectively.

Table 3
Percentage errors from the estimate of f_v0,k using models (Equations 1, 12 and 13).
Tabela 3
Erros percentuais da estimativa da f_v0,k ao se utilizar os modelos (Equações 1, 12 e 13).

ID	Er (%) (Equation 1)	Er (%) (Equation 12)	Er (%) (Equation 13)	ID	Er (%) (Equation 1)	Er (%) (Equation 12)	Er (%) (Equation 13)
1	55.31	13.94	3.16	16	41.62	11.73	24.73
2	46.96	2.54	20.05	17	39.64	15.84	36.47
3	49.36	3.18	0.26	18	54.09	16.02	8.80
4	34.62	20.65	4.60	19	48.51	3.37	11.86
5	33.64	30.37	11.58	20	50.66	7.54	7.78
6	57.91	20.05	1.49	21	40.66	9.57	5.58
7	50.33	5.01	22.98	22	44.83	4.67	11.99
8	53.49	7.15	6.36	23	49.08	1.43	4.33
9	49.53	1.78	3.41	24	57.64	17.74	29.32
10	48.34	0.23	10.84	25	51.28	0.80	43.28
11	47.48	0.37	9.00	26	34.99	21.99	34.14
12	51.82	10.13	3.10	27	42.21	11.96	2.26
13	57.40	17.15	16.04	28	37.69	12.52	4.35
14	49.68	6.56	10.10	29	37.72	14.51	3.98
15	53.23	15.49	13.22	30	37.40	19.64	17.98

• Source: Author's data
• Fonte: Dados do autor.

(Eq. 13) $f_{v0,k}=1.33+0.14\cdot \left(f_{M,k}\right)$

(Eq. 14) $Er\left(\%\right)=100\cdot \frac{\left|f_{v0,k}{}^{(experimental)}-f_{v0,k}{}^{(estimated)}\right|}{\left|f_{v0,k}{}^{(experimental)}\right|}$

4. DISCUSSION

With respect to ANOVA result that revealed the Brazilian ratio to be inaccurate to estimate f_v0,k, this is in line with results presented in Christoforo et al. (2019) and Couto et al. (2020), but not in accordance with Matos and Molina (2016). The reason why this last work does not agree to the results herein found out may be due the fact that only one species was investigated, and given the natural variability of wood, it was not representative.

Regarding the estimate of f_v0,k as a function of f_c0,k, results (Figure 1) pointed to geometric model as the most accurate equation (R² = 80.80%.). This type of regression is not in accordance to the linear equation adopted in ABNT NBR 7190-1 (2022). It is worth mentioning that even when comparing the normative linear ratio to the linear regression found out (R² = 78.86%), the second is much more accurate, which emphasizes the poor prediction power of the normative one.

Results presented concerning f_v0,k estimated in terms of f_M,k (Figure 2) confirms that the linear regression (R² = 74.19%) was the more accurate equation determined, being in accordance to the regression type prescribed by the European standard EN 384 (2019) that utilizes f_M,k as independent variable. Besides, both exponential and geometric regression also presented R² larger than 70%.

Concerning errors calculated for estimations (Equations 1, 12 and 13) in comparison to the experimental results, outcome evinces the good accuracy of the estimates of f_v0,k using the proposed models of regression, especially when being estimated as a function of f_c0,k. Then, f_c0,k showed to be a more precise variable than f_M,k, which is recommended by EN 384 (2019).

This better accuracy of f_v0,k through f_c0,k (Brazilian standard) may be explained by anatomical differences between hardwood and softwood, since the correlation given in EN 384 (2019) is purposely calibrated for the last one, and there is no available estimate for hardwoods. However, as already claimed, the good accuracy of the European estimate makes it useful for Brazilian hardwoods as well.

5. CONCLUSION

The analysis of variance revealed the divergence between f_v0,k (experimental) and 0.12·f_c0,k groups, since the model (Equation 1) currently admitted in the calibration of the Brazilian standard ABNT NBR 7190-1 (2022) does not give accurate estimates of f_v0,k.

All models of regression applied for the estimate of f_v0,k through f_c0,k and f_M,k were significant. The suggested models (Equations 12 and 13) showed a wider coverage of shear strength due to the very representative number of hardwood species under evaluation in this study.

In the estimate of f_v0,k, when compared to the model (Equation 1) given implicitly by ABNT NBR 7190-1 (2022), the suggested models (Equations 12 and 13) provide relatively lower errors. This finding indicates the good accuracy of the models proposed, which lead to a more accurate structural design when compared to the current correlation admitted in the Brazilian standard. Therefore, results found out justifies the adoption of these ratios/correlations in the future update of normative recommendations.

6. REFERENCES

• Associação Brasileira de Normas Técnicas – ABNT. NBR 7190: Projeto de estruturas de madeira. Rio de Janeiro, Brazil: 1997.
• Associação Brasileira de Normas Técnicas – ABNT. NBR 7190-1: Projeto de estruturas de madeira – Parte 1: Critérios de dimensionamento. Rio de Janeiro, Brazil: 2022.
• Associação Brasileira de Normas Técnicas – ABNT. NBR 7190-3: 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, Brazil: 2022.
• Almeida AS, Lanini TLS, Caetano JA, Christoforo AL, Lahr FAR. Evaluation of Stiffness in Compression Perpendicular to Grain of Brazilian Tropical Wood Species. Current Journal of Applied Science and Technology. 2018; 28(5): 1-7. doi:10.9734/CJAST/2018/42945
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Publication Dates

• Publication in this collection
  26 June 2023
• Date of issue
  2023

History

• Received
  16 Nov 2022
• Accepted
  09 Mar 2023