ABSTRACT
The present study aims to compare the characteristic values of shear strength parallel to grain obtained through different test methods described in Documents 3 [1] and 4 [2] of ABNT NBR 7190:2022. Compression and shear parallel to grain tests were carried out on specimens from five Brazilian wood species, in order to classify the batches according to their compression strength, to compare the test methods for determining shear strength parallel to grain, as established in the referred documents and evaluating the relationships between shear and compression strengths parallel to grain proposed by the Brazilian standard. The experimental program used batches composed of thirty-six specimens, twelve of which were assigned to compression parallel to grain tests and determination of apparent density, and the remaining twenty-four to shear parallel to grain tests, with twelve used for each test method. Strength characteristic values were determined, statistical equivalence between the methodologies was evaluated, and the existence of a correlation between compression and shear was verified. The results show that the methodology of Document 3 [1] provides significantly higher strength values than those obtained with the methodology described in Document 4 [2], and that there is no statistical equivalence between the two test methods.
Keywords:
Timber properties; shear strength parallel to grain; standardization
1. INTRODUCTION
Wood has the inherent ability to absorb carbon dioxide during tree growth rather than releasing it into the environment, in addition to being a fully renewable material [3,4,5]. In contrast, life-cycle assessments of materials such as concrete and steel indicate opposite behavior, reinforcing the use of wood as a sustainable and viable alternative for the urgent mitigation of climate change [6]. Moreover, among the materials most commonly used in civil construction, wood exhibits an excellent ratio of mechanical strength to density, as well as a favorable relationship between embodied energy and mechanical performance [7, 8].
Technical standardization refers to the systematic establishment and application of procedures aimed at obtaining consistent and comparable results within a given context [9]. Normative documents are developed through consensus among interested parties, based on consolidated scientific knowledge, prepared by Technical Committees, and approved by a recognized body, such as the Brazilian Association of Technical Standards (ABNT) in Brazil. Taking the Brazilian standard ABNT NBR 7190:2022 as a reference, two methods are prescribed for determining shear strength parallel to grain.
The first method is the shear parallel to grain test performed on small clear specimens of Brazilian tropical hardwoods subjected to uniform loading [1]. A similar test configuration is also prescribed in ASTM D143:1982 [10] and in COPANT 463:1972, the latter being no longer valid and used only for reference purposes.
This methodology is based on the classical formulation of pure shear stress from Strength of Materials, which is typically applied to glued joints, screws, nails, or situations in which two members slide relative to each other, regardless of the material properties. In this formulation, stresses act tangentially to the contact plane between the members (resisting area), parallel to the longitudinal axis of the element.
According to MATOS and MOLINA [11], the specimen geometry adopted for the shear parallel to grain test standardized by ABNT NBR 7190:2022-3 [1] has been the subject of debate for two main reasons. First, the asymmetry of the specimen geometry introduces eccentricities that lead to complex stress concentrations associated with bending moment effects during testing – effects that are undesirable when the objective is to evaluate pure shear stress [12,13,14]. Second, the shear strength values obtained with this method are significantly higher than those reported in other normative documents and in studies that adopt alternative test configurations, which may indicate substantial inaccuracies when this methodology is employed [15].
The second method is the static three-point bending test standardized by ABNT NBR 7190:2022-4 [2] for determining longitudinal shear strength in bending. This test consists of applying a concentrated load at midspan to structural-sized sawn timber specimens, typically from plantation-grown species of the genera Pinus and Eucalyptus. This test configuration provides a realistic representation of the behavior of beams subjected to bending under service conditions in civil construction. However, as noted by IDO et al. [16], bending induces a combination of stresses – compression parallel to grain on the upper face, tension parallel to grain on the lower face, and longitudinal shear near the neutral axis – which may cause specimens to fail in tension rather than in shear, thereby leading to an underestimation of the true shear strength.
A similar procedure is described in ISO 13910:2014 [17], which adopts the classical Strength of Materials expression for shear stress in bending, , where V is the shear force, S is the first moment of area, I is the second moment of area about the horizontal axis, and b is the width of the cross-section at the section under consideration. For rectangular cross-sections, this expression is simplified to , which corresponds to the maximum shear stress acting in the plane of the centroidal axis (coincident with the neutral axis), considering that V = F/2, , and A = b · h, as indicated in the referenced documents.
This test method provides consistent values of failure load, since the theoretical shear force along the beam remains constant in magnitude over each half-span, with only a sign reversal at midspan, which does not affect the evaluation of the results. Nevertheless, the shear stress expression used in this method is derived under the assumptions of homogeneous, isotropic, and linear-elastic material behavior and therefore has an approximate character. As a result, its application to heterogeneous and anisotropic materials such as wood is subject to inherent limitations and potential inaccuracies.
In addition, compression strength parallel to grain is experimentally determined in this study, as it is used to classify wood species batches into strength classes according to ABNT NBR 7190:2022-3 [1]. This classification provides the reference basis for the comparison of mechanical properties and for the analysis of the normative ratios between shear and compressive strengths.
In this context, it is evident that both test methods prescribed by ABNT NBR 7190:2022 [1, 2] for the determination of shear strength parallel to grain present inherent limitations related to specimen geometry, stress distribution, and the theoretical assumptions on which their evaluation expressions are based. While the small clear specimen test aims to represent pure shear conditions, its geometric configuration may induce secondary stress effects that compromise the results validity. Conversely, the bending test on structural-sized specimens provides a more realistic representation of structural behavior, but relies on simplified shear stress formulations derived from classical beam theory, which may not be fully applicable to anisotropic and heterogeneous materials such as wood. Therefore, the aim of this study is to critically compare these two test methodologies, as well as to discuss the implications of these differences for the interpretation and reliability of shear strength values used in structural design.
2. MATERIALS AND METHODS
For the experiments, the following batches of Brazilian tropical hardwood species were used: Caixeta (Simarouba amara Aubl.), Sucupira Amarela (Enterolobium schomburgkii (Benth.) Benth.), Tamboril (Enterolobium contortisiliquum (Vell.) Morong), Cambará (Moquiniastrum polymorphum (Less.) G. Sancho), Cupiúba (Goupia glabra Aubl.), totaling five different species subjected to the experimental analyses.
According to Item 4.5 of ABNT NBR 7190:2022-3 [1], the minimum strength characterization of lesser- known native tropical species requires twelve specimens for each type of test. In the present study, this corresponds to thirty-six specimens per wood species batch: twelve for compression parallel to grain, twelve for shear parallel to grain according to ABNT NBR 7190:2022-3 [1], and twelve for shear parallel to grain according to ABNT NBR 7190:2022-4 [2]. As five species were evaluated, a total of one hundred and eighty specimens were tested (Figure 1).
A caliper with an accuracy of 0.01 mm was used to measure specimen dimensions, and a precision balance with an accuracy of 0.01 g was used for mass measurements. Compression parallel to grain tests and both shear parallel to grain tests were performed using an AMSLER universal testing machine with a capacity of 250 kN. Moisture content determination was carried out using a MA035 drying oven. All equipment was provided by, and all tests were conducted at, the Wood and Timber Structures Laboratory (LaMEM), Department of Structural Engineering (SET), School of Engineering of São Carlos (EESC), University of São Paulo (USP).
The experimental program was divided into the following stages: execution of the tests in accordance with ABNT NBR 7190:2022-3 [1] and ABNT NBR 7190:2022-4 [2], including the determination of moisture content, apparent density, and compression strength parallel to grain, as well as shear strength parallel to grain. Subsequently, characteristic values were calculated, and potential correlations between the obtained results were investigated.
Finally, statistical analyses of the shear strength parallel to grain obtained from both test methods were performed using Minitab 19 software to evaluate whether the mean strength values differed statistically at a significance level of α = 5% (95% confidence level). The applied statistical procedures included the Anderson- Darling test for normality assessment, Levene’s test for homogeneity of variances, and the t-test for comparison of means.
For the compression strength parallel to grain test, specimens were prepared with a prismatic shape and specific dimensions, as shown in Figure 2, with an allowable dimensional tolerance of 0.1 mm. Loading was applied monotonically at a rate of approximately 10 MPa/min. Twelve specimens per species batch were tested, totaling sixty specimens in this stage of the study.
After being measured, the specimen must be weighted for the determination of apparent density from Equation 1.
Where ρap is the apparent density [kg/m3]; m is the specimen mass [kg]; and V is the specimen volume [m3] Compression strength parallel to grain value is given by Equation 2.
Where fc0 is the compression strength parallel to grain [MPa]; Fc0,máx is the maximum compressive load [N]; and A is the initial cross-sectional area [mm2].
To determine shear strength parallel to grain, the critical shear plane of the specimen must be oriented parallel to the direction of the applied load. The load is applied monotonically in a single loading cycle at a rate of approximately 2.5 MPa/min, inducing shear stresses in the resisting area that defines the failure plane of the specimen. The standardized specimen geometries prescribed by the normative documents are illustrated in Figure 3. At this stage of the study, twenty-four specimens per species batch were tested, with twelve specimens assigned to each test method, totaling one hundred and twenty specimens.
Shear strength parallel to grain value is given by Equations 3 [1] and 4 [2].
Where fv0 is the shear strength parallel to grain [MPa]; Fv0,máx is the maximum shear load [N]; and Av0 is the cross-sectional area, parallel to the applied load [mm2]
Where fv0 is the shear strength parallel to grain [MPa]; Fv0,máx is the maximum shear load [N]; and Av0 is the cross-sectional area [mm2]
After completion of the destructive tests, the specimens were oven-dried at 103 °C ± 2 °C, as specified in Document 3 [1]. The dry mass was then recorded to determine the moisture content using the gravimetric method described in Equation 5.
Where U is the relative moisture content [%]; mi is the specimen initial mass [g]; and ms is the specimen dry mass [g].
It is noteworthy that the standardized specimens for moisture content determination, with dimensions of 2 × 3 × 5 cm, were not used. In the present study, moisture content was determined using specimens from the compression strength parallel to grain tests, following the same drying procedure, in order to ensure consistency between mechanical testing and moisture assessment.
Tests for determining the mechanical properties of wood are conducted on specimens at an equilibrium moisture content corresponding to the standard reference condition (U = 12%). However, as the moisture content at the time of testing may differ slightly from this reference value, mechanical strength results must be adjusted when the moisture content is between 10% and 25%, in accordance with Item 5.6.1 of ABNT NBR 7190:2022-1 [18], using Equation 6. Apparent density values are adjusted using the Kollmann diagram, as specified in Item 5.2.4 of ABNT NBR 7190:2022-3 [1].
Where f12 is the strength value at the reference moisture content [MPa]; fU% is the strength at the test moisture content [MPa]; and U% is the moisture content of the specimen at the moment of testing [%].
The characteristic values of the mechanical properties of wood are obtained according to Item 4.6 of ABNT NBR 7190:2022-3 [1] as described in Equation 7.
For the proper application of this formula, the test results must first be arranged in ascending order (x1 ≤ x2 ≤... ≤ xn). If the number of specimens is odd, the highest value is disregarded. The characteristic value xwk must not be lower than the minimum value x1, nor lower than 0.7 times the mean value of the complete sample (0.7 · xm), and must not exceed the mean value (xm). Accordingly, xwk is defined as the greatest value among x1, 0.7 · xm, and the value obtained from Equation 7, provided that all of them are lower than xm. Otherwise, the value taken for xwk shall be 0.7 · xm.
Limits x1, xm and 0.7 · xm result from the assumption that strength values follow a Gaussian normal probability distribution, symmetric about the mean value (xm).
To obtain the lower characteristic strength, corresponding to the 5% quantile of the normal distribution of strengths, with z = –1.645, the factor 0.7 that multiplies the mean results from Equation 8 given below:
Where xwk is the characteristic value [MPa]; xm is the mean value [MPa]; z is the 5% quantile of the standard normal distribution; and C.V. is the coefficient of variation.
According to Item 4.3 of ABNT NBR 7190:2022-3 [1], coefficients of variation of up to 18% are permitted for strength properties associated with normal stresses (tension and compression), while coefficients of variation of up to 28% are allowed for properties associated with tangential stresses (shear), in order to classify wood species batches as homogeneous. The higher allowable coefficient of variation for shear reflects the more brittle and less predictable failure behavior of wood under shear loading when compared to normal stresses.
By substituting these limiting coefficients of variation into Equation 8, pessimistic strength values of 0.7039 · xmfor normal stresses (compression parallel to grain) – which is consistent with the value of 0.7 indicated in the description of Equation 7 – and 0.5394 · xm for tangential stresses (shear parallel to grain) are obtained. The latter differs significantly from the commonly adopted value of 0.7.
Therefore, the actual coefficients of variation obtained experimentally were used in Equation 8, rather than adopting the normative value of 0.7, in order to more accurately determine the characteristic strength values.
Figure 4 shows the configuration for each done test.
3. RESULTS
Tables 1–5 show the strength class, minimum, maximum, mean and characteristic values (adjusted for content moisture of 12%) for the properties of density, compression strength parallel to grain and shear strength parallel to grain, according to the methodologies of Documents 3 [1] and 4 [2], in addition to their respective standard deviation and coefficient of variation values, for each wood species batch tested.
Table 6 presents the p-values for the normality test, homoscedasticity test, and comparison of means for the shear strength parallel to grain obtained by both test methods for the wood species batches tested.
For the specimens tested according to Document 3 [1], only pure shear was observed as the failure mode (Figure 5a). In contrast, the specimens tested according to Document 4 [2] exhibited two failure modes: tension in the lower grain (Figure 5b) and shear in bending (Figure 5c).
Table 7 presents the predominance of each shear failure mode for the wood species batch tested.
Table 8 shows an overview of the strength values and the fv0,k/fc0,k ratio, both for the methodology of Document 3 [1], and for the methodology of Document 4 [2], obtained for each wood batch tested.
4. DISCUSSION
The coefficients of variation reported on Tables 1–5 indicate that all wood species batches can be classified as homogenous, since the coefficients of variation of the strength properties comply with Item 4.3 of ABNT NBR 7190:2022-3 [1], being less or equal to 18% for compression parallel to grain and less or equal to 28% for shear parallel to grain.
According to Table 6, the statistical analysis shows that the mean shear strength values obtained using methodologies [1] and [2] differ significantly for all evaluated wood species batches, as the t-test p-values are lower than 0.05.
From Table 7, it is observed that the predominant failure mode in all wood species batches for the specimens tested according to the methodology of Document 4 [2] is tensile failure in the lower grain, with the shear capacity not being reached in most cases.
Although species anatomy and physical properties may influence failure modes in bending, such effects could not be assessed in the present study. Neither Document 3 [1] nor Document 4 [2] specifies the orientation of growth rings relative to the specimen faces, and no control of anatomical directions or detailed anatomical characterization was performed. Consequently, the observed failure modes could not be directly correlated with the wood’s anatomical structure or physical properties.
Based on the summary presented in Table 8, the shear strength parallel to grain obtained using the methodology of Document 3 [1] are significantly higher than those obtained using the methodology of Document 4 [2]. The average value of 9.2 MPa for Document 3 [1] and 4.3 MPa for Document 4 [2], corresponding to an average reduction of 47.9% when the latter methodology is adopted.
Item 6.4.2 of ABNT NBR 7190:2022-1 [18] establishes a fixed ratio between the design shear strength parallel to grain and the design compressive strength parallel to grain, fv0,d/fc0,d = 0.10, regardless of strength class and applicable to both native and plantation-grown hardwood species. According to Item 5.8.3 of the same standard [18], design strength values are obtained from characteristic values using the expression . Item 5.8.5 [18] assigns different partial safety factors to tangential and normal stresses, namely γw= 1.8 for shear stresses and for normal stresses.
Since the modification factor kmod is related to design conditions and is applied equally to both strength properties, it cancels out when the ratio between shear and compressive strengths is considered. Moreover, the symbol fw refers generically to both fv0 and fc0. Therefore, the ratio between characteristic values can be obtained from the ratio between design values by accounting only for the different partial safety factors, resulting in fv0,k/fc0,k = 0.13.
It is observed that only the values obtained using the methodology of Document 4 [2] approach the fv0,k/fc0,k ratio of 0.13 derived from Document 1 [18], with an average of 0.14. Although slightly higher in most cases, this result contrasts with the mean ratio of 0.29 obtained from the methodology presented in Document 3 [1].
Comparing the values of the fv0,k/fc0,k ratio reported in the literature, COUTO et al. [19] obtained mean values of 0.24 for class D20, 0.29 for class D30, 0.18 for class D40, and 0.27 for class D60, using the methodology of ABNT NBR 7190:1997 [20], which is equivalent to the method currently prescribed in ABNT NBR 7190:2022-3 [1]. Similarly, RODRIGUES et al. [21] obtained mean values of 0.26 for class D30 and 0.10 for class D40, also based on the methodology of ABNT NBR 7190:2022-3 [1]. In both studies, the values are higher than the normative value of 0.13 derived from ABNT NBR 7190:2022-1 [18] and are relatively close to those obtained in the present study.
On the other hand, MORITANI et al. [22], using the methodology of ABNT NBR 7190:2022-4 [2], obtained mean values of 0.11 for class D30 and 0.12 for class D40, which are close to the value of 0.13 derived from ABNT NBR 7190:2022-1 [18] and consistent with the results of this study.
5. CONCLUSIONS
Values of shear strength parallel to grain obtained using the test methodologies contained in ABNT NBR 7190:2022 differ significantly from each other in statistical terms. While the methodology proposed by Document 3 [1] yields considerably higher values, ranging from 6.5 to 12.4 MPa, with a mean value of 9.2 MPa, and results in pure shear failure in 100% of cases, the shear strength values are reduced, ranging from 2.8 to 5.2 MPa, with a mean value of 4.3 MPa, and the predominant failure mode for the methodology proposed by Document 4 [2] is tensile failure in the lower grain (67% to 83% in the tested wood species batches).
Results obtained from the shear strength parallel to grain test proposed by Document 4 [2] were shown to be closer to the fv0,k/fc0,k ratio of hardwoods of 0.13 given by Document 1 [18], ranging from 0.09 to 0.16, with a mean value of 0.14, whereas the results obtained from the test proposed by Document 3 [1] are significantly higher, ranging from 0.21 to 0.39, with a mean value of 0.29.
It is emphasized that both methodologies used in this study to determine the shear strength parallel to grain present inherent inaccuracies associated with the specimen geometry and the failure modes resulting from the type of test performed. While the results obtained through the test method proposed by Document 4 [2] approach the values related to species originating from plantation forests, the results obtained through the test method proposed by Document 3 [1] differ significantly from the values related to species originating from native forests, both contained in tables presented in Document 1 [18]. This indicates the need for revising the values of shear strength parallel to grain proposed for wood species from native forests.
6. ACKNOWLEDGMENTS
To the professors, technicians, and other staff members of the Wood and Timber Structures Laboratory (LaMEM) of the Department of Structures (SET) of the School of Engineering of São Carlos (EESC), at the University of São Paulo (USP - São Carlos).
The authors also would like to thank the financial support provided by the National Council for Scientific and Technological Development (CNPq) (No 130898/2024-4 and No 313198/2023-3), by the São Paulo Research Foundation (FAPESP) (No 2024/01522-5), and by the Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES) (No 88887.968336/2024-00).
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