Modelos para a estimativa da resistência característica à tração inclinada de madeiras folhosas
Almeida, João Paulo Boff
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Due to the anisotropic characteristics, wood has distinct mechanical performance when requested in longitudinal, radial and tangential directions. In structural design, the longitudinal direction is considered to be parallel to the grains (0°) and the radial and tangential directions are considered normal to the grains (90°). In Brazil, the Brazilian Standard NBR 7190 (ABNT, 1997) establishes the test methods for obtaining strength properties in the parallel (f0) and normal (f90) directions to the wood grains. For this, formulations from the theory of mechanics of materials, developed for isotropic materials, are used. The estimation of strength properties in intermediate directions (off-axis strengths, 0° < θ < 90°) can be performed using empirical models or failure criteria (mathematical models) developed for anisotropic materials. These criteria, such as the Tsai and Wu criterion (1971) and the Tsai-Hill criterion (Azzi and Tsai, 1965), because they are little known by the technical community, are rarely used to estimate wood failure. On the other hand, the empirical models, adjusted according to the exponent n of the trigonometric terms, have been developed and incorporated in several standards documents. Among such, NBR 7190 (ABNT, 1997) recommends the use of Hankinson's empirical model (1921) to estimate the normal off-axis stresses (θ > 6°). Because it was developed through compression tests on softwoods, Hankinson's (1921) model, in its original form (exponent n = 2), may not be a good estimator of the characteristic off-axis tensile strength (ftθ,k) of hardwoods. In this context, this research has the main objective of determining, for hardwoods, models that lead to good estimates of the ftθ,k. Aiming at comprehensive results, 5 species, distributed in the hardwood resistance classes and 6 grain inclination angles (0°, 10°, 20°, 45°, 60° and 90°) were adopted. The statistical analysis showed that the Hankinson model (1921), with an exponent n equal to 2, does not lead to accurate estimates of ftθ,k. With the exception of linear, all regression models tested were significant and with good fits (coefficient of determination - R2 > 96%). Compared to empirical models and failure criteria present in the literature, the model obtained in this research proved to be, for the grouping of species, the most accurate in estimating ftθ,k. Furthermore, the use of the proposed model requires only the knowledge of the characteristic tensile strength parallel to the grains; therefore, this model is easy use in the development of wooden structures projects.
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