Relações entre propriedades de rigidez de madeiras do grupo das folhosas
Almeida, João Paulo Boff
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For a correct timber structures design, it is necessary to know the physical and mechanical properties of the material. Among these properties, the modulus of elasticity is highly important, in view of its use in the Ultimate Limit State (ULS - stability) and the Serviceability Limit State (SLS – excessive deformation) safety checks. In Brazil, the Brazilian Standard ABNT NBR 7190 establishes the test methods to obtain these properties, however, the premises require procedures performed in specialized and high-cost laboratories. In the impossibility of determining experimental results, the normative document itself establishes relation between mechanical properties, aiming to simplify the characterization of the material. But, the relation prescribed between the modulus of elasticity in compression (Ec0) and parallel tension to the grain (Et0) [Ec0 = Et0] makes no distinction between hardwoods and softwoods. In addition, the current relation between the Ec0 and the modulus of elasticity in bending (EM) [EM = 0.90∙Ec0] was based on the ancient normative reference MB-26: 1940 (Brazilian Standard NBR 6230) which determined different specimens dimensions on bending test, conditioning to another calculation model (Timoshenko’s beams theory) and not to the one used by the Brazilian standard (Euler Bernoulli’s beams theory). In this context, this research aimed to investigate, through Analysis of Variance (ANOVA), the effectiveness of the relations among stiffness properties prescribed by the Brazilian Standard for hardwoods, as well as verifying, through regression models, the possibility of estimating Ec0, Et0 and EM by of density at 12% moisture content (ρap,12%). To this end, defect-free specimens from ten hardwoods species were adopted. The ANOVA results showed that Ec0 and Et0 were statistically equivalent, and relation between EM and 0.90∙Ec0 was not statistically equivalent, implying the determination of the ideal coefficient equal to 0.98 by the least squares method. This coefficient was 8.89% higher than the Brazilian standard. In addition, all regression models tested were significant and with well adjust. The linear regression model resulted in the best fit in the estimate of Ec0(ρap,12%) and Et0(ρap,12%) with coefficient of determination (R²) equal to 80.71% and 84.95%, respectively. While the logarithmic model was the most accurate in estimating the EM(ρap,12%) with R² equal to 86.62%. These results showed the possibility of estimating the stiffness properties by the density at 12% moisture content.
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