Analysis of relations between the moduli of elasticity in compression, tension, and static bending of hardwoods

Abstract

Accurate estimation of average modulus of elasticity in compression parallel to the grain (Ec0) is of paramount importance for rational sizing of timber structures, given the use of this property in the estimation of stability of compressed parts (ultimate limit state, ULS) and in calculation of excessive strains (serviceability limit state, SLS). In Brazil, if values cannot be experimentally determined, ABNT NBR 7190 (1997) allows for estimation of Ec0 through relations to average modulus of elasticity both in tension parallel to the grain (Et0) (Ec0 = Et0) and in bending (EM) (Ec0 = EM/0.90). This research aimed to access the efficiency of these relations by testing 30 tropical wood species. The analysis of variance results showed that Ec0 and Et0 were statistically equal. However, Ec0 and EM/0.90 were not statistically equal, and the method of least squares resulted in a coefficient of 0.98, which was 8.89% higher than the one suggested by ABNT NBR 7190 (1997) and close to 1, thus, validating the results of ANOVA, which pointed on the equivalence between Ec0 and EM (Ec0 = EM). As an alternative to simplified equations of the standard, two-parameter regression models were used. The geometric model with R² = 91.67% proved to be the model of best fit, which demonstrated that Ec0 could be calculated as a function of EM.