Probability models that relate nondestructive test methods to lumber design values of plantation loblolly pine

Abstract

Within-grade variability in mechanical properties for visually graded lumber has led to increased deployment of nondestructive testing (NDT) methods, even though the relationships between static bending and NDT-predicted values are often highly variable. Dynamic modulus of elasticity (MOE dyn) was measured using two acoustic velocity instruments and one transverse vibration instrument, along with specific gravity, for 819 pieces of visually graded loblolly pine lumber. Static modulus of elasticity (MOE) and bending strength (F b) were measured via destructive testing. The probability of meeting design values was compared using (1) normal distribution linear and power regression models and (2) binomial distribution logistic regression models; the parameters of both models were fit using maximum likelihood estimation. For the normal distribution models, the standard error of the estimate, which ranged from 1.28 to 1.82 GPa for MOE and 4.47 to 5.07 MPa for F b, was incorporated into predictions in order to calculate the probability of meeting design values. At 50 per cent probability, transverse vibration MOE dyn values of 10.9 (normal) and 11.0 (binomial) GPa would meet the No. 2 MOE design value (9.7 GPa). At probabilities of 75 per cent and 95 per cent, the required values were 12.1 and 13.8 (normal) GPa and 12.0 and 13.5 (binomial) GPa, respectively. The normal and binomial approaches required similar NDT values to meet thresholds, although the advantage of the normal approach is that the regression parameters do not need to be recalculated for each threshold value, but at the expense of increased model complexity.