Modeling spatial variability of localized lumber properties

Abstract

The primary objective of this research was to develop stochastic models of localized modulus of elasticity (MOE) and tensile strength (T) for laminating lumber. Detailed information on the variability of localized MOE and T is needed for Monte Carlo simulation models that predict the reliability of glued-laminated beams. Spatial variability of localized MOE and T was investigated for two high quality visual grades of Douglas fir laminating lumber: 302-24 and L1. Research results indicated that MOE and T varied along the length of the lumber specimens with significant spatial correlations between these localized values. A model was developed for simulating the spatial variation in MOE and T for 8-ft long lumber. This model simulated random vectors of correlated localized MOE and T from a multivariate normal distribution. These multivariate normal vectors were then transformed so that the individual segment M0E's and segment T's had the correct univariate probability distributions. This transformation preserved the univariate probability distributions and the correlation matrices for localized MOE and T. The model was also used to predict long-span tensile strength. Simulated long-span tensile strengths agreed well with actual long-span tensile test results and confirmed the existence of a tensile strength-length effect. The original model was modified to simulate localized MOE and T for lumber up to 26-ft in length. This embellishment required the expansion of the original correlation matrices. These matrices were expanded by assuming that the spatial correlation functions for MOE and T followed autoregressive processes. The embellished model also preserved the probability distributions of localized MOE and T and the expanded correlation matrices. A secondary research objective was to evaluate a stress wave technique as a means of collecting field measurements of localized MOE. Localized stress wave velocity was used to calculate stress wave MOE. Although stress wave MOE was highly correlated to bending MOE, there was not a one-to-one correspondence between the two quantities. Correlation between stress wave MOE and bending MOE agreed with previous research results. A bending test, if feasible, would be a more accurate method of determining information on the spatial variability of MOE.