Stochastic Model for Localized Tensile Strength and Modulus of Elasticity in Lumber

Localized modulus of elasticity (MOE) and tensile strength (T) were modeled for two visual grades of Douglas-fir laminating lumber. These material property models will be used as input to other structural analysis models that predict the strength and reliability of glued-laminated beams. Tensile strength and MOE are important material properties since most glued-laminated (glulam) timber beam failures initiate in the tension zone. Localized MOE and T exhibited significant within-piece variability as well as between-piece variability. These localized properties were also spatially correlated. A method that uses a transformation of the multivariate normal distribution was developed to simulate these localized properties for lumber up to 8-ft long. This method preserved the probability distributions of localized MOE and T as well as the spatial correlations between the localized property values. Procedures were described for expanding the model to simulate boards of any length. The method was also used to simulate long-span tensile strength. Mean simulated tensile strengths compared favorably with test results. Test results also confirmed a reduction in tensile strength as test span increased.