Modeling glulams in linear range with parameters updated using Bayesian inference

A stochastic hierarchical model of a glued laminated timber beam loaded in bending is formulated in this paper. Being attributed to the limited number of observed data the model captures both the inherent variability of the elastic properties of individual timber boards making up the laminated beam and the uncertainty of the parameters controlling their probability distributions. Apart from the deflection measurements obtained from the full scale displacement-controlled, four point bending tests the model also incorporates the data from numerous nondestructive macroindentation measurements. The forward deterministic model of laminated beam is based on the Mindlin beam theory combined with the finite element method to simulate the laboratory measurements numerically. The inference of the model parameters is performed in the framework of Bayesian statistics. Apart from improved posterior distributions of material data, we also offer an improved formula for estimating the longitudinal elastic modulus from indentation measurements.