Variation of mechanical properties in oak boards and its effect on glued laminated timber : application to a stochastic finite element glulam strength model

Abstract

The renewable material wood and hereof derived structural engineered wood products (EWPs) is widely acknowledged as being the major pillar of sustainable building construction. Due to the strongly increasing demand and technical assets the wood resource hardwoods, previously less used as compared to softwoods, is gaining a high momentum for EWPs. Here, the species white oak (Quercus robur, petraea) representing beside beech (Fagus sylvatica) the largest hardwood stocks in Europe is investigated. This work addresses the need of improved understanding and modeling of the variability of stiffness and strength along and between boards and the resulting impact on the size-effect of glued laminated timber (GLT) made of oak. A set of 53 oak boards (Quercus robur) was used to study the variation of mechanical properties along the board's main axis. For each board, detailed information regarding size and position of knots was obtained, which was then used to digitally reproduce the geometry of the knots. The modulus of elasticity (MOE) parallel to the fiber was measured in tension along each board in 15 consecutive segments of 100 mm in length. The boards were tested in tension until failure and the remnants were then tested in secondary tension tests, when possible. Thus, multiple values for tensile strength were obtained per board. Based on the MOE results, a first order autoregressive [AR(1)] model for the simulation of local MOE profiles within board was developed. The model considers the non-stationarity of the MOE profiles by means of a two step method. Firstly, a Gaussian AR process is conducted and then mapped to the normalized MOE distribution. In a second step, the result in scaled to fit a specified global MOE value. The tensile strength data was analyzed by means of survival analysis, where different parametric and regression type statistical models were fitted. The tensile strength models were coupled to the localized MOE AR(1) model by means of a cross-correlation coefficient, thus obtaining a modified vector autoregressive (VAR) model for the local MOE and tensile strength along board. Numerical simulations with the fitted tensile strength models predicted a relatively high size effect, i.e. length effect, characterized by a size-effect exponent of around 0.23 at the 5%-quantile level. A stochastic finite element model for the analysis of GLT beams was developed. The model considers the local variation of mechanical properties within each lamination, simulated by the derived VAR model, as well as the stochastic distribution of finger-joints connecting adjacent boards. A simple energy-based failure mechanism is considered for the evolution of tensile damage in wood and finger-joint elements. The model was calibrated with experiments of oak GLT beams of three different cross-sections tested at the MPA, University of Stuttgart, and then applied to simulate a second database of oak GLT beams tested at FCBA, France. The results obtained with the model are in good agreement with the experiments. In particular, the size effect of beam depth is correctly represented. The influence of the used material models for wood and finger-joints was analyzed parametrically. It is shown that the lower tail of the local tensile strength distribution, which can be estimated rather accurately by survival analysis dominates the GLT bending strength. This is fortunate, as the lower tails can be estimated by means of survival analysis in a rather accurate manner, while the upper tails require further assumptions. The author hopes that the presented work contributes to stimulate the discussion on modelling of structural timber elements made of hardwoods.