Bending strength predictions of cross-laminated timber plates subjected to concentrated loading using 3D finite-element-based limit analysis approaches

Cross-laminated timber (CLT) is an innovative wood product with increasing utilisations. It is well known that the orthotropic and inhomogeneous strength properties of wooden boards have a strong influence on the load bearing capacity of CLT plates, especially when the complex wood fibre distribution due to randomly occurring knots is considered. Thus, high safety factors are used in current standards and a generally accepted numerical tool for the strength prediction of CLT plates is still not available. In this paper, we combine recent advances in 3D numerical limit analysis and a knot reconstruction algorithm, where not only the bending strength of CLT plates under concentrated loading is estimated using the numerical approach, but also the scatter of strength properties resulting from the material's inhomogeneities is investigated using a stochastic approach. For the latter, data collected during the grading process of wooden boards are condensed into so-called strength profiles for single wooden boards. The limit analysis approach then allows a time-efficient simulation of a large number of randomly assembled CLT plates. The comparison of the resulting strength predictions to experiments shows good agreement with respect to both the mean load bearing capacity and the statistical scatter of strength.