Stochastic FE analysis of stress concentrations in curved glulam beams due to the uncertainty of material direction

When curved glulam beams are subjected to bending, tension perpendicular to grain is introduced. In this work, Monte-Carlo analysis is conducted to study the influence of the annual-ring orientation of individual board on stress concentration in the radial direction. A virtual cutting program is developed which simulates the sawing processes of boards and yields a database of sawn boards, each with a characterized material direction with respect to the pith location. Lamellas are randomly selected from the database to construct curved glulam beams in FE models for Monte-Carlo simulation. Parameters including lumber diameter distribution, taper function, orthotropic elastic properties are considered for four common wood genera in Europe: spruce, pine, larch, and beech. Statistical analysis shows that when the annual-ring effect is considered, the average radial stress in the middle height area of the glulam beams can reach up 1.56 times (even higher on the middle width and height area) compared to the common practice, where wood is usually simplified as transverse isotropic material. Such stress concentration, which can trigger early damage of the structure, indicates an underestimation of stress perpendicular to grain in common practice. Moreover, parameter studies show that the stress redistribution depends not only on the mechanical properties of wood species but also on the width of the board layer.