Out-of-plane cross-angle bending stiffness of cross-laminated timber

The increasing use of cross-laminated timber (CLT) in construction worldwide can be attributed to its combination of sustainability, structural efficiency, biaxial strength and stiffness, short construction times, and architectural flexibility. However, when applied in free-form structures, CLT panels may exhibit irregular element geometries, resulting in deviations from their major or minor strength axes. The required out-of-plane cross-angle bending stiffness is not addressed by commonly used design methods. This study addresses this gap by examining the cross-angle bending stiffness of CLT panel segments using experimental, analytical, and numerical methods. Three different lay-ups (3-ply, 4-ply, and 5-ply) and five cross-angles (ranging from 0 degrees to 90 degrees) were tested under 3-point bending, demonstrating the nonlinear relation between cross-angle and out-of-plane bending stiffness. The lowest stiffness was observed for intermediate cross-angles and not when loaded along the minor strength direction. A proposed analytical model that combines the shear analogy with Hankinson's equation yielded adequate approximations. The model was verified by numerical simulations and then applied to predict the out-of-plane cross-angle bending stiffness of a wide range of CLT layups. This research provides valuable insights for working with CLT in complex geometrical designs, enhancing preliminary design.