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This paper presents the formulation of strain-based finite elements for modelling composite beams with finger joints considering slip between the layers. The finite elements are derived according to Reissner beam theory based on the modified principle of virtual work where the displacements and rotations are eliminated from the problem and the axial deformation, shear deformation and curvature of the layers remain only functions to be approximated within the finite element. Lagrange polynomials are used as shape functions to approximate the deformations and various interpolation methods are applied to numerical examples, with the Lobatto integration scheme giving slightly better results than Equidistant. The experimentally measured mechanical properties needed as input data for the numerical model are given for the four glued laminated beech beams. The numerical model is thoroughly verified and validated. The results show that the presented finite element formulation is an efficient tool for practical and accurate calculations.

Finger joints with standard geometries and adhesives used for joining coniferous wood are not sufficient in terms of strength when gluing beech wood. A numerical model of finger joined beech lamellas was prepared and simulations of tension tests were made. Parametric studies with multiple variables referring to geometrical properties of finger joints and two different types of applied adhesives were performed. The results showed a high influence of the finger joint geometrical parameters. Experimental tests on the tension strength of the finger joints were performed. To validate the numerical model, 20 mm long finger joints were produced and tested. Two types of adhesives were used, MUF and PRF. The finger joints were pressed under two different pressures. Prior to tension testing, the dynamic modulus of elasticity was measured with a strength grading machine and strength grade assignments were made. The influence of joining of the boards on the dynamic modulus of elasticity was analysed. The results of the tension tests of the finger joints showed a clear influence of the finger joint geometry, where highest strengths were obtained with longer and thinner fingers, while the influence of the adhesive seems to decrease with the length of finger joints