Glued-in-rod timber joints: analytical model and finite element simulation

In this paper, a closed form analytical solution for glued-in-rod (GiR) joints is derived by solving the governing differential equations and accurately applying the boundary conditions in a cylindrical coordinate system for a GiR joint comprising of a rod, adhesive (glue) and timber. The results of the analytical model are compared with 3D continuum finite element simulations and it is shown that the closed-form solution developed can estimate the stress distribution in the adhesive and adherents (rod and timber) with good accuracy. Furthermore, the stiffness of GiR timber joints can be obtained from this analytical model. Closed-form solutions for pull-pull and pull-push test setup configurations are compared and it is shown that the maximum shear stress in the adhesive-adherent interface in a pull-push configuration is around 20% higher than that of the pull-pull counterpart. The typically (around 20%) lower strength of GiR joints in pull-push experiments compared to that of pull-pull tests can be attributed to this higher maximum shear stress which is predicted by the analytical model. A parametric study is carried out using the FE and analytical models and the effects of different variables on the distribution of stresses in the adhesive and adherents are studied.