Computational model of adhesive scarf joints in timber beams

The subject of this paper is the general formulation of a model for scarf adhesive joints in timber beams within the framework of plane linear elasticity. It is assumed that wood is orthotropic. The joint can be subjected to a complex loading state including an axial force, a bending moment and a shear force. The joint model is given in displacements by means of a set of four partial differential equations of the second order. Boundary conditions cater for sharp edges in the adherends. Complete solutions to theory of elasticity equations are presented and discussed. The manner in which the joint transmits the axial force, the bending moment and the shear force is presented. It is shown that the scarf joint does not feature stress concentrations and that there exists an approximate equivalence of displacements and stress states in scarf jointed and continuous elements.