An elasto-plastic model for the deformation of dowel-type fasteners based on Johansen’s theory

In timber structures, the stiffness of a connection is of considerable importance in terms of the distribution of forces and deformations within the structural system, and therefore requires an appropriate design method. The existing European standard, and its second generation, provide equations for the prediction of deformation for connections with dowel-type fasteners. However, these empirical equations differ significantly in the influencing parameters from the theory to determine load-bearing capacity according to Johansen. Since that approach is based on ideal-plastic assumptions for the embedment stiffness and the bending moment of the fastener, no deformation can be obtained. This paper presents an extension of Johansen theory, considering an elastic–plastic assumption of the material parameters, which allows to obtain the deformation of the connection considering the same parameters as for the prediction of the ultimate load. These new derived basic equations are solved numerically, resulting in a force–deformation curve that reflects the elastic–plastic behaviour of a given connection. In order to validate this approach, a comparison of the results with experimentally determined curves and with the well-established beam-on-foundation method (BOFM) is presented. The results demonstrate that the extended theory can be employed to achieve outcomes that are highly comparable to those attained by the BOFM. However, minor deviations were observed when the connection configuration was within the transition state between two failure modes. For configurations with a force-fibre angle of α = 60° , the results of the extended Johansen theory accurately describe the initial stiffness but underestimate the force in plasticised areas. This can be attributed to the bedding curve being oversimplified when a rising branch is observed after the timber material’s yield strength is reached. • Extension of the Johansen theory with elastic–plastic material properties. • Multilinear input parameters. • Numerical solution of extended basic equations. • Comparison of numerical solution with results obtained by the beam-on-foundation method.