An analytical model for embedment stiffness of a dowel in timber under cyclic load

The fundamental part of a dowel-type connection is the embedment of a steel dowel into the timber that surrounds it, and the stiffness of the timber in embedment is represented by the foundation modulus. A standard experimental method for identifying the foundation modulus under static load is modified to assess the secant stiffness exhibited under one-sided cyclic load. It is shown that the steady-state secant stiffness is significantly higher than the static stiffness under initial loading, and that, if the amplitude of the cyclic component of the load is sufficiently small, a simple analytical elastic model predicts the foundation modulus well. The analytical model is based on a complex stress function for the timber in embedment and the frictional interaction between the dowel and the timber. The foundation modulus calculated in this way can be used to predict the stiffness of complete connections for analysis of vibration in frames modelled with semi-rigid joints. Although the application of the model is limited to vibration about a non-zero mean load, with no load-sign reversal, this form of vibration encompasses various important types of in-service vibration of structures, such as that induced by turbulent wind or footfall.