Timber-to-timber and steel-to-timber screw connections: Derivation of the slip modulus via beam on elastic foundation model

The aim of this paper is to propose formulations for the slip modulus prediction of timber-to-timber connections (TTC) and steel-to-timber connections (STC) with inclined screws and possible interlayers. The beam on elastic foundation model, previously developed for timber-to-concrete connections, was extended to consider the flexibility of both media where the screw is inserted. Since a significant influence of the fastener diameter on the foundation modulus was observed in tests, an interpolating formula correlating the foundation modulus with timber density and the fastener diameter was derived. The exact solution of the timber-to-timber analytical model was found to agree well with experimental results for total and double thread screws. A parametric study was undertaken to prove that connections with inclined screws have significantly higher slip modulus and lower degradation of performance as the diameter decreases or the thickness of the intermediate layer increases compared to connections with screws perpendicular to the sliding plane. Furthermore, the slip modulus of inclined screws was found to be limited by the weakest timber layer. Closed form expressions for the prediction of the slip modulus were derived by interpolation for the most important cases of technical interest. These formulas can be proposed for the implementations in codes of practice such as the Eurocode 5, since simplified formulas of the slip modulus are currently missing for connections with inclined fasteners and interlayers.