Analysis and design of timber-to-timber connections based on the lower bound theorem of the theory of plasticity

Abstract

Over the last few years, the structural analysis of timber elements in relation to the service state has evolved significantly. Indeed, several static calculation procedures have been developed. On the contrary, no standard procedure has been developed to support the static calculation concerning the ultimate limit state of timber elements, which focuses on the definition of the collapse load. Indeed, in the structural analysis of the service state, many factors influencing the ultimate limit state are not adequately considered. The paper discusses the development of the static calculation procedure of the ultimate limit state of timber structures. The ultimate limit state is determined with the support of the theory of plasticity, and particularly through the lower bound theorem. At first, the yield conditions of timber are developed. The yield conditions, governed by a few material-related parameters, are composed of different regimes, each representing a different failure mode. By introducing anisotropic yield conditions, the plastic theory allows considering the anisotropy of the material effectively. Afterwards, the defined yield conditions are implemented in the analysis and design of interlocking timber-to-timber connections. The use of the theory of plasticity allows determining in an illustrative way the respective stress state in the element, thus facilitating the proper development of the connections and the integration of structural performance with additional requirements (e.g. assembly).