A simplified bilinear <i>M-θ</i> theoretical model for through-tenon joints in historic Chinese wooden structures

The through-tenon joint (TTJ), exhibiting semi-rigid behavior, serves as a pivotal connection component in historic Chinese wooden structures. However, in engineering applications, research on simplified mechanical models applicable to this joint is still insufficient. Based on the wood embedding and compressing theory and mechanical characteristics of tenon joints, this study formulates geometric relationships, physical relationships, and equilibrium equations governing the joint under bending loads, and derives the M-θ theoretical model via solving simultaneous equations. Subsequently, the theoretical model is simplified using Taylor’s formula, and a simplified M-θ bilinear theoretical model of the TTJ is proposed. Through comparative analysis with test data and finite element models, the accuracy and applicability of the proposed model are verified, which can provide theoretical support for new construction and renovation of traditional wooden structures. On this basis, the research further conducts parametric analysis on the joint dimensions. Results show that increasing tenon width and height has the most significant effect on improving the yield and peak moment and delaying its yielding and failure, while the increase in the initial gap of the joint lead to a decrease in the yield and peak moment. Based on these conclusions, references for preliminary design or parametric analysis can be provided for engineering.