Modeling the strength of the mortise-and-tenon joint in the «Seat rail – rear leg» assembly of a wooden chair
DOI:
https://doi.org/10.36930/42265212Keywords:
beechwood; wooden chair; skeletal furniture; mortise-and-tenon joint; seat rail; rear leg; tenon length; tenon thick-ness; maximum failure bending moment; strength; mathematical modelling; regression model; rational geometric parametersAbstract
Ensuring the strength of critical joints in skeletal furniture products is an important task in structural design because the geometric parameters of the joints directly determine the ability of the furniture frame to withstand service loads. The study aimed to establish the relationships between the length and thickness of a single tenon and the strength of the «Seat rail – rear leg» joint of a beechwood chair and to develop a mathematical model for predicting its load-bearing capacity. Tenon length l=25–35 mm and tenon thickness δ=8–12 mm were selected as variable factors. The maximum failure bending moment Mmax, N·m, was adopted as the strength criterion. The experiment was implemented using a two-factor B-plan matrix with five replications for each experimental condition. The mean Mmax values ranged from 170.028 to 211.075 N·m. A second-order polynomial regression model incorporating linear and quadratic effects as well as factor interaction was obtained. A nonlinear extremal relationship Mmax=f(l,δ) was established: increasing the tenon length and thickness initially improves joint strength; however, after a rational combination of the parameters is reached, their further increase does not result in a corresponding improvement in load-bearing capacity. The predicted maximum of Mmax≈212.5 N·m occurs at approximately l=33.2 mm and δ=10.6 mm. Among the experimentally tested combinations, the highest value of 211.075 N·m was obtained for a tenon length of 35 mm and thickness of 10 mm. A rational range of tenon geometric parameters was identified as l≈32–35 mm and δ≈10–11 mm. The established relationships enable a transition from empirical selection of tenon dimensions to predictive design of joint geometry based on the strength criterion and provide a basis for further investigations of the reliability and durability of skeletal furniture structures made of beechwood
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