Use of lower tolerance limits for designing chair frames with round-end mortise and tenon joints

Abstract

In this study, the reliability of the mortise-tenon (MT) joints was examined experimentally and numerically. The joint strength has been determined empirically and numerically, but the reliability of the joint does not rely on a single asset - mean and standard deviation. The prediction of its strength also refers to a single value in the future population, but tolerance limits are related to a portion of the future population. Therefore, ensuring joint reliability comes into prominence not only for empirical data but also for theoretical and numerical analysis. For this purpose, the moment capacity of the T-shaped MT joints constructed of white oak was determined, and the lower tolerance limits (LTLs) approach was used to construct confidence/proportion (gamma/beta) levels for reliability. According to the results, the moment capacity of the MT joints was 341 Nm. The LTL values at 0.95/0.95, 0.99/0.95, 0.95/0.99, and 0.99/0.99 gamma/beta levels were 231, 226, 187 and 181 Nm, respectively. The normal stresses at each gamma/beta level were calculated based on the moment capacity and tenon sizes and were compared with the finite element method (FEM). Experimental and numerical results varied from 0.3% to 13.4%. Furthermore, a side frame was imposed to a vertical load of 1000 N on the front leg, and the moment of the joint on the side rail to the back post was measured (196 Nm). The side frame was modeled on ABAQUS - FEM software - and subjected to a moment of 196 Nm on the side rail. The theoretical and numerical results of stresses on joints differed from - 4.3% to 5.8%. The study showed that the reliability value is known, and; the joints could be designed by using FEM.