## 5 Conclusions  
Through the on-site survey of a Chinese traditional timber structure, the probability analysis of the gap value and four typical gap values are determined. The full-scale mortise-tenon joint under different loose conditions, the following conclusions can be drawn:  
1. The gap is primarily distributed within the 5-15 mm range, the proportion of joint with this gap value reaches 44%. Four typical gap values including 5 mm, 10 mm, 25 mm and 50 mm are selected to study the effects of the gap on the mechanical properties of the PMT joint;
2. The loose joint slips firstly when subjected to repeated loads. Once the tenon overcomes the free rotation angle, the mortise and tenon compress together. The predominant deformation of the joint is the partial pulling out of the tenon, and the contact portion between mortise and tenon has noticeable compression deformation. The failure stage is characterised by wood fibre tearing at the variable cross-section of the tenon at the negative loading. No obvious compression deformation of the column, fang and mortise occurs;
3. The hysteresis curve of restoring moment and rotational angle of LJ-1 and LJ-2 is an inverse \"Z\" shape with obvious pinching effect and the hysteresis loop is asymmetrical. The mortise-tenon joint undergoes slipping, elastic, strengthening and the failure stage in order. Hysteresis curves of the restoring moment and rotational angle of LJ-3 and LJ-4 are shriveled and the sliding length is longer than that of LJ-1 and LJ-2. It is worth noting that mortise-tenon joints mainly rely on compression force to resist external load and friction force to consume energy;
4. The bending bearing capacity and rotational stiffness of loose joints have a certain drop with the increase in gap. The limit angle of the loose joint lags behind that of the regular joint. The rotational stiffness of a loose joint with a large gap is essentially zero during loading, indicating that the mortise-tenon joint has almost no resisting capability. Because its stiffness is low, an acceptable processing method is required to improve the joint's rotational performance under loose conditions. The limitation gap value is given, which can provide a reference to the protection and repair of the traditional timber structure. The proposed three-parameter power function model is noted to be consistent with experimental results, which shows that the proposed model can reflect the mechanical behaviour of joints;
5. The stress states of penetrated mortise-tenon joints with different loose conditions are discussed. Compression deformations are mainly located at the tenon. The smaller the degree of loosening, the greater the stress of the component. If the degree of loosening is large, the stress of joint is very small, indicating that the joint has almost no resistance to external load. [PERSON] and [PERSON] carried out the experiments and investigated their results. [PERSON] and [PERSON] wrote the manuscript in consultation with [PERSON]-[PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript. This work was supported in part by grants from the National Natural Science Foundation of China (Grant NO. 51978038) and the Overseas Expertise Introduction Project for Discipline Innovation (B13002). The study was conducted in accordance with the Declaration of Helsinki, and approved by the Institutional Review Board. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **LJ-1** & **LJ-2** & **LJ-3** & **LJ-4** \\ \hline \(\sigma^{+}_{\text{max}}\) (MPa) & 4.18 & 4.18 & 3.25 & 0.84 \\ \hline \(\sigma^{-}_{\text{max}}\) (MPa) & 4.18 & 4.18 & 1.539 & 0.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The comparisons of maximum Mises stress of joints under different loose degrees. **Informed Consent Statement**: Not applicable. **Data Availability Statement**: Not applicable. **Acknowledgments**: The authors would like to thank the financial support from NSFC and 111 projects. **Conflicts of Interest**: The authors declare no conflict of interest.