## 4 Discussion Statement
### Stress State of the Loose Joint  
The penetrated mortise-tenon joint with different loose conditions are established by ABAQUS. The size and load of the FEM are same as the experimental models. The elastic-plastic model is needed in this model as it is hard to observe plastic deformation in ABAQUS with the FEM with the orthotropic material. Material parameters of the timber parallel to the grain are applied to the column, and material parameters of the timber perpendicular to the grain are applied to fang. The mortise mainly depends on the timber parallel to the grain and the tenon depends on the timber perpendicular to the grain to bear compression force. The stress-strain relationship can be simplified to the bilinear constitutive model [27]. Column and fang are assigned with different material properties separately. Column and fang are divided into different parts to mesh. The discretisation of both column and fang consists of 8-node hexahedral finite elements (element C3D8R of ABAQUS), as this element can avoid the \"hourglass\" phenomenon. In this simulation, the contact pressure is calculated by using the hard contact model implemented in ABAQUS. The friction coefficient is taken as 0.5 [28]. The interaction type of the mortise and tenon is defined as the surface to surface contact with finite sliding. The boundary conditions are shown in Figure 28. The FEM of LJ-2 is subjected to the verification of corresponding experimental results [27]. Figure 27: Curves of restoring moment and rotational angle. (a) LJ-1. (b) LJ-2. (c) LJ-3. (d) LJ-4. The stress nephogram and deformation of LJ-1, LJ-2, LJ-3 and LJ-4 at the 120 mm loading level are extracted and shown in Figure 29. It can be seen that the main deformation occurs to the tenon, and stress of the right side of the tenon is high due to mutual interactions of the mortise and tenon. It is noted that significant compression deformations are mainly located at the tenon. Figure 28: Boundary conditions. Figure 29: Cont. In addition, it can be seen that the stress of LJ-1 and LJ-2 are maximum. The compression area of LJ-1 is bigger than that of LJ-2. The stress of LJ-4 is the minimum. The stress of LJ-3 takes second-place. The elements exhibiting the maximum stress under positive and negative loading are located at the tenon necks on both sides of the lower tenon. In the experiment for specimens, the failure of the tenon is due to a crack located at the tenon neck under the tenon, which means that the numerical prediction is in agreement with experimental evidence. The stresses of the column and fang body are lower than that of the tenon and mortise, which corresponds coincidental with the experimental phenomenon. The loose condition can impact the stress state of the loose joint. The smaller the degree of loosening is, the greater the stress of the component is. 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. The maximum missed stresses of joints are listed in Table 5. \(\sigma_{\text{max}}^{+}\) and \(\sigma_{\text{max}}^{-}\) are the maximum missed stresses under positive and negative rotations. The maximum stresses of the LJ-1 and LJ-2 are almost equal. It shows that the mortise and tenon of the two joints have experienced sufficient mutual compression. The maximum stresses of the LJ -3 under positive and negative rotation are 3.25 MPa and 1.54 MPa, which are 22.2% and 63.8% lower than that of LJ-1. It is noted that the gap weakens the mutual compression of the mortise and tenon. The maximum stresses of the LJ-4 under positive and negative rotation are 0.84 MPa, which are 80% lower than that of LJ-1. It is noted that the gap strongly weakens the mutual compression of the mortise and tenon. Additionally, necessary measures should be taken to repair the loose joints. Figure 29: Stress nephogram of loose joints. (**a**) Positive loading of LJ-1. (**b**) Negative loading of LJ-1. (**c**) Positive loading of LJ-2. (**d**) Negative loading of LJ-2.