PSI - Issue 37

712 Pan Yu et al. / Procedia Structural Integrity 37 (2022) 706–713 Pan Yu / Structural Integrity Procedia 00 (2021) 000 – 000 7 for validation of the proposed beam element model of this timber frame. It is modeled only by the C3D8R elements with size 25 × 25 × 25 mm 3 near the MT joints, 25 × 25 × 50 mm 3 and 50 × 50 × 50 mm 3 for the rest of the frame and stone bases.

Figure 8 - solid model of timber frame from ABAQUS The lateral force-displacement relationship of the two models is presented in Fig. 9, the two results have a basic agreement with each other. There are three critical points shown in the curve, and the corresponding horizontal displacements are 0.011m, 0.105m and 0.199m, respectively. The restoring moments at two CF and MT joints are normalized by the total bending moment at all joints at the same moment, and the proportion of the restoring moments at these joints at the first critical point is shown in Fig.10 (a), the ‘CF1’ and ‘MT1’ denote the left CF and MT joints, and ‘CF2’ and ‘MT2’ denote the right CF and MT joints of the timber frame. The proportion of the restoring moment at left CF is about 0.83, which shows that lateral resistance of the frame is mainly provided by the left CF. The restoring moment of right CF joint is small, this is because the right column dose not rotate until that the lateral loading displacement is 0.011 due to the two horizontal gaps (0.005m); the restoring moments of two MT joints are small, this is because the tenon is not locked inside the mortise in rotational direction due to vertical gaps. The proportion of the restoring moments at the four joints at the second critical point is shown in Fig. 10(b), the restoring moments at left and right CF joints which are basically equal are much larger than those at the two MT joints. The lateral stiffness is negative because of the obvious P- ∆ effect of the two columns with large lateral displacement. The lateral stiffness changes from negative to positive when the lateral loading displacement is larger than the value at the third moment, this is because the tenon starts to be locked inside the mortise in rotational direction. When the loading displacement is 0.199m, there is frictional slip occurring at the left timber column, then the lateral loading ends at this moment. The proportion of the restoring moments of the four joints at the third critical point is shown in Fig. 10(c), the results shows that main components of restoring moment are provided by the two MT joints, the restoring moment at the right MT joint is larger than that at the left MT joint, because the right MT joint is locked earlier in rotational direction than the left MT joint.

(0.199,1.56 × 10 4 )

(0.011,1257)

(0.105,1124)

Figure 9 - lateral force-displacement relationship of the timber frame