PSI - Issue 37

Pan Yu et al. / Procedia Structural Integrity 37 (2022) 706–713 Pan Yu / Structural Integrity Procedia 00 (2021) 000 – 000

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3.2. Hybrid finite element with CF joint The bending moment-angle relationship of CF joint is presented in section 2.2, and the rotational stiffness of it is derived by taking the derivative of result in Eq. 2 with respect to the angle . Then the stiffness matrix of the hybrid finite element with CF joint can be expressed as = [ 11 12 13 21 22 23 31 32 33 + 14 15 16 24 25 26 34 35 36 41 42 43 51 52 53 61 62 63 44 45 46 54 55 56 64 56 66 ] (7) where 11 and other notations are the components of the stiffness matrix of the beam element (Yu, 2021). 4. Modeling of the timber frame The timber portal frame serves as a basic lateral-resisting component of heritage timber building, it is established in this section for illustration of modeling of a heritage timber frame. A rigid timber frame model can be directly established through the beam elements as shown in Fig. 7, the rigid frame is assembled by 12 beam elements with 0.75m length. Then the timber frame with MT and CF joints can be obtained by replacing the elements 5 and 8 as the hybrid finite elements with MT joints in section 3.1 and replacing the elements 1 and 12 as hybrid finite elements with CF joint in section 3.2. The vertical and horizontal gaps inside the MT joints are both 5mm. The cross sections of the beam and column are 0.3m × 0.2m and 0.3m × 0.3m , respectively. And the material of the frame is Hemlock with a density of 0.506 3 ⁄ , the more detailed material property of the wood is referred from the literature (Yu, 2021). There are two vertical loads P=35KN at the column heads, the direction of the horizontal load F is along the central axis of the beam.

P=35KN

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Stone base

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Figure 7 - modelling of the timber frame Moreover, a solid element (SE) model with MT and CF joints in ABAQUS as shown in Fig. 8 is also established Rigid frame Timber frame ① ①