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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2. Semirigid joints 2.1. MT joint

The MT joint is commonly used for connecting the column and beam in heritage Chinese timber structure. The tenon at the end of beam is placed inside the mortise directly as shown in Fig. 2. The frictional slip-contact behavior is allowed between the tenon and mortise in the plane of the MT joint under external loads. There are three degrees of freedoms (axial, vertical and rotational directions) for the mortise-tenon joint, and the compressive and frictional forces would be generated at the contact interface between the mortise and tenon with relative rotation as shown in Fig. 3, The equilibrium equation in three directions in Fig. 4 can be obtained as (Yang, 2020) { = − 1 + 1 + 2 + 2 + 3 + 3 = 1 − 2 + 3 − 3 = 1 1 + 1 1 + 2 2 + 2 2 + 3 3 + 3 3 (1) where 1 , 2 and 3 are the compressive forces derived from compressive deformation volumes V t1 and V t2 at the tenon and V at the column, 1 , 2 and 3 are the corresponding frictional force at the contact surfaces. 1 , 2 and 3 denote the lengths of the moment arm of the forces 1 , 2 and 3 relative to the center of rotation at Point O 2 . 1 , 2 and 3 lengths of the moment arm of the forces 1 , 2 , and 3 relative to the center of rotation in Fig. 3(c) (Yang, 2020).

Line5

C(C x ,C y )

Beam

D(D x ,D y )

V t1

Line6

B(B x ,B y )

Line4

P f1

A(A x ,A y )

y

P C1

Line1

o 2 (X,Y)

Line2

x

P

h t

h m

o 1 (0,0)

¦ È

P C2

N

E(E x ,E y )

h b

Line3

P f2

Tenon

M

F(F x ,F y )

V t2

Line7

G(G x ,G y )

Mortise

J(J x ,J y )

P f3

H(H x ,H y )

N(N x ,N y ) M(M x ,M y ) V c

P C3

l t

K(K x ,K y )

Line8

Column

Figure 3 - geometry of compressive deformation of MT joint

a

b

c

Beam

Beam

Beam

V t1

V t1

V t1

P f1

P f1

P C1

y

P C1

y

y

P C1

o 2 (X,Y)

x

o 2 (X,Y)

o 2 (X,Y)

x

x

o 1 (0,0)

¦ È

P C2

o 1 (0,0)

¦ È

o 1 (0,0)

¦ È

Tenon

P C2

P C2

Tenon

Axial force

Tenon

Vertical force

P f2 P f3

V t2

V t2

Mortise

V t2

Bending moment

Mortise

P f3

Mortise

P C3

P C3

P C3

Column

V c

Column

V c

Column

V c

P f3

Figure 4 - compressive and frictional forces due to external forces in (a) axial; (b)vertical; (c) rotational directions