Strength of Shape-Adhesive Joints

Strength of Dowel Joints

Joints with dowel connectors are particularly recognised in furniture due to the many significant benefits, including:

• reducing material consumption by the size of tenons,

• the simple technological process,

• the uncomplicated construction.

The literature on the subject recognises the model of a bent 2-D angular dowel joint (Fig. 6.50) (Dzi^gielewski and Smardzewski 1995; Smardzewski 1998a). This model assumes that the total load is transferred only by the dowels, while there are no interactions between the connected elements. The bending moment in this case can be broken down into two equal, in terms of value, normal forces acting in the axes of the dowels; therefore, the neutral axis of bending is in the middle of the distance between the dowels. Then, the strength conditions of a structural node can be expressed as follows:

shearing strength of the dowels:

4T

nnd2 ’

bending strength of the dowels:

M, d

jy ^kd > where

J = 2(ja + Aa2), pd2 pd4

A = T ’ Jo = 64 ’

hence,

,d 16M

kg – Pd4T4Pd2C2(c + d);

where

M, T bending moment, cutting force, d dowel diameter,

a distance of dowel axis from the neutral axis,

c spacing between the dowel axes,

p distance of extreme fibres from the neutral axis, n number of connectors,

kd shearing strength of the wood,

kg bending strength of the wood.

By choosing the greater diameters d of the calculated values, we proceed to determine the length of a dowel. It depends mainly on the strength of the glue-line, which occurs on the side of the dowel, on the wall. The state of loading a dowel with normal forces is illustrated in Fig. 6.50. It shows that the maximum normal force concentrates only in one dowel and amounts to:

N M

Nmax = + ; (6.160)

2 c

where

N normal force.

Therefore, we calculate the shearing stress for the smaller length of the dowel embedded in the two elements, by using the equation:

from which we determine the length of the dowel:

where

kk shearing strength of the adhesive glue-line, whereby

where

L length of the dowel.

The conditions adopted in the model are met when between the joined elements there is a gap preventing or limiting immediate contact of the elements, or when the load of the node is insignificant in relation to the stiffness of the glue-line. The results in accordance with the above analytical description were obtained in the works (Smardzewski and Dzi^gielewski 1994; Smardzewski 1990). However, in these works, only those connections specified in the range of loads were studied, not providing, in both cases, what part of the interim strength of the joint was constituted by the upper limit of the applied force. Additionally, the authors (Smardzewski and Dzi^gielewski 1994) reported that in the studied samples, due to technological reasons, there was a gap between the connected elements.

As can be seen from the author’s studies, as the load value gets closer to the interim strength limit of the joint, there is a displacement of the neutral axis of bending in the direction of the lower part of the joint. Such a state of the structural node takes into account the mathematical model for which the scheme of forces is shown in Fig. 6.51. Then, contact stresses arise between the joined elements, the resultant of which is as follows:

Qn = 4xzhdy. (6.164)

where

dy the width of the contact surface.

This value remains in close connection with the location of the neutral axis z and the distance of the resultant Qn from the centre of the distance between the dowels:

Qn(t – z) = Nm2(z + 0.5c) + Nmi(z – 0.5c), (6.165)

while the location of the neutral axis is expressed by the equation:

2QJ c(Nm2 Nm1)

Nm2 + Nm1 + 2Qn

where in turn

qxz (0.5Й1 – z)2dy = M.

The strength conditions in such a model can be expressed as follows:

k > —

k > nd2 ’

k > 2;5N+M

‘ 0;5ndL

A further build-up of the load leads to a case where the growing stress between elements is focused along the lower edge of the contact surface of the elements (Fig. 6.52).

When considering the system of forces in the plane XZ, such a stress can be expressed as a reaction Qn of a spring of the stiffness k. Then,

Qnz = Nm-(0;5c + 0 ; 5hi – z) + Nmi(0;5hi – 0 ; 5c – z), (6 ;171)

Qnz = M,

while the strength conditions are in accordance with the previous equations.