ultimate bending strength and stiffness under compression test of

ultimate bending strength and stiffness under compression test of

1
ULTIMATE BENDING STRENGTH AND STIFFNESS UNDER
COMPRESSION TEST OF END CORNER MITER JOINTS CONSTRUCTED
OF SOLID WOOD
Vassil JIVKOV
Assia MARINOVA
INTRODUCTION
One of the strongest and most permanent joints made in carpentry and cabinet-making,
where pieces of wood are fastened together, is the miter joint. The miter joint is a good way of
efficiently joining wood and wood related materials like MDF, plywood, particleboard, etc. A
cabinet with a face frame with miter joints immediately conveys a high level of quality and
craftsmanship. Solid wood frame is a good solution for many other furniture structures like frames
for upholstery furniture or bed support frame and therefore the strength of joints is of first priority.
There are many studies dealing with strength and stiffness of joints constructed of wood.
Some studies has been carried out for dowel joints [2,4,5,6,14,16] and other for mortise and tenon
joints [1,3,7,8,9,10,11,13,15]. But very less data was found for the strength of miter joints [4]. Most
of researchers have tested T-type joints and not end corner joints. Miter joints could be constructed
in traditional way like dowels or mortise and tenon or in specific way with dovetail joints.
This study was carried out to establish more information about bending strength and
stiffness coefficient under compression test of different miter joints constructed from different wood
species, designed for use in wooden cabinet doors or other furniture frames.
MATERIALS AND TEST METHODS
All specimens for this study have been made from alder, pine and walnut wood. Four types
of end corner miter joints constructed with open mortise and tenon; two-pin dowels, plastic dovetail
keys with glue and plastic dovetail keys without glue. Polyvinyl acetate glue has been used for
assemble of joints. The type, shape, and dimensions of test samples are shown in Figure 1.
All specimens have been tested under compression bending test (Fig. 2). The specimens’
sizes are given in Figure 2a.
Figure. 1. Typ,e shape and dimensions of test samples.
For each type of joints 10 samples were manufactured. The samples were tested under
compression bending loading in the Laboratory for Furniture Structural Design at the University of
Forestry, Sofia, using the universal testing machine FP 100. The requirement of a static loading that
the time for the testing of each sample had to be within the interval of 60±30 s was met.
The type, dimensions and scheme of loading and deformation of the tested samples under
compression bending loading are shown in Fig. 2.
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Figure 2. Dimensions, type of loading and deformation of the tested samples
The samples were loaded step by step in the compression bending test. For each value of the
loading forces has been measured the change of the distance between the applied points of the
forces and have been determined the changed under loading angle between the arms of the joints
and the changed arm of bending, as well. The loading has been applied in the range corresponded to
the linear section of the curve expressed the relationship between the bending moment and the
semi-rigid rotation of the joint. In accordance with the results of the previous investigations this
linear section of the curve corresponds approximately to the range of 20% to 60% of the failure
bending moment.
As it can be seen on the Fig. 2 b, c, in the compression bending test both the right angle
between the two arms of the joints and the arm of the bending forces l were changed. The linear
displacement f i of the applied points of the loading forces Fi has been measured for each test
sample at each level of the loading. It is a sum of a displacement as a result of rotation of the arms
of the joint and an additional displacement ∆ i as a result of bending deflection of the arms (See
Figure 2 b). The displacement ∆ i has been calculated by the formula
(1)
∆i =
Fi a 3
,
3EI
where:
Fi is the magnitude of the loading forces in the compression bending test, N;
а - the axial length of the joints arms (Fig. 2), m, ( а =141,4 mm);
E - the modulus of longitudinal elasticity, N/m2;
I - the axial moment of inertia of the cross-section of the joints arms, m4,
which has been calculated by the formula
(2)
I=
δb 3
12
,
where:
b is the width of the arms, m, ( b =50 mm);
δ - the thickness of the arms, m, ( δ =20 mm).
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The distance between the applied points of the forces (Fig. 2 b, c) at each level of loading
has been determined by the expression
(3)
Li = L − f i + ∆ i ,
where before the deformation of the samples the size L = 200 mm (Fig. 2 a).
The changed under loading angle α i between the joints arms has been calculated in radians
by the formula
(4)
α i = 2 arcsin
Li
L − fi + ∆i
.
= 2 arcsin
2a
2a
The changed arm of bending l i has been determined by the expression
(5)
l i = a cos
αi
2
.
As a result of deformation through the compression bending test the semi-rigid rotation in
radians of the arms of the joints is
(6)
γi =
π
2
− αi .
For each value of the loading force Fi the bending moment of the joint in [Nm] has been
calculated by the formula
M i = Fi l i .
(7)
The stiffness coefficient c i [Nm/rad] in the compression bending test has been calculated by
the formula
ci =
(8)
∆M i
.
∆γ i
In (8) have been used the symbols
(9)
∆M i = M i − M 0 ,
∆γ i = γ i − γ 0 ,
where in the compression tests M i and γ i have been determined according to (7) and (6),
respectively, for the value of the loading force Fi , and M 0 , γ 0 - according to (7) and (6) for the
starting magnitude of the loading force F0 .
The stiffness coefficient с as a stiffness characteristic of the corner joint in the compression
test has been determined as an average value of the obtained from (8) values for each sample at
each level of loading in the range of loading corresponded to the linear section of the curve
expressed the relationship between the bending moment and the semi-rigid rotation of the joint.
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The testing of each sample has been extended until the failure load was reached. The
ultimate bending moment can be calculated by the formula (7) with the maximum value of the
loading force. In this way, by the testing of the samples at the same scheme of compression loading
can de determined simultaneously the strength and the stiffness characteristics of the joints.
RESULTS AND ANALISIS
The results of bending moments under compression test are given in Table 1.
Results from the test indicate that type of joints and type of wood species have considerable
influence on the ultimate bending strength. Highest bending moment has joint constructed with
open mortise and tenon of walnut 284.8 Nm. This is due to two reasons. First, this is because of
huge gluing area in this joint. On the other hand walnut wood has the best mechanical properties in
comparison with other wood species. Typical type of failure of open mortise and tenon joints can be
seen in Figure 3. In most of test samples the joint failed due to a split failure of the tenon.
Figure 3. Type of failure of end corner miter joints with open mortise and tenon
The next highest ultimate bending moment with approximately 31-32% lower strength is
determined in the corner joint constructed of walnut wood with two-pin dowel joints (196 Nm) and
in the one constructed again of walnut wood with dovetail key joint (195.2 Nm). Close in
magnitude is the ultimate bending moment of alder wood corner joint with open mortise and tenon
joints with 191.5 Nm. The following group has 38 to 52% lower bending strength and consists of
joints with ultimate bending moment from 136.8 to 179.6 Nm. These joints are constructed of pine
and alder wood with open mortise and tenon, two-pin dowels and dovetail key joints. All joints
constructed with dovetail keys failed due to shear failure in the area of the dovetail key (See Figure
4).
Figure 4. Type of failure of end corner miter joints with dovetail keys
The results for joints bending strength indicate clearly that dovetail joints with unglued keys
are very weak and they should be recommended only in case of usage in none-load-bearing frames.
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Table 1. Ultimate bending moments and stiffness coefficients of tested end corner joints
from 3 different wood species under compression tests
Type of joints/
Wood species
Ultimate bending moment, М
Coefficient of
Mean x , Nm
variation v, %
I. End corner miter joint with open mortise and tenon:
1. Alder
191,5
11,1
2. Pine
179,6
9,3
3. Walnut
284,8
9,5
II.: End corner miter joint with two-pin dowels:
4. Alder
174,9
9,9
5. Pine
144,5
7,4
6. Walnut
196,0
12,1
III. End corner miter joint with dovetail keys with glue:
7. Alder
160,6
15,0
8. Pine
136,8
14,8
9. Walnut
195,2
11,3
IV. End corner miter joint with dovetail keys without glue:
10. Alder
73,1
14,6
11. Pine
58,8
18,0
12. Walnut
103,5
5,3
Stiffness coefficient, с
Coefficient of
Mean x ,
variation v, %
Nm/rad
4252,3
3475,2
5416,4
17,9
17,8
17,9
4965,3
3689,5
6385,4
15,4
13,6
15,7
4181,0
3251,5
6211,0
17,7
19,0
14,4
2268,9
1459,6
2561,8
19,2
18,7
13,0
Ultimate bending strength
300
250
200
Nm 150
Alder
Pine
100
Walnut
50
0
I
II
III
IV
Type of joints
Figure 5. Ultimate bending moments of end corner miter joints constructed of alder, pine
and walnut wood. I - open mortise and tenon joint; II – two-pin dowel joint; III – dovetail key joint
with glued key; IV – dovetail key joint with unglued key
A clear relationship between ultimate bending strength and stiffness coefficient can be
observed in the test results. Stiffness coefficient of joints follows the trend from ultimate bending
strength with some exceptions. Two-pin dowel and dovetail with glued key joints constructed of
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walnut have higher strength compare to open mortise and tenon joints. Also two-pin dowel joints
have higher stiffness in comparison to open mortise and tenon joints.
Stiffness coeficients
7000
6000
5000
Nm/rad
4000
Alder
3000
Pine
2000
Walnut
1000
0
I
II
III
IV
Type of joints
Figure 6. Stiffness coefficients of end corner miter joints constructed of alder, pine and
walnut wood. I - open mortise and tenon joint; II – two-pin dowel joint; III – dovetail key joint with
glued key; IV – dovetail key joint with unglued key
CONCLUSIONS
From the results of this study for evaluating the ultimate bending moment and stiffness
coefficient under compression test of end corner miter joints constructed from alder, pine and
walnut wood following conclusions can be done:
1. Type of joints and type of wood species have considerable influence on the ultimate
bending strength and stiffness of tested end corner miter joints.
2. Highest ultimate bending moment and stiffness were obtained with joints constructed of
walnut wood.
3. Open mortise and tenon joints showed the highest ultimate bending strength among the
four types of joints tested within each wood species.
4. No significant difference in bending strength and stiffness was observed among two-pin
dowel joints and dovetail joints with glued keys.
5. The application of dovetail miter joints with unglued key should be very limited because
these types of joints showed three times lower strength and stiffness among all evaluated joints.
6. The results of this study on bending moments and stiffness coefficient under compression
test of end corner miter joints can be used for norm and strength design of furniture and other
structural elements, for furniture construction analyses and for quality control.
References:
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Author's addresses:
Vassil Jivkov, Associate Professor
Assia Marinova, Associate professor
Department of Furniture and Interior Design
University of Forestry
Kliment Ohridski Blvd 10
1756 Sofia
Bulgaria
e-mail: [email protected], [email protected]
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