191 452 1 SM
191 452 1 SM
191 452 1 SM
Journal of Science
19(4): 191-203 (2006)
www.gujs.org
ABSTRACT
In this study, the strength properties of glued-dowel joined sofa frames constructed of solid wood and wood based
composite materials were investigated. Furthermore, the place of the stretcher was optimized in the side frame of
the sofa. Scotch pine (Pinus Sylvestrs Lipsky) and Turkish beech (Fagus Orientalis Lipsky) were used as solid
wood materials. Oriented strandboard (OSB), okoume (Aucoumea klaineana pierre) plywood (PLY) and medium
density fiberboard (MDF) were used as wood composites. Specimens were tested under static load according to
the principles of TS 9215 by applying both seat and backrest loads which the sofa can be imposed upon in service.
The finite element method was utilized for analyzing the sofa frames. As a result, it has been observed that the
three dimensional structural analysis by means of the finite element method gives reasonable estimates of the
overall strength performances of the sofa frames. Furthermore; it was concluded that the wood composite
materials could be used instead of solid wood materials in the production of the frame construction furniture,
especially in the upholstered seating furniture frames.
Key Words: Frame construction, strength design of furniture, wood composite, finite element method, structural
analysis.
1. INTRODUCTION
Today, the world population is increasing rapidly.
Furniture demand by the customers has developed
parallel to this situation. Gradually, decreasing of the
forest resources requires more efficient use of wood
materials in frame furniture production and better
proofing of the furniture to ensure its durability. Within
this scope, a number of appropriate performance test
methods have been developed for furniture by bringing
up the concep of furniture engineering [1].
Today, strength (engineering) design of furniture can be
accomplished by utilizing solid modeling and structural
analysis softwares. All members of the product can be
modeled parametrically and required changes can
readily be optimized via advantages that are provided
by the solid modeling. Likewise, strength calculations
of the designed product could be made by means of the
computer aided structural analysis software [2].
When the recent studies have been investigated, it has
been seen that the software, especially finite element
method (FEM) have been commonly utilized in
structural analysis of the furniture systems.
*
192
193
Thickness
18
18
18
18
18
18
18
18
194
e.
f.
g.
-
195
I. Type
II. Type
III. Type
Figure 3. Nodes of the sofa frames tested (D1, D2,D3, D4, D5, D6, D7,......D18: Member nodes and / or supports).
In the description of the materials, some technological
properties of the materials utilized for the construction
Table 2. The technological properties of the test materials entered into the program
Modulus of
Modulus of
rigidity (G)
Poison
Thermal
elasticity
(N/mm2)
ratio
conductivity
Material
(E) (N/mm2)
()
(kcal/mhC)
12250
0,05
0,3
0,54
Beech
11760
0,05
0,3
0,54
Pine
7730
0,05
0,3
0,54
PLY
5498
0,05
0,3
0,54
MDF
6530
0,05
0,3
0,54
OSB
In the description of the materials, the sectional
properties of the members that integrate the furniture
system were entered into the program. These properties
are cross sectional area, moment of inertia around (Y)
Jd
Jd
U
K
Density
(g/cm3)
0,65
0,52
0,57
0,69
0,59
Ultimate
bending
strength (e)
(N/mm2)
129,672
73,244
64,998
32,121
32,876
(2.1)
196
Member Type
Cross
sectional
area
(mm2)
1260
1260
Moment of
inertia
(Izz)
(mm4)
514500
34020
Moment of
inertia
(Iyy)
(mm4)
34020
514500
Form
constant for
shearing (SAy)
(SAz)
1,5
1,5
Torsional
constant
(J)
(mm4)
114043
114043
I. Type
II. Type
III. Type
Figure 4. Member codes of the sofa frames (E1, E2,E3, E4, E5, E6, E7, E8, E9, E10, E11...... E27 : Members of the
system)
In the solution phase, firstly the support types (degrees
of freedom constraints) of the points which touch the
floor was determined. As the actual tests, the stump was
supported as pin (pin support), and the back post was
supported as roller (roller support) to the floor. There
are six degrees of freedom at each joint (node). In other
words, all joints can carry the axial forces, shear forces,
and the bending moments.
I. Type
II. Type
Figure 5. Applying the test loads to the sofa frames in the computer program
In the solution part, reaction forces, axial forces, shear
forces, and bending moments acting on each member,
the stress values that occur along the materials of the
solved systems were taken from the program.
III. Type
197
Compression
strength
(N/mm2)
79,1
49,7
37,8
Shear
strength
(N/mm2)
10,3
6,2
8,9
18,7
5,5
16,6
5,6
Bending
strength
(N/mm2)
129,6
73,2
60,2
64,9
24,7
32,1
19,4
32,8
Modulus of
elasticity
(N/mm2)
12250
11760
3413
7730
2290
5498
2450
6530
198
Beech
Pine
PLY
MDF
OSB
I. Type
II. Type
III. Type
I. Type
II. Type
III. Type
I. Type
II. Type
III. Type
I. Type
II. Type
III. Type
I. Type
II. Type
III. Type
Sum of
squares
3917003,200
3851798,578
701701,867
343250,000
8813753,644
Mean squares
F Value
979250,800
1925899,289
87712,733
11441,667
85,5864
168,3233
7,6661
Probably
(p < 0,05)
0,0000
0,0000
0,0000
Table 7. Means comparison of the load bearing capacity values for material types
Force ( N)
Material type
(X)
HG
1622
A
Beech
1318
B
Pine
1397
BC
PLY
1223
C
MDF
731
D
OSB
LSD 103 N
X: Mean value
HG: Homogenous groups
The other important factor for providing a strong
bonding concerning the material is the surface
smoothness. The specific adhesion between the smooth
surface and the glue line can be stronger. It is expected
that the solid wood materials give smoother surface
than the wood composites after processing with the
cutters. For this reason, the adhesion between the solid
wood materials and the glue line is stronger than the
Table 8. Means comparison of the load bearing capacity values for side frame types
Sdie frame type
Force ( N)
(X)
861
I. Type
1557
II. Type
1356
III. Type
LSD 79, 77 N
According to Table 8; it has been found that the
presence of the side slat between the arm and the side
rail and this members place has significantly affected
HG
C
A
B
Although, the I. type and II. type side frames have the
same number of joints, the sofa frames constructed of
III. type side frames gave better performance than the
sofa frames constructed with side frame of I. type.
Hence, the effective properties are as follows; despite
Table 9. Reaction forces occurred in the supports (N)
Material
Direction
D1
0
X
Beech
792,3
Y
0
Z
0
X
Pine
752,6
Y
0
Z
0
X
PLY
757,2
Y
0
Z
0
X
MDF
795,9
Y
0
Z
0
X
OSB
560,3
Y
0
Z
D1: Right back post support
D8: Left back post support
After obtaining the support reaction forces; the axial
forces which act upon the all members of the sofa
frames and consequential axial stresses were analyzed
199
D3
489,5
-375
130,9
451
-336
125,4
455.5
-340
134,5
493
-379
147
264,5
-143
101,4
D8
D10
0
489,5
792,3
-375
0
-130
0
451
752,6
-336
0
-125
0
455,5
757,2
-340
0
-134
0
493
795,9
-379
0
-147
0
264.5
560,3
-143
0
-101
D3: Right stump support
D10: Left stump support
as the second phase. Obtained normal force diagrams
from the analysis results were presented in Figure 6.
200
I. Type
II. Type
III. Type
Table 10. Comparison of the maximum axial stresses values and axial design stresses (N/mm2)
Tension
Test
Tension
Compression
Test
Compression
Material
member
tension
design
Result
member
compression
design stress
stress
stress
stress
Stump
Back post
Beech
0,729
43
+
1,060
53
bottom
bottom
Stump
Back post
Pine
0,583
25
+
0,914
33
bottom
bottom
Stump
Back post
PLY
0,599
21
+
0,929
25
bottom
bottom
Stump
Back post
0,520
9
+
0,851
12,5
bottom
bottom
MDF
Stump
Back post
0,244
9
+
0,575
11
bottom
bottom
OSB
(+): Passed
(): Failed
The section sizes of the members that integrate the sofa
frames constructed of solid wood and wood composites
were found to be strong enough for safely carrying the
axial forces. The shear forces in direction (Y) which act
I. Type
Figure 7. Shear force diagrams of the sofa frames
II. Type
Result
+
+
+
+
+
III. Type
201
Table 11. Comparison of the maximum shear stresses and shear design stresses
Shear design stress
Test shear stress
Material
Shear member
(N/mm2)
(N/mm2)
Stump bottom
1,210
3,5
Beech
Stump bottom
0,997
2
Pine
Stump bottom
1,020
3
PLY
Stump bottom
0,906
2,4
MDF
Stump bottom
0,504
2,5
OSB
It has been determined that, for the section sizes of the
members which are used in construction of the sofa
frames, they have sufficient strength for carrying the
shear forces. In the last phase, the bending moments in
I. Type
II. Type
Result
Passed
Passed
Passed
Passed
Passed
III. Type
Table 12. Comparison of the maximum bending stresses and bending design stresses (N/mm2)
Bending
Test bending stress
Bending design
Material
member
stress
Stump bottom
60,476
43
Beech
Stump bottom
49,851
25
Pine
Stump bottom
50,982
22
PLY
Stump bottom
45,298
11
MDF
Stump bottom
25,208
11
OSB
The maximum bending stresses occurred in the tops of
the members of stump bottom (E2,E9) where they
were joined to the member of side rail (E18,E19).
Therefore, the most critical places of the sofa frames are
the joints where the stump connected to the side rail.
Determined bending stresses values which act upon the
mentioned joints have exceeded the allowable bending
design stresses determined for each material. The
bending strength of these joints and sectional properties
Result
Failed
Failed
Failed
Failed
Failed
202
The optimum place for the side slat has been found at
the mid point between the side rail and arm like II. type
side frame in the production of the sofa frames
evaluated in this study. The most critical joints have
been determined as stumpside rail connections. If it is
necessary, the load bearing capacity of each three types
of sofa frames can be augmented by increasing the
strength of the joints.
203
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