Study on the numerical analysis for structural detail of timber frame ...

<strong>Study</strong> on the numerical analysis for structural detail of timber frame
based on partial compressive strain behavior of the joints
Shinya Matsumoto 1 , Yoshinobu Fujitani 2 , Yoshiyuki Suzuki 3
ABSTRACT: The joints are very important structural element in timber frame structures. However, the nonlinear
characteristics of joints are complicated and it is not clear that the design method for structural detail of timber frame on
the member joints. The reason for that wood is the anisotropic material, and the frictional contact problems are existing
between the each members joint etc. In this study, we investigate the simple modeling of timber joints for partial
compressive strain behavior by experimental test, and ascertain by the lateral compressive tests for Japanese cedar testpieces.
The partial compressive behaviors of joints are investigated experimentally by changing the angle of the
pressure plate of testing equipment from 0 to 10 degree. The shearing force caused by inclination of the pressure plate is
measured by the 3 component force sensor using the crystal piezoelectric type. And the difference of friction force is
compared using the Polytetrafluoroethylene (PTFE) sheet to reduce the friction resistance force between pressure plate
and timber. And we illustrate the modeling for structural detail of timber frame based on partial compressive strain
behavior of the joints.
KEYWORDS: structural detail, anisotropy, compressive strain inclined to the grain, friction
1 INTRODUCTION 123
The various types of joints are existing in Japanese
tradition timber structures. It is important to grasp the
structural behaviour of these joints for earthquake
resisting. In the past analytical research on the whole
behavior for the traditional timber structures, the
techniques which modeling the mass system or
segmented beam element based on the frame level
analysis are mainly used.
Today, the effect of the joint detail of traditional timber
structures has not been clarified analytically. The
mechanical behavior is complicated because of the joints
detail originated from anisotropy, heterogeneity, and
contact problem for the connection shape, etc. It is
necessary to examine the level of the modeling for the
whole timber structures. The reason is the necessities of
the structural detail modeling have increased as well as
considering the micro material model, it become the
complicated physical phenomenon.
In this study, the effects of the structural detail on the
whole timber structures are investigated. We carried out
1 Shinya Matsumoto, Department of Social and Environmental
Engineering, Hiroshima University, 1-4-1, Kagamiyama,
Higashi-Hiroshima,739-8527, Japan. Email:
mshin@hiroshima-u.ac.jp
2 Yoshinobu Fujitani, Hiroshima International University, Kure,
Japan. Email: y-fujita@it.hirokoku-u.ac.jp
3 Yoshiyuki Suzuki, Ritsumeikan University, Kusatsu, Japan.
Email: suzuki-y@fc.ritsumei.ac.jp
the basic experiment in order to develop the simple
analysis method. In this paper, we investigate the basic
timber characteristics for the compressive strain inclined
to the grain and partial nonlinear behavior based on the
orthotropic theory.
2 PARTIAL COMPRESSION TEST
2.1 EXPERIMENT OUTLINE
Partial compression test for the wood fiber orthogonal
direction was carried out in order to simulate the
orthotropic material, and to obtain the basic properties
for the numerical analysis.
Figure 1 shows the shape and size of the test piece (100
100 300mm). The test piece used non-knot cedar
wood (average width of annual rings = 2.6mm, surface
water content = 10.4%, air-dried density = 0.40g/cm 3 ,
measured in laboratory). Partial compression test was
carried out for fiber radial direction (R direction) and
tangential direction (T direction) shown in Figure 2. The
pressure plate jigs are made 3 angle patterns which slope
from 0°, 5°, to 10°. In this test, to measure the shearing
force in the pressure head with the changing for the
degree of angle, 3 component force sensor (crystal
piezoelectric type) was equipped in the pressure head.
The vertical compressive force and the shearing force in
the pressure head were measured, at the same time the
strain in each position (1-8) were measured as shown in
Figure 1. Strain gauge was stuck at both sides of test

piece, and the mean value was obtained on the each
point 1-6.
In this test, the partial compression test was carried out
by inserting the Polytetrafluoroethylene (PTFE) sheet
between pressure plate and surface of test piece in order
to reduce the effect of the friction. The list of the test
specimen is shown in Table 1.
100
7
15
Figure 1: Partial compression test
R
Figure 2: Load direction
Table 1: List of the test specimen
No. Symbol
Load
direction
Angle
(deg.)
1 R00T
0
2 R05T Radial 5
3 R10T 10
4 T00T
0
5 T05T Tangential 5
6 T10T 10
P
Q
300
1 2 3
4 5 6
45 45 15
2.2 RESULT OF THE EXPERIMENT
The vertical load - vertical displacement relation for the
R direction loading test is shown in Figure 3. Also, the
vertical load - vertical displacement relation for the T
direction loading test is shown in Figure 4. From these
figures, it is proven that the initial rigidity for load-
8
T
15
35
50
(Units : mm)
displacement relation becomes low with the increase of
angle of the pressure plate changing to 0°, 5°, 10°.
Load P (kN)
70
60
50
40
30
20
10
0
R00T
R05T
R10T
0 5 10 15
Displacement (mm)
Figure 3: Vertical load - vertical displacement relation
(R00T, R05T, R10T)
Load P (kN)
80
70
60
50
40
30
20
10
0
T05T
T00T
0 5 10 15
Displacement (mm)
T10T
Figure 4: Vertical load - vertical displacement relation
(T00T, T05T, T10T)
Figure 5 shows the horizontal load - vertical
displacement relation for R direction test measured by
the 3 component force sensor. From the Figure, it is
proven that the shearing force in the pressure head tends
to decrease when the pressure plate angle grows
comparison 5° with 10°.
Shearing force Q (kN)
3
2.5
2
1.5
1
0.5
0
R05T
R10T
0 5 10 15
Displacement (mm)
Figure 5: Horizontal load - vertical displacement relation
(R05T R10T)

Load-compressive strain relation of test (R00T) is shown
in the Figure 6, Figure 7.
Load (kN)
Figure 6: Load-compressive strain (1, 2, 3) relation
(R00T)
Load (kN)
Figure 7: Load-compressive strain (4,5, 6) relation
(R00T)
Load (kN)
Figure 8: Load-compressive strain (1, 2, 3) relation
(R10T)
Load (kN)
40
35
30
25
20
15
10
5
0
40
35
30
25
20
15
10
5
0
40
35
30
25
20
15
10
5
0
1
0 1000 2000 3000
Compressive strain (μ)
2
3
0 1000 2000 3000
40
35
30
25
20
15
10
5
0
6
4
Compressive strain (μ)
5
-500 500 1500 2500
6
Compressive strain (μ)
4
3
2
5
1
0 1000 2000 3000
Compressive strain (μ)
Figure 9: Load-compressive strain (4, 5, 6) relation
(R10T)
Load-compressive strain relation of test (R10T) is shown
in the Figure 8, Figure 9.
Load-tensile strain relation of test (R00T) and (R10T) is
shown in the Figure 10, Figure 11.
Load (kN)
Figure 10: Load-tensile strain (7, 8) relation (R00T).
Load (kN)
40
35
30
25
20
15
10
5
0
-500 500 1500 2500
40
35
30
25
20
15
10
5
0
7
8
Tensile strain (μ)
8
7
-500 500 1500 2500
Tensile strain (μ)
Figure 11: Load-tensile strain (7, 8) relation (R10T).
The strain of each part for change of the sinkage angle
was shown from these figures. For the reference, the
compressive strain inclined to the grain for R direction
test are shown in Figure 12-Figure 14

Figure 12: Compressive strain inclined to the grain
(R00T)
Figure 13: Compressive strain inclined to the grain
(R05T)
Figure 14: Compressive strain inclined to the grain
(R10T)
3 CROSS-SHAPED FRAME TEST
3.1 EXPERIMENT OUTLINE
In this study, cross-shaped frame is made using non-knot
cedar wood with column cross section 100100mm and
nuki-beam cross section 40100mm. The column upper
and bottom ends are restricted by the pin support as
shown in Figure 15.
Intertru
ss
振れ止め
Load P 1
Disp. 1 Disp. 2 200 200
DG3
DG5
+
-
DG1
50 50
DG7
DG4
100
300
DG6
100
DG8
250 250
500
250 250
300
160
DG10 DG11
DG12 DG13
160
DG9
50
50
200
振れ止め
DG2
Intertru
ss
Load P 2
-
+
Figure 15: Test specimen dimension and displacement
measurement position
The loading test was carried out by using two electronic
control actuators to applied antisymmetric vertical
displacement for the nuki beam ends.
Cotter pin
40
60
304030
140
140
2060
20
込栓(15×15) 304030
20
60
40
2060 20
20
くさび Wedge
20
Wedge くさび
Wedge
くさび
Model A
(Complete nuki joint)
Model B
(Link nuki joint)
Model C
(Link nuki joint with cotter pin)
Figure 16: The details of the each test specimen juncture
The frame models were made 3 types which different of
the joint detail as shown in Figure 16. The model A is
complete continuous beam joint, and the horizontal beam
member is one part element (it is called complete nuki
joint). Model B is the joint processing the right and left
members like key-shape, and consist of discontinues
beam (it is called link nuki joint). Model C is stricken the
cotter pin to the linke nuki joint, and the discontinuous
beam is fixed in the connection inside (it is called link
nuki joint with cotter pin). These joints have also fixed
by driving two wedges (zelkova material) on the upper
clearance between column and beam. The details of each
part are shown in Figure 16.
The whole view of Model A is shown in Figure 17. The
Model A has been bound the 1/3 span from the edge of
the horizontal bracing for out-of-plane deformation by
steel pipes (intertruss braceing) which covered PTFE
sheet to reduce the friction.

Figure 17: Test specimen Model A
The loading program is shown in Figure 18, and the
target displacement each 3 cycles (for deformation
angle: 1/50rad, 1/20rad, 1/15rad, 1/450rad,
1/300rad, 1/200rad, 1/150rad, 1/100rad,
1/75rad ) is antisymmetric displacement control which
repeatedly increased. Throughout this paper, the load
and displacement of left side is described by symbol P1
and 1, the load and displacement of right side is
described by symbol P2 and 2. The sign was defined for
the direction of the arrow respectively shown in Figure
15.
Target displacement(mm)
80
60
40
20
0
-20
-40
-60
-80
1/450 1/300 1/200 1/150 1/100 1/75 1/50 1/20 1/15
0 6 12 18 24 30
Cycles
36 42 48 54 60
Figure 18: The loading program
3.2 RESULT OF THE EXPERIMENT
Figure 19 shows the load P1- displacement 1 relation
and Figure 20 shows the load P2- displacement 2
relation for Model A. The sign of the load and
displacement are defined the direction of the arrow as
shown in Figure 15. From these figures, it is proven that
the mechanical characteristics under the loading region
for displacement 15mm (for deformation angle: 1/50rad)
in Model A is approximately symmetric behavior.
Figure 21 shows the load P1- displacement 1 relation
and Figure 22 shows the load P2- displacement 2
relation for Model B. From these figures, It is proven
that the mechanical characteristics under the loading
region for displacement 15mm (for deformation angle:
1/50rad) in Model B is unsymmetrical behaviour
different from Model A. Also, it tends to show the
linearity deformation and low rigidity for the positive
load and deformation in the direction for the first
quadrant of the graph. But, it tends to show the large slip
hysteresis curve for negative load and deformation in the
direction for the third quadrant of the graph. These are
supposed the effect of the discontinuous beam
connection shape and driving two wedges in the Model
B.
Load P1(kN)
0.8
0.6
0.4
0.2
0
-50 -30 -10 10 30 50
‐0.2
‐0.4
‐0.6
‐0.8
Displacement (mm)
Figure 19: The load P1- displacement 1 relation (Model
A).
Load P2(kN)
0.8
0.6
0.4
0.2
0
-50 -30 -10 10 30 50
‐0.2
‐0.4
‐0.6
‐0.8
Displacement (mm)
Figure 20: The load P2- displacement 2 relation (Model
A).
Load P1(kN)
0.8
0.6
0.4
0.2
0
-50 -30 -10 10 30 50
‐0.2
‐0.4
‐0.6
‐0.8
Displacement (mm)
Figure 21: The load P1- displacement 1 relation (Model
B).
Load P2(kN)
0.8
0.6
0.4
0.2
0
-50 -30 -10 10 30 50
‐0.2
‐0.4
‐0.6
‐0.8
Displacement (mm)
Figure 22: The load P2- displacement 2 relation (Model
B).
Figure 23 shows the load P1- displacement 1 relation
and Figure 24 shows the load P2- displacement 2
relation for Model C. From these figures, more

symmetrical mechanical characteristic is shown in
Model C compared with Model B. It is considered that
Model C is stricken the cotter pin to the discontinuous
beam.
Load P1(kN)
Figure 23: The load P1- displacement 1 relation (Model
C).
Load P2(kN)
-50 -30 -10 10 30 50
‐0.2
‐0.4
‐0.6
‐0.8
Displacement (mm)
Figure 24: The load P2- displacement 2 relation (Model
C).
The final state of each tests are shown in Figure 25-
Figure 27.
Figure 25: The final state of Model A
Figure 26: The final state of Model B
0.8
0.6
0.4
0.2
0
0.8
0.6
0.4
0.2
0
-50 -30 -10 10 30 50
‐0.2
‐0.4
‐0.6
‐0.8
Displacement (mm)
Figure 27: The final state of Model C
4 CONCLUSIONS
In this paper, the basic experimental tests for timber
were carried out to investigate the effects of the
structural detail. And we investigated the basic timber
characteristics for the compressive strain inclined to the
grain and partial nonlinear behaviour. These
experimental results are important data for the numerical
analysis based on the orthotropism theory.
ACKNOWLEDGEMENT
This work was supported by JSPS KAKENHI 19106010.
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