development of ductile semi-rigid joints...
TRANSCRIPT
DEVELOPMENT OF DUCTILE SEMI-RIGID JOINTS WITH
LAGSCREWBOLTS AND GLUED-IN RODS.
Yoshiaki Wakashima 1, Kenho Okura
2, Kazuo Kyotani
3
ABSTRACT: Although the ductility of joints is important from the viewpoint of the seismic response, joints with
lagscrewbolts or glued-in rods normally exhibit very stiff elastic behavior that causes brittle failure of wood. The
purpose of this study is to obtain ductile semi-rigid portal frame joints using lagscrewbolts or glued-in rods such that
brittle failure of the joints is prevented. We developed two types of leg and beam-column joints. With regard to ductility,
the performance of the joints is governed by the yield and plastic deformation of steel. The diameters of connecting
bolts, which penetrate the lagscrewbolts, are chosen such that the connecting bolts yield under the shear strength of the
joint panel. Similarly, for joints using glued-in rods, threaded steel rods have a reduced cross-section in a certain length
so as to yield the thinner part. Cyclic loading tests were conducted for the developed joints and for portal frames having
these joints. A large deformation was observed with little damage of the wood members. Analytical models of the joints
were examined considering prestress in the bolts. An analytical model of the portal frames was also examined
considering the shear deformation of the joint panel and bending property of the column. The calculated results were in
good agreement with the experimental results.
KEYWORDS: Portal frame, Semi-rigid joint, Lagscrewbolt, Glued-in Rod, Ductility
1 INTRODUCTION 123
Axial fasteners such as glued-in rods and lagscrewbolts
normally exhibit very stiff elastic behavior under tensile
forces without any particular consideration [1].
Therefore, joints with the fasteners parallel to the grain,
such as leg joints, are very brittle. Similarly, when the
fasteners are embedded perpendicular to the grain, such
as in a beam column joint, the joints generally turn out to
be brittle due to shear failure in the joint panel. For the
above reasons, in order to obtain a ductile joint, which is
an important requirement from the viewpoint of the
seismic response, it is necessary to ensure that the tensile
strength of the fastener is controlled so that brittle failure
is prevented. One of the authors has investigated joints
composed of glulam frames and special steel connectors,
where glued-in rods attach the connectors to the frame
[2]. The yield strength of the steel connectors was
designed to be lower than the strengths of the glulam
frames and glued-in rods so that most of the damage
would be concentrated within the steel connectors. These
joints showed reasonable ductility and energy
1 Yoshiaki Wakashima, Toyama Prefectural Forest Products
Research Institute, 4940 Kurokawa-shin, Imizu 939-0311
Japan. Email: [email protected] 2 Kenho Okura, GrandWorks Corporation, 452 Oenoki,
Namerikawa 936-0874 Japan. Email: k-
[email protected] 3 Kazuo Kyotani, Laminate-lab Corporation, 10
Kusajimaazafurukawa, Toyama 930-2201 Japan. Email:
absorption; however, since the connector was completely
exposed to the exterior, an architectural design problem
arose.
In this study, we examined joints, the ductility of which
is governed by the yield strength of the bolts that are
inserted in timber so as to minimize the exposure of the
steel materials to the exterior.
2 JOINTS
2.1 STRUCTURE OF NEW JOINT SYSTEMS
We developed two types of leg joints shown in Figure 1.
RC-type joints consist of glued-in rods that have reduced
cross-sections without ribs in a certain length so that the
rods yield. The material of the rods is mild steel. Nuts
are also installed between the column and the steel base
so that the rods resist compressive forces. Lagscrewbolts
are used for LC-type joints. Their performance is
governed by the yield strength and plastic deformation of
the anchor bolts.
Two types of beam-column joints are developed as
shown in Figure 2. In C-type joints, the bolts, which pass
through the central hole of the lagscrewbolts embedded
in the column, are connected to the lagscrewbolts
embedded in the beam. In B-type joints, a hole having a
particular length is punched in the lagscrewbolts
embedded in the beam, and the bolts are connected from
a steel plate to the inner hole of the lagscrewbolts. A
detailed illustration of the plates is shown in Figure 3.
For both the beam-column joints, the diameter of the
connecting bolts is decided such that the bolts yield
under the shear strength of the joint panel. The anchor
bolts and the connecting bolts for beam-column joints
described as ABR490 in Figures 1 and 2 are roll
threaded bolts. The effective sectional area of the bolts is
almost same between body and thread, which lead to
yielding of bolts uniformly and large plastic deformation.
Nominal diameter of the lagscrewbolts using above
joints is 35 mm.
2.2 JOINT TESTS
Static cyclic loading tests were performed
for the developed joints. Figures 4 and 5
illustrate the details of the test specimens
and set-ups. Table 1 lists the specifications
of the investigated test specimens. The
nominal diameters of the anchor bolts are 14
mm and 16 mm for LR300 and LR450,
respectively. The effective elongations of
the bolts (shown in Figure 2) are 279.5 mm
and 192 mm for CL300 and BL450-type
joints, respectively.
The relationships between moment and joint
rotation for leg joints are illustrated in
Figure 6. Since the failure of the RC-type
joint was fracture of the rods, reasonable
plastic behavior was observed. The observed
ultimate moment exceeded the reference strength of the
glulam. Because of the reaction of the nuts to
compressive forces, little slip behavior was observed in
the hysteresis loop.
Tensile failure of the anchor bolts occurred in the LC-
type joint; we obtained a large rotation angle exceeding
0.1 rad. However, unlike RC-type joints, slip behavior is
observed in the hysteresis loop because the anchor bolts
Glue-in rod
Column
Reduced diameter
Nuts for reacting to
compression force
(a)RC-type (b)LC-type
Figure 1: Developed leg joints. JSS: Japan Steel Standard
Column
Lagscrewbolt
Shear Key
Steel Column Base Plate
Anchor BoltsJSS ABR490
Sill
Foundation
(a)C-type (b)B-type
Figure 2: Developed beam column joints Figure 3: Steel plates for B-type joints
Column
Lagscrewbolt
Steel Gusset
BoltJSS ABR490
Drift-pin
Beam
Lagscrewbolt
Lag Bolt
Effective elongation
length of bolt
Column
LagscrewboltSteel Plate
Lagscrewbolt
Drift-pin Beam
BoltJSS ABR490
Steel Plate
Shear Key
Shear Key
Effective elongation
length of bolt
(a)RC-type (b)LC-type Figure 4: Test specimens for leg joints. JIS: Japan Industrial Standard
Figure 5: Test set-up for beam column joints
Table 1:Specification of joint specimens
Code
nameWood material JAS grade
Cross section
(mm)
RC Glulam(Sugi) E65-F225 180×450
LR300 Glulam(Red pine) E105-F300 105×300
LR450 Glulam(Red pine) E105-F300 105×450
CL300 Glulam(Red pine) E105-F300 105×300
BL450 Glulam(Red pine) E105-F300 105×450
Leg joint
Beam
column joint
Steel column
baseNut
Column
GIR(M20)JIS SS400
φ15
1800
70
P
1,419
Shear Key
Steel Column Base
Anchor Bolt
Column
Foundation Jig
(H-Shaped Steel)
Lagscrewbolt
JSS ABR490
Elongation Length of Ancor Bolt =385mm
P
Column
Beam
1500
2000
1630
Actuator
Pin support bar
P
do not resist compressive forces.
The rotational rigidity of the leg joints is calculated
using the analytical model proposed by Koizumi et al [3].
In order to determine the maximum strength of the joints,
a neutral axis, which varies according to yield conditions
of the bolts, should be decided. When the rods on the
tensile side are in the yield condition as shown in Figure
7(a), the neutral axis λ is expressed in the form of equation (1)
)(1244()2(2
1 2
uuuu
u
eKwhebKdPeKweb
δδδδ
λ ++++
=
± 2))(2)(1(4( uuuu KdPeKwheb δδδ +++
))))21(12(21)(2(4 22
uuuu KdggPhKwhebeKweb δδδ ++++−
(1)
where γ is length of the yield section of wood, Kd is the
slip modulus of the glued-in rod, δ is the slip of glued-in
rod, δu is the ultimate slip of the glued-in rod, Pu is the
yield strength of the glued-in rod, Kw is the embedded
rigidity of wood, e is yield embedded displacement of
wood, and b is the width of the column.
The above equation is derived assuming that the
embedment resistance of wood and the tensile resistance
of the rods are perfectly elasto-plastic. The calculated
results are shown in Figure 6(a) as dotted lines. The
experimental and theoretical results were in good
agreement.
As mentioned above, a large ultimate moment was
observed. This may be because of two reasons. One
reason is that the yield stress in the joints is distributed
as shown in Figure 7(a), which leads to the stress being
restrained in the outer laminations of glulam. Another
probable reason is that the longitudinal stress of wood
near the fixed end of the column is not sufficiently large
so that little failure occurs due to bending. This
assumption is mentioned in following section.
Since plastic deformation of the anchor bolts causes
deformation of the leg joint, equation (2) is applied to
estimate the rotational rigidity of LC-type joints [4].
( )bB
ctbt
l
ddAnEsKbs
α+
= (2)
where dt, dc, and lb are as illustrated in Figure 7(b). Es is
Young’s modulus of the anchor bolt, AB is the cross-
sectional area of the anchor bolt, and nt is the number of
anchor bolts on the tensile side. The value of αB is
generally 2 for bending deformation of the base plate
and deformation of concrete on the compression side [4].
However, αB is ignored in this study because the base
plate has sufficient thickness and because H-shaped steel
jig is used as a substitute for the concrete foundation.
The calculated results and the experimental results are in
good agreement as shown in Figure 6(b) and 6(c). Since
the bending of the base plate and deformation of the
foundation jig are ignored, it seems that further
verification is necessary to simulate
the actual situation by setting a leg
joint on concrete.
The experimental results for beam-
column joints are illustrated in
Figure 8. From the results, a large
deformation could be obtained by
plastic deformation of the bolts
without any visible failure of the
glulam. Slip behavior is not clearly
observable in the hysteresis loop for
L-type joints. The reason for this
result is that the bolts that are
(a)RC-type (b)LR300-type (c)LR450-type
Figure 6: Moment- rotation relationships for leg joint specimens
λ γ
Pu
δu Pu
Kd・δ
Reaction forces
g1
g2 h1
(a)RC-type (b)LR-type Figure 7: Yield condition of leg joint at the maximum strength
M
Q
Reaction forces dt dc
lb
(a)CL300-type (b)BL450-type
Figure 8: Moment- rotation relationships for beam column joint specimens
-20
-15
-10
-5
0
5
10
15
20
25
-0.05 0 0.05 0.1 0.15 0.2
Rotation (rad.)
Mom
ent
(kN
・m
)
ExperimentCaluculate
-50
-40
-30
-20
-10
0
10
20
30
40
50
-0.05 -0.03 -0.01 0.01 0.03 0.05 0.07 0.09 0.11
Rotation (rad.)
Mom
ent
(kN
・m)
ExperimentCaluculate
-200
-150
-100
-50
0
50
100
150
200
-0.01 0 0.01 0.02 0.03 0.04 0.05
Rotation (rad.)
Mom
ent
(kN
・m
)
-40
-30
-20
-10
0
10
20
30
40
-0.05 0 0.05 0.1 0.15 0.2 0.25
Rotation (rad.)
Mom
ent
(kN
・m
)
-60
-40
-20
0
20
40
60
80
-0.05 0 0.05 0.1 0.15 0.2
Rotation (rad.)
Mom
ent
(kN
・m
)
connected to the lagscrewbolts embedded in the beam
are considered to resist both tensile and compressive
forces, because the bolts behave as buckling-restrained
members in the lagscrewbolts embedded in the column.
It is considered that the rotational rigidity of beam-
column joints subjected to open-mode moment is
different from that of joints subjected to close-mode
moment. Figure 9 shows the mechanical models for
joints subjected to open- and close-mode moment. From
the equilibrium of moments, equation (3) and (4) are
obtained for the opening and closing modes, respectively,
by assuming a beam to be a rigid body in the section of
the joint.
( ) ( )Lac
hKdghLac
gKdhLac
bKwM δ
λλ
δλ
λλλδ
λ −−−+
−+
+−+= 2)(13
2
2
(3)
( ) ( ) ( )hgLach
KdLacg
KdgLacb
KwM +−−
−−
+
+−= δλλ
δλλλ
δλ
2132
(4)
where λ is the neutral axis, b is the width of the column,
Kw is the embedment rigidity of wood, Kd1 is the
tensile slip modulus of the fastener, Kd2 is the
compressive slip modulus of the fastener, and δc is the
embedded displacement at the beam end.
The above equation can be expressed in the form of a
cubic equation as a function of λ when b0, c0, and d0 are
appropriately introduced.
0000 32 =+++ λλλ bcd (5)
Then, equation (5) can be solved using the solutions for
cubic equations. For example, the following notations
can be introduced.
3
00
2bcp −= 0
3
00
27
02 3
dcbb
q +−= pr
3
4−=
+
−=32
320
pqD
If D0 > 0, then
3
0])
3[
3
1
3
2(
b
rp
qArcCosrCos −−=
πλ
(6)
The compressive force C, which is produced due to the
compression of the bolts and the embedment of wood, is
expressed as
cgKd
cKwbC δλλ
λδ)(1
2
1 −+= (7)
The tensile bolt force T is
cgKd
T δλ
λ)(2 −= (8)
From equilibrium condition 0=++− PTC
( )λλλ
δKwbKdKdKdhKdg
Pc
+++−−=
22122212
2 (9)
The joint moment is
( )λ−+= 1hLaPMj (10)
From equations (6), (9), and (10), the rotational rigidity
of joints is obtained as
( )λδ /c
MjKj =
(11)
When F is a shear force that occurs at the joint panel as
shown in Figure 9, C is equal F for the opening mode
and T is equal F for the closing mode. The shear strain γ
produced by F is
( )AwGwF /αγ = (12)
where Gw is the shear modulus of the column, Aw is the
cross-sectional area of the column, and α is the shear
coefficient.
Equation (13) is the rotational rigidity of the joint
considering shear deformation of the column in the joint.
( )γλδ +=
/c
MjKj
(13)
Because the effect of bending deformation of the column
in the joints is ignored in the above equations, finite
element (FE) analysis, in which the column is assumed
to be a beam on an elastic foundation as illustrated in
Figure 10, was carried out to evaluate the effect of
bending deformation. Figure 11 shows the calculated
displacements at h1 and g1 obtained from equation (9)
and FE analysis. From these results, it is clear that the
location of the neutral axis and the displacements at h1
and g1 are almost coincident and the assumption that the
column is a rigid body in the section of the joint seems to
be appropriate.
Since a tightening torque of 100 Nm is applied to the
bolts that are used to assemble the beam and column, it
is considered that the effect of prestress in the bolts
should be taken into account in order to estimate the
rigidity of C-type joints. When the beam is embedded in
the column as shown in Figure 12(a), equation (15) is
obtained from the moment equilibrium.
(a)Opening mode (b)Closing mode Figure 9: Mechanical model for beam-column joins
Elastic
Foundation
Beam
P
Glue-in rods
Figure 11: Calculated displacements at h1 and g1
Figure 10: Beam on elastic foundation model for beam-column joints
-0.02
-0.01
0
0.01
0.02
0.03
Displacement(mm)
FE analysis
Calculate
h1 g1
Neutral Axis
La
λ
δc
Column
Beam
Joint panel
δc
La
λ
Column
Beam
Joint panel
( ) ( ) ( )hgLac
hKdLac
gKdgLac
bKwM +−
−−
−+
+−= δλλ
δλ
λλδ
λ21
32
( ) ( )
−+++−
−+−
3
2
2
2 λλδ
λλ gh
gLacghb
Kw
(15)
When the bolts reach their tensile strength as shown in
Figure 12(b), the equations corresponding to the
equilibrium of the moments for opening and closing
modes are expressed by equation (16) and (17),
respectively.
)2
(3
)(2)( 2121
γγλλ −+−
−+−+−−+−= hLaCwhLaCwghLaQLaQM
(16)
)2
(3
)()( 2121
γγλγ +−−
−++−−−++−= gLaCwgLaCwghLaQLaQM
(17)
The initial rigidity of the joints calculated from equations
(3), (4), and (15) and the ultimate moment calculated
from equations (16) and (17) are illustrated in Figure 8
as dotted lines. The calculated results obtained using
equation (15), which considers the effect of prestress, are
lower than the experimental results as shown in Figure
8(a). One possible reason for this result is that some
measurement error may have occurred when the
measurement points were set near the interface between
the column and beam, since these points are moved
following the recover of the embedded displacement of
wood that is generated by embedding the beam to the
column due to the prestress.
Although the yielding points of the joints in the opening
and closing modes differ by 10–15%, the calculated
results can satisfactorily describe this phenomenon. The
difference in the ultimate moments of the opening and
closing mode is not significant; however, the shear force
produced in the joint panel at the closing mode is 30%
larger than that at the opening mode. These are important
results that help designers to appropriately design joints
that do not undergo failure in the joint panel.
3 PORTAL FRAMES
3.1 PORTAL FRAME TESTS
In order to evaluate the performance of the developed
joints, static cyclic loading tests were carried out on
portal frames using the developed joints. Table 2 lists the
specifications of the test specimens used in the portal
frame tests. Figure 13 shows an example test setup and
the actual test setup for the 8P2F specimen. The
specimens are laid on the test floor and column bases are
fixed on H-shaped steel jigs. The beam was subjected to
push-and-pull cyclic loading and Ai distribution was
applied to calculate the shear force of second story [5].
Ai is a vertical distribution coefficient of seismic story
shear coefficients.
T
TA i
i
i31
2)
11(1
+−++= α
α
(18)
δc
La
λ
Torque
Colum
Beam
λ
δy
Figure 12: Mechanical models for beam-column joints
(a)Considering torque influence
(b)Final failure condition by fracture of rods
Table 2: Specification of portal frame specimens
(a)Schematic diagram (b)Photograph showing testing feature
Figure 13: Test set-up for full-scale portal frame specimen
3P:27308P:7280
2777
81
2696
2730
Beam
Beam
Column
Column
Foundation jig
(H-shaped steel)
P
P
Code nameSpan
(mm)
Height
(mm)
Red pine glulam
(mm)Leg joint
Beam-
column joint
3P1F 2730 1F:2777105 x 300
JAS-grade:E105-F300LR300 CL300
8P1F 72801F:2777
2F:2730
105 x 300
JAS-grade:E105-F300LR450 BL450
3P2F 2730 1F:2777105 x 300
JAS-grade:E105-F300LR300 CL300
8P2F 72801F:2777
2F:2730
105 x 300
JAS-grade:E105-F300LR450 BL450
Where αi=Wi/W, W is weight above ground level, T is
fundamental natural period. Figure 14 shows the relation
between load and shear deformation obtained from the
tests. The shear deformation of 3P2F due to plastic
deformation of joint bolts was so large that the test
terminated by the stroke limit of the actuator. Both side
of the leg joints became pin condition after splitting of
the wood around the lagscrewbolts for 8P2F, although, a
relatively large shear deformation occurred.
The relationships between the moment and rotation
angle of the joints are illustrated in Figure 15 and 16.
The calculated results are also
plotted. The joint moment is
determined from the distribution
of bending strain obtained from
strain gauges and Young’s
modulus of glulam measured
using the Timoshenko-Goens-
Hearmon (TGH) method [6]. The
maximum rotation angle of the
leg joint on the left side could not
be obtained, since the
displacement transducer separated
from the specimen before the test
ended. These results indicate that
the shapes of the hysteresis loops
are almost identical to the
corresponding loops obtained
from the joints tests. The loops of
the beam-column joints for 8P2F
show a wider area (indicating the
energy absorption ability) as
compared to the results of the
joint test, since the frame
specimen was subjected to a large
cyclic shear deformation.
The rigidity and strength of the
beam-column joints are calculated
as mentioned previously; however,
moment equilibrium is calculated
considering shear forces that act
on both sides of the joint in the
first story. With the assumption
that joint failure is caused by bolt
fracture, the maximum angle of
joint rotation is determined from
the strain data obtained by tensile tests of bolts. The
calculated values for leg joints are also given as stated
above. The axial forces on the columns, which are
necessary to estimate the strength of the leg joints, are
determined from the measured shear strain values of the
beams. The strain data of the anchor bolts obtained from
the frame tests are used for calculating the maximum
rotation angle of the leg joints.
The observed and calculated results show good
agreement. The yield moments differ by 10%–15%
between the opening and closing mode for the beam-
-20
-15
-10
-5
0
5
10
15
20
-0.2 -0.15 -0.1 -0.05 0 0.05
Rotation (rad.)
Mom
ent
(kN
・m)
-20
-15
-10
-5
0
5
10
15
20
25
-0.05 0 0.05 0.1 0.15 0.2
Rotation (rad.)
Mom
ent
(kN
・m
)
-30
-20
-10
0
10
20
30
-0.05 0 0.05 0.1 0.15 0.2
Rotation (rad.)
Mom
ent
(kN
・m
)
-30
-20
-10
0
10
20
30
-0.2 -0.15 -0.1 -0.05 0 0.05
Rotation (rad.)
Mom
ent
(kN
・m)
(e)Left side leg joint (f) Right side leg joint
Figure 15: Moment-rotation relationships obtained from 3P2F. ―:Experiment,
－：Calculate.
(c)Left side joint of 1st story (d) Right side joint of 1
st story
(a)Left side joint of 2nd
story (b) Right side joint of 2nd
story
(a)3P2F (b)8P2F
Figure 14: Load-shear deformation obtained from experimental tests
-30
-20
-10
0
10
20
30
40
-15 -10 -5 0 5 10 15 20 25 30 35
Shear Deformation (cm)
Shea
r Forc
e (k
N)
2nd story
1st story
2D FEM(1st) 2D FEM(2nd)
-80
-60
-40
-20
0
20
40
60
80
-10 -5 0 5 10 15 20
Shear Deformation (cm)
Shear
Forc
e (
kN)
2nd story
1st story 2D FEM(1st)
2D FEM (2nd)
-30
-20
-10
0
10
20
30
40
-0.05 0 0.05 0.1 0.15
Rotation (rad.)
Mom
ent
(kN
・m
)
-30
-20
-10
0
10
20
30
40
-0.05 0 0.05 0.1 0.15
Rotation (rad.)
Mom
ent
(kN
・m
)
column joints of the second story. Because of the effects
of the axial forces of the columns, the ultimate moments
of the leg joints differed by about 30% for 3P2F and
10% for 8P2F between the right and left side. This
indicates that a large ratio of span to story height
decreases the strength of leg joints.
The relation between load and shear deformation in one-
story specimens is shown in Figure 17. Large
deformations were obtained for both 3P1F and 8P1F due
to plastic deformation of the joint bolts. The final mode
of failure was fracture of the
anchor bolts and splitting of wood
in the beam-column joints.
The shear deformation of timber
portal frames can be calculated by
treating them as semi-rigid portal frame. The initial stiffness
including the effect of shear
deformation of the timber
elements is illustrated in Figure
17 as dotted lines. The calculated
and experimental results are
observed to be in good agreement.
However, it is considered that the
shear strain of the joint panel
should be included in the
estimation of the deformation of
portal frames. Figure 18 shows
the comparison between the shear
strain of the joint panel and the
joint moment, which are obtained
from the beam-column joint of
3P1F. Although the observed
shear strain was relatively small,
it is considered that this strain
should not be ignored when
calculating the deformation of
frames. Thus, the effect of shear
strain is considered for estimating
the rotational rigidity of beam-
column joints in this study.
Another problem in estimating the
deformation of portal frames is
the bending property of the timber
in which lagscrewbolts are
embedded parallel to the grain.
Figure 19 shows the longitudinal strain distribution of a
leg joint specimen simulated by FE analysis. The result
shows that the maximum tensile strain of the wood
occurs around the top of the lagscrewbolts, and the strain
decreases on approaching the column end. In Figure 20,
the column deflections obtained from the FE analysis
results are compared to the values calculated considering
the column as a cantilever beam. The FE analysis values
are smaller than the calculated values. When the part of
the timber in which lagscrewbolts are embedded is
-50
-40
-30
-20
-10
0
10
20
30
40
50
-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04
Rotation (rad.)
Mom
ent
(kN
・m)
-50
-40
-30
-20
-10
0
10
20
30
40
50
-0.05 -0.03 -0.01 0.01 0.03 0.05 0.07 0.09
Rotation (rad.)
Mom
ent
(kN
・m)
-50
-40
-30
-20
-10
0
10
20
30
40
50
-0.11 -0.09 -0.07 -0.05 -0.03 -0.01 0.01 0.03 0.05
Rotation (rad.)
Mom
ent
(kN
・m
)
-50
-40
-30
-20
-10
0
10
20
30
40
50
-0.05 -0.03 -0.01 0.01 0.03 0.05 0.07 0.09
Rotation (rad.)
Mom
ent
(kN
・m
)
-80
-60
-40
-20
0
20
40
60
80
-0.05 -0.03 -0.01 0.01 0.03 0.05 0.07 0.09 0.11
Rotation (rad.)
Mom
ent
(kN
・m)
-80
-60
-40
-20
0
20
40
60
80
-0.05 -0.03 -0.01 0.01 0.03 0.05 0.07 0.09
Rotation (rad.)
Mom
ent
(kN
・m)
(e)Left side leg joint (f) Right side leg joint Figure 16: Moment-rotation relationships obtained from 8P2F.
―:Experiment, －：Calculate.
(c)Left side joint of 1st story (d) Right side joint of 1
st story
(a)Left side joint of 2nd
story (b) Right side joint of 2nd
story
(a)3P1F (b)8P1F
Figure 17: Load-shear deformation obtained from experimental tests. －:Experiment, ･･･:Calculated as semi-rigid
portal frame, －:2D FE analysis results in consideration of the shear strain of the joint panel and the assumption as
a composite beam.
-40
-30
-20
-10
0
10
20
30
40
50
-20 -10 0 10 20 30 40 50
Shear Deformation (cm)
Shear
Forc
e (kN
)
-80
-60
-40
-20
0
20
40
60
80
100
-15 -10 -5 0 5 10 15 20 25
Shear Deformation (cm)
Shear
Forc
e (kN
)
assumed to be a composite beam comprising timber and
lagscrewbolts, the calculated results agree well with the
FE analysis results, as indicated by the dotted line in
Figure 20. The strain distribution is not linear between
the timber and the lagscrewbolts, which indicates that
the above assumption does not represent the actual
bending behavior of the column. However, this
assumption is applied as a simplified method to estimate
the deflection in this study. Figure 21 shows the 2D FE
analysis model employed above assumptions. Initial
stiffness of the portal frames obtained from this model is
shown in Figures 14 and 17. The experimental results
and the 2D FE analysis results are in better agreement
than without the considerations of above effects.
4 CONCLUSION
This study investigated the development of new semi-
rigid joints having performances that are governed by the
yield and plastic deformation of steel fasteners. Large
rotational angles were obtained in experimental tests.
The calculated rotational rigidity of the joints for both
open- and closed-mode moment showed good agreement
with the experimental results. Cyclic loading tests of
portal frames using the developed joints also proved
sufficiently ductility. Calculated initial stiffness of portal
frames in consideration of the effects of the joint panel
and the bending property of timber showed good
agreement with the experimental results.
REFERENCES [1] Gehri E.: Ductile behaviour and group effect of
glued-in steel rods. In: Proceeding of 2001-
International RILEM Symposium on “Joint in
timber Structure”, 333-342, 2001
[2] Wakashima Y., Sonoda S., Ishikawa K., Hata M., Okazaki Y., Hasegawa K.: Development of response
technique for timber frame structure. In:8th World
Conference on Timber Engineering, 449-452, 2004
[3] Koizumi A., Sasaki T., Jensen J. L., Iijima Y., Komatsu K.: Moment-resisting Properties of Post-
to-sill Joints Connected with Hardwood Dowels.
Mokuzai Gakkaishi, 47(1):14-21, 2001.
[4] Architecture Institute of Japan: Recommendation for Design of Connections in Steel Structures.
Architecture Institute of Japan, Tokyo, 2001.
[5] Architecture Institute of Japan: Recommendation for Load on Building. Architecture Institute of Japan,
Tokyo, 2004.
[6] Kubojjima Y., Yoshihara H., Ohta M., Okano t.: Examination of the Method of Measuring the Shear
Modulus of Wood Based on the Timoshenko Theory
of Bending. Mokuzai Gakkaishi, 42(12):1170-1176,
1996.
Figure 18: Shear strain of joint panel and joint moment relationships for 3P1F
-20
-15
-10
-5
0
5
10
15
20
25
30
-0.004 -0.002 0 0.002 0.004 0.006
γ
Mom
ent
(kN
・m)
ExperimentCalculate
Figure 19: Longitudinal strain distribution of leg joint specimen obtained by FE analysis
Figure 20: Comparison of the deflection of beam among FE analysis results and calculated results
P Longitudinal
strain
Figure 21: 2D FE analysis model
Glulam element
Semi-rigid joint element
(Rotational rigidity of
leg joint)
Semi-rigid joint element
(Rotational rigidity of
beam column joint
in cosideration of joint panel)
Composite beam element
Rigid body element
0
1
2
3
4
5
6
7
8
9
0 200 400 600 800 1000 1200 1400
Distance from fixed end (mm)
Difrection (mm)
FE analysis
Simple beam
Composite beam