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RESISTING CHARACTERISTICS OF HYBRID CENTER CORE SHEAR WALL
SYSTEMS
Takayoshi YAMAKAJI1 And Minoru YAMADA2
SUMMARY
In order to present the data of resisting characteristics of various kinds of hybrid center core shear
wall systems in rigid frames for the antiseismic structural design, tests and analysis were carried
out and compared directly with the corresponding moment frame systems for the estimation of
antiseismic behaviours. Hybrid center core shear wall were made of steel panel with and without
concrete covers. Steel profile and steel profile encased reinforced concrete composite moment
frames were tested for the direct comparison of the resisting behaviours with the center core shear
wall systems. Center core hybrid shear wall systems show 3 to 7 times higher initial stiffnesses and
2 to 3 times higher resistances than corresponding moment frames. However, the fracture ductility
of center core hybrid shear wall systems show only very small fracture ductility 0.01 to 0.02 i.e.
0.1 of corresponding moment frames, and consequently very small energy dissipation capacity.
Computed results coincide very well with test results. From the test results of 3 span 9 story rigid
frames with and without hybrid center core shear wall systems it was shown very clearly the fact
that center core shear walls are effective to increase their stiffness and resistances but cause the
lack of ductility. This fact may enable to give the evaluation base of seismic performance of
structures.
INTRODUCTION
There are yet few researches on steel panel shear wall [Mimura and Akiyama (1977), Elgaaly, Caccese and Du
(1990, 1993), and Yamada (1992, 1996)]. Therefore there are very few researches on hybrid structure using
steel panel shear wall. But the authors had proposed steel panel shear wall as one of the best antiseismic
structural element [Yamada and Yamakaji, 1997]. Practically, it has already reported that center core steel panel
shear wall set in the New Kobe City Hall of 32 stories of 132m heights showed good resisting behaviour
subjected to severe ground motion at the last Kobe earthquake, 17. Jan. 1995, in Kobe, Japan [Yamada, 1996].
The hybrid structure to be proposed in this paper is structure in which both of steel frame and steel wall, or only
frame is covered by concrete. The elasto-plastic deformation and fracture characteristics of each hybrid structure
depends on the pattern of concrerte covering. On the basis of behaviours of infilled steel structures of simple
material for comparison, the behaviours of hybrid structures may be extrapolated, so that those behaviours can
be estimated by the application of foregoing method [Cardan, 1961].
1
2
Structural Engineering Department, Newjec Inc., Osaka, Japan Email:[email protected]
Department of Architecture, Faculty of Engineering, Kansai University, Osaka, Japan, Fax:+81-75-724-8043
Steel Panel 0.4 encased in Concrete Wall
Steel
04
Panel
Steel
19*10*1 2*1 2
Profile
120 each
240
h
[Type A]
[Type
[Type C]
[Type
[Type E]
Steel Profile 19*10*1.2*1.2 encased in Concrete
30*30
Steel
Figure 1 : Specimens
EXPERIMENT
[Type
Profile
(Unit : mm)
Table 1 : Material properties
Specimens
properties
P
H
H/3
specimens
A
B
C
Type
D
E
F
•
yielding
strength of
steel profile
336
336
328
336
328
328
(Unit : MPa)
yielding
strength of
steel panel
238
238
238
P : cyclic
incremental
repeated
horizontal load
2H/
3
Tests were carried out on six specimens of 9 story 3 span
with the same scale under the same loading condition.
Six specimens are shown in Figure 1. Type A is steel
profile encased reinforced concrete rigid frame with
center core steel panel shear wall with concrete covering.
Type B is steel profile encased reinforced concrete rigid
frame with steel panel shear wall without concrete
covering. Type C is steel profile encased reinforced
concrete rigid frame. Type D is steel profile rigid frame
with steel panel shear wall. Type E is steel profile rigid
frame. Type F is steel profile rigid frame with center core
steel X-shape brace with the same cross section. The
mechanical properties of each material used for these six
specimens are indicated in Table 1. Horizontal force P
were loaded by incremental cyclic sway angles
amplitudes of 0.001, 0.002, 0.003, 0.005, 0.007, 0.010,
0.015, 0.020, 0.030 and 0.100.
compressiv
e strength
of concrete
22.4
42.5
35.9
R
•: horizontal displacement
tl d
i t
Figure 2 : Testing and Measuring method
Loading processes and Test results
Loading processes and test results are described as follows and are shown in Figure 3. Type A, shear wall in 1st
to 6th story and the side columns cracked as one block. The crack pattern shows an inclination of 45 degree in
2nd to 6th story and, in 1st story, is similar to crack near fixed end like contilever. Type B formed diagonal
tension field in buckled waves with a inclination of 45 degree as found in Type D. The buckled waves in Type
D penetrated into its beams while the buckled waves in Type B is formed in each story independently. Type C
shows remarkable incremental stiffness degradation due to concrete crack, development and so on after reversed
loading. This characteristics is indicated in all of hybrid structure with concrete covering. Type C and Type E,
without center core, shows more stable behaviour than the other structures with center core. All type structures
show hysteresis loops symmetrical with regard to original point of P-R coodinates. The Comparison of skelton
loop of each structure is shown in Figure 4. This diagram indicates that Type C and Type E have much more
ductile than the structure with center core. Type A, B and D, horizontal stiffness and energy dissipation capacity
increase in proportion to number of hybrid member. It can be assumed that the center core in Type B and Type
D resist by the diagonal tension steel panel shear wall, that the center core in Type A resists by the conjugate
diagonal tension and compression of steel panel shear wall and concrete shear wall, relatively and that the center
core in Type F resists by the conjugate diagonal tension and compression of X-steel brace. From the results, the
behaviours of hybrid structures of with concrete covering may be extrapolated and can be simplified into models
adequately.
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36
P(kN)
30
P
P
R
R
24
20
12
10
R(rad)
0
-0.03
P(kN)
-0.015
0
0.015
0.03
-0.03
-0.015
0
-12
-10
-24
-20
[Type A]
-36
18
R(rad)
0
0.015
-30
[Type B]
20
P(kN)
0.03
P(kN)
P
P
R
15
R
12
10
6
5
R(rad)
0
-0.1
-0.05
0
0.05
R(rad)
0
-0.02
0.1
-0.01
0
0.01
0.02
-5
-6
-10
-12
-15
12
18
P(kN)
8
12
4
6
R(rad)
0
-0.06
-0.03
0
0.03
-4
0.06
[Type D]
-20
[Type B]
-18
P(kN)
R(rad)
0
0.09
-0.01
0
-6
P
0.01
0.02
P
R
R
-8
-12
-12
[Type E]
-18
[Type F]
H
2H/3 H/3
Figure 3 : Experimental P-R relationship of each structure
P(kN )
40
P
Type
F
R
20
Type
A Type
BType
D
0
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
Type
C
Type
E
0.06
R(rad)
0.08
0.1
-20
-40
Figure 4 : Comparison of experimental envelopes of hysteresis loops
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ANALYSIS
Models for Analysis
Horizontal sway behaviours of hybrid structures can be estimated by the application of foregoing method. Type
A is simplified into a free-standing cantilever, such as shown in figure 5 (a) [Cardan, 1961], subjected to
horizontal load of external excitation, horizontal and bending reaction by surrounding frame at each story and
beams adjacent to center core [Yamada, 1980]. The structural elements of center core are 2nd to 9th walls
differentiated in each story and the couple of side columns, which are deformed by sway and rotation around the
center of gravity of 1st story-wall, and 1st wall deformed by sway deformation and the couple of side columns
deformed by sway and bending deformation. This model is named Core wall system. While Type B and Type C
are simplified into rigid members and hinges for rigid frame [Yamada and Kawamura et al., 1984] and shear
spring for steel panel shear wall at each story, as shown in Figure 5 (b). For Type B, the stiffness of shear spring
at each story can be put at arbitrary numerical values greater than zero. For Type C, the stiffness of shear spring
at each story is put at zero as initial condition. In general, this model for Type B and Type C is named Frame
system model.
P
P
K iR=1
R
`9
K iF=1
K S : shear stiffness of hybrid wall at each story
`9
K R : rocking stiffness by reaction beam
K Si = 2
`9
K F : horizontal stiffness by frame at each story
K 1S , K 1B
[Type
A]
K B : bending stiffness by side couple columns
of hybrid wall at 1st story
(a) Core wall system
P
P
P
R
[K ] : band stiffness matrix of horizontal
R
[K ]
[Type B]
stiffnesses of steel panel shear walls
and hinges at both edges of rigid
members
[Type
C]
(b) Frame system
Figure 5 : Modeling of structures
Fundamental Equations
For core wall system, the incremental equation (1) that is derived from the shear equation at each story and the
moment equation of the cantilever in the center of height at the 1st story is given as follows:
1
KF  6
KF
11 − S 1 F  − ∑ S i F
2
K1 + K 1  i = 2 K i + K i
∆θ1B =
⋅ ∆P
∑ K iR + K1B + K1S ⋅ K1F + 9 KSi ⋅ K iF
∑
h
4(K1S + K1F ) i =2 K Si + K iF
(1
)
where K F and K R are the horizontal spring stiffness by surrounding rigid frame reaction at each story and the
rocking stiffness by bending reaction of beams adjacent to center core, respectively. K S and K1B are shear
stiffness of shear wall at each story and bending stiffness by the couple of side columns at the 1st story,
st
B
respectively. ĢĮ
1 and ĢP are incremental bending angle of 1 story of the couple of side columns and shear
load, respectively. For frame system, the matrix equation (2) that is derived from the differential equation
among the general story, the upper story and lower story is given as follows:
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{ĢR}= [K ] {ĢP}
|1
(2
where {ĢR} and {ĢP} are the vector of incremental sway angle and shear load at each story, respectively. [K ])|1 is
the band matrix, which is the horizontal stiffness of structure composed of rotation stiffness of hinges at both
edges of rigid members and shear spring stiffness of steel panel shear walls at each story. For equation (1) and
(2), incremental numerical analysis was carried out..
Structural elements
For core wall system with Type A, the relationship between shearing force and sway angle on each hybrid wall
at 2nd to 9th story can be given as additional property in Figure 6 (a). On the basis of this relationship, hysteresis
loop can be assumed mathematically. For simplified top and bottom of hybrid columns and both ends of hybrid
beams with Type A, B and C, the relationship between bending moment and rotation angle can be given as
degrading tri-linear hysteresis loop. Degraded inclination, which results from increase in concrete crack,
development and so on experimentally, is simplified to aim at the last unloading point in having loaded in the
same direction as the present in such a point that crack has closed. For Type C, Figure 6 (c) indicates that the
mechanism and the assumed loop of steel panel shear wall. This diagram represents that, at the elastic stage,
steel panel shear wall makes the formation of diagonal tension field in one direction after the shear buckling and
come up to the yielding point of steel at last. And controlling point which describes the constant tension stress is
decreased by given reversed deformation, and at last this tension field becomes compression field to buckle.
From this stage, steel panel shear wall starts to make the formation of diagonal tension field in the conjugate
direction and to lose the compression field at the same time. After the event, it is similar to the behaviour from
the first stage. In solving equation (1) and (2) composed of stiffness of these assumed hysteresis, each time
controlling points reach to boundary points, stiffness must be changed to continue to compute the other equation
(1) and (2)
Analytical results
Figure 7 shows tested P-R relationship of compared with computed results of Type A, B and C. Type A,
analysis underestimates the ultimate strength. Within about the sway angle of 0.010 at which cantilever yields at
1st story, computed values follow tested both qualitatively and quantitatively. Type B and C, computed values
QW
resistance property added wholly
comp. field of concrete shear wall
tens. field of steel panel shear wall
θS
0
rigid member
hinge of
and
brace A and B in being
formed and extinguished,
brace B forming comp.
field
brace A forming tens. field
Q
Qy
Qy/6
brace A in being
unloaded elasticaly
R
(a) steel panel shear wall with concrete covering
My M
brace B in being unloaded
elasticaly
Ry/6
My/3
Ry
brace A forming comp. field
θ
θy
(b) Hinge at the end of both edge
of beams or columns
brace B and A in being
formed
brace B forming tens.
field
(c) shear spring of steel panel shear wall
Figure 6 : Hysteresis Loop Formation Process
also coincide with tested value fairy good. Especially, non-linearity of whole behaviour due to change in system
with steel panel shear wall and degrading-stiffness property with concrete is represented by analysis. And it is
found that parallel damper of steel panel shear walls and serial damper of hinges each other in frame system
model for Type B and C may influences structural performance. Figure 8 shows sway deflection curves with
each model. Type A, horizontal displacement varies linearly throughout 1st to 9th story while Type B and C
horizontal displacement varies with S-shape of inflection point in 2nd or 3rd story. Type A, B and C, sway
deflection curves nearly symmetrical with the line of displacement of zero are presented at all. Figure 9 shows
distribution of
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P
R
36
P(kN)
24
[Type
A]
12
R(rad)
0
-0.03
-0.015
0
0.03
-12
Tested
-24
Computed
30
-36
P
0.015
P(kN)
R
20
10
[Type B]
R(rad)
0
-0.03
-0.015
0
0.015
0.03
-10
Tested
-20
Computed
-30
18
P
P(kN)
R
12
6
[Type
C]
R(rad)
0
-0.1
-0.05
0
0.05
0.1
-6
Tested
-12
Computed
-18
Figure 7: Comparison of P-R relationship between tested and computed values
story sway angle. Type A, thinking along with linearly deflection in Figure 8, bending deformation is larger than
shear deformation at 1st story. Type B and C, it is found that shear deformation at 2nd or 3rd story is the largest of
all stories. This indicate that steel panel shear wall in Type B starts to yield from the middle of story. And Type
B, it is slightly found that forced deformation in one and the other direction gives reversing yielding turn of steel
panel shear wall especially between at 1st and 6th story.
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height (mm)
1080
960
840
720
600
480
360
240
[Type A]
120
0
-30
Nth story
9
8
7
6
5
4
3
2
[Type A]
1
0
-0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04
story sway angle (rad)
±2/1000
±3/1000
±5/1000
±7/1000
±10/1000
±20/1000
±30/1000
-20 -10
0
10
20
30
horizontal displacement (mm)
height (mm)
1080
960
840
720
600
480
±5/1000
360
±7/1000
±10/1000
240
±20/1000
120
[Type B]
±30/1000
0
-10 -8 -6 -4 -2 0 2 4 6 8 10 12
horizontal displacement (mm)
Nth story
9
8
7
6
5
4
3
2
[Type B]
1
0
-0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04
story sway angle (rad)
height (mm)
Nth story
9
1080
8
960
7
840
6
720
5
600
±7/1000
4
480
±10/1000
3
360
±20/1000
±30/1000
2
240
±50/1000
1
120
[Type C]
±100/1000
[Type C]
0
0
-40 -30 -20 -10 0 10 20 30 40
-0.12 -0.09 -0.06 -0.03 0 0.03 0.06 0.09 0.12
horizontal displacement (mm)
story sway angle (rad)
Figure 8 : Analytical deflection curves
Figure 9 : Analytical distribution of story sway angle
CONCLUSION
In order to make clear the elasto-plastic deformation and fracture characteristics of hybrid center core shear wall
system, tests and analysis were carried out. Hybrid structure Type A and B of steel panel shear wall with and
without concrete covering, respectively, gives the lower deformation capacity and the higher initial stiffness and
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ultimate strength as shown in reinforced concrete structure, compared with corresponding moment frame.
Experimental P-R relationship can be fairly well followed by incremental deformation method at which two
simplified models are proposed.
ACKNOWLEDGEMENTS
The authors would like to express their thanks to Mr. Masuda (Maeda Corporation) for his kind co-operations.
REFERENCES
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Loads”, Proc., 4U.S. National Conf., Earthquake Engrg., Vol.2 pp.895-904.
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