2i-0066 The 17th World Conference on Earthquake Engineering

17th World Conference on Earthquake Engineering, 17WCEE

Sendai, Japan - September 13th to 18th 2020
Paper N゜C000953
Registration Code: S-A00978

ANALYTICAL STUDY ON BEHAVIOR OF A R/C FRAME WITH WALLS

AND STRUCTURAL GAPS DUE TO EXCESSIVE EARTHQUAKE MOTION

M.Honaga (1), T. Mukai (2), H. Kinugasa (3), Y. Matsuda (4)

(1) Graduate Student, Tokyo University of Science, 7115123@gmgmail.com

(2) Senior Research Engineer, Building Research Institute, t_mukai@kenken.go.jp
(3) Professor, Tokyo University of Science, kinu@rs.noda.tus.ac.jp
(4) Assistant professor, Tokyo Univ. of Science, Japan, matsuda_y@rs.noda.tus.ac.jp

Abstract
Today, mainly for simple modeling, many buildings have structural gaps between frame and walls. Analysis for such
buildings and evaluation of their seismic safety are performed with the assumption that structural gaps will not become
blocked and the frames around them will not be badly affected. However, if an earthquake motion occurs that is larger
than expected in structural design, it is expected that horizontal response deformation will cause structural gaps to become
blocked and wall members to contact the frames around them. In this case, seismic evaluation for such buildings must be
performed while considering these phenomena; however, no such method has been established yet.
By creating an analytical model that takes contact into account, this study aims to understand the behavior of a
whole building when wall members contact the frames around them, and to evaluate seismic safety performance including
negative effects when contact is made.
Therefore, a nonlinear-pushover analysis is conducted for a full scale five-story reinforced concrete frame
specimen with walls and the gaps that exhibited the above behavior. The validity of modeling the behavior of wall
members contacting the frame around them as observed during the experiment is investigated by comparing the analytical
results with the test results in terms of the horizontal load–deformation relationship, the sequence in which structural
members make contact, and the representative deformation angle of the whole building at the time of contact, by
specifying a shear spring constant so that horizontal stiffness increases steeply after a certain level of horizontal
displacement is reached. Using the analytical results, parameters such as changes in the stress transferred by the contacting
peripheral members are checked, and evaluation the seismic safety performance for a whole building will be done.

Keywords: a full scale reinforced concrete building; rectangle-section wall; contact; structural gap; nonlinear pushover
analysis

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2i-0066 The 17th World Conference on Earthquake Engineering

17th World Conference on Earthquake Engineering, 17WCEE

Sendai, Japan - September 13th to 18th 2020

1. Introduction
This paper proposes a new type of structure [1] that can contribute to secure their continuous availability after
earthquakes. It is based on RC (reinforced concrete) structural technology that does not require advanced
technologies such as vibration control or seismic base isolation, and can be used with conventional structural
design methods. This structural type gives higher strength and rigidity to each layer than regular rigid-joint
frames. It works by modifying the columns of the rigid-joint frame with sleeve walls, which reduces the
maximum response displacement under seismic conditions. This reduction in seismic response can increase
the continuous availability of structures after earthquakes following damage to the non-structural parts of
buildings.
Experiments conducted by Fukuyama et al. (2015)[1] evaluated the ability of columns with sleeve walls
to provide structural gaps and prevent rectangular-section walls from shearing forces. However, the gaps
became blocked during the experiment and the rectangular-section walls contacted the spandrel wall and bore
shearing forces as a result. Although there is no need to assume that such contact will occur under the levels
of earthquake motion that are assumed during the design phase, such contact could occur with stronger
earthquakes. On the other hand, although the experiments of Mukai, Kawagoe et al. (2018) demonstrated a
modeling method [2, 3] that properly evaluated the behavior noted above, the behavior of a frame with
rectangular-sectioned walls in contact with spandrel walls (as described above) has not been investigated.
Accordingly, the purpose of this study was to build an analytical model that considers such contact and predicts
its behavior. In addition, this paper investigates the seismic safety of frames comprising this type of contact.

2. Outline of experiments
2.1 Outline of specimens
An outline of the specimen (Fukuyama et al. 2015[1]) analyzed in this paper is given in Fig.1. The specimen
was a full-scale, solid, five-story, reinforced concrete frame with two spans in the ridge direction
(pressurization in-plate direction) and one span in the span direction (pressurization off-plate direction). In
addition, it had a structural gap between the wing walls/spandrel walls or hanging partition walls, and between
the spandrel walls and rectangular-section walls, so that the wing wall was utilized as the only structural
skeleton. The width of the structural gaps between the wing walls/spandrel walls or between the hanging
partition walls was 45 mm, and the gaps between the spandrel walls/rectangular-section walls were 80 mm. In
Fig.1, the framing elevations in the ridge and span directions are specified in the upper-left and upper-right
areas, and a framing plan of a typical floor is specified in the lower-left area. The mechanical characteristics
of the reinforced steel and concrete used are specified in Tables 1 and 2, and a sectional view of the column
and beam member is given in Fig.2. Sectional views of a rectangular-section wall and wing wall attached to a
column are provided in Fig.3. Each wing wall had reinforcing detail on the same edge. Their projecting length
were 700 mm and the wall thickness was 200 mm. Reinforcing bars for the wall edge were 6-D16 bound with
enclosed-type reinforcing rods. Vertical reinforcement in the walls comprised doubly-arranged D10@200,
bound with width-fixing reinforcements (D10) installed in the orthogonal direction. Horizontal reinforcements
in the walls were fixed with 180° hooks and linearly fixed at the column cross-sections.
Spacings between the vertical reinforcements in the walls were doubly-arranged D10@100 in the first
floor (to control buckling of the vertical reinforcements) and D10@200 in the other floors. Figure 3 provides
a representative sectional view of the first floor. It can be computed that a certain degree of ductility capacity
is obtained, as the degree of shear allowance was calculated as 1.26 by calculating the flexural ultimate strength
based on Bernoulli-Euler theory, and the ultimate shear strength based on a segmentation cumulative equation
for the columns with sleeve walls in the first floor.
Figure 4 specifies the bar arrangement of the slab reinforcement. The slab thickness was 200 mm, with
D10@50 used for both top and bottom reinforcements in the ridge direction, D10 and D13 arranged alternately
at intervals of 150 mm for the top reinforcement, and D10@150 forming the bottom reinforcement in the span

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2i-0066 The 17th World Conference on Earthquake Engineering

17th World Conference on Earthquake Engineering, 17WCEE

Sendai, Japan - September 13th to 18th 2020

direction. Slab reinforcements within the effective width of the slabs in the span direction were placed in seven
rows, with 18.5 rows in the overall width (for both top and bottom reinforcements).

Table 1 – Material characteristics of the reinforced steel

6000 6000 6000
σy Es
Reinforced steel
(N/mm2) (N/mm2)
3150 3500 3500 3500 3500

D10 (Wall and slab) SD295 352 182600

D10 (Horizontal reinforcements
SD295 372 185100
in the wall)
D13 (Horizontal reinforcements
SD295 340 182000
in the column and beam)
D13 (Slab for top reinforcement) SD295 342 180600
D16 SD295 384 187100
D25 (1F column and beam) SD345 383 182000
700 300

D25 (2~5F column and beam) SD390 449 181000

σy:Yield strength of reinforced steel, Es:Young's modulus of reinforced steel
South Center North
column column column Table 2 – Material characteristics of the concrete
Concrete σB (N/mm2) Ec (N/mm2)
6000

5F 31.3 24700
4F 33.6 26200
3F 37.7 28500
2F 33.0 26100
Fig. 1 – Outline of the specimen (unit:[mm]) 1F 34.9 28600
σB:Compressive strength, Ec:Young's modulus of concrete

Column 1F 2F 3~5F Beam 2~4F 5・RF

700 700 700 500 500
163.5 115 71.5 163.5 115 71.5 163.5 115 71.5 105 105 105 105
71.5 115 163.5 71.5 115 163.5 71.5 115 163.5 75 140 75 75 140 75
163.5 115 71.5

433 100 96

96
71.5 115 163.5

Sectional view Sectional view

700

700
533
71

71

Vertical Vertical
16D25(SD345) 16D25(SD390) 8D25(SD345) 6D25(SD345)
reinforcements reinforcements
Horizonal Horizonal
4D13(SD295A)@100 2D13(SD295A)@100 2D13(SD295A)@100
reinforcements reinforcements

Fig. 2 – Sectional view of the column and beam (unit:[mm])

200
200

Rectangular-section wall 1~5F Wing wall attached to a column

Span direction
Span direction bottom reinforcements:
bottom reinforcements: D10@150D10@150
900 top reinforcements: D10
70 205 40 top reinforcements: D10 and D13and D13 arranged
arranged alternately
alternately at intervalsat@150
intervals @150
55 130 200 700 200 200
Sectional 55145 150 200 150 14555
view
59 8259
200

Sectional
Vertical view
D10(SD295@200)
reinforcements
Horizonal
D10(SD295@100)
reinforcements
Reinforcing bars
4-D13(SD295) Ridge direction D10@150 (both top and bottom reinforcements )
for the wall edge Ridge direction D10@150 (both top and bottom reinforcements )

Fig. 3 – Sectional views of a rectangular-section wall and Fig. 4 – The bar arrangement of the
wing wall attached to a column (unit:[mm]) slab reinforcement

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2i-0066 The 17th World Conference on Earthquake Engineering

17th World Conference on Earthquake Engineering, 17WCEE

Sendai, Japan - September 13th to 18th 2020

2.2 Loading plan

As shown in Fig.5, pressurization was conducted on 4F and RF with an actuator installed so that the center of
the slab thickness was the pressurization core, with a load ratio of 4F:RF = 2:1. Four actuators were installed
on both the RF and 4F and the external forces were controlled by the average value of the horizontal
displacement of the RF beam core position.
The pressurization cycle comprised positive and negative alternating cyclic loading at the representative
deformation angle Rr (horizontal displacement of R layer beam core height/distance from top end of the stub
to the R layer beam core height). Loads Rr = 1/1600 rad and 1/800 rad were applied once, Rr = 1/400 rad,
1/200 rad, 1/100 rad, 1/67 rad, and 1/50 rad were applied twice, then Rr = 1/37 rad was applied in the forward
direction.
2.3 Measurement plan
The horizontal deformation angle and representative deformation angle Rr of each layer were measured by a
horizontal displacement measuring device installed at the beam core position of each layer. The positions of
the horizontal displacement measuring devices are specified in Fig.5. Deformation was measured against the
main reinforcements of major column/beams, flexural reinforcing bars, and slab reinforcements in the
pressurization in-plate direction. Since the deformation of beam bars on the north side was used for
examination in this paper, their positions are specified in Figs.6 and 7.
2.4 Experimental results
Figure 8 shows the envelope curve representing the relationship of base shear to representative deformation
angle. The maximum strength before the rectangular-section wall contacted the spandrel wall was about 4400

- + ab
1 RF
2
3150 3500 3500 3500 3500

1 5F
7000

2
1 4F
2
1 3F
10400

2
1 2F
2
600

South Center North a b

column column column
The positions of the horizontal displacement measuring devices

Fig. 5 – Loading device and the positions of the horizontal Fig. 6 – Strain gauge position of beams near
displacement measuring devices (unit:[mm]) rectangular-section walls (unit:[mm])

Rectangular-section wall contacted the spandrel wall

a1 b1
6000
Base shear (kN)

5000
4000
a2 b2
3000
2000
1000
0
0 0.01 0.02 0.03 0.04
Strain gauge of beam Representative deformation angle (rad.)
Fig. 7 – Strain gauge position of north beam Fig. 8 – Relationship of base shear to
representative deformation angle
4

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17th World Conference on Earthquake Engineering, 17WCEE

Sendai, Japan - September 13th to 18th 2020

kN, demonstrating a maximum strength at the rectangular-section walls at a representative deformation angle
of +0.01 rad. In general, strength deterioration was not observed during this period, demonstrating tough
behavior. At the point near the representative deformation angle of +0.014 rad, the structural gap in the
specimen between the rectangular-section wall and the spandrel wall on the second and third layers was closed
and the walls contacted (as shown by the broken line in Fig.8). The rectangular-section wall bore the shearing
force by contacting the spandrel wall, and base shear increased at the distortion angle thereafter. In addition,
regarding contact between the components described above, since the floor height was 3500 mm while the
structural gaps between the rectangular-section and spandrel walls were 80 mm, it was assumed that they
would not make contact when the distortion angle reached 0.02 rad (the structural gap was wide enough
because 3500 mm × 0.02 = 70 mm). However, contact of the components was observed at a point earlier than
this. The cause can be considered to be interlayer deformation, as well as rotation of the rectangular-section
wall fitted to the beam that occurred due to deformation of the beam.

3. Outline of the analysis

3.1 Frame modeling
As shown in Fig.9, the frame had a solid frame with each component of the column/beam modeling by line
element at the core position of the structure, and nodes were mounted on the joints of each component. The
degrees of freedom in movement and rotation were constrained on nodes 1, 2, 3, 19, and 21, as specified in
Fig.9.As shown in Fig.9, in accordance with Mukai, Kawagoe et al. (2018)[2], the rigid areas of the columns
were on the beam face position, and those of the beams penetrated into the joint sides by only D/4 (where D
represents the component depth) from the face position of the columns with the sleeve wall. Dangerous cross-
sectional positions occurred on the face positions of the column, beam, and wall.
In addition, the rectangular-section walls were modeled as single columns. In doing so, they were
configured so that they would bear the yield strength when displaced enough to contact the spandrel wall. Here,
shear springs that caused contact (Figs.9 and 10) were installed. The upper part of the rectangular-section wall
was configured as a rigid zone with a length of 650 mm (shown as a bold line in Fig.10). Since the rectangular-
section wall contacted the entire spandrel wall in the experiment conducted by Fukuyama et al. (2015)[1], we
determined the node height of the lower part of the rectangular-section wall to be the center location of the
contacting surface. In addition, to transmit flexural stress to the beam that the rectangular-section wall was
attached to, the rectangular-section wall was treated as a stud and the attached beam was divided at the center
of the wall depth of the rectangular section of the wall and modeled. Since the divided beam was specified as
a single member, a rigid zone was not provided on the beam at the joint of the rectangular-section wall and
beam. Although models that have a rigid zone at the joint can be considered adequate, differences between the
modelled and experimental values of initial stiffness can arise when contact is made. Furthermore, since there
were only small differences in the results of the model without a rigid zone after contact, the study was
conducted with a model that did not have a rigid zone on the joint.
A rigid floor was assumed for horizontal pressurization and configured in accordance with the
pressurization results by making its center of gravity act as the pressurization point during the experiment. The
force strength and control methods were as follows.
・The horizontal force was configured on the center of gravity of the slab at core heights of 4F and RF so the
force strength became 4F:RF = 2:1.
・Displacement control was configured so that the horizontal displacement of the rigid floor built on the RF
slab core height increased by 0.1 mm per step.
Furthermore, although the external forces used in the experiment alternated between positive and
negative, a one-way load was used for this analytical model.

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17th World Conference on Earthquake Engineering, 17WCEE

Sendai, Japan - September 13th to 18th 2020

The axial force used to calculate the yield strength of the material was configured by estimating the
weight of the reinforcing steel and concrete used according to the controlling area of the floor for all nodes.
The weight of reinforcing steel and concrete was found by calculating the cubic volume based on the cross-
sectional area and floor height of each component. Then, the weight of reinforcing steel was estimated by
multiplying the unit volume weight by 76.93 kN/m3, while the weight of concrete was estimated by multiplying
the unit volume weight by 24.5 kN/m3. The PΔ effect was not considered in this analysis.
3.2 Element modeling
Columns were modeled by placing flexural springs on the edges of the material and placing shear springs and
axial springs at the center. The beams were modeled as single-axis springs by placing flexural springs at the
edges of the material and shear springs at the center. Flexural and shear springs were regarded as three
polygonal line models that took crazing strength and yield strength limits into account. Axial springs were
regarded as a two polygonal line model that took the elasticity of the compression side and the yield of
reinforcement steel at the tension side into account.
The rectangular-section wall was configured to bear moment and shearing forces. The shear spring used
for the consideration of the contact specified in Figs.9 and 10 was configured so that the rigidity would increase
suddenly (rigidity was defined as 100 MN/mm) and the rectangular-section wall would bear yield strength
once a certain displacement was reached, as shown in Fig.11, since the structural gap between the rectangular-
section and spandrel walls was 80 mm. Since this deformation dominated before a large enough stress that
could destroy the part that was contacted (because the rectangular-section wall was equipped with a hinge), a
simple model that transmits stress through a shear spring with a hard inclination was used in this paper.

875 4250 875 875 4250 875 28

8
2800 350 2800 350 2800 350 2800 350 2800 350

16 17 18
7
40

650
39

13
36
14
38
15
27
350

35 37
24

310
32 34
10 11 12 4 310
350

31 33 単位
23 5 mm
28 30
7 8 9
Fig. 10 – Details of frame model considering
350

27 29 rectangular-section walls
24 26
4 5 6
350

23 25
Force (kN)

20 22
1 2 3
19 21
…接触を考慮する為のせん断ばね 単位：mm
〇 Shear springs that cause contact
…節点番号
□ Node number -100 -80 -60 -40 -20 0 20 40 60 80 100
Horizontal deformation (mm)
Fig. 9 – Frame model considering
rectangular-section walls (unit:[mm]) Fig. 11 – Shear spring that cause contact

Regarding the flexural and shear springs of the columns, beam, and rectangular-section walls, the initial
stiffness of the flexural spring was calculated by Formula (1), while that of the shear spring was calculated by
Formula (2) according to a previous study[4]. In accordance with study[5], Formula (3) was used to calculate
the rate of rigidity decrease in the flexural springs used for the columns and beams, while Formula (4) was
used for the rectangular-section wall. Formula (5) was used to calculate the rate of rigidity decrease in the
shear spring used for the columns and beams in accordance with study[6], while Formula (6) was used for the
6

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Sendai, Japan - September 13th to 18th 2020

rectangular-section wall in accordance with study[5]. The flexural and cracking strengths of the columns, beams,
and rectangular-section walls were calculated by Formula (7) in accordance with study[5]. Also based on
study[5], the shear and crazing strengths were calculated with Formula (8) for the columns and with Formula
(9) for the columns for beams. In addition, Formula (10) was used for the shear and crazing strength of the
rectangular-section walls. In accordance with document[7], the ultimate flexural strength was calculated with
Formula (11) as a reset total solution. Ultimate shear strength was calculated with Formula (12) in accordance
with document[5]. Since the rectangular-section walls of the specimen used in this paper hung down to the
beams, the yield strength was calculated based only on the strength of the concrete and reinforcing steel, as for
the beams, with shaft force of 0. In addition, although the effective width of the slab was determined as 1 m in
the study conducted by Mukai, Kawagoe, et al. (2018)[2,3], to get close to the experiment value, the lengths
were modified in each floor by assuming the point where the slab reinforcement yielded to be the effective
width. Since the maximum yield strength before contact was observed at the point around the representative
deformation angle of +0.01 rad, the yielding state of the slab reinforcement at this point can be described by
Fig.12.
600 600 450
600 600

2F 3F 4F 5F RF

350 350 ● Strain gauge position ■ Slab reinforcement yielded

Fig. 12 – Yielding state of the slab reinforcement (representative deformation angle of +0.01 rad.)

Further, it was considered that the strength of the beam changes, since the shearing force borne by the
rectangular-section walls acts as a shaft force against the beam when the rectangular-section walls are
contacted. However, when the shearing force of the rectangular-section wall calculated during analysis was
entered into Formula (11), the change in yield strength was only about 7% compared with models without
shaft force. Therefore, fluctuation in the shaft force was not considered in this model.

𝐾𝑓 = 6𝐸𝑐 𝐼/𝐿 (1)

𝐾𝑠 = 𝐺𝐴/𝜅𝐿 (2)
𝑎 𝑑 2
(0.043 + 1.64𝑛𝑝𝑡 + 0.043 ( ) + 0.33𝜂0 ) ( )
𝐷 𝐷
𝛼𝑦 { 2
𝑎 𝑑
(−0.0836 + 0.159 ( ) + 0.169𝜂0 ) ( )
𝐷 𝐷

2.0 < upper formula if (a/D), 2.0 ≥ lower formula if (a/D) (3)
𝛼𝑦 = 𝑤𝑀 𝑦𝐶 𝑛 /𝐸 𝐼𝑤 𝜀𝑦 (4)

Here, 𝑤𝑀𝑦 = yield moment of rectangular section wall [N・mm], 𝐶𝑛 = the distance from the elastic neutral
axis when the second vertical reinforcement edge from the tension edge is at the yield point to the center of
gravity of the vertical reinforcement on the tension side [mm], E = Young's modulus of concrete [N/mm2], 𝐼𝑤
= cross-sectional secondary moment [mm4], and 𝜀𝑦 = yield strain of vertical reinforcement.

𝑄 𝑄
α = ( 𝛾𝑢𝑛 ) / ( 𝛾𝑐 ) (5)
𝑢 𝑐

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Sendai, Japan - September 13th to 18th 2020

0.46𝑝𝑤 𝜎𝑦
𝛽𝑢 ＝ 𝐹𝑐
+ 0.14 (6)

𝑀𝑐 = (0.56√𝜎𝐵 + 𝜎0 )𝑍𝑒 [N・mm] (7)

0 𝜎 0.085𝐾𝑐 (𝐹𝑐 +500)

𝑄𝑐 = (1 + 150 )( 𝑀 ) bj [kg] (8)
+1.7
𝑄𝑑

0.085𝐾𝑐 (𝐹𝑐 +500)

𝑄𝑐 = ( 𝑀 ) bj [kg] (9)
+1.7
𝑄𝑑

𝑉𝑐 = 𝜏𝑠𝑐𝑟 𝑡𝑤 𝑙𝑤 /𝑥𝑤 [N] (10)

Here, 𝜏𝑠𝑐𝑟 represents the shear crazing force of concrete [N/mm2], the tensile strength of concrete is 𝜎𝑡 (=
0.33√𝜎𝑏 , where 𝜎𝑏 represents the compressive strength of concrete), 𝑡𝑤 = the rectangular-section wall
thickness [mm], 𝑙𝑤 = 0.9 × inside length of the rectangular-section wall [mm], and 𝑥𝑤 = the section modulus,
which is the rectangular section multiplied by 1.5.

𝜎𝑎𝑣 𝑏(𝛽1 𝑥𝑛 ) 2
𝑀𝑢 = 𝐴𝑠𝑡 𝜎𝑠𝑡 𝑑 − 𝐴𝑠𝑐 𝜎𝑠𝑐 𝑑𝑐 − + Ng [N・mm] (11)
2

0.23
0.068𝑝𝑡𝑒 (𝐹𝑐 +18)
𝑄𝑢 = { 𝑀
+ 0.85√𝜎𝑤ℎ 𝑝𝑤ℎ + 0.1𝜎0 } 𝑡𝑒 𝑗 [kN] (12)
√𝑄𝐷+0.12

4. Comparison of analytical and experimental results

4.1 Evaluation of the load-deformation relationship
Figure 13 describes the base shear-representative deformation angle relationships obtained through experiment
and theoretical analysis. It shows that the load-deformation relationship is mostly reproducible by letting the
shear spring representing the contact bear horizontal force after contacting the rectangular-section wall. The
analysis shows that the base shear starts to increase in around a representative deformation angle of 0.013 rad.
In addition, Fig.13 shows that the rate of increase in base shear is not constant, which is because the
rectangular-section walls are making contact at different times. Analysis shows that the base shear increases
suddenly when the rectangular-section walls on 2F and 3F contact for the first time. The rectangular-section
wall produces flexural yielding near Point A in Fig.13 and the rigidity is reduced again. After this, the
rectangular-section walls on 1F, 4F, and 5F begin to make contact near Point B in Fig.13 and the base shear
increases by shearing force. Finally, the base shear stops increasing near Point C in Fig.13, when all
rectangular-section walls become flexural-yielding. It is thought that the reason why the yield strength becomes
constant is because the degree of shear allowance (ultimate shear strength/ultimate shear strength during
flexural) in the rectangular-section walls in this specimen is > 2. Therefore, the walls do not collapse, showing
that the specimen has high strength.
4.2 Evaluation of the starting point of contact between the rectangular-section and spandrel walls
This section analyzes the contact starting point through the horizontal displacement of nodes and verifies it by
comparison with the experimental data. Figure 14 describes the horizontal displacement of nodes for each
representative deformation angle between 2F and 3F. The point where the rate of increase in the horizontal
displacement of nodes 24 and 26 (refer to Fig.9) changes under the influence of the shear spring used to
consider the contact was regarded as the contact starting point. Figure 14 shows that the rectangular-section

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Sendai, Japan - September 13th to 18th 2020

wall on the north side contacted the spandrel wall slightly before south side rectangular-section wall. A similar
tendency was confirmed among other nodes as well.

Rectangular-section wall contacted the spandrel wall Contact Starting point

Horizonal deformation(mm)
6000
ab c 300
Node 24 (south side)
Base shear (kN)

5000
4000 200 Node 26 (north side)
3000
Contact starting point
2000 100
Experiment (south side)
1000 Contact starting point
Analysis result
0 (north side)
0
0 0.01 0.02 0.03 0.04
0 0.01 0.02 0.03 0.04
Representative deformation angle (rad.) Representative deformation angle (rad.)
Fig. 13 – Relationship of base shear to Fig. 14 – Horizontal displacement of nodes for
representative deformation angle representative deformation angle (2~3F)

The contact starting point in the experiment was estimated by distortion of the beam in the vicinity of
the rectangular-section wall. Since beam bar strain gauges were only attached to the rectangular-section walls
on the north side in the experiment, the contact starting point on the north side was assumed. The positions of
the strain gauges are shown in Figs.6 and 7. In these figures, the upper-left beam of each floor is denoted as
a1, the lower-left beam is a2, the upper-right beam is b1, and lower-right beam is b2. As shown in Fig.15,
which describes the moments before and after contact, the moment of the beams changes after contact with the
rectangular-section walls. Among the strain gauges in the vicinity of the rectangular-section walls, those at b1
and b2 change rapidly. The representative deformation angle at this point was defined as the contact starting
point for the experimental values. Figure 15 describes the moments of the rectangular-section wall on the north
side of 2F and its peripheral members. The values for beams b1 and b2 on 3F are described in Fig.16 and are
representative of the strains on beam bars in the vicinity of the rectangular-section walls. Further, Fig.16 shows
the relationship between strain and representative deformation angle within the range Rr = −0.01–0.015 rad. It
was confirmed that at locations b1 and b2, a rapid change in strain began at a representative deformation angle
of approximately 0.014 rad. The strains of the beams in the other floors were also assumed according to the
method above.

60 50
Berore contact Before contact
Before contact After contact 20 40
Strain (μ)

After contact
Strain (μ)

30 After contact
-20
20
-60 10
-100 0
-0.02 -0.01 0 0.01 0.02 -0.02 -0.01 0 0.01 0.02
Representative deformation angle (rad.) Representative deformation angle (rad.)

Fig. 15 – Moments before and after contact Fig. 16 – Strain on beam bars (Left:b1, right:b2)

The contact starting points determined by the method above are compiled in Table 3 so that the
experimental and theoretical values can be compared. Since only the contact starting point of the rectangular-
section wall on the north side was calculated experimentally, comparison is made with that wall. In addition,
contact starting points plotted on the load-deformation angle relationships are shown in Fig.17. In both the
experimental and theoretical data, the order of occurrence of contact starting points is 2F and 3F, followed by
1F and 4F, then 5F, which demonstrates that the evaluation was accurate. In addition, we confirmed that the
representative deformation angles at the contact starting points were within 0.013–0.020 rad, which is a
reasonable range.

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2i-0066 The 17th World Conference on Earthquake Engineering

17th World Conference on Earthquake Engineering, 17WCEE

Sendai, Japan - September 13th to 18th 2020

Table 3 – Comparison of representative 6000

deformation angles at which contact started

Base shear (kN)

Blue…Experiment
5000 Red…Analysis result
●：Contact starting point (1F)
Floor Experiment (rad.) Analysis result (rad.) △：Contact starting point (2F)
5F 0.020 0.017 4000 ×：Contact starting point (3F)
4F 0.018 0.015 ■：Contact starting point (4F)
◆：Contact starting point (5F)
3F 0.014 0.013 3000
2F 0.014 0.013 0.005 0.01 0.015 0.02 0.025
Representative deformation angle (rad.)
1F 0.018 0.016
Fig. 17 – Comparison of contact starting point

5. Investigation on seismic safety of frames after contact with rectangular-section walls

Flexural yielding occurred on the column bases and terminal members of the beams on 1F in the specimen.
Based on a determination that the beams bear the shearing force of the rectangular-section walls, which
endangers the beams, we focused on the degree of shear allowance (ultimate shear strength of beams/shearing
force of beams) to investigate the safety of the beams used in this study. Regarding calculation methods, we
used data such as the theoretical inflection point ratio to re-calculate the ultimate shear strength. The shearing
force borne by the beams is the sum of the shearing forces occurring when the beams have a flexural yield and
that borne by the rectangular-section walls. A value that accounts for the whole width of the slab as effective
width was calculated when estimating the flexural ultimate strength. In addition, calculations were carried out
with an assumption that the beams bear a shaft force due to contact with the rectangular-section walls. The
ultimate flexural strength and ultimate shear strength were re-calculated by taking the shaft force into account,
and calculations were carried out for two cases: 1) when the beams bore a compressive axial force and 2) when
the beams bore a tensile axial force. The results are shown in Table 4.

Table 4 – Degree of shear allowance (beam)

Effective width of the slab Effective width of the slab
(1m) (whole width)
Beam (2~4F) Beam (5F・6F) Beam (2~4F) Beam (5F・6F)
Before contact 2.05 2.48 1.59 1.80
Degree of shear allowance
After contact 1.51 1.72 1.25 1.36
（ultimate shear strength of beam
Compressive axial force consideration 1.46 1.67 1.21 1.32
/shearing force of beam）
Tensile axial force consideration 1.57 1.79 1.28 1.40

Table 4 shows that the degree of shear allowance decreased after contact compared to that before contact,
with the lowest value being 1.21. It can be confirmed from this that the possibility of shear fracture increases
when there is contact between members of the framework. It will be necessary to investigate the seismic safety
of the frame with consideration of earthquakes that are stronger than the expected level, which could cause
contact between members of the framework.
Since it can also be assumed that the possibility of shear fracture increases for the columns, we
investigated the columns in the first floor, whose column bases had flexural yield. Regarding calculation
methods, we used data from the theoretical analysis to re-calculate the ultimate shear strength, as with the
beams. We also used theoretical estimates for the shearing force of the columns. In addition, since the shearing
force of the columns can change according to the shearing force of the beams, calculations were carried out
for each calculation pattern of the beams. The results are shown in Table 5.
It can be confirmed that the degree of shear allowance decreased, as with the beams. Specifically, the
lowest value among the center columns in the first floor was 1.13, indicating that a sufficient degree of shear
allowance was not ensured.

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2i-0066 The 17th World Conference on Earthquake Engineering

17th World Conference on Earthquake Engineering, 17WCEE

Sendai, Japan - September 13th to 18th 2020

Table 5 – Degree of shear allowance (1F column)

South column Center column North column
(1F) (1F) (1F)
Before contact 1.76 1.51 2.32
Beam:Effective width of the slab (1m) 1.47 1.30 2.08
Degree of shear allowance
Beam:effective width of the slab (whole width) 1.29 1.15 1.93
（ultimate shear strength of column
Beam:axial force consideration
/shearing force of column） 1.45 1.29 2.08
(effective width of the slab (1m))
Beam:axial force consideration
1.27 1.13 1.93
(effective width of the slab (whole width))

5. Conclusions
We conducted a static nonlinear-pushover analysis of the specimen of Fukuyama et al. (2015)[1] with
consideration of the behavior occurring when rectangular-section walls contact a spandrel wall, and gained the
knowledge described below.
・ We were able to experimentally evaluate load-deformation relationships and the sequence in which
structural members make contact in a specimen comprising rectangular-section walls and spandrel walls. Shear
springs were used where the horizontal stiffness increased rapidly after the point where a specified horizontal
displacement was reached. In addition, by making comparisons with experimental values, we confirmed that
the representative deformation angle at the contact starting point estimated by theoretical analysis was within
a reasonable range.
・It will be necessary to secure slit widths at the design phase to prevent contact between framework members,
which can occur when structural gaps are closed during a major earthquake. It is possible to estimate the
necessary slit width by applying the model presented in this study.
・It is confirmed that the degree of shear allowance for column and beam members decreases when an
unexpectedly strong earthquake occurs, as members of the framework contact each other. From this, it is shown
that it is necessary to secure sufficient degrees of shear allowance for columns and beams when considering
unusually strong earthquakes.

Acknowledgments
This study was conducted as part of the research “Development of function continuation technologies for
disaster center building”, which is part of the Comprehensive Technological Development Project of the
National Institute for Land and Infrastructure Management, and as “Development of seismic-assessment
technologies for continual use of existing buildings after an earthquake”, a research task designated by the
Building Research Institute. All related parties are gratefully acknowledged.

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2i-0066 The 17th World Conference on Earthquake Engineering

17th World Conference on Earthquake Engineering, 17WCEE

Sendai, Japan - September 13th to 18th 2020

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