Cyclic Behavior of HPFRCC Coupling Beams with Bundled Diagonal Bars
International Journal of Concrete Structures and Materials
Cyclic Behavior of HPFRCC Coupling Beams with Bundled Diagonal Bars
Sang Whan Han
Coupled shear walls are efficient in resisting lateral forces induced by winds and earthquakes. However, it is difficult to construct coupled shear walls particularly because current design codes require complex reinforcing details within coupling beams. The objective of this study was to develop simple reinforcement details for diagonally reinforced coupling beams; reducing transverse steel by use of high-performance fiber-reinforced cementitious composites (HPFRCCs) and bundling diagonal bars are explored. Four coupling beam specimens with length-to-depth aspect ratios of 2.0 or 3.5 were fabricated and tested under cyclic lateral displacements. The test results revealed that HPFRCC coupling beams with bundled diagonal bars and widely spaced transverse reinforcement (one-half the amount of reinforcement required by current seismic codes) exhibited excellent seismic performance compared with ordinary concrete coupling beams having code-required distributed diagonal reinforcement and transverse reinforcement.
coupled shear wall; coupling beam; diagonal reinforcement; high-performance fiber-reinforced cementitious composite
Coupled wall systems consisting of separate shear walls
linked together by coupling beams at floor levels are
effective in resisting wind- and earthquake-induced forces in
(Paulay and Priestley 1992)
subjected to design-level earthquakes, coupling beams designed
according to current design codes
(NZS 1982; CEN 2004;
are expected to suffer substantial inelastic
deformations and to dissipate significant amount of energy
(MacGregor and Wight 2009)
; they play a key role in the
seismic performance of the entire coupled wall system.
Therefore, coupling beams should be equipped with
adequate reinforcement details that perform well during seismic
events, providing adequate ductility and energy dissipation,
as well as strength and stiffness
(Paulay and Priestley 1992;
MacGregor and Wight 2009)
Coupling beams reinforced by means of a conventional
detail, with longitudinal bars parallel to the span of the
beam, may experience sliding shear failure near the beam
ends at which flexural cracks caused by reversed cyclic
loading come across one another
reinforcement is not capable of preventing sliding shear
failure when flexural cracks propagate across the entire
depth of the beam between stirrups
(Paulay and Priestley
. Many studies have been conducted with the aim of
resolving this problem. Historically,
Paulay and Binney
first developed diagonal reinforcement for coupling
beams. Diagonally reinforced coupling beams strongly resist
sliding and have ductility, energy dissipation, and stiffness
retention capacities superior to those conventionally
reinforced coupling beams
(Paulay and Binney 1974; Barney
et al. 1980; Tassios et al. 1996; Galano and Vignoli 2000;
Harries et al. 2005; Fortney et al. 2008; Wallace 2012; Naish
et al. 2013)
Based on the previous studies mentioned above,
section 18.10.7 in ACI 318-14
confinement options for coupling beams with diagonal
reinforcement (Fig. 1). In the first option, each group of
diagonal reinforcement comprises at least four longitudinal
bars enclosed by densely spaced transverse reinforcement
(Fig. 1a). This confinement method entails a very intricate
arrangement of reinforcement, especially at the mid-span of
the beam where opposite diagonal reinforcement groups
meet each other. According to
Harries et al. (2005)
, the first
confinement option is practically difficult to construct wpheffiffinffi
the average shear stress in the beam is greater than 0:5 fc0
MPa, where f’c is the concrete compressive strength in MPa.
Due to such shortcomings, a second confinement option is
allowed by section 18.104.22.168(d) in ACI 318-14, in which
transverse reinforcement required for beams and columns of
Fig. 1 Diagonally reinforced coupling beams [a, b options specified in ACI 318-14
, and c option with bundled diagonal
special moment frames is provided for the entire cross
section of the beam, as a replacement for transverse
reinforcement directly enclosing diagonal bars (Fig. 1b). However,
reinforcement congestion remains a problem when he
second option is used, especially near the midspan of the beam,
where horizontal crossties conflict with diagonal bars.
In efforts to resolve the difficulty of fabricating diagonal
reinforcement in coupling beams, various reinforcing details
have been investigated and proposed to date
(Tassios et al.
1996; Galano and Vignoli 2000; Han et al. 2015)
Han et al.
recently tested the efficiency of bundled diagonal
reinforcement in reinforced concrete (RC) coupling beams.
Bundled diagonal reinforcement allows more internal space,
enhancing workability and allowing simple construction,
compared with code-specified diagonal reinforcement in
which spacers are needed to maintain the gaps between
separate diagonal bars. Bundling also increases the angle of
diagonal reinforcement measured from the longitudinal axis
of the beam, thereby increasing both flexural and shear
Han et al. (2015)
reported that coupling beams
having bundled diagonal reinforcement achieved greater
strength and energy dissipation than, and a similar
displacement ductility to, those with code-specified diagonal
During the last decade, research groups
(Canbolat et al.
2005; Parra-Montesinos et al. 2005; Parra-Montesinos 2005;
Naaman et al. 2007; Lequesne et al. 2010; Olsen and
Billington 2011; Shin et al. 2014)
have investigated the
effectiveness of high performance fiber-reinforced cement
composites (HPFRCCs) with respect to earthquake
resistance of structures. HPFRCCs are characterized by
strainhardening behavior in uniaxial tension by developing
numerous micro-cracks with the assistance of a small portion
of engineered fibers
(Li 2003; Naaman 2003; Kim et al.
2007, 2009; Li 2012)
. HPFRCCs generally show much
higher ductility than normal concrete, under both tension and
compression. Thus, the use of HPFRCC may relieve the
confinement requirements of members with highly
subjected to seismic forces, HPFRCCs are deemed to improve
energy dissipation by means of fiber bridging over
microcracks and excellent bonding between the reinforcing steel
and cement within the composite
Given the aforementioned concerns, the aim of the present
work was to develop simple reinforcement details for
diagonally reinforced coupling beams. For developing a simple
reinforcement details for coupling beams and improving
their seismic behavior, several studies have been also carried
out using fiber reinforced coupling beams
(Canbolat et al.
2005; Lequesne et al. 2010)
. This study also focused on
application of HPFRCC to diagonally reinforced coupling
beams. In particular, the effect of HPFRCCs in coupling
beams with bundled diagonal reinforcement is investigated
for the purpose of reducing the amount of transverse
reinforcement required. In addition, to simplify construction as
much as possible, the feasibility of precast coupling beam
construction was explored. Four approximately half scale
coupling beam specimens with the length-to-depth aspect
ratios of 2.0 or 3.5 were fabricated and tested under cyclic
2. Experimental Program
Four coupling beam specimens were constructed and
tested in the present study. The primary goal of the tests was
to investigate the cyclic behavior of HPFRCC coupling
beams having bundled diagonal reinforcement and widely
spaced transverse reinforcement.
2.1 Specimen Details
Figure 2 illustrates the dimensions and reinforcing details
of the specimens. All specimens were reinforced with
bundled diagonal reinforcement and also used the second
confinement option illustrated in Fig. 1c. The main test variables
were the use of conventional RC or the use of HPFRCC in
combination with reduced transverse reinforcement, and the
use of two different aspect ratios (ln/lnh.h) where ln and h are
the length and overall depth of the beam. Table 1
summarizes the test variables and specimen dimensions. The
HPFRCC used in this study contained polyvinyl alcohol
(PVA) fibers. The PVA fiber content in the HPFRCC was 2%
by volume. The reduced amount of transverse reinforcement
was about one half that required by section 22.214.171.124(d) in
ACI 318-14. The aspect ratio (ln/h) of coupling beams was
selected to be either 2.0 or 3.5 to respectively represent
typical deep or slender coupling beams in high-rise
The beam length was 1050 mm in all specimens, and the
beam depth was 525 or 300 mm. The total area of diagonal
bars was determined so that the average shear stress inpthffiffieffi
coupling beam would be limited to approximately 0:5 fc0
MPa. The spacing of transverse reinforcement was 120 and
110 mm in the specimens with ln/h of 2.0 and 3.5
respectively, not exceeding six times the diagonal bar diameter as
required in ACI 318-14 section 126.96.36.199(d). The inclination
angles of bundled diagonal reinforcement in the specimens
with the aspect ratios of 2.0 and 3.5 were about 22.1 and
10.7 , respectively. ACI 318-14
horizontal reinforcement in diagonally reinforced coupling
beams (Fig. 1), mainly used to provide anchorage for
horizontal crossties, shall not develop the yield strength at walls.
In this study, the embedment length of horizontal
reinforcement into the top and bottom stubs was 50 mm in all
specimens. For producing the sufficient anchorage of
bundled diagonal bars, they were sufficiently extended to the top
and bottom concrete stubs. The coupling beams with large
extending bars may not be effective for construction.
However, the focus of this study was to propose simple details for
HPFRCC diagonally reinforced coupling beams by using
bundled diagonal reinforcement and reducing transverse
reinforcement. No simple detail for extended bundled bars
was proposed in this study.
Figure 3 shows reinforcement cages assembled inside the
coupling beam formworks before concrete placement. For
comparison, the figure shows both Specimens RC-ACI-2.0
(Han et al. 2015)
diagonal reinforcement designed according to section 188.8.131.52
in ACI 318-14.
Specimens RC-2.0 and RC-3.5 were RC coupling beams
having the same reinforcement details as RC-ACI-2.0 and
RC-ACI-3.5 respectively, except that they had bundled
diagonal reinforcement. Specimens HC-2.0 and HC-3.5
represent HPFRCC coupling beams having bundled
diagonal reinforcement and one half the code-required amount of
transverse reinforcement. It is clearly demonstrated that both
bundled diagonal reinforcement and widely spaced
transverse reinforcement would make coupling beam
It is difficult to arrange reinforcement for diagonal
reinforced coupling beams in construction sites due to the
complexity of their reinforcement and to cast concrete due to
the reinforcement congestion in the coupling beam. Precast
concrete (HPFRCC) coupling beams could alleviate the
problem associated with constructing in situ coupling beams.
To study the feasibility of precast construction of coupling
beams, the beam portion was constructed first, and the stubs
at the ends of the beam representing in situ shear walls were
fabricated in the next step. It is noted that precast concrete
coupling beams with large extended diagonal bundled bars
may not be efficient for installing the beam in the
construction site. However, this study did not attempt to
investigate the anchorage method of bundled diagonal bars.
This study focused on the use of HPFRCC, bundled
diagonal reinforcement that increases inner space of the beam,
and widely spaced transverse reinforcement in diagonally
reinforced coupling beams.
To ensure adequate load transfer between the beam and
stubs, 50 mm deep rectangular shear keys were crafted at the
beam ends, and ‘‘U’’-shaped reinforcement was also added at
the interfaces between the beam and stubs (Fig. 2). To
prevent the stubs from being damaged, they were built using
concrete of a compressive strength of 60 MPa and sufficient
2.2 Loading Frame, Protocol, and Measurements
Figure 4 illustrates the test setup and loading protocol. The
test setup was intended to represent the behavior of coupling
beams subjected to lateral loading. The coupling beam was
arranged vertically, and the steel frame rigidly connected to
the top stub was loaded horizontally by a hydraulic actuator.
Since coupling beam specimens were cast horizontally and
then tested vertically, a prestressing force was applied in the
specimen due to the weight of the specimen.
The weight of the top stub and beam, which was
associated with the prestressing force, was 29.1 kN, which is only
0.01 Agfc0 where Ag is the gross sectional area of the
coupling beam specimen and fc0 is the measured compressive
strength of the concrete or HPFRCC; thus, the prestressing
effect due to the weight of the specimen was neglected in
this study. The bottom stub was fixed to the strong floor with
anchors. In order to enforce zero moment at the mid-span of
the coupling beam, the axis of the actuator was arranged to
pass through the mid-span. Also, two roller supports were
installed near the ends of the steel frame to prevent the top
stub from rotation but allow horizontal translation. Also, the
supports were to restrain the elongation of the coupling
beam. In a coupled wall system, coupling beams tends to
elongate axially when lateral loading causes severe cracking
in concrete and inelastic residual strains in the longitudinal
bars. However, such elongation was restrained due to large
in-plane stiffness and strength of adjoining shear walls,
consequently imposing compression in the coupling beams
(Barbachyn et al. 2012)
. Stoppers were installed at the ends
of the bottom stub to prevent the specimen from sliding.
Quasi-static reversed cyclic loading was applied with
controlled displacement as shown in Fig. 4b. The drift ratio is
defined as the lateral displacement between the ends of the
coupling beam divided by the beam length. For each drift ratio,
two consecutive cycles of the same drift amplitude were applied
to assess strength and stiffness degradations. The same loading
protocol was used in all tests. Figure 5 displays the positions of
linear variable differential transformers (LVDTs) installed on
The lateral displacement of the coupling beam was
measured by using two LVDTs (marked ‘‘Top’’ and ‘‘Bottom’’)
installed horizontally at the top stub; the two yielded similar
displacements throughout testing. To monitor the possible
sliding of the specimen, a horizontal LVDT (marked ‘‘Base’’)
was installed at the bottom stub. To assess flexural and shear
deformations of the specimen, multiple vertical and diagonal
LVDTs were installed at one side of the beam. Also,
fixedend rotations at the interfaces between the beams and stubs
were monitored by using four vertical LVDTs (L5, L6, L7,
and L8) located on the top and bottom faces of the beam.
The actuator load was measured by a load cell, and the shear
force in the coupling beam was assumed to be equal to the
actuator load. Strain gauges were installed at selected
locations on the diagonal, transverse, and horizontal
2.3 Material Tests
Compression and uniaxial (direct) tension tests were
conducted to examine the properties of the normal concrete
and HPFRCC used to construct the coupling beam
specimens. Table 2 lists the proportions of the HPFRCC mixture.
PVA fibers in the HPFRCC were 2.0% by volume. The
water/PCM ratio was approximately 20%, where ‘‘PCM’’
stands for dry premixed cement mortar consisting of binder,
fillers, and chemical admixtures. Table 3 summarizes the
physical properties of the PVA fibers used in the HPFRCC.
In the normal concrete, the maximum aggregate size was
25 mm, whereas the HPFRCC contained neither coarse nor
For the compression tests, three cylindrical specimens
having 100 mm in diameter and 200 mm in height were
fabricated according to ASTM C39, and cured under the
same condition as the coupling beam specimens. Three
LVDTs in parallel were installed around the perimeter of the
specimen in the loading direction to estimate the average
compressive strain, with the gage length of approximately
Figure 6a shows the compressive stress–strain curves of
the HPFRCC and normal concrete acquired after 28 days of
curing. Both the HPFRCC and normal concrete showed
slightly higher strengths than the design compressive
strength of 40 MPa. The compressive stress–strain
relationships indicated that the HPFRCC was much more ductile
than the normal concrete; the strain measured at failure was
approximately 67% greater for the HPRCC. On the other
hand, the secant modulus of elasticity of the normal concrete
was about 24% greater than that of the HPFRCC. The secant
modulus was calculated according to ACI 318-14, which is
the slope of a line passing through 45% of the maximum
compressive strength in the stress–strain curve.
For direct tension tests, three dog-bone shaped specimens
were fabricated, similar to those used by the University of
Michigan research group
LVDTs in parallel were mounted along the sides of the
specimen to estimate the average tensile strain, with the gage
length of approximately 180 mm.
Figure 6b shows the tensile stress–strain curve and
cracking pattern of the HPFRCC used in this study. Under
tension, the HPFRCC specimens showed ductile behavior by
means of strain hardening, developing numerous
well-distributed micro-cracks with the effect of fiber bridging
2003; Naaman 2003; Kim et al. 2007, 2009; Li 2012)
maximum tensile strain exceeded 2.5%, and the tensile
strength was approximately 4.3 MPa. Table 4 summarizes
the compressive and tensile strengths of the HPFRCC and
normal concrete measured at the curing age of 28 days.
The properties of reinforcing bars used in the coupling
beam specimens were examined under uniaxial tension.
Stress–strain curves of the reinforcing bars are shown in
Fig. 7, and Table 5 summarizes the mechanical properties
acquired from the tension tests.
3. Test Results and Observations
3.1 Cracking Damages and Failure Modes
Figure 8 shows cracking damages in the two specimens
with the span-to-depth ratio of 2.0. In both specimens, a few
horizontal (flexural) cracks formed at the beam ends in the
very early stages; later, as the drift ration increased, inclined
(diagonal tension) cracks spread over the entire span.
In specimen RC-2.0, made with normal concrete, bundled
diagonal reinforcement and code-specified transverse
reinforcement, inclined cracks began to develop at
approximately 0.25% drift. By 2% drift, the width of inclined cracks
increased to about 1.5 mm (Fig. 8a), and most diagonal bars
underwent yielding near the beam-stub interfaces. At 5%
drift, the inclined cracks widened to greater than 4.5 mm,
and some spalling of concrete under compression occurred at
the beam ends (Fig. 8b). Slight buckling in the diagonal
bundled bars was observed. Eventually, at about 7% drift,
RC-2.0 started to collapse owing to the rupture of some
diagonal bars (Fig. 8c). It is noted that the crack patterns
were somewhat asymmetric (Fig. 8) even though the
rotation of the top stub (reaction block) was restrained by the
supports of the guide columns. This may be resulted from an
imperfect installation of the test setup.
Specimen HC-2.0, made with the HPFRCC, bundled
diagonal reinforcement and one-half the code-specified
transverse reinforcement, showed a pattern of flexural and
diagonal tension cracks that was generally similar to that of
Specimen RC-2.0. However, the inclined cracks in HC-2.0
were much narrower and more numerous than those in
RC2.0, as shown in Figs. 8d–f. Even at 5% drift, the inclined
cracks remained less than 2 mm in width (Fig. 8e), less than
half the cracks in RC-2.0 at the same drift. No buckling in
the diagonal bars occurred in this specimen. Also, almost no
spalling damage was observed in HC-2.0 by 7% drift
(Fig. 8f), even though the specimen had completely failed,
with the rupture of some diagonal bars.
Figure 9 shows cracking damage in the two specimens of
a span-to-depth ratio of 3.5; these specimens underwent
more flexural cracks near the beam ends than the specimens
of a span-to-depth ratio of 2.0. The standard specimen
RC3.5 having code-specified transverse reinforcement suffered
inclined cracking from about 0.75% drift. The inclined
cracks widened to about 2 mm by 2% drift (Fig. 9a), with
most diagonal bars yielding near the beam-stub interfaces.
At 5% drift, the cracks widened to more than 5 mm, and
some concrete spalled from the compression zones at the
beam ends (Fig. 9b). Finally, RC-3.5 started to collapse from
10% drift, when several diagonal bars ruptured and severe
concrete spalling occurred (Fig. 9c). In this specimen,
buckling was clearly observed in the diagonal bundled bars.
The HPFRCC specimen HC-3.5, which was reinforced
with bundled diagonal reinforcement and one-half the
amount of code-specified transverse steel, showed early
flexural cracks at 0.25% drift. By about 2% drift, numerous
diagonal tension cracks spread over the entire span (Fig. 9d),
and most diagonal bars underwent yielding. However, the
cracks were less than 0.5 mm wide at 2% drift, only
onefourth the width of cracks in RC-3.5 at the same drift. As in
the specimens of aspect ratio 2.0, the cracks in HC-3.5 were
much narrower and fewer than those in RC-3.5, as shown in
Figs. 9d–f. No buckling in diagonal bars was observed in
HC-3.5. Also, HC-3.5 did not suffer any spalling damage,
until it started to collapse with the rupture of some diagonal
bars at 10% drift (Fig. 9f).
Considering that Specimens RC-2.0 and RC-3.5
maintained a steady strength up to about 6 and 10% drift
respectively, the use of bundled diagonal reinforcement in
combination with code-specified transverse reinforcement
was considered to be an efficient solution for building
coupling beams to resist cyclic lateral loading. Also, the test
results suggested that the use of HPFRCC enabled a 50%
reduction in the code-required amount of transverse
reinforcement by providing effective confinement for bundled
diagonal reinforcement, controlling the width of cracks and
avoiding spalling damage.
3.2 Load–Displacement Responses
Figure 10 shows the cyclic shear-drift responses of the
coupling beam specimens. The right side vertical axis of this
figure indicates the normalized shear stress, namely, the ratio
of shear force in the coupling beam, taken equal to the
actuator load, to the product of the beam cross-sectional area
(Acw) and the square root of the concrete compressive
strength (f0c). Table 6 summarizes the yield load (Vy), yield
drift ratio (hy), maximum load (Vu), maximum drift ratio
(hu), and ductility ratio (l) of each specimen. The yield and
maximum drift ratios were determined according to the work
Pan and Moehle (1989)
. The yield drift ratio corresponds
to the point of intersection between the secant line
connecting the origin to the point of 2/3 of the maximum load
and the horizontal line at the point of the maximum load.
The maximum drift ratio was measured when the strength
reduced to 80% of the maximum load. The ductility ratio is
defined as the maximum drift divided by the yield drift.
Specimens RC-2.0 and RC-3.5 of normal concrete,
composed of standard RC, having bundled diagonal
reinforcement and code-specified transverse reinforcement exhibited
stable load-drift behavior up to about 4 and 8% drift
respectively, without considerable drop in strength. Between
the two, the slender beam specimen showed much more
ductility and had more full load-drift loops. The RC-2.0
specimen suffered significant and successive strength drops
from the second cycle to 5% drift, when some diagonal and
transverse reinforcement ruptured. In contrast, the
higheraspect-ratio specimen RC-3.5 sustained more than 80% of its
maximum load up to the first positive loading cycle of 10%
drift ratio. Thus, the ductility ratios of Specimens RC-2.0
Fig. 10 Hysteretic shear-drift responses.
and RC-3.5 for loading in the positive direction were
approximately 3.0 and 5.7 in, respectively.
Specimens HC-2.0 and HC-3.5, composed of HPFRCC,
having bundled diagonal reinforcement and one half the
amount of code-specified transverse reinforcement, showed
load-drift responses that were generally similar to those of
the normal concrete specimens discussed above. HC-2.0 and
HC-3.5 exhibited stable behavior up to 5 and 8% drift,
respectively. HC-2.0 underwent large strength drops from
the first cycle up to 6% drift, and completely collapsed
during the 7% drift cycles, owing to rupture of the diagonal
reinforcement. On the other hand, HC-3.5 started to become
unstable only from the 10% drift cycles. The ductility ratios
of Specimens HC-2.0 and HC-3.5 for loading in the positive
direction were approximately 3.7 and 5.6, respectively.
It is noted that the normalized shear stress greatly exceeded
the design limit of 0.83 for diagonally reinforced coupling
beams as specified in section 184.108.40.206(a) of ACI 318-14
(2014). Therefore, the test results suggest that bundled diagonal
reinforcement was applicable in both deep and slender coupling
beams, and that the HPFRCC was effective in allowing the
amount of transverse reinforcement required by
section 220.127.116.11(d) in ACI 318-14 to be reduced by half. It should
be noted that the measured strengths of all the specimens in the
tests are significantly larger than the calculated strengths per
ACI 318-14. This is on agreement with the results of previous
(Lequesne et al. 2010; Han et al. 2015)
overstrength must be accounted for in the seismic design of
diagonally reinforced coupling beam themselves and also adjoining
walls. Otherwise, significant damage could not be avoided in
adjoining walls during design-level earthquakes.
4. Cyclic Deterioration, Energy Dissipation, and Shear Distortion
4.1 Strength and Stiffness Degradations
Figure 11 shows the envelopes of the cyclic shear-drift
response curves for the four coupling beam specimens.
Among both pairs of specimens with the same aspect ratio,
the RC and HPFRCC specimens not only achieved similar
maximum loads, but also underwent similar strength
degradation histories. In addition, the primary cause of
sudden strength drops in all four specimens was the rupture
of diagonal reinforcement with no buckling. Therefore,
combining the use of HPFRCC and half the amount of
coderequired transverse steel appeared to provide confinement
equivalent to that of the code-required transverse
reinforcement. This figure also included the envelop curve
for code-compliant specimens RC-ACI-2.0 and RC-ACI-3.5
with distributed diagonal bars. It is observed that the envelop
curves of RC-ACI specimens with distributed diagonal
reinforcement were close to those of corresponding RC and
HPFRCC specimens with bundled diagonal bars.
Figure 12 shows the stiffness degradation histories of the
four specimens, from which the degree of stiffness retention
can be assessed. The normalized stiffness in the vertical axis
was determined by dividing the stiffness of the specimen
during the first cycle (of two consecutive cycles) under a given
drift by the initial stiffness in the first cycle under 0.25% drift.
The stiffness of the specimen during a loading cycle was taken
to be the slope of the line connecting the two points at the
positive and negative peak drifts on the load–displacement
curve (i.e., peak-to-peak stiffness) as illustrated in Fig. 12.
For both pairs of specimens having the same aspect ratio,
the RC and HPFRCC specimens exhibited similar stiffness
retention capacities throughout the tests, although the
stiffness retention capacity of HPFRCC specimens appeared to
be slightly better than RC specimens. HPFRCC specimens
also had similar stiffness retention capacity to RC specimen
with distributed diagonal reinforcement.
4.2 Energy Dissipation
Energy dissipation capacity was investigated among the
four specimens subjected to the same loading history. In
general, higher energy dissipation corresponds to better
seismic resistance. Figure 13 presents cumulative energy
dissipation for the four specimens. The amount of energy
dissipated during a loading cycle was taken as the area
surrounded by the load–displacement curve for the cycle; see
illustration in Fig. 13. The accumulated energy in the
vertical axis of Fig. 13 is the sum of dissipated energy in all
cycles up to the indicated drift.
Between the two deep coupling beam specimens, the
HC2.0 specimen dissipated consistently larger amounts of
energy, with about 20% greater energy dissipation than
RC2.0 (RC-ACI-2.0) up to the 7% drift cycles (Fig. 13a), even
though its transverse reinforcement had been reduced by
k1 :1st cycle stiffness
k2 :2nd cycle stiffness
area per cycle
50%. In contrast, the two slender specimens, RC-3.5 and
HC-3.5, dissipated very similar amount of energy up to 10%
drift (Fig. 13b). They dissipated more energy than specimen
RC-ACI-2.0 with distributed diagonal bars. At a given drift,
dissipated energy was much larger in the deep specimens
than in the slender specimens because of the greater strength
of deep specimens. Note that the inclination angle of the
diagonal bars in the deep coupling beams (ln/h = 2.0) was
larger than that in the slender coupling beams (ln/h = 3.5).
4.3 Shear Deformation
The degree of shear cracking damage in a specimen was
quantified by the amount of shear deformation. The shear
deformation of the specimen was assessed by using the data
acquired from the LVDTs installed at one side face of the
coupling beam (D1–D2, L1–L4 for the deep beams as
illustrated in Fig. 5a, and D1–D4, L1–L4, L9–L12 for the
slender beams as illustrated in Fig. 5b). For each shaded
region shown in Fig. 14, the average shear deformation c
was estimated as follows:
c1 þ c2
Here, c1 and c2 are the angular changes in the two initially
90 angles of each shaded region (e.g., at points 2 and 3 in
Fig. 5c). The angular changes were estimated by using the
deformed lengths of the two initially right triangles (having a
common hypotenuse, e.g., between points 1 and 4) formed
by the LVDTs. It was assumed that during testing there was
no change in length along the transverse axis of the beam
(e.g., between points 1 and 2, and between points 3 and 4 in
Figure 14 presents the shear distortion responses of all
four specimens up to the 5% drift cycles, plotted with respect
to the lateral load. Regardless of the length-to-depth aspect
ratio (ln/h), the HPFRCC specimens generally underwent
less shear distortion than the RC specimens, even though the
HPFRCC specimens had 50% less transverse reinforcement.
This is in accordance with the results that the RC specimens
suffered more intensive shear cracking damage than the
HPFRCC specimens. This suggests that the HPFRCC was
effective in bridging shear cracks to control the crack widths.
In the specimens of aspect ratio 2.0, the peak shear
distortion occurring during the 2% drift cycles was about 0.007
and 0.002 rad in RC-2.0 and HC-2.0, respectively, that
occurring during the 5% drift cycles was about 0.028 and
0.010 rad in RC-2.0 and HC-2.0, respectively. At each drift
level, the shear distortion in HC-2.0 was less than about 1/3
that of RC-2.0. In the specimens of aspect ratio 3.5, the beam
ends generally suffered larger shear distortions than the
middle parts, which was not the case in the specimens of
aspect ratio 2.0. During the 5% drift cycles, Specimens
RC3.5 and HC-3.5 had the peak shear distortions of about 0.027
and 0.009 rad at the ends of the beams.
In this study, experimental tests were conducted to assess
the cyclic behavior of HPFRCC coupling beams with
bundled diagonal reinforcement and widely spaced transverse
reinforcement. Their cyclic performance was compared with
that of concrete coupling beams with bundled and
distributed diagonal bars and full amount transverse
reinforcement required in ACI 318-14 as well as that of
codecompliant concrete coupling beams (RC-ACI) with
distributed diagonal bars and full amount of transverse
reinforcement. Both deep (ln/h = 2.0) and slender (ln/h = 3.5)
coupling beams were considered. Important findings and
conclusions are summarized as follows:
(1) The HPFRCC coupling beams had similar lateral
strengths to those of the RC coupling beams and
superior seismic capacities (e.g., ductility, energy
dissipation), even though the HPFRCC specimens
had bundled diagonal reinforcement and only half the
code-required amount of transverse reinforcement.
This suggests that the amount of transverse
reinforcement required by ACI 318-14
reduced by half with the use of HPFRCC, which
supplied adequate confinement for the bundled
diagonal bars. Moreover, distributed diagonal reinforcement
can be replaced by bundled diagonal reinforcement.
2. Concrete coupling beam specimens RC-2.0 (ln/h = 2.0)
and RC-3.5 (ln/h = 3.5), which had bundled diagonal
reinforcement, achieved the maximum drift ratio of
about 5.37 and 10.04, respectively. Also, no substantial
strength drop occurred until the bundled diagonal bars
ruptured in these specimens. This indicates that the use
of bundled diagonal reinforcement was effective in
ensuring suitable seismic performances of both deep and
slender coupling beams; this design also enables
3. HPFRCC specimens HC-2.0 and HC-3.5 having
bundled diagonal reinforcement and half the transverse
reinforcement required in ACI 318-14 produced the
maximum drift ratio of about 5.98 and 10.79,
respectively. Therefore, the superior seismic performance of
coupling beams can be maintained by using HPFRCC,
bundled diagonal reinforcement and reduced transverse
4. In all specimens studied in the present work, the
coupling beam portion was precast first, and the stubs at
the ends of the beam that represented in situ shear walls
were constructed later, allowing cold joints between the
beam and stubs. Nevertheless, none of these specimens
experienced sliding at the beam-stub interfaces during
the tests. This implies that the bundled diagonal
reinforcement provided sufficient friction shear strength
to resist sliding. Therefore, precast construction of these
concrete coupling beams turned out to be feasible.
Authors acknowledge the financial supports provided by the
N a t i o n a l r e s e a r c h f o u n d a t i o n o f K o r e a ( N R F
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