Journal of Building Engineering 34 (2021) 101937

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Journal of Building Engineering

journal homepage: http://www.elsevier.com/locate/jobe

Experimental study on cyclic response of concrete frames reinforced by

Steel-CFRP hybrid reinforcement
Shoutan Song a, b, Guan Wang d, Xinzhe Min a, Ning Duan a, Yongming Tu a, b, c, *
a
School of Civil Engineering, Southeast University, 211189, Nanjing, PR China
b
National Prestress Engineering Research Center, Southeast University, 211189, Nanjing, PR China
c
Division of Structural Engineering, Luleå University of Technology, SE, 97187, Luleå, Sweden
d
China Construction Infrastructure Co., Ltd., 100044, Beijing, PR China

A R T I C L E I N F O A B S T R A C T

Keywords: A novel section with Steel-carbon fiber reinforced polymer (CFRP) hybrid reinforcement is introduced. CFRP
Carbon fiber reinforced polymer (CFRP) longitudinal reinforcements are placed in the outer layer of the section, while steel reinforcements are arranged
Steel-CFRP hybrid Reinforcement in the inner layer. The new type section is utilized to reduce the residual deformation of anti-seismic structures
Concrete frame
and improve the durability of structures. Cyclic loading tests are conducted on the four concrete frame structure
Seismic performances
Residual deformation
with an axial compression ratio of 0.31. Seismic performances of concrete frames with steel reinforcements, steel-
CFRP hybrid reinforcements and CFRP reinforcements are compared and studied. The major objectives of study
are focus on the performance of CFRP reinforcements under the axial compression ratio of 0.31 and the ductility,
energy dissipation, strength degradation, unloading stiffness, residual deformation of the frame structure with
different reinforcement modes. Test results showed that as compared with the steel reinforced concrete frame,
Steel-CFRP hybrid reinforced concrete frame exhibited excellent post-earthquake repairabilities, comparable
hysteretic energy dissipation abilities and reasonable strength degradation. Furthermore, when the axial
compression ratio is 0.31, the ultimate tensile strength of CFRP reinforcements calculated in accordance with the
bearing capacity is 27.2%–32% of the static ultimate tensile strength. The concrete frame with ideal mechanical
properties can be obtained by reasonable allocation of steel and CFRP reinforcement.

1. Introduction segmental precast with unbonded post-tensioned tendons [6–9],

steel-GFRP hybrid reinforcement [10]、steel-FRP composite bar (SFCB)
Performance-based seismic design targets at achieving different [11–14], external FRP jacket with steel-BFRP hybrid reinforcement [15,
performance levels of structures subjected to different magnitudes of 16], segmental precast with steel-BFRP hybrid reinforcement [17]. In
earthquakes. Post-earthquake repairability and stability of damage those research, the application of Steel-FRP composite bar/hybrid
development are the focus of structural seismic design. Post-yield stiff­ reinforcement [10–17] not only plays the energy dissipation charac­
ness ratio (the ratio of post-yield stiffness to initial elastic stiffness) is a teristics of steel bars but also can use FRP bars to enhance the post-yield
key index for above two aspects [1–3]. Pettinga et al. [3] suggested that stiffness of the column. FRP materials have high corrosion resistance
when the post-yield stiffness ratio of pier column structures was greater [18,19]. Placing FRP reinforcement on the outer layer and steel rein­
than 5%, the stability of structural damage and residual displacement forcement on the inner layer with a larger thickness of concrete cover
under different types of earthquakes was improved. can improve the durability of the structure. The inward-moving steel
Pettinga et al. [3] summarized three methods to enhance the reinforcement make the structure have less plastic deformation at the
post-yield stiffness ratio: utilizing new materials; redesigning section same loading displacement. The existing research of steel-FRP hybrid
and initial seismic characteristics of the structure; introducing a sec­ reinforcement structure mainly focuses on the beams under static
ondary elastic frame to act in parallel with the primary system. Several loading [20–30] and the columns with axial compression ratio of 0–0.2
approaches were adopted to enhance the post-yield stiffness ratio, under cyclic loading [10–17]. The seismic performance of RC structure
including application of unbonded post-tensioned tendons [4,5], has a great relationship with the axial compression ratio. Compared with

* Corresponding author. School of Civil Engineering, Southeast University, 211189, Nanjing, PR China.
E-mail address: yongming.tu@ltu.se (Y. Tu).

https://doi.org/10.1016/j.jobe.2020.101937
Received 1 April 2020; Received in revised form 29 September 2020; Accepted 26 October 2020
Available online 6 November 2020
2352-7102/© 2020 Elsevier Ltd. All rights reserved.
S. Song et al. Journal of Building Engineering 34 (2021) 101937

steel bars, the damage evolution of FRP bars under pressure is more steel reinforcements are arranged on the inside. Thickness of concrete
complex. It is necessary to study the strength of FRP reinforcement and cover is 25 mm. For the frame CF1 and CF2, the spacing between two
the strength degradation of structures with steel-FRP hybrid reinforce­ layers of reinforcement is 25 mm. The stirrups in the test specimens are
ment under the cyclic loading with higher axial compression ratio. all made of steel with a diameter of 8 mm. At both ends of the frame
Considering that most of the large axial compression ratios are beam and column, the shear capacity of the structure is improved by
applied in frame structures, the seismic mechanical properties of con­ reducing the stirrup spacing (Fig. 1). 135-degree hooks (135-degree
crete frame with steel-CFRP hybrid reinforcement with an axial hooks) are used to form rectangular closed stirrups. Due to the form of
compression ratio of 0.31 are studied in this paper. Under cyclic loading, double-layer reinforcement, the frame CF1 and CF2 stirrups are added
differences in the mechanical properties of steel reinforced concrete with single-limb hoop reinforcement on the basis of closed stirrups.
frame, Steel-CFRP hybrid reinforced concrete frame and CFRP rein­ Details of section reinforcement are shown in Fig. 2 and Table 1.
forced concrete frame are compared, and seismic performances of frame Tested frames are fixed on the rigid ground by 4 vertical ground
structures with different steel-CFRP reinforcement ratios are studied. anchors, and concrete blocks are placed on its left side. Meanwhile, the
This paper focuses on: (1) the performance of CFRP reinforcements horizontal movement of the frame specimens is restricted by the tensile
under the axial compression ratio of 0.31; (2) bearing capacity, hyster­ anchor on the right side of the base beam (Fig. 3). The compressive
etic energy dissipation, post-yield stiffness ratio and ductility of differ­ strength of the concrete cube (150 × 150 × 150 mm) blocks used in the
ently reinforced structures; (3) residual displacement and unloading tested frame under the standard 28-day curing condition is 31.2 MPa. In
stiffness of the frame structure. the same manner, its cylinder compressive strength is 25.0 MPa. The
axial compression ratio of the tested frame columns is 0.31, based on the
2. Testing scheme cylinder compressive strength and the concentrated load of 575 kN
supplied by the two piercing jacks placed under the top beam of the
2.1. Basic information on test specimens frame column. A trolley is arranged on the beam at the top of the frame
column to ensure free sliding in the horizontal direction. At the three-
The test specimen is a 1:2 scale component of the original frame with divided points of the frame beam, two concentrated forces of 15 kN
a span of 7200 mm and a height of 3600 mm. The test specimen is a are applied to simulate the secondary beam load through the suspended
single-span frame with a distance of 3600 mm between the center of the heavy block. Horizontal load is exerted on the beam by MTS actuator of
left and right frame column, a net height of the frame column of 1500 50 t. The specific loading device is illustrated in Fig. 3.
mm. In the test frame, the one-sided reinforcement ratio of column is
0.8%, the reinforcement ratio of beam top is 0.67%, and reinforcement 2.2. Loading system
ratio of beam bottom is 0.45%. The dimension of column section is 250
mm × 300 mm, upper frame beam section 150 mm × 300 mm, and the The constant vertical load is first applied by a hydraulic jack to the
base beam section 300 mm × 500 mm. Specification details are given in specimen for predetermining axial pressure. Subsequently, lateral
Fig. 1. According to the different longitudinal reinforcement of the displacement exerted by the MTS system is applied to the frame. LVDT
frame beams and columns, the test specimens are named C, CF1, CF2 testing frame displacement was set on the right end of the frame beam
and F respectively. For frame C, all longitudinal reinforcements are steel and the base beam to monitor the displacement (Fig. 3). In order to
bars. For frame F, the longitudinal reinforcements are CFRP bars. The accurately capture the crack point and yield point, the lateral
longitudinal reinforcement of frames CF1 and CF2 are steel-CFRP hybrid displacement spacing is 0.5 mm before the crack point and is 3 mm
reinforcement. Frame CF1 is formed by replacing 1/3 of the reinforce­ before the yield point. After the concrete column yielded, loading was
ment area of the frame column, 1/3 of the reinforcement area of the established through measured lateral displacement of loading point at
beam upper, and 1/2 of the reinforcement area of the beam lower part multiple intervals of the column yield displacement. The loading
with CFRP bars. In order to ensure identical reinforcement area and displacement spacing is increased to 6 mm. The entire loading process is
reasonable layout, multiple small diameter CFRP reinforcements divided into three stages (Fig. 4):
(diameter 8 mm) are utilized (Fig. 2). CF2 has a higher proportion of Stage I: Cyclic loading is conducted with an increase of 0.5 mm per
CFRP reinforcements, formed by replacing 2/3 of the steel re­ level until the frame is cracked. Cyclic loading is repeated once per level.
inforcements, 2/3 of the reinforcement area of the beam upper, and 1/2 Stage II: To focus more on frame column damage, after the frame
of the reinforcement area of the beam lower part with CFRP re­ column cracks (The displacement measured in this paper is 3 mm), 3 mm
inforcements. In frame CF2, multiple small diameter steel re­ is added in each level progressively for cyclic loading until reinforce­
inforcements (diameter 8 mm) are utilized to ensure identical ment yielding (about 18 mm). Cyclic loading is repeated three times per
reinforcement area and reasonable layout. In the cross sections of frame level.
CF1 and CF2, CFRP reinforcements are arranged on the outside, and Stage III: After 18 mm, 6 mm per level is increased progressively for
cyclic loading until the horizontal frame strength is reduced to 80% of
the maximum strength. Cyclic loading is repeated three times per level.

2.3. Material property

The geometrical dimensions of CFRP reinforcements are shown in

Fig. 5. The pouring sleeve is set at the end of the CFRP reinforcements to
complete the strength test (Fig. 6). The grade of steel reinforcement is
hot-rolled ribbed bar with a yield strength of 400 MPa (HRB400). The
results of the reinforcement properties are displayed in Table 2. The
average ultimate compressive strength of 6 concrete cube (150 × 150 ×
150 mm) blocks is 31.2 MPa. The test method is carried out in accor­
dance with the provisions of Chinese code (GB/T50081-2019) [31].

Fig. 1. Dimension of tested frames and arrangement of stirrup.

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S. Song et al. Journal of Building Engineering 34 (2021) 101937

Fig. 2. Schematic diagram of the reinforcement in the beam and column (Left: 1-1; Right: 2-2).

following phenomena and conclusions are obtained: (1) For frame C, the
Table 1
bending failure site undergoes concrete collapse after the yield of tensile
Details of tested specimens.
steel reinforcements, the bearing capacity of the structure slowly de­
Specimen Column Beam Column Beam creases to 80% of the peak value, and the compressive reinforcements
Steel CFRP Steel bars CFRP bars As /Af As /Af present a buckling state during failure (Fig. 8a). (2) The failures of frame
bars bars CF1, CF2 and F are consistent. The bending failure site first shows mild
C 6Φ16 – 6Φ8+1Φ16 – – – concrete peeling, and then local damage of CFRP reinforcements. After
CF1 4Φ16 8Φ8 6Φ8 4Φ8 2 1.5 the peak load is reached, the concrete in the compression zone will
CF2 8Φ8 4Φ16 4Φ8 6Φ8 0.5 0.667 spalling in a large area. The FRP reinforcements will buckling due to the
F 6Φ16 6Φ8+1Φ16 0 0
lack of constraints of surrounding concrete (Fig. 8b), and the structural
– –

Notes：Af is the area of CFRP reinforcement; As is the area of steel strength will rapidly decline to 80% of the peak strength. (3) Shear
reinforcement. failure occurs at the bottom of the right column of frame CF2 because the
bending hook at the closure of the stirrup is 90◦ (other specimens are
3. Test results 135◦ ) and the closures are all located on the same side (Fig. 7c). Defects
of seismic stirrups reduce the shear capacity of the structure, resulting in
3.1. Test phenomena and crack distribution bending-shear failure.

In the loading process, the frame beam cracks before the frame col­
umn. As the load increases, plastic hinges appear at the bottom of the 3.2. Hysteresis curve
column and the end of the frame beam. In addition to shear failure after
bending plastic hinge occurs at the bottom of the right column of CF2 The measured load-lateral-displacement (V − δ) hysteretic curves of
frame, all the other tested frames are subject to column bottom bending four-truss specimens are shown in Fig. 9, and the skeleton curves are
failure. The final crack distribution and failure conditions are illustrated obtained according to the peak points of the hysteretic curves. The
in Fig. 7. Through observation and analysis of the experiment, the hysteretic curve of frame C is the fullest, indicating that the energy
dissipation capacity of the structure is better than those of the other

Fig. 3. Layout and loading diagram of tested specimens.

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S. Song et al. Journal of Building Engineering 34 (2021) 101937

Fig. 4. Loading schematic.

Fig. 6. Strength test of CFRP reinforcements.

load and displacement of each frame correspond to the horizontal load

and displacement when the columns are cracked. Yield load and
displacement are data on steel reinforcements yielding of column. In this
study, the equalenergy approach [32] (bilinear approximation) was
adopted to determine the yield points (Fig. 11). The ultimate displace­
Fig. 5. Geometric dimensions of CFRP reinforcements. ment is the corresponding horizontal displacement when the horizontal
load falls to 80% of the peak load. The positions of key points on the
three specimens. When the displacement is loaded to the vicinity of 2 skeleton curves are shown in Fig. 10.
mm, the frame beam first cracks, and then the frame column cracks at As can be observed in the data in Table 3, with the increase of the
the displacement of 3 mm. As the load displacement close to 18 mm, the CFRP reinforcement ratio, the bearing capacity of the frame structure is
reinforcements began to yield. When the displacement reaches 30 mm, also enhancing. Compared with frame C, the peak strengths of frame
the concrete cover in the compression zone at the bottom of the column CF1, CF2 and F are increased by 1.8%, 4.1% and 8.0% respectively. In
will collapse and spalling. After that, the bearing capacity begins to order to obtain the stress in CFRP reinforcement, the Opensees software
decline slowly until the load reaches 80% of the peak load. When the is used to establish a nonlinear analysis model of the frame structure
horizontal displacement of frame CF1, CF2 and F reaches 2 mm and 3 based on the fiber cross-section method, and the monotonic load is
mm, the frame beam and column crack respectively. Under the applied to the model to obtain the CFRP reinforcement stress at the peak
displacement of 30 mm, the concrete cover in the compression zone at load point. In the analysis model, Scott-Kent-Park concrete constitutive
the bottom of the column will collapse and spalling, and the CFRP re­ model is adopted which considers the influence of the stirrup constraint
inforcements will suffer initial damage. At this time, the bearing ca­ on the peak stress and strain of the concrete and the unloading rate of the
pacity will increase slowly. With the loading displacement of 36 mm, a softening stage. Steel reinforcement is regarded as a perfect elastoplastic
large area of concrete spalling occurs at the bottom of column, and the material and CFRP reinforcement is represented by a linear elastic ma­
bearing capacity begins to decline. When the displacement reaches terial. According to the calculation of the internal force at the bottom
42–45 mm, a complete crack occurs in the FRP reinforcements, and the section of the column under the corresponding peak load, when the axial
loading ends when the bearing capacity rapidly drops to 80% of the peak compression ratio is 0.31, the stresses of CFRP reinforcements in frame
load. CF1, CF2 and F are about 640 MPa, 572 MPa and 543 MPa respectively.
CFRP reinforcements do not fully exert their axial static tensile strength.
4. Discussions The reason is that after the concrete is crushed, CFRP reinforcements in
the compression zone lack the constraint of concrete, and buckle under
4.1. Envelope curves and post-yield stiffness ratios pressure, resulting in the damage of the reinforcements. In the limit
state, the inter-layer displacement angles of CF1, CF2 and F frames are
The average (push and pull) skeleton curves of each tested frame are close to or over 3%, which demonstrates that the structures possess
shown in Fig. 10. Data of key points of the load-displacement curve of satisfactory displacement capacities.
each specimen are shown in Table 2, where Vcr , Vy , Vp , Vu represent Based on the key points data of the skeleton curve in Table 3, data
cracking load, yield load, peak load and ultimate load respectively. δcr , related to stiffness and ductility of the structure can be obtained. The
δy , δp , δu symbolize cracking displacement, yield displacement, peak definition of stiffness in each stage is shown in Fig. 11. The post-yield
load displacement and ultimate displacement respectively. The cracking stiffness of a concrete column, k2 , can be calculated using Eq. (1):

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S. Song et al. Journal of Building Engineering 34 (2021) 101937

Table 2
Material properties.
Type Elastic modulus (GPa) Yield strength (MPa) Tensile strength (MPa) Density (kg/m) Elongation rate (%) Cross-section area
（mm2）

CFRP (8 mm) 163 – 2312 0.079 1.4 45.3

CFRP (16 mm) 162 – 1943 0.316 1.2 191
Steel (8 mm) 200 402 570 0.395 15.0 50.3
Steel (16 mm) 200 410 570 1.590 15.0 201

ratio k2 and post-yield stiffness ratio rc of the frame gradually increase.

According to the analytical results, the post-yield stiffness ratio k2 and
post-yield stiffness ratio rc of the frame C with full steel reinforcement
should be the smallest. The main reason why the test results differ from
the analytical results is that there is a small difference in the values of
bearing capacity near the peak load point, leading to the difference in
the determination of the peak point. Peak point has a great influence on
the value of k2 and rc . For frame C, there is a slight fluctuation (1.3%) in
the bearing capacity when the loading displacement ranges from 30 mm
to 36 mm. The bearing capacity at 30 mm is slightly larger, so it is
positioned as the peak point. The peak point displacements of CF1, CF2,
and F are all 36 mm. Post-yield stiffness ratio rc of the three frames with
CFRP reinforcements exceeds 0.17, indicating that the damage devel­
opment of the structures is highly stable. The absolute value of stiffness
after the peak load k3 in frame CF1, CF2 and F is greater than that of
frame C, mainly due to the great damage and the rapid decrease of the
structural strength caused by the buckling of CFRP reinforcements after
Fig. 7. Crack distribution and failure mode of tested frames [(a). C; (b). CF1;
peak load. Of all tested specimens, frame C has the best ductility. The
(c). CF2; (d). F]. ductility coefficient of all test specimens exceeds 2.5.

4.2. Equivalent damping ratio

Under the action of an earthquake, the structure has a continuous

process of energy absorption and dissipation. Energy dissipation ca­
pacity of a structure is an important index to evaluate its seismic prop­
erty. The higher the energy dissipation capacity of the structure, the
better the seismic property will be. Equivalent damping ratio he [33] is
adopted as the index to evaluate the energy dissipation performance of
the tested frames, whose expression is shown in Eq. (4), and its sche­
matic diagram of calculation is shown in Fig. 12.
1 Ahs
he = ⋅ (4)
2π Ase
Fig. 8. Damage details of steel and CFRP reinforcements.
where Ahs is the energy dissipated in a hysteretic cycle and the area of
Vp − Vy S(ABC+ADC) in Fig. 12, while Ase represents the maximum strain energy,
k2 = = rc k1 (1) which is half of the area of S(OBE+ODF) .
δp − δy
According to the test load-displacement hysteresis curve, the
where rc is the post-yield stiffness ratio between k2 andk1 , and k1 is equivalent damping ratio under each loading cycle is obtained. The
initial stiffness of the concrete column. equivalent damping ratio of the structure is the average value of the
k3 is the stiffness after the peak load, and μ is the ductility coefficient, three times of loading under the same displacement. As can be seen from
which can be calculated using Eqs. (2) and (3) respectively: Fig. 13, the development of the equivalent damping ratios of the four
specimens can be divided into two stages: pre-yield and post-yield
Vu − Vp
k3 = (2) stages. In pre-yield stage, there is no significant differences in the
δu − δp
equivalent damping ratio of each specimen, basically maintained at
δu around 5%. In this stage, the equivalent damping ratio increases first
μ= (3) and then declines with the increase of displacement, and the peak value
δy
coours at the displacement of 6 mm. The above reason is that when the
Stiffness and ductility data of each stage of the tested frames are loading displacement reaches 6 mm, additional cracks appear in the
summarized in Table 4. Based on the load-displacement skeleton curve frame concrete to dissipate part of the energy, while after 6 mm, the new
of the structure in Fig. 10 and the key points data in Table 3, the cracks became stable, and the equivalent damping ratio decreases. After
following conclusions can be drawn: With the increase of CFRP rein­ the steel reinforcements yields, the equivalent damping ratio of each
forcement ratio, the initial stiffness k1 has a tendency to decrease. tested specimen starts to show significant differences. The equivalent
Among all tested specimens, the stiffness of frame C is the largest, fol­ damping ratio of frame C increases faster than the other three speci­
lowed by frame CF1. Frame CF2 and F are smaller than CF1, and the data mens. The equivalent damping ratio of frame CF2 and F are smaller than
of the two specimens are relatively close. In addition to frame C, with the CF1, and the data of the two specimens are relatively close. Equivalent
increase of the ratio of CFRP reinforcements, the post-yield stiffness damping ratio of frame CF1 under the same displacement is about 70%–

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S. Song et al. Journal of Building Engineering 34 (2021) 101937

Fig. 9. Hysteretic curve of horizontal load-displacement of the tested frames

[(a). C; (b). CF1; (c). CF2; (d). F].

Fig. 11. Key points and stiffness of the specimen.

Fig. 10. Skeleton curve. CFRP reinforcements can ensure that the energy dissipation capacity of
the structure is not lower than 70% of the all-steel reinforcement
85% of that of frame C. Due to shear failure in the right column of frame structure.
CF2, the equivalent damping ratio at the later stage of loading is less
than that of frame F. The equivalent damping ratio of frame F under the
same displacement is about 60%–77% of that of frame C. On account of 4.3. Strength degradation
the above data, increasing the ratio of CFRP reinforcements will reduce
the energy dissipation of the structure. Reasonable design of the ratio of When the horizontal cyclic load is applied, the structural material
damage increases with the increase of loading times under the same

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S. Song et al. Journal of Building Engineering 34 (2021) 101937

Table 3
Summary of key points data in load-displacement curve.
Specimen Vcr (kN) δcr (mm) Vy (kN) δy (mm) Vp (kN) δp (mm) Vu (kN) δu (mm)

C 99.11 2.93 246.05 15.57 290.28 30.05 232.22 49.17

CF1 104.83 3.28 247.47 16.49 295.48 36.06 236.39 45.13
CF2 103.90 3.19 249.96 17.65 302.17 36.04 241.74 48.02
F 98.20 3.00 260.83 18.37 313.41 35.95 250.73 47.41

displacement, and the strength of the frame decreases constantly. The

Table 4
degradation of structural strength can be expressed by the ratio of the
Stiffness and ductility data of tested specimens.
third cyclic peak load of the same displacement to the first cyclic peak
Specimen k1 k2 k3 rc μ load. After steel reinforcement yields, the strength degradation coeffi­
C 15.799 3.055 − 3.036 0.193 3.157 cient λj of the frame structure is defined as Eq. (5):
CF1 15.004 2.454 − 6.516 0.164 2.736
Vj,3
CF2 14.159 2.840 − 5.045 0.201 2.720 λj = (5)
F 14.198 2.991 − 5.471 0.211 2.581 Vj,1

where Vj,3 means the strength of the third cycle under displacement
loading of grade j; Vj,1 is the strength of the first cycle under displace­
ment loading of grade j.
The strength degradation coefficient of tested specimens in this
paper is shown in Fig. 14, from which we can seen the following phe­
nomenons: (1) With the increase of loading displacement, the strength
degradation of each test specimen increases in general trend. Before
concrete spalling (displacement at 30 mm), there is no significant dif­
ference in the strength degradation of each test specimens. (2) The
strength degradation of frame C is stable and less than those of the other
three specimens. For the frame with CFRP reinforcement, the strength
degradation rate is obviously accelerated in large load displacement
stage. Especially for frame F, the strength degradation coefficient de­
creases significantly when the loading displacement exceeds 30 mm.
The explanation for this phenomenon is that the concrete is crushed
seriously after the peak load, and the CFRP reinforcements lack the re­
straint protection of concrete, leading to the large buckling damage and
the premature rupture of CFRP reinforcements. (3) When the peak load
is reached, the strength degradation coefficients of CF1 and CF2 are
0.944 and 0.937 respectively, and slightly less than frame C. In the limit
state, the strength degradation is no more than 6.5% for frame C and
27% for frame F. The strength degradation of hybrid reinforced frame
(CF1 and CF2) is between frame C’s and frame F’s, which is no more
Fig. 12. Schematic diagram of equivalent damping ratio.
than 13%. We can draw the following conclusions: In terms of the
strength degradation, the mechanical perforcemance of steel-CFRP
hybrid reinforced frame is better than that of CFRP reinforced frame

Fig. 13. Comparison of equivalent damping ratio.

Fig. 14. Comparison of strength degradation.

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S. Song et al. Journal of Building Engineering 34 (2021) 101937

and slightly worse than steel reinforced frame. α is the coefficient taking the influence of FRP reinforcement ratio
into consideration, and its model is shown in Eq. (9):

4.4. Degradation of unloading stiffness α=a + b

Af
(9)
As + Af
Unloading stiffness in the hysteresis curve can affect the residual
displacement, which is an important index to evaluate the structural where a and b are the corresponding coefficients. WhenAf = 0, the
repairability. The unloading stiffness Ku,test is calculated as follows: formula is degraded to TK model. In order to determine the parameters
of a and b, the least square method was used to fit the test data. Under
Ku,test =
Vu,test
(6) the condition of a = 0.4, the result is more appropriate when b = 0.24.
δu − δu,0 The unloading stiffness of frame C is calculated by Eq. (7), and the
correlation coefficient between the calculated results and the test results
where Ku,test is unloading stiffness; Vu,test is unloading load; δu is is 0.998. Eqs. (8) and (9) are used to calculate the unloading stiffnesses
unloading displacement; of frame CF1, CF2 and F, and the calculated results are compared with
δu,0 is the residual deformation when the load is zero. the test results. The correlation coefficients are 0.995, 0.997 and 0.984,
With the same maximum displacement, the smaller the unloading respectively. The ratio of the calculation result of Eq. (7) and Eq. (8) to
stiffness is, the smaller the residual displacement will be. Takeda [34] the test result is shown in Table 5. According to the data in Table 5, the
presented the calculation model of unloading stiffness ku of reinforced calculation result of Eq. (8) has better prediction accuracy than Eq. (7).
concrete columns, which is called TK model, the expression of unloading
stiffness is shown in Eq. (7):
( )− 0.4 4.5. Residual displacement ratio
δmax
ku = × k1 (7)
δy The repairability of post-earthquake structures is the focus of
research on seismic performance of structures, which can be evaluated
where δy is the yield displacement; δmax represents the maximum loading
by residual displacement. Under the same loading displacement, the
displacement; k1 is the initial stiffness.
smaller the residual displacement is, the better the repairability of the
The relationship between the average unloading stiffness and
structure will be. In this paper, the average residual displacement δr,j is
loading displacement of the four tested frames is shown in Fig. 15. When
used as the residual displacement of the corresponding load, as shown in
the ratio of δmax /δy is less than 1.5, there is no significant difference in
Eq. (9).
unloading stiffness of each specimen. When the ratio is greater than 1.5,
∑ ∑⃒ ⃒
the unloading stiffness of frame C is the largest, while that of frame F is δr,j+ + ⃒δr,j− ⃒
the smallest. There is no significant difference in unloading stiffness of δr,j = ∑ ∑ (10)
nj+ + nj−
steel-CFRP hybrid reinforcement concrete frames CF1 and CF2, sug­
gesting that the residual displacement of the structure can be reduced by where δr,j+ and δr,j− are the residual displacements of the positive and
the configuration of CFRP reinforcements. When the ratio of δmax / δy is negative loading of grade j respectively; nj+ and nj− are the times of
2.2, the unloading stiffnesses of frame CF1, CF2 and F are 90.2%, 93% positive and negative loading of grade j respectively.
and 79.8% of that of frame C respectively. To better describe the The expression of the residual displacement ratio of the structure is
unloading stiffness of pier columns with FRP reinforcements, the shown in Eq. (10):
unloading stiffness calculation of FRP pier columns is proposed
δr,j
considering the influence of FRP reinforcement ratio, as shown in Eq. γ r,j = (11)
L
(8):
(
δmax
)− α where L is the height from the bottom of frame column to the center line
ku− FRP = × k1− FRP (8) of frame beam, which is 1650 mm.
δy
The residual displacements of the four tested frames are described in
where k1− FRP is the initial stiffness of corresponding FRP structures; Af Fig. 16, from which it can be seen that: before yield displacement (18
and As are the section areas of FRP reinforcements and steel re­ mm), there is little difference in residual displacements of the four
inforcements respectively. specimens. Residual displacement increases slowly with the increase of
loading displacement, and the residual displacement at yield displace­
ment is no more than 2 mm. After the steel reinforcement yields, the
residual displacement of frame C increases rapidly with the increase of
the loading displacement. When the loading displacement reaches 48
mm, the residual displacement ratio γ r,j reaches 1% (16.5 mm),
exceeding the limit of the repairable residual displacement stipulated by
the Japanese Code (JSCE 2000, JRA 2012) [35,36]. After the loading
displacement exceeds the yield displacement, the residual displacements
of frame CF1, CF2 and F increase with the increase of loading dis­
placements, and the growth rates are much lower than that of frame C.
When the loading displacement reaches 45 mm, the residual displace­
ments of frame CF1, CF2 and F are 55.1%, 38.3% and 48.2% of the re­
sidual displacement of frame C. Throughout the loading process, the
residual displacements of frames CF1 and F is basically the same.
Compared with frame CF1 and F specimens, the residual displacements
of CF2 is consistent with the two specimens before the peak load and is
slightly smaller than the two specimens after the peak load. The use of
CFRP reinforcement can greatly reduce the residual displacements. The
ratio of CFRP reinforcements has little effect on residual displacements.
Fig. 15. Average unloading stiffness of push and pull. None of the residual displacements exceeds 1% of the frame height until

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S. Song et al. Journal of Building Engineering 34 (2021) 101937

Table 5
Comparison of Unloading stiffness data.
δ(mm) Unloading stiffness ratio

C CF1 CF2 F

Eq. (8) Eq. (7) Eq. (8) Eq. (7) Eq. (8) Eq. (7) Eq. (8) Eq. (7)
/Test /Test /Test /Test /Test /Test /Test /Test

18 1.000 1.000 0.939 0.945 0.938 0.941 0.927 0.923

24 0.892 0.892 0.990 1.020 0.958 1.006 0.920 0.981
30 0.816 0.816 1.059 1.111 0.999 1.087 0.943 1.061
36 0.758 0.758 1.144 1.218 1.058 1.186 0.992 1.166
42 0.713 0.713 1.294 1.394 1.158 1.330 1.095 1.336
45 0.693 0.693 1.482 1.606 1.237 1.437 – –
48 0.676 0.676 – – 1.350 1.584 1.390 1.750
51 0.660 0.660 – – – – – –
Mean 1.196 1.196 1.151 1.216 1.100 1.224 1.044 1.203
S.D. 0.176 0.176 0.187 0.226 0.143 0.218 0.165 0.279

tensile strength (2000 MPa). With the increase of the loading

displacement, the strength degradation of the of CFRP reinforced
concrete frame (F) is larger than frame with steel reinforcement
(C, CF1, CF2). Before the peak load, the maximum degradation of
the strength of steel-CFRP hybrid reinforced concrete frames
(CF1, CF2) is controlled within 6.3%. In the limit state, the
strength degradation of steel-CFRP hybrid reinforced concrete
frames (CF1, CF2) is no more than 13%. In terms of the strength
degradation, the mechanical perforcemance of steel-CFRP hybrid
reinforced frame is better than that of CFRP reinforced frame and
slightly worse than steel reinforced frame.
(4) In the limit state, the residual displacement ratios of Steel-CFRP
hybrid reinforced concrete frame and CFRP reinforced concrete
frame are less than 1%, and the residual displacement ratios of
frames with different CFRP reinforcement ratios are about
38.3%–55.1% of steel reinforced concrete frame. The calculated
results of unloading stiffness model of FRP pier structures with
different steel-FRP reinforcement ratios are highly consistent
with the test results.
(5) The change of CFRP reinforcement ratios has no effect on the
Fig. 16. Comparison of average residual lateral drift ratio. equivalent damping ratios before yield load, and the smaller the
ratio of CFRP reinforcement is, after yield load, the larger the
the loading failure of the three specimens, which displays good equivalent viscous damping ratio and the stronger the energy
repairability. dissipation capacity of the structure will be. The concrete
cracking and the energy dissipation of steel reinforcements
5. Conclusions yielding will affect the equivalent viscous damping ratio.
Reasonable design of CFRP reinforcement ratio can ensure at
In this paper, the horizontal cyclic loading tests are conducted for least 70% of the energy dissipation capacity of the steel rein­
steel-CFRP hybrid reinforced concrete, CFRP reinforced concrete and forced structure.
steel reinforced concrete frames with the axial compression ratio being
0.31. The following conclusions can be drawn from the test results and CRediT authorship contribution statement
analysis:
Shoutan Song: Conceptualization, Methodology, Software, Writing -
(1) The bending failure of steel reinforced concrete frames is mainly original draft, Writing - review & editing. Guan Wang: Data curation,
caused by concrete crushing after steel yielding, and the bending Formal analysis. Xinzhe Min: Visualization, Investigation. Ning Duan:
failure of steel-CFRP hybrid reinforced concrete frame and CFRP Software, Validation. Yongming Tu: Conceptualization, Supervision,
reinforced concrete frame is the decrease of strength caused by Project administration, Writing - review & editing, Funding acquisition.
concrete crushing and CFRP reinforcement fracture. Unreason­
able layout of steel stirrups will reduce the seismic shear capacity
Declaration of competing interest
of the structure, eventually resulting in shear failure.
(2) The higher the CFRP reinforcement ratio is, the higher the post-
The authors declare that there is no conflict of interests regarding the
yield stiffness ratio and the damage development stability of
publication of this article.
Steel-CFRP hybrid reinforced concrete frame will be.
(3) Cyclic loading affects the limit strength of CFRP reinforcement,
Acknowledgements
which further affects the strength degradation of the frame. With
the axial compression ratio being 0.31, the ultimate strengths of
The authors gratefully acknowledge the financial support from Na­
CFRP reinforcements of frame CF1, CF2 and F under peak load
tional Key Research and Development Program of China
are 640 MPa, 572 MPa and 543 MPa, which are about 32%,
(No.2017YFC0703006-01), and Jiangsu Planned Projects for Post­
28.6% and 27.2% of the ultimate strength of static uniaxial
doctoral Research Funds (No. 1601148B). The authors also acknowledge

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S. Song et al. Journal of Building Engineering 34 (2021) 101937

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