experimental study on hysteretic behavior of concrete

36
Experimental Study On Hysteretic Behavior of Concrete Filled Square CFRP Steel Tubular Beam- Column Wang Qing-li University of Science and Technology Liaoning Kuan Peng ( [email protected] ) Southwest Petroleum University Guo Yi-Huan University of Science and Technology Liaoning Shao Yong-bo Southwest Petroleum University Research Article Keywords: Square CFRP concrete ヲlled steel tube, Middle section lateral force-deァection curve, Hysteretic behavior, Finite element simulation Posted Date: November 10th, 2021 DOI: https://doi.org/10.21203/rs.3.rs-1023075/v1 License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License

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Page 1: Experimental Study On Hysteretic Behavior of Concrete

Experimental Study On Hysteretic Behavior ofConcrete Filled Square CFRP Steel Tubular Beam-ColumnWang Qing-li 

University of Science and Technology LiaoningKuan Peng  ( [email protected] )

Southwest Petroleum UniversityGuo Yi-Huan 

University of Science and Technology LiaoningShao Yong-bo 

Southwest Petroleum University

Research Article

Keywords: Square CFRP concrete �lled steel tube, Middle section lateral force-de�ection curve, Hystereticbehavior, Finite element simulation

Posted Date: November 10th, 2021

DOI: https://doi.org/10.21203/rs.3.rs-1023075/v1

License: This work is licensed under a Creative Commons Attribution 4.0 International License.  Read Full License

Page 2: Experimental Study On Hysteretic Behavior of Concrete

Experimental study on hysteretic behavior of concrete filled 1

Square CFRP steel tubular Beam-Column 2

Wang Qing-li1,2, Peng Kuan3, Guo Yi-Huan1, Shao Yong-bo4 3

(1. School of Civil Engineering, University of Science and Technology Liaoning, Anshan, 114051, 4

P. R. China 5

2. School of Civil Engineering, Shenyang Jianzhu University, Shenyang, 110168, P. R. China 6

3. School of Mechatronic Engineering, Southwest Petroleum University, Chengdu, 610500, P. R. 7

China 8

4. School of Civil Engineering and Geomatics, Southwest Petroleum University, Chengdu, 610500, 9

P. R. China ) 10

Abstract: In order to study the hysteretic behavior of concrete filled square CFRP steel tubular 11

Beam-Column under different influence factors, 12 specimens were designed, and the failure 12

mode, middle section lateral force-deflection(P-) curve, middle section bending 13

moment-curvature(M-) curve and middle section deflection-deformation(') curve were 14

studied. Axial compression ratio and longitudinal CFRP reinforcement coefficient as influencing 15

factors, the effects of axial compression ratio and longitudinal CFRP reinforcement coefficient on 16

P- skeleton curve, M- skeleton curve, strength and stiffness degradation, ductility, cumulative 17

Page 3: Experimental Study On Hysteretic Behavior of Concrete

energy consumption and other indexes were studied; the P- curve and deformation mode of the 18

specimens were simulated by ABAQUS, and the effects of axial compression ratio, slenderness 19

ratio and other main parameters on the hysteretic performance of the members were studied. The 20

test results show that CFRP has good lateral restraint and longitudinal reinforcement effect on 21

CFST, and the local buckling of CFST is delayed. The P- curve and M- curve of all specimens 22

are full. In addition, the steel tube and CFRP have good synergy in both longitudinal and 23

transverse directions. The change of axial compression ratio and longitudinal CFRP reinforcement 24

coefficient has no significant effect on the strength degradation. The increase o f axial compression 25

ratio and longitudinal CFRP reinforcement coefficient can improve the flexural capacity and 26

stiffness of the specimens, and slow down the stiffness degradation, but reduce the ductility and 27

cumulative energy consumption of the specimens. The finite element software ABAQUS is used to 28

simulate the P- curve and deformation mode of specimens. It is found that the simulation results 29

are in good agreement with the experimental results. Based on the model analysis of the main 30

parameters, it is found that the increase of steel yield strength and CFRP layers can improve the 31

bearing capacity of the specimens, and the axial compression ratio has the most significant effect 32

on the specimens. 33

Key words: Square CFRP concrete filled steel tube; Middle section lateral force-deflection curve; 34

Hysteretic behavior; Finite element simulation 35

Page 4: Experimental Study On Hysteretic Behavior of Concrete

1 Introduction and research significance" 36

In recent years, earthquakes are more and more widespread in the world. The distribution of 37

seismic zones is not uniform, but they are widely distributed. Some scholars have carried out 38

extensive and in-depth research on the seismic design of building structures, and the 39

earthquakes have caused huge economic losses and casualties. To deal with the threat of 40

earthquake disaster to buildings, the research on hysteretic behavior of building structures is 41

more and more extensive [1-2]. Nowadays, the most commonly used composite structure is 42

steel-concrete composite structure. It is a composite structure composed of steel and concrete, 43

which mainly uses the advantages of compressive performance of concrete and tensile 44

performance of steel [3-4]. This composite structure is not only convenient for construction, 45

but also saves a lot of materials, so as to achieve the goals of reducing the cost, reducing the 46

weight of components and shortening the construction period. Therefore, the steel -concrete 47

composite structure is widely used in practical engineering[5]. 48

Liu Y et al. [6] carried out the torsion tests of 16 circular CFRP concrete filled steel tubes. 49

The results show that the failure modes of the specimens bonded with longitudinal CFRP and 50

circumferential CFRP are different. Ling ZG et al. [7] carried out experimental research and 51

finite element theoretical analysis on torsion performance of 18 CFRP square section 52

Page 5: Experimental Study On Hysteretic Behavior of Concrete

concrete-filled steel tubular members. The results show that the steel tube and CFRP can work 53

together, and the deformation of the component approximately conforms to the plane section 54

assumption. Han LH et al. [8] deduced the axial force torque correlation equation of concrete 55

filled steel tubular members, described the moment torque correlation equation, and analyzed 56

the whole process of such specimens. Tao et al. found that square CFRP-CFST specimens’ 57

bearing capacity was reduced significantly after fire damage, while concrete -filled CFRP-steel 58

tube specimens’ fire resistance was better than that of ordinary concrete-filled steel tube 59

specimens [9-10]. In practical application, members often also bear hysteretic loads, such as 60

wind and earthquake load[10-11]. 61

In view of this, 12 groups of square CFRP concrete-filled steel tubular specimens are 62

designed in this paper. Referring to the hysteretic test of concrete -filled steel tubular, the failure 63

mode, P- curve, M- curve and ' curve of each group of specimens are studied. The axial 64

compression ratio and longitudinal CFRP reinforcement coefficient are taken as the influencing 65

factors to study their influence on P- skeleton curve and M- skeleton curve. ABAQUS is used 66

to simulate the P- curve and deformation mode of the specimens. On this basis, the influence of 67

axial compression ratio, slenderness ratio and other main parameters on the hysteretic 68

performance of the member is studied, so as to provide some theoretical reference for engineering 69

Page 6: Experimental Study On Hysteretic Behavior of Concrete

practice. 70

2 Raw material performance and experimental design 71

2.1 Performance of raw materials 72

(1) Steel 73

Cold-formed steel tubes were used for the S-CF-CFRP-ST specimens, in which the inner 74

chamfer radius at the bending angle was 5mm. The steel tubes’ material properties are shown 75

in Table 1. 76

Table 1 The material properties of steel tube used in experiment 77

Section fy/MPa fu/MPa Es/GPa sy/ vs '/%

Square 298 425 199 2502 0.28 27

(2) Concrete 78

Portland cement with a strength grade of 42.5 was used in the experiment. Medium coarse 79

sand was used as fine aggregate. The particle size of the coarse aggregate gravel was 5 ~15mm, 80

and a water reducer with 1% cement weight was added. The specific ratio of the concrete is 81

shown in Table 2. 82

Table2 Specific ratio of concrete kg/m3 83

Cement Water Fine Aggregate Coarse Aggregate

Page 7: Experimental Study On Hysteretic Behavior of Concrete

490 171.5 661.5 1078

After 28 days of standard curing, the concrete cube’s compressive strength (fcu) was 47.8MPa 84

and the elastic modulus (Ec) was 34.6GPa. The cube’s compressive strength was 77.7MPa 85

during the hysteretic test. 86

(3) CFRP and viscose 87

Carbon fiber fabric is a unidirectional fabric woven with carbon fiber made in China. Its main 88

properties are shown in Table 3. 89

The adhesive and base adhesive are building structural adhesives produced by China Institute 90

of construction science and technology in the test. 91

92

Table 3 Basic Performance Parameters of CFRP 93

Thickness of single

layer (mm)

Weight (g/m3) Elongation at

break(%)

Tensile strength of

monofilament (GPA)

0.111 200 2.1 4.9

2.2 Experimental design 94

A total of twelve S-CF-CFRP-ST specimens was designed, and their hysteretic behavior was 95

tested. The main parameters included the axial compression ratio (n), and strengthening factor 96

of longitudinal CFRP (. n is defined by the following equation: 97

Page 8: Experimental Study On Hysteretic Behavior of Concrete

n=N0/Nu, cr (1) 98

In which: N0 is the axial compression applied to the specimens. 99

The specimens’ calculated length (L) was 2000mm. The steel tube’s outer length (Bs) was 100

140mm. The tube’s wall thickness (ts) was 4mm, and the number of transverse CFRP layers 101

(mt) was 1, where ml was the number of longitudinal CFRP layers, and y was the specimens’ 102

displacement in the yield state. All specimens’ specific parameters are shown in Table 4. 103

Table 4 The parameters of S-CF-CFRP-ST specimens with hysteretic behavior 104

Order Number n ml/layers N0/KN y/mm

1 A0 0 0 0 0 16.1

2 A1 0 1 0.17 0 14.1

3 A2 0 2 0.34 0 14.1

4 B0 0.2 0 0 263 10.1

5 B1 0.2 1 0.17 268 11.1

6 B2 0.2 2 0.34 273 14.1

7 C0 0.4 0 0 526 9.1

8 C1 0.4 1 0.17 536 9.1

Page 9: Experimental Study On Hysteretic Behavior of Concrete

9 C2 0.4 2 0.34 546 8.1

10 D0 0.6 0 0 789 5.1

11 D1 0.6 1 0.17 804 7.1

12 D2 0.6 2 0.34 819 8.1

CFRP’s adhesion is extremely important to the experimental results. It is necessary to ensure 105

that the steel tube is hooped by the longitudinal CFRP in the preparation process, so that it can 106

maintain the cooperation with the steel tube. In addition, the longitudinal CFRP was hooped 107

by transverse CFRP to avoid premature stripping of the longitudinal CFRP [12]. 108

The experiment was carried out at the Structural Engineering Laboratory. The loading 109

equipment in the experiment is shown in Fig. 1. 110

111

Fig. 1 Loading equipment of hysteretic performance test of S-CF-CFRP-ST specimens 112

Page 10: Experimental Study On Hysteretic Behavior of Concrete

Before the experiment, the specimens were placed horizontally and hinged at both ends. The 113

axial loading (1250KN) was exerted by the actuator of Electro-hydraulic Servo-system that 114

was installed horizontally. At the same time, the cyclic loading (500KN) was exerted by the 115

actuator that was installed vertically in the midsection. The actuator was connected to the 116

specimens through a rigid fixture. To avoid the specimen’s instability during loading, a set of 117

4-piece lateral support devices was designed, which were installed at two quarter points of the 118

specimen, respectively. The sliding plate was arranged on the side of the equipment, which 119

contacted the specimen to ensure its unimpeded vertical movement in the plane during the 120

loading process. The lateral support was connected rigidly with the ground anchor. 121

The method to control loading-displacement was used in the experiment [13]. In the initial 122

stage of the experiment, the loading was controlled and classified. The specimens were loaded 123

at 0.25Puc (Puc is defined as the estimated lateral bearing capacity), 0.5Puc, and 0.7Puc, 124

respectively, and each stage loading was circulated for 2 times. Thereafter, displacement 125

control and step loading were adopted, and the specimens were loaded with 1.0, 1.5, 2.0, 3.0, 126

5.0, 7.0, and 8.0Δy. The loading of the first three levels was cycled 3 times, and that of the 127

other levels was cycled 2 times, where Δy=Puc/K0.7 and K0.7 is the secant stiffness of the P- 128

skeleton curve at 0.7Puc. The criteria for termination of the experiment were set that P dropped 129

Page 11: Experimental Study On Hysteretic Behavior of Concrete

to 50% of the peak loading; the displacement ductility coefficient reached 8, and the 130

displacement was close to the range of the actuator. 131

In the process of the test, P and were collected directly by the INV-306D intelligent signal 132

acquisition system, which was connected to the vertical actuator of Electro-hydraulic 133

Servo-system, and the P- curves were drawn at the same time. N0 and ' were collected 134

directly by the INV-306D intelligent signal acquisition system, which was connected to the 135

horizontal actuator of Electro-hydraulic Servo-system. The deflection was measured at two 136

quarter points close to the two supports. One transverse and one longitudinal strain gauge 137

were pasted on the top and bottom outermost edges of the steel tube’s midsection, respectively, 138

and one transverse and one longitudinal strain gauge were also pasted on the top and bottom 139

outermost edges of the CFRP’s midsection to measure the strain. 140

3 Test results and analysis 141

3.1 Test phenomena 142

During the 1y~2y period, some tiny cracks appeared between the transverse CFRPs in the 143

longitudinal tensile zone near the midsection. With the increase in displacement, the cracks 144

continued to expand from the upper and lower edges to the neutral axis, and some new cracks 145

Page 12: Experimental Study On Hysteretic Behavior of Concrete

also appeared. Thereafter, the axial compression ratio affected the experimental phenomenon 146

greatly. 147

When the specimens with a small axial compression ratio (n 0.2) were loaded to 3y, a slight 148

deformation occurred in the compression area near the midsection. With unloading and 149

reverse loading, the convex deformation flattened again, and the increases in the convex 150

deformation were proportional to the increase in displacement. At this time, the transverse 151

CFRP at the bending angle began to fracture sporadically. When they were loaded to 5y, the 152

convex deformation developed significantly and the sound of the CFRP splitting could be 153

heard. At this time, a large number of transverse CFRPs fractured at the bending angle, and 154

then the longitudinal CFRPs also fractured, as shown in Fig. 2(a). When loaded to 7y~8y, a 155

large number of them fractured, and finally, the steel tube was destroyed. In the specimens 156

without longitudinal CFRP, when the deflection was large during the later stage of loading, a 157

large number of transverse CFRPs fractured at the bending angle, and finally, the steel tube 158

was destroyed swiftly, as shown in Fig. 2(b). 159

160

Steel tube

Fracture of transverse CFRP

Steel tube

Page 13: Experimental Study On Hysteretic Behavior of Concrete

(a) Longitudinal CFRP of A1 (b) Transverse CFRP and steel tube of A0 161

Figure 2. Fracture of CFRP of specimens with a small axial compression ratio 162

When the specimens with a large axial compression ratio (n 0.4) were loaded to 3y, a slight 163

deformation occurred in the compression zone near the midsection. When loaded to 5y, the 164

deformation developed significantly, and at this time, the transverse and longitudinal CFRP at 165

the bending angle fractured gradually, as shown in Fig. 3(a). When loaded to 7y, a large 166

number of transverse and longitudinal CFRP fractured at the bending angle with a continuous 167

crackling sound. When loaded to 8y, obvious convex deformation occurred in the tube’s 168

midsection. The experimental results of specimens without longitudinal CFRP were the same 169

as those of specimens with a small axial compression ratio. When the deflection was large at 170

the end of loading, many transverse CFRP fractured at the bending angle, as shown in Fig. 171

3(b). 172

173

(a) C1 test results (b) C0 test results 174

Fig 3. CFRP fracture and steel tube failure of specimens with a large axial compression ratio 175

Longitudinal CFRP fracture Transverse CFRP fracture Buckling of steel tube

Transverse CFRP fracture

Page 14: Experimental Study On Hysteretic Behavior of Concrete

Figs. 4(a) and 4(b) separately show the failure status of the steel tube and concrete in 176

S-CF-CFRP-ST specimens with n =0.2, n =0.6. The figures show that as the axial compression 177

ratio increased, the extent of the damage to the steel tube and concrete decreased. Because the 178

concrete is confined by the CFRP and steel tube, the plastic filling showed good performance. 179

180

(a) The failure status of the steel tube and concrete in specimen with n =0.2 181

182

(b) The failure status of the steel tube and concrete in specimen with n =0.6 183

Figure 4. Failure of specimens with different axial compression ratio 184

In general, as the and n increased, the extent of the specimen’s damage decreased. Fig. 5 185

shows the hysteretic behavior of the S-CF-CFRP-ST specimens after loading. 186

187

Figure 5. Hysteretic behavior of the S-CF-CFRP-ST specimens after loading. 188

3.2 The curve of P-189

3.2.1 The hysteresis curve of P- 190

Convex

Crushing

Slight Crushing

Convex

Page 15: Experimental Study On Hysteretic Behavior of Concrete

Fig. 6 shows the S-CF-CFRP-ST specimens’ P-curves when ml=1. It can be seen that the 191

specimens’ hysteretic curves were relatively full. During the initial stage of loading, the 192

specimens were in the elastic stage, and the hysteretic curves changed linearly. After the 193

yielding stage was reached, the residual deformation was inversely proportional to the 194

stiffness. In the process of unloading to reverse loading, the stiffness did not change obviously. 195

During the final stage of loading, the S-CF-CFRP-ST specimens’ bearing capacity decreased 196

gradually. 197

-120

-80

-40

0

40

80

120

-150 -100 -50 0 50 100 150 / mm

P /

kN

-120

-80

-40

0

40

80

120

-120 -80 -40 0 40 80 120 / mm

P /

kN

(a) P- curve of A1 (b) P- curve of B1

-120

-80

-40

0

40

80

120

-75 -50 -25 0 25 50 75 / mm

P /

kN

-120

-80

-40

0

40

80

120

-60 -40 -20 0 20 40 60 / mm

P /

kN

(c) P- curve of C1 (d) P- curve of D1

Figure 6. P-curves of specimens with ml=1 198

3.2.2 Skeleton curve of P- 199

Figs. 7 (a) and 7 (b), respectively, show the S-CF-CFRP-ST specimens’ P- skeleton curves, 200

which are related to the axial compression ratio (n) and strengthening factor of longitudinal 201

CFRP (). It can be seen that as the n increased, both the specimens’ stiffness in the elastic 202

Page 16: Experimental Study On Hysteretic Behavior of Concrete

stage and their lateral bearing capacity decreased, and the curves showed a descending section 203

during the later stage of loading. As the increased, the specimens’ bearing capacity 204

increased, while the stiffness remained unchanged in the elastic stage. 205

-150 -100 -50 0 50 100 150-120

-80

-40

0

40

80

120

P /

kN

/ mm

A0

B0

C0

D0

-60 -40 -20 0 20 40 60-120

-80

-40

0

40

80

120

P /

kN

/ mm

D0

D1

D2

(a)Specimen of =0 (b)Specimen of n=0.6

Figure 7. Effect of n and on P- skeleton curves 206

3.3 M-skeleton curve 207

Figure 8 shows the deflection curve shape of the most representative A2 specimen. In this 208

paper, the curvature and bending moment of the middle section of the specimen are calculated by 209

formula (2) and (3), respectively: 210

2

2

L

um (2) 211

M=PL/4+N0 (3) 212

Page 17: Experimental Study On Hysteretic Behavior of Concrete

where: is the curvature of the middle section, um is the deflection of the middle section, L is 213

the calculated length of the specimen, M is the bending moment of the middle section, P is the 214

lateral bearing capacity, and N0 is the axial force. 215

0 500 1000 1500 2000-120

-80

-40

0

40

80

120

u /

mm

L / mm

+0.5Pu

-1y

+1.5y

-2y

+3y

-5y

+7y

-8y

Sine curve

216

Fig. 8 Deflection curve of A2 specimen 217

3.3.1 M- hysteresis curve 218

-75

-50

-25

0

25

50

75

-0.45-0.30-0.15 0.00 0.15 0.30 0.45

/ m-1

M /

kNm

-75

-50

-25

0

25

50

75

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

/ m-1

M /

kNm

(a) curve of A0 (b) curve of B0

-75

-50

-25

0

25

50

75

-0.24-0.16-0.08 0.00 0.08 0.16 0.24

/ m-1

M /

kNm

-75

-50

-25

0

25

50

75

-0.15-0.10-0.05 0.00 0.05 0.10 0.15

/ m-1

M /

kNm

Page 18: Experimental Study On Hysteretic Behavior of Concrete

(c) curve of C0 (d) curve of D0

Fig. 9 curve of partial specimens 219

It can be seen from Fig.9 that the M- hysteretic curves of specimens are shuttle shaped, and 220

there is no obvious pinch phenomenon. When the force control is adopted at the initial stage of 221

loading, the deformation of the specimen is elastic deformation, When the displacement control is 222

adopted, the component produces a less obvious "Bauhinia" effect. 223

3.3.2 M- skeleton curve 224

-0.45-0.30-0.15 0.00 0.15 0.30 0.45-75

-50

-25

0

25

50

75

M /

kNm

/ m-1

A1

B1

C1

D1

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3-75

-50

-25

0

25

50

75

M /

kNm

/ m-1

B0

B1

B2

(a) =0.17 specimens (b) n=0.2 specimens

Fig. 10 Effect of axial compression ratio and longitudinal CFRP reinforcement coefficient on

M- skeleton curve of specimens

Fig. 10 shows the influence of axial compression ratio and longitudinal CFRP 225

reinforcement coefficient on the M-skeleton curve of specimens hysteretic behavior. It can be 226

seen that the increase of axial compression ratio and longitudinal CFRP reinforcement coefficient 227

Page 19: Experimental Study On Hysteretic Behavior of Concrete

can improve the bending capacity of the specimens, and the change of axial compression ratio is 228

more sensitive to the bending capacity of the specimens. 229

3.4 Deformation of axial direction 230

Figures 11 (a) ~ (d) show the lateral deflection axial deformation (-') curves of four groups 231

specimens with different axial compression ratios. For A2 specimens without axial compression 232

ratio, it can be found that ' increases with the increase of at the initial stage of loading . ' 233

decreases with the increase of at the later stage of loading. For B2, C2 and D2 specimens with 234

axial compression ratio, ' increases with the increase of . 235

-12 -6 0 6 12-12

-8

-4

0

4

8

12

/ y

' / mm

0 8 16 24-12

-8

-4

0

4

8

12

/ y

' / mm

(a)axial deformation of A2 specimen (b)axial deformation of B2 specimen

0 12 24 36-12

-8

-4

0

4

8

12

/ y

' / mm

0 12 24 36-12

-8

-4

0

4

8

12

/ y

' / mm

(c)axial deformation of C2 specimen (d)axial deformation of D2 specimen

Fig. 11 -'curves of partially specimens 236

3.5 Strain relationship 237

3.5.1 Strain of steel tube and CFRP 238

In order to ensure the accuracy of the test results, the transverse strain curves (P-t curves) of 239

steel tube and CFRP at two test points of A1 group specimens are taken, as shown in Fig. 12 (a) 240

and Fig. 12 (b). Similarly, the longitudinal strain curve (P-1 curve) at the same two test points of 241

Page 20: Experimental Study On Hysteretic Behavior of Concrete

group A2 are taken, as shown in Fig. 12 (c) and Fig. 12 (d). st and cft are the transverse strains of 242

steel tube and CFRP. sl and cfl are the longitudinal strains of steel tube and CFRP. It can be seen 243

from Figure 12 that the transverse and longitudinal strains of steel tube and CFRP are consistent, 244

which indicates that under the action of hysteretic force, steel tube and CFRP can keep 245

cooperation in both transverse and longitudinal directions. 246

-120

-80

-40

0

40

80

120

-2000 -1000 0 1000 2000 3000

t /

P /

kN

st

cft

-120

-80

-40

0

40

80

120

-2000 0 2000 4000 6000

t /

P /

kN

st

cft

(a) P-t curve of A1 specimen at point 1 (b) P-t curve of A1 specimen at point 2

-90

-60

-30

0

30

60

90

-12000-8000 -4000 0 4000 8000

l /

P /

kN

sl

cfl

-90

-60

-30

0

30

60

90

-8000 -4000 0 4000 8000 12000

l /

P /

kN

sl

cfl

(c)P-1 curve of A2 specimen at point 1 (d)P-1 curve of A2 specimen at point 2

Fig. 12 P-t and P-1 curves of steel tube and CFRP at two test points

3.5.2 Comparison of transverse and longitudinal strain of steel tube 247

Fig. 13 is the comparison curve (P-s curve) of transverse and longitudinal strain of steel tube. 248

It can be seen from Figure 13 that the longitudinal strain sl and transverse strain st of each group 249

of specimens at the same point are different. When they are subjected to longitudinal tensio n, they 250

Page 21: Experimental Study On Hysteretic Behavior of Concrete

are subjected to transverse compression at the same time. 251

-120

-80

-40

0

40

80

120

-4000 0 4000 8000 12000

s /

P /

kN

sl

st

-120

-80

-40

0

40

80

120

-4200 -2100 0 2100 4200

s /

P /

kN

sl

st

252

(a) P-s curve of A2 specimen (b) P-s curve of D1 specimen 253

Fig.13 P-s curves of partially specimens 254

4. Analysis of main indicators 255

4.1 Strength degradation 256

According to the method of reference[7], the strength degradation coefficient ji is 257

determined. Figure 14 shows the strength degradation of the specimen. It is obvious from Figure 258

15 that the strength degradation of the specimen is not obvious. 259

0 3 6 9-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

ji

/ y

A0

B0

C0

D0

(a) =0 specimens

0 3 6 9-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

ji

/ y

A1

B1

C1

D1

(b) =0.157 specimens

0 3 6 9-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

ji

/ y

A2

B1

C1

D1

(c) =0.314 specimens

Fig.14 Strength degradation of specimens 260

4.2 Stiffness degradation 261

Page 22: Experimental Study On Hysteretic Behavior of Concrete

The stiffness EI of each cycle was determined according to the method of reference [11]. Figs. 262

15 (a) and (b) show the effects of axial compression ratio and longitudinal CFRP reinforcement 263

coefficient on the stiffness degradation of specimens, respectively, where EI=0 is the initial 264

stiffness of the specimens. It can be seen from Figure 15 that the increase of axial compression 265

ratio can delay the stiffness degradation of the specimen. In addition, the increase of longitudinal 266

CFRP reinforcement coefficient can delay the stiffness degradation of the specimen. 267

0 3 6 90.0

0.4

0.8

1.2

EI

/ E

I =

0

/ y

A2

B2

C2

D2

0 3 6 90.0

0.5

1.0

1.5E

I /

EI

=0

/ y

C0

C1

C2

(a) =0.34 specimens (b) n=0.4 specimens

Fig. 15 Effect of axial compression ratio and longitudinal CFRP reinforcement coefficient on 268

stiffness degradation of specimens 269

4.3 Displacement ductility factor 270

The ductility of the specimen is calculated by the following displacement ductility coefficient μ: 271

y

uu

(4) 272

where, Δu is the corresponding displacement when the load on the skeleton line decreases by 15%. 273

Page 23: Experimental Study On Hysteretic Behavior of Concrete

The comparison of the ductility coefficient of each group of specimens is shown in Fig. 16. 274

Since the load of n = 0 specimen does not drop to 85% of its peak bearing capacity at the end of 275

the test, it is impossible to determine its ductility coefficient, which is taken as a larger value in 276

comparison. It can be seen from Figure 16 that, in terms of the overall trend, the increase of axial 277

compression ratio and longitudinal CFRP reinforcement coefficient will reduce the ductility of the 278

specimen. The reason is that the larger the axial compression ratio and the longitudinal CFRP 279

reinforcement coefficient, the more the failure mode of the specimen tends to the brittle failure 280

mode of the concrete being crushed. 281

0.0 0.2 0.4 0.60

3

6

9

n

=0

=0.17

=0.34

282

Fig. 16 Comparison of specimens’ displacement ductility coefficient 283

4.4 Cumulative energy consumption and energy dissipation 284

Fig. 17 (a) and Fig. 17 (b) respectively show the influence of axial compression ratio and 285

longitudinal CFRP reinforcement coefficient on the cumulative energy dissipation E of 286

specimens [14-15]. It can be seen that the increase of axial compression ratio will reduce the 287

Page 24: Experimental Study On Hysteretic Behavior of Concrete

energy dissipation capacity of the specimens, which is due to the poor ductility of the specimens 288

with large axial compression ratio. The residual bearing capacity of the specimens with large axial 289

compression ratio is lower than that of the specimens with small axial compression ratio. In 290

addition, the increase of longitudinal CFRP reinforcement coefficient can improve the energy 291

dissipation capacity of the specimens. 292

0 3 6 90

80

160

240

E /

kNm

/ y

A0

B0

C0

D0

0 3 6 90

60

120

180

E /

kNm

/ y

B0

B1

B2

(a) =0 specimen (b) n=0.2 specimen

Fig. 17 Effect of axial compression ratio and longitudinal CFRP reinforcement coefficient on

cumulative energy dissipation

According to the method of reference [14-15], the energy dissipation coefficient he is determined. 293

Figure 18 shows the relationship between energy dissipation coefficient and displacement of 294

=0.34 specimen in the last cycle of each load level. It can be seen from the figure that when the 295

specimen yields, the energy dissipation coefficient of the specimen with axial compression ratio is 296

Page 25: Experimental Study On Hysteretic Behavior of Concrete

greater than that of the specimen without axial compression ratio, which indicates that the axial 297

compression ratio is beneficial to the seismic performance of the specimen within a certain range. 298

0 3 6 90

6

12

18

hE

/ y

A2

B2

C2

D2

299

Fig.18 Effect of n on energy dissipation of specimens 300

5 Finite element simulation 301

5.1 Stress strain relationship of materials 302

In the process of using ABAUQS finite element modeling, steel tube adopts the mixed 303

hardening model provided by ABAUQS software, and concrete adopts the plastic damage model 304

provided by ABAUQS finite element software. Both of them adopt the stress -strain relationship 305

provided by reference[16-21]. The parameters are determined as follows: the tensile plastic 306

damage parameter bt is 0.6~0.8, the compressive plastic damage parameter bc is 0.6~0.8; the 307

tensile stiffness recovery coefficient t is 0, and the compressive stiffness recovery coefficient c 308

is 0.4~0.95 according to the different axial compression ratio. 309

5.2 Finite element calculation model 310

Page 26: Experimental Study On Hysteretic Behavior of Concrete

The element selection, mesh generation and interface model treatment method of specimens 311

are consistent with those of CFST members. Figure 19 shows the boundary conditions for the 312

finite element simulation of specimens. 313

314

Fig. 19 Boundary conditions for the specimens’ finite element simulation 315

According to the symmetry of the geometry and boundary conditions of the component, the 316

quarter model of the actual component is taken for analysis, and the symmetrical constraint 317

conditions are imposed on the symmetry plane of the calculation model. The boundary condition is 318

that the surface load is applied on the end plate and the lateral hysteretic force is applied on the 319

middle section. In order to ensure that the loading mode is consistent with that in the test process, 320

the loading-displacement control mode is adopted. 321

5.3 Comparison of finite element simulation and test results 322

Fig. 20 and Fig. 21 show the comparison between the simulation results and the test results of 323

P- curve and P- skeleton curve of partially S-CF-CFRP-ST specimens, respectively. Fig. 22 (a) 324

y

x

z

Constraint point of displacement and rotation

Y-Z symmetry plane

X-Y symmetry plane

Hysteretic load

N0

Page 27: Experimental Study On Hysteretic Behavior of Concrete

and Fig. 22 (b) show the actual failure modes and the finite element simulation failure modes of 325

the steel tube in the specimens, respectively. Fig. 23 (a) and Fig. 23 (b) show the failure modes of 326

concrete in specimens and those of finite element simulation, respectively. It can be seen that the 327

simulation results are in good agreement with the experimental results. The test results of each 328

group are basically consistent with the finite element simulation results, which shows that the 329

simulation results of the established model are in good agreement with the actual test results. 330

331

-120

-80

-40

0

40

80

120

-180 -120 -60 0 60 120 180

/ mm

P /

kN

Test result

FE result

-120

-80

-40

0

40

80

120

-120 -80 -40 0 40 80 120

/ mm

P /

kN

Test result

FE result

332

(a) A1 specimen (b) B1 specimen 333

-120

-80

-40

0

40

80

120

-90 -60 -30 0 30 60 90

/ mm

P /

kN

Test result

FE result

-120

-80

-40

0

40

80

120

-75 -50 -25 0 25 50 75

/ mm

P /

kN

Test result

FE result

334

(c) C1 specimen (d) D1 specimen 335

Page 28: Experimental Study On Hysteretic Behavior of Concrete

Fig. 20 Comparison of simulation results and experimental results of 336

P-curves of partially specimens 337

-120

-80

-40

0

40

80

120

-150 -100 -50 0 50 100 150

/ mm

P /

kN

Test result

FE result

(a) A0 specimens

-135

-90

-45

0

45

90

135

-105 -70 -35 0 35 70 105

/ mm

P /

kN

Test result

FE result

(b) B0specimens

-120

-80

-40

0

40

80

120

-90 -60 -30 0 30 60 90

/ mm

P /

kN

Test result

FE result

(c) C0specimens

-120

-80

-40

0

40

80

120

-60 -40 -20 0 20 40 60

/ mm

P /

kN

Test result

FE result

(d) D0specimens

-120

-80

-40

0

40

80

120

-75 -50 -25 0 25 50 75

/ mm

P /

kN

Test result

FE result

(e) D1specimens

-120

-80

-40

0

40

80

120

-75 -50 -25 0 25 50 75

/ mm

P /

kN

Test result

FE result

(f) D2specimens

338

Fig. 21 Comparison of simulation results and experimental results of 339

P-skeleton curves of partially specimens 340

341

342

(a) Test result (b) FE result 343

Convex Convex

Page 29: Experimental Study On Hysteretic Behavior of Concrete

Fig.22 Failure modes of steel tube with middle section 344

345

(a) Test result (b) FE result 346

Fig.23 Failure modes of concrete with middle section 347

6 Parameter analysis

348

Axial compression ratio, slenderness ratio, number of CFRP layers, steel yield strength, 349

concrete strength and steel ratio are the main indexes to evaluate the performance of 350

S-CF-CFRP-ST specimens, which have significant influence on the skeleton curve of members 351

with compression bending hysteretic behavior. Therefore, a typical example is used to analyze the 352

influence of the above parameters on the p-Δ skeleton curve of members. 353

6.1 Influence of axial compression ratio n and slenderness ratio 354

Figure 24 shows the effect of axial compression ratio on the P- skeleton curve of members. 355

It can be seen that with the increase of n, the bearing capacity and the stiffness of the elastic stage 356

of the member decrease significantly. The shape of the curve also has obvious changes: when n=0, 357

there is no descending segment in the P- skeleton curve. With the increase of n, the second-order 358

effect of axial force is more obvious, and the descending segment appears in the curve, and the 359

Crushed Crushed

Page 30: Experimental Study On Hysteretic Behavior of Concrete

amplitude of the descending segment increases. Effect of on P- skeleton curve of specimens is 360

shown in Figure 25. It can be seen that the bearing capacity and the stiffness of the elastic stage of 361

the member decrease significantly with the increase of and the shape of the curve also has 362

obvious changes: the stability coefficient decreases with the increase of and the second-order 363

effect caused by the constant axial force is more obvious. 364

-120

-80

-40

0

40

80

120

-60 -40 -20 0 20 40 60

/ mm

P /

kN

n=0.0

n=0.1

n=0.2

n=0.3

n=0.4

n=0.5

n=0.6

n=0.7

n=0.8

-240

-160

-80

0

80

160

240

-45 -30 -15 0 15 30 45

/ mm

P /

kN

=25

=33

=50

=66

Fig.24 Effect of n on P- skeleton curve of

specimens

Fig.25 Effect of on P- skeleton curve of

specimens

6.2 Effect of CFRP layers 365

Figure 26 shows the effect of the number of longitudinal CFRP layers on the P- skeleton 366

curve of members. It can be seen that with the increase of ml, the shape of the skeleton curve and 367

the stiffness of the elastic stage are basically unchanged, and the bearing capacity of the member 368

is slightly improved. Figure 27 shows the effect of the number of transverse CFRP layers on the 369

P- skeleton curve of members. It can be seen that with the increase of mt, the shape of the 370

skeleton curve and the stiffness of the elastic stage have no obvious changes, and the bearing 371

capacity of the member increases slightly. 372

Page 31: Experimental Study On Hysteretic Behavior of Concrete

-120

-80

-40

0

40

80

120

-40 -20 0 20 40

/ mm

P /

kN

ml=0

ml=2

ml=4

-120

-80

-40

0

40

80

120

-45 -30 -15 0 15 30 45

/ mm

P /

kN

mt=2

mt=4

mt=6

Fig.26 Effect of m1 on P- skeleton curve of

specimens

Fig.27 Effect of mt on P- skeleton curve of

specimens

6.3 Influence of steel yield strength and concrete strength 373

Figure 28 shows the effect of steel yield strength on the P- skeleton curve of members. It 374

can be seen that with the increase of fy, the shape of the skeleton curve and the stiffness of the 375

elastic stage are basically unchanged, and the bearing capacity of the component is improved. 376

Figure 29 shows the effect of concrete strength on the P- skeleton curve of members. It can be 377

seen that with the increase of fcu, the shape of skeleton curve and the stiffness of elastic stage are 378

basically unchanged, and the bearing capacity of members is slightly improved. 379

-120

-80

-40

0

40

80

120

-60 -40 -20 0 20 40 60

/ mm

P /

kN

fy=235MPa

fy=345MPa

fy=390MPa

-120

-80

-40

0

40

80

120

-60 -40 -20 0 20 40 60

/ mm

P /

kN

fcu

=40MPa

fcu

=60MPa

fcu

=80MPa

Fig.28 Effect of fy on P- skeleton curve of Fig.29 Effect of fcu on P- skeleton curve of

Page 32: Experimental Study On Hysteretic Behavior of Concrete

specimens specimens

7 Conclusion 380

(1) CFRP has a good lateral restraint and longitudinal strengthening effect on CFST, and the local 381

buckling of steel tube is delayed. The P- curve and M-curve of the specimen are full, showing 382

good hysteretic behavior, and the deflection curve of the specimen is approximate to sine half 383

wave curve, and the steel tube and CFRP can keep cooperation in both longitudinal and transverse 384

directions. 385

(2) The increase of axial compression ratio and longitudinal CFRP reinforcement coefficient can 386

improve the flexural capacity and stiffness of the specimens, and decrease the rate of stiffness 387

degradation, but the ductility and cumulative energy consumption of the specimens were reduced. 388

The axial compression ratio is beneficial to the seismic performance of the specimens in a certain 389

range. During the loading process, the strength of each group of specimens has a certain 390

degradation trend. 391

(3) ABAQUS can be used to simulate the load-deformation curves and deformation modes of 392

members. The P- hysteretic curves of members established by ABAQUS can be used to analyze 393

the stress distribution of the components of members, and the simulation results are in good 394

agreement with the experimental results. 395

Page 33: Experimental Study On Hysteretic Behavior of Concrete

(4) The results of parametric analysis show that the increase of steel yield strength and steel ratio 396

can significantly improve the bearing capacity of members, and the increase of concrete strength 397

and CFRP layers can only slightly improve the bearing capacity. With the increase of slenderness 398

ratio or axial compression ratio, the bearing capacity and elastic stiffness of the members decrease 399

significantly, while the shape of load-deformation curve also has obvious change. 400

Data Availability Statement 401

Some or all data, models, or code that support the findings of this study are available from the 402

corresponding author upon reasonable request. 403

Acknowledgements 404

The research reported in the study are supported by Project For Talent of Liaoning Province (No. 405

XLYC1902009) and PHD Start-up Fund of Natural Science Foundation of Liaoning Province, 406

China (20170520139). 407

408

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