Experimental and analytical studies on CFRP strengthened circular thin-walled CFST stub columns under eccentric compression

Thin-Walled Structures 127 (2018) 102–119

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Experimental and analytical studies on CFRP strengthened circular thinwalled CFST stub columns under eccentric compression

T

⁎

Jingfeng Wanga,b, , Qihan Shena, Fengqin Wanga, Wei Wanga a b

School of Civil Engineering, Hefei University of Technology, Anhui Province 230009, China Anhui Civil Engineering Structures and Materials Laboratory, Anhui Province 230009, China

A R T I C L E I N F O

A B S T R A C T

Keywords: Concrete-filled thin-walled steel tube (CFST) Carbon fiber reinforced polymer (CFRP) Eccentric compressive behavior Finite element (FE) modeling Simplified empirical formulas

Carbon fiber reinforced polymer (CFRP) strengthened concrete-filled thin-walled steel tubular (CFST) column can improve its load carrying capacity and resolve local bugles or corrosion of thin-walled steel tube. However, little attention to CFRP strengthened CFST columns has been paid. This paper reported an experimental and numerical analysis on eccentric compressive behavior of circular CFST stub columns partially-wrapped by CFRP strips. A series of circular composite columns, including nine CFRP strengthened CFST stub columns and one bare CFST stub column, were tested subjected to eccentric compression. Moreover, a nonlinear finite element (FE) modeling in considering contact interactions of the composite columns was developed and verified by the test results in terms of eccentric load (N) - longitudinal shortening (δ) curves and failure patterns. Then, the influence of extensive parameters on the eccentric compressive behavior of CFRP strengthened circular CFST columns was also evaluated. Meanwhile, a simplified empirical method on the eccentrically-loaded stub composite columns was proposed on the basis of unified theory. The experimental and analytical data indicated that the eccentric compressive strength of CFRP strengthened circular CFST stub column was obviously influenced by load eccentricity, CFRP confinement factor, steel strength, core concrete strength and CFRP strength. The proposed simplified empirical formulas may provide a considerable approach for designing this type of composite structures in engineering practice.

1. Introduction Nowadays, concrete-filled thin-walled steel tube (CFST) members were popularly applied for multi- and high-rise buildings, and they were sincerely favored and recommended by many engineers and scholars due to their excellent combination action provided by outside steel tube and infill concrete [1–5]. However, the deterioration in load carrying capacity caused by outward local buckling or corrosion on thin-walled steel tube was observed as well. Although a series of strengthening methods including welding steel plates [6] and attaching bars [7,8] to the inside surface of steel tubes were proposed to prevent the above problems, some drawbacks including increase in weight, difficulty in construction and deterioration in durability were also discovered. In an attempt to avoid these problems and to prevent outward bugles or corrosion, wrapping carbon fiber reinforced polymer (CFRP) strips on outside surface of the thin-walled steel tube was suggested by Alam et al. [9] because of their outstanding advantages of high tensile strength, light weight and construction convenience [10–12].

⁎

Over the past decades, CFRP was widely used in reinforced concrete (RC) buildings or bridges and was proved to be an effective application for RC members as it could substantially improve their load-carrying capacity and ductility [13–15]. However, investigation on CFRP strengthened CFST members was lagging with respect to the development of the type of composite structures. Besides, the limited experimental studies were mainly focused on the performance of CFST members fully-wrapped by CFRP. For example, Park and Choi [16] conducted experiments on CFRP strengthened CFST columns under axial compression. Yu et al. [17] and Park et al. [18] examined the structural behavior of CFST columns strengthened by CFRP subjected to axial cyclic load. Zhang et al. [19] and Yu et al. [20] completed cyclic lateral tests on the type of composite columns as well. Tao et al. [21], Tao and Han [22] made some experimental researches on the axial compressive and flexural performance of fire-exposed CFST beams and columns strengthened by CFRP. All test results demonstrated that the load carrying capacities of CFST members were dramatically enhanced by the setting of CFRP strip. However, literatures on the behavior of CFRP strengthened circular CFST columns in a partial encased approach

Corresponding author at: School of Civil Engineering, Hefei University of Technology, Anhui Province 230009, China. E-mail address: [email protected] (J. Wang).

https://doi.org/10.1016/j.tws.2018.01.039 Received 19 October 2017; Received in revised form 22 December 2017; Accepted 31 January 2018 0263-8231/ © 2018 Published by Elsevier Ltd.

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or subjected to eccentric compression were scarce. Only Zand et al. [23] and Sundarraja and Prabha [24] studied the behaviors of various CFST members partially-wrapped by CFRP. Owing to complex process and large expense of experimental models and apparatus, the extensive experimental study on CFRP strengthened CFST members was limited. Hence, numerical analysis would be an extremely powerful and effective way for in-depth study to better understand the performance of CFRP strengthened CFST members. Ahmed et al. [25] established a finite element (FE) analysis modeling to explore the effect of different parameters on the flexural behavior of the CFST beams strengthened by CFRP. Choi and Xiao [26] proposed a computer-aided model to analyze the axial compressive behavior of CFRP fully-wrapped circular CFST columns. However, little attention has been paid to the FE analysis on eccentric compressive performance of circular CFST columns partially-wrapped by CFRP strips. Therefore, in order to efficiently explore the structural behavior of CFRP strengthened CFST columns, the necessity of developing a FE modeling on the type of composite column was emerged. The main objective of this study is to investigate the performance of CFRP partially-wrapped circular thin-walled CFST columns under eccentric compressive load. A total of nine circular CFST stub columns strengthened by CFRP strips and one bare circular CFST stub column subjected to eccentric compression were conducted. Moreover, in order to efficiently explore the eccentric compressive behavior of CFRP strengthened circular CFST columns and to figure out the complex interaction between the different components, a nonlinear FE analysis modeling of the type of composite columns was developed and verified through test results. In addition, an extensive parametric analysis on CFRP partially-wrapped circular thin-walled CFST stub columns under eccentric load was carried out. Finally, a simplified calculation approach on load-carrying capacity of the eccentrically-loaded stub composite columns was proposed according to the unified theory method.

Table 2 Material properties of CFRP. Type

Basic weight (g/m2)

Tensile stress Pf (MPa)

Fracture strainεFRP (%)

Elastic modulus EFRP (GPa)

CFRP

296.0

3510

1.44

243.0

material properties of CFRP strip. For the inner core concrete, commercially available self-compacting concrete (SCC) was used to avoid the necessity for vibrating and to cast conveniently. A same batch of SCC was used for the infill concrete of all specimens. Three group tests were carried out to observe the material properties of the infill concrete. Three concrete cubes in each group with the size of 150 × 150 × 150 mm for cube compressive strength and the size of 100 × 100 × 300 mm for elastic modulus according to specification GB/T 50081 [29]. Test results showed that the average cube compressive strength (fcu) of SCC was 31.2 N/mm2 and the elastic modulus (Ec) was 30,521.3 N/mm2 at 28 days. The characteristic compressive strength (fck) of the infill concrete is defined as 0.67fcu, which is determined according to specification ACI Committee 318 [30]. 2.2. Test specimens In an attempt to investigate the influence of steel strength (fy), number of CFRP layer (n) and spacing of CFRP strip (a) on the eccentric compressive behavior of circular CFST stub columns partially-wrapped by CFRP, a total of nine stub composite columns and one bare CFST stub column were tested and analyzed. Details of the columns are listed in Table 3. Fig. 1 displays the two types of eccentrically-loaded stub composite columns, including circular CFST stub columns fully- and partially-wrapped by CFRP strips. 2.3. Test setup and measurement

2. Experimental investigation

A schematic diagram of test arrangement and a test field photograph are illustrated in Fig. 2(a) and (b). Lasers and water levels were employed to carefully centralize the specimens and other components. Then a hydraulic machine of 500 t in capacity was used to exert the vertical load to the column end. To make the experiments going smoothly, the specimen was subjected to progressively increasing eccentric load. Each 0.1Nue (Nue was the eccentric compressive strength of the composite column estimated by FE modeling) was taken to the column end and was hold for 2 min before the pressure load was up to 0.6Nu. After that, each 0.05Nu was applied to the column end and was hold for 4 min until the load reaching Nue. The test procedure was terminated when the load fell to 0.85Nu or severe damage occurred.

2.1. Materials and properties Table 1 shows the material properties of steel tubes. Steel tubes with nominal yield strength of 235 MPa and 345 MPa were respectively employed to study the influence of steel strength. The material properties of steel were determined by the tensile coupon tests and three tensile coupons were cut from each steel tube wall to obtain the actual strength and elastic modulus in compliance with specification GB/T 228 [27]. It showed that the average yield stress (fy) of the steel tube was 240.8 MPa and 348.6 MPa; and the ultimate stress (fu) was 379.2 MPa and 487.3 MPa. The elastic modulus of steel was 198 GPa and 202 GPa. Similarly, a tensile coupon test of CFRP strip was conducted in accordance with ASTMD 3039 [28]. The test results indicated that the CFRP strip was a linear elastic material and its average ultimate tensile strength and elastic modulus were 3510 MPa and 234 GPa. It should be noted that the CFRP had an average fracture strain (εFRP) of 1.44% with an effective thickness of 0.167 mm per layer. Table 2 displays the

2.4. Experimental results and analysis In this section, the eccentric compressive performance of circular thin-walled CFST stub columns fully- or partially-wrapped by CFRP strips were investigated based on the test results. Failure patterns and force-displacement relationship curves of all test specimens were examined and compared. The typical failure patterns of test specimens are shown in Fig. 3. Fig. 4 displays the photographs of all circular CFST stub columns partially wrapped by CFRP following the tests. For the stub composite columns, inward bugles were prevented by the application of infill core concrete, so that outward local buckling turned out to be the main failure mode of eccentrically-loaded composite columns. It was worth noting that the outward bugles mainly appeared at the unwrapped zone of the column, which meant that outward local buckling could be effectively prevented by lateral-wrapped CFRP strip. In addition, colloid

Table 1 Material properties of steel. Steel

Thickness t (mm)

Yield stress fy (N/ mm2)

Ultimate stress fu (N/mm2)

Elastic modulus Es (N/ mm2)

Poisson's ratio ν

Elongation at fracture (%)

Q345

6

348.6

487.3

0.28

13.8

Q235

6

240.8

379.2

2.02 × 105 1.98 × 105

0.25

15.3

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Table 3 Information of circular steel tubes, concrete and CFRP. Specimen

D/mm

L/mm

t/mm

e/mm

n

a/mm

fcu

fck

fy

fu

Configuration of CFRP

ES11 ES12 ES21 ES22 ES23 ES31 ES32 ES33 ES41 ES42

140 140 140 140 140 140 140 140 140 140

450 450 450 450 450 450 450 450 450 450

6 6 6 6 6 6 6 6 6 6

30 30 30 30 30 30 30 30 10 50

3 3 0 1 5 3 3 3 3 3

50 50 0 50 50 0 30 150 50 50

31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2

20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9 20.9

240.8 348.6 348.6 348.6 348.6 348.6 348.6 348.6 348.6 348.6

379.2 487.3 487.3 487.3 487.3 487.3 487.3 487.3 487.3 487.3

Partially wrapped Partially wrapped No CFRP Partially wrapped Partially wrapped Fully wrapped Partially wrapped Partially wrapped Partially wrapped Partially wrapped

specimens, the strengthen index and ductility index were used and defined as follow:

peeling and severe rupture of CFRP were observed on the type of stub composite columns. These phenomena indicated that the outstanding tensile property of CFRP was fully used in stub columns and relative slip displacement actually existed between CFRP strips and steel tube. To explore the failure pattern of the infill core concrete, CFRP strips and the steel tubes of columns were removed after the tests. Crumbling of concrete on compressive side and tensile cracks on tensile side were observed around the mid-height of the stub composite column. In general, the failure patterns of CFRP strengthened circular CFST stub columns under eccentric compression mainly included: (1) outward local bugles; (2) severe rupture of CFRP strips; (3) colloid peeling; (4) concrete cracking and crumbling. Fig. 5 and Table 4 show the comparison on eccentric load (N) longitudinal shortening (δ) curves and strength enhancement indexes (SEI, defined in Eq. (1)) of specimens. It can be seen that the strength of the eccentrically-loaded circular CFST stub column was substantially improved with the increase of steel strength and number of CFRP layer, while opposite results were observed with the increasing of spacing of CFRP and load eccentricity. The strength enhancement index (SEI) of each specimen is defined as follows:

SEI =

N FRP, ue − N CFST, ue N CFST, ue

SI = Nue / Nu0

(2)

DI = δu/ δ y

(3)

where Nu0 is the average axial compressive strength of CFRP partiallywrapped CFST column; Nue is the average eccentric compressive strength of CFRP partially-wrapped CFST column; δy is the longitudinal shortening corresponding to the yield compressive strength of the composite column, as defined in Ref. [24]; δu is the longitudinal shortening corresponding to the ultimate compressive strength. The summaries of SI and DI of CFRP strengthened circular CFST columns were listed in Table 4 as well. The analytical results indicated that the SI of the type of composite column was dramatically enhanced by the decreasing of load eccentricity, while the steel strength, number of CFRP layer and spacing of CFRP had little impact on the SI of the stub composite columns. For the DI of the type of column, it decreased with the increase of steel strength and layer of FRP strips, while it was improved by the increasing of load eccentricity. Fig. 6 depicts the typical strain responses of the circular CFST stub columns strengthened by CFRP in the mid-height section, and compressive and tensile sides. The results indicated that the longitudinal strains on the compressive and tensile sides of the steel tube were basically symmetrical. Moreover, the longitudinal and transverse strains on the tensile and compressive sides were clearly greater than those on the middle side at the same load level. It should be noted that the CFRP tensile strains in the middle-height section of the stub column could reach the ultimate strain with increasing load pressure, corresponding to severe CFRP rupture in stub columns. These results demonstrated that the lateral-wrapped CFRP could make full use of its tensile strength

(1)

where NFRP,ue is the ultimate eccentric compressive strength of CFRP strengthened CFST column; NCFST,ue is the ultimate eccentric compressive strength of bare CFST column. Because of the abrupt tearing failure of CFRP strip, a typical sudden "drop" was discovered from the N-δ curves of all specimens. Thus, the ductility of FRP strengthened CFST stub column subjected to eccentric load was lower than that of bare CFST stub column. To evaluate the eccentric compressive strength and ductility of test

Knife hinge

b

D

a

Core concrete L

CFRP strip

Steel tube Steel tube A

A

A Rigid plate

(a) Fully-wrapped

CFRP strip

A (c) A-A

(b) Partially-wrapped

Fig. 1. Detail of circular CFST column strengthened by CFRP.

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Hydraulic machine

tearing rupture of CFRP strips, etc. Therefore, literatures on FE analysis of circular CFST columns strengthened by CFRP strips are scarce. In order to resolve these problems, numerical modeling of this type of composite columns were developed in this section.

N

3.1. Description of FE modeling Loading plate

3.1.1. Element types Because of the solid characteristic of the core concrete, 8-node reduced integration brick elements with three degrees of freedom per node (C3D8R) would be an effective element type to simulate its deformation features. For the steel tube wall, both solid element type and shell element type are appropriate to reflect the deformation and local buckling characteristic. However, the shell thickness would be much smaller than the size of elements if thick steel tube was used; this will significantly influence the accuracy of FE modeling. Using C3D8R will make the steel tube meshes follow the curved contacting boundary and express the deformation of circular steel hollow section (SHS). For the CFRP strips, using S4R shell elements would be proper for analyzing the stress and strain features due to the papery characteristic of CFRP strip.

CFST column

CFRP strip

LVDT Knife hinge Base

N (a) Schematic diagram of test arrangement

Loading plate

3.1.2. Boundary conditions Two rigid plates with a Poisson's ratio of 0.0001 and elastic modulus of 1 × 1012 N/mm2 were set up at the top and bottom of the CFRP strengthened CFST column. The vertical load and boundary conditions were respectively applied to the rigid plates. Moreover, knife hinges were also employed in FE modeling to realize the pinned joints of the CFRP strengthened composite columns. After then, the displacement of the bottom rigid plate in three directions were fixed, whereas the rotation in three directions were allowed. For the top rigid plate, the displacement in x and y axis were restrained while displacement in the z axis and rotation in three directions were allowed. The "tie" option was taken as the contact behavior between the rigid plate and surface of the column end.

CFRP

CFST stub column LVDTs LVDTs Knife hinge

3.1.3. Interactions between various components To consider the contact interaction between the inner core concrete and the SHS, surface-to-surface contact option was used in the FE model. Based on the test result of bare CFST column, the influence of friction coefficients along the tangential direction on the eccentric compressive behavior of circular CFST columns was studied. Different friction coefficients were taken as 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6 in this section. The comparison demonstrated that the friction coefficient taken as 0.3 coincided better with the test results (seen in Fig. 7a). The same friction coefficient was also employed in Ref. [31,32]. The interaction between the CFRP strip and the circular SHS was discussed as well. Though most numerical modeling took perfect bond in regard to the interaction between the CFRP strip and the RC members [13–15] and used 'tie' option for them, the relative slip did exist in real specimens which was corresponded to the failure pattern of colloid

(b) Test field photograph Fig. 2. Experimental setup.

in stub columns. 3. Finite element modeling With respect to the experimental tests, the numerical analysis method for studying the performance of CFRP strengthened circular CFST column is an effective approach to cut down time and money consumed on further investigations. However, FE modeling for CFST columns strengthened by CFRP strips is a little difficult as it needs to respond to much complex nonlinear behavior including cracking, crumbling and plasticity of concrete, local bugles of steel tube and

Rupture of CFRP Colloid peeling

c

a

Crack of concrete

d

Concrete crumbling Local buckling

b Fig. 3. Failure patterns of eccentrically-loaded circular stub composite column.

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Fig. 4. Overview failure photos of specimens after the tests.

ratios ranged from 0.1 to 0.3 were discussed in this FE modeling. Results shown in Fig. 7c demonstrated that the Poisson's ratio had little influence on the eccentric compressive behavior of the type of composite columns, which is similar to the investigation conducted by Dai and Lam [31].

peeling. On the condition that the Coulomb friction coefficient of 0.3 was employed for the contact behavior of steel tube inside surface to core concrete outside surface, surface-to-surface contacts were also used to estimate the interaction between the CFRP strips and the steel tube wall. "Hard contact" option was employed for normal direction behavior, and general bond behavior was set through friction coefficient in tangential direction. Different friction factors ranged from 0.3 to 0.8 were discussed in the FE modeling (shown in Fig. 7b). Compared with the test data of all specimens, it indicated that the FE analytical results with a friction coefficient of 0.7 satisfied well with the experimental results. Moreover, the numerical analysis indicated that the eccentric compressive strength of the CFRP strengthened CFST column was improved with the increasing of friction factor in tangential direction. Thus, using excellent cohesive colloid between the fiber and steel tube could significantly reduce the relative slip and enhance the strength of the eccentrically-loaded composite column. For the concrete infill, the effect of concrete Poisson's ratio (υ) on the eccentric compressive behavior of CFRP strengthened circular CFST columns was investigated. The infilling concrete types with Poisson's

3.2. Material modeling For the common carbon steel, an elastic-plastic stress-strain (σ)-(ε) model proposed in Ref. [33] was applied to describe the constitutive behavior of the circular steel tube wall. For the CFRP used in the above experiments, it is generally considered as isotropic material which is a subset of an orthotropic material. Jiang and Teng [13] investigated the material property of CFRP and proposed a simplified constitutive relationship (Lamina behavior) for the CFRP. The Lamina behavior in ABAQUS defines transversely isotropic material that requires five constitutive constants to define stress-strain relationship unlike nine constants in orthotropic material. Detailed information can be seen in Table 2.

Fig. 5. Load (N) versus longitudinal shortening (δ) curves of CFRP strengthened circular CFST stub columns.

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Table 4 Information summary of test specimens. Specimen

Nue/kN

SEI

Nu0/kN

SI

δy/mm

δu/mm

DI

Nu,FE/kN

Nu,FE/Nue

Nu,c/kN

Nu,c/Nue

ES11 ES12 ES21 ES22 ES23 ES31 ES32 ES33 ES41 ES42

1186.2 1325.1 1086.0 1154.0 1457.5 1523.9 1411.0 1270.3 1847.0 991.0

– 22.0% 0% 6.3% 34.2% 40.3% 29.9% 17.0% 70.1% − 8.7%

2007.1 2352.0 2048.4 2140.6 2478.6 2594.0 2441.7 2150.8 2352.0 2352.0

0.54 0.57 0.53 0.53 0.59 0.59 0.58 0.59 0.79 0.47

3.1 3.2 3.1 3.1 3.4 3.3 3.3 2.4 3.0 2.6

15.3 14.5 23.9 15.6 14.0 14.3 14.5 13.8 11.4 15.5

4.9 4.5 7.7 5.0 4.1 4.3 4.4 5.8 3.9 5.9

1162.5 1311.8 1085.4 119.6 1428.4 1462.9 1368.7 1244.9 1828.8 942.1

0.98 0.99 1.00 0.97 0.98 0.96 0.97 0.98 0.99 0.95

1034.2 1260.2 1080.5 1135.3 1335.3 1404.0 1310.8 1140.5 1825.0 962.4

0.87 0.93 0.99 0.98 0.92 0.92 0.93 0.90 0.99 0.97

Note: Nu,FE is the predicted eccentric compressive strength of CFRP strengthened CFST stub column.

In the above algorithm, fc′ is the cylinder strength of the core concrete, and ξ is the confinement coefficient. As, Ac are the cross sectional area of the steel tube and inner concrete, respectively. fy is the yield strength of the steel tube. fck is the characteristic compressive strength of core concrete and fck is taken as 0.67 fcu, where fcu is the cube compressive strength of unconfined concrete. The initial elastic modulus of the confined concrete is taken as 4700 fc′ (N/mm2) (the unit of fc′ is N/mm2). Both of them are determined in compliance with the recommendations in ACI Committee 318 [30]. Typical FE modeling of the eccentrically-loaded circular CFST column partially-wrapped by CFRP is shown in Fig. 8.

Nowadays, relative literatures mainly focus on CFRP strengthened RC members, investigations on the constitutive relationship of the infill core concrete in CFRP strengthened circular CFST column were scarce. Therefore, using the confined concrete model proposed by Han [33] to analyze the mechanical behavior of the type of composite columns would obtain a constitutive result and behave a proper accuracy. The stress-strain model of concrete in Ref. [33] is expressed as follows:

y=

2 (x ≤ 1) ⎧ 2x − x x ( ⎨ β (x − 1) η + x x > 1) ⎩

where,

x=

ε , ε0

εc = (1300 + 125fc′ )⋅10−6 .

(4)

y=

σ , σ0

σ0 = f ′c ,

ε0 = εc +

800ξ 0.210−6 ,

For circular CFST, 7 β = (2.36 × 10−5)[0.25 + (ξ − 0.5) ]⋅(fc′ )0.5⋅0.5 ≥ 0.12 , ξ = Asfy/(Acfck).

η = 2,

Fig. 6. Typical eccentric load (N) versus strain (ε) of CFRP strengthened circular CFST stub columns.

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Fig. 7. Effect of various friction factors or Poisson's ratio on eccentric compressive strength.

Fig. 10 displays the force-displacement curves observed by the experiments and numerical modeling. Similar test results on CFRP strengthened square CFST stub columns were also compared with the FE analytical results, as illustrated in Fig. 11. The results indicated that the predicted force-displacement curves were in good agreement with the test curves. Table 4 shows that only a maximum difference of 5% was discovered between the predicted and observed results. The difference between the FE analytical and experimental results was possibly arisen from the difference in the imperfection, site condition and material property between the test specimens and FE models. Generally speaking, the prediction had a tendency to safety with respect to test results. Therefore, the FE modeling proposed in this paper could be used as an accurate and efficient way for the further study. 4. Parametric analysis In this section, an extensive parameter analysis on the performance of CFRP strengthened circular thin-walled CFST stub columns was conducted (seen in Table 5). Steel tubes with diameter-to-thickness ratios (D/t) ranging from 20 to 100 were specially analyzed to explore the influence of CFRP strengthened thin-walled CFST columns according to specification AS 4100 [34] and GB 50018 [35]. A total of ten parameters included:

Fig. 8. FE modeling of CFRP strengthened circular CFST column.

3.3. Validation of FE model To evaluate the accuracy of numerical modeling, FE analytical results were compared with the experiments in terms of the failure modes and force-displacement curves. Failure patterns including local buckling, rupture of CFRP, concrete crumbling and cracking were respectively reflected in FE models (seen in Fig. 9) and they behaved a good consistent with the test results.

• Material parameters: steel tube strength (f ), concrete strength (f ) and CFRP strength (f ); and • Geometric parameters: diameter-to-thickness ratio (α = D/t), y

cu

FRP

number of CFRP layer (n); spacing of CFRP (a); width of CFRP (b), load eccentricity (e) and scale effect; and

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Fig. 9. Observed and predicted failure modes of CFRP strengthened circular CFST stub columns.

• Load parameters: pre-tightening force of CFRP (p ).

eccentric compressive strength and initial stiffness of the stub column with a fcu of 30 MPa respectively reduced by 21.8% and 17.1%. When fcu increased to 60, 80 and 100 MPa, the eccentric compressive strength of CFRP strengthened CFST columns respectively increased by 8.5%, 28.7% and 57.4%. Similarly, the initial stiffness had an improvement of 16.9%, 20.5% and 74.8%, respectively.

f

The detailed information is shown in Table 5. 4.1. Steel strength (fy) The effect of different steel strength on the force-displacement curves of eccentrically-loaded circular thin-walled CFST stub columns partially-wrapped by CFRP strips is illustrated in Fig. 12a. The results indicated that the eccentric compressive strength of CFRP strengthened by CFST stub column was improved with an increase of steel strength while the initial stiffness almost remained constant. Compared to the composite column with a fy of 345 MPa, the eccentric compressive strength of the column with a fy of 235 MPa decreased by 10.7%. For the stub composite columns with fy of 420 MPa and 550 MPa, the eccentric compressive strength respectively increased by 10.2% and 19.2% with respect to the stub column with a fy of 345 MPa.

4.3. FRP strength (fFRP) Fig. 12(c) depicts the influence of CFRP strength (fFRP) on the eccentric compressive behavior of CFRP strengthened thin-walled CFST stub columns. According to the numerical results, the eccentric compressive strength of the type of composite column increased with an increase of fFRP while initial axial stiffness was seldom changed. The strength of the columns with fFRP of 1500, 2500 and 3000 MPa were respectively 13.1%, 5.9% and 3.7% lower than that of the column with a fFRP of 3500 MPa. When the fFRP increased to 4500 MPa, the eccentric compressive strength of the column would increased by 5.4%.

4.2. Concrete strength (fcu) 4.4. Diameter-to-thickness ratio (α) Various concrete strength (30, 50, 60, 80 and 100 MPa) were analyzed in this section. Fig. 12b displays the impact of concrete strength (fcu) on the eccentric compressive behavior of the type of composite column. Both the eccentric compressive strength and initial stiffness were obviously heightened by the increasing of concrete strength. Compared with the stub composite column with a fcu of 50 MPa, the

The diameter-to-thickness ratios (α) taken as 10, 14, 20, 28.6, 40, 50, 70 and 100 (the corresponding steel tube thicknesses were 14, 10, 7, 4.9, 3.5, 2.8, 2 and 1.4 mm, respectively) were investigated. As shown in Fig. 12(d), the eccentric compressive strength and initial stiffness of CFRP strengthened thin-walled CFST stub columns raised with the 109

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Fig. 10. Comparison on test and FE results of CFRP strengthened circular CFST stub columns.

decreasing of α. The eccentric compressive strength of the composite columns with α = 100, 70 and 50 were 18.0%, 14.3% and 6.6% lower than that of the stub composite column with α = 40, while the initial stiffness of the them were respectively 5.1%, 3.5% and 1.0% lower than that of the latter. When α decreased from 40 to 28.6, 20, 14 and 10, the load carrying capacities values of the stub composite columns increased by 16.6%, 47.6%, 90.0% and 164.1%, respectively; whereas the improvements of the initial stiffness were respectively found to be 31.6%, 54.9%, 73.7% and 141.5%.

compressive strength of CFRP strips partially-wrapped thin-walled CFST stub columns, the number of CFRP layer ranged from 0 to 5 was explored in this section (seen in Fig. 12e). Compared to the circular thin-walled CFST stub column strengthened by zero layer (specimen ES21) of CFRP namely that the specimen was a bare CFST stub column, the eccentric compressive strength of the stub composite columns with 1, 2, 3, 4 and 5 layers of CFRP were respectively improved by 11.8%, 19.9%, 30.0%, 41.5% and 45.7% and their initial stiffness respectively increased by 11.0%, 34.2%, 45.1%, 76.5% and 81.7%. The result indicated that both the eccentric compressive strength and initial stiffness of CFRP strengthened circular CFST stub column were enhanced with the increasing of CFRP layer.

4.5. Number of CFRP layer (n) To evaluate the influence of number of CFRP layer on the eccentric 110

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Fig. 10. (continued)

4.6. Spacing of CFRP strip(a)

4.8. Scale effect

The influence of spacing of CFRP strip on the eccentric compressive behavior of the thin-walled stub composite column strengthened by CFRP is shown in Fig. 12f. The numerical models with spacing of CFRP strip a = 0, 30, 50 and 100 mm were conducted. The decrease of CFRP spacing enhanced the eccentric compressive strength of the composite column and had a little effect on the initial stiffness. Compared to the CFST stub column partially-wrapped by CFRP in 100 mm spacing, the eccentric compressive strength of the stub composite columns with CFRP strip spacing of 0, 30 and 50 mm respectively increased by 17.7%, 12.5% and 8.9% while the initial stiffness were respectively improved by 18.7%, 12.6% and 9.3%.

Fig. 12h displays the scale effect on eccentric compressive strength of CFRP strengthened thin-walled CFST stub column. The columns with dimensions ranging from 100 × 2.0 × 200 mm to 2400 × 48.0 × 4800 mm were analyzed in this section. Results revealed that the eccentric compressive strength and initial stiffness of the thin-walled stub composite columns were significantly enhanced with the increasing of the cross-section area. The eccentric compressive strength of the thinwalled stub composite columns with scale of 140 × 2.8 × 280 mm, 200 × 4.0 × 400 mm, 400 × 8.0 × 800 mm, 600 × 12.0 × 1200 mm, 1200 × 24.0 × 2400 mm and 2400 × 48.0 × 4800 mm were respectively 1.83, 2.54, 16.58, 26.51, 138.61 and 616.29 times of that of the stub composite column with a dimension of 100 × 2.0 × 200 mm. Similarly, the initial stiffness was 1.35, 1.72, 4.27, 6.68, 13.09 and 23.57 times of the latter.

4.7. Width of CFRP strip (b) Different widths of CFRP strip including 30, 50 and 100 mm were investigated in this section. Fig. 12g shows that the eccentric compressive strength of the thin-walled CFST stub column partiallywrapped by CFRP strips in width of 30 mm was respectively 9.7% and 16.5% lower than that of CFST stub columns partially-wrapped by CFRP in width of 50 and 100 mm. The initial stiffness of the CFST stub column with CFRP width of 30 mm was 5.6% and 13.2% smaller than that of the columns with CFRP width of 50 and 100 mm. The result demonstrated that the width of CFRP strip had a great impact on the eccentric compressive strength of the thin-walled stub composite column. However, the initial stiffness raised slightly.

4.9. Pre-tightening force of CFRP (P) Analytical results for CFRP pre-tightening force of 0, 0.1Pf, 0.2Pf, 0.3Pf, 0.4Pf and 0.5Pf are captured in Fig. 12i. Here, the ultimate strength of CFRP (Pf) was 3510 MPa. The eccentric compressive strength and initial stiffness of thin-walled stub composite columns with CFRP pre-tightening force of 0.1Pf, 0.2Pf, 0.3Pf, 0.4Pf and 0.5Pf were slightly influenced when compared with the CFRP strengthened CFST stub column without pre-tightening force. However, the displacement corresponding to eccentric compressive strength of the column was gradually reduced with the increase of CFRP pre-tightening force. It can be observed that the ductility of circular thin-walled CFST columns 111

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Fig. 11. Comparison on experimental [24] and FE analytical results.

composite columns with load eccentricities of 20 mm, 30 mm, 40 mm, 50 mm, 60 mm, 70 mm, 105 mm and 140 mm (corresponding to eccentricity ratios of 0.29, 0.43, 0.57, 0.71, 0.86, 1.00, 1.50 and 2.00) were respectively reduced by 17.5%, 32.0%, 48.2%, 54.3%, 58.7%, 62.9%, 71.8% and 77.2% with respect to the column with a load eccentricity of 17.5 mm (corresponding to eccentricity ratios of 0.14).

partially-wrapped by CFRP was greatly affected by the pre-tightening force of CFRP strip. 4.10. Load eccentricity (e) To comprehend the effect of load eccentricity on eccentric compressive behavior of the type of stub composite column, a variety of load eccentricities ranging from 0 to 140 mm were analyzed (shown in Fig. 12j). The results indicated that the eccentric compressive strength of CFRP strengthened CFST stub column was impaired by the increasing of load eccentricity. The eccentric compressive strength of the type of 112

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Table 5 Parameters of FE models. Specimens

Dimensions D × t × L/mm

fy/MPa

fcu/MPa

fFRP/MPa

b/mm

n

a/mm

e/mm

δ/mm

K/kN/mm

NFE /kN

ES-S-11 ES-S-12 ES-S-13 ES-S-14 ES-f-11 ES-f-12 ES-f-13 ES-f-14 ES-C-11 ES-C-12 ES-C-13 ES-C-14 ES-t-11 ES-t-12 ES-t-13 ES-t-14 ES-t-15 ES-t-16 ES-t-17 ES-t-18 ES-l-11 ES-l-12 ES-l-13 ES-l-14 ES-l-15 ES-l-16 ES-w-11 ES-w-12 ES-w-13 ES-w-14 ES-a-11 ES-a-12 ES-a-13 ES-a-14 ES-cs-11 ES-cs-12 ES-cs-13 ES-cs-14 ES-cs-15 ES-cs-16 ES-cs-17 AS-11 ES-e-11 ES-e-12 ES-e-13 ES-e-14 ES-e-15 ES-e-16 ES-e-17 ES-e-18 ES-0.0Pf ES-0.1Pf ES-0.2Pf ES-0.3Pf ES-0.4Pf ES-0.5Pf

140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 1.4 × 450 140 × 2.0 × 450 140 × 2.8 × 450 140 × 3.5 × 450 140 × 4.9 × 450 140 × 7.0 × 450 140 × 10.0 × 450 140 × 14.0 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 100 × 2.0 × 200 140 × 2.8 × 280 200 × 4.0 × 400 400 × 8.0 × 800 600 × 12.0 × 1200 1200 × 24.0 × 2400 2400 × 48.0 × 48000 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450

235 345 420 550 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345

50 50 50 50 50 50 50 50 30 60 80 100 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50

3510 3510 3510 3510 1500 2500 3000 4500 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510

50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 0 30 50 100 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 1 2 3 4 5 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 0 50 50 50 50 50 50 50 50 50 0 30 50 100 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50

30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 21.4 30 42.9 85.7 128.6 257.1 514.3 0 10 20 40 50 60 70 105 140 30 30 30 30 30 30

15.1 15.0 14.8 14.6 14.0 14.5 14.8 15.3 15.6 14.9 14.3 14.0 14.3 14.7 14.9 15.0 15.3 16.2 18.1 20.6 21.8 18.6 16.5 15.0 14.8 14.1 21.8 16.8 15.0 14.3 14.1 14.8 15.0 15.3 6.9 9.1 14.2 28.4 42.6 80.2 157.9 0.0 13.9 14.5 15.6 16.2 16.6 17.1 17.4 17.5 15.0 14.8 14.5 14.1 13.6 13.1

411.3 420.1 421.8 425.2 431.7 437.8 452.2 465.1 348.4 490.9 506.4 734.4 398.6 405.2 415.8 420.1 552.8 650.9 729.6 1014.5 289.6 321.5 388.7 420.1 511.2 526.3 289.6 377.0 390.7 418.7 532.8 505.4 490.7 448.9 513.1 692.9 881.9 2192.1 3429.6 6718.2 12,094.1 940.7 753.4 595.4 421.6 357.9 315.6 275.6 206.0 166.1 420.1 421.4 420.8 422.3 420.3 420.7

906.4 1014.5 1117.6 1209.3 882.1 954.4 976.7 1069.3 793.1 1101.2 1305.4 1596.8 831.8 869.1 947.6 1014.5 1183.4 1497.8 1927.1 2679.5 780.2 872.6 935.8 1014.5 1104.1 1136.7 780.2 924.2 1014.1 1076.4 1096.4 1048.2 1014.1 931.6 516.7 947.6 1827.4 9084.2 14,212.7 72,135.4 318,953 1749.3 1442.6 1189.3 906.1 798.7 721.6 649.2 493.7 398.2 1014.1 1069.5 1104.2 1137.8 1170.4 1206.7

Note: The b, n, a respectively stand for the width, the layer and the spacing of CFRP strip.

5. Discussion

column consisted of thin-walled steel tube. The results indicated that the small improvement in the experiments may be because of thick steel tube wall and small confinement provided by CFRP. Therefore, the wrapping scheme of CFRP-confined thin-walled steel tube is suggested in this paper. Moreover, slight damage of CFRP strips adjacent to the top and bottom column ends demonstrated that the high-strength tensile property of CFRP was not fully used. In an attempt to avoid this problem, applying pre-tightening force for the lateral-wrapped CFRP was suggested by some scholars. Mortazavi et al. [14] and Yamkawa et al. [36] explored the structural behavior of RC columns strengthened by lateral pre-tensioned CFRP. The results confirmed that wrapping columns by pre-tensioned CFRP strips could significantly improve the load

5.1. Wrapping scheme Compared with the experimental result of specimen ES12, greater strength enhancement index was observed with a thinner steel tube while the CFST columns were set with a same amount of CFRP strips. For the specimen ES12, its strength enhancement index was 22.0%. However, the strength enhancement indexes were respectively up to 24.1%, 28.6%, 30.4%, 32.7% and 40.1% when the steel tube thickness decreased from 6.0 mm to 4.9 mm, 3.5 mm, 2.8 mm, 2.0 mm and 1.4 mm. Besides, according to Ref. [21,22], a great improvement of eccentric compressive strength took place when the type of composite 113

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Fig. 12. Influence of various parameters on N-δ curves of CFRP strengthened CFST columns.

(1) The elastic stage (OA). During the preceding loading, the circular SHS and the core concrete were subjected to the eccentric load separately. The eccentric compressive load would have a approximate linear relationship with the longitudinal shortening before the vertical compressive pressure reached the point A (seen in Fig. 13). (2) The elastic-plastic stage (AB). With the load and displacement increasing, cracks of the core concrete were developed. The force undertaken by the core concrete showed a nonlinear relationship with the displacement. This phenomenon indicated that the CFRP confined circular CFST stub column stepped into elastic-plastic stage. Moreover, as the core concrete was confined by the SHS, the lateral deformation of the inner concrete was restrained by the SHS.

carrying capacities of the columns. Based on these above studies, using pre-tensioned CFRP strip for CFST stub columns was suggested to improve the strengthening effect as well.

5.2. Analysis of N-δ curves A standard N-δ curve of CFRP partially-wrapped thin-walled CFST stub column under eccentric compression was observed based on amounts of test results and numerical analysis (seen in Fig. 12). FE results indicated that the shape and trend of the N-δ curve had something to do with the CFRP confinement coefficient (ξFRP) and each curve could be divided into five parts: 114

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Fig. 12. (continued)

tightening force of CFRP strip. Besides, local buckling was mainly located at the unwrapped zone due to the lack of confinement. (4) The sudden descent stage (CD). Owing to the tearing rupture of CFRP strip, the N-δ curves of the CFRP strengthened CFST stub columns under eccentric load exhibited a feature of sudden descent beyond the peak load. Experimental and numerical data indicated that the degree of the descent was related to the ξFRP. The higher ξFRP, the larger level of descent was. When the N-δ curve arrived at point D, the CFRP strips wrapped at the mid-height of the column would be invalid (seen in Fig. 13). (5) The horizontal stage (DE). In this stage, the outward bugles were observed at the mid-height of the thin-walled CFST stub column immediately with the confinement effect of CFRP disappearing. Therefore, the strength of the composite column could be hardly improved with the increasing of longitudinal shortening.

Fig. 13. Typical N-δ curve of CFRP strengthened CFST stub columns under eccentric load.

The standard N-δ curve of bare CFST stub column under eccentric load was also depicted (shown in Fig. 14) to compare with that of CFRP strengthened CFST stub column. The comparison revealed a distinct difference between the two types of columns. For the curve of bare CFST stub column, the reserve of ductility (defined as the horizontal distance of points B and C) was related with ξsc and was much larger than that of stub composite column. While the vertical distance of points B and C (named as enhancement) was relative with the load eccentricity and ξsc. The enhancement of the bare CFST column was smaller than that of the same type of stub composite column because of the setting of lateral-confined high-strength CFRP strips. After reaching the ultimate compressive strength, the eccentric load of the bare CFST column decreased slowly which showed a feature of gentle descent.

The restriction effect would keep increasing with the development of longitudinal shortening. Finally, the steel stress got to the yielding strength with the N-δ curve reaching point B. (3) The strain-hardening stage (BC). As inward bugles and outward bugles of the SHS were respectively prevented by the inner core concrete and the outside CFRP strips, the ultimate eccentric compressive strength of the type of stub composite column was dramatically improved. The ultimate stress of the steel tube would be obviously higher than the result of the tensile coupon tests. Numbers of analytical results demonstrated that the enhancement of steel stress increased with the increasing of ξFRP. The horizontal distance of points B and C was related with the degree of pre-

115

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where e is load eccentricity of the column; Li is the initial imperfection of the composite column. For the stub column, Li = 0. For the slender column, Li = L/1000; L is the length of the column. Thus, the curve relating the eccentric load to the uniaxial bending moment is defined. Based on the numerous FE analytical results, the resistance of the CFRP strengthened circular CFST column is defined by moment-eccentric load interaction curves. The curve was derived using numerical integration to determine the level of bending moment that could be sustained for a given axial load, assuming a fully plastic distribution of stresses and that the concrete did not act in tension. In this section, the calculating model with conditions of D × t × L mm = 140 × 3.5 × 450 mm, a = 50 mm, b = 50 mm, n = 3, fy = 345 MPa, fFRP = 3510 MPa, fcu = 50 MPa was presented to figure out the design resistance of the type of composite column (shown in Fig. 15).

Fig. 14. Typical N-δ curve of bare CFST stub columns under eccentric load.

6. Prediction of the strength Presently, the design method for CFRP strengthened circular CFST stub columns under eccentric compression was seldom suggested by some scholars although simplified calculating formulas on the eccentrically-loaded bare CFST columns are available. While the behavior of CFRP strengthened CFST column is similar to that of bare CFST columns. Therefore, the approach for the bare circular CFST columns recommended in Ref. [33] could also provide a reference to predict the strength of CFRP strengthened circular CFST stub columns which can be defined as follows: when N/Nu0 ≥ 2η0 ,

α⋅βm M N + ≤1 Nuo Muo

(6)

when N/Nu0 < 2η0 ,

Fig. 15. Moment-load interaction curve for the specimen ES-S-12.

−

β M bN 2 cN − + m ≤1 Nu0 Mu0 Nu2 0

(7)

ζ 0)/η20 ;

which, α = 1 − 2η0 ; b = (1 − c = [2(ζ 0 − 1)]/η0 ; ⎧ 0.5 − 0.245ξ sc (ξ sc ≤ 0.4) η0 = ; ⎨ 0.1 + 0.14ξ −sc0.84 (ξ sc > 0.4) ⎩ ζ 0 = 0.18ξ −sc1.15 + 1; η0 and ζ 0 respectively represent the coefficients related with confinement factor of steel-to-concrete (ξ sc ); βm is the equivalent bending moment. In this paper, βm = 1; N is the eccentric load; M is the uniaxial bending moment; Nu0 is the axial compressive strength of CFRP strengthened circular CFST stub column; Mu0 is the bending moment of the type of composite column subjected to pure bending. Based on the above formulas, both of Nu0 and Mu0 need to be defined before ensuring the eccentric load and uniaxial bending moment of the eccentrically-loaded composite column. According to some investigations conducted by Refs. [21,22], the strengthening effect for the beams is quite limited because of using unidirectional CFRP strips to confine the circular CFST members. As the CFRP strips were set along the lateral direction, the excellent high tensile strength of CFRP strips can hardly be fully used. Therefore, the Mu0 for the circular CFST beam could be approximately regarded as that of bare CFST beam which can be described as follows: In

Fig. 16. Comparison of ultimate eccentric compressive strength between observed and predicted results.

This phenomenon was attributed to the excellent ductility property of CFST members which was contrary to the brittle rupture of CFRP strips. A similar description on typical N-δ curve of eccentrically-loaded bare CFST stub column can be seen in Ref. [36] as well.

Mu0 = γm fsc Wsc

(8)

5.3. Typical M-N curves

fsc = (1.14 + 1.02ξ sc)f ck

(9)

For the eccentrically-loaded circular CFST stub columns partiallywrapped by CFRP, the effect of combined compression and uniaxial bending must be accounted for. The design moment (Mue) arising from the application of eccentric load (Nue) is defined as:

where γm is the bending strength index, γm = 1.1 + 0.48 ln(ξ sc + 0.1) ; Wsc is the section modulus of the CFST beam, Wsc = πD3/32 . For the axial compressive strength of circular CFST stub column partially-wrapped by CFRP strips, a simplified calculating approach for the type of stub composite column was proposed in accordance with the unified theory approach. The approach was a simplified model taking

Mue = Nue (e + Li )

(5) 116

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Table 6 Comparision of predicted and extensive FE analysis result. Dimensions D × t × L /(mm)

fy (MPa)

fcu (MPa)

ξsc

fFRP (MPa)

ξcf

b

n

a

NFE (kN)

Nc (kN)

Nc/NFE

140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 1.4 × 450 140 × 2.0 × 450 140 × 2.8 × 450 140 × 4.9 × 450 140 × 7.0 × 450 140 × 10.0 × 450 140 × 14.0 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 140 × 3.5 × 450 100 × 2 × 300 200 × 4.0 × 400 600 × 12.0 × 1200 1200 × 24.0 × 2400 2400 × 48.0 × 48000 200 × 4.0 × 400 200 × 4.0 × 400 200 × 4.0 × 400 200 × 4.0 × 400 200 × 4.0 × 400 200 × 4.0 × 400 200 × 4.0 × 400 200 × 4.0 × 400 200 × 4.0 × 400 200 × 4.0 × 400 200 × 4.0 × 400 200 × 4.0 × 400 200 × 4.0 × 400 200 × 4.0 × 400 200 × 4.0 × 400 200 × 2.0 × 400 200 × 5.0 × 400 200 × 8.0 × 400 400 × 4.0 × 800 400 × 4.0 × 800 400 × 4.0 × 800 400 × 2.0 × 800 400 × 5.0 × 800 400 × 8.0 × 800 600 × 5.0 × 800 600 × 5.0 × 800 600 × 5.0 × 800

235 345 420 550 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 235 420 550 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345 345

50 50 50 50 50 50 50 50 30 60 80 100 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 30 80 100 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50

0.508 0.745 0.907 1.188 0.745 0.745 0.745 0.745 1.242 0.621 0.466 0.373 0.285 0.412 0.587 1.078 1.619 2.492 3.881 0.745 0.745 0.745 0.745 0.745 0.745 0.745 0.745 0.745 0.745 0.745 0.587 0.587 0.587 0.587 0.587 0.978 0.367 0.293 0.400 0.715 0.936 0.587 0.587 0.587 0.587 0.587 0.587 0.587 0.587 0.587 0.285 0.745 1.252 0.285 0.285 0.285 0.140 0.358 0.587 0.236 0.236 0.236

3510 3510 3510 3510 1500 2500 3000 4500 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510 3510

1.113 1.113 1.113 1.113 0.476 0.793 0.952 1.427 1.856 0.928 0.696 0.557 1.046 1.065 1.090 1.162 1.241 1.368 1.570 0 0.371 0.742 1.485 1.856 1.113 1.113 1.113 1.113 1.113 1.113 1.526 0.763 0.254 0.127 0.064 1.272 0.477 0.382 0.763 0.763 0.763 0.254 1.272 2.035 0.763 0.763 0.763 0.763 0.763 0.763 0.732 0.779 0.831 0.366 0.610 0.977 0.598 0.617 0.636 0.404 0.404 0.404

50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 0 30 100 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 30 80 100 50 50 50 50 50 50 50 50 50 50 50 50

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 1 2 4 5 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 5 8 3 3 3 3 3 3 3 3 3 3 5 8 5 5 5 5 5 5

50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 0 50 50 0 30 100 50 50 50 50 50 50 50 50 50 50 50 50 50 50 10 30 80 50 50 50 50 50 50 50 50 50 50 50 50 30 80 100

906.4 1014.5 1117.6 1209.3 882.1 954.4 976.7 1069.3 793.1 1101.2 1305.4 1596.8 831.8 869.1 947.6 1183.4 1497.8 1927.1 2679.5 780.2 872.6 935.8 1104.1 1136.7 780.2 924.2 1076.4 1096.4 1048.2 931.6 516.7 1827.4 14,212.7 72,135.4 318,953 1293.7 2314.1 2941.0 1583.6 1900.8 2021.7 1482.6 1892.8 2083.8 1859.3 1847.7 1742.6 1605.1 1845.8 1883.4 1668.2 1863.1 2284.1 5979.3 6377.9 6884.2 3874.4 5752.2 6121.3 13,741.3 13,466.7 13,227.7

892.3 981.6 1054.5 1188.6 873.2 929.4 955.8 1028.1 790.2 1080.6 1292.9 1526.5 904.2 866.0 914.3 1142.6 1421.4 1884.5 2634.8 780.2 853.6 920.7 1036.1 1084.3 759.3 944.2 1012.4 1009.2 1006.7 929.1 499.3 1755.7 14,079.4 69,449.9 316,915 1267.8 2304.1 2852.0 1553.6 1732.7 1921.7 1458.6 1792.8 1983.8 1608.3 1645.7 1608.4 1605.1 1645.7 1643.4 1628.2 1763.1 2234.1 5909.3 6317.9 6884.2 3870.4 5652.2 6021.3 13,541.3 14,466.7 14,527.7

0.98 0.97 0.94 0.98 0.99 0.97 0.98 0.96 1.00 0.98 0.99 0.96 1.09 1.00 0.96 0.97 0.95 0.98 0.98 1.00 0.98 0.98 0.94 0.95 0.97 1.02 0.94 0.92 0.96 1.00 0.97 0.96 0.99 0.96 0.99 0.98 1.00 0.97 0.98 0.91 0.95 0.98 0.95 0.95 0.87 0.89 0.92 1.00 0.89 0.87 0.98 0.95 0.98 0.99 0.99 1.00 1.00 0.98 0.98 0.99 1.07 1.10

the concrete strength, steel strength, CFRP strength, number of CFRP layer and wrapping ratio of the column into consideration. The prediction can be described as follows:

ξsc = As f y /(Ac fcu )

(12)

ξcf = Afrp f frp /(Ac fcu )

(13)

Nu0 = Asc fscf , u

β = b/(a + b)

(14)

(10)

where fscf,u is the unified strength of composite section; ffrp is the ultimate strength of CFRP strip; As, Ac and Afrp are respectively the crosssection area of steel tube, core concrete and CFRP strip; ξsc and ξcf are the ultimate confinement coefficient of the CFST columns provided by

fscf , u = (1.14 + 1.02ξsc + 0.265β − 0.068ξcf − 0.902β 2 − 0.053ξcf2 + 1.092βξcf ) fcu

(11) 117

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steel tube and CFRP, respectively; β is the CFRP wrapping ratio along the height of the composite column; a and b are respectively spacing and width of CFRP strip. According to scope of the test and FE analysis, Eqs. (10)–(14) were suitable for the partially-wrapped circular CFST stub columns namely that diameters ranged from 140 mm to 2400 mm, diameter-to-thickness ratios ranged from 20 to 100, steel strength ranged from 235 MPa to 550 MPa, concrete strength ranged from 30 MPa to 100 MPa, CFRP strength ranged from 1500 MPa to 4500 MPa, CFRP wrapping ratio ranged from 0 to 1, number of CFRP layer ranged from 0 to 5 and load eccentricity ratio ranged from 0 to 2. Fig. 16, and Tables 4, 6 respectively show the predicted capacity versus the experimental and numerical results. The result showed that the eccentric compressive strength calculated by the simplified empirical formulas coincided well with the test and FE results.

in Western Sydney University. The authors would like to acknowledge the Dr. Jiaxin Wang and the assistance of Xuezhou Wu of Hefei University of Technology as well. References [1] Z.B. Wang, Z. Tao, Q. Yu, Axial compressive behavior of concrete-filled double-tube stub columns with stiffeners, Thin-Walled Struct. 120 (1) (2017) 91–104. [2] F. Yuan, M.C. Chen, H. Huang, L. Xie, C. Wang, Circular concrete filled steel tubular (CFST) columns under cyclic load and acid rain attack: test simulation, Thin-Walled Struct. 122 (2018) 90–101. [3] M.F. Hassanein, V.I. Patel, M. Elchalakani, H.T. Thai, Finite element analysis of large diameter high strength octagonal CFST short columns, Thin-Walled Struct. 123 (2018) 467–482. [4] C.C. Hou, L.H. Han, Q.L. Wang, C. Hou, Flexural behavior of circular concrete filled steel tubes (CFST) under sustained load and chloride corrosion, Thin-Walled Struct. 107 (2016) 182–196. [5] R. Wang, L.H. Han, J.G. Nie, et al., Flexural performance of rectangular CFST members, Thin-Walled Struct. 79 (2) (2014) 154–165. [6] H. Ge, T. Usami, Strength of concrete-filled thin-walled steel box columns: experiment, ASCE J. Struct. Eng. 118 (11) (1992) 3036–3054. [7] C.S. Huang, Y.K. Yeh, G.Y. Liu, et al., Axial load behavior of stiffened concrete-filled steel columns, ASCE J. Struct. Eng. 128 (9) (2002) 1222–1230. [8] J. Cai, Z.Q. He, Axial load behavior of square CFT stub column with binding bars, J. Constr. Steel Res. 62 (5) (2006) 472–483. [9] M. Alam, S. Fawzia, X.L. Zhao, et al., Performance and dynamic behaviour of FRP strengthened CFST members subjected to lateral impact, Eng. Struct. 147 (2017) 160–176. [10] L. Waal, D. Fernando, V.T. Nguyen, et al., FRP strengthening of 60 year old prestressed concrete bridge deck units, Eng. Struct. 143 (2017) 346–357. [11] D.H. Lee, S.J. Han, K.S. Kim, et al., Shear strength of reinforced concrete beams strengthened in shear using externally-bonded FRP composites, Compos. Struct. 173 (1) (2017) 177–187. [12] A. Godat, F. Ceroni, O. Chaallal, et al., Evaluation of FRP-to-concrete anchored joints designed for FRP shear-strengthened RC T-beams, Compos. Struct. 176 (2017) 481–495. [13] T. Jiang, J.G. Teng, Theoretical model for slender FRP-confined circular RC columns, Constr. Build. Mater. 32 (4) (2012) 66–76. [14] A.A. Mortazavi, K. Pilakoutas, K.S. Son, RC column strengthening by lateral pretensioning of FRP, Constr. Build. Mater. 17 (6–7) (2003) 491–497. [15] A. Ganganagoudar, T.G. Mondal, S.S. Prakash, Analytical and finite element studies on behavior of FRP strengthened RC beams under torsion, Compos. Struct. 153 (2016) 876–885. [16] J.W. Park, S.M. Choi, Structural behavior of CFRP strengthened concrete-filled steel tubes columns under axial compression loads, Steel Compos. Struct. 14 (5) (2013) 453–472. [17] T. Yu, Y.M. Hu, J.G. Teng, FRP-confined circular concrete-filled steel tubular columns under cyclic axial compression, J. Constr. Steel Res. 94 (94) (2014) 33–48. [18] J.W. Park, Y.K. Hong, S.M. Choi, Behaviors of concrete filled square steel tubes confined by carbon fiber sheets (CFS) under compression and cyclic loads, Steel Compos. Struct. 10 (2) (2010) 187–205. [19] B. Zhang, J.G. Teng, T. Yu, Experimental behavior of hybrid FRP-concrete-steel double-skin tubular columns under combined axial compression and cyclic lateral loading, Eng. Struct. 99 (2015) 214–231. [20] T. Yu, Y.M. Hu, J.G. Teng, Cyclic lateral response of FRP-confined circular concretefilled steel tubular columns, J. Constr. Steel Res. 124 (2016) 12–22. [21] Z. Tao, L.H. Han, L.L. Wang, Compressive and flexural behaviour of CFRP-repaired concrete-filled steel tubes after exposure to fire, J. Constr. Steel Res. 63 (8) (2007) 1116–1126. [22] Z. Tao, L.H. Han, Behaviour of fire-exposed concrete-filled steel tubular beam columns repaired with CFRP wraps, Thin-Walled Struct. 45 (1) (2007) 63–76. [23] A.W.A. Zand, H.W.B. Wan, A.A. Mutalib, S.J. Hilo, Rehabilitation and strengthening of high-strength rectangular CFST beams using a partial wrapping scheme of CFRP sheets: experimental and numerical study, Thin-Walled Struct. 114 (2017) 80–91. [24] M.C. Sundarraja, G.G. Prabha, Experimental study on CFST members strengthened by CFRP composites under compression, J. Constr. Steel Res. 72 (5) (2012) 75–83. [25] W. Ahmed, Z. Al, H.W.B. Wan, A.M. Azrul, et al., Finite element analysis of square CFST beam strengthened by CFRP composite material, Thin-Walled Struct. 96 (2015) 348–358. [26] K.K. Choi, Y. Xiao, Analytical model of circular CFRP confined concrete-filled steel tubular columns under axial compression, J. Compos. Constr. 14 (1) (2010) 125–133. [27] GB/T228-2010, Metallic Materials-Tensile Testing at Ambient Temperature, Architecture Industrial Press of China, Beijing, 2010 (in Chinese). [28] ASTM D3039, Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials, American Society for Testing of Materials, 2000. [29] GB/T50081-2002, Standard for Test Method of Mechanical Properties on Ordinary Concrete, Architecture Industrial Press of China, Beijing, 2002 (in Chinese). [30] ACI 318-02, Building Code Requirements for Reinforced Concrete and Commentary, American Concrete Institute, Farmington Hills, MI, USA, 2002. [31] X. Dai, D. Lam, Numerical modeling of the axial compressive behaviour of short concrete-filled elliptical steel columns, J. Constr. Steel Res. 66 (7) (2010) 931–942. [32] X.H. Dai, D. Lam, N. Jamaluddin, et al., Numerical analysis of slender elliptical concrete filled columns under axial compression, Thin-Walled Struct. 77 (4) (2014)

7. Conclusions This paper studied the eccentric compressive performance of CFRP partially-wrapped circular CFST stub columns. A nonlinear FE modeling was developed and verified by test data, and then an extensive parametric analysis on CFRP strengthened circular thin-walled CFST stub column was conducted. Finally, a simplified empirical method to calculate the eccentric compressive strength of CFRP strengthened CFST stub columns was proposed in accordance with the unified theory. According to the experimental and analytical results in this paper, the following conclusions can be drawn: (1) The experimental results demonstrated that using CFRP in lateral direction could significantly improve the eccentric compressive behavior of thin-walled circular CFST stub column. The eccentric load - longitudinal shortening curve for the CFST stub column partially-wrapped by CFRP exhibited a feature of sudden descent beyond the peak load; it was related with the tearing rupture of CFRP. (2) Failure modes of the CFRP strengthened circular CFST stub columns under eccentric load mainly included: the outward bulges of steel tube wall, the rupture of CFRP strips, the colloid peeling, the concrete cracking and crumbling. Moreover, outward local bulges of the type of composite columns were mainly located at the unwrapped zone, so that it indicated that using CFRP for the stub composite columns could obviously prevent the outward bulges on the steel tubes. (3) The strength of the eccentrically-loaded thin-walled stub composite columns was obviously improved with the increasing of the steel tube strength, the CFRP strength, the concrete strength, the number of CFRP layer and the cross-section area, while the opposite results were observed with the increase of the diameter-to-thickness ratio, the spacing of FRP and the load eccentricity. (4) A FE modeling in considering contact interactions of the circular CFST stub columns strengthened by CFRP was developed and validated against the test dates. The proposed FE modeling could be used to predict the eccentric compressive behavior of the FRP strengthened CFST columns in a proper precision. (5) Based on the unified theory, a simplified empirical method to calculate the eccentric compressive strength of CFRP strengthened circular thin-walled CFST stub columns was proposed and verified by the test and FE results. The simplified calculation formulas may provide an effective approach to use CFRP strips for CFST structures. Acknowledgments This work described in this paper is supported by the National Natural Science Foundation of China (Project 51478158) and the New Century Excellent Talents in University (Project NCET-12-0838), which is greatly appreciated. Especially gratitude is also paid to Professor Tao 118

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Architecture Industrial Press of China, Beijing, 2002 (in Chinese). [36] T. Yamkawa, M. Banazadeh, S. Fugikawa, Emergency retrofit of shear damaged extremely stub RC columns using pre-tensioned aramid fiber belts, J. Adv. Concr. Technol. 3 (1) (2005) 95–106.

26–35. [33] L.H. Han, Concrete Filled Steel Tubular Structures—Theory and Practice, 3rd edition, Science Press, Beijing, 2016 (in Chinese). [34] AS4100-1998, Steel Structures, Standards Australia, Sydney, 1998. [35] GB 50018-2002, Technical Code of Cold-formed Thin-walled Steel Structures,

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