Behavior of ECC-encased CFST columns under eccentric loading

Journal Pre-proof Behavior of ECC-encased CFST columns under eccentric loading Jingming Cai, Jinlong Pan, Jiawei Tan, Brecht Vandevyvere, Xiaopeng Li PII:

S2352-7102(19)32005-4

DOI:

https://doi.org/10.1016/j.jobe.2020.101188

Reference:

JOBE 101188

To appear in:

Journal of Building Engineering

Received Date: 24 September 2019 Revised Date:

12 January 2020

Accepted Date: 13 January 2020

Please cite this article as: J. Cai, J. Pan, J. Tan, B. Vandevyvere, X. Li, Behavior of ECC-encased CFST columns under eccentric loading, Journal of Building Engineering (2020), doi: https://doi.org/10.1016/ j.jobe.2020.101188. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

Jingming Cai: Conceptualization, Methodology, Writing – original draft. Jinlong Pan: Funding acquisition, Supervision Jiawei Tan: Validation, Investigation. Brecht Vandevyvere: Writing-review & editing, Investigation. Xiaopeng Li: Writing-review & editing, Investigation.

Behavior of ECC-encased CFST columns under eccentric loading Jingming Cai a,b, Jinlong Pana*, Jiawei Tanb, Brecht Vandevyvereb, Xiaopeng Lic a

Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education,

Southeast University, Nanjing, China b

Department of Civil Engineering, KU Leuven, Bruges, Belgium

c

Department of Civil and Environmental Engineering, University of California, Irvine, USA

Abstract In this paper, the eccentric load behavior of engineered cementitious composite (ECC)-encased concrete filled steel tube (CFST) is analyzed

based on

ABAQUS/standard solver. A finite element (FE) model was established with consideration of different constitutive models, and the accuracy of proposed FE model was verified with experimental results. Failure mechanisms of ECC-encased CFST columns under eccentric loading were investigated; it was found that the eccentricity ratio has a great influence on the failure processes of the composite column, also the confinement effect decreased as eccentricity ratio increased. Based on the proposed FE model, parameter analysis was conducted to investigate the influences of different material strength and sectional dimensions. Based on stress analysis from the proposed FE model, a theoretical model for predicting sectional capacity of ECC-encased CFST columns has also been proposed and verified. Key words: ECC; Composite columns; Finite element analysis; Eccentric loading

Nomenclature steel ratio of CFST longitudinal reinforcement ratio stirrup confinement index for ECC first cracking strength of ECC first cracking strain of ECC ultimate tensile strain of ECC



peak strain of ECC cross-sectional area of ECC-encased CFST column cross-sectional area of concrete cross-sectional area of steel tube cross-sectional area of longitudinal bar cross-sectional area of inner CFST side length of column outer diameter of steel tube eccentric distance the thickness of ECC layer confined by stirrup elasticity modulus of ECC elasticity modulus of steel elasticity modulus of concrete cylinder strength of concrete characteristic strength of core concrete cylinder strength of ECC yield strength of stirrup yield strength of steel yield strength of steel tube stirrup confinement index

k

confinement coefficient ultimate axial load of ECC-encased CFST column ultimate moment of ECC-encased CFST column stirrup spacing thickness of steel tube volume of stirrup volume of ECC

1.Introduction

ECC, which is short for engineered cementitious composite, is a kind of novel fiber reinforced cementitious material which has gained increasing attention from researchers and engineers in recent years. Due to its unique multiple-cracking and strain-hardening behaviors, different structural composite members containing ECC material have been proposed and investigated, such as steel reinforced ECC beams [1], steel reinforced ECC columns [2], FRP reinforced ECC composite beams [3]. It was found that ECC composite members have both higher ductility and strength under static and quasi-static loading. Additionally, ECC composite members may be much safer and more durable than conventional concrete composite members, since ECC materials have better fire resistance [4-5] and durability [6-7]. As a typical ECC composite member, ECC-encased concrete filled steel tube (CFST) column has been proposed and investigated by the authors recently. The ECC-encased CFST column was consisted of two parts, i.e., the inner CFST component and outer steel reinforced ECC (R/ECC) component. Compared with conventional CFST columns, the outer R/ECC component could serve as a protective layer, which can greatly improve its fire resistance and durability. Compared with the R/ECC column, the inner CFST column increases its stiffness and also decreases its cost since ECC materials generally show lower elastic modulus and have a higher price [8]. For ECC-encased CFST columns under both uniaxial and eccentric compressive loading, it was found that the composite columns failed in a ductile mode with about 30% higher compressive strength than concrete-encased CFST columns [9-10]. For ECC-encased CFST columns under cyclic loading, results showed that ECC-encased CFST column has higher ductility and doubled cumulative energy dissipation compared with same-sized concrete-encased CFST columns [11]. The typical failure modes for ECC and concrete-encased CFST columns are shown in Fig.1. It can be inferred that ECC-encased CFST column have better composite effects than concrete-encased CFST column. However, due to the limited number of test specimens, the failure mechanism as well as the influences of different parameters on the mechanical behaviors of ECC-encased CFST columns still need more investigation.

Set against this background, the eccentric behaviors of ECC-encased CFST columns were investigated in this paper. The finite element(FE) model was established and the constitutive models for different materials were explored. After the FE model was verified with the experiment results, the influences of different parameters were investigated.

(a) Concrete-encased CFST columns

(a) ECC-encased CFST columns

Fig.1 Typical failure modes for composite columns under cyclic loading

2. Finite element analysis (FEA) modeling The FE model of ECC-encased CFST column under eccentric loading is shown in Fig.2, which is based on the ABAQUS/standard solver. In this model, the nonlinear behavior of each material as well as the contact behavior of each component was fully considered. As shown in Fig.2, the composite column consists different types of materials, such as core concrete, steel, normal unconfined ECC and stirrup confined ECC. The constitutive model for each material has a tremendous influence on the accuracy of FE model.

(a) FE model

(b) Geometry

Fig.2 The FE model and geometry of ECC-encased CFST column

2.1 Constitutive model for steel All the steel components, including longitudinal reinforcement, stirrup and steel tube, are described with the same constitutive model due to its isotropic behaviors. In this paper, a five-stage constitutive model shown in Fig.3 was applied to characterize E ε ε < ε % * + ε + , ε < ≤ # − . < ≤ = $ /1 + 0.6 45 6478 : ≤ * < 479 6478 # 1.6 ε > ; "

the elastoplastic behavior of steel [12], which is expressed as follows:

where B=2A

=0.8 /

.,

C=0.8

modulus of steel.

> ,

+A

,

. =1.5 *

-B

,

* =10

and

. ,

>

.

; =100

*

;

(1)

.,

A=0.2

/(

.

−

)* ,

are the the yield stress and elastic

Stressσ

fy

0 εe εe1 εe2

Strain ε

εe3

Fig.3 Typical constitutive model for steel

2.2 Constitutive model for core concrete Unlike normal concrete, the core concrete in ECC-encased CFST column was confined by steel tube which has both higher ductility and strength. The constitutive model proposed by Tao et.al [13] which considered the confinement effect during different stages was applied in this paper, as shown in Fig.4. It was noticed that the confinement effect decreased with the increase of eccentricity, thus the eccentricity ratio was also considered in the constitutive model [14]. During the initial stage from Point O to Point A, the constitutive model for core concrete was given by: where X = J ; A= J

KL

MK JKL NDK

= .G(E6*)FG(H6.)F 8

A

BCD

O6.8

; B=

.PP

0< ε ≤

EFGHF 8

(2)

− 1; εQ =0.00076+R(0.626fQ − 4.33) × 106X .

During the second stage from Point A to Point B, the constitutive model was

expressed as:

4CC

4CL

= YZ

where m= (2.9224-0.00367 )( BD ) k = 0.12 + 0.88Ymn6P

B[ C

/;

.;.*\G .

.

<ε≤

*BCD

;

^

=

cL.L8de f

.*P (.G . *XB_ )`ab

.G..g∗. ciL (BCD )j.d

(3) ;

During the last stage from Point B to point C, the model was expressed as : σ=

where

= 0.7x1 − Ymn6..;y

k = 0.12 + 0.88Ymn6P

/;

.

+(

zK

−

)exp [−(

464CC ..* ) ] t

{ ; = 0.04 − .G

|

. ;g

ε≥

}.Ld~•K c9.j€

; ξ = E

（ 4）

E5 B_

C BC~

.

In above formulas, k is the confinement coefficient; e is the eccentricity ratio which was defined as

/ , where

is the eccentric distance and

length of the composite column;

and

strength of core concrete, respectively;

is the side

are the characteristic and cylinder

and

are the cross-sectional areas of

concrete and steel tube, respectively. The elastic modulus (

‚)

of concrete was taken as 4730R

and the Poisson’s

ratio of concrete was set as 0.2 according to ACI 318-11[15]. For composite columns under compressive loading, the tensile constitutive model of concrete was simplified as the fracture energy model proposed for the convenience of convergence [16]. σ A B

Stressσ

f'c

e=0 C

e=1 Oε

c0 εcc

Strain ε

ε

Fig.4 Stress–strain curves for core concrete with different eccentricity ratios

2.3 Constitutive model for ECC The uniaxial compressive stress–strain curve for ECC is shown in Fig.5(a), in which the influence of stirrup confinement effect was taken into account. For those ECC with no stirrup confinement, the ascending stage from being elastic to being elastoplastic can be expressed by [17]: < 0.4ε 4 = ƒ (1 − 0.308 BDL + 0.124) 0.4 < ≤ C7

where

and

(5)

are the cylinder strength and elasticity modulus of ECC. As shown

in Fig.5(a), the bilinear curves were applied to depict the post-peak behavior of ECC

material, the parameters for the curves are shown in Table 1. It has been reported that ECC possesses a higher ductility as well as a higher strength with the confinement of stirrup [18], thus the peak strain ( are expressed by:

) and peak stress (

) for ECC confined by stirrup

where

=



= 1.12Y 6X.X*„7 ,

(6)

=

= 1.03Y 6….;X„7 ,

= (1 − . *

*†C‡ˆ

)*

‰ŠB_‹ D Œ• BC7

(7) .

and

are derived from regression analysis with the experimental data provided by Ref.[18]. is the stirrup confinement index which considered the thickness of ECC layer confined by stirrup (

), stirrup spacing( ), yield strength of stirrup (

the volume of the stirrup( ) and ECC(

) as well as

).

As shown in Fig.5(b), the uniaxial tensile stress–strain curves for ECC was simplified as bilinear curves and could be expressed as: where

and

=Ž

4 •C < ε

+(

A

•C

−

) (4

464•C

•• 64•C

)

<

≤



(8)

are the initial cracking strength and ultimate tensile strength of

ECC. Correspondingly, ε

and

are initial cracking strain and ultimate tensile

strain of ECC, respectively. The parameters for ECC under uniaxial tension are also shown in Table 1. The tensile descending stage of ECC material was not considered according to the uniaxial tensile test. Table 1 Material parameters for ECC

0.0021

σcp

（ ε'

cp

3.2 MPa

0.05

5 MPa

0.005

0.03

,σ' ） cp

σtu

0.5σcp 0.4σcp

Normal un-confined ECC

σtc

Stirrup confined ECC

0.4εcp

εcp

εcu

1.5εcp

（ a） Compressive

0 εtc

（ b） Tensile

Fig.5 Typical stress–strain curve for ECC

εtu

2.4 Modeling process and boundary conditions The FE model of ECC-encased CFST column under eccentric loading is shown in Fig.2. Two rigid plates with infinite stiffness were attached on both ends of the composite columns. The “ Tie contact” was applied to define the interactions between composite column and rigid plates. The element type of C3D8R was applied to define both rigid plates and composite column. The steel tube has two contact surfaces with both core concrete and outer ECC. The “Hard contact” was adopted to define the normal direction between steel tube and ECC while the “Mohr–Coulomb friction model” was adopted to define the tangential direction. The friction coefficient for the contact surface between steel tube and core concrete was set as 0.25 [14]. By contrast, it has been reported that ECC and section steel have a higher bond strength due to ECC’s superb ductility [19]. Thus, the friction coefficient between ECC and steel tube was set as 0.5 after multiple trials. In addition, compared with normal concrete, ECC was reported to have a more reliable bond behavior with steel reinforcement [20]. Therefore, the “Embedded element” was applied to define the contact behavior between ECC and steel reinforcements. As shown in Fig.2, the eccentric loading was applied along the loading line with displacement increments. All degrees of freedom for the loading line, except the axial displacement along Z-axis and rotation around Y-axis, were constrained. A symmetrical bearing line was arranged at the bottom rigid plate, in which only the rotation around Y-axis was not constrained.

2.5 Verification of the FE model The verifications of the FE model are threefolds. First, the ultimate eccentric compressive strength extracted from both experiment and FE model are shown in Table 2 and the maximum error is lower than 10%. Second, Fig.6 shows the experimental and simulational load–displacement curves for ECC-encased CFST columns with different eccentricity ratios, it can be seen that the accurate prediction of initial stiffness as well as carrying capacity were obtained. Third, Fig.7 shows the

failure modes derived from both experiment and FE model. For the specimen with different eccentricity ratios, the simulation result has very similar failure modes in both tensile and compressive sides. According to the analysis above, it is feasible to simulate the eccentric behaviors of ECC-encased CFST columns based on the proposed FE model. Therefore, the failure mechanism of the composite column can be further analyzed.

Table 2 The comparison of eccentric compressive strength Specimens

Experimental（

Simulation（

）

B/

B）

3671

3536

0.96

C1-0.4

2768

2643

0.95

C1-0.6

1846

1711

0.93

C1-0.8

1178

1130

0.96

4000

3000

3500

2500

3000

Load(kN)

Load(kN)

C1-0.2

2500 2000 1500 1000

Experiment Simulation

500 0

0

2

4

6

8

10

12

14

Displacement(mm)

2000 1500 1000

Experiment Simulation

500

16

0

18

0

2

4

6

8

10

12

14

16

18

Displacement(mm)

(a) C1-0.2

(b) C1-0.4

2000

1000

1500

Load(kN)

Load(kN)

1200

1000

Experiment Simulation

500

0

800 600 400

0 0

2

4

6

8

10

12

14

Displacement(mm) (c) C1-0.6

16

Experiment Simulation

200

18

0

2

4

6

8

10

12

14

16

Displacement(mm) (d) C1-0.8

18

Fig.6 Comparison of load–displacement curves

(a)Y=0.2

(b)Y=0.4

(c)Y=0.6

Fig.7 Comparison of failure model between experiment and FE model

3. Failure mechanism Three typical failure modes, i.e., compression-controlled, tension-controlled and balanced failure modes were observed and defined previously [10]. The proposed FE model was further applied to analyze the failure mechanism of ECC-encased CFST columns with different failure modes. 3.1 Longitudinal reinforcement The stress development for the longitudinal reinforcement at both tensile and compressive sides are shown in Fig.8, in which the abscissa indicates the axial displacement of the composite column while the ordinate represents the stress of the longitudinal reinforcement. In addition, the axial displacement corresponding to the peak load of the composite column was plotted as a dashed line. For the composite column that features compression-controlled failure mode, as shown in Fig.8(a), it was noticed that the longitudinal reinforcement at the compressive side yielded obviously earlier than that at tensile side. When the axial displacement was 2.3 mm, the longitudinal reinforcement at compressive side yielded. By contrast, the longitudinal reinforcement at tensile side is still under its elastoplastic phase. For the composite column that features balanced failure mode, as shown in Fig.8(b), the yielding of longitudinal reinforcement at both tensile and compressive sides were almost simultaneous as the composite column reached its peak load. This

conclusion is also consistent with the previous experimental results in Ref.[10]. For the composite column that features tension-controlled failure mode, as shown in Fig.8(c), the longitudinal reinforcement at tensile side yielded before the peak load. After that, the load gradually transferred to the compressive side and the longitudinal reinforcement at compressive side yielded after the composite column

400

300

300

Tensile side

200 100

Peak load

0 -100

Compressive side

-200 -300 -400

400 300

Tensile side

200 100

Peak load

0 -100 -200

Stress(MPa)

400

Stress(MPa)

Stress(MPa)

reached its peak load.

Compressive side

-300 0

5

10 15 Displacement(mm)

20

-400

0

5

10 15 Displacement(mm)

20

200

Tensile side

100

Peak load

0 -100

Compressive side

-200 -300 -400

0

5

10 15 Displacement(mm)

20

Compressive side

(a)Compression-controlled failure (b) Balanced failure

(c) Tension-controlled

failure Fig.8 The stress development of longitudinal reinforcement

3.2 Steel tube The stress development of steel tubes are shown in Fig.9, in which the abscissa is the axial displacement of the composite column and the ordinate is the stress of the steel tube. The stress development for both compressive and tensile sides of the steel tube were plotted with different colors. For the composite column that features compression-controlled failure mode, as shown in Fig.9(a), both tensile and compressive sides of the steel tube were under compressive stress initially. With the increase of axial displacement, the steel tube in the compressive side gradually yielded before the peak load of the composite column. By contrast, the steel tube in the tensile side was governed by tensile stress and yielded as the composite column reached its peak load. For composite columns features balanced failure mode, as shown in Fig.9(b), the tensile side of the steel tube was under tensile stress initially and then the steel tube in both tensile and compressive sides yielded as the composite column reached its peak load. For the composite columns that features tension-controlled failure mode, as shown in Fig.9(c),

the yield of the steel tube in the tensile side was further advanced before the composited column reached its peak load.

100

Tensile side

-100

Compressive side

-200

Tensile side

200 100

Peak load

0 -100

Compressive side

-200

0

5

10 15 Displacement(mm)

20

-400

200

Tensile side Peak load

100 0 -100 -200

Compressive side

-300

-300

-300

Stress(MPa)

Stress(MPa)

Stress(MPa)

200

0

300

300

Peak load

300

-400

400

400

400

-400

0

5

10 15 Displacement(mm)

20

0

5

10 15 Displacement(mm)

20

(a)Compression-controlled failure (b) Balanced failure (c) Tension-controlled failure Fig.9 The stress development of steel tube

3.3 Contact stress The steel tube contacted with both core concrete and ECC component, thus two different types of contact stress were shown in Fig.10. The contact stress P1 was defined as the contact between steel tube and inner concrete, and P2 is defined as the contact stress between steel tube and ECC component. Three typical positions were selected as shown in Fig.11, where Point 1 and Point 3 are typical points in tensile and compressive sides, respectively.

(a) Steel reinforced ECC

(b) Steel tube Fig.10 Type of contact stress

(c) Core concrete

Fig.11 Typical locations of steel tube 3.3.1 The contact stress between steel tube and core concrete (P1) The contact stress between steel tube and core concrete for different composite columns are shown in Fig.12. For the composite column that features compression-controlled failure mode, as shown in Fig.12(a), the P1 value at different locations were all constant as zero during the initial stage because the Poisson's ratio of the steel tube was slightly higher than the core concrete thus the steel tube gradually departed from core concrete. As the axial displacement increased, P1 at different locations increased gradually. Among these different points, the tensile contact stress (Point 1) is the largest with a peak contact stress of 14.3MPa. This is because the tensile side of core concrete might crack during the initial stage thus the steel tube would have a higher confinement effect on the plastic deformation of the core concrete in the tensile side. For the composite column that featured balanced failure mode, as shown in Fig.12(b), P1 at different locations were constant as zero during the initial stage. When the axial displacement was 2 mm, P1 at different locations increased gradually. The contact stress in the compressive side (Point 3) almost kept constant after the composite column reached its peak load, while the contact stress in the tensile side (Point 1) is about three times higher than that in the compressive side. In can be inferred that the core concrete was subjected to uneven hoop constrain, where concrete in the tensile side was more effectively constrained than in the compressive

side. For the composite column that features tension-controlled failure mode, as shown in Fig.12(c), P1 at the different locations were kept as zero during the initial stage. As the axial displacement increased, the contact stress began to increase slowly. However, the peak contact stress was only about 5 MPa, which is significantly lower than Fig.12(a) and Fig.12(b). It can be seen that for ECC-encased CFST columns that featured tension-controlled failure mode, the core concrete was not effectively confined by steel tube. This result is consistent with the constitutive model of core concrete applied in this paper, in which the influence of eccentricity ratio was considered, as shown in Eq.(3) and Eq.(4). The eccentricity has great influences on the mechanical behaviours of concrete composite columns, which also have been reported by other researchers[21-22].

16

12 10 8 6

3 2 1

4 2 0

0

5

10 15 Displacement(mm)

20

3 2 1

14 12

5

Contact Stress(MPa)

14

Contact Stress(MPa)

Contact Stress(MPa)

16

10 8 6 4

4 3

3 2 1

2 1

2 0

0

5

10 15 Displacement(mm)

20

0

0

5

10 15 20 Displacement(mm)

25

(a)Compression-controlled failure (b) Balanced failure (c) Tension-controlled failure Fig.12 Distribution of contact stress P1 at different locations 3.3.2 The contact stress between steel tube and ECC (P2) The contact stress between steel tube and ECC are shown in Fig.13. The maximum value for P2 was only 5 MPa, which is much lower than the contact stress between steel tube and core concrete (P1). For the composite column that featured compression-controlled failure mode, as shown in Fig.13(a), P2 was very low during the initial stage, indicating the confinement effect was negligible during the initial stage. When the axial displacement was about 7 mm, the contact stress in the compressive side (Point 3) increased rapidly. This is because the steel tube in the compressive side exhibited local outward buckling and the steel tube was re-contacted with ECC component.

When the axial displacement was about 14 mm, the contact stress in the tensile side (Point 1) increased rapidly. This is because the steel tube in the tensile side exhibited a large degree of outward buckling and then was confined by ECC component. By contrast, the contact stress at Point 2 was constantly kept at 0.2 MPa. It can be concluded that confinement effct between steel tube and ECC was also not uniform. For the composite column that features balanced failure mode, as shown in Fig.13(b), the contact stress was significantly reduced compared with the results shown in Fig.13(a). The contact stress between steel tube and ECC were negligible during the initial stage. When the axial displacement of the composite column reached 4 mm, the contact stress in the compressive side increased rapidly. This is because of the local outward buckling of steel tube. When the axial displacement was about 10 mm, the composite column reached its peak load and the contact stress in the compressive side reduced significantly and then maintained at about 1.7 MPa. It can be attributed to the reason that ECC at compressive side was not crushed, which could restrain the steel tube continuously during the whole stage. For the composite column that features tension-controlled failure mode, as shown in Fig.13(c), the contact stress between steel tube and ECC were further reduced. At the initial stage, the contact stress at different locations were negligible as well. When the axial displacement was about 5 mm, the contact stress in the compressive side increased rapidly with a maximum value of 0.9 MPa. When the axial displacement was about 12 mm, the composite column reached its peak load and the contact stress at the compressive side reduced significantly. After the peak load, the contact stress at the compressive side raised remarkably with a maximum value of 1.4 MPa, once again demonstrating that ECC in the compressive side could restrain the steel tube during the whole loading stage. 3.0

3

3 2 1

2 1 0

0

5

10 15 Displacement(mm)

20

1.5

2.5 2.0 1.5

3 2 1

1.0 0.5 0.0

0

5

10 15 Displacement(mm)

20

Contact Stress(MPa)

4

Contact Stress(MPa)

Contact Stress(MPa)

5

1.0

3 2 1

0.5

0.0

5

10 15 Displacement(mm)

20

(a)Compression-controlled failure (b) Balanced failure

(c) Tension-controlled

failure Fig.13 Distribution of contact stress P2 at different locations

4. Parameter analysis According to the proposed FE model, the axial load ( (

) and moment capacities

) for ECC-encased CFST columns can be computed. Based on the proposed FE

model, the effects of different parameters on the

−

curves were discussed. The

main parameters can be summarized as: (1) core concrete strength ( ); (2) steel tube

ratio ( ); (3) steel tube strength ( ); (4) longitudinal bar ratio ( ); (5) ultimate tensile strain of ECC ( ); (6) compression strength of ECC (

).

4.1 Compressive strength of core concrete As

shown

in

Fig.14(a),

for

the

composite

columns

that

feature

compression-controlled failure mode, the loading carrying capacity increased with the increase of core concrete strength. However, as the eccentricity ratio increased, the composite columns were governed by tension-controlled failure and the tensile failure was the controlling factor thus the influence of core concrete strength was negligible.

4.2 Steel tube ratio The steel tube ratio was defined as the cross-sectional area ratio between steel tube and core concrete. As can be seen in Fig.14(b), for the composite column governed by both compression-controlled and tension-controlled failure modes, the loading carrying capacity as well as the ductility increased gradually as the steel tube ratio increased. It may be attributed to the reason that the confinement effect increased with the increase of steel tube ratio.

4.3 Steel tube strength

As shown in Fig.14(c), the increase of steel tube strength has similar effects with steel tube ratio, both loading carrying capacity and ductility increased with the increase of steel tube strength. It may be attributed to the reason that the passive confinement effect provided by steel tube increased with the increase of steel tube strength.

4.4 Longitudinal bar ratio The longitudinal bar ratio is defined as cross-sectional area of the longitudinal bar, ECC-encased CFST column and

=

⁄( −

), where

is the

is the cross-sectional area of

is the cross-sectional area of inner CFST. As can

be seen in Fig. 14(d), the loading and moment carrying capacity would increase with the increase of longitudinal bar ratio during the whole stage, especially when the column features tension-controlled failure mode.

4.5 Ultimate tensile strain of ECC As can be seen in Fig.14 (e), the ultimate tensile strain of ECC material has negligible effect on the carrying capacity for those columns which feature compression-controlled failure mode. While for those columns governed by tension-controlled failure mode, since the controlling factor was tensile fracture at tensile side, the carrying capacity of the composite column increased gradually with the increase of tensile strain of ECC.

4.6 Effect of compression strength of ECC Generally, the compression strength of ECC is similar to that of concrete, while ECC material with lower water-cement ratio or appropriate volume of silica fume possesses higher compression strength. Fig.14(f) shows the

−

curves for the

ECC-encased CFST columns with different compressive strength of ECC. It seems that the compressive strength of ECC has a positive influence on the axial load and moment capacities of columns when the columns feature compression-controlled failure mode. This is reasonable since the failure process is governed by the

compression behavior of ECC material in this case. However, with the increase of eccentricity, the columns tend to fail in tensile side. Therefore, the increase of compressive strength of ECC has negligible influences on the load-carrying capacity

6000

f 'c=25 MPa

6000

αs=0.5%

5000

f 'c=35 MPa

5000

αs=1%

4000

MPa

3000

3000

2000

2000

1000

1000

0 0

100

200

300

Mu(kN.m)

100

(a)

αl=1%

200

300

Mu(kN.m)

1000

0

0

200

250

300

350

(d)

400

400

f 'ce=32 MPa f 'ce=52 MPa f 'ce=72 MPa

Nu(kN)

3000

1000

Mu(kN.m)

300

4000

2000

2000

200

Mu(kN.m)

5000

εt=5.5%

4000 3000

3000

100

6000

εt=3.5%

Nu(kN)

Nu(kN)

4000

150

0 0

400

εt=1.5%

5000

αl=2.2%

100

2000

(c)

αl=1.6%

5000

50

3000

(b)

6000

0

fyt=542MPa

4000

1000

0 0

400

fyt=442MPa

5000

αs=1.5%

4000

fyt= 342MPa

6000

Nu(kN)

f 'c=45

Nu(kN)

Nu(kN)

of the column.

2000 1000

0

50

100

150

200

250

300

350

400

0

0

50

100

150

200

250

300

350

400

Mu(kN.m)

Mu(kN.m)

(e) Fig.14 Effects of different parameters on

−

(f)

curves

5.Theoretical models

5.1Basic assumptions As shown in Fig.13, the outer ECC component has lower contact stress with inner CFST columns, indicating the slip as well as composite effect between them are negligible. Thus, the sectional capacity of ECC-encased CFST column can be divided into two parts, which are inner CFST component and outer R/ECC component shown as follows:

=

=

+

+

B

B

(9) (10)

where

and

are the ultimate compression and moment carrying capacity of

the composite column,

and

are the ultimate compression and moment B

carrying capacity of the outer steel reinforced ECC,

and

ultimate compression and moment carrying capacity of the inner CFST.

B

are the

Following assumptions are made in this paper: (1) The cross-section remained plane during the loading process, therefore the strain for different components are proportional to the distance from the neutral axis; (2) The bond between steel reinforcement and ECC is perfect and the bond-slip effect was ignored; (3) The tensile stress of concrete was ignored. (4) The stress–strain relationship for the longitudinal bar and steel tube is idealized as an elastic-plastic relation. (5) Both inner CFST component and outer R/ECC component have the same neutral axis.

and

5.2 For the outer steel reinforced component (

)

In order to simplify the theoretical model, as can be seen in Fig.15, the outer R/ECC component is simplified as an approximately I-shaped section. It should be guaranteed that the R/ECC component has the same area after simplification, thus the area ’. should be equal to ’* .

Fig.15 Cross-section simplification The constitutive models for ECC and steel reinforcements are shown in Fig.16, which is given by [23]:

where k. =

ACL 4CL

=Ž

, k* =

k. (0 ≤ ≤ ) + k* ( − ) ( ≤ ≤ ) + k; ( − ) ( ≤ ≤ )

AC“ 6ACL 4C“ 64CL

, k; =

AC• 6AC“ 4C• 64CL

,

elastic strain and corresponding stress, respectively;

and

and

(11) are the maximum are the peak strain

and corresponding stress, respectively;

and

are the ultimate strain and

corresponding stress, respectively. k\ (0 ≤ ≤ ) + kP ( − ) ( ≤ ≤ )

The tensile constitutive model for ECC is expressed as: where k\ =

stress;

and

A•L 4•L

=”

, kP =

A••c A•• 4•• 64•L

,

and

(12)

are the first cracking strain and

are the ultimate strain and stress. The constitutive model for steel

reinforcement is shown in Fig.16(c). σ

σ

σ

σcp

σtu

σy

σc0

σt0

σcu

εcp

εc0

0

εcu ε

εtu

0 εt0

(a)

(b)

ε 0

εy

εsu

ε

(c)

Fig.16 Constitutive models for (a) ECC in compression; (b) ECC in uniaxial tension; (c) steel Fig.17 shows the strain distribution when the outermost layer of ECC reached its ultimate strain (

). The so-called balanced failure model is defined as follows: the

steel reinforcement in the tension side yielded and the outmost fiber of compressive ECC reached its ultimate strength simultaneously. According to the assumptions illustrated above, the compression part of ECC can be expressed as: m•– = 4

4C•

C• G4_

ℎ

(13)

where m•– is the depth of ECC under compression stress with balanced failure

mode;

is the yield strain of steel rebar in the tension side; ℎ is the effective

height shown in Fig.17. It is obvious that the cross section is subjected to compression controlled failure when m• ≥ 4

4C•

C• G4_

controlled failure when m• ≤ 4

compression stress.

4C•

ℎ , while the cross-section is subjected to tension

C• G4_

ℎ , m• represents the depth of ECC under

Fig.17 Strain distributions along the cross section. 5.2.1 Tension-controlled failure When the reinforced ECC column with I-shaped cross-section fails in tension-controlled failure, the stress distribution model can be divided into two types, as shown in Fig. 18.

(a) Type 1

(b) Type 2

Fig. 18 Stress distribution of R/ECC in tension-controlled failure (1)Type 1 Based on the force equilibrium, the axial load is expressed as: =˜

|š

™ ( ) m − ˜|

›c8ˆ 8 š

›•8ˆ

8 ™ ( ) m − ˜›c8ˆ 8

( ) m − ˜›•8ˆ ™ ( ) m + œ

8

−

(14)

Also, according to the moment equilibrium, the bending moment bearing capacity is expressed as:

=˜

|š

™ ( ) ž − mŸ m + ˜|

›c8ˆ 8 š

*

ℎ

œ *

Ÿ m + ˜›•8ˆ ™ ( ) žm − Ÿ m + *

ℎ

œ

ž − a Ÿ +

*

8

*

ℎ

8

›

8 ™ ( ) ž − mŸ m + ˜›c8ˆ

›•8ˆ 8

( ) ž − mŸ m + ˜› œ

ž −a Ÿ

*

8

( ) žm −

*

ℎ

(15)

ℎ

where a and a are the cover thickness of R/ECC column at compressive and tensile side, respectively. (2)Type 2 Based on the force equilibrium, the axial load is expressed as: =˜

›c8ˆ 8

š ™ ( ) m + ˜›c8ˆ

|

8

( ) m − ˜|

( ) m − ˜›•8ˆ ™ ( ) m +

›•8ˆ 8 š

œ

8

−

(16)

According to the moment equilibrium, the bending moment bearing capacity is expressed as: =˜

›c8ˆ 8

š ™ ( ) ž − mŸ m + ˜›c8ˆ

|

*

ℎ

8

Ÿ m + ˜›•8ˆ ™ ( ) žm − Ÿ m + *

ℎ

œ

8

*

ℎ

( ) ž − mŸ m + ˜|8

›

*

ℎ

ž − a Ÿ + *

ℎ

š

ž −a Ÿ *

ℎ

›•8ˆ 8

( ) ž − mŸ m + ˜› œ *

8

( ) žm −

(17)

5.2.2 Compression-controlled failure When the reinforced ECC column with I-shaped cross section features compression-controlled failure mode, the stress distribution model can also be divided into two types which are shown in Fig.19. Based on the plane-section remaining assumption, the stress of the steel reinforcement can be calculated as follow =

=(

œL 6|š

=

|š

)

œL 6|š |š

(18) (19)

(a) Type 3

(b) Type 4

Fig. 19 Stress distribution of R/ECC in compression-controlled failure (3)Type 3 Based on the force equilibrium, the axial load is expressed as: =˜

›c8ˆ 8

( ) m − ˜|

š ™ ( ) m + ˜›c8ˆ

( ) m − ˜›•8ˆ ™ ( ) m +

›•8ˆ 8 š

|

8

œ

8

−

(20)

The bending moment bearing capacity is expressed as: =˜

›c8ˆ 8

›

8 ™ ( ) ž − mŸ m + ˜›c8ˆ

œ *

8

Ÿ m + ˜| ™ ( ) žm − Ÿ m + œ

œ *

œ

œ *

8

ž − a Ÿ + œ

*

š

›•8ˆ 8

( ) ž − mŸ m + ˜› *

š ( ) žm − Ÿ m + ˜›•8ˆ ™ ( ) žm −

|

œ

ž −a Ÿ œ

*

8

*

(21)

(4)Type 4 Based on the force equilibrium, the axial load and moment is expressed as:

=˜

=˜

›c8ˆ 8

›c8ˆ 8

›•8ˆ

8 ™ ( ) m + ˜›c8ˆ 8

š ( ) m + ˜›•8ˆ

›

8 ™ ( ) ž − mŸ m + ˜›c8ˆ

œ *

8

*

œ

8

œ *

œ

8

›•8ˆ 8

( ) ž − mŸ m + ˜›

Ÿ m + ˜›•8ˆ ™ ( ) žm − Ÿ m + œ

( ) m − ˜| ™ ( ) m +

|

œ *

8

ž − a Ÿ + œ *

š

−

(22)

š ( ) žm − Ÿ m + ˜›•8ˆ ™ ( ) žm −

ž −a Ÿ œ *

œ *

|

8

(23)

All the parameters in above four types can be computed according to the proposed constitutive models. 5.3 For the inner CFST component (NQNŠ¢ and MQNŠ¢ )

The simplified calculation method for CFST column has been proposed by An et.al [24], which is shown as follow:

=¤

B

where m

,

=¤

B

,

,

+ k.

,

,

(0.5™ − m

,

) + 2k*

§

H6m

γ=Ž m 6 0.12 ¨ ©

©ª H6m¨

−0.3 ©ª

H6©

+ 1 0.5(B +

H6©ª .P(H6©ª )

+ 0.73 (0.5(B − *

|

H

k. = [ž−3 + 4.6Ÿ © H

H

|š H

© H

©

|

¯. = Ž

H

© *

|

H

H

*

© H

−22.2 ž šŸ + 29.4 |

© *

H

|š H

|š H

H

«)

*

≤ m¨ ≤ B

< m¨ < 0.5(B +

« ))

+ (1.6 − 2.9)](

< 0.5)

© H

;\P B_5

)

.;y

(0.5≤

H

© *

− 12 (

|š H

|š H

≤ 1)

< 0.5)

H

is

;\P

H

H

fixed, the

B_5



,

=

;\P

B_5

,

assumption show in Fig.20, where

≤ 1)

（27） （28）

（31） |

H

−3.9 ž Ÿ + 5.3 − 0.46 − 0.7 (0.5 ≤ š ≤ 1) H H B_5 H ¯; = ° © * © ;\P |š −2.1 ž Ÿ + 3.5 + 0.22 − 1.9 ( < 0.5) ©

H

（26）

（29）

9.1 ž Ÿ − 11.8 + 0.6 + 2.3 (0.5 ≤ š ≤ 1) H H B_5 H ¯* = ° © * © ;\P |š 13.7 ž Ÿ − 19.4 − 0.76 + 9.7( < 0.5) ©

m¨

« ))

（30）

−5.3 ž Ÿ + 6.7 − 1.8 (0.5 ≤ H

«)

m¨

+ (1.5 − 2.3)] (

k* = ¯. ( š)* + ¯* ( š )* + ¯;

,

(25)

¨ ª ž−0.16 + 0.5Ÿ « + (0.5(B + « ) ≤ m¨ ≤ B) H6©ª * =Ž m¨ 6 .PHG .P©ª H6©ª ž−0.04 + 0.46Ÿ (m¨ − 0.5 + 0.5 « ) + (0.5(B − « ) < m¨ < 0.5(B +

k. = [ž2.8 − 4.2Ÿ ž š Ÿ + ž−4.6 + 7.9Ÿ

when m

(24)

(m¨ − m

|

H

（32）

（33）

can be deduced based on the plane-section « )/m¨

Fig.20 Stress distribution of inner CFST

（34）

,

Then the corresponding

can be computed by the constitutive relation of

steel tube reinforced concrete shown as following:

where m =

47,C‡ˆ7 4L

, ² =

²=ƒ

A7,C‡ˆ7 AL



y = 2m − m * (m ≤ 1)

1 + ³xm

..´

|

− 1{ (µ ≤ 1.12)

¶(|6.)8 G|

and

(µ > 1.12)

（35）

（36）

are the peak stress and the corresponding

strain, respectively; µ is the confinement factor of CFST which can be calculated as (

,

)/(

). This stress-strain model has been widely applied and other

parameters can be found in the reference [24]. −

5.4

curves for ECC-encased CFST columns

Based on the proposed calculation methods, the load and moment carrying capacities for the composite columns with different eccentricity ratios can be computed when the specimen dimensions are fixed. The flow chart to determine and

is shown in Fig.21. Firstly, we should “Input column dimension and

materials properties”, this is the first step and all the parameters have been given above. According to the proposed model (equation 14 to equation 36), it can be found that

−

and

are the functions of m• . With the inputting of different m• , the

can be plotted as shown in Fig.22. The black dots in Fig.22 represent the

experimental results of different columns. Generally, it can be seen that the calculation results are in good agreement with the experimental results. As can be seen in Table 3, the maximum error between experimental value ( (

·

) and calculation value

) was controlled within 12%. It was also found that the compressive strength

derived from FE modeling (

B ) has higher accuracy.

It is reasonable since the nonlinear

behavior of materials as well the composite effects between different components were considered in the FE modelling.

and

Fig.21 Flow chart to determine

6000 5000

Nu(kN)

4000

•

C1-0.2

C1-0.4 •

3000 2000

e=0.2 e=0.4 e=0.6 e=0.8

1000

• C1-0.6

•

C1-0.8

0 0

−

Fig.22

50

100

150

200

250

300

350

400

Mu(kN.m)

curve for ECC-encased CFST column

Table 3 Comparison of the compressive strength Specimens

Experimental（

）

FEA(

B)

Computational（

）

/

B/

C1-0.2

3671

3536

3789

1.032

0.9632

C1-0.4

2768

2643

2571

0.929

0.9548

C1-0.6

1846

1711

1759

0.953

0.9269

C1-0.8

1178

1130

1270

1.078

0.9593

C2-0.4

2643

2465

2341

0.886

0.9326

C3-0.4

3055

2973

2807

0.919

0.9732

C4-0.4

2586

2386

2324

0.905

0.9225

Conclusions Based on the simulational methods, the eccentric behaviors of ECC-encased CFST columns were studied. The key conclusions are summarized as follows: (1) The FE model for ECC-encased CFST columns under eccentric loading was established with the considerations of different constitutive models. The accuracy of FE model was verified with the experimental results. (2) The failure mechanism of ECC-encased CFST column was investigated with the proposed FE model. It was found that the eccentricity ratio has a significant influence on the yielding processes and composite effect between each component. (3) The influences of different parameters on the eccentric behavior of the composite column were discussed. It was found that the steel tube ratio ( ), steel tube strength (

) and longitudinal reinforcement ratio (

) influenced the load capacity of

ECC-encased CFST column regardless of their failure modes. By contrast, the core concrete strength (

) and compression strength of ECC (

) influenced those

columns which feature compression-controlled failure mode. By contrast, the ultimate tensile strain of ECC ( ) influences those columns which feature tension-controlled

failure mode.

(4) A theoretical model was developed and compared with the experimental results. The maximum error between experimental value (

) and calculation value (

·

) was

controlled within 12%, the accuracy of the proposed theoretical model was verified.

Acknowledgments This work was financially supported by Natural Science Foundation of China (No. 51778131 and No. 51908117) and Jiangsu Planned Projects for Postdoctoral Research Funds (2019K042).

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Highlights:

(1) A new FE model was proposed to investigate the eccentric behaviour of ECC-encased CFST column. (2) The failure mechanisms of the composite column were discussed with the proposed FE model. (3) The influences of different parameters were investigated with the proposed FE model. (4) A theoretical model for predicting the sectional capacity of ECC-encased CFST columns was also proposed and verified.

Conflict of Interest We wish to draw the attention of the Editor to the following facts which may be considered as potential conflicts of interest and to significant financial contributions to this work. We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us. We confirm that we have given due consideration to the protection of intellectual property associated with this work and that there are no impediments to publication, including the timing of publication, with respect to intellectual property. In so doing we confirm that we have followed the regulations of our institutions concerning intellectual property and there is no conflict of interest for this paper. Yours sincerely, Jinlong Pan Professor Department of Civil Engineering Southeast University，China Mobile: (86) 13645178762 Fax: (86) 25 83791225 E-mail: [email protected]