Behaviour of short CFRP-steel composite tubed reinforced normal and high strength concrete columns under eccentric compression

Engineering Structures 205 (2020) 110096

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Behaviour of short CFRP-steel composite tubed reinforced normal and high strength concrete columns under eccentric compression

T

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Tianxiang Xua,b, Jiepeng Liua,b, Xuanding Wanga,b, Ying Guoa,b, , Y. Frank Chenc a

School of Civil Engineering, Chongqing University, Chongqing 400045, China Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China c Department of Civil Engineering, The Pennsylvania State University, Middletown, PA 17057, USA b

A R T I C LE I N FO

A B S T R A C T

Keywords: CFRP-steel composite tubed reinforced concrete (C-STRC) High-strength concrete (HSC) Short column Eccentric compression Lateral displacement Load capacity

The use of steel tubed reinforced concrete (STRC) column maximizes the confinement effectiveness of steel tube as the steel tube is disconnected at the beam-column joint. However, for high-strength and high performance concrete, the confinement from the steel tube would be limited. Also, certain measures need to be implemented to prevent the corrosion of steel tube. Carbon fibre reinforced polymer (CFRP) has the advantages of high strength-to-weight ratio and good corrosion resistance. However, the complicated construction procedures and relatively brittle post-peak behaviour limit its application to new concrete buildings. The combination of CFRP and STRC column is a good alternative to solve the concerning problems. This study experimentally investigated the behaviour of CFRP-steel composite tubed reinforced concrete (C-STRC) columns under eccentric compression. The observed failure modes, load-deformation curves, and load-stress curves of the steel tube and longitudinal reinforcing bars are presented. The test results show that the load capacity and deformability of the CSTRC columns with normal concrete strength are enhanced due to the use of CFRP and steel tube. The plastic stress distribution method was employed to analyse the axial load versus moment interaction curves and the results were found to be generally in good agreement with the test ones.

1. Introduction Concrete filled steel tube (CFST) columns [Fig. 1(a)] have been widely used because the confinement from the steel tube enhances the load capacity and deformability of core concrete [1–4]. However, the steel tube in a CFST column needs to be thick enough to avoid a potential outward local buckling [5]. Steel tubed concrete (STC) column is another type of composite columns, in which the steel tube does not pass through the beam-column joint and thus carries no direct axial load, providing mainly the lateral confinement to the core concrete [6–9]. This results in a relatively thinner steel tube and simpler joint construction, compared with CFST columns. However, in most practical occasions, the columns are subjected to eccentric loading, in which strain gradients along the section height will result in the non-uniform confinement. Therefore, longitudinal bars or steel shapes are added to resist the bending moment. Steel tubed reinforced concrete (STRC) column was proposed by Tomii et al. [10], as shown in Fig. 1(b). The confinement from the thin-walled steel tube would be limited for highstrength concrete (HSC) and high performance concrete (HPC) due to their high strength and/or high deformation capacity [11,12]; while a

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thick-walled steel tube is uneconomical and will result in heavier structures and require an improved confinement type. In addition, corrosion is generally a concern for metal structures such as CFST and STRC columns. Carbon fibre reinforced polymer (CFRP) material has been widely adopted to enhance the load bearing capacity and ductility of core concrete due to its high strength-to-weight ratio, good corrosion resistance, and fatigue resistance [13–16]. However, the CFRP is a brittle material as it usually fails by sudden rupture. In addition, the construction procedure of CFRP is quite complicated for a new concrete structure as the surface of concrete needs to be cleaned, followed by the wrapping of CFRP on site, consuming both time and labour. The CFRP-steel composite tubed reinforced concrete (C-STRC) column is a novel composite member, in which the CFRP is wrapped around the steel tube of a STRC column, thus it takes the advantages of both CFRP and STRC columns. The steel tube can be prefabricated into any desired shape with the CFRP wrapped around it in a shop. The CFRP-steel composite tube can then be used as framework for core concrete pouring. The outer CFRP-steel composite tube provides the lateral confinement to the core concrete and the potential inward and

Corresponding author at: School of Civil Engineering, Chongqing University, Chongqing 400045, China. E-mail address: [email protected] (Y. Guo).

https://doi.org/10.1016/j.engstruct.2019.110096 Received 23 July 2019; Received in revised form 5 December 2019; Accepted 13 December 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

Mp N n0 Np tcf ts tv αb αt Δ δ δp

Notations D Dc e Ec Ecf Esa fcc fco fcu,m fl fy fya h hc Kε L l lm

the diameter of steel tube the diameter of inner concrete the load eccentricity the elastic modulus of unconfined concrete the elastic modulus of CFRP the elastic modulus of longitudinal rebars the confined concrete strength the unconfined concrete strength the cubic compressive strength of concrete the confining pressure the yielding strength of steel tube the yielding strength of longitudinal rebars the distance from a certain point to the centre of the longitudinal rebar located in the extreme tension region the compressive depth of the cross section in the plastic stress distribution method the strain efficiency factor of CFRP the length of a specimen the location of a certain section along the height of column the length at mid steel tube

δu εf εfu εsa εya σh σsa σv σz

the bending moment at the peak load the axial load the number of CFRP layers the measured load capacity of a specimen the thickness of CFRP the thickness of steel tube the thickness of V-block the longitudinal reinforcement to concrete area ratio the steel tube to concrete area ratio the axial shortening of a specimen the measured lateral displacement of a certain section the measured lateral mid-span displacement of a specimen at the peak load the measured lateral mid-span displacement of a specimen when the load decreases to 80% of the peak load the lateral strain of CFRP at the middle section during the loading process the ultimate strain of CFRP the axial strain of longitudinal rebars the yielding strain of longitudinal rebars the transverse stress of steel tube the axial stress of longitudinal rebars the longitudinal stress of steel tube the equivalent stress of steel tube

Fig. 1. Comparison of CFST column and STRC column.

eccentricity, CFRP confinement factor, and strength of concrete and CFRP. In addition, an empirical formula was proposed for the calculation of eccentric compressive strength. For CFRP-steel composite tubed concrete (C-STC) columns, Liu et al. [11,33] tested 16 circular specimens with normal strength concrete and 19 circular specimens with high-strength concrete under concentric compression and provided practical design recommendations. Previous studies demonstrated that the combination of FRP and steel tube can significantly enhance the load bearing capacity and deformability of core concrete. However, studies on the behaviour of either CFRP confined CFST columns or C-STRC columns under eccentric compression are rather limited. Therefore, as a preliminary study on the behaviour of C-STRC columns under eccentric compression, 16 such columns with normal and high strength reinforced concrete were concentrically and eccentrically tested. The observed failure modes, load versus deformation curves, and load versus stress curves of the steel tube and longitudinal reinforcing bars (rebars) were analysed and discussed in this paper in detail.

outward local buckling of steel tube will be suppressed by the core concrete and CFRP, respectively. Moreover, the CFRP prevents the corrosion problem of steel tube and its post-peak behaviour is enhanced by the presence of steel tube. A number of studies have been conducted on the axial behaviour of fibre reinforced polymer (FRP) confined CFST columns. The influence of FRP layers, diameter-to-thickness ratio of steel tube, concrete strength and cross-sectional shape on the compressive behaviour of FRP confined CFST short columns was experimentally studied [17–24]. Wang et al. [25,26] investigated the influence of slenderness ratio and longitudinal CFRP layers on the circular and square CFRP confined CFST columns under concentric compression. Li et al. [27] performed a compression test on 7 CFRP confined CFST columns with different slenderness ratio and CFRP layers. In addition, the stress-strain relationship of FRP confined CFST columns has been theoretically studied [28–31]. However, only limited study has been conducted on the behaviour of CFRP confined CFST columns under eccentric compression. Wang et al. [32] tested 9 CFST columns partially-wrapped by CFRP strips under eccentric compression and concluded that the load bearing capacity of specimens was significantly influenced by the load 2

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2. Experimental program 2.1. Specimens In total, 20 specimens were prepared and tested to failure under concentric or eccentric compression, including 16 CFRP-steel composite tubed reinforced concrete (C-STRC) columns, 2 steel tubed reinforced concrete (STRC) columns, and 2 CFRP confined reinforced concrete (CRC) columns. The system parameters considered include three concrete strength grades (C40, C60, C80), four numbers of CFRP layers (2, 3, 4, 5), and five load eccentricities (25, 37.5, 50, 62.5, 75 mm). Specimen details are listed in Table 1 along with the test results, in which D is the outer diameter of specimen (excluding the negligible CFRP thickness), L is the height of specimen, ts is the thickness of steel tube, n0 is the number of CFRP layers, fco is the uniaxial concrete compressive strength, e is the load eccentricity, αt is the ratio of steel tube to gross concrete area, and αb is the ratio of longitudinal reinforcement to gross concrete area. The specimen designation begins with the type of specimens (STRC, CRC, or C-STRC), followed by the diameter of steel tube (mm), design concrete strength (MPa), number of CFRP layers, and load eccentricity (mm). For example, CRC-200-80-425 represents a CRC column with 200 mm tube diameter, 80 MPa concrete strength, 4 CFRP layers, and 25 mm load eccentricity. The geometry of the specimens is illustrated in Fig. 2. The circular steel tubes were fabricated by rolling plain steel plates and the butt seam was strengthened by a 50 mm (width) × 2 mm (thickness) steel plate to prevent a premature weld failure. The reinforcement cage consists of eight 14 mm Φ symmetrically arranged longitudinal rebars and 8 mm Φ stirrups evenly spaced at 200 mm on centres. It was placed into the steel tube with one 16 mm thick end plate welded first (Fig. 2). The longitudinal rebars were welded to the end plates to ensure the transferring of bending moments. All specimens were cast from the same batch of concrete and another end plate was welded to the steel tube after ten days of concrete curing. The steel tube was disconnected by two 10 mm stripes with each at 100 mm from the respective steel tube end (Fig. 2). After that, the CFRP was wrapped around the steel tube (C-STRC columns) or the concrete (CRC columns) with an overlapping length of 150 mm via a wet lay-up process (fibres were oriented in the hoop direction only), and the overlapping zone was symmetric with respect to the butt seam.

Fig. 2. Geometry of the specimens.

2.2. Material properties Concrete cubes and prisms were prepared and cured under the same condition as the specimens to obtain the cubic compressive strength (fcu,m) and elastic modulus of the concrete (Ec), respectively, as presented in Table 2. The uniaxial concrete compressive strength (fco) used in calculations can be obtained by converting the fcu,m to cubic characteristic strength through some coefficients according to GB500102010 [34], which is then converted into fco according to the EC2-1-1 [35]. Details of the transferring method is presented in Appendix A. Tensile coupons were tested to determine the mechanical properties of reinforcing steel and steel tube [36], while the mechanical properties of CFRP were provided by the manufacturer. The material properties of reinforcing steel (longitudinal rebar and stirrup), steel tube, and CFRP are summarized in Table 3. The thickness of steel tube and each CFRP layer are 2 mm and 0.167 mm, respectively. 2.3. Instrument and measuring scheme All specimens were tested under monotonically increasing axial displacements using a 10,000 kN hydraulic compression machine (Fig. 3). The knife-edge plates and adjustable V-blocks were applied to provide the required end eccentricities and pin supports. Three linear variable differential transformers (LVDTs) were installed on the middle

Table 1 Specimen details. Specimens

D (mm)

L (mm)

ts (mm)

n0

fco (MPa)

e (mm)

Longitudinal bars

Stirrups

αt

αb

STRC-200-80-25 STRC-200-80-50 CRC-200-80-4-25 CRC-200-80-4-50 C-STRC-200-40-4-0 C-STRC-200-40-4-25 C-STRC-200-40-4-50 C-STRC-200-60-4-25 C-STRC-200-60-4-50 C-STRC-200-60-4-75 C-STRC-200-80-2-50 C-STRC-200-80-2-62.5 C-STRC-200-80-3-25 C-STRC-200-80-3-50 C-STRC-200-80-4-0 C-STRC-200-80-4-25 C-STRC-200-80-4-37.5 C-STRC-200-80-4-50 C-STRC-200-80-5-25 C-STRC-200-80-5-50

200 200 196 196 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200

600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600

2 2 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

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

75.2 75.2 75.2 75.2 45.7 45.7 45.7 63.0 63.0 63.0 75.2 75.2 75.2 75.2 75.2 75.2 75.2 75.2 75.2 75.2

25 50 25 50 0 25 50 25 50 75 50 62.5 25 50 0 25 37.5 50 25 50

8Φ14 8Φ14 8Φ14 8Φ14 8Φ14 8Φ14 8Φ14 8Φ14 8Φ14 8Φ14 8Φ14 8Φ14 8Φ14 8Φ14 8Φ14 8Φ14 8Φ14 8Φ14 8Φ14 8Φ14

Φ8@200 Φ8@200 Φ8@200 Φ8@200 Φ8@200 Φ8@200 Φ8@200 Φ8@200 Φ8@200 Φ8@200 Φ8@200 Φ8@200 Φ8@200 Φ8@200 Φ8@200 Φ8@200 Φ8@200 Φ8@200 Φ8@200 Φ8@200

4.2% 4.2% 0 0 4.2% 4.2% 4.2% 4.2% 4.2% 4.2% 4.2% 4.2% 4.2% 4.2% 4.2% 4.2% 4.2% 4.2% 4.2% 4.2%

4.1% 4.1% 4.1% 4.1% 4.1% 4.1% 4.1% 4.1% 4.1% 4.1% 4.1% 4.1% 4.1% 4.1% 4.1% 4.1% 4.1% 4.1% 4.1% 4.1%

3

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Table 2 Material properties of concrete. Concrete grade

fcu,m (MPa)

fco (MPa)

Ec (MPa)

C40 C60 C80

58.7 80.3 98.3

45.7 63.0 75.2

38,800 47,000 49,100

segment of the steel tube to monitor the lateral displacements of the specimens, in which two LVDTs were arranged adjacent to the stripes on the compression side (to avoid the influence of separation between concrete and steel tube near the girth gap) and another one located in the middle on the tension side (to avoid the influence of buckling of steel tube at the middle of steel tube). Two additional LVDTs were used to measure the overall axial displacement of a specimen (Fig. 3). To monitor the specimen strains, five axial strain gauges were installed on the longitudinal rebars numbered as B1-B5 from the tension region to the compression region [Fig. 4(a)], and four pairs of strain gauges were applied to steel tubes at the middle section [Fig. 4(b)]. Furthermore, only transverse strain gauges were used at quarter locations (Sections ae, Fig. 3) to measure the strains of the CFRP (Fig. 5), and the strain gauges at the middle section were numbered as C1-C8 [Fig. 5(c)]. 2.4. Test procedures Fig. 3. The testing machine and layout of LVDTs.

The axial load applied to the specimens consists of two stages: loadcontrol stage and displacement-control stage. The load was applied at a rate of 3kN/s in the load-control stage as the displacement was relatively small. Once the yielding of longitudinal bars or steel tube was observed, the load was applied according to the displacement-control method, in which the mid-span displacement was increased at a rate of 2 mm/min. It should be noted that the steel tube was judged to be yielded once the transverse strain or the longitudinal strain reached the yielding strain of steel tube. The test was generally terminated when the rupture of CFRP occurred, but for the specimens with CFRP ruptured near the peak load, the loading process was terminated when the load decreased to be lower than 85% of the peak load.

Fig. 4. Layout of strain gauges on longitudinal bar and steel tube.

3. Experimental results

characterized as a bending failure mode. Furthermore, diagonal shear cracks were also observed in the compression region in Specimen CSTRC-200-60-4-25 and the specimens with the concrete strength grade of C80. It should be noted that rupture of CFRP occurred at the middle section for specimens with relative small load eccentricity [e = 0 mm and 25 mm, Fig. 6(a–e)], while that happened at the end of mid steel tube for specimens with load eccentricity larger than 50 mm [e.g., Fig. 6(f)]. The plastic deformation of STRC specimens developed not so fully as that of C-STRC specimens, which might be caused by the inadequate confinement provided by the steel tube. Flexural cracks in the tension region and shear cracks in the compression region were also observed on the surface of concrete [Fig. 7(a)]. However, flexural cracks appeared at the upper end for Specimen STRC-200-80-50. Fig. 7(b) shows the typical failure modes of CRC specimens in which the deformation of concrete was the most serious among the three types of specimens. Concrete crushing occurred in the compression region, and wider and

3.1. Failure modes Fig. 6 shows the typical failure modes of C-STRC specimens subjected to concentric and eccentric loads. The concentrically-loaded CSTRC specimens [Fig. 6(a and b)] failed by the explosive rupture of CFRP. A critical diagonal concrete crack was observed on the surface of Specimen C-STRC-200-80-4-0 [Fig. 6(b)]. Generally, for the specimens under eccentric loading [Fig. 6(c-f)], the rupture of CFRP occurred in the compression region at the peak load, followed by the rapidly increasing deformation in the steel tube and concrete. It should be stressed that for the specimens with the higher concrete strength of C80, the rupture of CFRP actually occurred beyond the peak load. This may be caused by the brittleness of high-strength concrete, resulting in a relatively small deformation at the peak load. The concrete crushed in the compression region and the flexural cracks were noticed in the tension region after removing the steel tube, which was hence Table 3 Material properties of reinforcing steel, steel tube and CFRP. Material

Yielding strength (MPa)

Ultimate strength (MPa)

Elastic modulus (MPa)

Longitudinal rebars Stirrups Steel tube CFRP

489.7 510 334 –

623.7 558 454 3410

1.87 2.14 1.67 2.31

4

× × × ×

105 105 105 105

Ultimate strain (με) – – – 16,100

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Fig. 5. Layout of strain gauges on CFRP.

more concentrated flexural cracks were noticed in the tension region. Typical lateral deformation shapes of different types of specimens (C-STRC, STRC, and CRC) are shown in Fig. 8, which are generally in better agreement with a second-order parabola. The thickness of Vblock (tv = 95 mm) was considered as part of the specimen length because the valley of V-block is a fixed point in reality. Unlike the specimens with steel tubes, the lateral deformation of Specimen CRC200-80-4-25 increased dramatically when the load reached 90% of the peak load. The deformations of C-STRC and CRC columns were larger than those of STRC columns. However, the lateral displacement at l = 195 mm was distant from the parabola curve for Specimens STRC-

200-80-50, C-STRC-200-60-4-75, C-STRC-200-80-2-50/62.5, and CSTRC-200-80-3-50, caused by the failure section near the mid tube end. Plane section is usually assumed to determine the sectional capacity, which means the originally plane section remains plane after deformation. The strain distribution of longitudinal rebars was investigated to verify this assumption. Fig. 9 shows the strain distribution of rebars along the height of the section during the loading process till the peak load, in which h is the distance from a certain point to the centre of the longitudinal rebar located in the extreme tension region [Fig. 4(a)]. As shown in Fig. 9, the section generally remains plane before the peak load, with strains at some testing points becoming

Fig. 6. Failure modes of C-STRC specimens. 5

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Fig. 7. Failure modes of STRC and CRC specimens.

Fig. 8. Typical lateral deformed shapes along the height of specimens.

Fig. 9. Typical strain distribution of longitudinal bars along the depth of section.

Mp=Np(e+δp)

discrete at the peak load. This may be caused by the following two reasons: (1) the plastic deformations of concrete and longitudinal bars increase dramatically when approaching the peak load, leading to the inaccurate readings from damaged strain gauges; and (2) another possible consequence of the plastic deformation of concrete is that the longitudinal bars are vulnerable to the buckling problem. In addition, the tension region of Specimen C-STRC-200-60-4-50 (e = 50) is larger than that of Specimen C-STRC-200-60-4-25 (e = 25).

(1)

These curves can be generally classified into three types: bi-linear, elastic-plastic, and linear-parabolic. The bi-linear type is more likely for the specimens with lower concrete strength and smaller load eccentricity. As shown in Fig. 10, the lateral deformation increases linearly with the axial load at the initial stage, and in most occasion, yielding of rebar occurs in the compression region (indicated by rhombic red dots in Fig. 10, based on the stress analysis results presented in Section 3.5), followed by the yielding of steel tube in the compression region (circular red dots, based on the stress analysis results presented in Section 3.4). The N-δ curves then enter into the second stage as the plastic deformation of concrete increases. The yielding of steel tube (square red dots) and rebar (five-pointed star red dots) in the tension region occur after their yielding in the compression region. For the specimens with lower concrete strength and smaller load eccentricity (Specimens CSTRC-200-40-4-25, C-STRC-200-40-4-50, and C-STRC-200-60-4-25), there is an ascending branch of N-δ curves after the yielding of steel tube in the compression region. The initial stiffness and Np of C-STRC columns decrease with an increasing load eccentricity, while δp and δu tend to increase. The number of CFRP layers, concrete strength, and confinement types seem to have little influence on the initial stiffness of C-STRC columns (Figs. 11–13). For specimens with concrete strength of C80, the increase of CFRP layers has little influence on Np and δp when

3.2. Load versus deformation curves Figs. 10-12 show the relationships between load (N) and mid-span lateral displacement (δ) for various C-STRC specimens and the effects of the respective influencing factors (i.e., load eccentricity, number of CFRP layers, and concrete strength). Fig. 13 shows the influence of confinement types on N–δ curves. In addition, the key test results are summarized in Table 4, in which Np and δp are respectively the axial load and mid-span displacement of a specimen at peak load, δu is the mid-span displacement when the load decreases to 80% of Np, and Mp is the bending moment at peak load and determined by Eq. (1). It should be noted that the type of load versus deformation curves represents respectively the type of load-axial shortening curves and N-δ curves for specimens under concentric load and eccentric load. 6

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Fig. 10. Influences of load eccentricity on the N-δ curves.

e = 25 mm; while δp is significantly enhanced with increasing CFRP layers despite of the slight increase of Np when e = 50 mm (Fig. 11). In addition, δu tends to increase with the increase of CFRP layers. Np increases as the concrete strength increases, but δp and δu decrease dramatically and the ascending branch of N-δ curves no longer exists with higher concrete strength (Fig. 12). Fig. 13 compares the specimens with different confinement types. The N-δ curves experience a similar initial stage up to the point where CRC specimens change to the next branch. Then, C-STRC specimens enter into the branch of N-δ curves approximately after the peak load of STRC specimens, and CRC specimens possess a relatively brittle post-peak behaviour. In addition, δp and δu

are significantly improved due to the use of CFRP. Fig. 14 shows the load (N) versus axial shortening (Δ) curves for the C-STRC columns under concentric compression, in which Δ is averaged from the two vertical LVDTs. For Specimen C-STRC-200-40-4-0, the N-Δ curve increases linearly at the initial and later stages and the steel tube and rebar yield approximately at the initial point of the ascending branch. However, the rebar of Specimen C-STRC-200-80-4-0 yields during the initial stage, while the steel tube yields near the peak load, and then the load gradually decreases.

Fig. 11. Influences of CFRP layers on the N-δ curves. 7

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Fig. 12. Influences of concrete strength on the N-δ curves.

initially, and then σh increases quickly with the development of plastic deformation of core concrete, followed by the yielding of steel tube. Typical steel tube stresses in the tensile region, on the central axis, and in the compression region for the C-STRC columns under eccentric compression are shown in Fig. 17(c–e). These stresses increase gradually with the load initially, especially σv. Then, σh increases slightly with the plastic deformation of concrete before the peak load. The steel tube yields first in the compression region before reaching the peak load, followed by the yielding of steel tube in the tension region. As shown in Fig. 18, the variation of tube stresses in the SRTC columns are similar to those in the C-STRC columns. However, the yielding of steel tube occurs near the peak load in the compression region, after the peak load along the central axis, and at a later time in the tension region.

3.3. Load versus strain curves of CFRP Typical load (N) versus strain (εf) curves for CFRP at the mid-section of C-STRC columns are shown in Fig. 15. As shown in Fig. 15(a), the lateral strain of the CFRP in a C-STRC column under concentric compression increases linearly with the increasing axial load initially and then increases rapidly with the increasing plastic deformation of concrete. The variation trends of N-εf curves are similar despite of some discrete data. For the C-STRC columns under eccentric compression [Fig. 15(b–d)], the strain gauges in the compression region are in tensile state due to the dilation of concrete and steel tube, while those in the tension region tend to be in compression. The steel tube at the midsection is in plane stress status, and the vertical strain of steel tube is in tensile state in the tension region. Thus, the transverse strain of steel tube tends to be in compressive state, leading to the compressive strain of CFRP in the tension region. The strain gauge near the extreme compression fibre (C5) appears to have larger tension strain. While Specimens C-STRC-200-80-4-25 and C-STRC-200-80-4-50 show the opposite trend, which may be due to the damage in the strain gauge caused by the large compressive deformation. Similar N-εf relationships are found in CRC specimens, as shown in Fig. 16. Namely, the lateral strain increases linearly with the increasing load, followed by the rapid increase until the peak load is reached.

3.5. Stresses in the longitudinal rebars The longitudinal rebars are assumed as an ideal plastic material, represented by Eq. (3) where σsa and εsa are respectively the stress and strain of the rebars during the loading and fya , Esa , and ε ya are respectively the yielding strength, elastic modulus, and yielding strain of the rebars.

Esa εsa εsa < ε ya σsa = ⎧ εsa ≥ ε ya ⎨ fya ⎩

3.4. Stresses in the steel tube

Typical load versus stress curves for the longitudinal rebars in the CSTRC columns are shown in Fig. 19. For the C-STRC columns subjected to concentric compression [Fig. 19(a)], the rebar stresses increase approximately linearly with increasing loads initially and then yield almost simultaneously. For the C-STRC columns under eccentric compression [Fig. 19(b–d)], the longitudinal rebars in the tension region are more likely to be in tensile state initially for the specimens with larger load eccentricity. As the load increases, the originally compressive rebars in the tension region gradually turn tensile. The longitudinal rebar at the extreme compression fibre yields first, followed by the progressive yielding of the rebars from compression to tension regions. The rebars subjected to tension generally yield near the peak load.

Based on the measured strains of steel tube, the elastic-plastic method [37] was employed to analyse the stresses of steel tube at the mid-height of a specimen (Section c, Fig. 3). Typical load (N) versus stress (σ) curves for the C-SRTC columns at the middle section are shown in Fig. 17 where σv, σh and σz are respectively the longitudinal stress, hoop stress, and equivalent stress of steel tube. σz is used to determine the yield of steel tube and can be calculated by Eq. (2).

σz =

σv2 + σh2 − σv σh

(3)

(2)

Fig. 17(a and b) show the stresses in the steel tube of the C-STRC columns under concentric compression. As seen, σv is higher than σh

Fig. 13. Influences of confinement types on the N-δ curves. 8

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Table 4 Test results. Specimens

n0

e (mm)

fco (MPa)

Np (kN)

δp (mm)

δu (mm)

Mp (kN·m)

Type of load versus deformation curves

STRC-200-80-25 STRC-200-80-50 CRC-200-80-4-25 CRC-200-80-4-50 C-STRC-200-40-4-0 C-STRC-200-40-4-25 C-STRC-200-40-4-50 C-STRC-200-60-4-25 C-STRC-200-60-4-50 C-STRC-200-60-4-75 C-STRC-200-80-2–50 C-STRC-200-80-2-62.5 C-STRC-200-80-3-25 C-STRC-200-80-3-50 C-STRC-200-80-4-0 C-STRC-200-80-4-25 C-STRC-200-80-4-37.5 C-STRC-200-80-4-50 C-STRC-200-80-5-25 C-STRC-200-80-5-50

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

25 50 25 50 0 25 50 25 50 75 50 62.5 25 50 0 25 37.5 50 25 50

75.2 75.2 75.2 75.2 45.7 45.7 45.7 63.0 63.0 63.0 75.2 75.2 75.2 75.2 75.2 75.2 75.2 75.2 75.2 75.2

2691 1650 2624 1529 3532 2503 1733 2613 1730 1005 1695 1382 2851 1821 4378 2900 2452 1859 2872 2001

3.56 4.58 11.26 – – 19.19 27.98 12.44 7.44 19.38 8.66 5.41 5.19 7.64 – 6.99 12.01 7.18 6.40 8.98

9.16 11.39 12.67a – – 23.10 47.59 17.81 25.04 19.42a 15.55 13.17a 14.08 11.13 – 12.56 19.17a 19.16 23.18 21.11

76.85 90.06 95.15 80.66 0 110.62 135.15 97.84 99.38 94.85 99.43 93.86 86.06 104.96 0 92.76 121.39 106.30 90.17 118.01

Linear-parabolic Linear-parabolic Elastic-plastic Linear-parabolic Bi-linear Bi-linear Bi-linear Bi-linear Elastic-plastic Linear-parabolic Linear-parabolic Linear-parabolic Linear-parabolic Linear-parabolic Elastic-plastic Elastic-plastic Elastic-plastic Linear-parabolic Linear-parabolic Linear-parabolic

a

The load has not decreased to 80% of Np.

Fig. 14. Load versus axial shortening curves for the C-STRC columns under concentric compression.

Fig. 15. Typical load versus strain curves of CFRP at the mid-section for C-STRC columns.

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As with the stress results of the longitudinal rebars in C-STRC columns, the variations of rebar stresses in CRC and STRC columns are similar (Fig. 20). Compared with C-STRC columns and CRC columns, the longitudinal rebars of STRC columns in the tension region yield during the post-peak stage, indicating that the strength of rebars is utilized more efficiently for the specimens with CFRP sheets. 4. Axial load versus moment interaction diagram Plastic stress distribution method was employed to simulate the axial load (N) versus moment (M) interaction diagram. The following usual assumptions are employed to establish the analysis model: (1) All the longitudinal bars in tension and in compression reach their yield stress (fya); (2) The concrete of C-STRC specimens in compression reaches the confined concrete strength (fcc), and fcc of C-STRC specimens with bi-linear and parabolic types of stress-strain curves under concentric compression can respectively be determined by Eq. (4) [33] and Eq. (5) [11], in which fl is the confining pressure; (3) The confining

Fig. 16. Load versus strain curves of CFRP at the mid-section for Specimen CRC-200-80-4-25.

Fig. 17. Typical load versus stress curves for the steel tube of C-SRTC columns. 10

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Fig. 18. Load versus stress curves for the steel tube of Specimen STRC-200-80-25.

As shown in Fig. 21, the N-M interaction diagrams are generated by gradually increasing the compressive depth of the cross section (hc). It should be noted that gross area of concrete is used, which is reasonable as αb is relatively small. Fig. 22 shows the influence of CFRP layers and concrete strength on N-M interaction diagrams of C-STRC columns, in which P and T represent the predicted and tested results, respectively. As shown in Fig. 22, the predicted results are higher than the test ones. This may be caused due to the strain gradients along the height of the column under eccentric compression, which results in the non-uniform confinement. In addition, for specimens with the CFRP ruptured beyond the peak load, the confining stress at the peak load will be overestimated when the rupture strain of CFRP and the yield strength of steel tube are used. To this end, a reduction factor equal to 0.65 is used to calculate the confining stress, and the predicted results are shown in the Fig. 22 (represented by Pm), which are generally in good agreement with the test results except for Specimens C-STRC-200-40-4-25 and CSTRC-200-40-4-50, this may be caused by the large plastic deformation of specimens with a concrete strength of C40, resulting in a large lateral deformation. The CFRP layers and concrete strength have little influence on the pure bending bearing capacity. The axial load bearing capacity increases with increasing CFRP layers and concrete strength.

pressure is computed by Eqs. (6), in which fy is the yielding strength of steel tube, kε is the strain efficiency factor valued respectively as 0.594 [33] and a mean value of 0.145 [11] for specimens with bi-linear and parabolic types of stress-strain curves under concentric compression, εfu is the ultimate strain of CFRP, Ecf is the elastic modulus of CFRP, and Dc is the diameter of inner concrete; (4) The classification of the stressstrain curves under concentric compression is determined by the confinement ratio (fl/fco) suggested by Liu et al. [11], but it should be noted that kε is valued as 0.594 when determining the types of stress-strain curve; (5) The confinement of stirrups is negligible because the stirrups used in this study have relatively large spacing and small diameter; and (6) The steel tube provides lateral confining stress only and has negligible longitudinal stress due to the following two reasons: (a) the steel tube is disconnected at both ends without bearing any direct axial load; and (b) the steel tube has a relatively larger diameter-to-thickness ratio (1 0 0), resulting in a small steel ratio.

f fcc =fco ⎜⎛1+3.5 l ⎞⎟ fco ⎠ ⎝

(4)

f f ⎞ ⎛ fcc =fco ⎜-0.413+1.413 1+11.4 l -2 l ⎟ f f co co ⎠ ⎝

(5)

fl =

5. Conclusions

2(ts fy + kε tcf εfu Ecf ) Dc

(6)

In this study, 20 specimens were tested to failure to firstly

Fig. 19. Typical load versus stress curves for the longitudinal rebars in C-STRC columns. 11

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Fig. 20. Typical load versus stress curves for the longitudinal rebars in CRC and STRC columns.

The bi-linear type is more likely for the C-STRC columns with lower concrete strength and smaller load eccentricity. (5) The yielding of the steel tube in C-STRC columns in the compression region generally occurs approximately at the initial point of the second branch of load versus mid-span lateral displacement curves, followed by the yielding of steel tube in the tension region. (6) The load capacity and deformability of the specimens with lower concrete strength are significantly improved due to the use of CFRP. The load capacity decreases with an increasing load eccentricity, while the deformability increases accordingly. In addition, the load bearing capacity increases with the increasing concrete strength, but the deformability decreases dramatically. For the specimens with the concrete strength of C80, increasing the number of CFRP layers does not significantly improve the load capacity and deformability unless the load eccentricity is large enough. (7) The N-M interaction diagrams are generated by the plastic stress distribution method, in which a reduction factor of 0.65 is used to calculate the confining stress. The predicted results are generally in good agreement with the test results. The pure bending moment is almost the same with different CFRP layers and concrete strengths, while the axial load bearing capacity increases with the increase of CFRP layers and concrete strength.

Fig. 21. Generation of N-M curves.

investigate the behaviour of the CFRP-steel composite tubed reinforced concrete stub columns under eccentric compression. Experimental results including failure modes, load versus deformation curves, and load versus stress curves of steel tube and longitudinal rebars were obtained and are discussed in detail. The study results manifest the following major findings. (1) All C-STRC columns fail by the explosive rupture of CFRP, occurring at the peak load for the specimens with concrete strength of C40 and C60 and after the peak load for the specimens with concrete strength of C80. The failure mode is characterized as bending failure with the concrete crushed in the compression region and flexural cracks in the tension region. The deformation of the concrete in CRC columns is most serious among the three types of columns studied. (2) The lateral deformation shape of C-STRC columns matches well with the second-order parabola. The increase in the lateral deformation is more evident for the specimens with CFRP than those without CFRP. (3) The section of C-STRC columns subjected to eccentric loading remains plane after bending, and the usual plane section assumption remains valid. (4) Three basic types of load versus mid-span lateral displacement curves are observed: bi-linear, elastic-plastic, and linear-parabolic.

CRediT authorship contribution statement Tianxiang Xu: Conceptualization, Data curation, Investigation, Methodology, Project administration, Software, Validation, Writing original draft, Writing - review & editing. Jiepeng Liu: Conceptualization, Formal analysis, Funding acquisition, Project administration, Supervision, Validation, Writing - original draft, Writing review & editing. Xuanding Wang: Methodology, Supervision, Validation, Writing - original draft, Writing - review & editing. Ying Guo: Conceptualization, Investigation, Project administration, Supervision, Validation, Writing - original draft, Writing - review & editing. Y. Frank Chen: Writing - original draft, Writing - review & editing.

Fig. 22. Influence of CFRP layers and concrete strength on N-M interaction diagrams. 12

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Table A.1 Variation coefficient of concrete. fcu,k δ 1

15 0.21

20 0.18

25 0.16

30 0.14

35 0.13

40 0.12

45 0.12

50 0.11

55 0.11

60 0.1

65 0.1

70 0.1

75 0.1

80 0.1

85 0.11

90 0.11

95 0.11

100 0.11

105 0.11

The variation coefficient of concrete over C80 is determined by the linear extension of the coefficients.

Table A.2 Concrete strength relationship. fcu,k fck

15 12

20 16

25 20

30 25

37 30

45 35

50 40

55 45

60 50

67 55

75 60

85 70

95 80

105 90

Declaration of Competing Interest

Acknowledgements

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (51622802, 51438001).

Appendix A. Transferring of concrete strength First, the cubic characteristic strength of concrete (fcu,k) is calculated using the average measured cubic concrete strength (fcu,m) [34] according to Eq. (A.1).

fcu,k = fcu,m (1 − 1.645δ )

(A.1)

where δ is the variation coefficient of concrete [38], with the representative values listed in Table A.1. Note that the linear interpolation is permitted to determine a δ value. fcu,k is then converted into the characteristic cylinder strength (fck) based on the relationship between fcu,k and fck (EC2-1-1 2004), as shown in Table A.2. Finally, the unconfined concrete strength (fco) is calculated by Eq. (A.2) (EC2-1-1 2004).

fco = fck + 8

(A.2)

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