# Experimental Study on CFRP-Confined Circularized Concrete-Filled Square Steel Tube Short Columns

Authors: Yuchuan Wen; Zhongjun Hu; Anningjing Li; Quanheng Li; Xuepeng Li; Yan Xu
Journal: Advances in Materials Science and Engineering
 (2021)

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## Abstract

This study investigates the suitability of the circularization technique for strengthening square concrete-filled square steel tube (CFSST) short columns. A total of 16 specimens were tested under axial compression. The main parameters under investigation were concrete strength, the thickness of arc cement mortar layer components (CAM), and the layers of carbon fiber-reinforced polymer (CFRP) sheets. Test results indicated that the failure mode of CFRP-confined circularized CFSST (C-C-CFSST) columns was similar to that of CFRP-confined concrete columns. The CFRP-confined circularized strengthening method can increase confinement efficacy and reduce the stress concentration at the corners of CFSST columns. Three existing CFRP-confined concrete stress-strain models were evaluated using the test results. The predictions of the Lam and Teng stress-strain model agree well with the test data.


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## Body

## 1. Introduction

Concrete-filled steel tube (CFST) has the advantages of high bearing capacity and ductility and is widely used in civil structures [1, 2]. However, the exposed CFST structures are easily failed by corrosion in engineering practice, especially in the moisture environment [3–5]. When the corrosion occurs on steel tube, the durability and bearing capacity of CFST will degrade [6]. Consequently, finding a method to enhance the corrosion resistance of CFST columns is necessary [7].Fiber-reinforced polymer (FRP) composites have been widely used in retrofitting existing columns [8, 9]. FRP-confined concrete has been proven to be feasible in theoretical research and engineering practice [10]. Strengthening CFST columns with FRP material has the dual advantages of improving bearing capacity and durability [11–13].In recent years, concrete-filled square steel tube (CFSST) has been increasingly applied in various building structures because of its advantages of easy joint connection and construction [14–16].Tao, Han, and Wang studied the section shape influence on the axial compression performance of CFRP-confined CFST short columns. The results indicated that the CFRP confinement efficacy of a CFSST column is lower than a circular CFST column because of the stress concentration at the corners of the square steel tube and the reduction of the effective area of the confined section [17, 18].To improve the confinement efficiency of CFSST columns by CFRP jackets and to reduce stress concentration, the circularizing technique has been proven to be an effective method before FRP wrapping by some scholars. The experimental study of Priestley and Seible first indicated that shape modification by bonding concrete segments can improve the confinement efficiency of CFRP jackets [19]. Hadi et al. carried out relevant research on the CFRP-confined arc-treated concrete rectangular columns; the results show that using precast concrete arc-treated components as transitions between CFRP and rectangular columns could significantly reduce stress concentration and enhance the effective constraint area of the cross section [20, 21]. The above studies showed that circularizing concrete columns by bonding precast segments can increase the axial load capacity and change the stress-strain curve from softening to hardening the branch of reinforced concrete (RC) columns [20].Yang et al. performed an experimental study on the axial compressive performance of rectangular concrete-filled FRP-steel composite tube columns for various corner radiuses and proposed that FRP-confined CFSST concrete stress-strain curve can be divided into four phases (i.e., initial linear phase, transition to yield phase, hardening phase, and residual phase). Different corner radii significantly affect the confinement effectiveness and the third phase of the FRP-confined CFSST stress-strain curve [22]. Most of the existing CFSST columns have sharp corners, which cause stress concentration, and the CFSST columns cannot round the corners similar to RC columns in practical engineering. Therefore, shape modification before FRP wrapping may effectively reduce stress concentration. To solve this problem further, an experimental study was undertaken to investigate the suitability of the circularization technique for strengthening CFSST short columns. This study utilizes the bonding CAM components between FRP and the CFSST column as a circularizing method. Sixteen specimens were tested under axial compression to study the influence of different CAM thicknesses (the middle height of CAM component), layers of CFRP, and concrete strength on bearing capacity, deformation performance, and stress-strain relationship.


## 2. Experimental Program

### 2.1. Test Specimens

All of the specimens were 100 mm × 100 mm in cross section and 300 mm in height. Twelve specimens were C-C-CFSST columns, two specimens were CFRP-confined CFSST columns, and two specimens were CFSST columns. Sixteen specimens were divided into two groups according to the concrete strength. The specimens of group 1 were C20, and those of group 2 were C30. Each group had six C-C-CFSST specimens with 5, 10, and 15 mm CAM thickness. The corresponding radius of rounded corners was 20, 30, and 40 mm. T700 CFRP sheets with 1.72% elongation were used in this test. The performances of steel tubes, epoxy adhesive, and CFRP sheets were tested in a structural laboratory, as shown in Table1. The test specimens are listed in Table 2. The cross section and FRP bonding position of specimens are shown in Figure 1.Table 1
Material properties.
MaterialsThickness (mm)Yield strength (MPa)Tensile strength (MPa)Tensile elastic modulus (MPa)Steel tube2313.9392.62.07 × 105CFRP0.167—30942.44 × 105Epoxy resin——582.584 × 103Table 2
Test parameters of specimens.
SpecimenCAM thicknessConfinement conditionC20-0-0-1——C20-0-1-2—1-layer CFRP confinementC20-5-1-35 mm1-layer CFRP confinementC20-5-2-45 mm2-layer CFRP confinementC20-10-1-510 mm1-layer CFRP confinementC20-10-2-610 mm2-layer CFRP confinementC20-15-1-715 mm1-layer CFRP confinementC20-15-2-815 mm2-layer CFRP confinementC30-0-0-9——C30-0-1-10—1-layer CFRP confinementC30-5-1-115 mm1-layer CFRP confinementC30-5-2-125 mm2-layer CFRP confinementC30-10-1-1310 mm1-layer CFRP confinementC30-10-2-1410 mm2-layer CFRP confinementC30-15-1-1515 mm1-layer CFRP confinementC30-15-2-1615 mm2-layer CFRP confinementFigure 1
Cross sections of specimens. (a) CFSST column. (b) CFRP-confined CFSST column. (c) C-C-CFSST column.
(a)(b)(c)The concrete specimens were prepared with Portland cement. The diameter of the coarse aggregate was 5–10 mm, which was used for fine aggregate in continuous grading and medium sand. The axial compressive strength measured values of two groups’ specimens were 20.7 and 27.1 MPa.The main processes of specimen preparation are as follows: (1) Prefabricated CAM was configured with a high mark cement mortar, and the CAM mold was made with a PVC tube and a plate. The specimen and the CAM should have similar strength values to satisfy the equal-strength principle. The test using CAM strength was slightly higher than the specimen. (2) The epoxy resin was smeared on the surface of the steel tube, and the CAM was bonded on corresponding positions. (3) The CAM components were fixed to dry using adjustable circular steel rings for 48 h. (4) The specimens were wrapped with CFRP sheets after circularizing. The overlap length of the CFRP was 100 mm. The making process of specimen is shown in Figure2.Figure 2
Production process of specimens. (a) CFSST column. (b) CAM bonding. (c) CAM fixing. (d) CFRP wrapping.
(a)(b)(c)(d)


### 2.2. Test Setup and Instrumentation

All specimens were tested under axial compression using a pressure testing machine with 2000 kN capacity. Four axial strain gauges and four hoop strain gauges were pasted on the mid-height of the specimen. Four linear variable differential transducers (LVDTs) were used to monitor the axial deformation of specimens. The LVDTs were installed at the corner of the specimen and covered the mid-height of the specimen. The layout of the test setup and measuring point are shown in Figure3. The loading program was based on standard for test method of concrete structures (GB/T 50152–2012) [23]. To avoid the premature failure of specimens, the top and bottom ends of specimens were wrapped with additional two layers of CFRP with 50 mm width.Figure 3
Loading apparatus and LVDTs.


## 2.1. Test Specimens

All of the specimens were 100 mm × 100 mm in cross section and 300 mm in height. Twelve specimens were C-C-CFSST columns, two specimens were CFRP-confined CFSST columns, and two specimens were CFSST columns. Sixteen specimens were divided into two groups according to the concrete strength. The specimens of group 1 were C20, and those of group 2 were C30. Each group had six C-C-CFSST specimens with 5, 10, and 15 mm CAM thickness. The corresponding radius of rounded corners was 20, 30, and 40 mm. T700 CFRP sheets with 1.72% elongation were used in this test. The performances of steel tubes, epoxy adhesive, and CFRP sheets were tested in a structural laboratory, as shown in Table1. The test specimens are listed in Table 2. The cross section and FRP bonding position of specimens are shown in Figure 1.Table 1
Material properties.
MaterialsThickness (mm)Yield strength (MPa)Tensile strength (MPa)Tensile elastic modulus (MPa)Steel tube2313.9392.62.07 × 105CFRP0.167—30942.44 × 105Epoxy resin——582.584 × 103Table 2
Test parameters of specimens.
SpecimenCAM thicknessConfinement conditionC20-0-0-1——C20-0-1-2—1-layer CFRP confinementC20-5-1-35 mm1-layer CFRP confinementC20-5-2-45 mm2-layer CFRP confinementC20-10-1-510 mm1-layer CFRP confinementC20-10-2-610 mm2-layer CFRP confinementC20-15-1-715 mm1-layer CFRP confinementC20-15-2-815 mm2-layer CFRP confinementC30-0-0-9——C30-0-1-10—1-layer CFRP confinementC30-5-1-115 mm1-layer CFRP confinementC30-5-2-125 mm2-layer CFRP confinementC30-10-1-1310 mm1-layer CFRP confinementC30-10-2-1410 mm2-layer CFRP confinementC30-15-1-1515 mm1-layer CFRP confinementC30-15-2-1615 mm2-layer CFRP confinementFigure 1
Cross sections of specimens. (a) CFSST column. (b) CFRP-confined CFSST column. (c) C-C-CFSST column.
(a)(b)(c)The concrete specimens were prepared with Portland cement. The diameter of the coarse aggregate was 5–10 mm, which was used for fine aggregate in continuous grading and medium sand. The axial compressive strength measured values of two groups’ specimens were 20.7 and 27.1 MPa.The main processes of specimen preparation are as follows: (1) Prefabricated CAM was configured with a high mark cement mortar, and the CAM mold was made with a PVC tube and a plate. The specimen and the CAM should have similar strength values to satisfy the equal-strength principle. The test using CAM strength was slightly higher than the specimen. (2) The epoxy resin was smeared on the surface of the steel tube, and the CAM was bonded on corresponding positions. (3) The CAM components were fixed to dry using adjustable circular steel rings for 48 h. (4) The specimens were wrapped with CFRP sheets after circularizing. The overlap length of the CFRP was 100 mm. The making process of specimen is shown in Figure2.Figure 2
Production process of specimens. (a) CFSST column. (b) CAM bonding. (c) CAM fixing. (d) CFRP wrapping.
(a)(b)(c)(d)


## 2.2. Test Setup and Instrumentation

All specimens were tested under axial compression using a pressure testing machine with 2000 kN capacity. Four axial strain gauges and four hoop strain gauges were pasted on the mid-height of the specimen. Four linear variable differential transducers (LVDTs) were used to monitor the axial deformation of specimens. The LVDTs were installed at the corner of the specimen and covered the mid-height of the specimen. The layout of the test setup and measuring point are shown in Figure3. The loading program was based on standard for test method of concrete structures (GB/T 50152–2012) [23]. To avoid the premature failure of specimens, the top and bottom ends of specimens were wrapped with additional two layers of CFRP with 50 mm width.Figure 3
Loading apparatus and LVDTs.


## 3. Test Results and Discussion

### 3.1. Main Test Results

The key test results of axial compression specimens are shown in Table3. fc0 is the compressive strength of unconfined concrete columns, fco′ is the compressive strength calculated value of CFSST, and N is the ultimate bearing capacity of specimens.Table 3
Experimental results of specimens.
Specimenfc0 (MPa)fco′ (MPa)N (kN)C20-0-0-120.745.82488.0C20-0-1-220.745.82542.7C20-5-1-320.745.82650.5C20-5-2-420.745.82765.0C20-10-1-520.745.82760.0C20-10-2-620.745.82875.6C20-15-1-720.745.82800.4C20-15-2-820.745.821019.3C30-0-0-927.153.39539.9C30-0-1-1027.153.39631.6C30-5-1-1127.153.39738.3C30-5-2-1227.153.39867.1C30-10-1-1327.153.39843.9C30-10-2-1427.153.39950.3C30-15-1-1527.153.39893.4C30-15-2-1627.153.391069.8


### 3.2. Test Failure Modes

The typical failure mode of specimens is shown in Figure4. The tested CFRP-confined CFSST columns failed by CFRP jacket rupture near the corners. These ruptures occurred in the mid-height region of all the specimens. The failure mode of C-C-CFSST columns was similar to CFRP-confined concrete columns.Figure 4
Failure mode of some specimens.The specific breakpoint locations of test specimens after loading are shown in Figure5. L is the horizontal distance from the breakpoint to the corner. The CFRP-confined CFSST column failed by CFRP rupture at the corner of the steel tube because of stress concentration. The CFRP breakpoints of C-C-CFSST columns occurred away from the corner when CAM thickness increases from 5 mm to 15 mm. The changing position of CFRP breakpoints showed that the stress concentration of the steel tube corner gradually reduced with the increasing CAM thickness.Figure 5
Influence of CAM thickness on CFRP breakpoint location.


### 3.3. Load-Strain Response

Figure6 shows the load-strain curves of C-C-CFSST specimens (group 2). The axial and hoop strains were obtained by the average of four axial strain gauges and four hoop strain gauges, respectively. For specimens C30-5-1-11, C30-10-1-13, and C30-15-1-15, the ultimate load is 738.3, 843.9, and 893.4 kN, respectively. For specimens C30-5-2-12, C30-10-2-4, and C30-15-2-16, the ultimate load is 867.1, 950.3, and 1069.8 kN, respectively. Similar to those FRP-confined concrete load-strain curves, all specimens’ curves showed the same trend with a bilinear shape and a monotonically ascending characteristic. When the load was less than 80% of the ultimate load, the axial and hoop strain developed slowly. When the load was more than 80% of the ultimate load, the curves came into the plastic stage, and the deformation grew rapidly. The hoop rupture failure of CFRP occurred when reaching the ultimate loads of specimens, and the ultimate hoop strain slightly increased with the increasing CAM thickness.Figure 6
Test load-strain curves. (a) Specimens warped with one-layer CFRP. (b) Specimens warped with two-layer CFRP.
(a)(b)


### 3.4. CAM Influence on Bearing Capacity and Vertical Displacement

Figures7 and 8 show vertical displacement and bearing capacity of test specimens with different CAM thickness. When the CAM thickness increases from 5 mm to 15 mm, the bearing capacity and vertical displacement increase gradually. Compared with C20-0-1-2, the bearing capacity of C20-5-1-3, C20-10-1-5, and C20-15-1-7 increased by 19.9%, 40.2%, and 47.5%, respectively. Compared with C30-0-1-10, the bearing capacity of C30-5-1-11, C30-10-1-13, and C30-15-1-15 increased by 16.9%, 33.6%, and 41.4%, respectively. The increasing bearing capacity and vertical displacement showed the great effectiveness of CAM between CFRP sheets and CFSST columns. The increase of the CAM thickness generally leads to an increase in the bearing capacity and vertical displacement, which indicated that the circularization technique for strengthening CFSST short columns is a suitable and alternative strengthening method in engineering.Figure 7
The effects of CAM thickness on vertical displacement.Figure 8
The effects of CAM thickness on bearing capacity.


## 3.1. Main Test Results

The key test results of axial compression specimens are shown in Table3. fc0 is the compressive strength of unconfined concrete columns, fco′ is the compressive strength calculated value of CFSST, and N is the ultimate bearing capacity of specimens.Table 3
Experimental results of specimens.
Specimenfc0 (MPa)fco′ (MPa)N (kN)C20-0-0-120.745.82488.0C20-0-1-220.745.82542.7C20-5-1-320.745.82650.5C20-5-2-420.745.82765.0C20-10-1-520.745.82760.0C20-10-2-620.745.82875.6C20-15-1-720.745.82800.4C20-15-2-820.745.821019.3C30-0-0-927.153.39539.9C30-0-1-1027.153.39631.6C30-5-1-1127.153.39738.3C30-5-2-1227.153.39867.1C30-10-1-1327.153.39843.9C30-10-2-1427.153.39950.3C30-15-1-1527.153.39893.4C30-15-2-1627.153.391069.8


## 3.2. Test Failure Modes

The typical failure mode of specimens is shown in Figure4. The tested CFRP-confined CFSST columns failed by CFRP jacket rupture near the corners. These ruptures occurred in the mid-height region of all the specimens. The failure mode of C-C-CFSST columns was similar to CFRP-confined concrete columns.Figure 4
Failure mode of some specimens.The specific breakpoint locations of test specimens after loading are shown in Figure5. L is the horizontal distance from the breakpoint to the corner. The CFRP-confined CFSST column failed by CFRP rupture at the corner of the steel tube because of stress concentration. The CFRP breakpoints of C-C-CFSST columns occurred away from the corner when CAM thickness increases from 5 mm to 15 mm. The changing position of CFRP breakpoints showed that the stress concentration of the steel tube corner gradually reduced with the increasing CAM thickness.Figure 5
Influence of CAM thickness on CFRP breakpoint location.


## 3.3. Load-Strain Response

Figure6 shows the load-strain curves of C-C-CFSST specimens (group 2). The axial and hoop strains were obtained by the average of four axial strain gauges and four hoop strain gauges, respectively. For specimens C30-5-1-11, C30-10-1-13, and C30-15-1-15, the ultimate load is 738.3, 843.9, and 893.4 kN, respectively. For specimens C30-5-2-12, C30-10-2-4, and C30-15-2-16, the ultimate load is 867.1, 950.3, and 1069.8 kN, respectively. Similar to those FRP-confined concrete load-strain curves, all specimens’ curves showed the same trend with a bilinear shape and a monotonically ascending characteristic. When the load was less than 80% of the ultimate load, the axial and hoop strain developed slowly. When the load was more than 80% of the ultimate load, the curves came into the plastic stage, and the deformation grew rapidly. The hoop rupture failure of CFRP occurred when reaching the ultimate loads of specimens, and the ultimate hoop strain slightly increased with the increasing CAM thickness.Figure 6
Test load-strain curves. (a) Specimens warped with one-layer CFRP. (b) Specimens warped with two-layer CFRP.
(a)(b)


## 3.4. CAM Influence on Bearing Capacity and Vertical Displacement

Figures7 and 8 show vertical displacement and bearing capacity of test specimens with different CAM thickness. When the CAM thickness increases from 5 mm to 15 mm, the bearing capacity and vertical displacement increase gradually. Compared with C20-0-1-2, the bearing capacity of C20-5-1-3, C20-10-1-5, and C20-15-1-7 increased by 19.9%, 40.2%, and 47.5%, respectively. Compared with C30-0-1-10, the bearing capacity of C30-5-1-11, C30-10-1-13, and C30-15-1-15 increased by 16.9%, 33.6%, and 41.4%, respectively. The increasing bearing capacity and vertical displacement showed the great effectiveness of CAM between CFRP sheets and CFSST columns. The increase of the CAM thickness generally leads to an increase in the bearing capacity and vertical displacement, which indicated that the circularization technique for strengthening CFSST short columns is a suitable and alternative strengthening method in engineering.Figure 7
The effects of CAM thickness on vertical displacement.Figure 8
The effects of CAM thickness on bearing capacity.


## 4. Stress-Strain Models of CFSST Columns

### 4.1. Axial Stress-Strain Curves

The axial stress-axial strain curves of all the test specimens are shown in Figure9. All the curves had an obvious bilinear shape with two segments. The first-segment slope of the curve was much bigger than the second-segment slope. The CAM thickness affected mainly the second segment of the stress-strain curve. The second-segment slopes of C-C-CFSST specimens became slightly larger with the increase of CAM thickness. The ultimate axial stress fcc′ was affected by the CAM thickness and the layers of CFRP. As for specimens with no CAM, fcc′ and the second-segment slope were the smallest. The stress-strain curve of C20-5-1-3 and C30-5-1-11 was close to the stress-strain curve of C20-0-1-2 and C30-0-1-11, respectively, showing that CFRP wrapping was less effective for specimens with a CAM thickness of 5 mm. The specimens with a CAM thickness of 10 or 15 mm increased the effectiveness of CFRP confinement. To ensure the strengthening effectiveness in practical engineering, the CAM thickness should be large. The layers of CFRP affected fcc′ and ductility. The ultimate axial strain εcc′and ultimate axial stress fcc′ of specimens with two layers of CFRP were significantly larger than those of specimens with one layer of CFRP.Figure 9
Test stress-strain curves. (a) Specimens of group C20. (b) Specimens of group C30.
(a)(b)


### 4.2. Existing Stress-Strain Models

The existing FRP-confined concrete stress-strain models are mainly separated into two types. The first type uses a single function to express the stress-strain relationship and includes the Mander model, Samaan model, Yu model, and Yang and Feng model [24–27]. The second type uses piecewise function to express the stress-strain relationship and includes the Lam and Teng model, Lai model, Miyauchi model, and Wei and Wu model [28–34]. Among all existing models, the Lam and Teng model, Lai model, and Yang model are appropriate to predict the stress-strain relationship of CFRP-confined circularized concrete columns according to the published literature [8, 27].


#### 4.2.1. Lam and Teng Model

The first segment of the Lam and Teng model is a parabolic type, and the second segment is a linear type. This model has a high degree of accuracy in predicting FRP-confined concrete strength. The model is described by the following equation:(1)σc=Ecεc−Ec−E24f0εc20≤εc≤εt,σc=fco′+E2εcεt≤εc≤εcu,where σc and εc are the axial stress and axial strain, respectively. The ultimate axial stress and the ultimate strain are calculated as follows:(2)fcc′fco′=1+3.3k1flfco′,εcuεco=1.75+12ksflfcoεruεco0.45,where εru is the confinement effectiveness coefficient k1 and transition strain εt is given as follows:(3)ks=1−b−2r2+h−2r23Acor,εt=2f0Ec−E2,where Ec=4730fco′ is the elastic modulus of the unconfined concrete, E2=fcc′−f0/εcu is the slope of the linear second portion, εco=0.002 is the axial strain with ultimate load, and ks is the constraint coefficient.


#### 4.2.2. Lai Model

The Lai model has a high accuracy to predict the CFRP-confined rectangular concrete column with corner radii, which is described by the following equation:(4)σz=εzA+Bεz+Cεz2,0≤εz≤εzb,σz=σzb+E2εz−εzb,εzb≤εz≤εzc.A, B, and C are given as follows:(5)A=1E0,B=1Ep−2E0+1EpE2Ep,C=1E0−1EpE2Ep1εt2,where Ep=σzb/εzb.FRP-confined concreteE2/Ec in different sections is given as follows:(6)E2Ec=0.0331lnβj−0.0564,βj≥5.6,0.1217lnβj−0.2091,βj<5.6.Constraint stiffnessβj is given as follows:(7)βj=EftffcR,where R represents the radii of equivalent circle = 2(b + h)/2π.Transition stress and strain are given as follows:(8)σzbfc,m=0.0568βj0.46+1,εtεcu=0.011βj+1.


#### 4.2.3. Yang and Feng Model

The Yang and Feng model is different from the two above models, which have no obvious transition segment. This model has high accuracy to predict the CFRP-confined concrete column, which is given as follows:(9)σc=εc/εcc∗fcc∗rr−1+εc/εcc∗r,r=EcEc−fcc∗/εcc,fcc∗εcc=1+3.33σlfco′0.9,εcc∗εcc=1+17.4σlfco′1.07.where fcc∗ and εcc∗ are the peak axial stress and corresponding axial strain of concrete under a specific level of lateral confining stress.


### 4.3. CFSST Column Strengthfco′

CFSST column strengthfco′ is given in technical code for concrete filled steel tubular structures (GB50936-2014) [35]. It is calculated as follows:(10)fco′=1.212+Bθsc+Cθsc2fco,B=0.131fy235+0.723,C=−0.07fck14.4+0.026,θsc=αscffc,αsc=AsAc,where As and Ac are the steel tube area and core concrete area, respectively; fy and f are the tensile strength standard value and design value, respectively; αsc and θsc are the steel ratio and confinement coefficient of the specimen, respectively; B and C are the influence coefficients.


### 4.4. Effective CFRP Confinement Coefficientke

The theoretical fracture strainεfu can be calculated as fiber strength divided by the elastic modulus. However, the actual fracture strain εru is much smaller than the theoretical fracture strain. Lam and Teng suggested that εru can be calculated from εfu as follows:(11)εru=keεfu,where the effective CFRP confinement coefficient k of the circular column is approximately 0.586 [15] and was taken as 0.5, 0.53, and 0.56 corresponding with CAM thickness of 5, 10, and 15 mm, respectively, according to the test results.


### 4.5. Intercept of the Stress Axis by the Linear Second Portionf0

Lam and Teng showedf0/fco′=1.09 from the test and suggested that f0=fco′ approximately [15]. However, this method ignores the influence of FRP confinement. The intercept f0 was affected by the confinement effectiveness, which can be calculated by confinement stiffness ratio βj and confining factor ξ. Yu [26] suggested that f0 can be calculated as follows:(12)f0=1+1.1ξfc′.However, for FRP-confined CFSST columns, confining factorξ should value FRP and steel tube confining factor, and f0 is given as follows:(13)f0fco'=1+kξ,where k is modified based on the test results. The linear fitting between f0/fco′ and ξ is shown in Figure 10, and k = 0.04854.Figure 10
Relationship betweenf0/fco′ and ξ.


### 4.6. Stress-Strain Model Verification

The experimental stress-strain curves of 12 C-C-CFSST columns were compared with the calculation curves of the Lam and Teng model, Lai model, and Yang and Feng model. The comparison of calculated stress-strain curves with experiment curve is shown in Figures11 and 12.Figure 11
Comparison of calculated stress-strain curves with the experiment curve of group C20. (a) C20-5-1-3. (b) C20-5-2-4. (c) C20-10-1-5. (d) C20-10-2-6. (e) C20-15-1-7. (f) C20-15-2-8.
(a)(b)(c)(d)(e)(f)Figure 12
Comparison of calculated stress-strain curves with the experiment curve of group C30. (a) C30-5-1-11. (b) C30-5-2-12. (c) C30-10-1-13. (d) C30-10-2-14. (e) C30-15-1-15. (f) C30-15-2–16.
(a)(b)(c)(d)(e)(f)The Lam and Teng model had the highest fitting grade on C-C-CFSST column stress-strain curves among three models. The Yang and Feng model fitted well in some situations, such as C20-10-2-6, C20-15-1-7, C30-5-1-11, and C30-15-2-16. The Lai model had a big deviation compared with other models. The stress-strain curves of the C-C-CFSST column can be separated into three segments, as shown in Figure13.Figure 13
Proposed stress-strain model for C-C-CFSST.In segment I, the Lam and Teng model shows a great prediction on the stress-strain relationship of the C-C-CFSST column. The Lai model and the Yang and Feng model generally underestimated the axial stress of specimens in segment I. The Lam and Teng model has an unobvious segment II slightly overestimating the axial stress. The Yang and Feng model has a similar trend to the experiential curves of segment II. Although similar to segment I, this model underestimates the axial stress of specimens. The Lai model also greatly underestimates the axial stress because of the inaccuracy of the calculated transition strain. In segment III, the ultimate axial stressfcc' calculated from the Lam and Teng model and the Yang and Feng model is well estimated to the test value. The stress-strain curves calculated from the Lam and Teng model are dramatically close to the test curves. In conclusion, the Lam and Teng model has the greatest prediction for the stress-strain relationship of the C-C-CFSST column among the three models. The Yang model has a more accurate prediction, while CAM thickness is increasing. The transition strain of the Lai model is always larger than the test transition strain, which leads to the inaccuracy of the calculated curves. A more accurate stress-strain model for C-C-CFSST columns should be developed in experimental and theoretical research.


## 4.1. Axial Stress-Strain Curves

The axial stress-axial strain curves of all the test specimens are shown in Figure9. All the curves had an obvious bilinear shape with two segments. The first-segment slope of the curve was much bigger than the second-segment slope. The CAM thickness affected mainly the second segment of the stress-strain curve. The second-segment slopes of C-C-CFSST specimens became slightly larger with the increase of CAM thickness. The ultimate axial stress fcc′ was affected by the CAM thickness and the layers of CFRP. As for specimens with no CAM, fcc′ and the second-segment slope were the smallest. The stress-strain curve of C20-5-1-3 and C30-5-1-11 was close to the stress-strain curve of C20-0-1-2 and C30-0-1-11, respectively, showing that CFRP wrapping was less effective for specimens with a CAM thickness of 5 mm. The specimens with a CAM thickness of 10 or 15 mm increased the effectiveness of CFRP confinement. To ensure the strengthening effectiveness in practical engineering, the CAM thickness should be large. The layers of CFRP affected fcc′ and ductility. The ultimate axial strain εcc′and ultimate axial stress fcc′ of specimens with two layers of CFRP were significantly larger than those of specimens with one layer of CFRP.Figure 9
Test stress-strain curves. (a) Specimens of group C20. (b) Specimens of group C30.
(a)(b)


## 4.2. Existing Stress-Strain Models

The existing FRP-confined concrete stress-strain models are mainly separated into two types. The first type uses a single function to express the stress-strain relationship and includes the Mander model, Samaan model, Yu model, and Yang and Feng model [24–27]. The second type uses piecewise function to express the stress-strain relationship and includes the Lam and Teng model, Lai model, Miyauchi model, and Wei and Wu model [28–34]. Among all existing models, the Lam and Teng model, Lai model, and Yang model are appropriate to predict the stress-strain relationship of CFRP-confined circularized concrete columns according to the published literature [8, 27].


### 4.2.1. Lam and Teng Model

The first segment of the Lam and Teng model is a parabolic type, and the second segment is a linear type. This model has a high degree of accuracy in predicting FRP-confined concrete strength. The model is described by the following equation:(1)σc=Ecεc−Ec−E24f0εc20≤εc≤εt,σc=fco′+E2εcεt≤εc≤εcu,where σc and εc are the axial stress and axial strain, respectively. The ultimate axial stress and the ultimate strain are calculated as follows:(2)fcc′fco′=1+3.3k1flfco′,εcuεco=1.75+12ksflfcoεruεco0.45,where εru is the confinement effectiveness coefficient k1 and transition strain εt is given as follows:(3)ks=1−b−2r2+h−2r23Acor,εt=2f0Ec−E2,where Ec=4730fco′ is the elastic modulus of the unconfined concrete, E2=fcc′−f0/εcu is the slope of the linear second portion, εco=0.002 is the axial strain with ultimate load, and ks is the constraint coefficient.


### 4.2.2. Lai Model

The Lai model has a high accuracy to predict the CFRP-confined rectangular concrete column with corner radii, which is described by the following equation:(4)σz=εzA+Bεz+Cεz2,0≤εz≤εzb,σz=σzb+E2εz−εzb,εzb≤εz≤εzc.A, B, and C are given as follows:(5)A=1E0,B=1Ep−2E0+1EpE2Ep,C=1E0−1EpE2Ep1εt2,where Ep=σzb/εzb.FRP-confined concreteE2/Ec in different sections is given as follows:(6)E2Ec=0.0331lnβj−0.0564,βj≥5.6,0.1217lnβj−0.2091,βj<5.6.Constraint stiffnessβj is given as follows:(7)βj=EftffcR,where R represents the radii of equivalent circle = 2(b + h)/2π.Transition stress and strain are given as follows:(8)σzbfc,m=0.0568βj0.46+1,εtεcu=0.011βj+1.


### 4.2.3. Yang and Feng Model

The Yang and Feng model is different from the two above models, which have no obvious transition segment. This model has high accuracy to predict the CFRP-confined concrete column, which is given as follows:(9)σc=εc/εcc∗fcc∗rr−1+εc/εcc∗r,r=EcEc−fcc∗/εcc,fcc∗εcc=1+3.33σlfco′0.9,εcc∗εcc=1+17.4σlfco′1.07.where fcc∗ and εcc∗ are the peak axial stress and corresponding axial strain of concrete under a specific level of lateral confining stress.


## 4.2.1. Lam and Teng Model

The first segment of the Lam and Teng model is a parabolic type, and the second segment is a linear type. This model has a high degree of accuracy in predicting FRP-confined concrete strength. The model is described by the following equation:(1)σc=Ecεc−Ec−E24f0εc20≤εc≤εt,σc=fco′+E2εcεt≤εc≤εcu,where σc and εc are the axial stress and axial strain, respectively. The ultimate axial stress and the ultimate strain are calculated as follows:(2)fcc′fco′=1+3.3k1flfco′,εcuεco=1.75+12ksflfcoεruεco0.45,where εru is the confinement effectiveness coefficient k1 and transition strain εt is given as follows:(3)ks=1−b−2r2+h−2r23Acor,εt=2f0Ec−E2,where Ec=4730fco′ is the elastic modulus of the unconfined concrete, E2=fcc′−f0/εcu is the slope of the linear second portion, εco=0.002 is the axial strain with ultimate load, and ks is the constraint coefficient.


## 4.2.2. Lai Model

The Lai model has a high accuracy to predict the CFRP-confined rectangular concrete column with corner radii, which is described by the following equation:(4)σz=εzA+Bεz+Cεz2,0≤εz≤εzb,σz=σzb+E2εz−εzb,εzb≤εz≤εzc.A, B, and C are given as follows:(5)A=1E0,B=1Ep−2E0+1EpE2Ep,C=1E0−1EpE2Ep1εt2,where Ep=σzb/εzb.FRP-confined concreteE2/Ec in different sections is given as follows:(6)E2Ec=0.0331lnβj−0.0564,βj≥5.6,0.1217lnβj−0.2091,βj<5.6.Constraint stiffnessβj is given as follows:(7)βj=EftffcR,where R represents the radii of equivalent circle = 2(b + h)/2π.Transition stress and strain are given as follows:(8)σzbfc,m=0.0568βj0.46+1,εtεcu=0.011βj+1.


## 4.2.3. Yang and Feng Model

The Yang and Feng model is different from the two above models, which have no obvious transition segment. This model has high accuracy to predict the CFRP-confined concrete column, which is given as follows:(9)σc=εc/εcc∗fcc∗rr−1+εc/εcc∗r,r=EcEc−fcc∗/εcc,fcc∗εcc=1+3.33σlfco′0.9,εcc∗εcc=1+17.4σlfco′1.07.where fcc∗ and εcc∗ are the peak axial stress and corresponding axial strain of concrete under a specific level of lateral confining stress.


## 4.3. CFSST Column Strengthfco′

CFSST column strengthfco′ is given in technical code for concrete filled steel tubular structures (GB50936-2014) [35]. It is calculated as follows:(10)fco′=1.212+Bθsc+Cθsc2fco,B=0.131fy235+0.723,C=−0.07fck14.4+0.026,θsc=αscffc,αsc=AsAc,where As and Ac are the steel tube area and core concrete area, respectively; fy and f are the tensile strength standard value and design value, respectively; αsc and θsc are the steel ratio and confinement coefficient of the specimen, respectively; B and C are the influence coefficients.


## 4.4. Effective CFRP Confinement Coefficientke

The theoretical fracture strainεfu can be calculated as fiber strength divided by the elastic modulus. However, the actual fracture strain εru is much smaller than the theoretical fracture strain. Lam and Teng suggested that εru can be calculated from εfu as follows:(11)εru=keεfu,where the effective CFRP confinement coefficient k of the circular column is approximately 0.586 [15] and was taken as 0.5, 0.53, and 0.56 corresponding with CAM thickness of 5, 10, and 15 mm, respectively, according to the test results.


## 4.5. Intercept of the Stress Axis by the Linear Second Portionf0

Lam and Teng showedf0/fco′=1.09 from the test and suggested that f0=fco′ approximately [15]. However, this method ignores the influence of FRP confinement. The intercept f0 was affected by the confinement effectiveness, which can be calculated by confinement stiffness ratio βj and confining factor ξ. Yu [26] suggested that f0 can be calculated as follows:(12)f0=1+1.1ξfc′.However, for FRP-confined CFSST columns, confining factorξ should value FRP and steel tube confining factor, and f0 is given as follows:(13)f0fco'=1+kξ,where k is modified based on the test results. The linear fitting between f0/fco′ and ξ is shown in Figure 10, and k = 0.04854.Figure 10
Relationship betweenf0/fco′ and ξ.


## 4.6. Stress-Strain Model Verification

The experimental stress-strain curves of 12 C-C-CFSST columns were compared with the calculation curves of the Lam and Teng model, Lai model, and Yang and Feng model. The comparison of calculated stress-strain curves with experiment curve is shown in Figures11 and 12.Figure 11
Comparison of calculated stress-strain curves with the experiment curve of group C20. (a) C20-5-1-3. (b) C20-5-2-4. (c) C20-10-1-5. (d) C20-10-2-6. (e) C20-15-1-7. (f) C20-15-2-8.
(a)(b)(c)(d)(e)(f)Figure 12
Comparison of calculated stress-strain curves with the experiment curve of group C30. (a) C30-5-1-11. (b) C30-5-2-12. (c) C30-10-1-13. (d) C30-10-2-14. (e) C30-15-1-15. (f) C30-15-2–16.
(a)(b)(c)(d)(e)(f)The Lam and Teng model had the highest fitting grade on C-C-CFSST column stress-strain curves among three models. The Yang and Feng model fitted well in some situations, such as C20-10-2-6, C20-15-1-7, C30-5-1-11, and C30-15-2-16. The Lai model had a big deviation compared with other models. The stress-strain curves of the C-C-CFSST column can be separated into three segments, as shown in Figure13.Figure 13
Proposed stress-strain model for C-C-CFSST.In segment I, the Lam and Teng model shows a great prediction on the stress-strain relationship of the C-C-CFSST column. The Lai model and the Yang and Feng model generally underestimated the axial stress of specimens in segment I. The Lam and Teng model has an unobvious segment II slightly overestimating the axial stress. The Yang and Feng model has a similar trend to the experiential curves of segment II. Although similar to segment I, this model underestimates the axial stress of specimens. The Lai model also greatly underestimates the axial stress because of the inaccuracy of the calculated transition strain. In segment III, the ultimate axial stressfcc' calculated from the Lam and Teng model and the Yang and Feng model is well estimated to the test value. The stress-strain curves calculated from the Lam and Teng model are dramatically close to the test curves. In conclusion, the Lam and Teng model has the greatest prediction for the stress-strain relationship of the C-C-CFSST column among the three models. The Yang model has a more accurate prediction, while CAM thickness is increasing. The transition strain of the Lai model is always larger than the test transition strain, which leads to the inaccuracy of the calculated curves. A more accurate stress-strain model for C-C-CFSST columns should be developed in experimental and theoretical research.


## 5. Conclusions

This study presents the results from an experimental investigation on the compressive behavior of 16 C-C-CFSST short columns. Based on test data, the effect of CAM thickness on the failure model and the axial stress-strain relationship is discussed. The following conclusions can be made:(1)
CFRP confinement using the CAM could effectively enhance the ductility and axial load carrying capacity of CFSST short columns. For the increasing CAM thickness, the bearing capacity of C20-5-1-3, C20-10-1-5, and C20-15-1-7 is improved by 19.9%, 40.2%, and 47.5%, respectively.(2)
The increasing CAM thickness leads to the CFRP breakpoint gradually moving far from the specimen corner, which led to the decrease of stress concentration of CFRP hoop stress in the corner of the square steel tube. The increasing CAM thickness also made the lateral stress well distributed. The effective fracture strain and constraint efficiency of CFRP increased well.(3)
The stress-strain curve characteristic of the C-C-CFSST column is similar to the CFRP-confined circular concrete column. The applicability of the existing model for FRP-confined concrete was evaluated and compared with the test data. The predictions of the Lam and Teng model agree well with the test data.



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*Source: 6620577-2021-03-17.xml*