# Seismic Performance of Concrete-Filled Square Steel Tubular Column-Steel Beam Sleeve Joint

Authors: Xiangong Huang; Man Xu; Nan Guo; Senwen Deng; Le Huang
Journal: Shock and Vibration
 (2022)

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## Abstract

The concrete-filled square steel tubular (S-CFST) structure has been widely used as a resistance system against earthquakes due to its good seismic performance. However, the application of the S-CFST structure is limited by its complex joint formulation. To overcome this shortcoming, a sleeve semirigid joint has been proposed, while its seismic performance has not been well examined. This study aims to discuss the behavior of sleeve joints with different parameters under low cyclic loading. The analysis results show that the simulation results of the finite element model established by ABAQUS were in good agreement with the experimental results, which further verified the good energy dissipation performance of the sleeve joint, and gave the design suggestions of the joint under different parameters to promote the engineering application of this type of joint.


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## Body

## 1. Introduction

The concrete-filled steel tube (CFST) has various advantages, such as high bearing capacity, good plasticity and toughness, easy processing, and convenient construction [1, 2]. However, the complexity of the design and construction of beam-column joints limits its application to some extent. In addition, almost all current joints are designed as rigid joints, but the semirigid joint under the action of cyclic loading shows a better energy dissipation performance and more stable seismic characteristics, which has attracted extensive attention of researchers [3–8].In recent years, researchers have conducted plenty of research on the types and mechanical properties of semirigid joints of concrete-filled steel tubes, and some achievements have been made. For example, Oh and Ai-Roda [9] carried out an experimental study on the connection of concrete-filled steel tubular column and H-shaped steel beam. T-cleat connections and bending steel plates with a centered hole were used to strengthen the stiffness of the connection, and the hysteretic performance of the connection was analyzed. It was found that the joint of bending steel plates with a centered hole demonstrates good deformation ability. Ricles et al. [10] conducted low reversed cyclic loading tests on 10 full-scale joints of concrete-filled square steel tubular (CFST) column and steel beam. They found that the flange joints of the T-shaped steel bolt connection and reinforced beam meet the design principle of “strong column and weak beam,” and the bolted end-plate connection can enhance the bolt hole strength, effectively reducing the slippage and the pinch phenomenon of hysteretic curves. Yang et al. [11] studied the mechanical properties of joints through diaphragms of concrete-filled rectangular steel tubular column and H-shaped steel plate under low cyclic loading. The results showed that such type of joint has good seismic performance, and the wedge-shaped plates on both sides of the flange have a significant influence on the joint ductility. Lv and Li [12] proposed a joint form with an octagonal ring beam outside the CFST column and designed three specimens to study its mechanical properties. The obtained results indicated that the three specimens all show high bearing capacity, good ductility, and energy dissipation capacity under cyclic loading. Mirza and Uy [13] used the experiment and finite element method to study the performance of bolted beams, columns, and horizontal end-plate joints. The mechanical properties of flat end joints of the composite beam-column under low-probability, high-consequence loading were investigated. Gao et al. [14] researched the mechanical characteristics and energy dissipation performance of different forms of large-size connections of CFST column and H-shaped steel beam. He concluded that the bearing capacity and energy dissipation performance of joints with inner diaphragms are better than those of joints with through diaphragms. France and Buick Davison [15] carried out static loading tests on the bolted end-plate joint of CFST column and steel beam and compared its performance with that of the square steel tubular column joint. Through experimental analysis, it was found that the strength and stiffness of the joint are significantly improved, but the joint ductility is reduced, and the failure mode of the joint is bolt pull out.For the simulation model and calculation theory of the concrete-filled steel tube column-steel beam semirigid joint, the research focus is mainly on the connection with bolts, and the deformation model of the connection element is established. Huang [16] used ABAQUS to establish two-element connectors to simulate the beam-column joint used in the bolted end-plate connection. Compared with the experiment data, this finite element model (FEM) effectively simulated the force exerted on the joint under high temperatures. In such conditions, the axial force of the beam end has an obvious influence on the force exerted on the joint. Hu et al. [17] studied the performance of T-shaped steel bolted joints under low cyclic loading and proposed a new mechanical calculation model for such joints. The model diagram is shown in Figure 1, where the mechanical model simulated T-shaped steel as a nonlinear spring element, and a multiline segment cyclic stiffness model was used to simulate the hysteretic performance of T-shaped steel components. By comparing the simulated results of this model with the experimental results, it was concluded that this model can accurately simulate the mechanical behavior of T-shaped steel bolted joints [17].Figure 1
Hu calculation model.Many achievements have been obtained in the connection test and theoretical study of semirigid joints of CFST column and steel beam, but the existing semirigid joint forms have their own limitations. It is difficult to find a joint form with both technical and economic advantages; thus, it is necessary to select the suitable joint type based on the application situation by developing the advantages and avoiding the disadvantages. In this paper, the sleeve joint form of concrete-filled square steel tubular column-steel beam was studied, and its mechanical properties under low cyclic loading are investigated using ABAQUS. This joint is shown in Figure2.Figure 2
Sketch of sleeve joint.


## 2. Model Design

The sleeve joint is formed by sheathing the steel sleeve at the joint position of concrete-filled square steel tubular column, welding the upper and lower edges of the sleeve with the steel tubular column, and then completely welding the steel beam with the sleeve, and the joint has clear force transmission and simple construction. To investigate the seismic performance of concrete-filled square steel tubular column-steel beam sleeve joint, three joint models of this type are designed.


### 2.1. Model Dimension

Three sleeve joint specimens of CFST column and steel beam, numbered from CFST-1 to CFST-3, were designed. The size of the square steel tubular column was300×300×8 mm (length × width × thickness), and the steel beams were made of HN244×175×7×11 mm hot-rolled H-beam. Strength grade Q235 steel was used for beams, columns, and sleeves, and concrete with strength grade C30 was filled in the square steel tube. The sleeve was welded with steel plates, and the type of electrode was E43. The upper and lower flanges and web at one end of the steel beam were completely welded on the sleeve. A 5 mm weld was left on the top and bottom of the sleeve to weld the sleeve on the square steel tubular column, the periphery of which was in full contact with the square steel tubular column. The variables were the thickness and height of the sleeve. The main parameters are shown in Table 1, and the detailed joint structure is shown in Figure 3.Table 1
Sleeve parameters of specimens height × side length × thickness (mm).
CFST-1CFST-2CFST-3488 × 312 × 6600 × 312 × 6488 × 320 × 10Figure 3
Detailed joint structure. (a) Elevation, (b) plan, and (c) profile.
(a)(b)(c)


### 2.2. Material Properties

Steel is simulated by the conventional ideal elastic-plastic model, and Q235 steel was adopted in this model, with an elastic modulus ofE=2.03×105 N/mm2, a Poisson ratio of 0.3, and a density of 78.5 g/mm2.The concrete constitutive model is the plastic damage model of square steel tubes proposed by Han et al. [18, 19], which considers the interaction between the inner wall of square steel tube and core concrete.


## 2.1. Model Dimension

Three sleeve joint specimens of CFST column and steel beam, numbered from CFST-1 to CFST-3, were designed. The size of the square steel tubular column was300×300×8 mm (length × width × thickness), and the steel beams were made of HN244×175×7×11 mm hot-rolled H-beam. Strength grade Q235 steel was used for beams, columns, and sleeves, and concrete with strength grade C30 was filled in the square steel tube. The sleeve was welded with steel plates, and the type of electrode was E43. The upper and lower flanges and web at one end of the steel beam were completely welded on the sleeve. A 5 mm weld was left on the top and bottom of the sleeve to weld the sleeve on the square steel tubular column, the periphery of which was in full contact with the square steel tubular column. The variables were the thickness and height of the sleeve. The main parameters are shown in Table 1, and the detailed joint structure is shown in Figure 3.Table 1
Sleeve parameters of specimens height × side length × thickness (mm).
CFST-1CFST-2CFST-3488 × 312 × 6600 × 312 × 6488 × 320 × 10Figure 3
Detailed joint structure. (a) Elevation, (b) plan, and (c) profile.
(a)(b)(c)


## 2.2. Material Properties

Steel is simulated by the conventional ideal elastic-plastic model, and Q235 steel was adopted in this model, with an elastic modulus ofE=2.03×105 N/mm2, a Poisson ratio of 0.3, and a density of 78.5 g/mm2.The concrete constitutive model is the plastic damage model of square steel tubes proposed by Han et al. [18, 19], which considers the interaction between the inner wall of square steel tube and core concrete.


## 3. Model Validation

### 3.1. Experimental Setup

Two MTS actuators were used to apply low cyclic load to the beam ends on both sides of the specimen, and the Jack on the column top was utilized to apply the axial force, while hinged supports were placed at the column bottom and column end to simulate the hinged boundary conditions. In the test, four H-shaped steel was installed as limit beams to ensure that the components do not have out-of-plane torsion and instability before failure and to limit the lateral displacement of the specimen during loading. It is specified in the test that the pushing direction of the actuator is positive and the pulling direction is negative, and the left and right beams were marked. During the test, firstly, a vertical axial force of 770 kN (axial compression ratio of 0.23) was applied on the column top with a Jack. Then, MTS actuators were utilized to apply displacement cyclic load on the left and right beam ends at the same time, with a displacement increment of 5 mm. When the specimen yielded, cyclic loading was continued three times with the same increment until any of the following conditions occurred: (1) the load is reduced to less than 80% of the peak load; (2) the steel tube in the joint area is locally damaged by shear or more than 70% of the local weld cracks; (3) the steel beam has obvious local buckling deformation or fracture, or the steel beam has out-of-plane instability.The stress distribution in the core area of the joint was measured by both the strain gauge and the stain rosette that are arranged according to Figure4. The displacement of the beam end was measured by a displacement sensor and collected synchronously and automatically by a computer. The test device is shown in Figure 5. Due to the sticking and measurement, the strain gauge and the stain rosette did not work well, so the measurement results of strain were not provided in this paper.Figure 4
Strain gauge arrangement. (a) Front view and (b) top view.
(a)(b)Figure 5
Diagram of the test device. (a) Model diagram and (b) physical diagram.
(a)(b)


### 3.2. Material Mechanical Properties

#### 3.2.1. Steel

According to the provisions in metallic materials–tensile testing–method of test at ambient temperature (GB/T 228.1–2010) [20] and steel and steel products–location and preparation of samples and test pieces for mechanical testing (GB/T 2975–2018) [21], three groups with two samples per group from the same batch of steel were taken to conduct tensile tests on the material universal testing machine. The performance parameters measured are shown in Table 2.Table 2
Performance parameters of steel.
Thickness (mm)Measured strength (MPa)Average strength (MPa)5.65Yield strength323.86322.72323.29Ultimate strength474.09473.42473.767.65Yield strength299.50282.88291.19Ultimate strength390.05392.82391.439.67Yield strength313.57319.68316.62Ultimate strength420.86427.45424.15


#### 3.2.2. Concrete

When pouring C30 concrete, three150×150×150 mm standard concrete test cubes and three 150×150×300 mm prismatic blocks were fabricated. After 28 days of curing under the same conditions as the joint specimens, the compressive test on the concrete cube was carried out, and then the average value was taken. Ultimately, the measured average compressive strength of concrete cubes was 40.59 MPa, the average axial compressive strength was 27.18 MPa, and the average elastic modulus was 31783 MPa.


### 3.3. FE Model

Solid element C3D8R in ABAQUS is used to build the model, including steel beam, steel tube, core concrete, and steel sleeve. The mesh of the connection area is encrypted by using structured mesh and considering the complex stress and calculation accuracy of the connection area. The mesh size of the joint connection area between steel tube and beam is 15 mm, and the rest parts are 60 mm. Steel sleeve is the key component of joint connection, which is divided by 15 mm. The size of core concrete is 160 mm.The normal attribute between steel pipe and concrete is “hard” contact, the tangential direction is defined as limited sliding, and the friction coefficient is 0.3. Except the weld joint area, the contact between the steel tube and the steel sleeve is defined as “hard,” which means that there is no immersion between the two faces.


### 3.4. Failure Mode

The failure phenomena of the three specimens under different loading displacements are shown in Table3, where 55 mm (1) represents the first circle load when the displacement of the beam end is 55 mm. The failure modes of these specimens are shown in Figure 6.Table 3
Failure phenomena of specimens.
No.Vertical loading displacementFailure phenomenaCFST-155 mm (1)The upper flange of the right beam and the lower flange of the left beam have large local buckling55 mm (2)The sleeve local buckling at the connection between the right beam and the sleeve and the left beam and the sleeve is about 15 mm and 20 mm, respectively55 mm (3)The upper flange weld of the right beam and the lower flange weld of the left beam crack60 mm (1)The base metals on the lower side of the right beam and the upper side of the left beam are torn60 mm (3)The base metals on the upper and lower flanges are torn65 mm (2)The connection between the sleeve and the upper flange and the sleeve and the lower flange of the right beam is torn about 30 mm and 8 mm, respectively; the connection between the sleeve and the upper flange of the left beam is torn about 40 mm65 mm (3)The specimen failure occursCFST-255 mm (1)The adhesion failure occurs between the concrete and steel tube wall60 mm (1)The base metal on the lower flange of the right beam is torn60 mm (2)The base metal on the upper flange of the left beam is torn, and the sleeve local buckling occurs65 mm (1)The sleeve of the right beam has a tear of about 2 mm65 mm (2)The upper flange of the left beam is partially separated from the sleeve65 mm (3)The flange on both sides of the beam is separated from the sleeve, and specimen failure occursCFST-365 mm (1)The upper flange of the right beam has a local buckling65 mm (2)The sleeve of the left beam has a local buckling of about 8 mm65 mm (3)The base metals on the lower side of the right beam and the upper side of the left beam are torn, and the sleeve of the left beam has a local buckling of about 12 mm70 mm (1)The left beam is distorted70 mm (2)The base metal has been torn, and the sleeve of the left beam has a crack of about 6 mm70 mm (3)The sleeve of the left beam is slightly damaged and has a local buckling, and the whole weld is torn75 mm (2)The flange on both sides of the beam is separated from the sleeve, and specimen failure occursFigure 6
Failure modes of specimens. (a) Sleeve local buckling; (b) base metal tearing of the left; (c) weld cracking; (d) base metal tearing of upper; (e) sleeve tearing; (f) joint failure.
(a)(b)(c)(d)(e)(f)The test phenomena, failure processes, and failure modes of three sleeve joint specimens were identical, belonging to the failure mode of semirigid joints with high stiffness. Therefore, the seismic performance of the joint can be improved by improving the design, welding process, and sequence or strengthening the strength check and quality inspection of the weld.A full finite element model was built by ABAQUS as shown in Figure7. The axial force was applied on the top of the column, and the cyclic load was applied on the beam end to simulate the test loading conditions. The displacement constraints in X and Y directions and rotation constraints in Y and Z directions were applied at the top of the column, and X, Y, Z displacement constraints and Y, Z rotation constraints were imposed at the bottom of the column.Figure 7
Loading conditions.Figure8 shows the comparison of joint failure modes of specimen CFST-1 between the simulated results and experimental results. It can be seen from the figure that the simulation failure mode of the sleeve joint is almost the same as the experimental result. The failure mode of the specimen is mainly the buckling and the tearing of the sleeve. However, because the material damage is not given in the material property, the tearing of the sleeve is not simulated in the finite element model. The place where the joint deformation is large is the place where the steel is torn. The ABAQUS finite element model established in this paper can accurately simulate the failure mode of joints.Figure 8
Failure mode.Figure9(a) shows the stress distribution of the steel beam. It can be seen from the figure that the flange of the beam is curved. This phenomenon also occurs in the specimen CFST-1, the sleeve buckling is obvious, and the flange of the beam is easier to bend. It shows that the specimen with thinner sleeve wall thickness is more prone to buckling under the same axial compression ratio.Figure 9
The stress distribution of steel beam and steel tube. (a) Steel beam and (b) steel tube.
(a)(b)The finite element analysis can simulate the stress distribution of the steel tube column inside the sleeve, which cannot be obtained in the test. Figure9(b) shows the stress distribution of steel tube under ultimate load. It can be seen that when the specimen was damaged, because the sleeve is only connected with the steel tube by the upper and lower welds, the corresponding part of the steel tube is also the part with the greatest stress in the loading process, and it is also the part most prone to deformation and buckling.Figure10 shows a comparison of failure modes between extended end-plate joints and sleeve joints. The extended end-plate joint is a typical semirigid joint [22, 23], and its main failure modes are shown in Figure 10(a). One kind of failure is that while the upper flange of the steel beam is taken as the rotation center, the end plate at the lower flange also has bending deformation, which is consistent with the failure mode of the sleeve joint. The other kind of failure is that the end plate below the upper flange of the steel beam is basically in a straight line; that is, the end plate has no obvious bending deformation, and the failure mode is consistent with the weld tearing failure mode of sleeve joint. From the analysis of rotation capacity and failure modes, the sleeve joint conforms to the connection characteristics of the semirigid joint.Figure 10
Comparison of failure modes of two semirigid joints. (a) Extended end-plate joint. (b) Sleeve joint.
(a)(b)


### 3.5. Hysteretic Curve

The load-displacement hysteretic curves of the specimen beam end are shown in Figure11, where the graph in the first and third quadrants is the hysteretic curve of the left beam end and the graph in the second and fourth quadrants is the hysteretic curve of the right beam end. Both graphs are shuttle-shaped, indicating good deformability, seismic performance, and energy dissipation capacity of the specimen. Since cyclic load is applied on both sides of the beam end, the corresponding hysteretic curves are symmetrically distributed. When the specimen reached the yield state, the hysteretic curve analysis showed that some specimens had buckled. After yielding, the first cyclic load value of each displacement level was higher than that of the next two cycles, indicating that the joint strength and stiffness degrade with loading. In terms of ultimate bearing capacity, specimen CFST-2 did not change much compared with specimen CFST-1, suggesting that increasing the sleeve height will not improve the bearing capacity. However, the area of hysteretic curves of specimen CFST-2 was larger than that of specimen CFST-1. It implicated that the energy dissipation capacity of joint specimen CFST-2 is higher than that of joint specimen CFST-1.Figure 11
Load-displacement hysteretic curves of the beam end. (a) CFST-1, (b) CFST-2, and (c) CFST-3.
(a)(b)(c)Figure12 shows that the simulated hysteretic curve is in good agreement with the experimental curve, which verifies the rationality of the finite element method [24, 25]. The load value of the simulated hysteretic curve was slightly higher than that of the experimental hysteretic curve. This is because the finite element model ignores the influence of the weld quality between the sleeve and the flange of the steel beam as well as the environment of the specimen. The initial stiffness of the joint in the finite element analysis was larger than that in the test, which is because the weld of the specimen basically appears in the part where one end of the steel beam is connected with the sleeve, while the weld is not considered in the finite element analysis.Figure 12
Comparison of hysteretic curves. (a) CSFT-1, (b) CFST-2, and (c) CFST-3.
(a)(b)(c)


### 3.6. Skeleton Curve

When applying cyclic load on the steel beam end, the skeleton curve can be obtained by successively connecting the maximum load in each stage of the hysteretic curve. The skeleton curves of three joint specimens are shown in Figure13. The skeleton curves of the joint specimen are basically S-shaped, and the sleeve joints undergo obvious elastic, elastic-plastic, and plastic failure processes during loading. However, the skeleton curves of the left and right beam ends are not completely symmetrical. This is because the quality of the welds on both sides of the beam end cannot be the same, and cumulative damage occurs at the joints. The initial stiffness, ultimate bearing capacity, and ultimate displacement of specimen CFST-3 were significantly higher than those of CFST-1 and CFST-2, indicating that increasing the sleeve thickness can effectively improve the seismic performance of the sleeve joint.Figure 13
Comparison of skeleton curves. (a) CFST-1, (b) CFST-2, (c) CFST-3, and (d) comparison of skeleton curves under different parameters.
(a)(b)(c)(d)As shown in Figure13, the simulated and experimental skeleton curves are both S-shaped, and the joint specimens have experienced three stages under low cyclic loading, that is, elastic, elastic-plastic, and plastic failure. The simulated and experimental skeleton curves were also roughly consistent in values, with a load value error within 10%, which further illustrates the rationality of the finite element method. By comparison, the simulated skeleton curve using FEM is more symmetrical, but the symmetry of the experimental skeleton curve is slightly worse. This is because there was residual deformation during loading; thus, the skeleton curve in positive and negative loading direction deviates slightly, but this influence factor is not considered in finite element simulation.


## 3.1. Experimental Setup

Two MTS actuators were used to apply low cyclic load to the beam ends on both sides of the specimen, and the Jack on the column top was utilized to apply the axial force, while hinged supports were placed at the column bottom and column end to simulate the hinged boundary conditions. In the test, four H-shaped steel was installed as limit beams to ensure that the components do not have out-of-plane torsion and instability before failure and to limit the lateral displacement of the specimen during loading. It is specified in the test that the pushing direction of the actuator is positive and the pulling direction is negative, and the left and right beams were marked. During the test, firstly, a vertical axial force of 770 kN (axial compression ratio of 0.23) was applied on the column top with a Jack. Then, MTS actuators were utilized to apply displacement cyclic load on the left and right beam ends at the same time, with a displacement increment of 5 mm. When the specimen yielded, cyclic loading was continued three times with the same increment until any of the following conditions occurred: (1) the load is reduced to less than 80% of the peak load; (2) the steel tube in the joint area is locally damaged by shear or more than 70% of the local weld cracks; (3) the steel beam has obvious local buckling deformation or fracture, or the steel beam has out-of-plane instability.The stress distribution in the core area of the joint was measured by both the strain gauge and the stain rosette that are arranged according to Figure4. The displacement of the beam end was measured by a displacement sensor and collected synchronously and automatically by a computer. The test device is shown in Figure 5. Due to the sticking and measurement, the strain gauge and the stain rosette did not work well, so the measurement results of strain were not provided in this paper.Figure 4
Strain gauge arrangement. (a) Front view and (b) top view.
(a)(b)Figure 5
Diagram of the test device. (a) Model diagram and (b) physical diagram.
(a)(b)


## 3.2. Material Mechanical Properties

### 3.2.1. Steel

According to the provisions in metallic materials–tensile testing–method of test at ambient temperature (GB/T 228.1–2010) [20] and steel and steel products–location and preparation of samples and test pieces for mechanical testing (GB/T 2975–2018) [21], three groups with two samples per group from the same batch of steel were taken to conduct tensile tests on the material universal testing machine. The performance parameters measured are shown in Table 2.Table 2
Performance parameters of steel.
Thickness (mm)Measured strength (MPa)Average strength (MPa)5.65Yield strength323.86322.72323.29Ultimate strength474.09473.42473.767.65Yield strength299.50282.88291.19Ultimate strength390.05392.82391.439.67Yield strength313.57319.68316.62Ultimate strength420.86427.45424.15


### 3.2.2. Concrete

When pouring C30 concrete, three150×150×150 mm standard concrete test cubes and three 150×150×300 mm prismatic blocks were fabricated. After 28 days of curing under the same conditions as the joint specimens, the compressive test on the concrete cube was carried out, and then the average value was taken. Ultimately, the measured average compressive strength of concrete cubes was 40.59 MPa, the average axial compressive strength was 27.18 MPa, and the average elastic modulus was 31783 MPa.


## 3.2.1. Steel

According to the provisions in metallic materials–tensile testing–method of test at ambient temperature (GB/T 228.1–2010) [20] and steel and steel products–location and preparation of samples and test pieces for mechanical testing (GB/T 2975–2018) [21], three groups with two samples per group from the same batch of steel were taken to conduct tensile tests on the material universal testing machine. The performance parameters measured are shown in Table 2.Table 2
Performance parameters of steel.
Thickness (mm)Measured strength (MPa)Average strength (MPa)5.65Yield strength323.86322.72323.29Ultimate strength474.09473.42473.767.65Yield strength299.50282.88291.19Ultimate strength390.05392.82391.439.67Yield strength313.57319.68316.62Ultimate strength420.86427.45424.15


## 3.2.2. Concrete

When pouring C30 concrete, three150×150×150 mm standard concrete test cubes and three 150×150×300 mm prismatic blocks were fabricated. After 28 days of curing under the same conditions as the joint specimens, the compressive test on the concrete cube was carried out, and then the average value was taken. Ultimately, the measured average compressive strength of concrete cubes was 40.59 MPa, the average axial compressive strength was 27.18 MPa, and the average elastic modulus was 31783 MPa.


## 3.3. FE Model

Solid element C3D8R in ABAQUS is used to build the model, including steel beam, steel tube, core concrete, and steel sleeve. The mesh of the connection area is encrypted by using structured mesh and considering the complex stress and calculation accuracy of the connection area. The mesh size of the joint connection area between steel tube and beam is 15 mm, and the rest parts are 60 mm. Steel sleeve is the key component of joint connection, which is divided by 15 mm. The size of core concrete is 160 mm.The normal attribute between steel pipe and concrete is “hard” contact, the tangential direction is defined as limited sliding, and the friction coefficient is 0.3. Except the weld joint area, the contact between the steel tube and the steel sleeve is defined as “hard,” which means that there is no immersion between the two faces.


## 3.4. Failure Mode

The failure phenomena of the three specimens under different loading displacements are shown in Table3, where 55 mm (1) represents the first circle load when the displacement of the beam end is 55 mm. The failure modes of these specimens are shown in Figure 6.Table 3
Failure phenomena of specimens.
No.Vertical loading displacementFailure phenomenaCFST-155 mm (1)The upper flange of the right beam and the lower flange of the left beam have large local buckling55 mm (2)The sleeve local buckling at the connection between the right beam and the sleeve and the left beam and the sleeve is about 15 mm and 20 mm, respectively55 mm (3)The upper flange weld of the right beam and the lower flange weld of the left beam crack60 mm (1)The base metals on the lower side of the right beam and the upper side of the left beam are torn60 mm (3)The base metals on the upper and lower flanges are torn65 mm (2)The connection between the sleeve and the upper flange and the sleeve and the lower flange of the right beam is torn about 30 mm and 8 mm, respectively; the connection between the sleeve and the upper flange of the left beam is torn about 40 mm65 mm (3)The specimen failure occursCFST-255 mm (1)The adhesion failure occurs between the concrete and steel tube wall60 mm (1)The base metal on the lower flange of the right beam is torn60 mm (2)The base metal on the upper flange of the left beam is torn, and the sleeve local buckling occurs65 mm (1)The sleeve of the right beam has a tear of about 2 mm65 mm (2)The upper flange of the left beam is partially separated from the sleeve65 mm (3)The flange on both sides of the beam is separated from the sleeve, and specimen failure occursCFST-365 mm (1)The upper flange of the right beam has a local buckling65 mm (2)The sleeve of the left beam has a local buckling of about 8 mm65 mm (3)The base metals on the lower side of the right beam and the upper side of the left beam are torn, and the sleeve of the left beam has a local buckling of about 12 mm70 mm (1)The left beam is distorted70 mm (2)The base metal has been torn, and the sleeve of the left beam has a crack of about 6 mm70 mm (3)The sleeve of the left beam is slightly damaged and has a local buckling, and the whole weld is torn75 mm (2)The flange on both sides of the beam is separated from the sleeve, and specimen failure occursFigure 6
Failure modes of specimens. (a) Sleeve local buckling; (b) base metal tearing of the left; (c) weld cracking; (d) base metal tearing of upper; (e) sleeve tearing; (f) joint failure.
(a)(b)(c)(d)(e)(f)The test phenomena, failure processes, and failure modes of three sleeve joint specimens were identical, belonging to the failure mode of semirigid joints with high stiffness. Therefore, the seismic performance of the joint can be improved by improving the design, welding process, and sequence or strengthening the strength check and quality inspection of the weld.A full finite element model was built by ABAQUS as shown in Figure7. The axial force was applied on the top of the column, and the cyclic load was applied on the beam end to simulate the test loading conditions. The displacement constraints in X and Y directions and rotation constraints in Y and Z directions were applied at the top of the column, and X, Y, Z displacement constraints and Y, Z rotation constraints were imposed at the bottom of the column.Figure 7
Loading conditions.Figure8 shows the comparison of joint failure modes of specimen CFST-1 between the simulated results and experimental results. It can be seen from the figure that the simulation failure mode of the sleeve joint is almost the same as the experimental result. The failure mode of the specimen is mainly the buckling and the tearing of the sleeve. However, because the material damage is not given in the material property, the tearing of the sleeve is not simulated in the finite element model. The place where the joint deformation is large is the place where the steel is torn. The ABAQUS finite element model established in this paper can accurately simulate the failure mode of joints.Figure 8
Failure mode.Figure9(a) shows the stress distribution of the steel beam. It can be seen from the figure that the flange of the beam is curved. This phenomenon also occurs in the specimen CFST-1, the sleeve buckling is obvious, and the flange of the beam is easier to bend. It shows that the specimen with thinner sleeve wall thickness is more prone to buckling under the same axial compression ratio.Figure 9
The stress distribution of steel beam and steel tube. (a) Steel beam and (b) steel tube.
(a)(b)The finite element analysis can simulate the stress distribution of the steel tube column inside the sleeve, which cannot be obtained in the test. Figure9(b) shows the stress distribution of steel tube under ultimate load. It can be seen that when the specimen was damaged, because the sleeve is only connected with the steel tube by the upper and lower welds, the corresponding part of the steel tube is also the part with the greatest stress in the loading process, and it is also the part most prone to deformation and buckling.Figure10 shows a comparison of failure modes between extended end-plate joints and sleeve joints. The extended end-plate joint is a typical semirigid joint [22, 23], and its main failure modes are shown in Figure 10(a). One kind of failure is that while the upper flange of the steel beam is taken as the rotation center, the end plate at the lower flange also has bending deformation, which is consistent with the failure mode of the sleeve joint. The other kind of failure is that the end plate below the upper flange of the steel beam is basically in a straight line; that is, the end plate has no obvious bending deformation, and the failure mode is consistent with the weld tearing failure mode of sleeve joint. From the analysis of rotation capacity and failure modes, the sleeve joint conforms to the connection characteristics of the semirigid joint.Figure 10
Comparison of failure modes of two semirigid joints. (a) Extended end-plate joint. (b) Sleeve joint.
(a)(b)


## 3.5. Hysteretic Curve

The load-displacement hysteretic curves of the specimen beam end are shown in Figure11, where the graph in the first and third quadrants is the hysteretic curve of the left beam end and the graph in the second and fourth quadrants is the hysteretic curve of the right beam end. Both graphs are shuttle-shaped, indicating good deformability, seismic performance, and energy dissipation capacity of the specimen. Since cyclic load is applied on both sides of the beam end, the corresponding hysteretic curves are symmetrically distributed. When the specimen reached the yield state, the hysteretic curve analysis showed that some specimens had buckled. After yielding, the first cyclic load value of each displacement level was higher than that of the next two cycles, indicating that the joint strength and stiffness degrade with loading. In terms of ultimate bearing capacity, specimen CFST-2 did not change much compared with specimen CFST-1, suggesting that increasing the sleeve height will not improve the bearing capacity. However, the area of hysteretic curves of specimen CFST-2 was larger than that of specimen CFST-1. It implicated that the energy dissipation capacity of joint specimen CFST-2 is higher than that of joint specimen CFST-1.Figure 11
Load-displacement hysteretic curves of the beam end. (a) CFST-1, (b) CFST-2, and (c) CFST-3.
(a)(b)(c)Figure12 shows that the simulated hysteretic curve is in good agreement with the experimental curve, which verifies the rationality of the finite element method [24, 25]. The load value of the simulated hysteretic curve was slightly higher than that of the experimental hysteretic curve. This is because the finite element model ignores the influence of the weld quality between the sleeve and the flange of the steel beam as well as the environment of the specimen. The initial stiffness of the joint in the finite element analysis was larger than that in the test, which is because the weld of the specimen basically appears in the part where one end of the steel beam is connected with the sleeve, while the weld is not considered in the finite element analysis.Figure 12
Comparison of hysteretic curves. (a) CSFT-1, (b) CFST-2, and (c) CFST-3.
(a)(b)(c)


## 3.6. Skeleton Curve

When applying cyclic load on the steel beam end, the skeleton curve can be obtained by successively connecting the maximum load in each stage of the hysteretic curve. The skeleton curves of three joint specimens are shown in Figure13. The skeleton curves of the joint specimen are basically S-shaped, and the sleeve joints undergo obvious elastic, elastic-plastic, and plastic failure processes during loading. However, the skeleton curves of the left and right beam ends are not completely symmetrical. This is because the quality of the welds on both sides of the beam end cannot be the same, and cumulative damage occurs at the joints. The initial stiffness, ultimate bearing capacity, and ultimate displacement of specimen CFST-3 were significantly higher than those of CFST-1 and CFST-2, indicating that increasing the sleeve thickness can effectively improve the seismic performance of the sleeve joint.Figure 13
Comparison of skeleton curves. (a) CFST-1, (b) CFST-2, (c) CFST-3, and (d) comparison of skeleton curves under different parameters.
(a)(b)(c)(d)As shown in Figure13, the simulated and experimental skeleton curves are both S-shaped, and the joint specimens have experienced three stages under low cyclic loading, that is, elastic, elastic-plastic, and plastic failure. The simulated and experimental skeleton curves were also roughly consistent in values, with a load value error within 10%, which further illustrates the rationality of the finite element method. By comparison, the simulated skeleton curve using FEM is more symmetrical, but the symmetry of the experimental skeleton curve is slightly worse. This is because there was residual deformation during loading; thus, the skeleton curve in positive and negative loading direction deviates slightly, but this influence factor is not considered in finite element simulation.


## 4. Parametric Analysis

### 4.1. Axial Compression Ratio

Axial compression ratio is the ratio of the axial pressure of the column to the compressive strength of the entire section of the column. During the test, an axial pressure of 770 kN (axial compression ratio of 0.23) was applied to the column. Since the change in the axial compression ratio is not considered in the test, in this section, the influence of different axial compression ratios on the joint specimens was simulated and analyzed. The axial compression ration can be calculated according to (1)n=NNu=NfyAs+fcAc,where N represents the axial load, Nu is the ultimate bearing capacity of concrete-filled steel tube column, fy is the yield strength of steel, fc is the compressive strength of concrete, and As and As are the area of the steel tube and the core concrete, respectively.Take the CFST-1 as an example. Figure14 shows the load-displacement curves of joints with different axial compression ratios. The load-displacement curves of all parametric analyses below are obtained under monotonic loading. The initial stiffness is calculated by the slope of the elastic segment of the load-displacement curve. The slopes (initial stiffness) of the four curves are 1.116 (n = 0.2), 1.246 (n = 0.4), 1.408 (n = 0.6), and 1.334 (n = 0.8), respectively. It can be seen from the figure that, under the same boundary and loading condition, the joint still has a good bearing capacity, and the axial compression ratio is the main factor influencing the initial stiffness of the joint. When the axial compression ratio is smaller than 0.6, the initial stiffness of the joint is positively correlated with the axial compression ratio, but when this ratio exceeds 0.6, the initial stiffness of the joint will be negatively correlated with the axial compression ratio. Therefore, it can be concluded that the joint achieves the optimal initial stiffness when the axial compression ratio n = 0.6.Figure 14
Load-displacement curves of joints with different axial compression ratios.It can be seen from Figure15 that the hysteretic curves with the axial compression ratio n = 0.2 and n = 0.4 are almost the same, but the hysteretic curve with the axial compression ratio n = 0.8 shows an obvious “pinch” phenomenon, which indicates that it is affected by slippage. When the axial compression ratio exceeds 0.6, the energy dissipation capacity of the joint will be affected.Figure 15
Hysteretic curves of joints with different axial compression ratios. (a)n = 0.2, (b) n = 0.4, (c) n = 0.6, and (d) n = 0.8.
(a)(b)(c)(d)


### 4.2. Influence of Concrete Strength Grade

The influence of different concrete strength grades on sleeve joints was analyzed, and the results are shown in Figure16. It can be seen from Figure 16 that the concrete with higher strength bears more load in the later stage of loading so that the local buckling of steel tubular wall filled with concrete of higher strength is smaller than that filled with ordinary strength concrete. Thus, it can be concluded that increasing the concrete strength has a better effect that the yielding of the steel tube will occur later.Figure 16
Load-displacement curves of joints with different concrete strength grades.Figure17 shows the hysteretic curves of joints with different concrete strengths. It can be seen from the figure that, compared with the initial hysteretic curve, the load increases by about 20% when the concrete strength increases. In addition, concrete strength has a significant influence on the overall elastic-plastic stage of the specimen, but before the elastic-plastic stage, the bearing capacity will not change significantly with increasing concrete strength.Figure 17
Hysteretic curves of joints with different concrete strength grades. (a) C20 concrete, (b) C25 concrete, (c) C30 concrete, and (d) C40 concrete.
(a)(b)(c)(d)


### 4.3. Influence of Sleeve Thickness

Due to the limited test condition, only a few specimens were carried out, and the optimal sleeve thickness was not found. Therefore, in finite element analysis, the thickness of the sleeve was taken as 6 mm, 8 mm, 10 mm, 12 mm, and 16 mm for analysis and comparison, while other conditions remained constant. Figure18 shows the load-displacement curves of joints with different sleeve thicknesses. As is observed, when the thickness of the sleeve is less than 10 mm, increasing the sleeve thickness can improve the stiffness and the ultimate bearing capacity. However, when the sleeve thickness exceeds 10 mm, the yield-bearing capacity and ultimate bearing capacity of the joints do not change significantly. The results show that when the thickness of the sleeve reaches 10 mm, the initial stiffness of the joint increases, but the increase is not obvious.Figure 18
Load-displacement curves of joints with different sleeve thicknesses.As shown in Figures18 and 19, when the sleeve thickness exceeds 10 mm, the yield-bearing capacity and ultimate bearing capacity do not change significantly, and the hysteretic curves do not change much, indicating that the energy dissipation performance of the joint changes slightly. The results show that the seismic performance of joints can be improved with the increase of sleeve thickness, but the improvement effect is not obvious when the thickness exceeds a certain value. Moreover, when the thickness of the sleeve is less than 10 mm, the ultimate load increases significantly, which also leads to local buckling of the sleeve. Therefore, it is not recommended to increase the thickness of the sleeve without restriction when designing joints, which may result in unnecessary waste.Figure 19
Hysteretic curves of joints with different sleeve thicknesses. (a)t = 6, (b) t = 8, (c) t = 10, (d) t = 12, and (e) t = 16.
(a)(b)(c)(d)(e)According to the test and finite element analysis, in order to meet the requirements that the joint strength should be higher than the members, the thickness of the sleeve needs to be greater than the thickness of the steel tube to ensure that the sleeve does not buckle before the column-steel tube. However, when the thickness of the sleeve reaches a certain degree, the impact on the bearing capacity of the joint decreases. At this time, increasing the thickness of the sleeve will cause a waste of materials. Therefore, it is suggested that the ratio of sleeve thickness to steel tube thickness ranges from 1.0 to 1.25.


### 4.4. Influence of Sleeve Height

Take 2 times the beam height as the initial height of the sleeve. 1.2 times, 1.5 times, and 1.8 times the sleeve height were taken to compare with the initial height. Figure20 shows the load-displacement curves of joints with different sleeve heights. As shown in the figure, when the height of the sleeve is increased while the sleeve thickness is unchanged, the initial stiffness of the sleeve joint slowly increases. Moreover, with the increase in sleeve height, the ultimate load and ultimate displacement do not change significantly. Therefore, it is not economical to improve the bearing capacity of the joint by increasing the sleeve height.Figure 20
Load-displacement curves of joints with different sleeve heights.Figure21 shows the hysteretic curves of joints with different sleeve heights. By comparing the hysteretic curves of joints with each height, it is found that there is no significant change. However, as the height of the sleeve height increases, the shuttle shape becomes more obvious, and the hysteretic curve becomes fuller. It suggests that increasing the height can improve the energy dissipation capacity and ductility of the joints but has no significant effect on changing the ultimate bearing capacity and ultimate displacement. Moreover, as the height increases, the fabrication of sleeve joint specimens becomes more difficult. Therefore, the seismic requirements of joints can be met only by appropriately increasing the sleeve height.Figure 21
Hysteretic curves of joints with different sleeve heights. (a) 1 h, (b) 1.2 h, (c) 1.5 h, and (d) 1.8 h.
(a)(b)(c)(d)


## 4.1. Axial Compression Ratio

Axial compression ratio is the ratio of the axial pressure of the column to the compressive strength of the entire section of the column. During the test, an axial pressure of 770 kN (axial compression ratio of 0.23) was applied to the column. Since the change in the axial compression ratio is not considered in the test, in this section, the influence of different axial compression ratios on the joint specimens was simulated and analyzed. The axial compression ration can be calculated according to (1)n=NNu=NfyAs+fcAc,where N represents the axial load, Nu is the ultimate bearing capacity of concrete-filled steel tube column, fy is the yield strength of steel, fc is the compressive strength of concrete, and As and As are the area of the steel tube and the core concrete, respectively.Take the CFST-1 as an example. Figure14 shows the load-displacement curves of joints with different axial compression ratios. The load-displacement curves of all parametric analyses below are obtained under monotonic loading. The initial stiffness is calculated by the slope of the elastic segment of the load-displacement curve. The slopes (initial stiffness) of the four curves are 1.116 (n = 0.2), 1.246 (n = 0.4), 1.408 (n = 0.6), and 1.334 (n = 0.8), respectively. It can be seen from the figure that, under the same boundary and loading condition, the joint still has a good bearing capacity, and the axial compression ratio is the main factor influencing the initial stiffness of the joint. When the axial compression ratio is smaller than 0.6, the initial stiffness of the joint is positively correlated with the axial compression ratio, but when this ratio exceeds 0.6, the initial stiffness of the joint will be negatively correlated with the axial compression ratio. Therefore, it can be concluded that the joint achieves the optimal initial stiffness when the axial compression ratio n = 0.6.Figure 14
Load-displacement curves of joints with different axial compression ratios.It can be seen from Figure15 that the hysteretic curves with the axial compression ratio n = 0.2 and n = 0.4 are almost the same, but the hysteretic curve with the axial compression ratio n = 0.8 shows an obvious “pinch” phenomenon, which indicates that it is affected by slippage. When the axial compression ratio exceeds 0.6, the energy dissipation capacity of the joint will be affected.Figure 15
Hysteretic curves of joints with different axial compression ratios. (a)n = 0.2, (b) n = 0.4, (c) n = 0.6, and (d) n = 0.8.
(a)(b)(c)(d)


## 4.2. Influence of Concrete Strength Grade

The influence of different concrete strength grades on sleeve joints was analyzed, and the results are shown in Figure16. It can be seen from Figure 16 that the concrete with higher strength bears more load in the later stage of loading so that the local buckling of steel tubular wall filled with concrete of higher strength is smaller than that filled with ordinary strength concrete. Thus, it can be concluded that increasing the concrete strength has a better effect that the yielding of the steel tube will occur later.Figure 16
Load-displacement curves of joints with different concrete strength grades.Figure17 shows the hysteretic curves of joints with different concrete strengths. It can be seen from the figure that, compared with the initial hysteretic curve, the load increases by about 20% when the concrete strength increases. In addition, concrete strength has a significant influence on the overall elastic-plastic stage of the specimen, but before the elastic-plastic stage, the bearing capacity will not change significantly with increasing concrete strength.Figure 17
Hysteretic curves of joints with different concrete strength grades. (a) C20 concrete, (b) C25 concrete, (c) C30 concrete, and (d) C40 concrete.
(a)(b)(c)(d)


## 4.3. Influence of Sleeve Thickness

Due to the limited test condition, only a few specimens were carried out, and the optimal sleeve thickness was not found. Therefore, in finite element analysis, the thickness of the sleeve was taken as 6 mm, 8 mm, 10 mm, 12 mm, and 16 mm for analysis and comparison, while other conditions remained constant. Figure18 shows the load-displacement curves of joints with different sleeve thicknesses. As is observed, when the thickness of the sleeve is less than 10 mm, increasing the sleeve thickness can improve the stiffness and the ultimate bearing capacity. However, when the sleeve thickness exceeds 10 mm, the yield-bearing capacity and ultimate bearing capacity of the joints do not change significantly. The results show that when the thickness of the sleeve reaches 10 mm, the initial stiffness of the joint increases, but the increase is not obvious.Figure 18
Load-displacement curves of joints with different sleeve thicknesses.As shown in Figures18 and 19, when the sleeve thickness exceeds 10 mm, the yield-bearing capacity and ultimate bearing capacity do not change significantly, and the hysteretic curves do not change much, indicating that the energy dissipation performance of the joint changes slightly. The results show that the seismic performance of joints can be improved with the increase of sleeve thickness, but the improvement effect is not obvious when the thickness exceeds a certain value. Moreover, when the thickness of the sleeve is less than 10 mm, the ultimate load increases significantly, which also leads to local buckling of the sleeve. Therefore, it is not recommended to increase the thickness of the sleeve without restriction when designing joints, which may result in unnecessary waste.Figure 19
Hysteretic curves of joints with different sleeve thicknesses. (a)t = 6, (b) t = 8, (c) t = 10, (d) t = 12, and (e) t = 16.
(a)(b)(c)(d)(e)According to the test and finite element analysis, in order to meet the requirements that the joint strength should be higher than the members, the thickness of the sleeve needs to be greater than the thickness of the steel tube to ensure that the sleeve does not buckle before the column-steel tube. However, when the thickness of the sleeve reaches a certain degree, the impact on the bearing capacity of the joint decreases. At this time, increasing the thickness of the sleeve will cause a waste of materials. Therefore, it is suggested that the ratio of sleeve thickness to steel tube thickness ranges from 1.0 to 1.25.


## 4.4. Influence of Sleeve Height

Take 2 times the beam height as the initial height of the sleeve. 1.2 times, 1.5 times, and 1.8 times the sleeve height were taken to compare with the initial height. Figure20 shows the load-displacement curves of joints with different sleeve heights. As shown in the figure, when the height of the sleeve is increased while the sleeve thickness is unchanged, the initial stiffness of the sleeve joint slowly increases. Moreover, with the increase in sleeve height, the ultimate load and ultimate displacement do not change significantly. Therefore, it is not economical to improve the bearing capacity of the joint by increasing the sleeve height.Figure 20
Load-displacement curves of joints with different sleeve heights.Figure21 shows the hysteretic curves of joints with different sleeve heights. By comparing the hysteretic curves of joints with each height, it is found that there is no significant change. However, as the height of the sleeve height increases, the shuttle shape becomes more obvious, and the hysteretic curve becomes fuller. It suggests that increasing the height can improve the energy dissipation capacity and ductility of the joints but has no significant effect on changing the ultimate bearing capacity and ultimate displacement. Moreover, as the height increases, the fabrication of sleeve joint specimens becomes more difficult. Therefore, the seismic requirements of joints can be met only by appropriately increasing the sleeve height.Figure 21
Hysteretic curves of joints with different sleeve heights. (a) 1 h, (b) 1.2 h, (c) 1.5 h, and (d) 1.8 h.
(a)(b)(c)(d)


## 5. Conclusions

In this paper, the method of numerical simulation analysis is used to design three concrete-filled steel tubal column-steel beam semirigid sleeve joints. The joint is composed of two steel plates and a sleeve welded together with the steel pipe column. The upper and lower flanges and webs at the end of the steel beam are welded by manual arc welding and completely welded on the sleeve. The validity of the finite element model is verified by comparison with experimental data, and the joints are subjected to low cyclic loading. The mechanical properties under different parameters are analyzed. Based on the analysis of this paper, the following conclusions can be drawn:(1)
The semirigid sleeve joint model is established by ABAQUS and compared with the hysteretic curves and skeleton curves of previous experiments, which verifies the applicability of the finite element model in simulating the seismic performance of the joint under low cycle load.(2)
The axial compression ratio and the height of the sleeve have little effect on the ultimate bearing capacity of the joint and have a small effect on the energy dissipation capacity. The design should be selected according to the economic principle.(3)
The thickness of the sleeve and the concrete strength grade are the main factors affecting the seismic performance of sleeve joints. When the thickness of the sleeve is increased or the concrete strength grade in the column is increased, the ductility and ultimate bearing capacity of the joint increase, and the energy consumption capacity is also improved.(4)
It is recommended that the thickness of the sleeve should be 1 to 1.25 times the thickness of the connecting steel tube. At the same time, according to the principle of economy, it is recommended that the height of the sleeve should not be greater than 2 times the height of the connecting steel beam.



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*Source: 3639936-2022-07-19.xml*