# Axial Compressive Behavior of Glass Fiber-Reinforced Hollow Concrete Columns

Authors: Xiangyang Jian; Ni Zhang; Qingwei Sun; Jian Liu
Journal: Advances in Materials Science and Engineering
 (2022)

---

## Abstract

To investigate the axial compression behavior of glass fiber-reinforced polymer tubes filled with reinforced hollow concrete members, the finite element model was established in ABAQUS. The correctness of the finite element model was verified by comparing the simulation results with the existing test results. On this basis, the influence of the main parameters such as GFRP tube wall thickness, filament winding angle, concrete strength grade, and hollow ratio on the axial compression behavior was analyzed. The calculation formula of the bearing capacity under axial compression of the GFRP tube filled with reinforced hollow concrete members was established. The results show that the load and strain curves and failure modes of the model and the established bearing capacity formula are in good agreement with the test results. The axial compression capacity of the hollow members increases with the increase in the thickness of GFRP tube wall thickness, filament winding angle, and concrete strength grade and decreases with the increase in the hollow ratio. The GFRP tube filament winding angle and hollow ratio have significant influence on the bearing capacity of axial compression, followed by the GFRP tube wall thickness and concrete strength grade. The radius ratio of hollow part should be 0.250.5. The axial compression bearing capacity of the hollow members can be compensated by properly increasing the GFRP tube wall thickness, filament winding angle, or concrete strength grade. The research conclusion can provide some reference for the design of the structure.


---

## Body

## 1. Introduction

Fiber-reinforced polymer (FRP) is a new material widely used in civil engineering in recent years [1, 5], among which filament wound pipe is the most representative one. The cost of glass fiber-reinforced polymer (GFRP) is lower than that of other FRP materials, which makes the structure have higher economic benefits. The glass fiber-reinforced polymer tube filled with reinforced hollow concrete structure is formed by setting a nonstressed mold in the glass fiber tube, then placing the longitudinal stressed reinforcement between the glass fiber tube and the mold, and finally, and pouring concrete between the glass fiber tube and the mold. The typical section form of the structure is shown in Figure 1. The excellent corrosion resistance of glass fiber tube can protect the internal longitudinal reinforcement and concrete, and the concrete strength is improved due to the restraint effect of glass fiber tube. The concrete is only poured between the glass fiber tube and the mold, which reduces the self-weight of the structure and is convenient for engineering transportation and installation. Due to its excellent performance, the structure has attracted extensive attention in the engineering field. The structure can better meet the needs of today’s engineering structures to withstand the harsh environment and the development requirements of heavy load, light weight, long span, and high strength. Therefore, it has been more and more widely used in underground engineering, civil buildings, bridges, and marine engineering [6, 9].Figure 1
Section form of the GFRP tube filled with reinforced hollow concrete structure.At present, researchers at home and abroad mainly study the mechanical properties of FRP-reinforced solid concrete structure, such as bending, axial compression, and eccentric compression [10, 23], while there are relatively few studies on the mechanical properties of FRP-reinforced hollow concrete structure [24 and 25]. Due to the limited test components, it is impossible to analyze each influencing factor in detail. In this paper, the axial compression calculation model of FRP-reinforced hollow concrete column is established through ABAQUS finite element analysis software, and the simulation results are compared with the existing test results to verify its correctness. On this basis, the effects of FRP wall thickness, filament winding angle, concrete strength, and void ratio on the axial compression performance of FRP-reinforced hollow concrete columns are analyzed.


## 2. Establishment of the Finite Element Model

### 2.1. Constitutive Model of the Glass Fiber Tube

The mechanical properties of the glass fiber tube in the elastic stage are based on the single-layer plate model in ABAQUS. The failure of glass fiber tube adopts the Hashin failure criterion [26]. The mechanical parameters of the glass fiber tube required to define Hashin criterion are obtained from [27], and the specific values are shown in Table 1.Table 1
Properties of the unidirectional GFRP tube.
XC/MPaXT/MPaYC/MPaYT/MPaG12/MPaE11/MPaE22/MPaυ12SL/MPa15035050140228701268084300.340


### 2.2. Constitutive Model of Concrete

The calculation model proposed by Lam and Teng [28] in 2003 is used as the constitutive model of concrete compression zone, as shown in Figure 2.(1)σc=Ecεc−Ec−E224fco′εc20≤εc≤εtfco′+E2εcεt≤εc≤εcc,εt=2fco′Ec−E2,E2=fcc′−fco′εcc,σRu=EfRεf,fcc′fco′=1+3.3σRufco′,σRufco′≥0.07fcc′fco′=1,σRufco′≤0.07,εccεco=1.75+12σRufco′εh,rupεco0.45.where Ec is the initial elastic modulus of concrete. E2 is the slope of the second curve. εt is the strain value at the dividing point of two curves. εcc and fcc′ are the peak strain and stress of concrete under restraint, respectively. εco and fco′ are the peak strain and stress of concrete without restraint, respectively. σRu is the circumferential limit binding force. εh,rup is the fracture strain in fiber material property test.Figure 2
Constitutive model of the concrete compression zone.The relationship model between stress and fracture energy provided by ABAQUS is used as the constitutive model of concrete in tensile zone to simulate the tensile softening performance of concrete. The tensile softening model of concrete is shown in Figure3.Figure 3
Tension softening model of concrete.


### 2.3. Constitutive Model of Reinforcement

The plastic analysis model provided by ABAQUS is used as the constitutive model of reinforcement, which meets the von Mises yield criterion. In the plastic analysis model, the relationship between uniaxial stress and strain of reinforcement needs to be input. The constitutive model of reinforcement adopts the calculation model proposed by Zhong [29] in 1994, as shown in Figure 4.Figure 4
Stress and strain relationship of steel.And, its relation is shown as follows:(2)σt=Etεt,−Aεt2+Bεt+C,fty,fty1+0.6εt−εte2εte3−εte2,1.6fty,εt≤εteεte<εt≤εte1εte1<εt≤εte2εte2<εt≤εte3εt>εte3,where fty is the yield strength of reinforcement. Et is the elastic modulus of reinforcement. A=0.2fty/εte1−εt2, B=2Aεte1, C=0.8fty+Aεte2−Bεte, εte=0.8fty/Et, εte1=1.5εte, εte2=10εte, and εte3=100εte.


### 2.4. Element Type, Contact Surface Relationship, and Loading Mode

The glass fiber tube uses composite shell element, and element type is S4R. The upper and lower end plates of components and concrete use solid element, and element type is C3D8R. The reinforcement uses three-dimensional truss element, and element type is T3D2. Friction contact is defined between glass fiber tube and concrete. The friction coefficient is set to 0.4. The Coulomb friction model is used in tangential direction, and “hard” contact is used in normal direction. The reinforcement is placed into the concrete by using the embedded region command, and the contact between the end plate and the concrete is constrained by binding tie. The displacement loading method is used in the loading process, and the incremental iterative method is used to solve the calculation. The calculation model is shown in Figure5.Figure 5
Finite element analysis model.The structural grid division method is adopted to discretize the components. The grid division density is very important to the calculation accuracy. If the grid is too large, the calculation accuracy will be reduced. If the grid is too dense, too much computer resources will be wasted. Therefore, the reasonable grid density should be determined in combination with the grid test.


## 2.1. Constitutive Model of the Glass Fiber Tube

The mechanical properties of the glass fiber tube in the elastic stage are based on the single-layer plate model in ABAQUS. The failure of glass fiber tube adopts the Hashin failure criterion [26]. The mechanical parameters of the glass fiber tube required to define Hashin criterion are obtained from [27], and the specific values are shown in Table 1.Table 1
Properties of the unidirectional GFRP tube.
XC/MPaXT/MPaYC/MPaYT/MPaG12/MPaE11/MPaE22/MPaυ12SL/MPa15035050140228701268084300.340


## 2.2. Constitutive Model of Concrete

The calculation model proposed by Lam and Teng [28] in 2003 is used as the constitutive model of concrete compression zone, as shown in Figure 2.(1)σc=Ecεc−Ec−E224fco′εc20≤εc≤εtfco′+E2εcεt≤εc≤εcc,εt=2fco′Ec−E2,E2=fcc′−fco′εcc,σRu=EfRεf,fcc′fco′=1+3.3σRufco′,σRufco′≥0.07fcc′fco′=1,σRufco′≤0.07,εccεco=1.75+12σRufco′εh,rupεco0.45.where Ec is the initial elastic modulus of concrete. E2 is the slope of the second curve. εt is the strain value at the dividing point of two curves. εcc and fcc′ are the peak strain and stress of concrete under restraint, respectively. εco and fco′ are the peak strain and stress of concrete without restraint, respectively. σRu is the circumferential limit binding force. εh,rup is the fracture strain in fiber material property test.Figure 2
Constitutive model of the concrete compression zone.The relationship model between stress and fracture energy provided by ABAQUS is used as the constitutive model of concrete in tensile zone to simulate the tensile softening performance of concrete. The tensile softening model of concrete is shown in Figure3.Figure 3
Tension softening model of concrete.


## 2.3. Constitutive Model of Reinforcement

The plastic analysis model provided by ABAQUS is used as the constitutive model of reinforcement, which meets the von Mises yield criterion. In the plastic analysis model, the relationship between uniaxial stress and strain of reinforcement needs to be input. The constitutive model of reinforcement adopts the calculation model proposed by Zhong [29] in 1994, as shown in Figure 4.Figure 4
Stress and strain relationship of steel.And, its relation is shown as follows:(2)σt=Etεt,−Aεt2+Bεt+C,fty,fty1+0.6εt−εte2εte3−εte2,1.6fty,εt≤εteεte<εt≤εte1εte1<εt≤εte2εte2<εt≤εte3εt>εte3,where fty is the yield strength of reinforcement. Et is the elastic modulus of reinforcement. A=0.2fty/εte1−εt2, B=2Aεte1, C=0.8fty+Aεte2−Bεte, εte=0.8fty/Et, εte1=1.5εte, εte2=10εte, and εte3=100εte.


## 2.4. Element Type, Contact Surface Relationship, and Loading Mode

The glass fiber tube uses composite shell element, and element type is S4R. The upper and lower end plates of components and concrete use solid element, and element type is C3D8R. The reinforcement uses three-dimensional truss element, and element type is T3D2. Friction contact is defined between glass fiber tube and concrete. The friction coefficient is set to 0.4. The Coulomb friction model is used in tangential direction, and “hard” contact is used in normal direction. The reinforcement is placed into the concrete by using the embedded region command, and the contact between the end plate and the concrete is constrained by binding tie. The displacement loading method is used in the loading process, and the incremental iterative method is used to solve the calculation. The calculation model is shown in Figure5.Figure 5
Finite element analysis model.The structural grid division method is adopted to discretize the components. The grid division density is very important to the calculation accuracy. If the grid is too large, the calculation accuracy will be reduced. If the grid is too dense, too much computer resources will be wasted. Therefore, the reasonable grid density should be determined in combination with the grid test.


## 3. Mechanical Performance Analysis

### 3.1. Verification of Numerical Simulation Results

In order to verify the correctness of the numerical simulation results, the simulated curve was compared with the load and longitudinal strain curve in the test in [25], as shown in Figure 6. It can be seen from Figure 7that the load and longitudinal strain curve of the numerical simulation results were in good agreement with the test results. It showed that the axial compression model of the FRP-reinforced hollow concrete column established by ABAQUS was correct, and the axial compression performance can be studied by this model.Figure 6
Comparison between calculated and experimental results: (a) GRCH1, (b) GRCH2, (c) GRCH3, (d) GRC4, (e) GRCH5, (f) GRCH6, and (g) GCH7.
(a)(b)(c)(d)(e)(f)(g)Figure 7
Load and strain curve.


### 3.2. Mechanical Behavior

In order to verify the effectiveness of the axial compression model of glass fiber-reinforced hollow concrete members, its stress mechanism was studied. Taking GRCH6 member in [30] as an example, the whole process of member axial compression failure is studied. And, the failure modes of simulated and tested members were compared, as shown in Figure 8.Figure 8
Test and simulated failure mode. (a) Failure mode of GRCH6 in [30]. (b) Simulation results.
(a)(b)Through the established axial compression model, the load and longitudinal strain relationship curve of GRCH6 is obtained, as shown in Figure7. In order to better observe the stress, three characteristic points are taken on the load and longitudinal strain curve. Point A is the end point of the first straight line segment, point B is the starting point of the third linear strengthening segment, and point C is the final failure point of the component. The stress distributions of glass fiber tube, reinforcement, and concrete in axial compression members at three characteristic points are given, respectively, as shown in Figures 9 and 10:(1)
Elastic stage OA: When the load is small, the load and longitudinal strain curve in this stage is straight and the axial compression member is in the elastic working stage. Glass fiber tube, reinforcement, and concrete are stressed separately. The transverse deformation of concrete is small, and the glass fiber tube has not yet restrained the internal concrete. At this stage, the stress of the glass fiber tube is evenly distributed along the whole length of the member and the reinforcement has not yet yielded (Point A in Figures10(b) and 10(c)).(2)
Elastoplastic stage AB: With the increasing load, the load and longitudinal strain curve begins to show a curve. With the continuous development of microcracks in concrete, the stiffness of axial compression members decreases. At this stage, the increase of transverse deformation of concrete makes the glass fiber tube under radial compression and circumferential tension. The glass fiber tube has a restraining effect on the internal concrete. Both longitudinal reinforcement and stirrup yield at point B (point B in Figure10(c)).(3)
Strengthen stage BC: With the increase of transverse deformation of concrete, the circumferential stress of glass fiber tube continues to increase. At this stage, the binding force of the glass fiber tube on the internal concrete is gradually strengthened. When point C is reached, the glass fiber tube reaches the ultimate tensile stress at 120240 mm from the upper and lower ends. The core concrete is crushed, and the glass fiber is broken. Finally, the axial compression member is damaged.Figure 9
The stress distribution of concrete.Figure 10
The stress distribution of each part. (a) The axial stress distribution in the core concrete. (b) GFRP pipe ring to the stress distribution. (c) The stress distribution of the reinforced skeleton.
(a)(b)(c)From the above analysis, the axial compression model of the FRP-reinforced hollow concrete column established in this paper can simulate the whole process of axial compression failure. Moreover, the failure model obtained by simulation is basically consistent with the tested one.


## 3.1. Verification of Numerical Simulation Results

In order to verify the correctness of the numerical simulation results, the simulated curve was compared with the load and longitudinal strain curve in the test in [25], as shown in Figure 6. It can be seen from Figure 7that the load and longitudinal strain curve of the numerical simulation results were in good agreement with the test results. It showed that the axial compression model of the FRP-reinforced hollow concrete column established by ABAQUS was correct, and the axial compression performance can be studied by this model.Figure 6
Comparison between calculated and experimental results: (a) GRCH1, (b) GRCH2, (c) GRCH3, (d) GRC4, (e) GRCH5, (f) GRCH6, and (g) GCH7.
(a)(b)(c)(d)(e)(f)(g)Figure 7
Load and strain curve.


## 3.2. Mechanical Behavior

In order to verify the effectiveness of the axial compression model of glass fiber-reinforced hollow concrete members, its stress mechanism was studied. Taking GRCH6 member in [30] as an example, the whole process of member axial compression failure is studied. And, the failure modes of simulated and tested members were compared, as shown in Figure 8.Figure 8
Test and simulated failure mode. (a) Failure mode of GRCH6 in [30]. (b) Simulation results.
(a)(b)Through the established axial compression model, the load and longitudinal strain relationship curve of GRCH6 is obtained, as shown in Figure7. In order to better observe the stress, three characteristic points are taken on the load and longitudinal strain curve. Point A is the end point of the first straight line segment, point B is the starting point of the third linear strengthening segment, and point C is the final failure point of the component. The stress distributions of glass fiber tube, reinforcement, and concrete in axial compression members at three characteristic points are given, respectively, as shown in Figures 9 and 10:(1)
Elastic stage OA: When the load is small, the load and longitudinal strain curve in this stage is straight and the axial compression member is in the elastic working stage. Glass fiber tube, reinforcement, and concrete are stressed separately. The transverse deformation of concrete is small, and the glass fiber tube has not yet restrained the internal concrete. At this stage, the stress of the glass fiber tube is evenly distributed along the whole length of the member and the reinforcement has not yet yielded (Point A in Figures10(b) and 10(c)).(2)
Elastoplastic stage AB: With the increasing load, the load and longitudinal strain curve begins to show a curve. With the continuous development of microcracks in concrete, the stiffness of axial compression members decreases. At this stage, the increase of transverse deformation of concrete makes the glass fiber tube under radial compression and circumferential tension. The glass fiber tube has a restraining effect on the internal concrete. Both longitudinal reinforcement and stirrup yield at point B (point B in Figure10(c)).(3)
Strengthen stage BC: With the increase of transverse deformation of concrete, the circumferential stress of glass fiber tube continues to increase. At this stage, the binding force of the glass fiber tube on the internal concrete is gradually strengthened. When point C is reached, the glass fiber tube reaches the ultimate tensile stress at 120240 mm from the upper and lower ends. The core concrete is crushed, and the glass fiber is broken. Finally, the axial compression member is damaged.Figure 9
The stress distribution of concrete.Figure 10
The stress distribution of each part. (a) The axial stress distribution in the core concrete. (b) GFRP pipe ring to the stress distribution. (c) The stress distribution of the reinforced skeleton.
(a)(b)(c)From the above analysis, the axial compression model of the FRP-reinforced hollow concrete column established in this paper can simulate the whole process of axial compression failure. Moreover, the failure model obtained by simulation is basically consistent with the tested one.


## 4. Influence of Design Parameters on Axial Compression Performance

Based on the correctness of the established finite element model, the axial compression performance of glass fiber-reinforced hollow concrete columns is analyzed. The basic parameters are set as follows: The wall thickness of glass fiber tube, the filament winding angle, the inner diameter, the radius of hollow concrete, and concrete strength grade are 5 mm, 70°, 200mm, 50mm, and C50, respectively. When other parameters are the same, the effects of changing the wall thickness, filament winding angle, concrete strength, and void ratio of glass fiber tube are studied.


### 4.1. Influence of Glass Fiber Tube Wall Thickness

The load and longitudinal strain curves of glass fiber tube-reinforced hollow concrete columns with different glass fiber tube wall thicknesses are shown in Figure11 when the glass fiber tube wall thicknesses are 3, 4, 5, 6, and 7 mm, respectively, and other conditions are the same. It can be seen that the load and longitudinal strain curves are basically the same at the initial stage of load action. When the load reaches 3545% Pu (3mm: 48%, 4mm: 43%, 5mm: 40%, 6mm: 36%, and 7mm: 34%), the change of glass fiber tube wall thickness affects the load and longitudinal strain curve. The load value of the member with large thickness is greater than that of the member with small thickness at the same strain value, and the curve slope of the member with large thickness is greater than that of the member with small thickness. The ultimate bearing capacity of glass fiber tube wall thicknesses 4mm, 5mm, 6mm, and 7mm is 10.5%, 20.6%, 31.0%, and 40.9% higher than that of 3mm, respectively. With the increase of the wall thickness of glass fiber tube, greater lateral force is required for glass fiber fracture. And the restraint of internal concrete is improved; that is, the axial compression bearing capacity increases with the increase of glass fiber tube wall thickness.Figure 11
The influence of GFRP tube thickness.


### 4.2. Influence of Filament Winding Angle of the Glass Fiber Tube

When the filament winding angles of the fiber glass tube is 10°, 30°, 50°, 70°, and 90°, respectively, and other conditions are the same, the load and longitudinal strain curves of glass fiber tube-reinforced hollow concrete columns with different filament winding angles of fiber glass tube are shown in Figure12. It can be seen that the load and longitudinal strain curves are basically the same at the initial stage of load action. When the load reaches 3050% Pu (10°: 48%, 30°: 43%, 50°: 39%, 70°: 34%, and 90°: 28%), the change of filament winding angle of glass fiber tube has an impact on the load and longitudinal strain curve. The curve slope of the member with large winding angle is greater than that of the member with small winding angle. It shows that the stiffness of the member increases with the increase of the filament winding angle of the glass fiber tube. The load value of the member with larger filament winding angle is greater than that of the member with smaller filament winding angle at the same strain value. The ultimate bearing capacity of the glass fiber tube with filament winding angles of 30°, 50°, 70°, and 90° is 10.8%, 21.7%, 41.5%, and 68.0% higher than that of 10°, respectively. With the increase of winding angle, the circumferential binding force of glass fiber tube increases; that is, the axial compression bearing capacity increases with the increase of fiber winding angle of glass fiber tube.Figure 12
The influence of the GFRP tube fiber winding angle.


### 4.3. Influence of the Concrete Strength Grade

When the concrete strength grade is C50, C45, C40, C35, and C30, respectively, and other conditions are the same, the load and longitudinal strain curves of glass fiber tube-reinforced hollow concrete columns under different concrete strength grades are shown in Figure13. It can be seen that the load and longitudinal strain curves are basically the same at the initial stage of load action. When the load reaches 30–35% Pu (C50: 29%, C45: 31%, C40: 32%, C35: 34%, and C30: 36%), the change of concrete strength affects the load and longitudinal strain curve. The curve slope of members with higher concrete strength is greater than that of members with lower concrete strength. It shows that the stiffness of members increases with the increase of concrete strength grade. The load value of the member with high concrete strength is greater than that of the member with low concrete strength at the same strain value. The ultimate bearing capacity of concrete strength C50, C45, C40, and C35 is 25.3%, 19.3%, 12.9%, and 6.4% higher than that of C30, respectively. With the increase of concrete strength, the axial compression bearing capacity increases gradually.Figure 13
The influence of strength grade.


### 4.4. Influence of Hollow Ratio

1When the hollow concrete has the radius of 0mm (solid), 25mm, 50mm, and 75mm, respectively, and other conditions are the same, the load and longitudinal strain curves of glass fiber tube-reinforced hollow concrete columns under hollow concrete with different radii are shown in Figure14. It can be seen that the load and longitudinal strain curves are basically the same at the initial stage of load action. When the load reaches 2535% Pu (0mm: 28%, 25mm: 29%, 50mm: 31%, and 75mm: 34%), the change of void ratio has an impact on the load and longitudinal strain curve. The curve slope of the member with small hollow ratio is greater than that of the member with large hollow ratio. It shows that the stiffness of the member increases with the decrease of hollow ratio. The load value of the member with small hollow ratio is greater than that of the member with large hollow ratio at the same strain value. The ultimate bearing capacity of hollow concrete with the radius of 0mm (solid), 25mm, and 50mm is 49.1%, 43.5%, and 27.4% higher than that of 75mm, respectively. With the increase of hollow ratio, the area of concrete gradually decreases, resulting in the reduction of bearing capacity of hollow columns; that is, the axial compression bearing capacity decreases with the increase of hollow ratio.Figure 14
The influence of hollow ratio.According to the above analysis, the axial compression bearing capacity of glass fiber tube-reinforced hollow concrete columns increases with the increase of the glass fiber tube wall thickness. When the wall thickness is increased from 3mm to 7mm, the bearing capacity is increased by about 41%. The bearing capacity increases with the increase of fiber winding angle of the glass fiber tube. The filament winding angle of glass fiber tube is increased from 10° to 90°, and the bearing capacity is increased by about 68%. The bearing capacity increases with the increase of concrete strength grade. The concrete strength grade is increased from C30 to C50, and the bearing capacity is increased by about 25%. The bearing capacity increases with the decrease of hollow ratio. The radius of concrete hollow decreased from 75mm to 0mm (solid), and the bearing capacity is increased by about 49%. The winding angle and hollow ratio of glass fiber tube have significant influence on the axial compressive capacity of glass fiber tube-reinforced hollow concrete column, followed by the wall thickness of glass fiber tube and concrete strength grade. The glass fiber-reinforced hollow concrete columns should not only consider that the hollow part can reduce the self-weight but also ensure that the axial compression bearing capacity cannot be too low. Therefore, the radius ratio of hollow part should be 0.25 0.5. The axial compression bearing capacity of hollow columns can be compensated by appropriately increasing the wall thickness of glass fiber-reinforced tube, filament winding angle, or concrete strength.


## 4.1. Influence of Glass Fiber Tube Wall Thickness

The load and longitudinal strain curves of glass fiber tube-reinforced hollow concrete columns with different glass fiber tube wall thicknesses are shown in Figure11 when the glass fiber tube wall thicknesses are 3, 4, 5, 6, and 7 mm, respectively, and other conditions are the same. It can be seen that the load and longitudinal strain curves are basically the same at the initial stage of load action. When the load reaches 3545% Pu (3mm: 48%, 4mm: 43%, 5mm: 40%, 6mm: 36%, and 7mm: 34%), the change of glass fiber tube wall thickness affects the load and longitudinal strain curve. The load value of the member with large thickness is greater than that of the member with small thickness at the same strain value, and the curve slope of the member with large thickness is greater than that of the member with small thickness. The ultimate bearing capacity of glass fiber tube wall thicknesses 4mm, 5mm, 6mm, and 7mm is 10.5%, 20.6%, 31.0%, and 40.9% higher than that of 3mm, respectively. With the increase of the wall thickness of glass fiber tube, greater lateral force is required for glass fiber fracture. And the restraint of internal concrete is improved; that is, the axial compression bearing capacity increases with the increase of glass fiber tube wall thickness.Figure 11
The influence of GFRP tube thickness.


## 4.2. Influence of Filament Winding Angle of the Glass Fiber Tube

When the filament winding angles of the fiber glass tube is 10°, 30°, 50°, 70°, and 90°, respectively, and other conditions are the same, the load and longitudinal strain curves of glass fiber tube-reinforced hollow concrete columns with different filament winding angles of fiber glass tube are shown in Figure12. It can be seen that the load and longitudinal strain curves are basically the same at the initial stage of load action. When the load reaches 3050% Pu (10°: 48%, 30°: 43%, 50°: 39%, 70°: 34%, and 90°: 28%), the change of filament winding angle of glass fiber tube has an impact on the load and longitudinal strain curve. The curve slope of the member with large winding angle is greater than that of the member with small winding angle. It shows that the stiffness of the member increases with the increase of the filament winding angle of the glass fiber tube. The load value of the member with larger filament winding angle is greater than that of the member with smaller filament winding angle at the same strain value. The ultimate bearing capacity of the glass fiber tube with filament winding angles of 30°, 50°, 70°, and 90° is 10.8%, 21.7%, 41.5%, and 68.0% higher than that of 10°, respectively. With the increase of winding angle, the circumferential binding force of glass fiber tube increases; that is, the axial compression bearing capacity increases with the increase of fiber winding angle of glass fiber tube.Figure 12
The influence of the GFRP tube fiber winding angle.


## 4.3. Influence of the Concrete Strength Grade

When the concrete strength grade is C50, C45, C40, C35, and C30, respectively, and other conditions are the same, the load and longitudinal strain curves of glass fiber tube-reinforced hollow concrete columns under different concrete strength grades are shown in Figure13. It can be seen that the load and longitudinal strain curves are basically the same at the initial stage of load action. When the load reaches 30–35% Pu (C50: 29%, C45: 31%, C40: 32%, C35: 34%, and C30: 36%), the change of concrete strength affects the load and longitudinal strain curve. The curve slope of members with higher concrete strength is greater than that of members with lower concrete strength. It shows that the stiffness of members increases with the increase of concrete strength grade. The load value of the member with high concrete strength is greater than that of the member with low concrete strength at the same strain value. The ultimate bearing capacity of concrete strength C50, C45, C40, and C35 is 25.3%, 19.3%, 12.9%, and 6.4% higher than that of C30, respectively. With the increase of concrete strength, the axial compression bearing capacity increases gradually.Figure 13
The influence of strength grade.


## 4.4. Influence of Hollow Ratio

1When the hollow concrete has the radius of 0mm (solid), 25mm, 50mm, and 75mm, respectively, and other conditions are the same, the load and longitudinal strain curves of glass fiber tube-reinforced hollow concrete columns under hollow concrete with different radii are shown in Figure14. It can be seen that the load and longitudinal strain curves are basically the same at the initial stage of load action. When the load reaches 2535% Pu (0mm: 28%, 25mm: 29%, 50mm: 31%, and 75mm: 34%), the change of void ratio has an impact on the load and longitudinal strain curve. The curve slope of the member with small hollow ratio is greater than that of the member with large hollow ratio. It shows that the stiffness of the member increases with the decrease of hollow ratio. The load value of the member with small hollow ratio is greater than that of the member with large hollow ratio at the same strain value. The ultimate bearing capacity of hollow concrete with the radius of 0mm (solid), 25mm, and 50mm is 49.1%, 43.5%, and 27.4% higher than that of 75mm, respectively. With the increase of hollow ratio, the area of concrete gradually decreases, resulting in the reduction of bearing capacity of hollow columns; that is, the axial compression bearing capacity decreases with the increase of hollow ratio.Figure 14
The influence of hollow ratio.According to the above analysis, the axial compression bearing capacity of glass fiber tube-reinforced hollow concrete columns increases with the increase of the glass fiber tube wall thickness. When the wall thickness is increased from 3mm to 7mm, the bearing capacity is increased by about 41%. The bearing capacity increases with the increase of fiber winding angle of the glass fiber tube. The filament winding angle of glass fiber tube is increased from 10° to 90°, and the bearing capacity is increased by about 68%. The bearing capacity increases with the increase of concrete strength grade. The concrete strength grade is increased from C30 to C50, and the bearing capacity is increased by about 25%. The bearing capacity increases with the decrease of hollow ratio. The radius of concrete hollow decreased from 75mm to 0mm (solid), and the bearing capacity is increased by about 49%. The winding angle and hollow ratio of glass fiber tube have significant influence on the axial compressive capacity of glass fiber tube-reinforced hollow concrete column, followed by the wall thickness of glass fiber tube and concrete strength grade. The glass fiber-reinforced hollow concrete columns should not only consider that the hollow part can reduce the self-weight but also ensure that the axial compression bearing capacity cannot be too low. Therefore, the radius ratio of hollow part should be 0.25 0.5. The axial compression bearing capacity of hollow columns can be compensated by appropriately increasing the wall thickness of glass fiber-reinforced tube, filament winding angle, or concrete strength.


## 5. Axial Compression Bearing Capacity

There are mainly unified theoretical method and limit equilibrium method for the calculation of axial compression bearing capacity of glass fiber-reinforced hollow concrete columns. Considering that the limit equilibrium method has relatively many analysis and calculation parameters and the stress analysis process is cumbersome, which is not convenient for practical application, a simple and practical bearing capacity calculation formula is established by using the unified theoretical method.


### 5.1. Unified Theory Method

Combined with the unified theory of concrete filled steel tubular model [24] and according to the failure mechanism and stress characteristics of glass fiber-reinforced hollow concrete column, concrete and glass fiber tube are taken as composite materials. We determine the formula for calculating the axial compression bearing capacity of glass fiber-reinforced hollow concrete columns.(3)Nu=A+Bθ+ρrfcAc,where A and B are undetermined coefficients. Ac is the concrete area. fc is the axial compressive strength of concrete. ρr is the reinforcement index, where ρr=ffAf/fcAc. Ar is the sectional area of reinforcement. fr is the yield strength of reinforcement. θ is the restraint index of the glass fiber tube, where θ=ffAf/fcAc. Af is the cross-sectional area of the glass fiber tube. ff is the yield strength of the glass fiber tube.Based on the correctness of the axial compression model of glass fiber tube-reinforced hollow concrete columns, a large number of calculation results are regressed and analyzed by changing the calculation parameters to determine the undetermined coefficients.A=1.093, and B=1.553.We substitute the calculation results of A and B into (3) and sort it out.(4)Nu=1.093+1.553θ+ρrfcAc.


### 5.2. Formula Validation

In order to verify the correctness of the established calculation formula, the calculation results are compared with the test results in the literature [25], as shown in Table 2.Table 2
Experiment results and calculated results.
Specimen nameNexp (kN)Nfem (kN)Ncal (kN)Nexp/NfemNexp/NcalGRCH12789274127601.0181.011GRCH22940291028441.0341.010GRCH32451237424461.0321.002GRC43246309430301.0491.071GRCH52889289528760.9981.005GRCH63095297029921.0421.034GCH72516244125271.0311.031Note. Nexp is the test result, Nfem is the finite element result, and Ncal is the calculation result.Compared with the experimental results, the average error of the analysis results by the finite element model is 1.029 and the mean square deviation is 0.033. The average error of is 1.018, and the mean square deviation is 0.030. It can be seen that the analytical results of the finite element model and the calculated results by the unified theory method are in good agreement with the test results, which shows that the established calculation formula of axial compression bearing capacity is reasonable.


## 5.1. Unified Theory Method

Combined with the unified theory of concrete filled steel tubular model [24] and according to the failure mechanism and stress characteristics of glass fiber-reinforced hollow concrete column, concrete and glass fiber tube are taken as composite materials. We determine the formula for calculating the axial compression bearing capacity of glass fiber-reinforced hollow concrete columns.(3)Nu=A+Bθ+ρrfcAc,where A and B are undetermined coefficients. Ac is the concrete area. fc is the axial compressive strength of concrete. ρr is the reinforcement index, where ρr=ffAf/fcAc. Ar is the sectional area of reinforcement. fr is the yield strength of reinforcement. θ is the restraint index of the glass fiber tube, where θ=ffAf/fcAc. Af is the cross-sectional area of the glass fiber tube. ff is the yield strength of the glass fiber tube.Based on the correctness of the axial compression model of glass fiber tube-reinforced hollow concrete columns, a large number of calculation results are regressed and analyzed by changing the calculation parameters to determine the undetermined coefficients.A=1.093, and B=1.553.We substitute the calculation results of A and B into (3) and sort it out.(4)Nu=1.093+1.553θ+ρrfcAc.


## 5.2. Formula Validation

In order to verify the correctness of the established calculation formula, the calculation results are compared with the test results in the literature [25], as shown in Table 2.Table 2
Experiment results and calculated results.
Specimen nameNexp (kN)Nfem (kN)Ncal (kN)Nexp/NfemNexp/NcalGRCH12789274127601.0181.011GRCH22940291028441.0341.010GRCH32451237424461.0321.002GRC43246309430301.0491.071GRCH52889289528760.9981.005GRCH63095297029921.0421.034GCH72516244125271.0311.031Note. Nexp is the test result, Nfem is the finite element result, and Ncal is the calculation result.Compared with the experimental results, the average error of the analysis results by the finite element model is 1.029 and the mean square deviation is 0.033. The average error of is 1.018, and the mean square deviation is 0.030. It can be seen that the analytical results of the finite element model and the calculated results by the unified theory method are in good agreement with the test results, which shows that the established calculation formula of axial compression bearing capacity is reasonable.


## 6. Conclusion

In this paper, the finite element model of glass fiber tube-reinforced hollow concrete columns under axial compression is established, and the correctness of the model is verified by the existing test results. On this basis, the effects of various parameters are analyzed:(1)
The finite element model established in this paper can simulate the whole process of axial compression failure, and the failure mode and load and longitudinal strain curve are basically consistent with the test results, which verifies the effectiveness of the axial compression model of the glass fiber tube-reinforced hollow concrete column.(2)
The radius ratio of the hollow part should be 0.25‐0.5, and the wall thickness, filament winding angle, or concrete strength of the glass fiber tube can be appropriately improved to make up for the axial compression bearing capacity of the hollow column.(3)
The calculation formula of axial compression bearing capacity is established by using the unified theory method. The calculation results are in good agreement with the test results, which can provide a certain reference basis for the design of the hollow structure.



---

*Source: 3315930-2022-12-16.xml*