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Abstract

In order to study the axial compression performance of the FRP (fiber reinforced polymer)-concrete-steel solid columns (FCSSC), the nonlinear analysis program of FCSSC was compiled in this paper. The program was verified by existing tests, and the impacts of FRP tube thickness, steel tube thickness, outer radius of steel tube, steel tube strength and concrete strength were examined. The outcomes showed that the calculated results agreed with the experimental results. It demonstrated the way that the program could precisely reflect the strain of FCSSC under various degrees of load and gauge a ultimate load of FCSSC. The increment of steel tube thickness, outer radius of steel tube and concrete strength on the bearing capacity of FCSSC were chiefly reflected in the increment of initial stiffness. The improvement of FRP tube thickness could provide greater constraining force. The increment of steel tube strength could expand the load at the inflection point on the load-longitudinal strain curve. The research results can give a reference to the use of the new structure.

Keywords

FRP tube concrete steel tube axial compression performance

Introduction

Fiber reinforced polymer (FRP) has been successfully used in fortifying the designs in view of its benefits like high strength, light weight major and corrosion resistance. Lately, FRP tubes, especially FRP tube concrete structure has been applied in civil engineering.^1–4 In the FRP tube concrete structure, FRP tube is a lightweight formwork, which can lessen the expense and the expulsion time and FRP tube can constraint the concrete in the circumference which can improve structural bearing capacity and ductility. However, there are also some disadvantages in FRP tube concrete structure, such as brittle failure, poor bearing capacity in construction stage and so on.

In view of the advantages and disadvantages of FRP tube concrete structure, the composite structure of FRP, steel and concrete has become the focus in recent years. Xiao⁵ proposed to utilize FRP tube to constraint the concrete-filled steel tube columns in 2003, giving full play to the benefits of FRP and steel tube to oblige the concrete, in order to compensate for the weaknesses of plasticity of FRP and erosion of steel tube. Tao et al.⁶ found this structure can improve the bearing capacity and ductility than the concrete structure or concrete-filled steel tube structure. Wang et al.^7–9 proposed FRP restricted shaped steel concrete columns in 2009. In this construction, I-shaped steel was in the FRP tube, and the concrete was filled the FRP tube. The FRP tube can constraint the circumferential and longitudinal deflection of the concrete, so the shaped steel can effectively avoid local buckling under the constraint of concrete. Then the buckling time of the shaped steel can be delayed and the ultimate bearing capacity of the structure can be improved.

Teng et al.¹⁰ proposed the hollow-core FRP-concrete-steel column in 2004, as displayed in Figure 1(a). The empty column was made out of FRP tube (in the outside), steel tube and concrete filled between the two tubes. The steel tube can likewise be filled with concrete to be the FRP-concrete-steel solid column, as displayed in Figure 1(b). The new composite column defeated the corrosion of concrete filled steel tube column and low ductility of concrete filled FRP tube column. The main use of FRP tube in the new composite column was the high strength and to give circumferential restricting power to the concrete, in order to work on the bearing capacity and ductility of composite column. It likewise protect the inner steel tube from corrosion and the concrete from premature fracture. The FRP tube can be used as the formwork in the construction phase and can moreover defend the steel tube to avoid buckling. The concrete in the composite column was in a three-dimensional stress state under the constraints of steel tube and FRP tube, and its definitive strength and strain can be greatly improved. The composite column had good durability, seismic resistance and ductility in engineering.

Figure 1.

Cross section of FRP steel concrete composite columns: (a) double-tube concrete column (DTCC) and (b) FRP-concrete-steel solid column (FCSSC).

Yu et al.¹¹ conducted an experimental study on the eccentric compression of double-tube concrete column and proposed a variable constraint model. In this model, the eccentric distance was introduced into the calculation of the slope of the straight section of concrete stress-strain curve to consider the influence of strain gradient on the FRP constraint effect. Louk Fanggi and Ozbakkaloglu¹² studied and analyzed the effects of FRP tube thickness, concrete strength, hollow rate and steel tube thickness/shape on ultimate stress and ultimate strain of concrete in double-tube concrete column based on the established database. A calculation model was proposed to determine the ultimate stress and strain of concrete in composite columns. This model was suitable for ordinary concrete and high strength concrete double-tube column. Ozbakkaloglu et al.¹³ proposed a model that can be used to predict the limit state of double-tube concrete column and FRP-concrete-steel solid column based on the established database of combined column axial compression tests. By introducing the effective factors of stress and strain, the model can be used to calculate the ultimate stress and strain of concrete in composite columns with circular and square circular cross sections. At the same time, the model also considered the influence of failure mode of steel tube on the ultimate state of composite column.

Numerous specialists have finished a movement of researches on FRP tube-concrete-steel tube composite columns. Most of these studies focused on the axial compression performance,^14–16 eccentric compression performance^17,18 and seismic performance^19,20 of hollow-core FRP-concrete-steel composite columns. Through the joint limit of FRP tube and inside steel tube, the buckling failure the inner steel tube can be effectively delayed. Furthermore the steel content of the column can be increased and the ductility of composite column is better than that of the FRP tube filled with concrete column.

In view of the explores, there were some studies on FRP-concrete-steel solid columns.^4,21 Basically focus on the experimental, theoretical research, the impact of the parameters of the research is not comprehensive. The core concrete in the solid column can prevent the buckling of the steel tube and increase the bearing capacity of the composite column. To compensate for the absence of test information of solid columns, a nonlinear analysis program of FRP-concrete-steel solid column under axial compression is used in this paper. The consequences of nonlinear analysis program had been confirmed by existing tests. The parameters such as FRP tube thickness, steel tube thickness, outer radius of steel tube steel tube strength and concrete strength were analyzed in this paper.

Calculation analysis

Basic assumptions

According to the mechanical characteristics of FSCSC, it is assumed to be that:

(1) There is no overall slip between FRP tube, steel tube and concrete.

(2) The longitudinal deflection coordination and the internal and external force equilibrium ought to be met during loading.

ε_{f} = ε_{c} = ε_{s}, N = σ_{f} A_{f} + σ_{c} A_{c} + σ_{s} A_{s}

Where, $σ_{f}$ and $ε_{f}$ are the longitudinal stress and strain of the FRP tube. $σ_{c}$ and $ε_{c}$ are the longitudinal stress and strain of the concrete. $σ_{s}$ and $ε_{s}$ are the longitudinal stress and strain of the steel tube. $A_{f}$ is the cross sectional area of the FRP tube. $A_{c}$ is the cross sectional area of the concrete. $A_{s}$ is the cross sectional area of the steel tube. $N$ is the axial load.

Constitutive model

Constitutive relation of the concrete

The stress and strain curve of concrete is shown in Figure 2. The constitutive relationship of confined concrete²² was :

f_{c} = \frac{(E_{1} - E_{2}) ε_{c}}{{1 + {[\frac{(E_{1} - E_{2}) ε_{c}}{f_{o}}]}^{1.5}}^{\frac{1}{1.5}}} + E_{2} ε_{c}

(1)

E_{1} = 3950 \sqrt{{f'}_{c}}

E_{2} = 245.61 f_{c}'^{0.2} + 1.3456 \frac{E_{f} t_{f}}{D}

f_{o} = 0.872 f'_{c} + 0.371 f_{r} + 6.258

f_{r} = \frac{2 f_{f} t_{f}}{D}

Figure 2.

Stress-strain relationship of concrete.

Where, $f_{c}$ and $ε_{c}$ are the longitudinal stress and strain of the concrete. $E_{1}$ and $E_{2}$ are the slope of the first and second curves. $f_{o}$ is the plastic stress at the turning point of the second curve. $f'_{c}$ is the peak stress of unconfined concrete. $f_{r}$ is the lateral restraint of concrete. $f_{f}$ is the circumferential strength of FRP tube. $E_{f}$ is the circumferential elastic modulus of FRP tube. $t_{f}$ is the FRP tube thickness. $D$ is the concrete diameter.

Constitutive relation of the FRP tube

The constitutive relationship of FRP²³ was:

σ_{f} = E_{fz} ε_{f} [1 - \frac{(υ_{c} - υ_{fz}) υ_{fh}}{\frac{(1 - υ_{c} - 2 υ_{c}^{2}) E_{fh} t}{E_{c} R} + (1 - υ_{fz} υ_{fh})}]

(2)

Where, $σ_{f}$ and $ε_{f}$ are the longitudinal stress and strain of the FRP tube. $E_{fh}$ and $E_{fz}$ are the circumferential and longitudinal elastic modulus of FRP tube. and $υ_{fz}$ are the circumferential and longitudinal Poisson’s ratio of FRP tube. $υ_{c}$ is the Poisson’s ratio of the concrete. $R$ is the concrete radius. $t$ is the FRP tube thickness.

Constitutive relation of the steel tube

The stress and strain curve of steel tube²⁴ is consist of two straight-line segments: elastic segment and strengthening segment, as shown in Figure 3.

Figure 3.

Stress-strain relationship of steel tube.²⁴

The expression of stress and strain is:

σ_{s} = {\begin{matrix} E_{t} ε_{s} (ε_{s} \leq ε_{ty}) \\ f_{ty} + 0.01 E_{t} (ε_{s} - ε_{ty}) (ε_{s} > ε_{ty}) \end{matrix}

(3)

Where, $σ_{s}$ and $ε_{s}$ are the stress and strain of the steel tube. $f_{ty}$ is the yield strength of the steel tube. $E_{t}$ is the elastic modulus of the steel tube.

Computational procedure

(1) Input the material characteristics, geometric dimensions and other parameters of FCSSC, for instance, elastic modulus and cross-sectional area of the FRP tube, concrete, steel tube, diameter and thickness of FRP tube and steel tube.

(2) Assuming the longitudinal initial strain value $ε$ , the stress is determined by the stress-strain constitutive model of FRP tube, concrete and steel tube.

(3) The longitudinal load is calculated as per the balance condition of force $N$ .

(4) By increasing the longitudinal strain value $Δ ε$ , the whole process curve of load and strain of FCSSC can be acquired. The computation steps are displayed in Figure 4.

Figure 4.

Calculation procedure.

Verification results

The consequence of the nonlinear analysis program is contrasted with the load and longitudinal strain curves of test specimens DTCC-NSC-G4-Q345, DTCC-NSC-G4-Q460, DTCC-NSC-G4-Q690, DTCC-NSC-G8-Q345, DTCC-NSC-G8-Q460, and DTCC-NSC-G8-Q690 in Qian and Liu,²⁰ as shown in Figure 5. The test parameters in Xu²⁵ are as follows: the height of specimen is 400 mm, the inner diameter of FRP tube is 200 mm, the layers of FRP tube are 4 and 8. The axial elastic modulus of FRP with four layers is 11.9 GPa, and the axial Poisson ratio is 0.14. The circumferential elastic modulus is 40.3 GPa and the circumferential Poisson ratio is 0.45. The axial elastic modulus of FRP with 8 layers is 13.2 GPa, and the axial Poisson ratio is 0.12. The circumferential elastic modulus is 44.2 GPa and the circumferential Poisson ratio is 0.37. The outer diameter of steel tube is 133 mm and the thickness is 4 mm. The theoretical yield strength of Q345 steel, Q460 steel, and Q690 steel are 345, 460, and 690 MPa, respectively. The 28 days compressive strength of concrete is 54.97 MPa. The modulus of elasticity of concrete is 2.92 × 10⁴ MPa, and the Poisson proportion is 0.202.

Figure 5.

Comparison between test and calculation results: (a) DTCC-NSC-G4-345, (b) DTCC-NSC-G4-Q460, (c) DTCC-NCS-G4-Q690, (d) DTCC-NSC-G8-Q345, (e) DTCC-NSC-G8-Q460, and (f) DTCC-NSC-G8-Q690.

With the increment of load, the load and longitudinal strain curve shows three stages: the linear section in the initial stage, the elastic-plastic section and the strengthened linear section. The specimen is in the elastic working stage at the initial stage of loading. At this stage, the transverse deflection of concrete is close to nothing, so the interaction among concrete and FRP tube isn’t clear and the curve augments straightforwardly at this stage. At the point when the load comes to 37% of the ultimate load, the constraint impact of FRP tube on concrete had changed. The curve is not linearly. Right now, the growth rate of longitudinal strain of FRP tube is more prominent than that of load. At this stage, the transverse deflection of concrete increments quickly, which results in radial pressure between FRP tube and concrete, and FRP tube would constrain the concrete. At the point when the load reaches 59% of the ultimate load, the curve was roughly directly. Figure 5 shows that the calculation result is in exceptional concurrence with the test result, which shows that it is feasible to take a gander at the axial compression performance of FCSSC by using the axial compression nonlinear analysis program.

Influence of parameters

Some parameters of FCSSC are set as follows: the thickness of FRP tube is 5 mm, and the inner diameter is 200 mm. The axial elastic modulus of FRP tube is 12.5 GPa, and the axial strength is 180 MPa. The circumferential elastic modulus of FRP tube is 44.5 GPa, and the circumferential strength is 450 MPa. The thickness of the steel tube is 5 mm, and the outer diameter is 90 mm. The elastic modulus of steel tube is 206 GPa, and the yield strength is 345 MPa. The strength of concrete is C40. The impact of the FRP tube thickness, steel tube thickness, outer radius steel tube, steel tube strength and concrete strength on the load and longitudinal strain curve of FCSSC is examined.

The thickness of FRP tube

The load and longitudinal strain curves of FCSSC under various FRP tube thicknesses are displayed in Figure 6. All curves are consistent at the initial stage of load. When the load gets 27%–40% of the ultimate load (FRP tube thickness is 3 mm: 39.8%, 4 mm: 35.5%, 5 mm: 32.1%, 6 mm: 29.3%, 7 mm: 26.8%), the stiffness of load and longitudinal strain curve with thick FRP tube is more prominent than that of specimens with thin FRP tube. At a tantamount longitudinal strain, the load of specimen with thick FRP tube is higher than that of specimens with thin FRP tube. The ultimate loads of specimens with 4, 5, 6, and 7 mm FRP tube thickness are 12.1%, 24.3%, 36.6%, and 49.0% higher than that of specimens with 3 mm FRP tube thickness. The thickness of FRP tube impacts little on the stiffness of FCSSC. With the augmentation of FRP tube thickness, the necessity effect of FRP tube on concrete bit by bit increases. That is on the grounds that FRP tube breaks requires larger circumferential force, the ultimate bearing capacity of FSCSC would be increment with the increment of FRP tube thickness. The increment of ultimate bearing capacity is similar with the FRP tube thickness tube increasing per 1 mm.

Figure 6.

Effect of thickness of FRP tube.

Figure 7 shows the ultimate load of FCSSC changes with the thickness of FRP tube under different steel tube thickness, outer radius of steel tube, steel tube strength and concrete strength. It shows that the effect of the FRP tube thickness on the ultimate load of FCSSC is generally roughly similar. The ultimate load increases with the increment of FRP tube thickness.

Figure 7.

The thickness of FRP tube: (a) FRP tube thickness-Steel tube thickness, (b) FRP tube thickness-outer Radius of steel tube, (c) FRP tube thickness-Steel tube strength, and (d) FRP tube thickness-concrete strength.

Figure 7(a) shows the ultimate load of FCSSC changes with the thickness of FRP tube under different steel tube thickness. When the thickness of the steel tube changes from 3 to 7 mm, the slope of the curves are generally similar. For a comparative thickness of steel tube, the ultimate load would increase about 314 kN when the thickness of FRP tube increases per 1 mm.

Figure 7(b) shows the ultimate load of FCSSC changes with the thickness of FRP tube under different outer radius of steel tube. When the outer radius of the steel tube changes from 35 to 75 mm, the slope of the curves are generally similar. For a comparative outer radius of steel tube, the ultimate load would increase about 310 kN when the thickness of FRP tube increases per 1 mm.

Figure 7(c) shows the ultimate load of FCSSC changes with the thickness of FRP tube under different strength of steel tube. When the steel tube strength changes from Q345 to Q690, the slope of the curves are generally similar. For a comparable strength of steel tube, the ultimate load would increases about 313 kN when the thickness of FRP tube increases per 1 mm.

Figure 7(d) shows the ultimate load of FCSSC changes with the thickness of FRP tube under different concrete strength. When the concrete strength changes from C30 to C50, the grade of the slope of the curves are generally similar. For a comparable concrete strength, the ultimate load would increases around 312 kN when the FRP tube thickness increases per 1 mm.

The thickness of steel tube

The load and longitudinal strain curve of FCSSC under various steel tube thickness are displayed in Figure 8. It shows that the initial slope of the specimens with thick steel tube are greater than that of the specimens with thin steel tub. The steel tube thickness has an impact on the stiffness and the stiffness increases with the increase of steel tube thickness. At a tantamount longitudinal strain, the load of the specimens with thick steel tube is higher than that of the specimens with thin steel tube. The ultimate bearing capacity of specimens with steel tube thickness of 4, 5, 6, and 7 mm is 2.6%%, 5.1%, 7.6%, and 10.0% higher than that of specimens with thickness of 3 mm. That is because that with the increase of steel tube thickness, the longitudinal section area of steel tube would increase, and the bearing capacity of steel tube would increase. The ultimate bearing capacity of FCSSC increases with the increment of steel tube thickness.

Figure 8.

Effect of steel tube thickness.

Figure 9 analyzes the ultimate load of FCSSC changes with the thickness of steel tube under different FRP tube thickness, steel tube radius, steel tube strength and concrete strength. It shows that the impact of the steel tube thickness on the ultimate load of FCSSC is basically same. The ultimate load increases with the augmentation of steel tube thickness.

Figure 9.

The thickness of steel tube: (a) steel tube thickness-FRP tube thickness, (b) steel tube thickness-outer radius of steel tube, (c) steel tube thickness-steel tube strength, and (d) steel tube thickness-concrete strength.

Figure 9(a) shows the ultimate load of FCSSC changes with the thickness of steel tube under different FRP tube thickness. When the thickness of the FRP tube changes from 3 to 7 mm, the slope of the curves is generally similar. For a comparable thickness of FRP tube, the ultimate load would increase about 72 kN when the thickness of steel tube increases per 1 mm.

Figure 9(b) shows the ultimate load of FCSSC varies with the thickness of steel tube under various outer radius of steel tube. When the outer radius of steel tube changes from 75 to 35 mm, the slope increases with the augmentation of the outer radius of steel tube. It shows that with the augmentation of the outer radius of the steel tube, the impact of the steel tube thickness on the ultimate load increases bit by bit. This is because that with the increment of the outer radius of the steel tube, the longitudinal segment region of the steel tube extends, the bearing capacity of the steel tube increases. When outer radius of steel tube is 35, 45, 55, 65, and 75 mm, the ultimate load would independently increase by 54, 73, 92, 111, and 130 kN when the thickness of steel tube increases per 1 mm.

Figure 9(c) shows the ultimate load of FCSSC changes with the thickness of steel tube under different steel tube strength. When the steel tube strength changes from Q345 to Q690, the slope increases with the augmentation of steel tube strength. It shows that with the augmentation of steel tube strength, the impact of steel tube thickness on ultimate load increases bit by bit. The utilization of high-strength steel tube can significantly improve the bearing capacity of FCS solid columns.

Figure 9(d) shows the ultimate load of FCSSC changes with the thickness of steel tube under different concrete strength. When the concrete strength changes from C30 to C50, the slope of the curves is generally similar. For a comparable concrete strength, the ultimate load would increase about 73 kN when the thickness of steel tube increases per 1 mm.

Outer radius of steel tube

The load and longitudinal strain curves of FCSSC under various outer radius of steel tube are displayed in Figure 10. It shows that the initial slope of the specimen with long outer radius of the steel tube is greater than that of the specimen with short outer radius of the steel tube. The steel tube outer radius affects the stiffness of the specimen, and the stiffness of the specimen would increase with the increment of the steel tube outer radius. At a comparable longitudinal strain, the load of specimens with long outer radius of steel tube is higher than that of the specimens with short outer radius of steel tube. The ultimate bearing capacity of specimens with outer radius of 45, 55, 65, and 75 mm is 2.5%%, 5.0%, 7.5%, and 10.0% higher than that of specimens with outer radius of 35 mm. With the increment of the outer radius of the steel tube, the cross-sectional area of the steel tube would bit by bit augment. The ultimate load of FCSSC would increase with the increment of the outer radius of steel tube.

Figure 10.

Effect of outer radius of steel tube.

Figure 11 analyzes the ultimate load of FCSSC changes with the outer radius of steel tube under different FRP tube thickness, steel tube thickness, steel tube strength and concrete. It shows that the effect of the steel tube thickness on the ultimate load of FCSSC is basically same. The ultimate load increases with the increment of steel tube thickness.

Figure 11.

Outer radius of steel tube: (a) radius of steel tube-FRP tube thickness, (b) radius of steel tube-steel tube thickness, (c) radius of steel tube-steel tube strength, and (d) radius of steel tube-concrete strength.

Figure 11(a) shows the ultimate load of FCSSC changes with the outer radius of steel tube under different FRP tube thickness. When the thickness of FRP tube changes from 3 to 7 mm, the slope of the curves is generally similar. It shows that the change of FRP tube thickness is similar to that of steel tube outer radius on the ultimate load of FCSSC, which changes roughly linearly.

Figure 11(b) shows the ultimate load of FCSSC changes with the outer radius of steel tube under different steel tube thickness. When the thickness of the steel tube changes from 3 to 7 mm, the effect of the outer radius of the steel tube on the ultimate load increases gradually. That is because that the specimens with thick steel tube have greater constraint effect on concrete than that of the specimens with small thickness of steel tube. When the outer radius of steel tube increases, the constraint effect of steel tube on concrete would increase. The ultimate load of specimens with thick steel tube would be more influenced by the outer radius of steel tube than that of specimens with thin steel tube. When the thickness of steel tube is 3, 4, 5, 6, and 7 mm and the outer radius of steel tube increases from 35 to 75 mm, the ultimate load of FCSSC would increase by 7.6%, 10.0%, 12.2%, 14.4%, and 16.5%.

Figure 11(c) shows the ultimate load of FCSSC changes with the outer radius of steel tube under different strength of steel tube. When the steel tube strength changes from Q345 to Q690, the effect of the outer radius of the steel tube on the ultimate load increases gradually. That is because that the specimens with long outer radius of steel tube have greater cross-sectional district. When the strength of steel tube extends, it would greatly influence the ultimate load. When the strength of steel tube is Q345, Q420, Q460, Q620, and Q690 and the outer radius of steel tube increases from 35 to 75 mm, the ultimate load of FCSSC increases by 10.0%, 12.2%, 13.3%, 17.6%, and 19.4% independently.

Figure 11(d) shows the ultimate load of FCSSC changes with the outer radius of steel tube under different concrete strength. When the concrete strength changes from C30 to C50, the slope of the curves is generally similar. It shows that the effect of the outer radius of steel tube on the ultimate load of FCSSC is equivalent and changes linearly.

Steel tube strength

The load and longitudinal strain curve of FCSSC under different steel tube strength is shown in Figure 12. It shows that the load at the inflection point would increase with the increment of steel tube strength. And the slope of the straight line has basically no change. The ultimate load with the steel tube strength of Q420, Q460, q620, and Q690 is 2.6%%, 3.9%, 9.4%, and 11.8% higher than that of Q345 respectively.

Figure 12.

Effect of steel tube strength.

Figure 13 analyzes the ultimate load of FCSSC changes with the strength of steel tube under different FRP tube thickness, steel tube thickness, outer radius of steel tube and concrete. It shows that the effect of the steel tube strength on the ultimate load of FCSSC is generally similar. The ultimate load increases with the increment of steel tube strength.

Figure 13.

Steel tube strength: (a) steel tube strength-FRP tube thickness, (b) steel tube strength-steel tube thickness, (c) steel tube strength-radius of steel tube, and (d) Steel tube strength-concrete strength.

Figure 13(a) shows the ultimate load of FCSSC changes with the strength of steel tube under different FRP tube thickness. When the thickness of the FRP tube changes from 3 to 7 mm, the slope of the curves is generally similar. It shows that the change of FRP tube thickness resembles the effect of steel tube outer radius on the ultimate load of FCSSC, both of them are roughly linearly.

Figure 13(b) shows the ultimate load of FCSSC changes with the strength of steel tube under different steel tube thickness. When the thickness of the steel tube changes from 3 to 7 mm, the effect of the outer radius of the steel tube on the ultimate load increases gradually. That is because that the specimens with thick steel tube have greater constraint effect on concrete than that of the specimens with thin steel tube. When the outer radius of steel tube extends, the constraint effect of steel tube on concrete would increase. The ultimate load of specimens with thick steel tube would be more influenced by the strength of steel tube than that of specimens with thin steel tube. When the thickness of steel tube is 3, 4, 5, 6, and 7 mm and the steel tube strength increases from Q345 to Q690, the ultimate load of FCSSC would augment by 9.2%, 11.8%, 14.2%, 16.5%, and 18.6% independently.

Figure 13(c) shows the ultimate load of FCSSC changes with the strength of steel tube under different outer radius of steel tube. When the outer radius of steel tube changes from 35 to 75 mm, the effect of the steel tube strength on the ultimate load increases gradually. The reason is that the cross-section area of specimens with long outer radius of steel tube is enormous. At the moment that the strength of steel tube increases, the effect on the ultimate load is more significant.

Figure 13(d) shows the ultimate load of FCSSC changes with the strength of steel tube under different concrete strength. When the concrete strength changes from C30 to C50, the slope of the curves is very similar. It shows that the effect of the outer radius of steel tube on the ultimate load of FCSSC is practically identical and changes linearly.

Concrete strength

The load and longitudinal strain curve of FCSSC under different concrete strength is shown in Figure 14. It shows that the ultimate load of the specimens with high concrete strength is greater than that of the specimens with low concrete strength. The concrete strength affects the stiffness and the stiffness would increase with the increment of concrete strength. At comparable longitudinal strain, the load of the specimens with high concrete strength is larger than that of the specimens with low concrete strength. The ultimate load of specimens with the concrete strength of C35, C40, C45, and C50 is 4.4%%, 8.8%, 13.2%, and 17.6% higher than that of the specimens with concrete strength of C30.

Figure 14.

Effect of concrete strength.

Figure 15 analyzes the ultimate load of FCSSC changes with the concrete strength under different FRP tube thickness, steel tube thickness, steel tube strength and outer radius of steel tube. It shows that the effect of the concrete strength on the ultimate load of FCSSC generally similar. The ultimate load increases with the increment of concrete strength.

Figure 15.

Concrete strength: (a) Concrete strength-FRP tube thickness, (b) concrete strength-steel tube thickness, (c) concrete strength-outer radius of steel tube, and (d) concrete strength-steel tube strength.

Figure 15(a) shows the ultimate load of FCSSC changes with the concrete strength under different FRP tube thickness. When the thickness of the FRP tube changes from 3 to 7 mm, the slope of the curves is generally similar. For a comparable thickness of FRP tube, the ultimate load would increase about 126 kN when the concrete strength increases per 5 MPa.

Figure 15(b) shows the ultimate load of FCSSC changes with the concrete strength under different steel tube thickness. When the thickness of steel tube changes from 3 to 7 mm, the curve is generally similar. For a comparable steel tube thickness, the ultimate load would increase about 125 kN when the concrete strength increases per 5 MPa.

Figure 15(c) shows the ultimate load of FCSSC changes with the concrete strength under different outer radius of steel tube. When the outer radius of the steel tube changes from 35 to 75 mm, the curve is generally similar. It shows that the change of outer radius of steel tube resembles the effect of concrete strength on the ultimate load of FCSSC, both of them are roughly linearly.

Figure 15(d) shows the ultimate load of FCSSC changes with the concrete strength under different steel tube strength. When the steel tube strength changes from Q345 to Q690, the curve is similar. For a comparable thickness of steel tube, the ultimate load would increase by about 4% when the concrete strength increases per 5 MPa.

Conclusions

In this paper, the axial compressive behavior of FRP-concrete-steel solid columns is concentrated by compiling the nonlinear analysis program. Furthermore, the accuracy of the results is confirmed by the tests. The impacts of FRP tube thickness, steel tube thickness, outer radius of steel tube, steel tube strength and concrete strength on axial compressive behavior are systematically analyzed. The conclusions are summed up as follows:

(1) The results of nonlinear analysis program are in great concurrence with the consequences of tests. It shows that the nonlinear analysis program can precisely reflect the longitudinal strain of FCSSC under various loads and it can assess the ultimate load of FCSSC.

(2) The load and longitudinal strain curve of FCSSC can be generally separated into three phases: the linear segment in the initial stage, the elastic-plastic segment and the strengthened linear segment. When the load comes to 37% of the ultimate load, the constraint of FRP tube on concrete would change.

(3) The ultimate load of FCSSC would increase with the increment of FRP tube wall thickness, steel tube wall thickness, steel tube outer radius, steel tube strength and concrete strength. The improvement of steel tube thickness, outer radius of steel tube and concrete strength on the bearing capacity of FCSSC is mostly reflected in the improvement of initial stiffness. The improvement of FRP tube thickness on the bearing capacity is principally to give more constraint on concrete. The improvement of steel tube strength on the bearing capacity is principally to improve load at the inflection point of load and longitudinal strain curve.

Footnotes

Handling Editor: Chenhui Liang

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was upheld by the Education Department of Liaoning Province (No. LJKQZ20222313) and Liaoning Provincial Department of Natural Science (No. 2022-MS-399).

ORCID iD

Wenyu Hou

Data availability statement

Some of all data, models, of code that support the findings of this study are available from the corresponding author upon reasonable request.

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Nonlinear analysis of FRP-concrete-steel solid columns

Abstract

Keywords

Introduction

Calculation analysis

Basic assumptions

Constitutive model

Constitutive relation of the concrete

Constitutive relation of the FRP tube

Constitutive relation of the steel tube

Computational procedure

Verification results

Influence of parameters

The thickness of FRP tube

The thickness of steel tube

Outer radius of steel tube

Steel tube strength

Concrete strength

Conclusions

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

Data availability statement

References