# Numerical Investigation of Carbon Fiber Reinforced Polymer Confined Concrete-Filled Steel Tube Columns under Eccentric Load

Authors: Brhanu Degefa Zewdu; Temesgen Wondimu Aure
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

Recently, Fiber Reinforced Polymer (FRP) materials have emerged as a viable alternative to confined columns due to their high ultimate tensile strength to weight ratio and corrosion resistance under harsh and corrosive environments. Many previous studies were focused on the confining capability of FRP on concentric axial loads. This study presents a nonlinear finite element (FE) investigation of the effects of the thickness of Carbon Fiber Reinforced Polymer (CFRP), the thickness of steel tube, cross-sectional shape, and slenderness effect of an FRP confined concrete-filled steel tube (FCCFST) column under eccentric load. The FE model was validated by comparing the results with experimental data available in the literature, and good agreement was found. From the FE results, it was found that the steel tube and CFRP confinement improved the load resistance capacity by about 34% to 39%, and the axial shortening of the column at the peak load, from 136% to 57%, in rectangular and circular cross-sections, respectively. The efficiencies of steel tube and CFRP confinement first increase with an increasing eccentricity of the axial load and then start to decrease as the failure mode of the column changes to stability.


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## Body

## 1. Introduction

Reinforced concrete (RC) structures deteriorate upon exposure to adverse environmental conditions, overloads, aging, design and construction errors, damage due to blasts, and collision or earthquake effects. This affects the strength and so reduces the overall design life of the structure. Thus, strengthening and retrofitting concrete structural elements are inevitable in situations where preventing potential vulnerability is required.Steel tube confinement is the commonly used strengthening technique first introduced by Tomii [1] to produce concrete and steel tube composite members. The concrete-filled steel tube (CFST) column is a type of composite structural member in which the full advantage of the characteristic behavior of concrete and steel is utilized. The steel tube gives uniform confinement along the cross-section and length of the column and thus enhances the strength of the core concrete and thereby the load-carrying capacity of the column [2, 3]. Since the steel tube is not continuous at the intersection with the slab. The axial load on the steel tube leads to the punching of the top or bottom slab. Therefore, the steel tube size has to be minimized by reducing its thickness or applying a small girth gap between the loading plate and the steel tube [3]. However, steel tube with thin wall thickness is prone to inelastic outward local buckling and corrosion, leading to the loss of their load-carrying capacity [4].Recently, fiber reinforced polymer (FRP) confinement material has emerged as a viable alternative to confine CFST column due to its high ultimate tensile strength to weight ratio, corrosion resistance under harsh environments, and flexibility in the postconstruction and maintenance of structures [5, 6]. FRP and steel tube confinement techniques are frequently used to achieve high load-carrying capacity and/or ductility of the column, with better confinement efficiency under circular than square sections [7, 8]. The combination of these materials yields FRP confined concrete-filled steel tube (FCCFST) columns.The cross section of the column is one important parameter in column design and confinement techniques for steel tubes and FRP materials. The results of experimental investigations conducted by Mirmiran et al. [9] on FRP confinement under axial compression load indicated that FRP wrapping is more effective in circular sections than in square sections, due to the uniform confinement effect of FRP on the circular sections. Columns may be subjected to flexure, in addition to axial loads, due to unbalanced moments at connecting beams, vertical misalignment during construction or architectural design, or lateral forces resulting from wind or seismic activity, eccentric loading, etc. [10]. FRP confinement enhanced the strength and deformation capacity of both short and slender columns under eccentric load [11, 12], but its efficiency decreases with increasing slenderness [13, 14]. Al-Nimry and Al-Rabadi [15] carried out an experimental investigation on FRP confined circular RC column under load eccentricity to diameter ratio of 0, 0.13, 0.26, and 0.34, and the results indicated a relative axial load resistance enhancement of 25–35% higher under eccentric load than under concentric load.Many experimental investigations on eccentrically loaded FRP confined columns have been carried out on circular columns [16–25] and noncircular columns [26–29]. It was found that eccentric loading highly influenced the mechanical behaviors of FRP confined concrete. The experimental investigations also confirmed that FRP confinement improves the load-carrying capacity and ductility of RC columns by postponing the crushing of concrete and yielding reinforcement under eccentric load [12, 15, 29, 30]. Its efficiency increased with increasing CFRP layer number but decreased with increasing concrete strength and the column failed due to the rupture FRP at their mid-height [4, 23, 31, 32]. It was suggested that the hybrid of two materials improves the performance of the column under concentric and eccentric load [20]. Thus, the interaction between the inner concrete core and the outer confinements materials has three confining pressure stages, namely steel-dominated confinement, dual-dominated (steel and FRP confinement), and FRP-dominated confining pressure stages [33]. Others studied the behavior of FRP-wrapped RC columns and developed the axial-flexural (P–M) interaction diagrams [34, 35].Overall, several numerical and experimental studies have been conducted on the behavior of FRP-wrapped concrete columns subjected to axial-flexural loads. However, the structural performance of fiber-reinforced polymer confined concrete-filled steel tube (FCCFST) RC columns under static load has not been investigated thoroughly. In light of such shortcomings, this paper presents a numerical investigation on the effect of thickness of CFRP and steel tube confinements, slenderness, axial load eccentricity, and cross-sectional shape of FCCFST RC column under static eccentric loads and plots axial-flexural (P M) interaction diagrams.


## 2. Materials and Methods

It is difficult to perform a large-scale experiment in developing countries because it is expensive in terms of laboratory resources, time, and material cost. However, finite element analysis (FEA) is the most powerful alternative computational tool to solve the nonlinear analysis of structural components generated from complex structures.This study used finite element analysis method to conduct parametric investigation on the effect of load eccentricity, height, FRP layer number, and slenderness of fiber reinforced polymer confined concrete filled steel tube reinforced concrete columns [3].


### 2.1. Description of Experimental Work used for Validation

The experiment conducted by Wang et al. [3] on the behavior of CFST circular RC column subjected to 0 mm, 25 mm, and 50 mm load eccentricities were used for the validation of stress-strain properties of concrete, steel tube, reinforcement, and loading conditions. The CFST column has 240 mm diameter, 720 mm height, 1.5 mm steel tube thickness, 20 mm diameter of longitudinal reinforcement bars, and 8 mm diameter of stirrups. The details of material properties and dimensions of the experimental study are summarized in Table 1 and Figure 1, respectively.Table 1
Materials Properties and dimension of the validation specimens.
ParameterNominal value of Wang et al. [3] expt.Average 100 mm cube strength of concrete,fcu, 10055.8 MPaAverage compressive strength of concrete,fco41.9 MPaCubic compressive strength of concretefcu′53.01 MPaElastic modulus of concrete,Ec34.4 GPaElastic modulus steel tube, rebars and stirrupsEs200 GPaYield strength of the longitudinal bar,fby477.2 MPaYield strength of the stirrup,fsy285.6 MPaYield strength of the steel tube,fty364.3 MPaFigure 1
CFST column detail [3].


### 2.2. Finite Element Modeling

ABAQUS version 2019 was used due to its wide range of nonlinear material models, element library, and contact formulations. The concrete and steel tube, and steel tube and external CFRP wrap were connected by a surface-to-surface tie constraint, while the reinforcement bars were embedded in the concrete host region. The detailed descriptions of the elements used in this study are listed in Table2.Table 2
Element types used in this study.
ComponentElement typeElement descriptionConcreteC3D8RAn 8-node linear brick, reduced integration, hourglass control.Steel tube and CFRPS4RA 4-node doubly curved thin or thick shell, reduced integration, hourglass control, finite membrane strains.Main bar and stirrupsT3D2A 2-node linear 3-D trussThe bottom of the column is fixed whereas the top of the column was prevented from translating in the plan, as shown in Figure2. The axial shortening displacement and lateral deflections (both directions) are recorded on the top and mid-height of the column, respectively.Figure 2
Column mode; (a) isolated column frame model; (b) FE model.
(a)(b)During testing, the eccentric load was applied with a V-shaped (knife edges) loading plate attached to the loading machine on the V-shaped grooves attached to the specimen prepared for the test [36]. Similarly, Chellapandian et al. [37] used knife edges but with an enlarged end for the eccentric load in the case of higher load eccentricity and reaction endplate to avoid stress concentration. In this study, to simulate the same, an analytical rigid plate was used on both ends of the column to avoid the concentration of stresses on concrete, premature failure, or local cracking due to the axial load.Based on the previous study [38], displacement control was used with a magnitude of 50 mm applied at the reference points created on the top analytical rigid plate as shown in Figure 2.The calibrated and default plasticity values and mesh sizes used in this study, after mesh sensitivity analysis are shown in Table3. The dilation angle was calibrated to the optimum during the validation stage, while the viscosity parameter was calibrated for convergence issue. The rest default plasticity parameter taken from Hafezolghorani et al. [39].Table 3
Plasticity parameters and elements mesh-sizes in the finite element model.
Plasticity parameterValueElementMesh size (mm)Dilation angle40 (calibrated)Concrete25fbo/fco, ratio2/3=0.67 (Default)CFRP and steel tube34Shape factor0.67 (default)Main bar and stirrups15Viscosity parameter0.0005 (calibrated)Eccentricity0.1 (default)


### 2.3. Concrete Constitutive Models in ABAQUS

The concrete damage plasticity (CDP) model is very versatile in simulating concrete under different loading conditions; therefore, it was used for all analyses performed in this study.In the CDP model, the uniaxial compressive behavior of concrete is assumed to follow the general stress-strain response shown in Figure3 and in the following equation:(1)σcfcm=k×η−η21+η−2×η,η=εcεc1,k=EciEc1,where σc is concrete compressive stress, fcm is the compressive strength of concrete, εc is concrete compressive strain, εc1 is the strain at the maximum stress, Eci is the initial tangent modulus, and Ec1 is the secant modulus from origin to the peak compressive stress.Figure 3
Response of concrete to uniaxial loading condition in compression [40].There are three approaches to define tension stiffening that can be used to characterize the postpeak uniaxial tensile response of concrete in the CDP model: (1) Postfailure stress-strain relation, (2) Fracture energy approach, and (3) Crack-opening-displacement approach. In this study, the crack-opening-displacement model was used. For uncracked normal-weight concrete subjected to tension a bilinear stress-strain relation as shown in Figure4(a) and in the equations (2)–(8) below are used:(2)σct=Eci×εct,for0.9×fctm,(3)σctfcm=1−0.1×0.00015−εct0.00015−0.9×fctm/Eci,for0.9×fctm<σct<fctm,where Eci is the tangent modulus of elasticity in MPa, εct is the tensile strain, σct is the tensile stress in MPa, and fctm is the tensile strength in MPa.Figure 4
Bilinear tensile stress-strain curve (a) uncracked section (b) cracked section [40].
(a)(b)The cracking of the concrete is simulated using a bilinear curve shown in Figure4(b).(4)σctfcm=1−0.8×ww1,forw≤w1,(5)σctfcm=0.25−0.05∗ww1,forw1<w<wc,where w is the crack opening in (mm).(6)w1=Gffctm.inmmand whenσct=0.2×fctm,(7)wc=5×Gffctm.inmmand whenσct=0,(8)fctm=2.12×ln1+0.1×fcm,wherefcm=fck+Δf,where Gf is the fracture energy in (N/mm), fck, and fctm are in (MPa), Δf=8MPa.The loss of the elastic stiffness during unloading is described by two damage variablesdc and dt for uniaxial compression and tension responses, respectively. The damage parameters can have values ranging from zero to one, with zero indicating that the material is undamaged and one indicating that the material has completely lost its strength. The CDP allows defining the compressive stress data as a function of the compressive inelastic strain εcin. This inelastic (crushing) strain εcin given by the following equation:(9)εcin=εc−εcoel,whereεc=σcEc,where, εcin is the inelastic strain, εc is the total compressive strain, εcoel is the elastic compressive strain corresponding to the undamaged material, σc is the compressive stress, and Ec is the initial undamaged modulus of elasticity.The inelastic strain values are positively increasing values, with the first value being zero (corresponding to the initial yield point). In the CDP model, the compressive damage is defined as a tabular function of the (inelastic) crushing strainεcin is given by the equation (9). The equivalent plastic strain for crushed concrete is(10)ε˜cpl=εc−εc,del,whereεc,del=σc1−dcEc.From equation (9), εc=εcin+εcoel, substituting in equation (10) yields:(11)ε˜cpl=εcin+εcoel−σc1−dcEc=εcin−σcEc×11−dc−1=εcin−dc1−dc×εcoel,The compressive damage variabledc can be computed using Hafezolghorani et al. [39] In the following equation:(12)dc=1−σcfc.It is assumed thatε˜cpl=0forσc<σcu.Also, the tensile damage variable can be defined as a tabular function of either the crack-opening-displacement (u˜tck) or the cracking strain (εtin). In both ways, similar to the compressive damage variable or the tensile damage variable can be computed using Hafezolghorani et al. [39] in the following equation:(13)dt=1−σtft.The plastic displacement can be determined using the following relationship:(14)ε˜tpl=u˜tck−dt1−dt×εtoel,whereεcoel=σtEc.The compressive and tensile damage parameters data can be provided in the concrete damaged plasticity model of the ABAQUS model in terms of inelastic (crushing) strain and plastic displacement relation, respectively. It is recommended to avoid using damage variables greater than 0.99, representing a 99% reduction of the elastic stiffness. In this thesis, the damage parameters were limited to 0.95, or 95% reduction of the elastic modulus.


### 2.4. Reinforcement, Steel Tube, and Loading Plate Modeling

Fiber reinforced polymer (FRP) material is considered as linear-elastic till it achieves the maximum tensile strength, i.e., the rupture of FRP material. The steel tube was modeled by shell element (S4R), and the reinforcement bar and stirrup were modeled by a truss (T3D2). The stress-strain model of steel tubes and reinforcement bars used in this study is shown in Figure5. The mathematical expression is expressed by the following equations:(15)σs=Es×εs,forεs≤εy,where, σs is the stress at strain εs, fy is the yield stress at the yield strain εy, andEs is elastic modulus of reinforcement bars.Figure 5
Stress-strain Model od Steel Tube, Reinforcing Bars and stirrups.In the experimental study used for validation, only the yield strength of the longitudinal reinforcement bar, stirrup, and steel tube is given. These properties are also used for parametric studies.


### 2.5. Parametric Study

The specimens used for the parametric study were named by their confinement type and thicknesses starting with the CFRP (C0, C1, C2, C3, C5, & C10) and then followed by the steel tube (S0 or S1), which yields unconfined (C0S0), only 1.5 mm steel tube confined (C0S1), one-ply CFRP and 1.5 mm steel tube confined (C1S1), three-ply CFRP and 1.5 mm steel tube confined (C3S1), and ten-ply CFRP and 1.5 mm steel tube confined (C10S1) columns. These specimens were repeated for each of the four heights (720, 1000, 2000, & 3000 mm) and each of the six eccentricities (i.e., 0, 25, 50, 80, 120, & 300 mm). A steel tube thickness of 1.5 mm is taken from the validation experiment [3].A total of 131 column specimens are numerically modeled to study slenderness, load eccentricity, cross-sectional shape, and the thickness of the CFRP and steel tube considered in the NLFEA. Among these, 122 of the 131 specimens are circular in cross-section and the rest nine specimens are rectangular with a corner radius of 30 mm. The rectangular section is tested for only 0, 25, and 50 mm eccentricities and for unconfined (C0S0), only steel tube confined (C0S1), and both steel tube and three-layer CFRP confined (C3S1) column. The rest material properties remain similar to the circular section.The 720 mm height steel tube confined (C0S1) specimen is selected as a control specimen in this study. The other specimens are developed from control specimens by varying the eccentricity of the axial monotonic load (with and without steel tube and CFRP laminate), the height of the column, and the thickness of the CFRP sheet. The detailed parametric study for the CFRP thickness, load eccentricity, and slenderness of all circular specimens is listed in Table4.Table 4
summary of the circular columns for the parametric study.
Eccentricity,e (mm)Height in (mm)720 mm1000 mm2000 mm3000 mme = 0C0S0C0S0C0S0C0S0C0S1C0S1C0S1C0S1C1S1C1S1C1S1C1S1C3S1C3S1C3S1C3S1C10S1C10S1C10S1C10S1e = 25C0S0C0S0C0S0C0S0C0S1C0S1C0S1C0S1C1S1C1S1C1S1C1S1C3S1C3S1C3S1C3S1C10S1C10S1C10S1C10S1e = 50C0S0C0S0C0S0C0S0C0S1C0S1C0S1C0S1C1S1C1S1C1S1C1S1C2S1C2S1——C3S1C3S1C3S1C3S1C5S1C5S1——C10S1C10S1C10S1C10S1e = 80C0S0C0S0C0S0C0S0C0S1C0S1C0S1C0S1C1S1C1S1C1S1C1S1C3S1C3S1C3S1C3S1C10S1C10S1C10S1C10S1e = 120C0S0C0S0C0S0C0S0C0S1C0S1C0S1C0S1C1S1C1S1C1S1C1S1C3S1C3S1C3S1C3S1C10S1C10S1C10S1C10S1e = 300C0S0C0S0C0S0C0S0C0S1C0S1C0S1C0S1C1S1C1S1C1S1C1S1C3S1C3S1C3S1C3S1C10S1C10S1C10S1C10S1For the parametric study, a combination of the two materials is used. The properties of longitudinal and transverse reinforcements, concrete, and steel tubes were taken from Wang et al. [3]. Similarly, the properties of FRP materials shown in Table 5 were taken from Sun et al. [41].Table 5
Mechanical properties of the T300/7901 CFRP lamiates [41].
ItemT300/7901ItemT300/7901ItemT300/7901E1125 GPaXt2000 MPaGftc180 N/mmE2E311.3 GPaXc1100 MPaGfcc100 N/mmv12v130.3Yt80 MPaGmtc4 N/mmv230.42Yc280 MPaGmcc10 N/mmG12G135.43 GPaS12S13120 MPaG233.979 GPaS2389.9 MPa


## 2.1. Description of Experimental Work used for Validation

The experiment conducted by Wang et al. [3] on the behavior of CFST circular RC column subjected to 0 mm, 25 mm, and 50 mm load eccentricities were used for the validation of stress-strain properties of concrete, steel tube, reinforcement, and loading conditions. The CFST column has 240 mm diameter, 720 mm height, 1.5 mm steel tube thickness, 20 mm diameter of longitudinal reinforcement bars, and 8 mm diameter of stirrups. The details of material properties and dimensions of the experimental study are summarized in Table 1 and Figure 1, respectively.Table 1
Materials Properties and dimension of the validation specimens.
ParameterNominal value of Wang et al. [3] expt.Average 100 mm cube strength of concrete,fcu, 10055.8 MPaAverage compressive strength of concrete,fco41.9 MPaCubic compressive strength of concretefcu′53.01 MPaElastic modulus of concrete,Ec34.4 GPaElastic modulus steel tube, rebars and stirrupsEs200 GPaYield strength of the longitudinal bar,fby477.2 MPaYield strength of the stirrup,fsy285.6 MPaYield strength of the steel tube,fty364.3 MPaFigure 1
CFST column detail [3].


## 2.2. Finite Element Modeling

ABAQUS version 2019 was used due to its wide range of nonlinear material models, element library, and contact formulations. The concrete and steel tube, and steel tube and external CFRP wrap were connected by a surface-to-surface tie constraint, while the reinforcement bars were embedded in the concrete host region. The detailed descriptions of the elements used in this study are listed in Table2.Table 2
Element types used in this study.
ComponentElement typeElement descriptionConcreteC3D8RAn 8-node linear brick, reduced integration, hourglass control.Steel tube and CFRPS4RA 4-node doubly curved thin or thick shell, reduced integration, hourglass control, finite membrane strains.Main bar and stirrupsT3D2A 2-node linear 3-D trussThe bottom of the column is fixed whereas the top of the column was prevented from translating in the plan, as shown in Figure2. The axial shortening displacement and lateral deflections (both directions) are recorded on the top and mid-height of the column, respectively.Figure 2
Column mode; (a) isolated column frame model; (b) FE model.
(a)(b)During testing, the eccentric load was applied with a V-shaped (knife edges) loading plate attached to the loading machine on the V-shaped grooves attached to the specimen prepared for the test [36]. Similarly, Chellapandian et al. [37] used knife edges but with an enlarged end for the eccentric load in the case of higher load eccentricity and reaction endplate to avoid stress concentration. In this study, to simulate the same, an analytical rigid plate was used on both ends of the column to avoid the concentration of stresses on concrete, premature failure, or local cracking due to the axial load.Based on the previous study [38], displacement control was used with a magnitude of 50 mm applied at the reference points created on the top analytical rigid plate as shown in Figure 2.The calibrated and default plasticity values and mesh sizes used in this study, after mesh sensitivity analysis are shown in Table3. The dilation angle was calibrated to the optimum during the validation stage, while the viscosity parameter was calibrated for convergence issue. The rest default plasticity parameter taken from Hafezolghorani et al. [39].Table 3
Plasticity parameters and elements mesh-sizes in the finite element model.
Plasticity parameterValueElementMesh size (mm)Dilation angle40 (calibrated)Concrete25fbo/fco, ratio2/3=0.67 (Default)CFRP and steel tube34Shape factor0.67 (default)Main bar and stirrups15Viscosity parameter0.0005 (calibrated)Eccentricity0.1 (default)


## 2.3. Concrete Constitutive Models in ABAQUS

The concrete damage plasticity (CDP) model is very versatile in simulating concrete under different loading conditions; therefore, it was used for all analyses performed in this study.In the CDP model, the uniaxial compressive behavior of concrete is assumed to follow the general stress-strain response shown in Figure3 and in the following equation:(1)σcfcm=k×η−η21+η−2×η,η=εcεc1,k=EciEc1,where σc is concrete compressive stress, fcm is the compressive strength of concrete, εc is concrete compressive strain, εc1 is the strain at the maximum stress, Eci is the initial tangent modulus, and Ec1 is the secant modulus from origin to the peak compressive stress.Figure 3
Response of concrete to uniaxial loading condition in compression [40].There are three approaches to define tension stiffening that can be used to characterize the postpeak uniaxial tensile response of concrete in the CDP model: (1) Postfailure stress-strain relation, (2) Fracture energy approach, and (3) Crack-opening-displacement approach. In this study, the crack-opening-displacement model was used. For uncracked normal-weight concrete subjected to tension a bilinear stress-strain relation as shown in Figure4(a) and in the equations (2)–(8) below are used:(2)σct=Eci×εct,for0.9×fctm,(3)σctfcm=1−0.1×0.00015−εct0.00015−0.9×fctm/Eci,for0.9×fctm<σct<fctm,where Eci is the tangent modulus of elasticity in MPa, εct is the tensile strain, σct is the tensile stress in MPa, and fctm is the tensile strength in MPa.Figure 4
Bilinear tensile stress-strain curve (a) uncracked section (b) cracked section [40].
(a)(b)The cracking of the concrete is simulated using a bilinear curve shown in Figure4(b).(4)σctfcm=1−0.8×ww1,forw≤w1,(5)σctfcm=0.25−0.05∗ww1,forw1<w<wc,where w is the crack opening in (mm).(6)w1=Gffctm.inmmand whenσct=0.2×fctm,(7)wc=5×Gffctm.inmmand whenσct=0,(8)fctm=2.12×ln1+0.1×fcm,wherefcm=fck+Δf,where Gf is the fracture energy in (N/mm), fck, and fctm are in (MPa), Δf=8MPa.The loss of the elastic stiffness during unloading is described by two damage variablesdc and dt for uniaxial compression and tension responses, respectively. The damage parameters can have values ranging from zero to one, with zero indicating that the material is undamaged and one indicating that the material has completely lost its strength. The CDP allows defining the compressive stress data as a function of the compressive inelastic strain εcin. This inelastic (crushing) strain εcin given by the following equation:(9)εcin=εc−εcoel,whereεc=σcEc,where, εcin is the inelastic strain, εc is the total compressive strain, εcoel is the elastic compressive strain corresponding to the undamaged material, σc is the compressive stress, and Ec is the initial undamaged modulus of elasticity.The inelastic strain values are positively increasing values, with the first value being zero (corresponding to the initial yield point). In the CDP model, the compressive damage is defined as a tabular function of the (inelastic) crushing strainεcin is given by the equation (9). The equivalent plastic strain for crushed concrete is(10)ε˜cpl=εc−εc,del,whereεc,del=σc1−dcEc.From equation (9), εc=εcin+εcoel, substituting in equation (10) yields:(11)ε˜cpl=εcin+εcoel−σc1−dcEc=εcin−σcEc×11−dc−1=εcin−dc1−dc×εcoel,The compressive damage variabledc can be computed using Hafezolghorani et al. [39] In the following equation:(12)dc=1−σcfc.It is assumed thatε˜cpl=0forσc<σcu.Also, the tensile damage variable can be defined as a tabular function of either the crack-opening-displacement (u˜tck) or the cracking strain (εtin). In both ways, similar to the compressive damage variable or the tensile damage variable can be computed using Hafezolghorani et al. [39] in the following equation:(13)dt=1−σtft.The plastic displacement can be determined using the following relationship:(14)ε˜tpl=u˜tck−dt1−dt×εtoel,whereεcoel=σtEc.The compressive and tensile damage parameters data can be provided in the concrete damaged plasticity model of the ABAQUS model in terms of inelastic (crushing) strain and plastic displacement relation, respectively. It is recommended to avoid using damage variables greater than 0.99, representing a 99% reduction of the elastic stiffness. In this thesis, the damage parameters were limited to 0.95, or 95% reduction of the elastic modulus.


## 2.4. Reinforcement, Steel Tube, and Loading Plate Modeling

Fiber reinforced polymer (FRP) material is considered as linear-elastic till it achieves the maximum tensile strength, i.e., the rupture of FRP material. The steel tube was modeled by shell element (S4R), and the reinforcement bar and stirrup were modeled by a truss (T3D2). The stress-strain model of steel tubes and reinforcement bars used in this study is shown in Figure5. The mathematical expression is expressed by the following equations:(15)σs=Es×εs,forεs≤εy,where, σs is the stress at strain εs, fy is the yield stress at the yield strain εy, andEs is elastic modulus of reinforcement bars.Figure 5
Stress-strain Model od Steel Tube, Reinforcing Bars and stirrups.In the experimental study used for validation, only the yield strength of the longitudinal reinforcement bar, stirrup, and steel tube is given. These properties are also used for parametric studies.


## 2.5. Parametric Study

The specimens used for the parametric study were named by their confinement type and thicknesses starting with the CFRP (C0, C1, C2, C3, C5, & C10) and then followed by the steel tube (S0 or S1), which yields unconfined (C0S0), only 1.5 mm steel tube confined (C0S1), one-ply CFRP and 1.5 mm steel tube confined (C1S1), three-ply CFRP and 1.5 mm steel tube confined (C3S1), and ten-ply CFRP and 1.5 mm steel tube confined (C10S1) columns. These specimens were repeated for each of the four heights (720, 1000, 2000, & 3000 mm) and each of the six eccentricities (i.e., 0, 25, 50, 80, 120, & 300 mm). A steel tube thickness of 1.5 mm is taken from the validation experiment [3].A total of 131 column specimens are numerically modeled to study slenderness, load eccentricity, cross-sectional shape, and the thickness of the CFRP and steel tube considered in the NLFEA. Among these, 122 of the 131 specimens are circular in cross-section and the rest nine specimens are rectangular with a corner radius of 30 mm. The rectangular section is tested for only 0, 25, and 50 mm eccentricities and for unconfined (C0S0), only steel tube confined (C0S1), and both steel tube and three-layer CFRP confined (C3S1) column. The rest material properties remain similar to the circular section.The 720 mm height steel tube confined (C0S1) specimen is selected as a control specimen in this study. The other specimens are developed from control specimens by varying the eccentricity of the axial monotonic load (with and without steel tube and CFRP laminate), the height of the column, and the thickness of the CFRP sheet. The detailed parametric study for the CFRP thickness, load eccentricity, and slenderness of all circular specimens is listed in Table4.Table 4
summary of the circular columns for the parametric study.
Eccentricity,e (mm)Height in (mm)720 mm1000 mm2000 mm3000 mme = 0C0S0C0S0C0S0C0S0C0S1C0S1C0S1C0S1C1S1C1S1C1S1C1S1C3S1C3S1C3S1C3S1C10S1C10S1C10S1C10S1e = 25C0S0C0S0C0S0C0S0C0S1C0S1C0S1C0S1C1S1C1S1C1S1C1S1C3S1C3S1C3S1C3S1C10S1C10S1C10S1C10S1e = 50C0S0C0S0C0S0C0S0C0S1C0S1C0S1C0S1C1S1C1S1C1S1C1S1C2S1C2S1——C3S1C3S1C3S1C3S1C5S1C5S1——C10S1C10S1C10S1C10S1e = 80C0S0C0S0C0S0C0S0C0S1C0S1C0S1C0S1C1S1C1S1C1S1C1S1C3S1C3S1C3S1C3S1C10S1C10S1C10S1C10S1e = 120C0S0C0S0C0S0C0S0C0S1C0S1C0S1C0S1C1S1C1S1C1S1C1S1C3S1C3S1C3S1C3S1C10S1C10S1C10S1C10S1e = 300C0S0C0S0C0S0C0S0C0S1C0S1C0S1C0S1C1S1C1S1C1S1C1S1C3S1C3S1C3S1C3S1C10S1C10S1C10S1C10S1For the parametric study, a combination of the two materials is used. The properties of longitudinal and transverse reinforcements, concrete, and steel tubes were taken from Wang et al. [3]. Similarly, the properties of FRP materials shown in Table 5 were taken from Sun et al. [41].Table 5
Mechanical properties of the T300/7901 CFRP lamiates [41].
ItemT300/7901ItemT300/7901ItemT300/7901E1125 GPaXt2000 MPaGftc180 N/mmE2E311.3 GPaXc1100 MPaGfcc100 N/mmv12v130.3Yt80 MPaGmtc4 N/mmv230.42Yc280 MPaGmcc10 N/mmG12G135.43 GPaS12S13120 MPaG233.979 GPaS2389.9 MPa


## 3. Results and Discussions

### 3.1. Validation of Finite Element Model

The modeling capability, boundary conditions, material properties, and loading procedure of the nonlinear finite element model with normal concrete and FRP were verified against the experimental tests of the CFST column under monotonic concentric and eccentric loads. The accuracy was evaluated by comparing nonlinear finite element analysis results of the specimen with its respective experimental result in terms of axial load-axial displacement, axial load-mid height lateral deflection response, and the failure pattern.The model prediction of the maximum load of the first specimen leads to an error of −2.24%, −2.83%, and 10.39%, for 50 mm, 25 mm, and 0 eccentricities, respectively. Figure6 confirms that the finite element response of the specimens is in agreement with the results reported from the experimental study under the given load eccentricities.Figure 6
Comparsion od this study with experimental data from Wang et al. [3].The comparison of the typical images of failure patterns in the specimens CFST circular column reported from the experimental study [3] and tested by NLFEA at failure load illustrates on Figures 7 and 8, respectively. The CFST specimen experienced continuous dilation in the mid-height region and localized outward buckling of the steel tube near the tube ends at large axial shortenings.Figure 7
Failures modes of the experimental specimen [3].Figure 8
FE failure modes of (a) concrete (b) steel tube (c) reinforcement bar.


### 3.2. Parametric Study

#### 3.2.1. Effects of Load Eccentricity

Load eccentricity increases from 0–80 mm, resulting in a 50.34% reduction in axial load-carrying capacity for the 720 mm unconfined column (C0S0), as shown in Table6. When 1.5 mm thick steel tube is added, the axial load-carrying capacity reduction decreased to 41.77%, in which steel tube confinement improves 8.57% of the axial load-carrying capacity to the unconfined column for the same range in eccentricity. In addition to this, when ten layers of CFRP lamina are added to C0S1, the percentage reduction will be 30.05%. This implies that both 1.5 mm steel tube and ten-layer CFRP (each 0.111 mm) confinement improve 20.29% in axial load-carrying capacity for 80 mm load eccentricity over the unconfined column. Specifically, ten-layer CFRP layer confinement shows an advance of 11.72% in axial load-carrying capacity over the CFST column. The rest specimens for all heights (i.e., H1000, H2000, & H3000E) show similar but with different sizes of the reduction. Figure 9 also shows clearly the effect of CFRP and steel tube confinement of the circular RC column under concentric and eccentric loads.Table 6
Effect of the CERP and steel tube confinement with increased load eccentricity.
Height of column (mm)Type of specimenEccentricity (mm)0255080120300720C0S03950.383324.682632.941961.831326.38431.19%−15.84−33.35−50.34−66.42−89.08C0S14542.433900.593264.752645.061870.38603.50%−14.13−28.13−41.77−58.82−86.71C3S14732.774273.103580.692891.551996.37625.86%−9.71−24.34−38.90−57.82−86.78C10S15141.424643.904162.723596.192365.91652.30%−9.68−19.04−30.05−53.98−87.31Figure 9
Effect of eccentricity on the load capacity of 720 mm FCCFST column.
(a)(b)(c)(d)CFRP and steel tube confinement increase the load-carrying capacity of the column under each load eccentricity. But, their efficiency first increases with increased eccentricity and then later starts to decrease. In other words, their efficiency increases up to an optimum value and then decreases, as shown in Table7. This indicates that when a column is subjected to increasing load eccentricity, the failure of the column shifts from material failure to stability or local failure, regardless of the slenderness ratio.Table 7
Percentage increase load-carrying od C10S1 column.
Electricity (mm)Height (mm)720100020003000030.1534.4933.0432.935058.1077.6974.3952.268083.3178.5778.2564.6512077.0276.0974.6966.0530051.2852.7052.3055.28Although the steel tube and CFRP confinement provided uniform confinement, the failure mode of the column depends on the magnitude of the axial load eccentricity. When the column was subjected to axial concentric loads, the column failed in the midheight region as a result of the lateral expansion of the concrete, similar to most of the experimental studies by explosive rupture of the CFRP wrap [33]. The confinement provided by the hoop FRP wraps allows the eccentrically loaded columns to attain higher axial resistance as they are deformed laterally with an increase of lateral deformation ability than their companion unconfined columns. Similar increases in the lateral deformation ability of hoop FRP confined columns were reported by Al-Nimry and Soman [42].


#### 3.2.2. Effects of Steel Tube Confinement Thickness

Figure10 shows the influence of steel tube thickness on the properties of 1000 mm height FCCFST specimens under 50 mm load eccentricity. From these curves, the ultimate load-carrying capacity of the FCCFST specimen increases with increasing steel tube thickness. However, increasing the thickness of the steel tube has no significant effect on the axial shortening under ultimate load [33]. The upper three curves in Figure 10 have similar axial deformation with a different ultimate load. Even though the C0S1 specimen has 1.5 mm steel tube confinement, it has different axial deformation due to the rest upper three curves in Figure 10 have additional five layers of CFRP wraps.Figure 10
Effect of steel tube thickness.


#### 3.2.3. Effects of CFRP Confinement Thickness

CFRP provides passive confinement, which becomes active after yielding of the steel tube confinement. The CFRP confined columns sustained higher axial displacements at ultimate resistance and recorded higher deformability compared to their companion control RC columns, as shown in Figure11. Its efficiency increases with the increase in eccentricity of the monotonic axial compressive load up to a certain level, then decreases.Figure 11
Axial deformation of the 720 mm column.The efficiency of both steel tube and CFRP hoop confinement in increasing the axial load-carrying capacity of columns confirmed by Figure12. An increment of 30.15% was recorded due to 1.5 mm steel tube and ten-layer CFRP confined 720 mm column under concentric load. For the same height, larger enhancements reaching up to 58.1 and 83.31% were observed, respectively, for the 50 & 80 mm axial load eccentricity. For the 720 mm column, the steel tube confinement only increases the load capacity by 14.99, 24, & 34.83%, for 0, 50 & 80 mm eccentricities, respectively. When three-ply CFRP confinement is added to the steel tube confinement, the column gets a strength increment of 19.8, 36 & 47.39% for the given range of eccentricity. Thus, the beneficial effects of both steel tube and CFRP confinement may be more significant for RC columns subjected to eccentrically loads than for concentric loaded concrete columns.Figure 12
Effect of confinement type and thickness on RC column.
(a)(b)(c)(d)


#### 3.2.4. Slenderness Effects

The difference in slenderness ratio values between gross (λg) and transformed (λt) cross-sectional area calculation methods is minor and can reasonably be neglected in the subsequent discussion. Thus, 2000 mm and 3000 mm columns are slender for the given cross-sectional geometry, reinforcement, and confinement condition.As the height of the column increases from 720 mm to 3000 mm, the confinement efficiency initially increases up to 1000 mm and later decreases for the 0, 25, and 50 mm eccentricities. For instance, the confinement efficiency increases from 30.15% to 34.49% and later decreases to 33.04 and 32.93% as the height increases from 720 to 3000 mm under concentric load (see Table7). But after 80 mm eccentricity, the efficiency anomaly decreases. Even though the steel tube and CFRP confinement increase the load-carrying capacity of all RC short and slender columns, their efficiency decreases in slender columns and at high eccentricity. This indicates that the steel tube and CFRP confinements are effective in short columns and at mild load eccentricity, as shown in Table 7 and Figure 13.Figure 13
Axial load versus lateral deflection curve for 720 mm column.
(a)(b)(c)(d)(e)


#### 3.2.5. Effects Cross-Sectional Shape

The load resistance capacity and axial deformation for the concentrically loaded members were greatly affected by the cross-sectional shape, ranging from 21.1% to 22.11% increase in load resistance capacity and 8.45% to 11.86% increase in axial deformation for the rectangular and circular cross-sections, respectively (see Table8). The CFRP wrap also enhanced the performance of the eccentrically loaded members with an increase in load resistance capacity ranging from 34.01% to 39.19% and in lateral deformation ranging from 136.05% to 57.29%, for the rectangular and circular cross-sections, respectively (see Table 9). For the given level of confinement and load eccentricities used in this study, circular sections exhibited lower gain in lateral deformation relative to the rectangular sections since circular sections have lower deflection capacity than rectangular or square sections, yet CFRP confinement is effective in the circular sections for the ultimate compressive load capacity.Table 8
Axial displacement versuaxial load response under concentric load.
C0S0 (control)C0S1C3S1Δ (mm)P (kN)Δ (mm)P (kN)Δ (mm)P (kN)Rectangular3.323732.153.504367.443.604519.46%5.6517.028.4521.10Circular3.313721.243.574370.613.714544.15%7.6517.4511.8622.11Table 9
Laterial deformation versus axial response under common eccentricity.
C0S0C0S1C3S1δ (mm)P (kN)δ (mm)P (kN)δ (mm)P (kN)Rectangular1.142567.632.443210.282.693440.81%114.4325.03136.0534.01Circular0.212535.970.313183.790.343529.76%45.3025.5557.2939.19Table9 shows the load versus mid-height lateral deflection of the eccentrically loaded members. The load capacity enhancement in rectangular and circular cross-sections due to steel tube confinement (C0S1) is 17.02 and 17.45% for concentrically loaded members and 25.03 and 25.55% for eccentrically loaded members, respectively. This indicates that the steel tube confinement shows a negligible variation in load-carrying capacity of both cross-sectional shapes. Whereas the axial deformation of these members increased by 5.65 and 7.65% for concentrically loaded members and 114.43 and 45.3% for eccentrically loaded members (see Table 9). As shown in Tables 7 and 8 steel tube and a combination of steel tube and CFRP confinement enhanced the axial load capacity of RC columns by 17.02 and 21.10% on concentrically loaded and 25.03 and 34.01% on eccentrically loaded rectangular columns, respectively. Therefore, steel tube and/or FRP confinements are effective under both concentric and eccentric loads, with slightly higher under eccentric loads.


### 3.3. Interaction Diagrams FCCFST Column

The P M interaction curves for the finite element results are computed as the peak load times the initial load eccentricity plus the additional deflection at 0.429L from the pin or roller end support. Mathematically,(16)M=P×e+Δ,where e is the initial eccentricity and Δ is the lateral deflection at peak load.The diagrams are constructed for C0S0, C0S1, C1S1, C3S1, and C10S1 columns. The interaction diagrams shown in Figure14 indicates the effectiveness of the steel tube and CFRP confinement. This assessment is in agreement with an earlier study [15] for the hoop FRP confinement, which allowed the eccentrically loaded columns to attain higher lateral deformations than that of unconfined columns at load eccentricities within the compression failure zone.Figure 14
Effect of steel tube and CFRP confinement in interaction diagram.
(a)(b)(c)(d)The difference in section capacity between an unconfined reinforced concrete column and a ten-layer CFRP confined CFST column reached 102.71% under pure compression.It is obvious that the load-carrying capacity of the column decreases with increasing slenderness ratio and axial load eccentricity, which is less pronounced under steel tube and CFRP confinement up to mild eccentricity. The NLFEA tests confirmed that FRP confinement improves the axial and flexural resistance of the columns as shown in Figure14.


## 3.1. Validation of Finite Element Model

The modeling capability, boundary conditions, material properties, and loading procedure of the nonlinear finite element model with normal concrete and FRP were verified against the experimental tests of the CFST column under monotonic concentric and eccentric loads. The accuracy was evaluated by comparing nonlinear finite element analysis results of the specimen with its respective experimental result in terms of axial load-axial displacement, axial load-mid height lateral deflection response, and the failure pattern.The model prediction of the maximum load of the first specimen leads to an error of −2.24%, −2.83%, and 10.39%, for 50 mm, 25 mm, and 0 eccentricities, respectively. Figure6 confirms that the finite element response of the specimens is in agreement with the results reported from the experimental study under the given load eccentricities.Figure 6
Comparsion od this study with experimental data from Wang et al. [3].The comparison of the typical images of failure patterns in the specimens CFST circular column reported from the experimental study [3] and tested by NLFEA at failure load illustrates on Figures 7 and 8, respectively. The CFST specimen experienced continuous dilation in the mid-height region and localized outward buckling of the steel tube near the tube ends at large axial shortenings.Figure 7
Failures modes of the experimental specimen [3].Figure 8
FE failure modes of (a) concrete (b) steel tube (c) reinforcement bar.


## 3.2. Parametric Study

### 3.2.1. Effects of Load Eccentricity

Load eccentricity increases from 0–80 mm, resulting in a 50.34% reduction in axial load-carrying capacity for the 720 mm unconfined column (C0S0), as shown in Table6. When 1.5 mm thick steel tube is added, the axial load-carrying capacity reduction decreased to 41.77%, in which steel tube confinement improves 8.57% of the axial load-carrying capacity to the unconfined column for the same range in eccentricity. In addition to this, when ten layers of CFRP lamina are added to C0S1, the percentage reduction will be 30.05%. This implies that both 1.5 mm steel tube and ten-layer CFRP (each 0.111 mm) confinement improve 20.29% in axial load-carrying capacity for 80 mm load eccentricity over the unconfined column. Specifically, ten-layer CFRP layer confinement shows an advance of 11.72% in axial load-carrying capacity over the CFST column. The rest specimens for all heights (i.e., H1000, H2000, & H3000E) show similar but with different sizes of the reduction. Figure 9 also shows clearly the effect of CFRP and steel tube confinement of the circular RC column under concentric and eccentric loads.Table 6
Effect of the CERP and steel tube confinement with increased load eccentricity.
Height of column (mm)Type of specimenEccentricity (mm)0255080120300720C0S03950.383324.682632.941961.831326.38431.19%−15.84−33.35−50.34−66.42−89.08C0S14542.433900.593264.752645.061870.38603.50%−14.13−28.13−41.77−58.82−86.71C3S14732.774273.103580.692891.551996.37625.86%−9.71−24.34−38.90−57.82−86.78C10S15141.424643.904162.723596.192365.91652.30%−9.68−19.04−30.05−53.98−87.31Figure 9
Effect of eccentricity on the load capacity of 720 mm FCCFST column.
(a)(b)(c)(d)CFRP and steel tube confinement increase the load-carrying capacity of the column under each load eccentricity. But, their efficiency first increases with increased eccentricity and then later starts to decrease. In other words, their efficiency increases up to an optimum value and then decreases, as shown in Table7. This indicates that when a column is subjected to increasing load eccentricity, the failure of the column shifts from material failure to stability or local failure, regardless of the slenderness ratio.Table 7
Percentage increase load-carrying od C10S1 column.
Electricity (mm)Height (mm)720100020003000030.1534.4933.0432.935058.1077.6974.3952.268083.3178.5778.2564.6512077.0276.0974.6966.0530051.2852.7052.3055.28Although the steel tube and CFRP confinement provided uniform confinement, the failure mode of the column depends on the magnitude of the axial load eccentricity. When the column was subjected to axial concentric loads, the column failed in the midheight region as a result of the lateral expansion of the concrete, similar to most of the experimental studies by explosive rupture of the CFRP wrap [33]. The confinement provided by the hoop FRP wraps allows the eccentrically loaded columns to attain higher axial resistance as they are deformed laterally with an increase of lateral deformation ability than their companion unconfined columns. Similar increases in the lateral deformation ability of hoop FRP confined columns were reported by Al-Nimry and Soman [42].


### 3.2.2. Effects of Steel Tube Confinement Thickness

Figure10 shows the influence of steel tube thickness on the properties of 1000 mm height FCCFST specimens under 50 mm load eccentricity. From these curves, the ultimate load-carrying capacity of the FCCFST specimen increases with increasing steel tube thickness. However, increasing the thickness of the steel tube has no significant effect on the axial shortening under ultimate load [33]. The upper three curves in Figure 10 have similar axial deformation with a different ultimate load. Even though the C0S1 specimen has 1.5 mm steel tube confinement, it has different axial deformation due to the rest upper three curves in Figure 10 have additional five layers of CFRP wraps.Figure 10
Effect of steel tube thickness.


### 3.2.3. Effects of CFRP Confinement Thickness

CFRP provides passive confinement, which becomes active after yielding of the steel tube confinement. The CFRP confined columns sustained higher axial displacements at ultimate resistance and recorded higher deformability compared to their companion control RC columns, as shown in Figure11. Its efficiency increases with the increase in eccentricity of the monotonic axial compressive load up to a certain level, then decreases.Figure 11
Axial deformation of the 720 mm column.The efficiency of both steel tube and CFRP hoop confinement in increasing the axial load-carrying capacity of columns confirmed by Figure12. An increment of 30.15% was recorded due to 1.5 mm steel tube and ten-layer CFRP confined 720 mm column under concentric load. For the same height, larger enhancements reaching up to 58.1 and 83.31% were observed, respectively, for the 50 & 80 mm axial load eccentricity. For the 720 mm column, the steel tube confinement only increases the load capacity by 14.99, 24, & 34.83%, for 0, 50 & 80 mm eccentricities, respectively. When three-ply CFRP confinement is added to the steel tube confinement, the column gets a strength increment of 19.8, 36 & 47.39% for the given range of eccentricity. Thus, the beneficial effects of both steel tube and CFRP confinement may be more significant for RC columns subjected to eccentrically loads than for concentric loaded concrete columns.Figure 12
Effect of confinement type and thickness on RC column.
(a)(b)(c)(d)


### 3.2.4. Slenderness Effects

The difference in slenderness ratio values between gross (λg) and transformed (λt) cross-sectional area calculation methods is minor and can reasonably be neglected in the subsequent discussion. Thus, 2000 mm and 3000 mm columns are slender for the given cross-sectional geometry, reinforcement, and confinement condition.As the height of the column increases from 720 mm to 3000 mm, the confinement efficiency initially increases up to 1000 mm and later decreases for the 0, 25, and 50 mm eccentricities. For instance, the confinement efficiency increases from 30.15% to 34.49% and later decreases to 33.04 and 32.93% as the height increases from 720 to 3000 mm under concentric load (see Table7). But after 80 mm eccentricity, the efficiency anomaly decreases. Even though the steel tube and CFRP confinement increase the load-carrying capacity of all RC short and slender columns, their efficiency decreases in slender columns and at high eccentricity. This indicates that the steel tube and CFRP confinements are effective in short columns and at mild load eccentricity, as shown in Table 7 and Figure 13.Figure 13
Axial load versus lateral deflection curve for 720 mm column.
(a)(b)(c)(d)(e)


### 3.2.5. Effects Cross-Sectional Shape

The load resistance capacity and axial deformation for the concentrically loaded members were greatly affected by the cross-sectional shape, ranging from 21.1% to 22.11% increase in load resistance capacity and 8.45% to 11.86% increase in axial deformation for the rectangular and circular cross-sections, respectively (see Table8). The CFRP wrap also enhanced the performance of the eccentrically loaded members with an increase in load resistance capacity ranging from 34.01% to 39.19% and in lateral deformation ranging from 136.05% to 57.29%, for the rectangular and circular cross-sections, respectively (see Table 9). For the given level of confinement and load eccentricities used in this study, circular sections exhibited lower gain in lateral deformation relative to the rectangular sections since circular sections have lower deflection capacity than rectangular or square sections, yet CFRP confinement is effective in the circular sections for the ultimate compressive load capacity.Table 8
Axial displacement versuaxial load response under concentric load.
C0S0 (control)C0S1C3S1Δ (mm)P (kN)Δ (mm)P (kN)Δ (mm)P (kN)Rectangular3.323732.153.504367.443.604519.46%5.6517.028.4521.10Circular3.313721.243.574370.613.714544.15%7.6517.4511.8622.11Table 9
Laterial deformation versus axial response under common eccentricity.
C0S0C0S1C3S1δ (mm)P (kN)δ (mm)P (kN)δ (mm)P (kN)Rectangular1.142567.632.443210.282.693440.81%114.4325.03136.0534.01Circular0.212535.970.313183.790.343529.76%45.3025.5557.2939.19Table9 shows the load versus mid-height lateral deflection of the eccentrically loaded members. The load capacity enhancement in rectangular and circular cross-sections due to steel tube confinement (C0S1) is 17.02 and 17.45% for concentrically loaded members and 25.03 and 25.55% for eccentrically loaded members, respectively. This indicates that the steel tube confinement shows a negligible variation in load-carrying capacity of both cross-sectional shapes. Whereas the axial deformation of these members increased by 5.65 and 7.65% for concentrically loaded members and 114.43 and 45.3% for eccentrically loaded members (see Table 9). As shown in Tables 7 and 8 steel tube and a combination of steel tube and CFRP confinement enhanced the axial load capacity of RC columns by 17.02 and 21.10% on concentrically loaded and 25.03 and 34.01% on eccentrically loaded rectangular columns, respectively. Therefore, steel tube and/or FRP confinements are effective under both concentric and eccentric loads, with slightly higher under eccentric loads.


## 3.2.1. Effects of Load Eccentricity

Load eccentricity increases from 0–80 mm, resulting in a 50.34% reduction in axial load-carrying capacity for the 720 mm unconfined column (C0S0), as shown in Table6. When 1.5 mm thick steel tube is added, the axial load-carrying capacity reduction decreased to 41.77%, in which steel tube confinement improves 8.57% of the axial load-carrying capacity to the unconfined column for the same range in eccentricity. In addition to this, when ten layers of CFRP lamina are added to C0S1, the percentage reduction will be 30.05%. This implies that both 1.5 mm steel tube and ten-layer CFRP (each 0.111 mm) confinement improve 20.29% in axial load-carrying capacity for 80 mm load eccentricity over the unconfined column. Specifically, ten-layer CFRP layer confinement shows an advance of 11.72% in axial load-carrying capacity over the CFST column. The rest specimens for all heights (i.e., H1000, H2000, & H3000E) show similar but with different sizes of the reduction. Figure 9 also shows clearly the effect of CFRP and steel tube confinement of the circular RC column under concentric and eccentric loads.Table 6
Effect of the CERP and steel tube confinement with increased load eccentricity.
Height of column (mm)Type of specimenEccentricity (mm)0255080120300720C0S03950.383324.682632.941961.831326.38431.19%−15.84−33.35−50.34−66.42−89.08C0S14542.433900.593264.752645.061870.38603.50%−14.13−28.13−41.77−58.82−86.71C3S14732.774273.103580.692891.551996.37625.86%−9.71−24.34−38.90−57.82−86.78C10S15141.424643.904162.723596.192365.91652.30%−9.68−19.04−30.05−53.98−87.31Figure 9
Effect of eccentricity on the load capacity of 720 mm FCCFST column.
(a)(b)(c)(d)CFRP and steel tube confinement increase the load-carrying capacity of the column under each load eccentricity. But, their efficiency first increases with increased eccentricity and then later starts to decrease. In other words, their efficiency increases up to an optimum value and then decreases, as shown in Table7. This indicates that when a column is subjected to increasing load eccentricity, the failure of the column shifts from material failure to stability or local failure, regardless of the slenderness ratio.Table 7
Percentage increase load-carrying od C10S1 column.
Electricity (mm)Height (mm)720100020003000030.1534.4933.0432.935058.1077.6974.3952.268083.3178.5778.2564.6512077.0276.0974.6966.0530051.2852.7052.3055.28Although the steel tube and CFRP confinement provided uniform confinement, the failure mode of the column depends on the magnitude of the axial load eccentricity. When the column was subjected to axial concentric loads, the column failed in the midheight region as a result of the lateral expansion of the concrete, similar to most of the experimental studies by explosive rupture of the CFRP wrap [33]. The confinement provided by the hoop FRP wraps allows the eccentrically loaded columns to attain higher axial resistance as they are deformed laterally with an increase of lateral deformation ability than their companion unconfined columns. Similar increases in the lateral deformation ability of hoop FRP confined columns were reported by Al-Nimry and Soman [42].


## 3.2.2. Effects of Steel Tube Confinement Thickness

Figure10 shows the influence of steel tube thickness on the properties of 1000 mm height FCCFST specimens under 50 mm load eccentricity. From these curves, the ultimate load-carrying capacity of the FCCFST specimen increases with increasing steel tube thickness. However, increasing the thickness of the steel tube has no significant effect on the axial shortening under ultimate load [33]. The upper three curves in Figure 10 have similar axial deformation with a different ultimate load. Even though the C0S1 specimen has 1.5 mm steel tube confinement, it has different axial deformation due to the rest upper three curves in Figure 10 have additional five layers of CFRP wraps.Figure 10
Effect of steel tube thickness.


## 3.2.3. Effects of CFRP Confinement Thickness

CFRP provides passive confinement, which becomes active after yielding of the steel tube confinement. The CFRP confined columns sustained higher axial displacements at ultimate resistance and recorded higher deformability compared to their companion control RC columns, as shown in Figure11. Its efficiency increases with the increase in eccentricity of the monotonic axial compressive load up to a certain level, then decreases.Figure 11
Axial deformation of the 720 mm column.The efficiency of both steel tube and CFRP hoop confinement in increasing the axial load-carrying capacity of columns confirmed by Figure12. An increment of 30.15% was recorded due to 1.5 mm steel tube and ten-layer CFRP confined 720 mm column under concentric load. For the same height, larger enhancements reaching up to 58.1 and 83.31% were observed, respectively, for the 50 & 80 mm axial load eccentricity. For the 720 mm column, the steel tube confinement only increases the load capacity by 14.99, 24, & 34.83%, for 0, 50 & 80 mm eccentricities, respectively. When three-ply CFRP confinement is added to the steel tube confinement, the column gets a strength increment of 19.8, 36 & 47.39% for the given range of eccentricity. Thus, the beneficial effects of both steel tube and CFRP confinement may be more significant for RC columns subjected to eccentrically loads than for concentric loaded concrete columns.Figure 12
Effect of confinement type and thickness on RC column.
(a)(b)(c)(d)


## 3.2.4. Slenderness Effects

The difference in slenderness ratio values between gross (λg) and transformed (λt) cross-sectional area calculation methods is minor and can reasonably be neglected in the subsequent discussion. Thus, 2000 mm and 3000 mm columns are slender for the given cross-sectional geometry, reinforcement, and confinement condition.As the height of the column increases from 720 mm to 3000 mm, the confinement efficiency initially increases up to 1000 mm and later decreases for the 0, 25, and 50 mm eccentricities. For instance, the confinement efficiency increases from 30.15% to 34.49% and later decreases to 33.04 and 32.93% as the height increases from 720 to 3000 mm under concentric load (see Table7). But after 80 mm eccentricity, the efficiency anomaly decreases. Even though the steel tube and CFRP confinement increase the load-carrying capacity of all RC short and slender columns, their efficiency decreases in slender columns and at high eccentricity. This indicates that the steel tube and CFRP confinements are effective in short columns and at mild load eccentricity, as shown in Table 7 and Figure 13.Figure 13
Axial load versus lateral deflection curve for 720 mm column.
(a)(b)(c)(d)(e)


## 3.2.5. Effects Cross-Sectional Shape

The load resistance capacity and axial deformation for the concentrically loaded members were greatly affected by the cross-sectional shape, ranging from 21.1% to 22.11% increase in load resistance capacity and 8.45% to 11.86% increase in axial deformation for the rectangular and circular cross-sections, respectively (see Table8). The CFRP wrap also enhanced the performance of the eccentrically loaded members with an increase in load resistance capacity ranging from 34.01% to 39.19% and in lateral deformation ranging from 136.05% to 57.29%, for the rectangular and circular cross-sections, respectively (see Table 9). For the given level of confinement and load eccentricities used in this study, circular sections exhibited lower gain in lateral deformation relative to the rectangular sections since circular sections have lower deflection capacity than rectangular or square sections, yet CFRP confinement is effective in the circular sections for the ultimate compressive load capacity.Table 8
Axial displacement versuaxial load response under concentric load.
C0S0 (control)C0S1C3S1Δ (mm)P (kN)Δ (mm)P (kN)Δ (mm)P (kN)Rectangular3.323732.153.504367.443.604519.46%5.6517.028.4521.10Circular3.313721.243.574370.613.714544.15%7.6517.4511.8622.11Table 9
Laterial deformation versus axial response under common eccentricity.
C0S0C0S1C3S1δ (mm)P (kN)δ (mm)P (kN)δ (mm)P (kN)Rectangular1.142567.632.443210.282.693440.81%114.4325.03136.0534.01Circular0.212535.970.313183.790.343529.76%45.3025.5557.2939.19Table9 shows the load versus mid-height lateral deflection of the eccentrically loaded members. The load capacity enhancement in rectangular and circular cross-sections due to steel tube confinement (C0S1) is 17.02 and 17.45% for concentrically loaded members and 25.03 and 25.55% for eccentrically loaded members, respectively. This indicates that the steel tube confinement shows a negligible variation in load-carrying capacity of both cross-sectional shapes. Whereas the axial deformation of these members increased by 5.65 and 7.65% for concentrically loaded members and 114.43 and 45.3% for eccentrically loaded members (see Table 9). As shown in Tables 7 and 8 steel tube and a combination of steel tube and CFRP confinement enhanced the axial load capacity of RC columns by 17.02 and 21.10% on concentrically loaded and 25.03 and 34.01% on eccentrically loaded rectangular columns, respectively. Therefore, steel tube and/or FRP confinements are effective under both concentric and eccentric loads, with slightly higher under eccentric loads.


## 3.3. Interaction Diagrams FCCFST Column

The P M interaction curves for the finite element results are computed as the peak load times the initial load eccentricity plus the additional deflection at 0.429L from the pin or roller end support. Mathematically,(16)M=P×e+Δ,where e is the initial eccentricity and Δ is the lateral deflection at peak load.The diagrams are constructed for C0S0, C0S1, C1S1, C3S1, and C10S1 columns. The interaction diagrams shown in Figure14 indicates the effectiveness of the steel tube and CFRP confinement. This assessment is in agreement with an earlier study [15] for the hoop FRP confinement, which allowed the eccentrically loaded columns to attain higher lateral deformations than that of unconfined columns at load eccentricities within the compression failure zone.Figure 14
Effect of steel tube and CFRP confinement in interaction diagram.
(a)(b)(c)(d)The difference in section capacity between an unconfined reinforced concrete column and a ten-layer CFRP confined CFST column reached 102.71% under pure compression.It is obvious that the load-carrying capacity of the column decreases with increasing slenderness ratio and axial load eccentricity, which is less pronounced under steel tube and CFRP confinement up to mild eccentricity. The NLFEA tests confirmed that FRP confinement improves the axial and flexural resistance of the columns as shown in Figure14.


## 4. Conclusion

This paper presents a finite element study aimed at gaining a further understanding of the behavior of FCCFST columns under eccentric load. The external FRP wrap is provided to constrain outward local buckling deformation of the steel tube and to better confine the concrete core. The accuracy of the nonlinear finite element model is evaluated by comparing the NLFEA result of two specimens with their respective experimental test result in terms of load-displacement response and failure pattern, which had agreed well. The tested parameters were the FRP layer number, the thickness of the steel tube, load eccentricity, the slenderness ratio, and the cross-sectional shape. Based on these nonlinear finite element analysis results, the following conclusions can be drawn:(1)
The axial load resistance of unconfined columns decreases with increasing slenderness ratio, axial compressive load, and load eccentricity. But this is less pronounced in the CFRP confined CFST column. The effect of both steel tube and CFRP confinement system is effective in enhancing the performance of the column by distributing the failure mode to its width or the whole section of the RC column.(2)
The increase in the steel tube thickness increased the ultimate load capacity of the FCCFST specimen but has no significant effect on the axial displacement of a specimen at ultimate load.(3)
The axial load resistance, the axial and lateral deformation capacity, and the overall performance of concrete-filled steel tube circular columns were improved by the CFRP wraps, under both concentric and eccentric loads. The external CFRP wraps delayed the outward local buckling deformation of the steel tube, and reinforcement bar and overall constrained the lateral expansion of the concrete column.(4)
The steel tube and CFRP confinement enhanced the performance of the eccentrically loaded members with an increase in load resistance capacity ranging from 34.01% to 39.19% and in lateral deformation ranging from 136.05% to 57.29% for the rectangular and circular cross-sections, respectively. Therefore, the efficiency of CFRP confinement in load-carrying capacity and lateral deformation is higher in circular and rectangular sections, respectively. In addition to this, the load-carrying capacity was reduced by 15.48, 14.89, and 12.51% under 25 mm load eccentricity and 31.2, 26.5, and 23.87% under 50 mm compared with the concentric load, consecutively for C0S0, C0S1, and C3S1 rectangular RC columns. Thus, CFRP confinement is more significant under eccentric load than under concentric load.



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*Source: 4807436-2022-05-14.xml*