# Finite Element-Based Performance Analysis of Encased Composite Columns under Monotonic Axial Compression Load

Authors: Kefiyalew Zerfu; Regasa Yadeta
Journal: Advances in Civil Engineering
 (2023)

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## Abstract

This paper presents the results of an investigation into the performance of fully encased composite columns under monotonic axial load using finite element simulation. The damage characteristics and the performance investigation of the specimen were mainly focused on the influence of the compressive strength of concrete and the size of reinforcement. The concrete material was modeled using concrete damage plasticity (CDP), which incorporates the hardening and softening behaviors, and the steel was modeled using metal plasticity. The results obtained from the current study were validated by using previously conducted experimental work and manual calculation based on Eurocode 4. According to the FEA result, damage to the concrete matrix was significantly minimized with the increase in the strength of the concrete. By keeping other parameters constant, an increase in longitudinal reinforcement diameter minimizes the equivalent plastic strain both in structural steel and reinforcement bars. Furthermore, the results showed that the numerical simulation fairly validated the analytical solution.


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## Body

## 1. Introduction

Due to its structural performance, especially in high-rise buildings and seismic-prone areas, composite construction is getting attention globally. Better functional and performance requirement of structural system is achieved by the utilization of steel-concrete structure. Due to their superior structural performance compared with conventional reinforced concrete (RC) columns, concrete-encased steel (CES) composite columns are gaining popularity in top-down or basement construction [1–3]. An advantage of composite structure construction is that the structure acquires its strength from the combined resistance of concrete and steel. Steel structures usually have improved ductility, high strength-to-weight, and stiffness-to-weight ratios [4–7]. Proper use of composite construction results in reductions in initial and life-cycle costs [8, 9]. High costs in the construction industry mainly occur due to labor costs and on-site temporary works. In the case of a high-rise building and bridge construction, the construction cost and time of temporary works significantly affect the effectiveness of conventional reinforced concrete construction. The construction process of reinforced concrete columns passes one of the critical paths. Thus, there is a need to reduce the cost and time of the on-site temporary works in the construction industry during the construction period [10, 11]. Composite construction, such as encased composite columns, is the most widely used type of composite construction. A fully encased composite column (FEC) provides improved strength, stability, stiffness, fireproofing, and corrosion protection [12–15].Basically, a steel-concrete composite column comprises either a concrete-encased steel section or a concrete-filled tubular steel section. Steel-concrete composites are generally used as load-bearing members in a composite-framed structure. The combined resistance to external loading in a composite column is enhanced by providing supplementary reinforcement. This prevents excessive spalling of the concrete under external load and fire conditions [16, 17]. So far, many studies have been conducted to study the performance of composite columns under different loading conditions, including combined action [1, 13, 18–24]. In addition, concrete-filled steel tubes under cyclic load were also reported in previous studies [24–26]. Previous studies showed that there are different factors that influence the performance of the composite column. For instance, an increase in the compressive strength of concrete yields an improved capacity for the composite column [4, 27–29]. The provision of confinement has also an effect on the load-carrying capacity, which depends on the steel section shape and the spacing between the transverse reinforcements [1, 30–32]. The effects of cross-section, column height, and confinement were also reported for different eccentricities and structural steel shapes [33–36]. Previous studies conducted on experimental and analytical studies of square composite columns with two interlocking spirals revealed an improved axial compressive capacity and ductility behavior of composite columns. The utilization of a circular and star-shaped spiral enhances the confinement effect for the core concrete [23, 24, 37–39]. According to Jin et al. [40], the constraint effect under concrete is enhanced as the confinement increases and the failure behavior of the column becomes less brittle. The cross-section of steel tubes and the addition of steel fiber also matter for the performance of a composite column. Zhang et al. [41] stated that the utilization of circular steel tubes is recommended over a square steel tube to meet the desired design strength requirement and provide better confinement to core concrete. Furthermore, Zhang et al. [41] quantified that the utilization of steel fibers effectively improved the ductility and reduced the crack width.Finite element analysis (FEA) is a widely utilized method to study the performance and failure characteristics of engineering structures. This computer-based analysis also helps to study the complex behavior that accounts for the material and geometric nonlinearity of steel-concrete composite columns. Earlier studies showed that FEA can fairly validate the results obtained from experimental tests [42–48]. The study result reported by Shih et al. [23] for a fully encased composite column (FEC) made of high-strength steel and concrete stated that finite element analysis reasonably validated the experimental result. Ellobody and Young [43] and Lai et al. [49] also quantified the nonlinear 3-D finite element model as an important tool to evaluate the performance of composite columns. Finite element analysis is applied to investigate the complex load transfer mechanism in composite structures such as a concrete-encased column [13, 18, 24, 50].The focus of this study is to investigate the damage and performance characteristics of an encased composite column under monotonic axial load. The strength of the concrete and the size of the reinforcing bars were used as the main parameters in this study. Nonlinear finite element analysis (FEA) was conducted for the damage behavior and load-carrying capacity of the composite column. Analytical design checks were carried out based on the simplified design method of the Eurocode 4 (EC4) plastic design approach. The FEA and analytical result verifications were conducted by comparing the experimental test reported by Lai et al. [1].


## 2. Material Data and Test Specimens

### 2.1. Material Data

The material definition and an appropriate material model is a crucial element in finite element modeling. The material properties for concrete structural steel and reinforcing bars should be defined with appropriate material parameters. During the finite element analysis, the nonlinear material behavior of these materials was included in the numerical simulation. The comprehensive details of material models were described in the following sections.


#### 2.1.1. Concrete Compressive Strength

Four classes of cylindrical compressive strength were utilized in this study, as shown in Table1. The concrete specimen having a compressive strength of 52.3 MPa was adopted from an experimental test reported by [1]. The encased composite column specimen with this compressive strength was used as a control for the validation study under the current study. However, the remaining concrete compressive strength classes were utilized as additional study parameters for the performance investigation of the encased composite columns. The modulus of elasticity and Poisson’s ratio of these specimens were calculated based on Eurocode-2 provisions for the design of concrete structures [51].Table 1
Mechanical properties of concrete.
Concrete gradeCylindrical compressive strength (MPa)Modulus of elasticity (GPa)Poisson’s ratioRemarkC5052.332.90.2∗C2525310.2∗∗C3030330.2∗∗C3535340.2∗∗∗Mechanical properties of concrete from experimental work [1]. ∗∗Mechanical properties of concrete based on Eurocode-2 provision [51].


#### 2.1.2. Damage Plasticity Modeling

ABAQUS© software offers mainly the following three crack model options to simulate the damage behavior of concrete(1) smeared crack model, (2) brittle crack model, and (3) concrete damaged plasticity model. The concrete damaged plasticity model was utilized in this study, incorporating the inelastic behavior of concrete under tension and compression, which incorporates damage parameters [52]. Thus, in ABAQUS© software, the concrete material is usually simulated under static and dynamic loading conditions using the concrete damaged plasticity model [53]. Tensile cracking and compressive crushing are the two main failure mechanisms considered for the damage plasticity model of concrete. The tensile and compressive behavior of concrete under uniaxial load is described by the damaged plasticity model [54]. During modeling, the degradation of the elastic stiffness in tension and compression is considered for analysis. Furthermore, under cyclic loading, stiffness recovery is accounted for by this model. The response of concrete presented in Figure 1 was utilized in the current study [53].Figure 1
Stress-strain behavior [53]: (a) compression and (b) tension.
(a)(b)The tensile and compressive damage parameters, (dc) and (dt), are calculated by equations (1) and (2), respectively. The value for the scalar damage variables, dt and dc, ranges from 0 (undamaged) to 1 (fully damaged) [55]. The compressive crushing and tensile cracking failure processes are considered in the damage model based on concrete plasticity.(1)σt=1−dtEOεt−εtpl,(2)σc=1−dcEOεc−εcpl.The strain hardening and softening behavior of the concrete were considered for the reinforced concrete during the analysis. To incorporate the complete tensile behavior of reinforced concrete, the input data for Young’s modulus (E0), stress (σt), cracking strain (εtck), and the damage parameter (dt) were considered during the simulation. The cracking strain (εtck) was calculated from the total strain using the following equation:(3)εtck=εt−εotel,where εotel=σt/Eo is the elastic strain and εt is the total strain.Again, the plastic strains are determined from the following equations:(4)εtpl=εtck−dt1−dt∗σtEo,(5)εcpl=εcck−dc1−dcσcE0,where E0 is the initial modulus of elasticity.Parameters describing the state of the material in which the concrete undergoes failure under biaxial compression were also used in this study. The ABAQUS user’s manual specifies that the default value for the ratio of the strength in the biaxial state to the strength in the uniaxial state (fb0/fc0) is equal to 1.16. The dilation angle, which is the angle of inclination of the failure surface towards the hydrostatic axis, measured in the failure plane, was also considered [24, 53]. The dilation angle, ψ, is physically interpreted as a concrete internal friction angle. Under this study, the dilation angles of ψ = 32°, 34°, 36°, and ψ = 38° were used for the corresponding concrete grades C25, C30, C35, and C50, respectively.


#### 2.1.3. Steel Material Modeling

The steel materials were modeled as an elastoplastic material as given in Eurocode 3, 2005, Abaqus manual, and Eurocode 2, 2005 [51, 53, 56]. Figure 2 shows the true stress and logarithmic strain graph that was utilized for the modeling of steel materials. To define the nonlinear behavior of the structural steel section and the reinforcement, the metal plasticity model was used. There true strain-stress behavior was used for steel material to account for the nonlinear behavior characteristics, which enable it to capture the postbehavior of the material [56]. The experimental stress and strain results of the uniaxial tension tests were converted to true stress and logarithmic plastic strain as inputs for the simulation using the following equations:(6)σtrue=σnom1+εnom,(7)εtrue=ln1+εnom,where εnom is the nominal or engineering strain and σnom is the nominal or engineering stress.Figure 2
Stress-strain curves for structural steel and reinforcement: (a) flange section; (b) web section; (c) longitudinal reinforcement; (d) transverse reinforcement.
(a)(b)(c)(d)The steel material properties used for the finite element simulation are given in Table2.Table 2
Steel material data [1].
MaterialYield stress (MPa)Ultimate stress (MPa)Density (kg/m3)Young’s modulus (MPa)Poisson’s ratioSteel sectionsFlange3755807,850226,6000.3Web4046117,850223,9000.3Reinforcement barsRebar5507257,850228,2000.3Stirrup5106677,850197,7000.3


### 2.2. Test Specimens’ Details

For the current study, an experimentally tested specimen by Lai et al. [1] was utilized as a control for analytical and FEA validation. The behavior of the specimens during the loading was examined based on the failure modes, peak load, and load-deflection plots. A column section given in Figure 3 was utilized as a control in an experimental test conducted by Lai et al. [1]. Analytical and finite element analyses were carried out in this column to investigate the structural performance under compressive load. The variables utilized were the compressive strength of the concrete, the height of the column, and the longitudinal and transverse reinforcement size effects.Figure 3
Dimension details of specimen [1].


## 2.1. Material Data

The material definition and an appropriate material model is a crucial element in finite element modeling. The material properties for concrete structural steel and reinforcing bars should be defined with appropriate material parameters. During the finite element analysis, the nonlinear material behavior of these materials was included in the numerical simulation. The comprehensive details of material models were described in the following sections.


### 2.1.1. Concrete Compressive Strength

Four classes of cylindrical compressive strength were utilized in this study, as shown in Table1. The concrete specimen having a compressive strength of 52.3 MPa was adopted from an experimental test reported by [1]. The encased composite column specimen with this compressive strength was used as a control for the validation study under the current study. However, the remaining concrete compressive strength classes were utilized as additional study parameters for the performance investigation of the encased composite columns. The modulus of elasticity and Poisson’s ratio of these specimens were calculated based on Eurocode-2 provisions for the design of concrete structures [51].Table 1
Mechanical properties of concrete.
Concrete gradeCylindrical compressive strength (MPa)Modulus of elasticity (GPa)Poisson’s ratioRemarkC5052.332.90.2∗C2525310.2∗∗C3030330.2∗∗C3535340.2∗∗∗Mechanical properties of concrete from experimental work [1]. ∗∗Mechanical properties of concrete based on Eurocode-2 provision [51].


### 2.1.2. Damage Plasticity Modeling

ABAQUS© software offers mainly the following three crack model options to simulate the damage behavior of concrete(1) smeared crack model, (2) brittle crack model, and (3) concrete damaged plasticity model. The concrete damaged plasticity model was utilized in this study, incorporating the inelastic behavior of concrete under tension and compression, which incorporates damage parameters [52]. Thus, in ABAQUS© software, the concrete material is usually simulated under static and dynamic loading conditions using the concrete damaged plasticity model [53]. Tensile cracking and compressive crushing are the two main failure mechanisms considered for the damage plasticity model of concrete. The tensile and compressive behavior of concrete under uniaxial load is described by the damaged plasticity model [54]. During modeling, the degradation of the elastic stiffness in tension and compression is considered for analysis. Furthermore, under cyclic loading, stiffness recovery is accounted for by this model. The response of concrete presented in Figure 1 was utilized in the current study [53].Figure 1
Stress-strain behavior [53]: (a) compression and (b) tension.
(a)(b)The tensile and compressive damage parameters, (dc) and (dt), are calculated by equations (1) and (2), respectively. The value for the scalar damage variables, dt and dc, ranges from 0 (undamaged) to 1 (fully damaged) [55]. The compressive crushing and tensile cracking failure processes are considered in the damage model based on concrete plasticity.(1)σt=1−dtEOεt−εtpl,(2)σc=1−dcEOεc−εcpl.The strain hardening and softening behavior of the concrete were considered for the reinforced concrete during the analysis. To incorporate the complete tensile behavior of reinforced concrete, the input data for Young’s modulus (E0), stress (σt), cracking strain (εtck), and the damage parameter (dt) were considered during the simulation. The cracking strain (εtck) was calculated from the total strain using the following equation:(3)εtck=εt−εotel,where εotel=σt/Eo is the elastic strain and εt is the total strain.Again, the plastic strains are determined from the following equations:(4)εtpl=εtck−dt1−dt∗σtEo,(5)εcpl=εcck−dc1−dcσcE0,where E0 is the initial modulus of elasticity.Parameters describing the state of the material in which the concrete undergoes failure under biaxial compression were also used in this study. The ABAQUS user’s manual specifies that the default value for the ratio of the strength in the biaxial state to the strength in the uniaxial state (fb0/fc0) is equal to 1.16. The dilation angle, which is the angle of inclination of the failure surface towards the hydrostatic axis, measured in the failure plane, was also considered [24, 53]. The dilation angle, ψ, is physically interpreted as a concrete internal friction angle. Under this study, the dilation angles of ψ = 32°, 34°, 36°, and ψ = 38° were used for the corresponding concrete grades C25, C30, C35, and C50, respectively.


### 2.1.3. Steel Material Modeling

The steel materials were modeled as an elastoplastic material as given in Eurocode 3, 2005, Abaqus manual, and Eurocode 2, 2005 [51, 53, 56]. Figure 2 shows the true stress and logarithmic strain graph that was utilized for the modeling of steel materials. To define the nonlinear behavior of the structural steel section and the reinforcement, the metal plasticity model was used. There true strain-stress behavior was used for steel material to account for the nonlinear behavior characteristics, which enable it to capture the postbehavior of the material [56]. The experimental stress and strain results of the uniaxial tension tests were converted to true stress and logarithmic plastic strain as inputs for the simulation using the following equations:(6)σtrue=σnom1+εnom,(7)εtrue=ln1+εnom,where εnom is the nominal or engineering strain and σnom is the nominal or engineering stress.Figure 2
Stress-strain curves for structural steel and reinforcement: (a) flange section; (b) web section; (c) longitudinal reinforcement; (d) transverse reinforcement.
(a)(b)(c)(d)The steel material properties used for the finite element simulation are given in Table2.Table 2
Steel material data [1].
MaterialYield stress (MPa)Ultimate stress (MPa)Density (kg/m3)Young’s modulus (MPa)Poisson’s ratioSteel sectionsFlange3755807,850226,6000.3Web4046117,850223,9000.3Reinforcement barsRebar5507257,850228,2000.3Stirrup5106677,850197,7000.3


## 2.1.1. Concrete Compressive Strength

Four classes of cylindrical compressive strength were utilized in this study, as shown in Table1. The concrete specimen having a compressive strength of 52.3 MPa was adopted from an experimental test reported by [1]. The encased composite column specimen with this compressive strength was used as a control for the validation study under the current study. However, the remaining concrete compressive strength classes were utilized as additional study parameters for the performance investigation of the encased composite columns. The modulus of elasticity and Poisson’s ratio of these specimens were calculated based on Eurocode-2 provisions for the design of concrete structures [51].Table 1
Mechanical properties of concrete.
Concrete gradeCylindrical compressive strength (MPa)Modulus of elasticity (GPa)Poisson’s ratioRemarkC5052.332.90.2∗C2525310.2∗∗C3030330.2∗∗C3535340.2∗∗∗Mechanical properties of concrete from experimental work [1]. ∗∗Mechanical properties of concrete based on Eurocode-2 provision [51].


## 2.1.2. Damage Plasticity Modeling

ABAQUS© software offers mainly the following three crack model options to simulate the damage behavior of concrete(1) smeared crack model, (2) brittle crack model, and (3) concrete damaged plasticity model. The concrete damaged plasticity model was utilized in this study, incorporating the inelastic behavior of concrete under tension and compression, which incorporates damage parameters [52]. Thus, in ABAQUS© software, the concrete material is usually simulated under static and dynamic loading conditions using the concrete damaged plasticity model [53]. Tensile cracking and compressive crushing are the two main failure mechanisms considered for the damage plasticity model of concrete. The tensile and compressive behavior of concrete under uniaxial load is described by the damaged plasticity model [54]. During modeling, the degradation of the elastic stiffness in tension and compression is considered for analysis. Furthermore, under cyclic loading, stiffness recovery is accounted for by this model. The response of concrete presented in Figure 1 was utilized in the current study [53].Figure 1
Stress-strain behavior [53]: (a) compression and (b) tension.
(a)(b)The tensile and compressive damage parameters, (dc) and (dt), are calculated by equations (1) and (2), respectively. The value for the scalar damage variables, dt and dc, ranges from 0 (undamaged) to 1 (fully damaged) [55]. The compressive crushing and tensile cracking failure processes are considered in the damage model based on concrete plasticity.(1)σt=1−dtEOεt−εtpl,(2)σc=1−dcEOεc−εcpl.The strain hardening and softening behavior of the concrete were considered for the reinforced concrete during the analysis. To incorporate the complete tensile behavior of reinforced concrete, the input data for Young’s modulus (E0), stress (σt), cracking strain (εtck), and the damage parameter (dt) were considered during the simulation. The cracking strain (εtck) was calculated from the total strain using the following equation:(3)εtck=εt−εotel,where εotel=σt/Eo is the elastic strain and εt is the total strain.Again, the plastic strains are determined from the following equations:(4)εtpl=εtck−dt1−dt∗σtEo,(5)εcpl=εcck−dc1−dcσcE0,where E0 is the initial modulus of elasticity.Parameters describing the state of the material in which the concrete undergoes failure under biaxial compression were also used in this study. The ABAQUS user’s manual specifies that the default value for the ratio of the strength in the biaxial state to the strength in the uniaxial state (fb0/fc0) is equal to 1.16. The dilation angle, which is the angle of inclination of the failure surface towards the hydrostatic axis, measured in the failure plane, was also considered [24, 53]. The dilation angle, ψ, is physically interpreted as a concrete internal friction angle. Under this study, the dilation angles of ψ = 32°, 34°, 36°, and ψ = 38° were used for the corresponding concrete grades C25, C30, C35, and C50, respectively.


## 2.1.3. Steel Material Modeling

The steel materials were modeled as an elastoplastic material as given in Eurocode 3, 2005, Abaqus manual, and Eurocode 2, 2005 [51, 53, 56]. Figure 2 shows the true stress and logarithmic strain graph that was utilized for the modeling of steel materials. To define the nonlinear behavior of the structural steel section and the reinforcement, the metal plasticity model was used. There true strain-stress behavior was used for steel material to account for the nonlinear behavior characteristics, which enable it to capture the postbehavior of the material [56]. The experimental stress and strain results of the uniaxial tension tests were converted to true stress and logarithmic plastic strain as inputs for the simulation using the following equations:(6)σtrue=σnom1+εnom,(7)εtrue=ln1+εnom,where εnom is the nominal or engineering strain and σnom is the nominal or engineering stress.Figure 2
Stress-strain curves for structural steel and reinforcement: (a) flange section; (b) web section; (c) longitudinal reinforcement; (d) transverse reinforcement.
(a)(b)(c)(d)The steel material properties used for the finite element simulation are given in Table2.Table 2
Steel material data [1].
MaterialYield stress (MPa)Ultimate stress (MPa)Density (kg/m3)Young’s modulus (MPa)Poisson’s ratioSteel sectionsFlange3755807,850226,6000.3Web4046117,850223,9000.3Reinforcement barsRebar5507257,850228,2000.3Stirrup5106677,850197,7000.3


## 2.2. Test Specimens’ Details

For the current study, an experimentally tested specimen by Lai et al. [1] was utilized as a control for analytical and FEA validation. The behavior of the specimens during the loading was examined based on the failure modes, peak load, and load-deflection plots. A column section given in Figure 3 was utilized as a control in an experimental test conducted by Lai et al. [1]. Analytical and finite element analyses were carried out in this column to investigate the structural performance under compressive load. The variables utilized were the compressive strength of the concrete, the height of the column, and the longitudinal and transverse reinforcement size effects.Figure 3
Dimension details of specimen [1].


## 3. Numerical Simulation

### 3.1. General

Basically, the finite element analysis (FEA) requires defining geometry, material properties, assigning a mesh, analysis type, and boundary conditions for a given model. Finite element analysis (FEA) resulted in refined results during the investigation of the flexural, fatigue, and axial performance of composite columns [20, 25, 42, 57]. The studies show that FEA is the best tool to understand the failure mechanism of a structural element under a given loading condition and even helps to predict the performance of structures under complex boundary, load, and geometrical conditions. Both material and geometric nonlinearity were considered in the analysis. The load was applied using several load increments during the simulation. This helps the structure to remain in equilibrium by controlling nonlinear fluctuations in the structure’s stiffness at the end of each increment [24].


### 3.2. Finite Element Modeling of Encased Composite Column

The modeling procedures for each constituent part of an encased composite column were described one by one in this section. The encased composite column is composed of a structural steel section, longitudinal reinforcement, transverse reinforcement, and concrete. The concrete and structural steel are modeled using a three-dimensional 8-noded hexahedral (brick) element with reduced integration (C3D8R). This helps the shear-locking effect during loading [34]. For the reinforcement, the T3D2 element was used [53]. The assembled view of the column is depicted in Figure 4.Figure 4
Assembled FEA model of encased composite column components.


### 3.3. Loading and Boundary Conditions

The FEA model was created based on the experimental setup as shown in Figure5. The bottom end of the column was fixed, and the axial load was applied through a rigid body reference node at the center of the top loading plate. The rotations and horizontal translations at the top surface were fixed, and translation along the longitudinal downward direction was allowed. The displacement control technique was used to apply the compressive crushing through the reference node at the center of the top loading plate. Figure 5 depicts the experimental setup, boundary, and loading conditions of the current study.Figure 5
Experimental setup and boundary condition: (a) experimental test setup and instrumentations [1]; (b) FEA boundary conditions.
(a)(b)


### 3.4. Interactions Properties

Kinematic relationships were considered to ensure compatibility between interacting bodies. The first interaction type used was an embedded constraint. The embedded constraint was defined for the interaction between concrete, structural steel, and reinforcement bar. The reinforcement bars and the structural steel were embedded under the concrete. Previous studies also stated that this option ensures a perfect bond between the concrete and embedded parts under the concrete [53, 58]. The concrete was defined as the host region, and the steel sections were defined as the embedded elements. The interaction between the encased composite column and the support and loading plate is defined as a tie. Another interaction type used in this study is general surface-to-surface contact, which is used to define two contacting bodies in general [24].


### 3.5. Mesh

Finite element results are highly dependent on mesh types, control, and sizes. Studies showed that the provision of coarse mesh yielded brittle failures [59–62]. The mesh size is one of the factors contributing to the convergence criteria. It has been also reported that mesh fineness and coarseness have a significant effect on computation time [58, 63–66]. The guideline for maximum mesh size was already stated in the previous report [58, 67]. However, the fines of mesh are usually determined by the convergence of results and practical considerations. A mesh size of 20 mm was used in this study.


## 3.1. General

Basically, the finite element analysis (FEA) requires defining geometry, material properties, assigning a mesh, analysis type, and boundary conditions for a given model. Finite element analysis (FEA) resulted in refined results during the investigation of the flexural, fatigue, and axial performance of composite columns [20, 25, 42, 57]. The studies show that FEA is the best tool to understand the failure mechanism of a structural element under a given loading condition and even helps to predict the performance of structures under complex boundary, load, and geometrical conditions. Both material and geometric nonlinearity were considered in the analysis. The load was applied using several load increments during the simulation. This helps the structure to remain in equilibrium by controlling nonlinear fluctuations in the structure’s stiffness at the end of each increment [24].


## 3.2. Finite Element Modeling of Encased Composite Column

The modeling procedures for each constituent part of an encased composite column were described one by one in this section. The encased composite column is composed of a structural steel section, longitudinal reinforcement, transverse reinforcement, and concrete. The concrete and structural steel are modeled using a three-dimensional 8-noded hexahedral (brick) element with reduced integration (C3D8R). This helps the shear-locking effect during loading [34]. For the reinforcement, the T3D2 element was used [53]. The assembled view of the column is depicted in Figure 4.Figure 4
Assembled FEA model of encased composite column components.


## 3.3. Loading and Boundary Conditions

The FEA model was created based on the experimental setup as shown in Figure5. The bottom end of the column was fixed, and the axial load was applied through a rigid body reference node at the center of the top loading plate. The rotations and horizontal translations at the top surface were fixed, and translation along the longitudinal downward direction was allowed. The displacement control technique was used to apply the compressive crushing through the reference node at the center of the top loading plate. Figure 5 depicts the experimental setup, boundary, and loading conditions of the current study.Figure 5
Experimental setup and boundary condition: (a) experimental test setup and instrumentations [1]; (b) FEA boundary conditions.
(a)(b)


## 3.4. Interactions Properties

Kinematic relationships were considered to ensure compatibility between interacting bodies. The first interaction type used was an embedded constraint. The embedded constraint was defined for the interaction between concrete, structural steel, and reinforcement bar. The reinforcement bars and the structural steel were embedded under the concrete. Previous studies also stated that this option ensures a perfect bond between the concrete and embedded parts under the concrete [53, 58]. The concrete was defined as the host region, and the steel sections were defined as the embedded elements. The interaction between the encased composite column and the support and loading plate is defined as a tie. Another interaction type used in this study is general surface-to-surface contact, which is used to define two contacting bodies in general [24].


## 3.5. Mesh

Finite element results are highly dependent on mesh types, control, and sizes. Studies showed that the provision of coarse mesh yielded brittle failures [59–62]. The mesh size is one of the factors contributing to the convergence criteria. It has been also reported that mesh fineness and coarseness have a significant effect on computation time [58, 63–66]. The guideline for maximum mesh size was already stated in the previous report [58, 67]. However, the fines of mesh are usually determined by the convergence of results and practical considerations. A mesh size of 20 mm was used in this study.


## 4. Result and Discussion

### 4.1. Manual Verification According to Eurocode 4

Before conducting the finite element analysis, the result from experimental work was verified by using manual calculation according to Eurocode 4 [30] for the composite column. Thus, the steps to design encased steel columns subjected to axial load are given as follows:(1)
Calculate the ultimate axial load,NEd(2)
Select a trial section and calculate geometrical properties(3)
Determine the buckling length of the column,Le(4)
Determine effective flexural stiffness,EIeff(5)
Determine plastic resistance,Npl,Rk(6)
Determine the relative slenderness of the sectionλ(7)
Choose the buckling curve and compute the reduction factor,χ(8)
Determine buckling resistance,Nb,Rd(9)
Check ifNEd<Nb,Rd, else return to step 2


#### 4.1.1. Given Data

NEd=4475.4kNSteel section UC152 × 152 × 30.Column cross-section,Ac=240×240mm2Characteristic cylindrical compressive strength of concrete,fck=50MPaLongitudinal reinforcement,8∅13Steel material properties are given in Table2Column height,l=600mm


#### 4.1.2. Design Checks

(a)
Geometrical properties of universal column (UC) sectionArea of UC section,Ag=3830mm2Radius of Gyration,iy=67.60mm and ix=38.30mmMoment of inertia,Iy=1748cm4 and Iz=560cm4,Effective length of the column = Le = 0.7∗ L = 0.7 ∗ 600 = 420 mm.(b)
Buckling length of the column (considering the bottom end is fixed and the top end is pinned)Le=0.7∗l=0.7∗600mm=420mm(c)
Effective flexural stiffness,EIeff, of the composite sectionEIeff=EaIa+EsIs+0.6EcmIcwhereEa=elasticmodulusofstructuralsteel=226,600MPa (from Table 2); Es=elasticmodulusofreinforcement=228,200MPa (from Table 2); Ecm=modulusofelasticityofconcrete=22fcm/100.3GPa=22∗50+8/100.3=37,278MPa (Eurocode 2 [51]); Ia=momentofinertiaofstructuralsteel; Ic=momentofinertiaofuncrackedconcretesection=b∗h3/12=240∗2402/12=2,764.8∗105mm4; Is=momentofinertiaofthe8∅13reinforcementbars=8∗π∗D4/64=11,215.88mm4Thus,(8)EIeff,y=226,600∗1748∗104+228,200∗11,215.88+0.6∗37,278∗2,764.8∗105N.mm2=10.1475∗1012N.mm^2,EIeff,z=226,600∗560∗104+228,200∗11,215.88+0.6∗37,278∗2,764.8∗105N.mm2=7.4555∗1012N.mm^2.(d)
Composite section plastic resistance(9)NPl,Rk=Agfy+0.85ACfck+Asfyk=3830∗375+0.85∗240∗240∗50+1061.86∗550=4468.27kN.(e)
Relative slenderness of the sectionThe relative slenderness,λi=Npl,Rk/Ncr, where Ncr,i=π2EIeff,i/Le2(10)Ncr,y=π2∗10.1475∗10124202∗10−3=567,754.03kN,Ncr,z=π2∗7.4555∗10124202∗10−3=417,136.26kN,λy=4,468.27567,754.03=0.089,λz=4,468.27417,136.26=0.1035.(f)
Buckling curve and the corresponding reduction factor,χCheckh/b=157.6/157.6=1.03<1.2, and tf<100mm (EN 1993-1-12005 [56])Thus, the buckling curve “b” for the y-y axis and the buckling curve “c” for the z-z axis were selected and α=0.34 for curve “b” and α=0.49 for curve “c” (EN 1993-1-12005 [56]).Reduction factor,χ=1/ϕ+ϕ2−λi2(11)ϕ=0.51+αλ−0.2+λ2,ϕy=0.51+0.340.089−0.2+0.0892=0.485,ϕz=0.51+0.490.1035−0.2+0.10352=0.482.Hence,(12)χy=10.485+0.4852−0.0892=1.04,χz=10.482+0.4822−0.10352=1.05,χy,yieldsthecriticalresistance.(g)
Determine the buckling resistance,Nb,RdNb,Rd=χy∗NPl,Rk=1.04∗4468.27kN=4647.00kN(h)
Check ifNEd<Nb,RdNEd<Nb,Rd⟶4475.40kN<4647.00kN,The deviation between the manual calculation and the experimental test becomes(13)⟶4647.00−4475.404647.00∗100%=3.7%.For this calculation, it can be seen that the experimental test fairly validates the analytical solution.


### 4.2. Finite Element Analysis Validation Study

To validate finite element analysis, an experimental work reported by Lai et al. [1] was used as a benchmark experiment. The encased composite column has a cross-section of 240 × 240 mm dimension with 600 mm height. A total of 8∅13 longitudinal reinforcement bars were provided, giving a reinforcement ratio of 1.84%. The transverse bars of ∅13 with a clear spacing of 120 mm, giving the volumetric ratio of 1.29% were used. The UC152 × 152 × 30 British steel section was adopted, which accounts for 6.56% of the entire section. This structural steel section is classified as class 1 according to EN1993-1-1, 2005 [56]. The characteristic cylindrical compressive strength of concrete is 50 MPa. The relevant material properties for the finite element analysis are presented in Section 2 under Tables 1 and 2. Furthermore, the finite element analysis instrumentation and modeling parameters are also depicted in Section 3.In this study, a mesh size of 20 mm fairly validates the experimental work. Results showed that the finite element analysis resulted in a close prediction of the experimental test with an accuracy of 95.20% for the ultimate load-carrying capacity of the encased composite column. The ultimate load obtained from finite element analysis (FEA) and experimental test were 4475.4 kN and 4701.01 kN, respectively. The deviation between the FEA and the experimental test is about 4.80%, which is within an acceptable range. Moreover, the comparative study shown in Figure6 shows that the simulation fairly traces the postfailure behavior of the encased composite column from the experimental test. Therefore, it has been observed that this validation result becomes a good starting point for the discussed parametric studies in the next sections.Figure 6
Comparative study between FEA and experimental test.


### 4.3. Effects of Concrete Strength

Obviously, it is a known fact that an increase in compressive strength yields enhanced load-carrying capacity of concrete structures; however, it is difficult to predict how much damage to the concrete matrix is minimized by improving the compressive strength of concrete. Thus, finite element analysis shows very precise information about how much of the concrete matrix is damaged at a given ultimate load. The geometrical and material properties used for the structural steel and reinforcement bar are identical to those given in Section4.2. Figure 7 clearly shows the effect of concrete strength on the damage characteristics of an encased composite column. The damage to the concrete is significantly minimized due to the increased strength of the concrete. The load-carrying capacity of the encased composite column increased with the increase in concrete compressive strengths, as shown in Figure 8. The load-carrying capacity of the column improved by about 6.38% and 5.93% for the concrete grades of fck=25 to fck=30 and fck=30 to fck=35, respectively. The capacity of the column improved by 11.93% on average as the compressive strength of concrete increased from fck=25 to fck=35, as depicted in Figure 8(b). From this study, we can understand that the damage to the concrete matrix can be minimized by increasing the compressive strength of the concrete. Furthermore, an increase in concrete strength improves the load-bearing capacity of an encased composite column, as expected.Figure 7
Effects of concrete strength on damage characteristics of the encased composite column: (a)fck=25; (b)fck=30; (c)fck=35.
(a)(b)(c)Figure 8
Comparative study: (a) load versus displacement study; (b) comparison in percentage.
(a)(b)


### 4.4. Effects of Reinforcement Ratio

The effect of longitudinal reinforcement is better understood by observing equivalent plastic strain (PEEQ), as shown in Figures9(a)–9(c). Keeping other parameters constant, an increase in the reinforcement ratio minimizes the equivalent plastic strain both in structural steel and reinforcement bars. The ultimate load of the encased composite column increased with the increase in reinforcement ratio, as shown in Figure 10. The finite element analysis also verified that the plastic resistance to compression of the composite section is directly proportional to the area of the reinforcing bar, as discussed in Section 4.1. The load-carrying capacity of the column improved by about 4.14% and 4.77%, for an increase in reinforcement ratio from 0.0157 to 0.0214 and 0.0214 to 0.0279, respectively. The capacity of the column improved by 8.91% on average when the reinforcement ratio increased from 0.0157 to 0.0279 while keeping the number of bars and other parameters constant, as depicted in Figure 9(b). Thus, from this study, we can understand that an increase in reinforcement ratio minimizes the plastic strain under structural steel and reinforcing bars in fully encased steel composite columns. A recent study also depicted that an increase in the reinforcement ratio tends to increase the ultimate load-carrying capacity [68].Figure 9
Effects of reinforcement ratio on damage characteristics of the encased composite column: (a)0.0157; (b) 0.0214; (c) 0.0279.
(a)(b)(c)Figure 10
Comparative study for reinforcement effect(a) load versus displacement study; (b) comparison in percentage.
(a)(b)


## 4.1. Manual Verification According to Eurocode 4

Before conducting the finite element analysis, the result from experimental work was verified by using manual calculation according to Eurocode 4 [30] for the composite column. Thus, the steps to design encased steel columns subjected to axial load are given as follows:(1)
Calculate the ultimate axial load,NEd(2)
Select a trial section and calculate geometrical properties(3)
Determine the buckling length of the column,Le(4)
Determine effective flexural stiffness,EIeff(5)
Determine plastic resistance,Npl,Rk(6)
Determine the relative slenderness of the sectionλ(7)
Choose the buckling curve and compute the reduction factor,χ(8)
Determine buckling resistance,Nb,Rd(9)
Check ifNEd<Nb,Rd, else return to step 2


### 4.1.1. Given Data

NEd=4475.4kNSteel section UC152 × 152 × 30.Column cross-section,Ac=240×240mm2Characteristic cylindrical compressive strength of concrete,fck=50MPaLongitudinal reinforcement,8∅13Steel material properties are given in Table2Column height,l=600mm


### 4.1.2. Design Checks

(a)
Geometrical properties of universal column (UC) sectionArea of UC section,Ag=3830mm2Radius of Gyration,iy=67.60mm and ix=38.30mmMoment of inertia,Iy=1748cm4 and Iz=560cm4,Effective length of the column = Le = 0.7∗ L = 0.7 ∗ 600 = 420 mm.(b)
Buckling length of the column (considering the bottom end is fixed and the top end is pinned)Le=0.7∗l=0.7∗600mm=420mm(c)
Effective flexural stiffness,EIeff, of the composite sectionEIeff=EaIa+EsIs+0.6EcmIcwhereEa=elasticmodulusofstructuralsteel=226,600MPa (from Table 2); Es=elasticmodulusofreinforcement=228,200MPa (from Table 2); Ecm=modulusofelasticityofconcrete=22fcm/100.3GPa=22∗50+8/100.3=37,278MPa (Eurocode 2 [51]); Ia=momentofinertiaofstructuralsteel; Ic=momentofinertiaofuncrackedconcretesection=b∗h3/12=240∗2402/12=2,764.8∗105mm4; Is=momentofinertiaofthe8∅13reinforcementbars=8∗π∗D4/64=11,215.88mm4Thus,(8)EIeff,y=226,600∗1748∗104+228,200∗11,215.88+0.6∗37,278∗2,764.8∗105N.mm2=10.1475∗1012N.mm^2,EIeff,z=226,600∗560∗104+228,200∗11,215.88+0.6∗37,278∗2,764.8∗105N.mm2=7.4555∗1012N.mm^2.(d)
Composite section plastic resistance(9)NPl,Rk=Agfy+0.85ACfck+Asfyk=3830∗375+0.85∗240∗240∗50+1061.86∗550=4468.27kN.(e)
Relative slenderness of the sectionThe relative slenderness,λi=Npl,Rk/Ncr, where Ncr,i=π2EIeff,i/Le2(10)Ncr,y=π2∗10.1475∗10124202∗10−3=567,754.03kN,Ncr,z=π2∗7.4555∗10124202∗10−3=417,136.26kN,λy=4,468.27567,754.03=0.089,λz=4,468.27417,136.26=0.1035.(f)
Buckling curve and the corresponding reduction factor,χCheckh/b=157.6/157.6=1.03<1.2, and tf<100mm (EN 1993-1-12005 [56])Thus, the buckling curve “b” for the y-y axis and the buckling curve “c” for the z-z axis were selected and α=0.34 for curve “b” and α=0.49 for curve “c” (EN 1993-1-12005 [56]).Reduction factor,χ=1/ϕ+ϕ2−λi2(11)ϕ=0.51+αλ−0.2+λ2,ϕy=0.51+0.340.089−0.2+0.0892=0.485,ϕz=0.51+0.490.1035−0.2+0.10352=0.482.Hence,(12)χy=10.485+0.4852−0.0892=1.04,χz=10.482+0.4822−0.10352=1.05,χy,yieldsthecriticalresistance.(g)
Determine the buckling resistance,Nb,RdNb,Rd=χy∗NPl,Rk=1.04∗4468.27kN=4647.00kN(h)
Check ifNEd<Nb,RdNEd<Nb,Rd⟶4475.40kN<4647.00kN,The deviation between the manual calculation and the experimental test becomes(13)⟶4647.00−4475.404647.00∗100%=3.7%.For this calculation, it can be seen that the experimental test fairly validates the analytical solution.


## 4.1.1. Given Data

NEd=4475.4kNSteel section UC152 × 152 × 30.Column cross-section,Ac=240×240mm2Characteristic cylindrical compressive strength of concrete,fck=50MPaLongitudinal reinforcement,8∅13Steel material properties are given in Table2Column height,l=600mm


## 4.1.2. Design Checks

(a)
Geometrical properties of universal column (UC) sectionArea of UC section,Ag=3830mm2Radius of Gyration,iy=67.60mm and ix=38.30mmMoment of inertia,Iy=1748cm4 and Iz=560cm4,Effective length of the column = Le = 0.7∗ L = 0.7 ∗ 600 = 420 mm.(b)
Buckling length of the column (considering the bottom end is fixed and the top end is pinned)Le=0.7∗l=0.7∗600mm=420mm(c)
Effective flexural stiffness,EIeff, of the composite sectionEIeff=EaIa+EsIs+0.6EcmIcwhereEa=elasticmodulusofstructuralsteel=226,600MPa (from Table 2); Es=elasticmodulusofreinforcement=228,200MPa (from Table 2); Ecm=modulusofelasticityofconcrete=22fcm/100.3GPa=22∗50+8/100.3=37,278MPa (Eurocode 2 [51]); Ia=momentofinertiaofstructuralsteel; Ic=momentofinertiaofuncrackedconcretesection=b∗h3/12=240∗2402/12=2,764.8∗105mm4; Is=momentofinertiaofthe8∅13reinforcementbars=8∗π∗D4/64=11,215.88mm4Thus,(8)EIeff,y=226,600∗1748∗104+228,200∗11,215.88+0.6∗37,278∗2,764.8∗105N.mm2=10.1475∗1012N.mm^2,EIeff,z=226,600∗560∗104+228,200∗11,215.88+0.6∗37,278∗2,764.8∗105N.mm2=7.4555∗1012N.mm^2.(d)
Composite section plastic resistance(9)NPl,Rk=Agfy+0.85ACfck+Asfyk=3830∗375+0.85∗240∗240∗50+1061.86∗550=4468.27kN.(e)
Relative slenderness of the sectionThe relative slenderness,λi=Npl,Rk/Ncr, where Ncr,i=π2EIeff,i/Le2(10)Ncr,y=π2∗10.1475∗10124202∗10−3=567,754.03kN,Ncr,z=π2∗7.4555∗10124202∗10−3=417,136.26kN,λy=4,468.27567,754.03=0.089,λz=4,468.27417,136.26=0.1035.(f)
Buckling curve and the corresponding reduction factor,χCheckh/b=157.6/157.6=1.03<1.2, and tf<100mm (EN 1993-1-12005 [56])Thus, the buckling curve “b” for the y-y axis and the buckling curve “c” for the z-z axis were selected and α=0.34 for curve “b” and α=0.49 for curve “c” (EN 1993-1-12005 [56]).Reduction factor,χ=1/ϕ+ϕ2−λi2(11)ϕ=0.51+αλ−0.2+λ2,ϕy=0.51+0.340.089−0.2+0.0892=0.485,ϕz=0.51+0.490.1035−0.2+0.10352=0.482.Hence,(12)χy=10.485+0.4852−0.0892=1.04,χz=10.482+0.4822−0.10352=1.05,χy,yieldsthecriticalresistance.(g)
Determine the buckling resistance,Nb,RdNb,Rd=χy∗NPl,Rk=1.04∗4468.27kN=4647.00kN(h)
Check ifNEd<Nb,RdNEd<Nb,Rd⟶4475.40kN<4647.00kN,The deviation between the manual calculation and the experimental test becomes(13)⟶4647.00−4475.404647.00∗100%=3.7%.For this calculation, it can be seen that the experimental test fairly validates the analytical solution.


## 4.2. Finite Element Analysis Validation Study

To validate finite element analysis, an experimental work reported by Lai et al. [1] was used as a benchmark experiment. The encased composite column has a cross-section of 240 × 240 mm dimension with 600 mm height. A total of 8∅13 longitudinal reinforcement bars were provided, giving a reinforcement ratio of 1.84%. The transverse bars of ∅13 with a clear spacing of 120 mm, giving the volumetric ratio of 1.29% were used. The UC152 × 152 × 30 British steel section was adopted, which accounts for 6.56% of the entire section. This structural steel section is classified as class 1 according to EN1993-1-1, 2005 [56]. The characteristic cylindrical compressive strength of concrete is 50 MPa. The relevant material properties for the finite element analysis are presented in Section 2 under Tables 1 and 2. Furthermore, the finite element analysis instrumentation and modeling parameters are also depicted in Section 3.In this study, a mesh size of 20 mm fairly validates the experimental work. Results showed that the finite element analysis resulted in a close prediction of the experimental test with an accuracy of 95.20% for the ultimate load-carrying capacity of the encased composite column. The ultimate load obtained from finite element analysis (FEA) and experimental test were 4475.4 kN and 4701.01 kN, respectively. The deviation between the FEA and the experimental test is about 4.80%, which is within an acceptable range. Moreover, the comparative study shown in Figure6 shows that the simulation fairly traces the postfailure behavior of the encased composite column from the experimental test. Therefore, it has been observed that this validation result becomes a good starting point for the discussed parametric studies in the next sections.Figure 6
Comparative study between FEA and experimental test.


## 4.3. Effects of Concrete Strength

Obviously, it is a known fact that an increase in compressive strength yields enhanced load-carrying capacity of concrete structures; however, it is difficult to predict how much damage to the concrete matrix is minimized by improving the compressive strength of concrete. Thus, finite element analysis shows very precise information about how much of the concrete matrix is damaged at a given ultimate load. The geometrical and material properties used for the structural steel and reinforcement bar are identical to those given in Section4.2. Figure 7 clearly shows the effect of concrete strength on the damage characteristics of an encased composite column. The damage to the concrete is significantly minimized due to the increased strength of the concrete. The load-carrying capacity of the encased composite column increased with the increase in concrete compressive strengths, as shown in Figure 8. The load-carrying capacity of the column improved by about 6.38% and 5.93% for the concrete grades of fck=25 to fck=30 and fck=30 to fck=35, respectively. The capacity of the column improved by 11.93% on average as the compressive strength of concrete increased from fck=25 to fck=35, as depicted in Figure 8(b). From this study, we can understand that the damage to the concrete matrix can be minimized by increasing the compressive strength of the concrete. Furthermore, an increase in concrete strength improves the load-bearing capacity of an encased composite column, as expected.Figure 7
Effects of concrete strength on damage characteristics of the encased composite column: (a)fck=25; (b)fck=30; (c)fck=35.
(a)(b)(c)Figure 8
Comparative study: (a) load versus displacement study; (b) comparison in percentage.
(a)(b)


## 4.4. Effects of Reinforcement Ratio

The effect of longitudinal reinforcement is better understood by observing equivalent plastic strain (PEEQ), as shown in Figures9(a)–9(c). Keeping other parameters constant, an increase in the reinforcement ratio minimizes the equivalent plastic strain both in structural steel and reinforcement bars. The ultimate load of the encased composite column increased with the increase in reinforcement ratio, as shown in Figure 10. The finite element analysis also verified that the plastic resistance to compression of the composite section is directly proportional to the area of the reinforcing bar, as discussed in Section 4.1. The load-carrying capacity of the column improved by about 4.14% and 4.77%, for an increase in reinforcement ratio from 0.0157 to 0.0214 and 0.0214 to 0.0279, respectively. The capacity of the column improved by 8.91% on average when the reinforcement ratio increased from 0.0157 to 0.0279 while keeping the number of bars and other parameters constant, as depicted in Figure 9(b). Thus, from this study, we can understand that an increase in reinforcement ratio minimizes the plastic strain under structural steel and reinforcing bars in fully encased steel composite columns. A recent study also depicted that an increase in the reinforcement ratio tends to increase the ultimate load-carrying capacity [68].Figure 9
Effects of reinforcement ratio on damage characteristics of the encased composite column: (a)0.0157; (b) 0.0214; (c) 0.0279.
(a)(b)(c)Figure 10
Comparative study for reinforcement effect(a) load versus displacement study; (b) comparison in percentage.
(a)(b)


## 5. Conclusions

In this study, nonlinear 3D finite element modeling of square-encased composite columns under monotonic axial compression load was performed. The concrete material was modeled using concrete damage plasticity (CDP), which incorporates the hardening and softening behaviors, and the steel was modeled using metal plasticity. The effects of concrete strength and reinforcement ratio were investigated to understand the capacity and stress-strain distribution under the composite column. The analysis result from the current study fairly validates the experimental result by capturing the postsoftening part of the test specimen. Furthermore, the result from experimental work was verified prior to FEA by using manual calculation according to Eurocode 4 and a simplified method to design encased steel columns under axial compression. Based on the analysis and discussion presented in this study, the following conclusions were drawn:(i)
A comparative study was conducted for finite element analysis to estimate the ultimate load-carrying capacity between analytical calculation according to Eurocode 4 and experiment test. It has been observed that the finite element analysis resulted in a close prediction of the experimental test with an accuracy of 95.20% for the ultimate load-carrying capacity of the encased composite column.(ii)
It has been observed that an appropriate material definition and mesh size selection during finite element analysis (FEA) helps to obtain refined postsoftening failure behavior of the composite volume form load versus displacement plot.(iii)
The increase in the compressive strength of concrete yields a reduction in the damage to the concrete matrix and improves the load-carrying capacity of the composite column. It has been observed that the capacity of the column improved by 11.93% on average as the compressive strength of concrete increased fromfck=25 to fck=35 by keeping other parameters constant.(iv)
An increase in reinforcement ratio minimizes the equivalent plastic strain both in structural steel and reinforcement bar, and it has been observed that the plastic resistance to compression of the composite section is directly proportional to the area of the reinforcing bar. The capacity of the column improved by 8.91% on average when the diameter of the bar increased from 0.0157 to 0.0279 while keeping the number of bars and other parameters constant.(v)
In general, nonlinear 3D finite element modeling is the finest tool to investigate the performance and damage behavior of composite structures by incorporating correct material modeling.



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*Source: 5974705-2023-01-27.xml*