Experimental Investigation and Numerical Analysis of the Axial Load Capacity of Circular Concrete-Filled Tubular Columns

Abstract

This paper focuses on the experimental investigation of the axial load capacity of CFT (concrete-filled steel tube) columns under actual construction conditions during building reconstruction. A total of four samples were loaded up to failure. The varied parameters were the column length and absence/presence of the concrete infill within the steel tube. Further, the analysis is extended to developing a numerical model in the finite element-based software ABAQUS version 6.9. This numerical model includes material and geometrical nonlinearities and was validated with the experimental results. The contribution of the concrete core to the column capacity and the concrete core confinement effect are discussed. Finally, the column capacity was calculated according to several design codes: the Eurocode 4 with and without considering the confinement effect, American specifications, Australian standards, the American Institute of Steel Construction, and the Architectural Institute of Japan. The Eurocode 4 considering the confinement effect provides the closest results to those obtained in the tests.

1. Introduction

Due to their constructive advantages, columns derived from steel hollow profiles filled with concrete (CFT columns) have found wide application in engineering practice. Compared to traditional concrete or steel columns, the advantages of these columns are numerous: higher load capacity, rigidity and ductility, and savings in space, material, and construction time.

Determining the ultimate bearing capacity of CFT columns is challenging due to many parameters which need to be investigated. First, the nonlinear behavior of the constitutive materials, steel and concrete, needs to be defined for application in numerical analysis. Further, the study should include the steel profile’s second-order influences, geometric imperfections, and residual stresses. Calculating the bearing capacity of CFT columns by current design codes and provisions uses simplified methods and is based on the calculation according to limit states.

In recent years, many authors have published works on the experimental and numerical analysis of the bearing capacity of CFT columns. Numerical analyses are mostly conducted using available finite element method (FEM) software. The majority of studies employed ABAQUS, as in [1,2,3,4], while certain studies utilized ANSYS [5,6,7] or LS-DYNA [8,9,10]. Further, many researchers provided a comparative analysis of their results with current design codes. The accuracy of calculating the bearing capacity of CFT columns is significantly affected by the adopted constitutive models for concrete and steel. Whole series of proposals for these relationships that more or less accurately describe the behavior of concrete and steel can be found in the literature [3,11,12,13,14,15,16,17]. Schneider [11] analyzed the influence of the section shape of the hollow steel profile and the steel quality on the CFT column load capacity on fourteen samples. Ehab Ellobody et al. [3] proposed constitutive models for confined concrete and steel for ABAQUS use. The numerically obtained results of the axial bearing capacity of CFT columns are compared with the results of experiments, as well as with the following design codes: EC4, ACI, and AISC. Giakoumelis and Lam [18] examined the effect of wall thickness, bond behavior of the hollow steel profile and concrete core, concrete shrinkage, and creep on the axial load capacity of circular CFT columns. In the paper [13], Hu proposed a constitutive model for the concrete core inside the CFT column, separately for circular and square sections. Liang and Fragomeni [19] presented constitutive models for the concrete and steel of normal- and high-strength materials. They conducted a parametric analysis to determine the influence of concrete confinement by the steel profile, the diameter-to-wall thickness ratio of the steel profile D/t, and the impact of concrete strength and steel quality on the bearing capacity of the CFT column of the circular section. Li et al. [20] analyzed the fundamental behavior of high-strength concrete-filled high-strength square steel tubular (HCFHSST) long columns under eccentric compression. Lin et al. [16] developed a new fiber beam element (FBE) model that applies to both small and large CFT and slender columns. Finally, attention should also be directed towards exploring new solutions and approaches, including innovative materials and sustainable solutions [21,22,23,24,25].

The CFT column’s slenderness, defined as the column length-to-dimeter ratio L/D, significantly influences its bearing capacity [26,27,28,29]. In the case of short columns (L/D ≤ 3.00) [26,30] the loss of bearing capacity may occur due to failure in the concrete material or yield of the steel profile.

The concrete core confinement effect-related research can be found in [18,19,31,32,33,34]. During the axial load, the inner concrete core gets strengthened by an outer steel profile that affects the bearing capacity of a composite column. This confinement decreases with the increased diameter-to-profile thickness ratio D/t, or with concrete strength, column slenderness, and load eccentricity. On the contrary, it rises with higher steel quality.

Oliveira et al. [26] presented experimental results from 32 axially loaded CFT columns, where the load was applied solely on the concrete core to assess the passive confinement provided by the steel tube. Abed et al. [35] conducted experimental and numerical studies on 16 CFT specimens, identifying the most influential factor on compressive behavior as D/t. Tao et al. [1] proposed an expression for determining lateral pressure in circular columns based on numerical tests with varying parameters. Han et al. [36] introduced the confinement factor, which relies on the cross-sectional areas and strengths of steel and concrete. However, instructions in the literature regarding when and how to consider confinement remain ambiguous today. This is partly due to challenges in direct measurement in experiments, leading some authors to provide algorithms for estimating this strengthening effect.

When creating a numerical model of the CFT column in ABAQUS, the bond behavior of two surfaces in a composite element should be defined. This contact is formed at the connection of the inner steel profile surface and the outer concrete core surface. This connection can be modeled using gap elements representing contact behavior in the longitudinal and tangential directions. It can be defined by setting the appropriate friction coefficient in the range of 0.2–0.6 [3,13,19]. The bond between the concrete core and the hollow steel profile decreases with increasing concrete strength [26,27]. This phenomenon occurs since higher-strength concrete has more significant shrinkage [3].

This research aimed to perform experimental tests on CFT columns on an actual reconstruction site to validate previous design calculations. Generally, there is a need for studies dealing with an empirical investigation conducted in conditions that may significantly differ from those achieved in laboratory settings. Moreover, this data may be valuable for validating other laboratory-performed tests or numerically obtained results. Finally, this study aimed to define a numerical 3D model which would successfully predict the structural behavior of a circular section’s axially loaded CFT column with reasonable accuracy. Nonlinear numerical analysis was performed in ABAQUS [37] using the proper concrete core and steel profile constitutive models, and aimed to include concrete confinement. The results of the study were validated with test results and compared with the relevant design codes: the EN-1994-1-1 (EC4) with and without considering the confinement effect [38], American specifications (ACI) [39], Australian standards (AS) [40,41], the American Institute of Steel Construction (AISC) [42], and the Architectural Institute of Japan (AIJ) [43]. Besides, design codes offer diverse instructions and criteria on how to account for the confinement effect. For instance, EC4 utilizes relative column slenderness, whereas AIJ employs the length-to-diameter (L/D) ratio.

The study introduces an experimental program designed to assess the axial load capacity of CFT columns under real construction conditions. The primary objective was to evaluate the effectiveness of concrete infill and steel tube confinement in strengthening the columns. Key parameters under investigation included column length and the impact of concrete infill on axial load capacity. The study tested the axial bearing capacity of four specimens: two hollow steel profiles with a D/t ratio of 101.6/2.7 mm and lengths of 0.5 m and 1.0 m, and two CFT columns consisting of identical steel profiles filled with C25/30 concrete. This approach allowed for measurement of the contributions of concrete infill and the calculation of steel tube confinement.

2. Experimental Research Program

2.1. Test Setup

The axial load capacity of steel and CFT columns was tested using a particular constructed set (Figure 1). It consists of a steel frame 2400 × 600 × 600 mm with two hydraulic 200 mm diameter presses. Hydraulic presses are driven by two electric motors (power 7 kW and 10 kW) with two hydraulic pumps (for lower and higher pressure). The total capacity of the press is 300 bar. The force was continuously measured using the C6A2MN dose device, which can measure a load of up to 2000 kN with an accuracy of ±0.1 kN. The column shortening was continuously measured with the W100 displacement gauge (inductive standard displacement transducer), which can measure the vertical displacement or shortening of the column with an accuracy of ±0.01 mm. Four gauges are placed on the top of the circular specimen in two perpendicular directions.

During the column’s concreting, the concrete core was left 1–2 cm longer than the steel profile and finely aligned with a concrete grinder on the testing day. The load was applied in steps via a rigid plate welded to the bottom and top ends of the steel column and the CFT column. This way, the load was applied simultaneously to the steel and concrete part of the column cross-section. The load applied in the tests was a quasistatic monotonically increasing centric axial load. A calotte device was used to achieve the centric introduction of the load. The loading process can be considered short-term as each sample’s failure took about 3 min.

The axial load capacity of four specimens was tested: two hollow steel profiles denoted as S₁ and S₂ and two CFT columns denoted as C₁ and C₂, as in

Table 1. Specimen details.

Specimen	L	D	t	$\overline{\mathit{\lambda }}$	NTEST	NFEM	NFEM/NTEST
-	[m]	[mm]	[mm]	-	[kN]	[kN]	[%]
S1	0.5	101.6	2.7	0.094	315.78	329.10	-
S2	1.0	101.6	2.7	0.187	297.84	328.09	-
C1	0.5	101.6	2.7	0.113	701.71	697.52	99.40
C2	1.0	101.6	2.7	0.227	555.57	568.65	102.35

. The ultimate load capacity of the steel columns and the corresponding CFT columns was analyzed, and the concrete infill’s contribution to the load capacity was eventually determined.

The specimen D/t ratio of all specimens was 37.63. The steel was S355 quality, and its characteristics were taken from the material specification. CFT column specimens C₁ and C₂ have the same length and steel characteristics as their empty reference columns S₁ and S₂. The concrete infill was C25/30 with a three-fraction granulometric composition made at the concrete plant. The specimen testing was performed on the construction site. The old “NAPRED” building in Belgrade was reconstructed using specifically CFT columns. The specimens were concreted in several layers and slumped with a metal rod. The concrete compressive strength was checked for three control cylinder samples 150 mm·300 mm, and the mean value f_c′ was 30.5 MPa.

A rigid steel plate at the bottom end of the specimens was also welded to the testing set. This way, the displacements and rotations of the samples are prevented by simulating fixed-end conditions. A rigid steel plate at the upper end of the specimen was also welded to the inner frame of the testing set to avoid rotation but allow movement in the loading direction. According to EC4 [38], the relative slenderness of the column was calculated using the following expression:

$$\overline{\lambda }=\sqrt{\frac{N_{pl,Rk}}{N_{cr}}}$$

(1)

where N_pl,Rk is the characteristic value of the plastic resistance of the composite section to the compressive normal force, and N_cr is the elastic critical normal force. The relative slenderness of the specimens is also shown in Table 1.

2.2. Failure Modes and Results

The axial load capacities of the four specimens obtained in tests N_test are reported in Table 1. Figure 2a shows the 0.5 m long hollow specimen S₁ and CFT column C₁ failure pattern. In these tests, the failure occurred due to the yielding of the steel profile and outward local buckling at both ends of the steel tube. Figure 2b shows the 1.0 m long hollow specimen S₂ and CFT column C₂ after testing. Here, the failure also occurred due to the outward local buckling of the steel profile at both ends of the column. The tests concluded once the pressure on the manometer began to decrease. At the same time, significant deformations in the steel tube were noted. Additionally, post-failure, the steel tubes of the CFT column specimens C₁ and C₂ were sectioned to inspect the inner concrete core. It was affirmed that the failure resulted from the yielding of the steel tube, as no evidence of concrete crushing was detected within the core. For longer specimens, besides the yielding of the steel tube, the signs of the overall column’s buckling could also be observed.

3. Numerical Modeling of Axial Bearing Capacity of CFT Columns Using FEM

3.1. General

The axial load capacity of circular CFT columns was determined using the finite element method-based software ABAQUS version 6.9 [37] (Figure 3). Three-dimensional C3D8R finite elements (8-node linear brick, reduced integration with hourglass control) were used for the concrete core. S4R finite shell elements (4-node general-purpose shell, reduced integration with hourglass control, finite membrane strains) were used to model the steel profile. An element size of 10 mm was chosen for both concrete and steel components based on the mesh sensitivity analysis [2]. The material nonlinear stress–strain relations are included within the constitutive materials. Finally, the connection of the steel profile with the concrete core was modeled using “surface-to-surface contact” elements [37].

The nonlinear analysis uses Newton’s direct method with a maximum of ten increments. The initial increment size is 0.1, the minimum increment size is 0.0001, and the maximum is 1.0. A linear extrapolation of the previous increment is adopted at the beginning of the next increment. The load was applied as a surface load in steps equivalent to the test’s applied pressure. The boundary conditions match the conditions from the experiment. At the bottom end of the CFT column, translation and rotation in all three directions are restrained, representing a rigid fastening. To apply the axial load, only vertical translation of the column is allowed at the upper end of the CFT column.

3.2. Constitutive Model for Concrete

The constitutive model for concrete significantly influences the accuracy of the obtained results. The model applied in this study was recommended by [3] (Figure 4), and it presents stress–strain (σ–ε) diagrams for both unconfined and confined concrete. The confined concrete model incorporates an increase in peak compressive concrete strength as well as improved ductility due to the presence of the steel casing.

The uniaxial compressive strength of unconfined concrete f_c′ was obtained in control tests as 30.5 MPa. The corresponding strain ε_c’ is taken as 0.003. The stress–strain relation of unconfined concrete is taken as linear until the value of 0.5·f_c′. The modulus of elasticity of concrete E_c is determined according to EN 1992-1-1 [44] based on the following expression:

$$E_c=\mathrm{22,000}\cdot {\left[\frac{{f_c}^{\prime }+8}{10}\right]}^{0.3}\left[\mathrm{MPa}\right]$$

(2)

The nonlinear part of the σ–ε diagram for unconfined concrete beyond 0.5·f_c′ is defined by the following equation, initially proposed by the author [45]:

$$\sigma =\frac{E_c\cdot \epsilon }{1+\left(R+R_E-2\right)\cdot \left(\frac{\epsilon }{{{\epsilon }_c}^{\prime }}\right)-\left(2\cdot R-1\right)\cdot {\left(\frac{\epsilon }{{{\epsilon }_c}^{\prime }}\right)}^2+R\cdot {\left(\frac{\epsilon }{{{\epsilon }_c}^{\prime }}\right)}^3}$$

(3)

where R_E and R are coefficients calculated as follows:

$$R_E=\frac{E_c\cdot {{\epsilon }_c}^{\prime }}{{f_c}^{\prime }}$$

(4)

$$R=\frac{R_E\cdot \left(R_{\sigma }-1\right)}{{\left(R_{\epsilon }-1\right)}^2}-\frac{1}{R_{\epsilon }}$$

(5)

where R_σ and R_ε in (5) equal 4 [46].

The tensile strength of concrete is taken as approximately 9% of the compressive strength of concrete f_c′. After reaching the peak value, the tensile stress decreases to zero at the strain of 0.001 [37].

The confinement effect significantly influences the axial bearing capacity of short circular CFT columns [30,47]. At the initial loading level, the influence of the steel part of the section on the concrete part is small, considering that steel has a higher Poisson coefficient. At an axial strain of approximately 0.001, micro-cracks appear in concrete, with the transverse strains in the concrete growing rapidly [48]. With a further increase in the load, the concrete gets strengthened by the steel profile. Consequently, the steel part of the section is in a biaxial stress state, while the concrete is in a triaxial stress state. It is known that the compressive strength of concrete increases in this condition. When this strengthening effect is considered, the CFT column’s load capacity is greater than the sum of the load capacity of the individual column elements.

To generate the σ–ε diagram of confined concrete, the previous E_c, f_c′, and ε_c′ defined in Equations (2)–(5) are replaced with a modulus of elasticity of confined concrete E_cc, compressive strength of confined concrete f_cc′, and the corresponding strain ε_cc′ [3,13,49], defined by the following expressions [50]:

$${f_{cc}}^{\prime }={f_c}^{\prime }+k_1\cdot f_l$$

(6)

$${{\epsilon }_{\mathrm{cc}}}^{\prime }={{\epsilon }_c}^{\prime }\cdot \left(1+k_2\cdot \frac{f_l}{{f_c}^{\prime }}\right)$$

(7)

where k₁ and k₂ are coefficients 4.1 and 20.5, respectively [51], while f_l is the lateral confining pressure, which depends on the ratio D/t and on the yield strength of steel f_y. It can be calculated in the following way [13]:

$$f_l=\left(0.043646-0.000832\cdot \frac{D}{t}\right)\cdot f_y$$

(8)

The decreasing branch of the confined concrete diagram is linear in the interval from ε_cc′ to 11∙ε_cc′. The reduction coefficient k₃ depends on the ratio D/t and the f_y and can be calculated as follows [13]:

$$k_3=1.00 \mathrm{for} D/t\le 40$$

(9)

$$k_3=0.0000339\cdot {\left(\frac{D}{t}\right)}^2-0.010085\cdot \left(\frac{D}{t}\right)+1.3491 \mathrm{for} 40<D/t\le 150$$

(10)

while r is the reduction coefficient that depends on the class of concrete. The reduction coefficient for concrete type C25/30 is 1.00 [13].

This model was then utilized within the concrete damaged plasticity formulation implemented in ABAQUS, with the dilation angle set at 20° [45]. The adopted Poisson’s ratio $\nu$ is 0.2 [1,3,13,52,53]. The material properties used in ABAQUS are shown in

Table 2. Material properties used in ABAQUS.

Concrete						Steel
Unconfined		Confined
${{\mathit{f}}_{\mathit{c}}}^{\mathit{\prime }}$	${\mathit{E}}_{\mathit{c}}$	${{\mathit{f}}_{\mathit{c}\mathit{c}}}^{\mathit{\prime }}$	${\mathit{E}}_{\mathit{c}\mathit{c}}$	$\mathit{\nu }$	${\mathit{f}}_{\mathit{y}}$	$\mathit{E}$	$\mathit{\nu }$
[MPa]	[MPa]	[MPa]	[MPa]	[-]	[MPa]	[MPa]	[-]
30.5	32,965	48.5	36,986	0.2	355	210,000	0.3

.

3.3. Constitutive Model for Steel

The von Mises model with isotropic hardening was applied in the paper. Figure 5 shows the adopted constitutive uniaxial model for structural steel [54].

Here, f_y is the yield strength 355 MPa for S355 steel quality, ε_y is the corresponding strain, f_u is the ultimate strength 490 MPa, and ε_u is the corresponding ultimate strain. Young’s modulus of elasticity of steel is 210 GPa, while Poisson’s ratio is 0.3.

3.4. The Connection between the Concrete Core and the Steel Profile

The bond connection of the steel profile with the concrete core can be modeled using “surface-to-surface contact” elements [11]. The model uses contact elements that simulate the behavior of the connection in the longitudinal and tangential directions. The first is defined using the “Hard Contact” option available in ABAQUS. It allows separation of the contact surfaces in tension but prevents penetration of materials in compression. For the tangential direction, the “Columb friction model” was adopted, whereby the coefficient of friction was set at 0.47 [55]. According to numerous authors, this coefficient is usually in the range of 0.2–0.6 [3,13,19], although it has little impact on axial response [2].

3.5. Numerical Results

The failure of both samples C₁ and C₂ occurred due to the yielding of the steel profile, and the axial load capacities N_FEM are reported in Table 1. The ultimate axial strength obtained for the C₁ is 697.52 kN. The ultimate strength sustained by the steel part of the column can be obtained by integrating the stress along the steel part in the cross-section. As it equals 329.10 kN, it was evident that the contribution of the concrete filling to the load capacity of the column was 53%. The compressive strength of the confined concrete is f_cc′ = 50.69 MPa. In this case, the lateral confining pressure is f_l = 4.92 MPa. The stress results for the specimen C₁ are shown in Figure 6a.

The ultimate axial strength obtained for the C₂ specimen is 568.65 kN, while the strength sustained by the steel part of the column is 328.09 kN. The contribution of the concrete infill to the bearing capacity of the column is 42%, meaning that the strength of the confined concrete is f_cc′ = 33.10 MPa. In this case, the lateral tension pressure is f_l = 0.63 MPa. The stress results for the specimen C₂ calculations are shown in Figure 6b.

4. Validation of Results

4.1. Comparison of N-ε Relations and Ultimate Strength Capacity Obtained in Tests and FEM

To validate the model presented in chapter 3 calculated using FEM, the results were compared with the experimental results. Figure 7 shows the ultimate force N-ε strain response for CFT specimens C₁ and C₂. A good agreement between the results can be observed. For CFT column C₁, the ultimate force N_FEM obtained by ABAQUS is 0.6% lower than the limit force obtained by experimental research. In Figure 7a, the axial force increases approximately linearly to about 400 kN and 0.0025 strain. With a further load increase, the specimen demonstrates plastic behavior with hardening and high strain levels achieved. For CFT column C₂, the ultimate force N_FEM is 2.3% higher than N_test. However, the inelastic behavior of the column occurs much earlier, at a force of about 200 kN and a strain of approximately 0.001, as shown in Figure 7b. This occurs because of the column’s global instabilities.

Moreover, it can be concluded that the column’s length significantly influences the axial load capacity of the CFT column. With a double increase in the column length from 0.50 m to 1.00 m, the limit force of the CFT column decreases 1.26 times.

4.2. Comparison of Steel Profile Contribution and Confinement Effect

Based on the results of the experimental tests, the ultimate axial capacity of steel column S₁ and CFT column C₁ are 315.78 kN and 701.71 kN, respectively. Based on these results, it can be concluded that the contribution of the concrete core to the load capacity of the column is 55%. Thus, the compressive strength of the concrete, initially measured at 30.5 MPa, increased to 53.10 MPa due to confinement provided by the outer steel tube. For the accepted value of k₁ = 4.1, the lateral confining pressure f_l according to Equation (6) is 5.51 MPa. A good agreement of the results can be observed considering the following:

$$\frac{f_{cc,test}^{\prime }}{f_{cc,FEM}^{\prime }}=\frac{53.10}{50.69}=1.047$$

(11)

Similarly, based on the results of the experimental tests, the ultimate axial capacity of steel column S₂ is 297.84 kN, while the capacity of CFT column C₂ is 555.57 kN. The concrete infill contribution to the column’s total load capacity is 46.4%. The strength of the confined concrete increased to 35.46 MPa, so the lateral confining pressure is 1.21 MPa. A good agreement between the results can also be noted, given the following:

$$\frac{f_{cc,test}^{\prime }}{f_{cc,FEM}^{\prime }}=\frac{35.46}{33.10}=1.071$$

(12)

Finally, the lateral confining pressure f_l registered for specimens C₁ and C₂ as 0.5 m and 1.0 m long, respectively, is compared in Equation (13). As also previously reported in the literature, it is confirmed that concrete confinement has a greater influence in shorter rather than in slender CFT columns, and so should be taken into account.

$$\frac{f_{l,test, C_1}}{f_{l,test, C_2}}=\frac{5.51}{1.21}=4.55$$

(13)

4.3. Comparison of the Obtained Results with Current Design Codes

Table 3. Ultimate values of axial forces of CFT column specimen C₁.

NTEST [kN]	NTEST/ NFEM	NTEST/ NEC4	NTEST/ NEC4, conf.	NTEST/ NACI/AS	NTEST/ NAISC	NTEST/NAIJ
701.71	1.006	1.351	1.049	1.443	1.380	1.420

and

Table 4. Ultimate values of axial forces of CFT column specimen C₂.

NTEST [kN]	NTEST/ NFEM	NTEST/ NEC4	NTEST/ NEC4, conf.	NTEST/ NACI/AS	NTEST/ NAISC	NTEST/NAIJ
555.57	0.977	1.069	0.946	1.143	1.093	1.124

show the comparison of experimental results N_TEST, results obtained in ABAQUS N_FEM for CFT specimens C₁ and C₂ with the N values calculated by the following design codes: EC4, EC4 considering the confinement, ACI/AS, AICS, and AIJ. Unit partial safety factors for the material are adopted.

Following the EC4 [38], the plastic resistance to compression N_pl,Rd of a composite cross-section should be calculated by adding the plastic resistances of its components as follows:

$$N_{pl,Rd}=A_a\cdot f_{yd}+A_c\cdot f_{cd}+A_s\cdot f_{sd}$$

(14)

where A_a, A_c, and A_s are the cross-sectional area of the steel profile, concrete, and reinforcement, respectively, and f_yd = f_y/γ_a, f_sd = f_sk/γ_s, and f_cd = f_ck/γ_c are the corresponding design values of the yield strength for steel and reinforcement and the compressive strength of concrete; f_y, f_sk, and f_ck are their characteristic values; γ_a, γ_s, and γ_c are the recommended values of the partial safety coefficients for the corresponding materials provided in EC2 [44] and EC3 [56], but here for validation all are taken as unity.

According to EC4, in the case of circular hollow steel profiles filled with concrete, the increase in concrete strength under pressure caused by the confining of the concrete by the steel profile can be taken into account if the following conditions are met [38]: relative slenderness $\overline{\lambda }\le 0.5$, $e/D<0.1$, where e is the load eccentricity. In that case, the plastic resistance to compression N_pl,Rd of a composite cross-section should be calculated as follows:

$$N_{pl,Rd}={\eta }_a\cdot A_a\cdot f_{yd}+A_c\cdot f_{cd}\cdot [1+{\eta }_c\cdot \frac{t}{D}\cdot \frac{f_y}{f_{ck}}]+A_s\cdot f_{sd}$$

(15)

Coefficients η_c and η_a include the concrete confinement effects introduced and depend on the relative slenderness and e/D ratio [16].

Applying ACI [39] and AS [40,41] the resistance to compression of the CFT column cross-section is also calculated without appropriate safety factors for the materials (unfactored axial bearing capacity) and is given by the following expression:

$$N_{ACI,AS}=A_a\cdot f_y+0.85\cdot A_c\cdot f_{ck}$$

(16)

As per AISC [42], the resistance of the cross-section under axial pressure is determined based on the following expression:

$$N_{AISC}=A_a\cdot f_y+C\cdot A_c$$

(17)

where C is the strength factor for concrete, and the rectangular CFT column amounts to 0.85·f_ck, while for the circular CFT column, 0.95·f_ck.

AIJ suggests the following expression for determining the ultimate bearing capacity of the cross-section of a CFT column under axial pressure [43]:

$$N_{AIJ}=0.85\cdot f_{cyl,100}\cdot A_c+(1+\eta )\cdot f_y\cdot A_a$$

(18)

where f_cyl,100 is the compressive strength of concrete tested on a cylinder sample with dimensions of 100 mm·200 mm, and η is the coefficient that considers the confinement effect and is 0.27. The confining effect can be considered if the following condition is met: $L/D \le 4$.

It can be observed that for a CFT column C₁, the EC4, taking into account the confinement effect, gives the closest results to the results obtained by experimental testing. On the other hand, the ACI/AS regulations give the most conservative results.

For a CFT column C₂, the confinement effect is significantly lower due to the increase in column slenderness. In this case, the ultimate value of the axial force of the CFT column obtained by experimental testing is lower than the calculated value proposed by EC4, considering the confinement effect. However, the same value N_{EC4, conf} again gives the closest results to the results of the experimental tests, while the ACI/AS norms provide the most conservative results.

5. Conclusions

This paper presents the experimental investigation of the CFT column’s axial capacity under construction conditions. The influence of the column’s length, the concrete infill on the total bearing capacity of the CFT column, and the concrete confinement effect were analyzed experimentally and numerically.

Using the developed numerical models in the finite element-based software ABAQUS, it is possible to determine the bearing capacity of CFT columns with satisfactory accuracy, considering geometric and material nonlinearities. The differences between the ultimate limit force of the CFT column obtained in FEM models and tests are within 0.6–2.3%. Regarding an increase in the CFT column’s length from 0.50 m to 1.00 m, the total limit force decreases by 26%. The ultimate axial capacity of a CFT column 0.50 m long compared to an empty steel column improves by 55%. For 1.0 m long specimens with greater relative slenderness, concrete infill improves the strength by 46.4%.

The obtained results of the experimental tests were also compared with relevant design codes: EC4, EC4 taking into account the confinement effect, ACI, AS, AICS, and AIJ. The EC4 considering the confinement effect gives the closest results to the results of the experimental tests, while the ACI/AS norms provide the most conservative results. Based on the experimental and numerical results, it is demonstrated that the confinement effect has a greater influence on CFT columns with the L/D ratio close to 4. As the column’s length increases, the confinement effect decreases significantly. This was obtained for specimen C₂ with an L/D ratio of approximately 10, where the lateral confinement pressure was found to be insignificant. However, it is recommended to consider the confinement effect in this specimen as per EC4 guidelines, and this criterion should be further examined. Future research should focus on a larger sample size of specimens with L/D ratios within the range of 4 to 10. This expanded scope of study would provide more accurate and informed design decisions.