Parametric Study on the Behavior of Steel Tube Columns with Infilled Concrete—An Analytical Study

Abstract

Concrete-filled steel tube (CFST) columns are used in tall buildings and bridges, and they provide more rigidity and higher bearing capacity, but buckling affects their behavior. There is an exceptional need to study the behavior of these columns under various conditions. The numerical method is beneficial in supplementing the experimental works and is used to explore the effects of various parameters because of the limitations in cost, apparatus, and time of the experimental program. The various parameters, such as the different slenderness ratios, i.e., column-height-to-cross-section-dimension (H/D), different steel-tube-thickness-to-column-dimension (D/t), and different compressive strength of concrete to yield strength of steel tube ratio (fc/fy) under concentric axial loading are considered in this current study. Firstly, a finite element model used the “ANSYS” software program and was constructed to validate the results of the experimental works. The extensive numerical models were carried out to extensively widen the study in this field. The numerical work was conducted on sixty-four specimens. Moreover, the analytical calculations from the different international codes/standards were compared with the numerical results to test their reliability in predicting the ultimate carrying loads. The study provided results that show the improvement effect of CFST columns with the high compressive strength of infilled concrete, while no remarkable enhancement effect with the high yield strength of steel tube was observed. Increasing the columns’ diameter is more effective in enhancing the load capacity (about three times more) than increasing the tube thickness (about 1.3 times). Ring stiffeners for long CFST columns (H/D > 12) do not lead to any enhancement of the column behavior due to yielding occurring firstly at the location of the rings. ECP205-2007 is the most conservative design code in predicting the load capacity of CFST columns, while the AIJ design code is good at predicting the ultimate load failure compared to the other codes/standards. Eurocode 4 provides underestimation values of the load-carrying capacity of CFST columns.

1. Introduction

Compared to conventional reinforced concrete columns, in concrete-filled steel tubes (CFSTs), the steel tube lies at the outer perimeter, enhances the stiffness, and has a much greater modulus of elasticity than the concrete. Additionally, it confines the concrete core, which increases the compressive strength and the ductility of the column. While the infilled concrete forms an ideal core to withstand the compressive load, it also delays and often prevents local buckling of the steel. Concrete-filled steel tube columns (CFSTs) were used for many decades as a composite structural element due to their numerous structural advantages, such as high strength, high ductility, fire resistance, and considerable energy absorption capacities. Nowadays, composite structures are considered to be an advantageous system for carrying loads in different building structures, such as bridges, high-rise buildings, subway stations, workshop buildings, electricity pylons and poles, and other types of structures. The sustainability of this type of construction has been investigated by many researchers [1,2,3,4]. In addition, the columns are subjected to concentric or non-concentric compressive forces, which are areas of extensive research studies using various experimental, numerical, or artificial intelligence methods [5,6,7,8]. Moreover, numerical modeling has shown a lot of promise in the area of composite elements under various loadings [9,10,11].

Composite columns of steel tubes filled with concrete provide more rigidity and higher bearing capacities, so several design methods and many studies have been developed to study the behavior of CFST columns under different loads. Their behavior has been investigated previously in a lot of past research. Stephen [12] tested fourteen specimens with different parameters to investigate the effect of the thickness of steel tubes and their shape on the ultimate strength of CFST columns, such as (L/D) and D/t. Susantha [13] investigated the complete stress–strain curve of concrete columns confined by different steel shapes (circular, box, and octagonal cross-sections) subjected to axial load and lateral pressure by using FEM analysis. The study showed that the circular-shaped columns were significantly confined in comparison to the box columns. Huang [14] examined the behavior of concrete-filled steel tube columns subjected to axial load and analytically verified the test results by using the nonlinear finite element analysis method. They noticed that the stiffening scheme enhanced and improved the confinement of the steel tube on the concrete core, and The Eurocode 4 specifications supplied a preservative estimate of the ultimate strength of circular CFST columns and even for D/t ≥ 150. Hsuan [15] showed that in circular CFST columns, the tubes could provide good restriction to the concrete essentially when the ratio of the width-to-thickness was small, D/t < 40, and the steel local buckling of the tube was not likely to occur. Giokoumelis and Lam [16] carried out tests on fifteen circular concrete-filled steel tube columns under axial loading. The study examined the effects of the bonding strength between the concrete infill and the tubular steel and the thickness of steel tubes in confinement. The experimental results were compared with the different code equations, such as Eurocode 4, the Australian standard, and American codes. It was found that the ratio between the experimental axial loading and the axial loading value calculated by Eurocode 4 was around unity, and it was noticed that Eurocode 4 supplied a good prediction for CFST columns. Zeghiche and Chaoui [17] investigated an experimental study on twenty-seven specimens of concrete-filled steel tube columns, and different parameters were considered. In this study, it is concluded that the increase in CFST columns’ slenderness ratio decreased the load-carrying capacity, and the use of high-strength concrete enhanced the load-carrying capacity of the tested columns, but the use of normal-strength concrete decreased the load-carrying capacity by a high rate. All of the tested CFST columns failed due to global buckling without any sign of local buckling. Zhi-Wu [18] carried out an experimental investigation on the behavior of circular concrete-filled steel tubular columns under concentric loading. Seventeen specimens of circular CFST columns with self-compacting concrete (SCC) and normal concrete (NC) were tested, and the study concluded that: an increase in concrete strength (SCC, NC) caused the development of an increase in load capacity but almost preserved a constant value in load capacity after failure. The measured axial load with strain ratio curves of the CFST columns proposed that a good confinement effect was presented for specimens after the load extended to the ultimate load capacity of columns. Liang and Fragomeni [19] prepared an analytical study on Circular CFST short columns subjected to axial loading by using nonlinear analysis methods to study their behavior (strength, ductility, and confining) and making a comparison between the analytical results with the experimental data. The study showed that increasing the ratio of diameter-to-thickness reduces the ultimate strength and the ductility of the axial performance of the CFST columns. It was found that proportionally increasing the compressive strength of concrete increased the ultimate loads, reducing the section and axial performance ductility of the CFST columns, and it was found that the axial loads of the CFST columns increased proportionally with the increasing yield strength of the steel tube. Goode [20] presented a study on concrete-filled steel tube columns to investigate their behavior under different loadings. The study concluded that Eurocode 4 predicted a safe method of strength estimation for long slender columns subjected to axial load and moment. They showed that the limitation of the code on concrete strength could be extended safely to 75 for circular CFST columns and noticed that in CFST columns that had thin tube thickness, the local buckling limits could be used if a factor of 0.75 was applied to the predicted resistance of Eurocode 4. Lai and Ho [21] studied the behavior of uniaxially loaded concrete-filled steel tube columns confined by external rings on thirty-five specimens experimentally and verified theoretically by calculations. The CFST columns specimens were categorized into groups according to the specimens that have the same parameters, such as concrete strength, the thickness and the diameter of the steel tube, and the heights of the columns. It was concluded from the study that the external stiffeners could resist the lateral dilation of CFST and develop the bonding condition. The external steel rings were more effective in restricting the lateral deformation of the core concrete and steel tube columns. Gupta and H. Singh [22] prepared an analytical study on the behavior of concrete-filled steel tube short columns by using the finite element software program ABAQUS Vr.6.9 against the experimental data. The study concluded that the change in effective length was not affected by the response of the CFST stub columns under axial compression load. The study noticed that the maximum pressure confinement value obtained by the ABAQUS v6.9 models was higher than the value obtained previously by the experimental test. Abdulhadi and Abbas [23] presented an experimental and analytical investigation for studying the behavior of concrete-filled steel tube columns under axial concentric loading. The study showed that the compressive strength of concrete was an important factor affecting the load deflection for CFST columns. Tiwary and Gupto [24] carried out an analytical study against an experimental work on CFST columns by using the finite element program ABAQUS/CAE to study their behavior. The study showed that the capacity of the CFST columns was increased with increasing column diameter. The deformation of the CFST columns was increased linearly when the ratio between the column length and the cross-section dimension (l/D) ranged from 4 to 6. It was also noticed that the CFST columns stresses were decreased with the increase in the outer steel tube thickness. Deifalla [25] developed an experimental study for twenty-seven specimens of CFST columns to study their behavior under concentric loading. Two loading methods were used on the CFST columns with different parameters that affect CFST columns, such as the global and local slenderness ratios, adding stiffeners, and the different ratios between the outer diameter of the tubes and their thickness to obviate local buckling, and these ratios were compared with the different limits of the maximum D/t ratio submitted by different codes. As a result, in this study, two failure modes of CFST columns occurred, yielding for short columns and global buckling for long columns; the ratios of columns’ diameters to their thickness and the ratios of the columns length to the cross-section dimension were inversely proportional to the ultimate load values. Alatshan [26] proposed an analytical study on circular CFST short columns that are confined by an external or spiral stiffener subjected to axial loading. They noticed that under axial loading, the circular CFST columns with external steel confinement supplied a better performance than increasing the steel tube thickness. The study demonstrated that the increase in the concrete compressive strength and the yield strength of steel, external confinement strength, and the decrease in the cross-section-to-thickness ratio provided the performance of circular CFST columns under axial loading. Abdel-zaher [27] carried out an analytical study and numerical investigation to study the behavior of CFST columns with different parameters, such as cross-sections and the ratios between the dimensions of column width-to-thickness. The study showed that when the slenderness ratio of CFST columns increased, the ultimate load, hardness, and ductility decreased. Azad and Uy [28] investigated the effect of concrete infill on the local buckling capacity on a hollow circular tube, and the study indicated different ratios of cross-section dimension, such as diameter-to-thickness, to verify whether member yielding or local buckling occurred first. The study presented that the concrete infill tube has little change in the tube at failure due to the local buckling failure mode, but the local buckling occurred largely in the hollow circular tube. Süleyman Ipek [29] developed an experimental and analytical study on CFST columns with different cross-sections to investigate their behavior against axial load; the study focused on the elliptical sections, and the study showed that three types of failure occurred in the elliptical section, shear failure, local buckling failure, and phenomena of the elephant foot buckling, which occurred nearly of the top and bottom of the CFST columns; finally, the study showed that the design codes formula of AISC and EC4 for (rectangular and circular) section were modified to be capable of expecting the axial load value for the elliptical section of the CFST columns. Lei Zhang [30] carried out an experimental study on CFST narrow rectangular columns to study their behavior under axial compressions loading. Twenty-four experimental specimens were tested to involve the behavior of CFST columns with a narrow rectangular section, The study showed that the local buckling failure of CFST occurred near the buckling ring, and the study demonstrated that when the ratios of D/B decreased, D/t increased the ductility index and the strength index improved remarkably; finally the study showed that more different codes have a good predictor to the safe design loads. Grzeszykowski and Szmigiera [31] conducted an experimental study on 21 CFST columns with square sections to investigate the vertical ductility of CFST columns subjected to axial load, a novel and vertical ductility was measured for the study. The study showed that the ductility of square CFST columns depends on the failure mode of these columns and demonstrated that when the volume of material increased, the ability of CFST columns to dissipate the energy loaded increased, and the study showed that the specimens that have a local failure mode were higher in comparison for ductility than the columns that have global failure. Erdoğan [32] presented an analytical study on CFST columns by using finite element modeling to investigate the ultimate strength of CFST columns; some parameters were studied, such as the thickness of the tube, the ratio of the cross-section dimension to thickness, concrete core compressive strength, and steel yielding strength. The study showed that the FE model is more effective than the empirical models in predicting the ultimate axial strength and demonstrated that the FE models have a good performance for CFST columns and close error values of the ultimate strength compared by the different design codes such as AIJ and EC4.

2. Research Significant

All of the previous studies focused on CFST short columns subjected to axial loads, but these did not cover CFST long columns when their height-to-cross-section-dimension ratios increased from the limitations of their dimension ratios. Accordingly, the current study presents an analytical verification against experimental data on the behavior of concrete-filled steel tube columns, which were subjected to concentric loading using the finite element software program ANSYS v19.0 [33]. The study will investigate the influence of different parameters on CFST columns when their height-to-cross-section dimension ratios increase from the limitation of their dimension ratios in different codes and make a comparison between the codes because these ratios vary from code to code. Some parametric studies were considered, such as the compressive strength of concrete, steel yield strength, the ratio of cross-section dimension to thickness D/t, the ratio of column length to cross-section dimension H/D, and the stiffener distribution along the specimen length.

3. Verification Study

Experimental work is a good technique for investigating and studying the behavior of any structure, but it is more expensive than analytical and numerical work. In recent decades, researchers have worked with computers for this analysis due to the expensive cost of the experimental work. In this research, the ANSYS V19.0 program was used to simulate three-dimensional finite element models to extend the study to the behavior of concrete-filled steel tube columns under various parameters. The finite element models’ results were compared and verified with the experimental data stated in the literature. This verification represents the model capabilities of the behavior of concrete-filled steel tube columns in the parametric study.

3.1. Previous Experimental Work

Deifalla [25] experimentally tested twenty-seven circular concrete-filled steel tube (CFST) column specimens subjected to concentric load. The outer diameter of the pipes was 127 mm, with a thickness of 2 mm and 4 mm, having D/T ratios equal to 63.5 and 31.8, respectively. The specimens’ lengths were 400 mm, 1000 mm, and 2000 mm, which corresponded to the H/D ratios of 3.14 (short columns), 7.874 (medium columns), and 15.748 (long columns), respectively.

The unstiffened columns consisted of 15 specimens, and the stiffened columns consisted of 12 specimens, as shown in Figure 1a. All of the stiffeners used in the stiffened specimens were square cross-sections of 10.5 mm × 10.5 mm, and the stiffener distribution along the lengths of the specimens had a spacing of 0.25 H and 0.5 H for columns with D/T equaling 63.5 and 31.8 and at 0.125, 0.167, and 0.33 H for columns with a D/T equal to 63.5.

Six specimens of steel tube without any concrete filling with D/T equal 63.5 and 31.8 were used as a control. Fifteen specimens filled with concrete; six for unstiffened columns with a D/T equal to 63.5 and 31.8, six for stiffened columns with a D/T equal to 63.5, and three for stiffened columns with a D/T equal to 31.8; and loaded on both the concrete core and the steel tube. Lastly, six specimens with a D/T ratio equal to 63.5, three for unstiffened columns and three for stiffened columns, consisted of sections filled with concrete and loaded through the steel shell only.

The study included two loading methods on the CFST sections: on the steel only and on the composite (i.e., both steel and infilled concrete). The case of loading on steel only is carried out by filling the tubes with concrete, except for 10 mm at both ends. The loading frames consisted of a horizontal I-section beam fixed with two I-section columns resting on the floor, as shown in Figure 1b. The specimens were positioned vertically, and the upper and lower ends were hinged at a strong frame. The loading was applied using a load cell with a capacity of 2000 kN.

Test coupons, according to DIN 50125 (2016), were conducted to establish the constitutive properties of the steel pipes. The obtained steel tube properties equaled 352 MPa for yielding strength (f_y) and 418 MPa for ultimate strength (f_u). The modulus of elasticity, E_s, was 200,000 MPa.

The properties of the concrete were determined using standard concrete cubes and cylinders to achieve the mean compressive strength. Six cubes with dimensions of 150 mm × 150 mm × 150 mm and six standard cylinders with a 150 mm diameter and 300 mm height were tested after 7 and 28 days. The average cube and cylinder strengths after 28 days were 42 MPa and 32.1 MPa, respectively.

3.2. Analytical Model

3.2.1. Element Types

The concrete core was modeled using the Solid65 element, and this was defined by eight nodes, and each node has three degrees of freedom: translations of nodes in the x, y, and z directions. This element type is suitable and capable of plastic deformation and cracking in a three-dimensional direction. Solid45 was used for the steel tube, and this was defined by eight nodes, and each node has three degrees of freedom: translations of nodes in the x, y, and z directions. The steel-plate loading and supporting were modeled using the Solid185 element, and this was defined by eight nodes, and each node has three degrees of freedom: translations of nodes in the x, y, and z directions.

3.2.2. Material Properties

Solid65 is the element type of the concrete core and requires linear and multilinear isotropic material for definition, as listed in

Table 1. Material properties of infilled concrete.

Linear Isotropic
EX	28,555 MPa
PRXY	0.2
Multilinear Isotropic
Point	Strain	Stress (MPa)
1	0.000000	0.00
2	0.000353	10.08
3	0.000604	16.16
4	0.000854	21.53
5	0.001105	25.83
6	0.001355	29.04
7	0.001605	31.27
8	0.001856	32.66
9	0.002357	33.60
Concrete
Shear Transfer Coef. for Opened Cracks		0.2
Shear Transfer Coef. for Closed Cracks		0.9
Uniaxial tensile Stress		3.89 MPa
Uniaxial compressive Stress		42 MPa

. The concrete modulus of elasticity Ex was calculated as Ex = 4400$\sqrt{{\mathrm{f}}_{\mathrm{cu}}}$, and f_cu is the specified cube compressive strength of the concrete and Poisson’s ratio for linear properties. The stress–strain curve of the concrete was used to develop the multilinear isotropic functions. The compressive stress–strain relationship for the concrete consisted of two parts. The first part shows the linear zone up to a point with stress equal to 0.3 ${\mathrm{f}}_{\mathrm{c}}^{\prime }$. The second part shows the elastic–plastic zone at the maximum compressive stress of the concrete material, which was obtained from stress f = $\frac{{\mathrm{E}}_{\mathrm{c}} \mathsf{\epsilon }}{1+{\left(\frac{\mathsf{\epsilon }}{{\mathsf{\epsilon }}_{\mathrm{o}}}\right)}^2}$, where the strain is at the ultimate compressive strength ${\mathsf{\epsilon }}_{\mathrm{o}}=\frac{2{\mathrm{f}}_{\mathrm{c}}^{\prime }}{{\mathrm{E}}_{\mathrm{c}}}$. The end point of the curve is defined at ${\mathrm{f}}_{\mathrm{c}}^{\prime }$ and ${\mathsf{\epsilon }}_{\mathrm{o}}$. In addition, the uniaxial cracking stress was determined using f_ctr = 0.6$\sqrt{{\mathrm{f}}_{\mathrm{cu}}}$.

It is required to specify the appropriate values of shear transfer in cases of open and closed cracks. The values of the open and closed shear transfer coefficients are between 0 and 1.0 [33]. The value of the closed shear transfer coefficient must be greater than the value of the open shear transfer coefficient. Several preliminary analyses were attempted with various values for the shear transfer coefficient within a range equal to 0.1 to 0.2 for open cracks, and 0.7 to 1 for closed cracks up to no deviation of results is observed. Therefore, the shear transfer coefficients for the open and closed cracks used in this study were equal to 0.2 and 0.9, respectively.

In

Table 2. Material properties of steel tube and stiffeners by.

Material Type	Property	Value
Linear Isotropic	EX	200,000 MPa
	PRXY	0.3
Multilinear Isotropic	Point	Strain	Stress (MPa)
	1	0.00	0.00
	2	0.00176	352
	3	0.00506	418

, Solid45 is the element type of steel tube and requires linear and multilinear isotropic material for definition. The steel modulus of elasticity is EX and Poisson’s ratio for the linear properties. The stress–strain curve of steel was used to develop the multilinear isotropic functions, where the strain hardening modulus E_t (after yielding stage up to the ultimate stage) is assumed to be the 0.1 initial moduli of elasticity E_s.

Solid185 is the element type of the loading and supporting steel plates and requires linear and multilinear isotropic material for definition. The steel modulus of elasticity is EX, and it is equal to 2 × 10⁸ MPa, and the Poissons’ ratio is PRXY and was assumed to be 0.3. Figure 2 shows the stress–strain curve for the (a) infilled concrete and (b) steel tube.

3.2.3. Modeling

The columns and the loading plates were modeled as volumes. The models of the CFST columns were created with different heights equal to 400, 1000, and 2000 mm, and the tube diameter was equal to 127 mm, with a thickness equal to 2 and 4 mm. For the stiffened columns, the external stiffeners have a cross-section of 10.5 mm × 10.5 mm. The loading and supporting steel plates were modeled with a diameter, thickness, and depth equal to 227 mm, 50 mm, and 50 mm, respectively, as shown in Figure 3.

3.2.4. Meshing, Boundary Conditions and Loading

A good result was obtained for Solid65, Solid45, and Solid185 in the model of the CFST column, and the Hex Sweep meshing was used. The mesh of the concrete core of the CFST column model in ANSYS is shown in Figure 4. The convergence of results is achieved by increasing the mesh density until it has a negligible effect on the results. So, the used element mesh size did not exceed 20 mm, which is less time-consuming and provides accurate results compared with previous experimental works. A full bond is assumed between the steel tube and the infilled concrete core, which represents the confinement of the steel tube to the concrete core.

The load on the columns was applied vertically and concentric as pressure over the column surface area. The displacement boundary conditions are provided to constrain the column’s support; at the bottom of the column, the degree of freedom of all nodes Ux, Uy, Uz = 0, and at the top of the column, the degree of freedom of Ux, Uz = 0, and is Uy simulated to be free in this direction. The load and supporting conditions of the CFST column model in ANSYS are shown in Figure 4f.

3.2.5. Analysis Type

The nonlinear static analysis type is performed using the Full Newton–Raphson method with a sufficiently large number of sub-steps during the loading process to capture the cracking, yielding, and failure stages. A convergence tolerance of 0.05 is assumed based on the displacement degree of freedom for concrete problems. The automatic time stepping is set to OFF to constrain the constant load sub-step. The typical commands for the nonlinear static analysis are listed in

Table 3. Commands used to control nonlinear static analysis.

Analysis Options	Small Displacement Static
Calculate prestress effects	No
Time at end of load step	2000
Automatic time stepping	Off
Time step size	200
Min time step	100
Max time step	10000
Frequency	Write every sub step
Write items to result file	All solution items

.

3.2.6. Results of Verification Study

Von Mises stresses are developed to compare the failure mode between the finite element models using ANSYS and the experimental specimens by Deifalla [25], as shown in Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11. It is noted that the FE models can capture the failure mechanisms and the associated deformed shape for the tested specimens, either local buckling failure for short columns, “elephant foot buckling at top or bottom end [18]”, as shown in Figure 5, or global buckling failure for slender columns. The existence of stiffeners with variable distributions has the same failure mode for short or slender columns. The yielding failure is shown for specimen C40-2-St2 (Figure 8) and global failure for specimen C100-2-St5 (Figure 9) based on the specimen height. In C200-2-St7, both yielding and global buckling was observed (Figure 10). As can be seen from these figures, the failure location in the FE models indicated by the max values of Von Mises stresses coincided with what occurred in the experimental ones.

Figure 12 shows the load–vertical deformation relationship for the unstiffened and stiffened CFST columns with (a) H/D = 3.14, (b) H/D = 7.87, and (c) H/D = 15.75 in both analytical end experimental tests, respectively. The comparisons between the failure loads obtained from the experimental tests and the finite element models by ANSYS are listed in

Table 4. Comparisons of ultimate axial loads calculated by ANSYS results and measured in existing testing.

	Specimen Code	t mm	D/t	H mm	H/D	Concrete Infill	Loading	Stiffeners Location	Axial Load Failure (KN)			Failure Mode
									PExp	PANSYS	PANSYS/PExp
1	S40-2-only	2	63.5	400	3.14	No	Steel	No	255	260	1.02 (+2%)	Local
2	S100-2-only			1000	7.87				230	220	0.96 (−4%)	Local
3	S200-2-only			2000	15.75				220	250	1.14 (+14%)	Global
4	S40-4-only	4	31.8	400	3.14	No	Steel		608	550	0.90 (−10%)	Local
5	S100-4-only			1000	7.87				580	530	0.91 (−9%)	Global
6	S200-4-only			2000	15.75				520	530	1.02 (+2%)	Global
7	C40-2	2	63.5	400	3.14	Filled	Composite		860	750	0.87 (+13%)	Yield
8	C100-2			1000	7.87				743	740	1.00 (0%)	Global
9	C200-2			2000	15.75				724	680	0.94 (−6%)	Global
10	C40-4	4	31.8	400	3.14				1260	1260	1.00 (0%)	Yield
11	C100-4			1000	7.87				1098	1080	0.98 (−2%)	Global
12	C200-4			2000	15.75				1078	1090	1.01 (+1%)	Global
13	S40-2	2	63.5	400	3.14		Steel		830	950	1.14 (+14%)	Yield
14	S100-2			1000	7.87				716	720	1.01 (+1%)	Local
15	S200-2			2000	15.75				713	660	0.93 (−7%)	Local
16	C40-2-St1	2	63.5	400	3.14		Composite	0.5 H	958	970	1.01 (+1%)	Yield
17	C100-2-St3			1000	7.87			0.25 H	816	790	0.97 (−3%)	Global
18	C200-2-St5			2000	15.75			0.25 H	802	760	0.95 (−5%)	Global
19	C40-2-St2			400	3.14			0.33 H	1075	1070	1.00 (0%)	Yield
20	C100-2-St5			1000	7.87			0.167 H	830	860	1.04 (+4%)	Global
21	C200-2-St7			2000	15.75			0.125 H	802	760	0.95 (−5%)	Combined
22	C40-4-St1	4	31.8	400	3.14			0.5 H	1295	1210	0.93 (−7%)	Yield
23	C100-4-St3			1000	7.87			0.25 H	1179	1160	0.89 (−11%)	Global
24	C200-4-St5			2000	15.75			0.25 H	1052	1090	1.03 (+3%)	Global
25	S40-2-St2	2	63.5	400	3.14		Steel	0.33 H	999	800	0.80 (−20%)	Yield
26	S100-2-St5			1000	7.87			0.167 H	882	1000	1.13 (+13%)	Global
27	S200-2-St7			2000	15.75			0.125 H	780	930	1.19 (+19%)	Global

. It is obvious that there is acceptable convergence for the load–vertical deformation relationships between the experimental and analytical results, especially in the first stage, for all of the tested columns, which are linear up to cracking load, while analytically, after this stage up to failure load, there are larger deformations corresponding to the approximate failure loads obtained from the experimental results by average differences, approximately 21%, 34%, and 45% for H/D = 3.14, 7.87, and 15.75, respectively. Additionally, from Table 4, it can be noted that the failure-load difference between the analytical and experimental specimens ranged from +13% to −11% for the CFST columns that are composite-loaded and ranged from +14% to −10% for the steel tube columns. However, for the CFST columns that are loaded on the steel tube, the differences ranged from +19% to −20%. Hence, the experimental tests for the CFST columns that are composite-loaded (the main core for this more extensive study) validate those which resulted from the FE ANSYS models and can be used for further parametric studies.

4. Parametric Study

Based on the verification study using ANSYS software to simulate the behavior of the CFST columns, the FE analysis with the same procedures is used widely to discuss the different parameters that cannot be permitted to be considered in a laboratory due to limited possibilities and may affect the behavior of the CFST columns under concentric loading.

Sixty-four finite element models of CFST columns with different parameters were modeled and analyzed by using the finite element program ANSYS version 19.0. The different parameters that were studied in this research are:

• Column-height-to-cross-section-dimension ratio (H/D), which (H) varied by 3000, 4000, and 5000 mm and (D) varying between 200 and 400 mm;
• Compressive strength of concrete to yield strength of steel tube (f_c’/f_y); (f_c’) in a range of 40, 50, and 60 MPa, and (f_y) in a range of 360, 420, and 520 MPa;
• Cross-section dimension to steel tube thickness (D/t); where (t) varied by 4, 8, and 12 mm;
• Stiffener distribution. The stiffeners were distributed over the column length every 250, 500, and 1000 mm.

In ANSYS, the material models for studying the effect of different concrete and steel material properties are listed in

Table 5. Material properties of infilled concrete in parametric study.

Cases	Case 1 fcu = 40 MPa		Case 2 fcu = 50 MPa		Case 3 fcu = 60 MPa
	Linear Isotropic
EX	31,112.7 MPa		34,785 MPa		38,105 MPa
PRXY	0.2		0.2		0.2
Multilinear Isotropic
Point	Strain	Stress (MPa)	Strain	Stress (MPa)	Strain	Stress (MPa)
1	0.0	0.0	0.0	0.0	0.0	0.0
2	0.000386	12.00	0.000431	15.00	0.000472	18.00
3	0.000659	19.24	0.000737	24.05	0.000807	28.86
4	0.000932	25.63	0.001042	32.04	0.001142	38.45
5	0.001205	30.74	0.001348	38.43	0.001476	46.12
6	0.001478	34.57	0.001653	43.21	0.001811	51.86
7	0.001752	37.22	0.001958	46.53	0.002145	55.84
8	0.002025	38.89	0.002264	48.61	0.002480	58.33
9	0.002298	39.75	0.002569	49.69	0.002815	59.62
10	0.002571	40.00	0.002875	50.00	0.003149	60.00
	Concrete
Shear Transfer Coef. for Opened Cracks	0.2		0.2		0.2
Shear Transfer Coef. for Closed Cracks	0.9		0.9		0.9
Uniaxial tensile Stress MPa	4.24		4.74		5.2
Uniaxial compressive Stress MPa	40		50		60

and

Table 6. Material properties of steel tube in parametric study.

Cases	Case 1 fy = 360 MPa		Case 2 Fy = 420 MPa		Case 3 Fy = 520 MPa
Linear Isotropic
EX	2 × 105 MPa
PRXY	0.3
Multilinear Isotropic
Point	Strain	Stress (MPa)	Strain	Stress (MPa)	Strain	Stress (MPa)
1	0	0	0	0	0	0
2	0.0018	360	0.0021	420	0.0026	520
3	0.0068	460	0.0061	500	0.0066	600

. Because of missing test information for the steel material, the ultimate strength f_u was determined using Equation (1) or Equation (2) obtained from [34].

$${\mathrm{f}}_{\mathrm{u}}=\left[1.6-2\times {10}^{-3}\left({\mathrm{f}}_{\mathrm{y}}-200\right)\right]{ \mathrm{f}}_{\mathrm{y}} \mathrm{if} 200 \mathrm{MPa} \le { \mathrm{f}}_{\mathrm{y}}\le 400 \mathrm{MPa}$$

(1)

$${\mathrm{f}}_{\mathrm{u}}=\left[1.2-3.75\times {10}^{-4}\left({\mathrm{f}}_{\mathrm{y}}-400\right)\right]{ \mathrm{f}}_{\mathrm{y}} \mathrm{if} 400 \mathrm{MPa} \le { \mathrm{f}}_{\mathrm{y}}\le 800 \mathrm{MPa}$$

(2)

According to

Table 7. Limits of cross-section-dimension-to-steel-tube-thickness (D/t) ratio for composite sections under different codes provisions.

Code	Local Slenderness Ratio D/t	Max D/t
ECP 205-2007(LRFD) ECP 203-2007	$\sqrt{{\left(8 {\mathrm{E}}_{\mathrm{s}}/{\mathrm{f}}_{\mathrm{y}}\right)}^{}}$	67.42
EC4	$90\times \sqrt{{\left(235/{\mathrm{f}}_{\mathrm{y}}\right)}^{}}$	73.54
AIJ	$35,250/f_y$	100.14

and

Table 8. Maximum and minimum limits of column-height-to-cross-section-dimension (H/D) ratio for composite sections under different codes provisions.

Code	Min H/D	Max H/D
EC4	<4 (short column)	>4 (long column)
AIJ	≤4 (short column)	≥12 (long column)

, the dimensions of the studied columns were selected based on the ECP205, EC4, and AIJ specifications to be a D/t range between 25 and 100 and a H/D range between 7.5 and 25 to be classified as the medium and long columns.

Table 9. Limits of infilled concrete compressive strength under codes of practice.

Code	Concrete Compressive Strength MPa
EC4	20–50
AISC	21–70

shows the limitations of the concrete compressive strengths under different codes of practice.

Table 10. Description of specimens modeled by ANSYS and summary of the results.

	Specimen Name	H mm	D mm	t mm	D/t	H/D	fcu MPa	fy MPa	Stiffener’s Location	Failure Load (KN)	V.L Deformation (mm)	Yielding Load (KN)	Yielding Deformation (mm)	Stiffness (KN/mm)		Ductility µ∆	Failure Mode
														Pre-Yielding K1	Post-Yielding K2
1	C1000-8-D400	1000	400	8	50	2.5	40	360	No stiffeners	7300	1.750	7100	1.55	4580.64	1000	1.129	Local
2	C1000-8-D200	1000	200	8	25	5				2700	1.728	2400	1.51	1533.33	1754	1.144	Local
3	C3000-8-D400	3000	400	8	50	7.5				7200	5.138	6400	4.29	1480.58	1.198	1.198	Local
4	C4000-8-D400	4000	400	8	50	10				7100	6.909	5900	6.1	1163.26	696.86	1.120	Local
5	C5000-8-D400	5000	400	8	50	12.5				7100	8.289	5900	6.9	964.05	553.25	1.201	Local
6	C3000-8-D200	3000	200	8	25	15				2600	5.552	2500	5.12	490.19	231.48	1.084	Local
7	C4000-8-D200	4000	200	8	25	20				2600	7.464	2500	6.8	367.65	150.602	1.097	Local
8	C5000-8-D200	5000	200	8	25	25				2600	9.375	2500	8.3	301.20	93.02	1.129	Global
9	C3000-4-D400	3000	400	4	100	7.5	40	360		5700	5.327	4500	3.43	1285.71	656.81	1.552	Local
10	C4000-4-D400	4000	400	4		10				5700	7.165	4500	4.80	937.5	507.399	1.492	Local
11	C5000-4-D400	5000	400	4		12.5				5700	9.004	4500	5.40	814.81	360.71	1.667	Local
12	C3000-4-D400-Fc50	3000	400	4	100	7.5	50	360		6500	5.751	5400	4.2	1261.9	773.69	1.369	Local
13	C5000-4-D400-Fc50	5000	400	4		12.5				6500	9.724	5400	7.5	786.67	269.78	1.297	Local
14	C3000-4-D400-Fy420	3000	400	4	100	7.5	40	420		5700	5.164	5200	4.30	1209.3	578.7	1.201	Local
15	C5000-4-D400-Fy420	5000	400	4		12.5				5700	8.721	5100	7.10	718.31	370.14	1.228	Local
16	C3000-4-D400-Fc60	3000	400	4	100	7.5	60	360		7000	5.333	6100	4.20	1452.4	796.46	1.269	Local
17	C5000-4-D400-Fc60	5000	400	4		12.5				7000	8.947	6100	7.50	813.33	621.98	1.193	Local
18	C3000-4-D400-Fy520	3000	400	4	100	7.5	40	520		5800	5.330	5200	4.30	1209.3	485.44	1.240	Local
19	C5000-4-D400-Fy520	5000	400	4		12.5				5800	9.002	5100	7.10	718.13	315.46	1.268	Local
20	C3000-12-D400	3000	400	12	33.3	7.5	40	360		9200	6.612	8700	4.90	1775.5	292.06	1.349	Local
21	C5000-12-D400	5000	400	12		12.5				9200	11.228	8700	8.60	1011.6	190.26	1.306	Local
22	C3000-8-D400-Fc50	3000	400	8	50	7.5	50	360		8000	5.483	7600	4.80	1583.3	585.65	1.142	Local
23	C5000-8-D400-Fc50	5000	400	8		12.5				7900	8.875	7500	7.30	1027.4	253.97	1.216	Local
24	C3000-8-D400-Fy420	3000	400	8	50	7.5	40	420		7400	5.437	6500	4.40	1477.3	867.89	1.236	Local
25	C5000-8-D400-Fy420	5000	400	8		12.5				7400	9.175	6900	7.80	884.62	363.64	1.176	Local
26	C3000-8-D400-Fc60	3000	400	8	50	7.5	60	360		8700	5.571	8200	4.90	1673.5	745.16	1.137	Local
27	C5000-8-D400-Fc60	5000	400	8		12.5				8600	9.118	8100	7.50	1080	309.02	1.216	Local
28	C3000-8-D400-Fy520	3000	400	8	50	7.5	40	520		7500	5.459	7000	4.41	1473.9	953.29	1.238	Local
29	C5000-8-D400-Fy520	5000	400	8		12.5				7500	9.332	7000	7.80	897.44	326.37	1.196	Local
30	C3000-4-D200	3000	200	4	50	15	40	360		1900	5.249	1800	4.20	387.1	166.94	1.129	Local
31	C4000-4-D200	4000	200	4		20				1900	7.073	1800	6.42	280.37	153.14	1.102	Local
32	C5000-4-D200	5000	200	4		25				1900	8.878	1800	7.90	227.85	102.25	1.124	Global
33	C3000-4-D200-Fc50	3000	200	4	50	15	50	360		2200	6.185	2100	5.2	403.85	101.52	1.189	Local
34	C5000-4-D200-Fc50	5000	200	4		25				2200	10.466	2100	8.90	235.96	63.857	1.176	Global
35	C3000-4-D200-Fy420	3000	200	4	50	15	40	420		1900	5.157	1800	4.80	375	280.11	1.074	Local
36	C5000-4-D200-Fy420	5000	200	4		25				1900	8.739	1800	8.10	222.22	156.49	1.079	Global
37	C3000-4-D200-Fc60	3000	200	4	50	15	60	360		2300	5.453	2100	4.90	428.57	180.83	1.113	Local
38	C5000-4-D200-Fc60	5000	200	4		25				2300	9.203	2100	8.30	253.01	221.48	1.109	Global
39	C3000-4-D200-Fy520	3000	200	4	50	15	40	520		1900	5.156	1800	4.80	375	280.11	1.074	Local
40	C5000-4-D200-Fy520	5000	200	4		25				1900	8.702	1800	8.19	222.22	196.46	1.062	Global
41	C3000-8-D200-Fc50	3000	200	8	25	15	50	360		2900	6.528	2700	5.12	527.34	142.05	1.275	Local
42	C5000-8-D200-Fc50	5000	200	8		25				2900	11.035	2800	8.55	327.49	40.24	1.291	Global
43	C3000-8-D200-Fy420	3000	200	8	25	15	40	420		2800	5.794	2600	5.10	509.8	288.18	1.136	Local
44	C5000-8-D200-Fy420	5000	200	8		25				2700	9.320	2600	8.60	302.33	138.89	1.084	Global
45	C3000-8-D200-Fc60	3000	200	8	25	15	60	360		3000	6.001	2800	4.95	575.76	142.72	1.212	Local
46	C5000-8-D200-Fc60	5000	200	8		25				3000	10.186	2800	8.60	331.4	94.57	1.184	Global
47	C3000-8-D200-Fy520	3000	200	8	25	15	40	360		2800	5.788	2600	5.10	509.8	290.7	1.135	Local
48	C5000-8-D200-Fy520	5000	200	8		25				2800	9.768	2600	8.60	302.33	85.616	1.136	Global
49	C1000-8-D400-@250	1000	400	8	50	2.5	40	360	Every 250 mm	7100	1.502	7000	1.30	5384.61	495.05	1.155	local
50	C1000-8-D400-@500	1000	400	8					Every 500 mm	7400	1.768	7100	1.30	5461.54	641.03	1.360	local
51	C3000-8-D400-@250	3000	400	8	50	7.5	40	360	Every 250 mm	6600	4.295	6100	3.75	1626.67	917.43	1.145	local
52	C3000-8-D400-@500	3000	400	8					Every 500 mm	7200	5.122	6200	4.30	1441.86	1216.54	1.191	local
53	C3000-8-D400-@1000	3000	400	8					Every 1000 mm	7200	5.135	6200	4.20	1476.2	1069.5	1.223	local
54	C5000-8-D400-@250	3000	400	8	50	12.5	40	360	Every 250 mm	6500	7.086	6000	6.10	984.13	381.68	1.125	local
55	C5000-8-D400-@500	3000	400	8					Every 500 mm	7100	8.352	6100	6.20	983.87	464.68	1.347	local
56	C5000-8-D400-@1000	3000	400	8					Every 1000 mm	7100	8.508	6100	6.20	983.87	433.28	1.372	local
57	C1000-8-D200-@250	1000	200	8	25	5	40	360	Every 250 mm	2800	1.794	2500	1.40	1785.71	761.42	1.281	local
58	C1000-8-D200-@500	1000	200	8					Every 500 mm	2700	1.652	2500	1.50	1666.67	1094.89	1.101	local
59	C3000-8-D200-@250	3000	200	8	25	15	40	360	Every 250 mm	2600	5.034	2400	4.55	527.47	413.22	1.106	local
60	C3000-8-D200-@500	3000	200	8					Every 500 mm	2600	5.323	2400	4.82	494.93	397.61	1.104	local
61	C3000-8-D200-@1000	3000	200	8					Every 1000 mm	2600	5.454	2400	4.91	488.8	367.65	1.111	local
62	C5000-8-D200-@250	3000	200	8	25	25	40	360	Every 250 mm	2600	8.482	2400	7.81	307.3	397.62	1.086	local
63	C5000-8-D200-@500	3000	200	8					Every 500 mm	2600	8.964	2400	8.41	292.68	261.78	1.093	local
64	C5000-8-D200-@1000	3000	200	8					Every 1000 mm	2600	9.192	2400	8.23	291.62	207.9	1.117	local

summarizes the FE analysis results for the CFST columns with different parameters. The results are measured by failure mode, failure load, and vertical deformation at the failure stage. There are measurements calculated to judge the results, such as pre-yielding stiffness, post-yielding stiffness, and ductility. The stiffness can be defined as the slope of the load–deflection curve. The pre-yield stiffness (K₁) and the post-yield stiffness (K₂) are given by Equations (3) and (4). Ductility is the ability of an element to change its shape without losing its strength or breaking. The ductility can be defined as the ratio between the deflection of the yield load to the deflection of the ultimate load. The ductility index (${\mathsf{\mu }}_{\Delta })$ can be calculated as shown in Equation (5).

$${\mathrm{K}}_1=\frac{{\mathrm{P}}_{\mathrm{y}}}{{\Delta }_{\mathrm{y}}}$$

(3)

$${\mathrm{K}}_2=\frac{{\mathrm{P}}_{\mathrm{u}}-{ \mathrm{P}}_{\mathrm{y}}}{{\Delta }_{\mathrm{u}}-{\Delta }_{\mathrm{y}}}$$

(4)

$${\mathsf{\mu }}_{\Delta }=\frac{{\Delta }_{\mathrm{u}}}{{\Delta }_{\mathrm{y}}}$$

(5)

where: K₁ = Pre–yield “Initial” Stiffness (kN/mm), P_y = Yielding Load (kN), ${\Delta }_{\mathrm{y}}$ = Yielding Deflection (mm), K₂ = Post–yield Stiffness “Effective” Stiffness (kN/mm), P_u = Ultimate Load (kN), and ${\Delta }_{\mathrm{u}}$ = Ultimate Deflection (mm).

4.1. The Effect of Infilled Concrete Compressive Strength

Different values of concrete compressive strength were used to study the behavior of the CFST columns with a normal compressive strength of 40 Mpa and high compressive strength of 50 and 60 Mpa. The effect of the compressive strength of the infilled concrete on failure load and vertical deformation for columns that have a D/t equal to 25, 50, and 100 and a H/D equal to 7.5, 12.5, 15, and 25 are shown in Figure 13. Figure 14 presents the column stiffness and ductility index for the CFST columns with different values of infilled concrete compressive strength.

It is shown that the effect of the concrete compressive strength on the CFST columns increased the load capacity of the CFST columns ([6,7,8,12,15]) by an average of 1.13 and 1.20 times for concrete compressive strength (f_cu) = 50 N/mm² and 60 N/mm² when compared with the case of f_cu = 40 N/mm². On the other hand, the vertical deformation is slightly increased by an average of 1.13 times for f_cu = 50 N/mm² and 1.05 times for f_cu = 60 N/mm² when compared with f_cu = 40 N/mm². In general, by increasing the compressive strength of the infilled concrete, the load capacity of the columns increased but reduced the vertical deformation due to the increase in column stiffness.

The pre-yielding stiffness increased by an average of 1.04 and 1.11 times, and the post-yielding stiffness is significantly increased by an average of 0.65 and 1.13 times for concrete compressive strength (f_cu) = 50 N/mm² and 60 N/mm² when compared with the case of f_cu = 40 N/mm². The column ductility is reduced by 1.01 and 0.95 times for concrete compressive strength (f_cu) = 50 N/mm² and 60 N/mm² when compared with the case of f_cu = 40 N/mm².

4.2. The Effect of Steel Tube Yield Strength

Different values of steel yield strength were used to study the behavior of the CFST columns, normal steel yield strength of 360 MPa, and high steel-yield strength of 420 and 520 MPa. The effect of the yield strength of the steel tube on failure load and vertical deformation for columns that have D/t equal to 25, 50, and 100 and a H/D equal to 7.5, 12.5, 15, and 25 are shown in Figure 15. Figure 16 presents the column stiffness and ductility index for the CFST columns with different values of steel tube yield strength. It is obvious that the effect of the steel tube yield strength on the CFST columns is not remarkable (opposite to finding in [8,15]); the increase in the yield strength of the steel tube led to a slight increase in the failure load for about 1.02 for f_y = 420 N/mm² and 1.04 for f_y = 520 N/mm² when compared with f_y = 360 N/mm². In addition, the same observation in the vertical deformation can be noted, i.e., the changes are about 1.01 for f_y = 420 N/mm² and 1.03 for f_y = 520 N/mm² when compared with f_y = 360 N/mm².

The pre-yielding stiffness is not affected by the material properties of the steel tube while the post-yielding stiffness is slightly decreased from 1.16 to 1.11 times for the steel-yielding strength (f_y) = 420 N/mm² and 520 N/mm² when compared with the case of f_y = 360 N/mm². The column ductility is slightly increased from 0.93 to 0.94 times for the steel-yielding strength (f_y) = 420 N/mm² and 520 N/mm² when compared with the case of f_y = 360 N/mm².

4.3. The Effect of D/t Ratio

Firstly, the effect of changing the tube thickness and maintaining the tube diameter constant is focused. Different values of tube thickness were used (4, 8, and 12 mm) with an outer diameter equal to 400 mm and D/t ratios equal to 33.3, 50, and 100, respectively. In addition, the CFST columns with tube thicknesses equal to 4 and 8 mm are used for columns with an outer diameter equal to 200 mm, which have D/t ratios equal to 25 and 50. The effect of tube thickness on the failure load and vertical deformation for columns that have a H/D equal to 7.5, 12.5, 15, and 25 are shown in Figure 17. Figure 18 represents the column stiffness and ductility index for the CFST columns with different values of tube thickness.

It is shown that the increase in the tube thickness with constant column diameter increases, i.e., the D/t value is reduced, the failure load and the vertical deformation of the CFST columns are largely [13,14,15] for H/D = 7.5, 12.5, 15, and H/D = 25 due to the increase in steel tube stiffness. The failure load is increased by 1.30, 1.25, and 1.60 for D/t = 25, 33.3 and 50, respectively when compared with D/t = 100. The vertical deformation is the same for D/t = 50 and there is amplification by 1.25 when D/t = 33.3 when compared with D/t = 100.

In addition, the effect of changing the tube diameter while maintaining the tube thickness constant is focused. Different values of the outer diameter were used (200 and 400 mm) with a constant tube thickness equal to 4 and 8 mm, i.e., the D/t ratio increased from 25 to 50 and 100. The effect of the outer diameter on the failure load and vertical deformation for columns that have a H/D equal to 7.5 and 15 for columns with a 3000 mm height, a H/D equal to 10 and 20 for columns with a 4000 mm height, and a H/D equal to 12.5 and 25 for columns with a 5000 mm height are shown in Figure 19. Figure 20 shows the column stiffness and ductility index for CFST columns with different values in tube diameter.

It is noted that increasing the outer diameter of the CFST columns while maintaining the tube thickness is constant, i.e., D/t is increased, leading to the increase in the failure load [15] by 2.77 when doubling the tube diameter, but the vertical deformation decreased by 8% for a column with a 3000 mm height, and by 12% for a column with 4000 and 5000 mm heights when doubling the tube diameter due to the increase in column stiffness (k = EA/L) by increasing the column cross-section (A).

4.4. The Effect of H/D Ratio

Different values of height were used to study the behavior of the CFST columns (3000, 4000, and 5000 mm) with tube thicknesses equal to 4 and 8 mm that have a D/t ratio equal to 25, 50, and 100, respectively. The compressive strength equals 40 MPa, and the steel-yield strength equals 360 Mpa. The effect of heights on the failure load and vertical deformation is shown in Figure 21. The column stiffness and ductility index for the CFST columns with different values of tube heights are shown in Figure 22.

It is shown that with increasing the column height while maintaining the column diameter and tube thickness constant, i.e., H/D increased from 7.5 to 25; the failure load is not different remarkably, while the deformation increased from 1.05 to 1.69 for different ratios of H/D when compared with the case with HD = 7.5. This is because decreasing the column stiffness (k = EA/L) by increasing the column height (L) is inversely proportional to deformation [16].

4.5. The Effect of Stiffeners Distribution

To study the effect of stiffener distribution on the CFST column behavior, the stiffener is a ring with a thickness of 40 mm transverse to the column length with a width of 40 mm parallel to the column length. The stiffeners are distributed along the column length at 250 mm, 500 mm, and 1000 mm. The columns have maintained constant values of the concrete compressive strength equal to 40 MPa, and the steel-yield strength equals 360 MPa. The studied specimens have different ratios of D/t equal to 25 and 50 and different ratios of H/D equal to 2.5, 5, 7.5, 12.5, 15, and 25 to study the efficiency of stiffeners in enhancing the load capacity of the CFST columns. Figure 23 shows the failure load–vertical deformation relationships for the CFST columns, unstiffened and stiffened, each 0.25, 0.5, and 1.0 m, with different values of H/D. Figure 24 shows the Von Mises stresses for the columns with different ratios of H/D that have no stiffeners, the stiffeners each 1.0 m, 0.5 m, and 0.25 m.

It is observed that the stiffened specimens are not affected by the development of the failure load and increased compared to the specimens that are unstiffened; for the short columns with H/D = 2.5, the failure load increased by 1% but decreased by 3% for the columns that have a stiffener every 500 mm and 250 mm, respectively. For H/D = 5, the failure load does not change for the columns that have a stiffener every 500 m but increases by 3% for columns that have a stiffener every 250 mm. At H/D = 7.5 and 12.5, with stiffener distribution along the column length, the failure load did not change and remained constant at distribution every 500 mm and 1000 mm, respectively, but the failure load decreased by 9% at a distribution of 250 mm compared to the unstiffened columns. At H/D = 15 and 25, the failure load does not change for every 250 mm, 500 mm, and 1000 mm.

In addition, the vertical deformation decreased [10], but not remarkably, for H/D = 2.5, 5, 7.5, 12.5, 15, and H/D 25 compared to the specimens that are unstiffened.

It can be considered from the behavior that the failure happened earlier than the unstiffened samples, and earlier too, for the stiffened specimens that have a stiffener every 250 mm compared to the unstiffened specimens, the earlier failure happened due to the failure in the stiffener [19] near the loading plate.

For the long columns, where H/D is more than 15, the stiffening with rings with different spacing between them along the column height does not enhance the behavior of the CFST column. It is suggested for future studies to stiffen CFST long columns with longitudinal steel strips.

5. Different Codes Provisions in Designing CFST Columns

Four different international code provisions addressing the design of the CFST columns were used. The following international standards are considered; American Standard-AISC-LRFD “AISC (2010) [35]”, The Egyptian Code of Practice for Steel Construction—Load and Resistance Factor Design “ECP 205-2007 (LRFD) [36]”, Eurocode 4 (EC4) [36] and Architectural Institute of Japan standards “AIJ (1997) [37]” and presented a full comparison between the failure load obtained by using the finite element program ANSYS version 19.0 and the different design codes.

5.1. International Codes Provisions

The AISC (2010) [35] code developed a formula that can be used to design and calculate the ultimate loads of the CFST columns (P_n). The ultimate load (P_n) can be calculated as follows:

$${\mathrm{P}}_{\mathrm{e} }\ge 0.44{ \mathrm{P}}_{\mathrm{o} }:{ \mathrm{P}}_{\mathrm{n}}={\mathrm{P}}_{\mathrm{o}}\left[ {0.658}^{\left({\mathrm{P}}_{\mathrm{o} }/{\mathrm{P}}_{\mathrm{e}}\right)}\right]$$

(6)

$${\mathrm{P}}_{\mathrm{e} }\le 0.44 {\mathrm{P}}_{\mathrm{o}}:{ \mathrm{P}}_{\mathrm{n}}=0.877{ \mathrm{P}}_{\mathrm{e} }$$

(7)

where:

$${\mathrm{P}}_{\mathrm{e} }={ \mathsf{\pi }}^2{ \mathrm{EI}}_{\mathrm{eff}}/{\left(\mathrm{KL}\right)}^2$$

(8)

$${\mathrm{EI}}_{\mathrm{eff}}={ \mathrm{E}}_{\mathrm{s} }{\mathrm{I}}_{\mathrm{s} }+0.5{\mathrm{E}}_{\mathrm{s} }{\mathrm{I}}_{\mathrm{sr} }+{\mathrm{C}}_{1 }{\mathrm{E}}_{\mathrm{c} }{ \mathrm{I}}_{\mathrm{c} }$$

(9)

$${\mathrm{C}}_{1 }=0.6+2\left[{\mathrm{A}}_{\mathrm{s} }/\left({\mathrm{A}}_{\mathrm{c} }+{\mathrm{A}}_{\mathrm{s} }\right)\right] \le 0.9$$

(10)

$${\mathrm{P}}_{\mathrm{o}}={ \mathrm{A}}_{\mathrm{s} }{\mathrm{F}}_{\mathrm{y}}+{ \mathrm{A}}_{\mathrm{sr} }{\mathrm{F}}_{\mathrm{yr}}+{ \mathrm{C}}_{1 }{\mathrm{A}}_{\mathrm{c} }{\mathrm{f}}_{\mathrm{c}}^{\prime }$$

(11)

where: ${\mathrm{E}\mathrm{I}}_{\mathrm{eff}}$: effective stiffness of the CFST member in N. mm²; ${\mathrm{I}}_{\mathrm{s} }$: the moment of inertia of the steel shape; ${\mathrm{I}}_{\mathrm{sr} }$: the moment of inertia of the reinforcing bars; ${ \mathrm{I}}_{\mathrm{c} }$: the moment of inertia of the concrete section; ${\mathrm{E}}_{\mathrm{c} }$: the modulus of elasticity of the concrete; ${\mathrm{E}}_{\mathrm{s} }$: the modulus of the elasticity of the steel; ${\mathrm{A}}_{\mathrm{s} }$: the area of the steel section; ${\mathrm{A}}_{\mathrm{c} }$: the area of the concrete; ${\mathrm{P}}_{\mathrm{n}}$: the nominal axial compressive strength; ${\mathrm{P}}_{\mathrm{e} }$: the elastic critical Euler buckling load; ${\mathrm{P}}_{\mathrm{o}}$: the nominal axial strength without consideration of the length effects; K: the buckling length factor according to the end conditions; L: the length of the column, and ${\mathrm{C}}_{1 }$: 0.95 for circular section.

ECP 205-2007(LRFD) [38] computes the design strength, Φ_cP_n, for symmetric axially loaded composite columns as:

$${\mathrm{P}}_{\mathrm{u} }={ \mathsf{\Phi }}_{\mathrm{c}}{ \mathrm{P}}_{\mathrm{n}}={ \mathsf{\Phi }}_{\mathrm{c}}{\mathrm{A}}_{\mathrm{s} }{\mathrm{F}}_{\mathrm{cr}}$$

(12)

$${\mathsf{\lambda }}_{\mathrm{m} }<1.1:{ \mathrm{F}}_{\mathrm{cr}}=\left(1-0.348{ \mathsf{\lambda }}_{\mathrm{m} }{}^2\right){ \mathrm{F}}_{\mathrm{ym}}$$

(13)

$${\mathsf{\lambda }}_{\mathrm{m} }\ge 1.1:{ \mathrm{F}}_{\mathrm{cr}}=0.648{ \mathrm{F}}_{\mathrm{ym}}/{\mathsf{\lambda }}_{\mathrm{m} }{}^2$$

(14)

$${\mathrm{F}}_{\mathrm{ym}}={ \mathrm{F}}_{\mathrm{y}}+{ \mathrm{C}}_{1 }{\mathrm{F}}_{\mathrm{yr}}\left({\mathrm{A}}_{\mathrm{r} }/{\mathrm{A}}_{\mathrm{s} }\right)+{ \mathrm{C}}_2{\mathrm{F}}_{\mathrm{cu}}\left({\mathrm{A}}_{\mathrm{c} }/{\mathrm{A}}_{\mathrm{s} }\right)$$

(15)

$${\mathsf{\lambda }}_{\mathrm{m} }={ \mathrm{L}}_{\mathrm{b}} {\left({\mathrm{F}}_{\mathrm{ym}}/{\mathrm{E}}_{\mathrm{m} }\right)}^{0.5} /\mathsf{\pi }.{ \mathrm{r}}_{\mathrm{m} }$$

(16)

where: ${\mathrm{r}}_{\mathrm{m} }$: the radius of gyration; ${\mathrm{F}}_{\mathrm{ym}}$: yield stress; ${\mathrm{E}}_{\mathrm{m} }$: Young’s modulus; ${\mathrm{C}}_{2 }$: numerical coefficient for tube and equal to 0.68; and ${\mathsf{\Phi }}_{\mathrm{c}}$: strength reduction factor for compression members and equal to 0.8.

Eurocode 4 [36] for the column’s slenderness ratio (${\mathsf{\lambda }}_{ }$) $\le$ 0.5 and the confinement effects are considered in the following equations:

$${\mathrm{Confinement} \mathrm{neglected} \mathrm{N}}_{\mathrm{PLRD} }={\mathrm{A}}_{\mathrm{a} }.{ \mathrm{f}}_{\mathrm{y}}/{\mathrm{g}\mathsf{\gamma }}_{\mathrm{a} }+{\mathrm{A}}_{\mathrm{c} }.{ \mathrm{f}}_{\mathrm{ck}}/{\mathsf{\gamma }}_{\mathrm{c} }+{\mathrm{A}}_{\mathrm{s} }{\mathrm{f}}_{\mathrm{sk}}$$

(17)

$${\mathrm{Confinement} \mathrm{considered} \mathrm{N}}_{\mathrm{PLRD} }={\mathsf{\eta }}_{2 }{\mathrm{A}}_{\mathrm{a} }.{ \mathrm{f}}_{\mathrm{y}}/{\mathsf{\gamma }}_{\mathrm{Ma} }+\left[1+{\mathsf{\eta }}_{1 }.\left(\mathrm{t}/\mathrm{D}\right). \left({\mathrm{f}}_{\mathrm{y}}/{\mathrm{f}}_{\mathrm{ck}}\right)\right]{ \mathrm{A}}_{\mathrm{c} }.{ \mathrm{f}}_{\mathrm{ck}}/{\mathsf{\gamma }}_{\mathrm{c} }$$

(18)

$${\mathsf{\eta }}_{1 }={ \mathsf{\eta }}_{10 }=4.9-18.5 \mathsf{\lambda } +17{ \mathsf{\lambda } }^2 \ge 0$$

(19)

$${\mathsf{\eta }}_{2 }={ \mathsf{\eta }}_{20 }=0.25(3+{ \mathsf{\lambda } }^2) \le 1$$

(20)

$$\mathsf{\lambda }=({\left({\mathrm{N}}_{\mathrm{PLRD} }/{\mathrm{N}}_{\mathrm{cr} }\right)}^{0.5}$$

(21)

$${\mathrm{N}}_{\mathrm{cr} }={ \mathsf{\pi }}^2{\left(\mathrm{EI}\right)}_{\mathrm{e}}/{\mathrm{L}}_{\mathrm{K} }{}^2$$

(22)

$${\left(\mathrm{EI}\right)}_{\mathrm{e}}={ \mathrm{E}}_{\mathrm{s} }{\mathrm{I}}_{\mathrm{s} }+0.8{ \mathrm{E}}_{\mathrm{cm} }{ \mathrm{I}}_{\mathrm{c} }$$

(23)

$${\mathrm{E}}_{\mathrm{cm} }=22 \left({\mathrm{f}}_{\mathrm{ck}}+8\right){ }^{1/3}$$

(24)

where: ${\mathrm{A}}_{\mathrm{a}}$: cross-sectional area of the steel; ${\mathrm{A}}_{\mathrm{c}}$: concrete sections; ${\mathrm{A}}_{\mathrm{s}}$: the area of the reinforced bars; ${\mathrm{f}}_{\mathrm{y}}$: the yield strength of the steel; ${\mathrm{f}}_{\mathrm{ck}}$: the compressive strength of the concrete cylinder; ${\mathrm{f}}_{\mathrm{sk}}$: the yield strength of the reinforcing bars; ${\mathsf{\gamma }}_{\mathrm{Ma}}$: the safety factor on the steel section and is taken to be 1.00; ${\mathsf{\gamma }}_{\mathrm{c}}$: the safety factor of the concrete section and is assumed to be 1.00, ${\mathrm{N}}_{\mathrm{PLRD}}:$ the plastic compressive resistance with unity safety factors; ${\mathrm{N}}_{\mathrm{cr}}:$ the elastic critical load. ${\left(\mathrm{EI}\right)}_{\mathrm{e}}$: the effective elastic flexural stiffness of the cross-section; ${\mathrm{E}}_{\mathrm{s}}$: modulus of elasticity of the steel tube; ${\mathrm{E}}_{\mathrm{cm}}$: modulus of elasticity of the concrete core; ${\mathrm{I}}_{\mathrm{s}}$: moment of inertia of the steel tube; and ${\mathrm{I}}_{\mathrm{c}}$: moment of inertia of the concrete core.

In AIJ (1997) [37]; the compressive strength of the CFST columns is calculated as shown:

$$\begin{array}{cc}\mathrm{Short} \mathrm{column} {\mathrm{l}}_{\mathrm{K}}/\mathrm{D}\le 4\hfill & \\ & {\mathrm{N}}_{\mathrm{C}1}={\mathrm{cN}}_{\mathrm{C}}+\left(1+\eta \right){\mathrm{sN}}_{\mathrm{C}}\hfill \end{array}$$

(25)

$$\begin{array}{cc}\mathrm{Medium} \mathrm{column} 4<{\mathrm{l}}_{\mathrm{K}}/\mathrm{D}\le 12\hfill & \\ & {\mathrm{N}}_{\mathrm{c}2}={\mathrm{N}}_{\mathrm{C}1}-0.125\times \left[{\mathrm{N}}_{\mathrm{C}1}-{\mathrm{N}}_{\mathrm{C}3}]\times [\left({\mathrm{l}}_{\mathrm{K}}/\mathrm{D}\right)-4\right]\hfill \end{array}$$

(26)

$$\begin{array}{cc}\mathrm{Long} \mathrm{column} {\mathrm{l}}_{\mathrm{K}}/\mathrm{D}>12\hfill & \\ & {\mathrm{N}}_{\mathrm{C}3}={\mathrm{cN}}_{\mathrm{C}}+{\mathrm{sN}}_{\mathrm{C}}\hfill \end{array}$$

(27)

$${\mathrm{l}}_{\mathrm{K} }/\mathrm{D} \le 4 { \mathrm{cN}}_{\mathrm{C}}= \mathrm{cA}.{ \mathrm{cf}}_{\mathrm{C}}= \mathrm{cA} \times { \mathrm{F}}_{\mathrm{c} }/{\mathrm{V}}_{\mathrm{c} }$$

(28)

$${\mathrm{l}}_{\mathrm{K} }/\mathrm{D}>12 { \mathrm{cN}}_{\mathrm{C}}={ \mathrm{cN}}_{\mathrm{Cr}}/{\mathrm{V}}_{\mathrm{c} }=\left(\mathrm{cA}.{ \mathrm{c}\mathsf{\sigma }}_{\mathrm{Cr}}\right)/{\mathrm{V}}_{\mathrm{c} }$$

(29)

$$\begin{array}{c}{\mathrm{cf}}_{\mathrm{C}}={\mathrm{F}}_{\mathrm{c}}/{\mathrm{V}}_{\mathrm{c}}\\ c{\lambda }_1\le 1 c{\sigma }_{\mathrm{Cr}}=2/[1+{\left(\mathrm{c}{\lambda }_1{}^4+1\right)}^{0.5}]\cdot {\mathrm{cr}}_{\mathrm{u}}\cdot {\mathrm{F}}_{\mathrm{c}}\end{array}$$

(30)

$${\mathrm{c}\mathsf{\lambda }}_{1 }>1 { \mathrm{c}\mathsf{\sigma }}_{\mathrm{Cr}}=0.83\exp \left[{\mathrm{C}}_{\mathrm{c} }\left(1-{\mathrm{c}\mathsf{\lambda }}_{1 }\right)\right].{ \mathrm{cr}}_{\mathrm{u}}.{ \mathrm{F}}_{\mathrm{c} }$$

(31)

$${\mathrm{c}\mathsf{\lambda }}_{1 }=\left(\mathrm{c}\mathsf{\lambda }/\mathsf{\pi }\right) \left(\mathrm{c}{\varepsilon }_{\mathrm{u}}\right){ }^{0.5}$$

(32)

$$\begin{array}{c}{\varepsilon }_{\mathrm{u}}=0.93{\left({\mathrm{cr}}_{\mathrm{u}}.{ \mathrm{F}}_{\mathrm{c} }\right)}^{0.25}. 10{ }^{-3}\\ { \mathrm{C}}_{\mathrm{c} }=0.568+0.00612{\mathrm{F}}_{\mathrm{c} } \end{array}$$

(33)

$${\mathrm{l}}_{\mathrm{K} }/\mathrm{D} \le 4 { \mathrm{sN}}_{\mathrm{C}}= \mathrm{sA}.{ \mathrm{sf}}_{\mathrm{C}}= \mathrm{sA} \times \mathrm{F}/\mathrm{sV}$$

(34)

$${\mathrm{l}}_{\mathrm{K} }/\mathrm{D}>12 \mathrm{and} \mathrm{s}\mathsf{\lambda } \le { \mathsf{\Lambda } \mathrm{cN}}_{\mathrm{C}}= \mathrm{sA} \left[1-0.4\left(\mathrm{s}\mathsf{\lambda }/\mathsf{\Lambda }\right){ }^2\right]\times \mathrm{F}/\mathrm{sV}$$

(35)

$$\mathrm{s}\mathsf{\lambda } >{ \mathsf{\Lambda } \mathrm{cN}}_{\mathrm{C}}= \mathrm{sA} \left(0.6 \mathrm{F}\right)/\left(\mathrm{s}\mathsf{\lambda }/\mathsf{\Lambda }\right){ }^2\times \mathrm{sV}$$

(36)

$$\mathsf{\Lambda } = \mathsf{\pi } \left(\mathrm{sE}/0.6 \mathrm{F}\right){ }^{0.5}$$

(37)

where: ${\mathrm{l}}_{\mathrm{K} }$: the effective length of the CFST columns; η: is a constant and equal to zero for rectangular and 0.27 for circular CFST column; ${\mathrm{N}}_{\mathrm{C}1},{ \mathrm{N}}_{\mathrm{c}2},{ \mathrm{N}}_{\mathrm{C}3}:$ are the allowable strengths of CFST column; $\mathrm{c}{\mathrm{N}}_{\mathrm{C}}$: the allowable strength of concrete column; cA: the cross-sectional area of the concrete column; $\mathrm{c}{\mathrm{f}}_{\mathrm{C}}$: the allowable compressive stress of concrete; ${\mathrm{F}}_{\mathrm{c} }$: the design standard strength of filled concrete; ${\mathrm{V}}_{\mathrm{c} }$: the safety factor of the concrete section and is equal to 1.00; ${\mathrm{c}\mathsf{\sigma }}_{\mathrm{Cr}}:$ the critical stress of the concrete column; $\mathrm{c}\mathsf{\lambda }:$ the slenderness ratio of the concrete column; $\mathrm{s}{\mathrm{N}}_{\mathrm{C}}$: the allowable strength of the steel tube column; sA: the cross-sectional area of the steel tube column; $\mathrm{s}{\mathrm{f}}_{\mathrm{C}}$: the allowable compressive stress of the steel tube column; $\mathrm{s}\mathsf{\lambda }:$ the effective slenderness ratio of the steel tube column; Λ: the critical slenderness ratio; sE: the modulus of elasticity of the steel tube column; F: the design standard strength of the steel tube column, and sV = 1.00.

5.2. Comparisons of the Analytical Results of Axial Loads with Different Codes

The different values of the axial loads obtained analytically by ANSYS and those obtained by the different design codes are listed in

Table 11. Comparisons of Ultimate Axial Loads between Analytical Results from ANSYS and obtained from Design Codes/standards.

Specimen Code	H/D	D/t	PANSYS (KN)	AISC (2010)		ECP 205-200 (LRFD)		EC 4		AIJ (1997)
				Pn (KN)	% Panlytical/Pn	Pn (KN)	% Panlytical/Pn	PPLRD (KN)	% Panlytical/PPLRD	Pc (KN)	% Panlytical/Pc
C400-2-D127	3.14	63.5	750	744	101% (+1)	612	123% (23)	781	96% (−4)	850	88% (−12)
C1000-2-D127	7.87		740	709	104% (+4)	593	125% (+25)	669	111% (+11)	772	96% (−4)
C2000-2-D127	15.75		680	597	114% (+14)	523	130% (+30)	708	96% (−4)	606	112% (+12)
C400-4-D127	3.14	31.75	1260	980	129% (+29)	857	147% (+47)	1143	110% (+10)	1158	108% (+8)
C1000-4-D127	7.87		1150	940	122% (+22)	830	113% (+13)	928	124% (+24)	1044	110% (+10)
C2000-4-D127	15.75		1190	810	146% (+46)	735	110% (+25)	975	122% (+22)	820	145% (+45)
C1000-8-D400	2.5	50	7300	7908	92% (−8)	6674	109% (+9)	9107	80% (−20)	9137	80% (−20)
C1000-8-D200	5	25	2700	2696	100% (0)	2425	111% (+11)	2989	90% (−10)	3189	85% (−15)
C3000-8-D400	7.5	50	7200	7572	95% (−5)	6472	111% (+11)	7473	96% (−4)	8361	86% (−14)
C4000-8-D400	10	50	7100	7289	97% (−3)	6296	113% (13)	7183	99% (−1)	7693	92% (−8)
C5000-8-D400	12.5	50	7100	6942	102% (+2)	6069	119% (+19)	7245	98% (−2)	6965	102% (+2)
C3000-8-D200	15	25	2600	2307	113% (+13)	2132	122% (+22)	2740	95% (−5)	2345	111% (+11)
C4000-8-D200	20	25	2600	2013	129% (+29)	1875	139% (+39)	3533	74% (−26)	3330	78% (−22)
C5000-8-D200	25	25	2600	1690	154% (+54)	1545	168% (+68)	4937	53% (−47)	2205	118% (+18)
C3000-4-D400	7.5	100	5700	6030	95% (−5)	4898	116% (16)	5745	99% (−1)	6539	87% (−13)
C4000-4-D400	10	100	5700	5771	99% (−1)	4760	120% (+20)	5611	102% (+2)	6046	94% (−6)
C5000-4-D400	12.5	100	5700	5454	105% (+5)	4581	124% (+24)	5675	100% (0)	5487	98% (−2)
C3000-4-D400-Fc50	7.5	100	6500	7070	92% (−8)	5672	115% (+15)	6668	97% (−3)	7658	85% (−15)
C5000-4-D400-Fc50	12.5	100	6500	6326	103% (+3)	5272	123% (+23)	6705	97% (−3)	6397	102% (+2)
C3000-4-D400-Fy420	7.5	100	5700	6295	91% (−9)	5175	110% (+10)	6038	94% (−6)	6877	83% (−17)
C5000-4-D400-Fy420	12.5	100	5700	5667	101% (+1)	4820	118% (+18)	6004	95% (−5)	5641	101% (+1)
C3000-4-D400-Fc60	7.5	100	7000	8101	86% (−14)	6442	107% (+7)	7602	92% (−8)	8777	80% (−20)
C5000-4-D400-Fc60	12.5	100	7000	7173	98% (−2)	5951	118% (+18)	7749	90% (−10)	7298	96% (−4)
C3000-4-D400-Fy520	7.5	100	5800	6735	86% (−14)	5634	103% (+3)	6519	89% (−11)	7439	78% (−22)
C5000-4-D400-Fy520	12.5	100	5800	6016	96% (−4)	5210	111% (+11)	6578	88% (−22)	6175	94% (−6)
C3000-12-D400	7.5	33.3	9200	9067	101% (+1)	8011	115% (+15)	9159	100% (0)	10146	91% (−9)
C5000-12-D400	12.5	33.3	9200	8363	110% (+10)	7518	122% (+22)	8782	105% (+5)	8409	109% (+9)
C3000-8-D400-Fc50	7.5	50	8000	8583	93% (−7)	7216	111% (+11)	8332	96% (−4)	9435	85% (−15)
C5000-8-D400-Fc50	12.5	50	7900	7808	101% (+1)	6734	117% (+17)	8244	96% (−4)	7831	101% (+1)
C3000-8-D400-Fy420	7.5	50	7400	8105	91% (−9)	7022	105% (+5)	8039	92% (−8)	9031	82% (−18)
C5000-8-D400-Fy420	12.5	50	7400	7383	100% (0)	6544	113% (+13)	7898	94% (−6)	7483	99% (−1)
C3000-8-D400- Fc60	7.5	50	8700	9586	91% (−9)	7957	109% (+9)	9202	95% (−5)	10508	83% (−17)
C5000-8-D400-Fc60	12.5	50	8600	8657	99% (−1)	7391	116% (+16)	9260	93% (−7)	8687	99% (−1)
C3000-8-D400-Fy520	7.5	50	7500	8986	83% (−17)	7930	95% (−5)	8963	84% (−16)	10142	74% (−26)
C5000-8-D400- Fy520	12.5	50	7500	8097	93% (−7)	7314	103% (+3)	9062	83% (−17)	8322	90% (−10)
C3000-4-D200	15	50	1900	1635	116% (+16)	1448	131% (+31)	1914	99% (−1)	1656	115 (+15)
C4000-4-D200	20	50	1900	1404	135% (+35)	1271	149% (+49)	2385	80% (−20)	2123	89% (−11)
C5000-4-D200	25	50	1900	1155	165% (+65)	1044	182% (+82)	3206	59% (−41)	1448	131% (+31)
C3000-4-D200-Fc50	15	50	2200	1829	120% (+20)	1601	137% (+37)	2196	100% (0)	1851	119 (+19)
C5000-4-D200-Fc50	25	50	2200	1253	176% (+76)	1119	196% (+96)	3706	59% (−41)	1531	144% (+44)
C3000-4-D200-Fy420	15	50	1900	1731	110% (+10)	1554	122% (+22)	2123	89% (−11)	1778	107% (+7)
C5000-4-D200-Fy420	25	50	1900	1192	159% (+59)	1079	176% (+76)	3827	50% (−50)	1448	131% (+31)
C3000-4-D200-Fc60	15	50	2300	2018	114% (+14)	1751	131% (+31)	2481	93% (−7)	2043	113% (+13)
C5000-4-D200-Fc60	25	50	2300	1342	171% (+71)	1185	194% (+94)	4210	55% (−45)	1600	144% (+44)
C3000-4-D200-Fy520	15	50	1900	1885	101% (+1)	1722	110% (+10)	2510	76% (−24)	1971	96% (−4)
C5000-4-D200-Fy520	25	50	1900	1243	153% (+53)	1106	172% (+72)	5032	39% (−61)	1448	131% (+31)
C3000-8-D200-Fc50	15	25	2900	2493	116 (+16)	2272	128% (+28)	3007	96% (−4)	2519	115% (+15)
C5000-8-D200-Fc50	25	25	2900	1792	162% (+62)	1615	180% (+80)	5453	53% (−47)	2274	126% (+26)
C3000-8-D200-Fy420	15	25	2800	2504	113% (+13)	2339	120% (+20)	3158	85% (−15)	2581	108% (+8)
C5000-8-D200-Fy420	25	25	2700	1774	152% (+52)	1606	168% (+68)	6187	44% (−56)	2205	122% (+22)
C3000-8-D200-Fc60	15	25	3000	2675	112 (+12)	2411	124% (+24)	3277	92% (+8)	2686	112% (+12)
C5000-8-D200-Fc60	25	25	3000	1887	159 (+59)	1678	179% (+79)	5976	50% (−50)	2330	129% (+29)
C3000-8-D200-Fy520	15	25	2800	2813	100% (0)	2664	105% (+5)	3952	71% (−29)	2956	95% (−5)
C5000-8-D200-Fy520	25	25	2800	1888	148% (+48)	1652	169% (+69)	8689	32% (−68)	2205	127% (+27)
Range				(−17) to (+76) %		(−5) to (+96) %		(−68) to (+24) %		(−26) to (+45) %
Average				114.7%		129.3%		86.1%		103.26%

.

5.2.1. Discussion for Results from AISC (2010) [35]

The comparison values of the AISC (2005) and the values obtained by the ANSYS results for columns with f_cu = 40 MPa and f_y = 360 MPa; at D/t = 25, the values of P_n equals the ANSYS failure load for H/D = 5, and increased by 13%, 29%, and 54% for H/D = 15, 20, and 25, respectively. At D/t = 33.3, the values of P_n increased by 1% and 10% for H/D = 7.5 and 12.5, respectively. At D/t = 50, the values of P_n decreased by 8% for H/D = 2.5 and decreased by 5%, and 3%, and increased by 2% for H/D = 7.5, 10, and 12.5, respectively, and the values of P_n increased by 16%, 35%, and 65% for H/D = 15, 20, and 25, respectively. In addition, at D/t = 100, the values of P_n decreased by 5%, and 1%, and increased by 5% for H/D = 7.5, 10 and 12.5, respectively.

At D/t = 25, in the case of f_cu = 50 MPa, the values of P_n increased by 16% and 62% for H/D = 15 and 25, respectively. For the case of using concrete with an fcu = 60 MPa as infill, the values of P_n increased by 12% and 59% for H/D = 15 and 25, respectively. In the case of f_y = 420 MPa, the values of P_n increased by 13% and 52% for H/D = 15 and 25, respectively, and for case of f_y = 520 MPa, the values of P_n equals the ANSYS failure load for H/D = 15 and increased by 48% for H/D = 25, respectively.

At D/t = 50, in the case of f_cu = 50 MPa, the values of P_n decreased by 7% and increased by 1% for H/D = 7.5 and 12.5, respectively, and increased by 20% and 76% for H/D = 15 and 25, respectively. For case of using concrete with an f_cu = 60 MPa as infill, the values of P_n decreased by 9% and 1% for H/D 7.5 and 12.5, respectively, and increased by 14% and 71% for H/D = 15 and 25, respectively. In the case of f_y = 420 MPa, the values of P_n decreased by 9% and 0% for H/D = 7.5 and 12.5, respectively, and the values of P_n increased by 10% and 59% for H/D = 15 and 25, respectively, and for case of f_y = 520 MPa the values of P_n decreased by 17% and 7% for H/D = 7.5 and 12.5, respectively, and the values of P_n increased by 1% and 53% for H/D = 15 and 25, respectively.

At D/t = 100, in the case of f_cu = 50 MPa, the values of P_n decreased by 8% and increased by 3% for H/D = 7.5 and 12.5, respectively. For the case of using concrete having f_cu = 60 MPa as infill, the values of P_n decreased by 14% and 2% for H/D 7.5 and 12.5, respectively, in the case of f_y = 420 MPa, the values of P_n decreased by 9% and increased by 1% for H/D = 7.5 and 12.5, respectively, and for the case of f_y = 520 MPa, the values of P_n decreased by 14% and 4% for H/D = 7.5 and 12.5, respectively.

It is noted that the AISC (2005) equations are more conservative for the slender sections (D/t = 100) than the compact sections (D/t = 25). The AISC (2005) equations are more conservative when the increasing column-height-to-diameter (H/D) ratio for compact sections and less conservative for slender sections. AISC (2005) equations are more conservative when increasing infill concrete and steel tube strengths for compact or slender sections. Finally, the failure load predicted from AISC (2005) code compared to analytical results from ANSYS ranges between (−17%) and (+76%) with an average ratio of 114.70%.

5.2.2. Discussion for Results from ECP 205-2007(LRFD) [38]

When comparing the analytical results from ANSYS with those obtained from the ECP 205-2007 code equations, it is found that at D/t = 25, the values of P_n increased by 11% for H/D = 5, and increased by 22%, 39%, and 68% for H/D = 15, 10, and 25, respectively. In the case of D/t = 33.3, the values of P_n increased by 15% and 22% for H/D = 7.5 and H/D 12.5 m, respectively. At D/t = 50, the values of P_n increased by 9% for H/D = 2.5 and increased by 11%, 13%, and 19% for H/D = 7.5, 10 and 12.5, respectively, and the values of P_n increased by 31%, 49%, and 82% for H/D = 15, 20 and 25, respectively. In addition, at D/t = 100, the values of P_n increased by 16%, 20%, and 24% for H/D = 7.5, 10, and 12.5, respectively.

At D/t = 25, for the case of using concrete with f_cu = 50 MPa, the values of P_n increased by 28% and 80% for H/D = 15 and 25, respectively. For the case of using concrete with f_cu = 60 MPa as infill, the values of P_n increased by 24% and 79% for H/D = 15 and 25, respectively. In the case of f_y = 420 MPa, the values of P_n increased by 20% and 68% for H/D = 15 and 25, respectively, and for the case of f_y = 520 MPa, the values of P_n increased by 5% and 69% for H/D = 15 and 25, respectively.

At D/t = 50, for the case of f_cu = 50 MPa, the values of P_n increased by 11% and 17% for H/D = 7.5 and 12.5, respectively, and increased by 37% and 69% for H/D = 15 and 25, respectively. In addition, when f_cu = 60 MPa, the values of P_n increased by 9%, and 16% for H/D = 7.5 and 12.5, respectively, and increased by 31% and 94% for H/D = 15 and 25, respectively. For the steel tube with f_y = 420 MPa, the values of P_n increased by 5% and 13% for H/D = 7.5 and 12.5, respectively, and the values of P_n increased by 22% and 76% for H/D = 15 and 25, respectively. In the case of a steel tube with f_y =520 MPa, the values of P_n decreased by 5% and increased by 3% for H/D = 7.5 and 12.5, respectively, and the values of P_n increased by 10% and 72% for H/D = 15 and 25, respectively.

At D/t = 100 and in the case of f_cu = 50 MPa, the values of P_n increased by 15% and 23% for H/D = 7.5 and 12.5, respectively. For the case of using concrete with f_cu = 60 MPa as infill, the values of P_n increased by 7% and 18% for H/D 7.5 and 12.5, respectively. In the case of a steel tube with f_y = 420 MPa, the values of P_n increased by 10% and 18% for H/D = 7.5 and 12.5, respectively, and for the case of f_y = 520 MPa the values of P_n increased by 3% and 11% for H/D = 7.5 and 12.5, respectively.

It can be obvious that the ECP 205-2007(LRFD) equations are more conservative for the slender sections (D/t = 100) than the compact sections (D/t = 25). With increasing (H/D), the ECP 205 equations are more conservative for compact sections and less conservative for slender sections. The ECP 205 equations are more conservative when increasing the infill concrete and steel tube strengths for the compact or slender sections. The failure load predicted from the ECP 205-2007 code compared to the analytical results from ANSYS ranges between (−5%) and (+96%), with an average ratio of 129.30%. These values are underestimated more than those obtained from the previous codes AISC (2005).

5.2.3. Discussion for Results from Eurocode 4 [36]

Comparing the analytical results from ANSYS with those obtained from the Eurocode 4 equations, it is found that for the case of using concrete with an f_cu equal to 40 MPa and a steel tube with an f_y equal to 360 MPa, and at D/t = 25, the values of failure load with respect to that obtained from ANSYS are decreased by 10% for H/D = 5 and decreased by 5%, 26%, and 47% for H/D = 15, 20, and 25, respectively, and at D/t = 33.3 the values of failure load increased by 0% and 5% for H/D = 7.5 and 12.5, respectively. In addition, at D/t = 50, the values of failure load decreased by 20% for H/D = 2.5 and decreased by 4%, 1% and 2% for H/D = 7.5, 10, and 12.5, respectively, and the values of failure load decreased by 1%, 20%, and 41% for H/D = 15, 20, and 25, respectively. In addition, at D/t = 100, the values of failure load decreased by 1% and increased by 2% and 0% for H/D = 7.5, 10 and 12.5, respectively.

At D/t = 2, 5 and with concrete of f_cu = 50 MPa, the values of failure load are decreased by 4% and 47% for H/D = 15 and 25, respectively. For the case of concrete with f_cu = 60 MPa as infill, the values of failure load decreased by 8% and 50% for H/D = 15 and 25, respectively. In the case of steel tube with f_y = 420 Mpa, the values of the failure load decreased by 15% and 56% for H/D = 15 and 25, respectively, and for the case of f_y = 520 MPa, the values of the failure load decreased by 29% and 68% for H/D = 15 and 25, respectively.

At D/t = 50, and with concrete of f_cu = 50 MPa, the values of failure load are decreased by 4% for both H/D = 7.5 and 12.5, respectively, and decreased by 0% and 41% for H/D = 15 and 25, respectively, and at f_cu = 60 MPa, the concrete infill values of failure load decreased by 5%, and 7% for H/D = 7.5 and 12.5, respectively, and decreased by 7% and 45% for H/D = 15 and 25, respectively. For f_y = 420 MPa, the steel tube values of failure load decreased by 8% and 6% for H/D = 7.5 and 12.5, respectively and decreased by 11% and 50% for H/D = 15 and 25, respectively, and at f_y = 520 Mpa, the values of failure load decreased by 16% and 17% for H/D = 7.5 and 12.5, respectively, and decreased by 24% and 61% for H/D = 15 and 25, respectively.

At D/t = 100, the values of failure load decreased by 3% for both H/D = 7.5 and 12.5, respectively. For the case of using concrete with f_cu = 60 MPa as infill, the values of the failure load decreased by 8% and 10% for H/D 7.5 and 12.5, respectively. In the case of a steel tube with f_y = 420 MPa, the values of failure load decreased by 6% and 5% for H/D = 7.5 and 12.5, respectively, and for the case of f_y = 520 MPa, the values of the failure load decreased by 11% and 22% for H/D = 7.5 and 12.5, respectively.

It can be noted that the EC4 equations are more conservative for slender sections (D/t = 100) than compact sections (D/t = 25). The EC4 equations are more conservative when increasing the column-height–to-diameter (H/D) for the compact sections and less conservative for slender sections. The EC4 equations are more conservative when increasing the infill concrete and steel tube strengths for compact or slender sections. The failure load predicted from the Eurocode 4 code compared to analytical results from ANSYS ranges between (−68%) and (+24%) with an average ratio of 86.10%. These values are underestimated more than that obtained from the previous codes AISC (2005) and ECP 205-2007(LRFD).

5.2.4. Discussion for Results from AIJ (1997) [37]

For the case of using concrete with an f_cu equal to 40 MPa and a steel tube with an f_y equal to 360 MPa, it is found that at D/t = 2,5 the values of failure load with respect to that obtained from ANSYS are decreased by 15% for H/D = 5 and increased by 11% and decreased by 22% for H/D = 15 and 25, respectively, and for H/D = 20 increased by 18%, and at D/t = 33.3 the values of failure load decreased by 9% and increased by 9% for H/D = 7.5 and 12.5, respectively. In addition, at D/t = 50, the values of failure load decreased by 20% for H/D = 2.5 and decreased by 14% and 8% and increased by 2% for H/D = 7.5, 10, and 12.5, respectively, the values of failure load increased by 15%, and decreased by 11%, and increased by 31% for H/D = 15, 20 and 25, respectively, and at D/t = 100 the values of failure load decreased by 13%, 6%, and 2% for H/D = 7.5, 10 and 12.5, respectively.

At D/t = 25 and with concrete having f_cu = 50 MPa the values of failure load with respect to that obtained from ANSYS are increased by 15% and 20% for H/D = 15 and 25, respectively. For the case of using high-strength concrete with f_cu = 60 MPa as infill, the values of failure load increased by 12% and 29% for H/D = 15 and 25, respectively. In the case of f_y = 420 MPa, the values of failure load increased by 8% and 22% for H/D = 15 and 25, respectively, and for the case of f_y = 520 MPa, the values of failure load decreased by 5% and increased by 27% for H/D = 15 and 25, respectively.

At D/t = 50, and with concrete having f_cu = 50 MPa, the values of the failure load with respect to that obtained from ANSYS are decreased by 15% and increased by 1% for H/D = 7.5 and 12.5, respectively, and increased by 19% and 44% for H/D = 15 and 25, respectively, and at f_cu = 60 MPa as a high-strength concrete, the values of failure load decreased by 17% and 1% for H/D = 7.5 and 12.5, respectively, and increased by 13% and 44% for H/D = 15 and 25, respectively. In the case of f_y = 420 MPa for the steel tube, the values of failure load decreased by 18% and 9% for H/D = 7.5 and 12.5, respectively and increased by 7% and 31% for H/D = 15 and 25, respectively and at f_y = 520 MPa the values of failure load decreased by 26% and 10% for H/D = 7.5 and 12.5, respectively and decreased by 4% and increased by 31% for H/D = 15 and 25, respectively.

At D/t = 10,0 and in case of f_cu = 50 MPa, the values of failure load decreased by 15% and increased by 2% for H/D = 7.5 and 12.5, respectively. For cases using high-strength concrete with f_cu = 60 MPa as in-fill, the values of failure load decreased by 20% and 4% for H/D 7.5 and 12.5, respectively, in case of f_y = 420 MPa, and the values of failure load decreased by 17% and increased by 1% for H/D = 7.5 and 12.5, respectively, and for cases of f_y = 520 MPa the values of failure load decreased by 22% and 6% for H/D = 7.5 and 12.5, respectively.

It can be observed that the AIJ (1997) equations are more conservative for the compact sections (D/t = 25 and 33) more than the slender sections (D/t = 50 and 100); opposite to the previous codes in 5.3.1, 5.3.2, and 5.3.3. In addition, the AIJ equations are more conservative for high values of concrete and steel strength in cases of short or long columns but with ratios less than that obtained from the previous codes in 5.3.1, 5.3.2, and 5.3.3. The average ratio of the failure load obtained by ANSYS compared to the AIJ code is 103.26%, and this demonstrated that the results obtained by the ANSYS program are in good agreement with AIJ, ranging between −26% and +45%.

5.2.5. Summary of Codes Provisions Comparisons

Figure 25 represents the comparisons of the analytical results with the results predicted by the AISC, ECP205, EC4, and AIJ Codes.

It is shown that the AIJ (1997) design code has good convergence compared to the other studied codes that cover the various ratios of the tube-diameter-to-thickness, column-height-to-diameter, and various values of the concrete infill material properties and steel tube material properties compared to the results obtained by the ANSYS models of the CFST columns. The load-carrying capacity of the CFST columns calculated from the Eurocode 4 design code underestimated the values, while the AISC and ECP 205 design codes overestimated them. The most divergent design code is ECP 205 when compared to the other studied codes.

For all of the studied codes, it was found that the equations are more conservative for the slender sections than for the compact sections. In addition, they are more conservative when increasing the column-height–to–diameter (H/D) ratio for the compact sections and less conservative for the slender sections. The different codes are more conservative for the high values of infill concrete strength and steel tube strength for either the compact or slender sections.

6. Conclusions

This paper discusses the behavior of concrete-filled tubes extensively. The main studied parameters are the H/D ratio, D/t ratio, the concrete and steel tube material properties, and the use of stiffeners with different spacings. The validation with the different code provisions is discussed. Analytical work, including sixty-four specimens, was carried out, and the main conclusions can be drawn as:

(1)

The ANSYS analytical models are in a good convergence to present the behavior and the failure modes of concrete-filled steel tube columns, either the yielding failure “the elephant foot buckling” for short ones or global buckling for long ones.

(2)

The effect of the compressive strength of the infilled concrete develops the behavior of the CFST columns gradually by increasing their load capacity but reducing the vertical deformation due to the increasing column stiffness.

(3)

The effect of the yielding strength of the steel tube on the CFST columns is not remarkable; the increase in the steel yield strength led to slight changes in failure load and vertical deformation.

(4)

The increase in the tube thickness of the CFST columns while maintaining the column diameter as a constant, i.e., D/t is reduced, the failure load is increased by 26–37%, but the vertical deformation is slightly affected by the tube thickness (about ± 6%).

(5)

Increasing the diameter of the CFST columns while maintaining the tube thickness is constant, i.e., D/t is increased, significantly increasing the load-carrying capacity by 2.7–3.00 times as doubling the column diameter but decreasing the vertical deformation due to the increase in column stiffness. These decreases in the vertical deformation is more markable in long columns (H/D > 12) than for the medium (4 < H/D < 12) and short columns (H/D < 4).

(6)

The vertical deformation increased, but the failure load is not remarkably different when increasing the column height-to-diameter ratio (H/D) while maintaining the column diameter and tube thickness as constants. This is because decreasing the column stiffness by increasing the column height is inversely proportional to the deformation.

(7)

The stiffened CFST long columns (H/D > 12) using rings as stiffeners do not increase the failure load sufficiently but may reduce the column capacity compared to the unstiffened CFST columns. This is due to the steel tube yielding first at the location of the rings.

(8)

The stiffened CFST long columns using rings with close spacing between them failed prior to those with widely spaced rings. This earlier failure happened due to the failure of the stiffeners near the loading plate.

(9)

For long columns (H/D > 12), stiffening with rings with different spacings between them along the column height did not enhance the behavior of the CFST column.

(10)

The load capacity obtained from the AISC (2010), ECP 205-2007 (LRFD), Eurocode 4, and AIJ (2008) codes/standards varied from (−17% to +76%), (−5% to +96%), (−68% to +24%), and (−26% to +45%), respectively, when compared with that which are obtained from ANSYS.

(11)

ECP205-2007 is the most conservative design code in predicting the load capacity of CFST columns compared to the other studied codes/standards, with differences averaging 29.3% when compared to that are obtained from ANSYS.

(12)

The Eurocode 4 design code has the most underestimation values of the load-carrying capacity for the CFST columns.

(13)

The AIJ (1997) design code closely predicts the load capacity of the CFST columns compared to the other studied codes/standards with the differences when compared to that which are obtained from ANSYS by an average of 3.3% for various studied parameters that cover the various ratios of the tube-diameter-to-thickness, column-height-to-diameter, and various values of concrete infill material properties and steel tube material properties.

(14)

All of the studied codes/standards are more conservative for slender sections than compact sections. In addition, they are more conservative when increasing column height–to–diameter (H/D) for compact sections and less conservative for slender sections. The different codes are more conservative for the high values of infill concrete strength and steel tube strength for either compact or slender sections.

7. Future Works

Different shapes of CFST columns can be studied. Double-skin tubular columns filled with concrete can be studied, as can different types of stiffeners for long CFST columns; for example, using shear connectors and using through bolts. The effect of the eccentricity of axial load on the CFST columns can be considered. Finally, the effect of the biaxial moment in addition to axial load in the CFST beam columns can be studied.