Effect of Preload on Box-Section Steel Columns Filled with Concrete under Axial Load: A Numerical Study

Abstract

External loads applied to a box-section steel column before it is filled with concrete to increase its efficiency due to modifications in structural systems or design errors may reduce its ultimate capacity and change its structural behavior. To examine this effect, finite element modeling (FEM) has been used to simulate these columns under preloading at different ratios with many variables in the geometric dimensions of the columns. The FEM results have been investigated using 38 experimental specimens obtained from previous studies without preloading. The results demonstrated high accuracy in modeling these columns in structural behavior and ultimate load capacity. After verifying the results, 84 Concrete-Filled Steel Columns (CFSC) were modeled under different preload ratios. The results indicated that some variables have directly affected the value of the decrease in column capacity in terms of its height, wall thickness, yield stress, and preload ratios, while others were inversely proportional in terms of the cross-section dimensions and concrete strength. The preload effect ratio had two separate limits, where when it reached 70%, the maximum value of the decrease in column capacity was 10.90%. The value increased sharply reaching 19.90% when there was a preload equal to 80%. New equations have been proposed to predict the ultimate capacity of CFSC under preloading with suitable accuracy with a correlation coefficient of no less than 0.949.

1. Introduction

Steel columns in structural systems may be defined as the backbone of steel buildings and great attention during design is given to them. Many shapes are used as steel columns, including I-sections, boxes (rectangles and squares), and built-up sections of angles or channels. These sections can be bonded to concrete by filling or encasing them to form a composite section. It might encounter certain problems that appear in the steel construction sites as a result of an increase in loads on the box columns as a result of a change in the structural system or an error in the design. It is categorically pivotal to build up these steel columns to resist any increase in the loads applied to them. Therefore, one of the strengthening methods is to use concrete to fill the box columns though they are under the influence of the already existing loads (preloading). Through literature review, it has been found out that many studies and even existing codes (ANSI/AISC 360-22 [1] and Eurocode-4 [2]) focused on this type of column labeled (composite section), but no preloading has been applied. That is, the column is just filled with concrete and then exposed to loads. This method of loading does not represent the application in reality if the columns are filled with concrete while they are under the influence of existing loads due to their presence in the current construction system.

Recently, many studies have paid attention to studying the behavior of Concrete-Filled Steel Columns (CFSC), whether it is a normal-strength [3,4,5] or high-strength concrete [6,7,8]. Among the normal-strength concrete studies was Schneider [9]. A number of 14 steel columns with different cross-sections consisting of 3 circular, 6 rectangular, and 5 square were tested under axial load. The concrete cylinder strength used ranged from 24 to 31 MPa and the yield stress ranged from 312 to 537 MPa. Different column wall thicknesses were used, which resulted in column width- or diameter-to-thickness ratios ranging from 17 to 50.8. The most important results are that the axial load behavior is greatly affected by the cross-section shape and the ratio of column dimensions to wall thickness. Uy [10] performed an experiment testing 19 square CFSC with concrete strength ranging from 28 to 32 MPa and a steel yield stress of 750 MPa. The test results indicated that the Eurocode-4 [2] approach was unsafe for the specimens exposed to pure axial load or bending. The reason was the Eurocode-4, which assumes concrete to be plastic (fully crushed) and steel to be elastic (fully yielded). Han [11] conducted experimental tests on 24 steel columns consisting of 20 rectangles and 4 squares tested under axial load. The concrete strength was 48.3 MPa and the steel yield stress ranged from 194 to 228 MPa. Han [11] concluded that the steel column behavior was influenced by the tube width ratio and material properties. Dondo [12] has conducted experimental studies on the behavior of 29 square steel tubes filled with concrete under compression load. The cross-section of the steel tubes ranges from 60 × 60 × 3.0 mm to 150 × 150 × 4.5 mm. The slenderness ratio ranges from 6.67 to 27.0, while the depth-to-wall column thickness ranges from 33.87 to 50.00. Specimens with high depth-to-wall thickness ratios (b/t) had more local buckling or bulging compared to those with small b/t ratios. All concrete-filled square columns experienced a decrease in their strength with an increase in the slenderness ratio. Further tests have been conducted by Shaker-Khalil and Molly [13] on concrete-filled rectangular hollow sections with 3 to 9 m heights with dimensions of 120 × 80 × 5 mm and 150 × 100 × 5 mm. The concrete strength ranged from 40.8 to 47.2 MPa while the steel yield stress ranged from 340 to 363 MPa. The conclusion showed that filling the section with concrete increased the capacity of the cross sections of columns 120 × 80 × 5 mm and 150 × 100 × 5 mm by 12% and 65%, respectively. Column failure occurred due to overall flexural buckling of the column with no sign of local buckling. Zhu et al. [14] have investigated the behavior of 30 square CFSC with concrete strength ranging from 24.47 to 26.58 MPa and yield stress ranging from 235 to 345 MPa. Five different cross-section designs, including unstiffened and stiffened cross-sections, have been identified. The results concluded that the inner stiffeners more significantly affected the failure mode, deformability, and overall strength of the composite columns. To study this type of composite columns with stiffened cross-section, Tao et al. [15,16,17] and Liu et al. [18,19] conducted experimental and numerical studies on thin-walled tube columns where the steel walls were stiffened to improve their structural behavior. Some other studies, including experimental tests [20,21,22,23,24] and numerical analysis [25,26,27], took the effect of concrete filling on double-skin steel tubular columns into consideration. Zhang et al. [28,29] studied the static and dynamic loads of steel columns with unstiffened and stiffened cross-sections with thicknesses of 1.25 to 1.48 mm. It was also observed that the ultimate capacity increased with the number of stiffeners, and the columns with more stiffeners had better ductility.

In recent years, much attention has been paid to the behavior of composite columns constructed from high-strength concrete and steel [30,31,32,33,34]. Based on the experimental test results of 41 circular steel columns with yield stress ranging from 410 to 435 MPa and concrete strength ranging from 58 to 96 MPa. Kilpatrick and Rangan [35] confirmed that the slenderness and load eccentricity significantly affected the strength of columns. Experimental testing of 22 specimens under axial compressive load was performed by Liu [36]. The test variables include a cross-section aspect ratio of 1.0 to 2.0, a steel-to-concrete volume ratio of 0.13 to 0.17, a steel yield stress of 495 MPa, and a concrete strength of 60 to 89 MPa. The confinement achieved by the steel section increases the strength of the concrete. Strength improvement is negatively affected by the section aspect ratio. Sakino et al. [37] axial loading tests have been performed on 48 square and 36 circular steel columns. The test parameters were material strengths with yield stress ranging from 262 to 853 MPa, concrete strength ranging from 25 to 91 MPa, and volumetric steel-to-concrete ratio from 0.09 to 0.26. The rest results showed that the strength improvement was attributed to the strain hardening of the steel section instead of the confinement effect. The concrete filling increased the strength of square columns more than the circular ones. In addition, some studies [10,38,39,40] have mainly focused on investigating the reliability of various existing codes, ANSI/AISC 360-22 [1] and Eurocode-4 [2], in predicting the ultimate capacity of CFSC.

For several reasons, many studies in the last three decades have relied directly on using a finite element modeling (FEM) system. It saved time and effort and reduced the costs of preparing experimental tests. There were some special tests such as preload or load cycle tests that were difficult to perform in the laboratory due to the unavailability of testing machines or preload systems. Added to this difficulty were the long duration of the tests and the lack of a safety factor while conducting these tests. Therefore, the researchers selected FEM programs with the highest accuracy in modeling structural elements to obtain the required reliability. FEM analysis was used to model steel tube columns whether unfilled [41,42,43] or filled with concrete [44,45,46,47,48,49,50] under the influence of axial load, or with the use of flexural load [51,52,53]. Wang et al. [43] conducted FEM analysis on 20 specimens of steel tube columns without concrete filling, and the results compared to experimental tests were very accurate. The average ultimate capacity ratio was 1.016 with a Coefficient of Variation, COV, equal to 5.66%. Dai and Lam [46] carried out FEM simulations on 21 specimens of concrete-filled steel tube columns with elliptical hollow sections. The results of comparing the FEM analysis with experimental tests were an excellent match in both structural behavior (load-axial shortening curve), failure mode, and ultimate load capacity. The average ultimate capacity ratio was 1.013 with COV equal to 2.75%. Tao et al. [49] have conducted a FEM analysis on 340 samples collected from previous studies. The results showed great accuracy using FEM analysis, as the average ultimate capacity reached 1.024, 1.009, and 1.037 for each of the 142 circular columns, 154 square columns, and 44 rectangular columns with a standard deviation equal to 0.065, 0.078, and 0.079, respectively. One of the applications of FEM analysis was the preload modeling. Sayed [54] has conducted a FEM study on reinforced concrete columns under preloading, which were strengthened using steel jacketing. The average ultimate capacity ratio of columns with or without strengthening was 1.003, with COV = 3.16% and a correlation coefficient, r, of 0.987. These results demonstrated the accuracy and reliability of using the FEM simulation system in modeling these structural elements. From the literature review, it was found that it was difficult to conduct experimental tests of these columns under the influence of preload due to the long time of the test and the method of representing the loads required for this. It was also found that using the FEM system had great accuracy in modeling this type of structural elements in obtaining the behavior of these elements and their ultimate capacity.

In this study, the FEM analysis will be applied to simulate these concrete-filled columns with or without preloading. Many of the previously mentioned variables will be used specifically compared to those that are likely to have an impact on the ultimate capacity of the steel columns under preload. These variables will be modeled in terms of column height, column wall thickness, yield stress, cross-section dimensions, and concrete strength under the influence of preload ratios equal to 40%, 60%, 70%, and 80% of the ultimate capacity of the steel column without concrete filling. First, the results of the FEM analysis will be verified through comparison with specimens available from previous studies [12,14,36,38,39] without preloading. Also, the results will be compared with the prediction of existing codes, ANSI/AISC 360-22 [1] and Eurocode-4 [2], to obtain the accuracy of their use in such columns and the extent of safety in the design. Second, the effect of preload ratios will be obtained with all these variables on the ultimate axial load capacity of CFSC. Thirdly, the possibility of proposing a new model that can predict the ultimate axial load capacity of CFSC under preloading is tangible, taking into account all the variables under study.

2. Existing Models

Many existing models, including international codes [1,2] or scientific papers, have provided equations that could predict the ultimate capacity of these types of structural elements, especially CFSC. The model is available through the ANSI/AISC 360-22 [1] in the chapter on designing composite elements, as in Equation (1). This model can predict the plastic axial compressive strength of CFSC without consideration of the column length effect.

$$N_{\mathrm{P}}=f_{\mathrm{y}}{A}_{\mathrm{s}}+K{f\prime }_{\mathrm{c}}{A}_{\mathrm{c}}$$

(1)

where f_y is steel column yield stress, A_s is the steel column cross-section, f′_c is the compressive strength of the concrete-filled steel column, A_c is the area of the concrete section, and K is a coefficient that depends on the cross-sectional shape of the steel column equal to 0.95 for columns with a round cross-section and 0.85 for other shapes. Some conditions have been set for using this model, as the concrete strength must not be less than 21 MPa and not more than 69 MPa. The yield stress of the steel column must not be more than 525 MPa. To take the column length into account, Equation (2) must be used to calculate the critical elastic buckling load.

$$N_{\mathrm{e}}={\pi }^2{\left(EI\right)}_{\mathrm{e}\mathrm{f}\mathrm{f}}/{L^2}_{\mathrm{c}}$$

(2)

where L_c is the effective column length, (EI)_eff is the effective stiffness of composite section calculated by Equation (3), E_s and E_C are the modulus of elasticity of steel and concrete, respectively, I_s and I_c are the moment of inertia of steel and concrete column, respectively, and C₃ is the coefficient for effective rigidity.

$${\left(EI\right)}_{\mathrm{e}\mathrm{f}\mathrm{f}}=E_{\mathrm{s}}{I}_{\mathrm{s}}+C_3{E}_{\mathrm{c}}{I}_{\mathrm{c}}$$

(3)

$$C_3=0.45+3\left({\displaystyle \frac{A_{\mathrm{s}}}{A_{\mathrm{c}}}}\right)\le 0.9$$

(4)

There are two column conditions based on the ratio between the width and the thickness of the steel column wall. The first is that the column is a compact section, when the ratio (λ = b/t) is less than Equation (5), in which the column nominal axial compressive strength N_no = N_P. The second case is that the column section is noncompact, when the ratio (λ = b/t) is less than Equation (6), so the N_no calculation is based on Equation (7).

$${\lambda }_{\mathrm{P}}=2.26\sqrt{{\displaystyle \frac{E_{\mathrm{s}}}{f_{\mathrm{y}}}}}$$

(5)

$${\lambda }_{\mathrm{r}}=3.00\sqrt{{\displaystyle \frac{E_{\mathrm{s}}}{f_{\mathrm{y}}}}}$$

(6)

$$N_{\mathrm{n}\mathrm{o}}=N_{\mathrm{P}}-\left(\left(\frac{N_{\mathrm{P}}-N_{\mathrm{y}}}{{\lambda }_{\mathrm{r}}-{\lambda }_{\mathrm{P}}}\right){\left(\lambda -{\lambda }_{\mathrm{P}}\right)}^2\right)$$

(7)

$$N_{\mathrm{y}}=f_{\mathrm{y}}{A}_{\mathrm{s}}+0.7{f\prime }_{\mathrm{c}}{A}_{\mathrm{c}}$$

(8)

To calculate the ultimate axial load capacity of the CFSC, two cases where the ratio between the column’s nominal axial compressive strength and the critical elastic buckling column load (N_no/N_e) are used, and their comparison is 2.25 where

$$N_{\mathrm{n}}=N_{\mathrm{n}\mathrm{o}}({0.658}^{\left(\frac{N_{\mathrm{n}\mathrm{o}}}{N_{\mathrm{e}}}\right)})\mathrm{When}{\displaystyle \frac{N_{\mathrm{n}\mathrm{o}}}{N_{\mathrm{e}}}}\le 2.25$$

(9)

$$N_{\mathrm{n}}=0.877N_{\mathrm{e}}\mathrm{When}{\displaystyle \frac{N_{\mathrm{n}\mathrm{o}}}{N_{\mathrm{e}}}}>2.25$$

(10)

To use the Eurocode-4 [2] in designing such a case, Equation (11) can be used. The axial compressive plastic resistance load of the composite column can be obtained as follows:

$$N_{\mathrm{n}}=f_{\mathrm{y}}{A}_{\mathrm{s}}+0.85{f\prime }_{\mathrm{c}}{A}_{\mathrm{c}}$$

(11)

Equation (11) applies to concrete partially and encased steel sections. For CFSC, the coefficient of 0.85 is replaced with 1.0. Therefore, the Equation (11) is modified to

$$N_{\mathrm{n}}=f_{\mathrm{y}}{A}_{\mathrm{s}}+{f\prime }_{\mathrm{c}}{A}_{\mathrm{c}}$$

(12)

3. Finite Element Model Study

3.1. Concrete Modeling and Properties

To perform the numerical analysis process, the ANSYS program was used. To model the concrete used to fill steel columns, the element SOLID65 is accordingly used [55]. This element contains eight points each containing three degrees of freedom (DOFs) in the X, Y, and Z directions. It can also provide high-accuracy modeling in deforming the plastic, breaking, and crushing in three directions. For the ANSYS program to employ the characteristics required for concrete modeling, some important characteristics must be defined. The stress–strain relationship for the concrete is used, as well as the shear transfers coefficient β, uniaxial tensile stress, modulus of elasticity, and Poisson’s ratio. The modulus of elasticity can be calculated from Equation (13), and through it, the rest of the characteristics of the stress–strain relationship in the elastic and plastic stages can be obtained [49,56].

$$E_{\mathrm{c}}=4700\sqrt{f_{\mathrm{c}}^{\prime }}$$

(13)

$$f_{\mathrm{e}\mathrm{l}}=0.30f_{\mathrm{c}}^{\prime }$$

(14)

$$E_{\mathrm{c}}=f_{\mathrm{e}\mathrm{l}}/{\epsilon }_{\mathrm{e}\mathrm{l}}$$

(15)

$${\epsilon }_0={\displaystyle \frac{2f_{\mathrm{c}}^{\prime }}{E_{\mathrm{c}}}}$$

(16)

$$f={\displaystyle \frac{E_{\mathrm{c}}\epsilon }{1+(\epsilon /{\epsilon }_{\mathrm{o}}{)}^2}}$$

(17)

wherein

• f_el = the stress at the elastic strain (ε_el) in the elastic range.
• ε_o = the strain at the ultimate cylinder compressive strength.
• f = the stress at any strain ε.

Regarding the shear transfer coefficient β [55], the values range from 0.0 for a smooth crack to 1.0 for a rough crack [57,58]. By reviewing previous studies [56,59], the best shear transfer coefficient was obtained, with the coefficient of open crack at, β_t = 0.2, and the coefficient of closed crack, β_c = 0.8. Also, the uniaxial tensile stress, f_r, can be calculated from Equation (18), and Poisson’s ratio of 0.2 for concrete was applied [49]. Through these equations, the stress–strain relationship for different grades of concrete can be calculated, which will be used in the FEM analysis process, as listed in

Table 1. The stress–strain relationships for concrete applied to the FEM analysis.

	Concrete Grade 25		Concrete Grade 26.6		Concrete Grade 28.8		Concrete Grade 46.6		Concrete Grade 60
	Stress (MPa)	Strain	Stress (MPa)	Strain	Stress (MPa)	Strain	Stress (MPa)	Strain	Stress (MPa)	Strain
	7.50	0.00032	7.98	0.00033	8.64	0.00034	13.98	0.00044	18.00	0.00049
	19.25	0.0010	20.07	0.0010	21.16	0.0010	28.68	0.0010	33.34	0.0010
	23.55	0.0015	24.78	0.0015	26.43	0.0015	38.00	0.0015	45.24	0.0015
	24.95	0.0020	26.49	0.0020	28.55	0.0020	43.53	0.0020	53.22	0.0020
	25.00	0.0021	26.60	0.0022	28.80	0.0023	46.08	0.0025	57.78	0.0025
	25.00	0.0025	26.60	0.0025	28.80	0.0025	46.60	0.0029	59.74	0.0030
	25.00	0.0030	26.60	0.0030	28.80	0.0030	46.60	0.0035	60.00	0.0033
									60.00	0.0035
Ec (GPa)	23.5		24.24		25.22		32.08		61.41
fr (MPa)	3.12		3.21		3.34		4.25		4.83

.

$$f_{\mathrm{r}}=0.623\sqrt{f_{\mathrm{c}}^{\prime }}$$

(18)

3.2. Steel Column Modeling and Characteristics

To model the steel columns, element SOLID185 was used [55]. This element contains eight points with 3-DOFs in three directions: x, y, and z. There are many properties of this element that it is capable of plasticity, creep, hyperelasticity, large deflection, and larger capabilities of strain. This is also suitable for asymmetric meshes and the ability to simulate deformations of elastic–plastic materials. The properties of the steel used to model the steel columns are introduced from the relationship between stress and strain, as well as the modulus of elasticity, based on the values included in previous studies from experimental tests [12,14,36,38,39]. A Poisson’s ratio of 0.3 for steel was used.

Table 2. The stress–strain relationships for steel applied to the FEM analysis.

	Young and Liu [39] (R1L)		Young and Liu [39] (R2L)		Young and Liu [39] (R3L)		Young and Liu [39] (R4L)		Young and Ellobody [38] (SHS2)
	Stress (MPa)	Strain	Stress (MPa)	Strain	Stress (MPa)	Strain	Stress (MPa)	Strain	Stress (MPa)	Strain
	350	0.0018	424	0.0022	366	0.0019	443	0.0023	448	0.00224
	381	0.009	477	0.011	398	0.013	482	0.011	474	0.013
	412	0.05	512	0.058	447	0.056	508	0.052	504	0.047
	449	0.09	540	0.11	514	0.14	550	0.13	574	0.13
	536	0.21	604	0.23	577	0.26	608	0.27	637	0.22
	626	0.45	661	0.41	629	0.43	659	0.41	676	0.31
	646	0.63	675	0.55	647	0.53	676	0.51	695	0.42
	649	0.72	676	0.61	648	0.64	678	0.61	699	0.5
	625	0.74	634	0.64	622	0.66	642	0.63	641	0.51
	601	0.75	571	0.66	581	0.68	596	0.64	596	0.52
Es (GPa)	198		194		193		194		200

shows the stress–strain relationship available in previous studies and used in modeling steel in the FEM analysis process.

The contact elements of TARGE170 and CONTA174 [55] were used to model the contact between the steel column wall and the filling concrete that functions as Coulomb’s friction model. CONTA174 applies to 3D geometrical elements with an 8-node intended for flexible–flexible and rigid–flexible contact analysis, which can be applied to the contact between solid bodies or shells. The CONTA174 contact element is associated with the 3D target segment element TARGE170 located on the surface of 3D solid elements. It has the same geometric characteristics as the underlying elements. TARGE170 was applied with 3D surface-to-surface contact elements with the CONTA174. In the basic Coulomb friction model (τ_lim = μP + b), two surfaces in contact can carry shear stresses, where μ = isotropic friction coefficient, p = normal contact pressure, and b = contact cohesion. Through the CONTA174 element, an option can be provided to specify the maximum equivalent frictional stress τ_max. Therefore, sliding will occur if the magnitude of the equivalent frictional stress reaches this value, and when the equivalent shear stress is less than the limit of frictional stress, no motion occurs between the two surfaces, which is known as sticking.

3.3. Model Studies of Structure

Using the ANSYS program, 122 specimens were modeled, as they contain many of the variables that were taken in this study. These specimens were divided into two main groups.

The first group numbers 38 specimens obtained through data available in previous studies from experimental tests [12,14,36,38,39], as listed in

Table 3. Summary of columns on previous studies used to verify FEM results.

FE Model Based on	Column Specimen	Steel Column Dimensions					fy (MPa)	Concrete f′c (MPa)
		a (mm)	b (mm)	t (mm)	L (mm)	a/b
Liu [36]	R1-1	120	120	4.00	360	1.0	495	60.0
	R2-1	150	100	4.00	450	1.5	495	60.0
	R3-2	180	90	4.00	540	2.0	495	60.0
	R4-2	130	130	4.00	390	1.0	495	60.0
	R5-1	160	110	4.00	480	1.5	495	60.0
	R6-1	190	100	4.00	570	1.9	495	60.0
	R7-1	106	106	4.00	320	1.0	495	89.0
	R8-1	130	90	4.00	390	1.4	495	89.0
	R9-2	160	80	4.00	480	2.0	495	89.0
	R10-1	140	140	4.00	420	1.0	495	89.0
	R11-1	160	125	4.00	480	1.3	495	89.0
Zhu et al. [14]	Pa-6-1	197	197	6.40	600	1.0	438	26.6
	Pa-10-1	201	201	10.10	600	1.0	382	26.6
Young and Ellobody [38]	SHS1C40	150.5	150.5	5.834	450	1.0	497	46.6
	SHS1C60	150.6	150.6	5.829	450	1.0	497	61.9
	SHS2C0	150.5	150.5	2.796	600	1.0	448	----
	SHS2C40	150.5	150.5	2.782	450	1.0	448	46.6
	SHS2C60	150.5	150.5	2.780	450	1.0	448	61.9
	RHS1C40	197.1	109.5	4.060	600	1.8	503	46.6
	RHS3C0	140.0	78.8	3.075	600	1.8	486	----
	RHS3C40	140.2	80.1	3.100	420	1.8	486	46.6
	RHS3C60	140.2	80.1	3.100	420	1.8	486	61.9
Dundu [12]	S1-101/1	101.6	101.6	3.00	1000	1.0	484	25.0
	S1-101/1.5	101.6	101.6	3.00	1500	1.0	484	25.0
	S1-120/1	120	120	3.50	1500	1.0	401	25.0
	S1-120/2	120	120	3.50	2000	1.0	401	25.0
	S1-150/1.5	150	150	3.50	1500	1.0	405	25.0
	S1-150/2	150	150	3.50	2000	1.0	405	25.0
	S1-150/2.5	150	150	3.50	2500	1.0	405	25.0
	S3-120/2.7	120	120	3.00	2700	1.0	401	28.8
	S3-150-3/2.7	150	150	3.00	2700	1.0	429	28.8
	S3-150-4.5/2.7	150	150	4.50	2700	1.0	335	28.8
Young and Liu [39]	R1L1200	120.1	40	1.94	1199	3.0	350	----
	R1L2000	120.2	40	1.95	2000	3.0	350	----
	R2L1200	119.7	39.9	5.31	1200	3.0	424	----
	R3L1200	119.9	80.1	2.82	1200	1.5	366	----
	R3L2000	120	80	2.80	2000	1.5	366	----
	R4L2000	120.1	80.4	6.02	2000	1.5	443	----

. Modeling of these steel columns was performed, whether they were filled with concrete (30 specimens) or not (8 specimens). These specimens contain many variables, including cross-section dimensions, height, concrete strength, yield stress, and wall thickness of the steel columns. All these specimens were tested to the failure point under axial load. This group will verify the accuracy of FEM analysis results in modeling this type of structural element under the influence of many variables.

The second group consists of 84 specimens that were selected based on some available data conducted as a literature review [12,14,36,38,39] and were modeled with dimensions similar to reality. These specimens were tested under three stages of axial load. The first stage is based on a hollow steel column without a concrete filling. The second stage uses CFSC without preloading. In the third stage, these columns were tested at four percentages of preload, where there was 40%, 60%, 70%, and 80% of the ultimate load of the steel column without concrete filling. Then, add concrete to the steel column after reaching this percentage of preload until the failure load.

Table 4. Summary of the columns created in this study by FEM analysis.

FEM Specimen	Steel Column Dimensions					fy (MPa)	Concrete f′c (MPa)
	b (mm)	t (mm)	L (mm)	b/t	Compact limit
R1-1	120	4	360	30	46.1	495	60
R1-L = 1500	120	4	1500	30	46.1	495	60
C1	200	5	4000	40	46.1	495	60
C2	150	5	4000	30	46.1	495	60
C3	250	5	4000	50	46.1	495	60
C4	200	5	3000	40	46.1	495	60
C5	200	5	5000	40	46.1	495	60
C6	200	8	4000	25	46.1	495	60
C7	200	10	4000	20	46.1	495	60
C8	200	12	4000	16.7	46.1	495	60
C9	200	5	4000	40	46.1	495	21
C10	200	5	4000	40	46.1	495	40
C11	200	5	4000	40	55.3	334.8	40
C12	200	5	4000	40	50.6	405	40

contains all the variables in terms of dimensions and characteristics of the materials used in this study.

3.4. Choosing the Optimal Mesh Convergence

The size of the elements used in FEM analysis plays a major role in the accuracy of the results and in the time taken to perform the analysis. Therefore, this section aims to determine the appropriate element mesh size in FEM analysis to obtain acceptable accuracy in the results with the least possible number of elements. To obtain this result, the density of the mesh was changed by changing the size of the elements from 2.5 mm to 20 mm, while monitoring the effect of this on the ultimate load capacity. The CFSC (S3-150-4.5/2.7) [12] was chosen as the largest specimen dimension for this operation. The relationship between the number of elements and the corresponding ultimate axial load capacity resulting from the FEM analysis is plotted, as shown in Figure 1. It is clear from Figure 1 that after the number of elements equals 389,680, the effect on the ultimate load capacity is not noticeable. From this result, the mesh dimensions corresponding to this number of elements can be adopted in conducting FEM analysis tests on the remaining specimens. Therefore, the FEM analysis model was divided into small elements with maximum typical dimensions of 5 mm in width, length, and height, respectively.

4. Verify the FEM Results and Existing Codes with Experimental Tests

4.1. Verify the FEM Results

The ultimate strength of structural elements is often the most important thing that can be obtained from testing and analyzing specimens. To verify the reliability and validity of the FEM analysis results, the ultimate axial load capacity results were compared with the experimental test results, as shown in

Table 5. Comparison of FEM results of CFSC and existing codes with experimental tests.

FE Model Based on	Column Specimen	NExp (kN)	FEM Results		ANSI/AISC 360-22		Eurocode 4
			NFEM (kN)	NFEM/NExp	NAISC (kN)	NAISC/NExp	NEC4 (kN)	NEC4/NExp
Liu [36]	R1-1	1701.0	1685.7	0.991	1555.9	0.915	1671.4	0.983
	R2-2	1778.0	1764.5	0.992	1618.9	0.911	1742.2	0.980
	R3-2	1795.0	1836.3	1.023	1746.2	0.973	1883.8	1.049
	R4-2	2018.0	2028.1	1.005	1754.1	0.869	1891.0	0.937
	R5-1	1982.0	1942.4	0.980	1822.1	0.919	1967.8	0.993
	R6-1	2049.0	2006.0	0.979	1959.7	0.956	2121.4	1.035
	R7-1	1749.0	1728.0	0.988	1531.4	0.876	1662.6	0.951
	R8-1	1752.0	1764.3	1.007	1590.3	0.908	1729.9	0.987
	R9-1	1878.0	1896.8	1.010	1734.4	0.924	1892.7	1.008
	R10-1	2752.0	2713.5	0.986	2390.5	0.869	2627.9	0.955
	R11-1	2580.0	2518.1	0.976	2434.5	0.944	2679.7	1.039
Zhu et al. [14]	Pa-6-1	2730.0	2710.9	0.993	2669.5	0.978	2780.8	1.019
	Pa-10-1	3980.0	3852.6	0.968	3432.9	0.863	3539.8	0.889
Young and Ellobody [38]	SHS1C40	2768.1	2690.6	0.972	2424.1	0.876	2562.8	0.926
	SHS1C60	2972.0	3037.4	1.022	2675.9	0.900	2859.8	0.962
	SHS2C40	1381.5	1376.0	0.996	1233.3	0.893	1381.9	1.000
	SHS2C60	1620.0	1660.5	1.025	1505.3	0.929	1702.7	1.051
	RHS1C40	1627.2	1685.9	1.036	1672.7	1.028	1813.8	1.115
	RHS3C40	1048.7	1021.4	0.974	951.9	0.908	1024.9	0.977
	RHS3C60	1096.9	1135.3	1.035	1079.2	0.984	1175.8	1.072
Dundu [12]	S1-101/1	718.9	745.5	1.037	751.7	1.046	797.1	1.109
	S1-101/1.5	691.2	720.3	1.042	738.1	1.068	797.1	1.153
	S1-120/1	997.2	968.3	0.971	903.5	0.906	970.1	0.973
	S1-120/2	899.7	933.8	1.038	889.2	0.988	970.1	1.078
	S1-150/1.5	1330.1	1316.8	0.990	1245.0	0.936	1338.6	1.006
	S1-150/2	1307.6	1312.8	1.004	1232.0	0.942	1338.6	1.024
	S1-150/2.5	1198.3	1224.6	1.004	1215.4	1.014	1338.6	1.117
	S3-120/2.7	825.2	812.0	0.984	821.4	0.995	937.0	1.136
	S3-150-3/2.7	1087.1	1095.8	1.008	1085.6	0.999	1187.9	1.093
	S3-150-4.5/2.7	1300.4	1292.3	0.994	1342.6	1.032	1449.4	1.115
Average ratio				1.022		0.945		1.024
COV				2.25%		5.74%		6.81%
r				0.999		0.998		0.998

, for CFSC while

Table 6. Comparison of FEM results for unfilled concrete steel columns and existing codes with experimental tests.

FE Model Based on	Column Specimen	NExp (kN)	FEM Results		ANSI/AISC 360-22		Eurocode 4
			NFEM (kN)	NFEM/NExp	NAISC (kN)	NAISC/NExp	NEC4 (kN)	NEC4/NExp
Young and Ellobody [38]	SHS2C0	408.6	409.8	1.003	405.2	0.992	405.8	0.993
	RHS3C0	558.2	563.2	1.009	552.9	0.991	557.0	0.998
Young and Liu [39]	R1L1200	167.0	169.0	0.988	189.6	1.135	154.4	0.925
	R1L2000	141.3	147.0	1.040	162.9	1.153	139.4	0.986
	R2L1200	717.4	730.3	1.018	567.6	0.791	646.6	0.901
	R3L1200	398.3	390.7	0.981	381.1	0.957	391.3	0.982
	R3L2000	394.0	382.2	0.970	361.4	0.917	389.1	0.987
	R4L2000	970.4	998.5	1.029	873.6	0.900	960.9	0.990
Average ratio				1.005		0.980		0.970
COV				2.41%		12.00%		3.62%
r				0.999		0.996		0.999

for steel columns is not filled (with concrete).

Table 5 shows the values of the ultimate axial load for both FEM analysis and experimental tests and the ratio between them, N_FEM/N_Exp, and the relationship is drawn in Figure 2. From Figure 2 and Table 5 for CFSC, the average ratio of N_FEM/N_Exp equals 1.002, with COV = 2.25% and r equal to 0.999. Also, according to Table 6 and Figure 2, for steel columns not filled with concrete, the average ratio of N_FEM/N_Exp equals 1.005, with COV equal to 2.41% and r equal to 0.999. From a statistical perspective, whether steel columns are filled with concrete or not, the reliability and validity of the results measured from the FEM analysis are an excellent match. This high accuracy and agreement in the results are consistent with the results of previous studies [43,44,45,46,47,48,49,50,51,52,53,54] that used FEM analysis in modeling such structural elements.

Through the load and axial shortening curves measured from the experimental tests and resulting from the FEM analysis of these specimens, the relationship between the load and axial shortening was drawn, as shown in Figure 3 and Figure 4. These specimens represent many considered variables. Where the compressive strength of concrete ranges from 26.6 to 89 MPa, the yield stress of steel ranges from 382 to 495 MPa, and the dimensions of columns range in ratios from 1.0 to 2.0; whereas, the wall thickness of columns ranges from 4.0 to 10.1 mm, as well as the height of the columns, which ranges from 360 to 600 mm. Figure 3 represents the relationship between load and axial shortening resulting from the FEM analysis, which has a very high accuracy when compared with the same experimental test results for these specimens (R1-1, R2-2, R3-2, R7-1, R8-1, and R9-1) provided in Liu [36]. Figure 4 represents the load-strain relationship obtained from FEM analysis, which is in excellent agreement with the same experimental test specimens Pa-6-1 and Pa-10-1 provided in Zhu et al. [14]. From Figure 3 and Figure 4, the accuracy resulting from comparing experimental results and FEM analysis of the behavior of the columns in applied load and axial shortening curves is an excellent match.

Here are the deformations and locations of the failure modes available through previous studies [14,36] from experimental tests and the same failure modes that can be obtained from FEM analysis. The degree of similarity between experimental tests and FEM analysis is an excellent match, as shown in Figure 5. A similar match of the deformation shape in Figure 5a was found with the same specimen Pa-6-1 available in Zhu et al. [14], and also in Figure 5b with the same specimen R4-2 available in Liu [36]. It clearly shows that the failure location most observed in these columns filled with concrete is the occurrence of local buckling, which is in the upper third of the column at the location of the applied load.

4.2. Verify the Existing Code Results

The most two important codes were selected from the existing codes, ANSI/AISC 360-22 [1] and Eurocode-4 [2], on which most models in studies or other codes are based, namely, ANSI/AISC 360-22 and Eurocode 4. The ultimate axial load of these steel columns was calculated through the equations provided in these codes, which appear in this study as Equations (1)–(12). These values were listed in Table 3 and Table 4, and a relationship was drawn between the calculated load and the experimental test results, as shown in Figure 6 for the ANSI/AISC 360-22, and Figure 7 for the Eurocode 4.

The tables and figures show that according to the ANSI/AISC 360-22, the ultimate capacity of columns filled with concrete can be predicted with an average ratio N_AISC/N_Exp equal to 0.945, with COV equal to 6.08% and r equal to 0.998. As for columns not filled with concrete, the average ratio N_AISC/N_Exp is equal to 0.980, with COV equal to 12.25%, and r equal to 0.996. From a statistical perspective, in most cases, the values calculated from the ANSI/AISC 360-22 are less than the ultimate capacity of steel columns, whether filled with concrete or not. This means that it is on the safe side of the design.

As for the Eurocode-4, the ultimate capacity of columns filled with concrete can be predicted with an average ratio N_EC4/N_Exp equal to 1.024, with COV equal to 6.65% and r equal to 0.997. As for columns not filled with concrete, the average ratio N_EC4/N_Exp is equal to 0.970, with COV equal to 3.73% and r equal to 0.996. It is clear from these results that Eurocode 4 predicts values greater than the ultimate capacity of CFSC, i.e., on the unsafe side of the design. However, it predicts values less than the ultimate capacity of steel columns not filled with concrete, i.e., on the safe side of the design. All these results relate to steel columns without preload.

5. Results and Discussion

To evaluate the effect of preload on the ultimate axial load capacity of CFSC, FEM analysis was performed on 84 specimens. Preloading was performed on the columns at ratios equivalent to 40%, 60%, 70%, and 80% of the ultimate load capacity of the steel columns not filled with concrete. In other words, these preload ratios were applied to the columns with several variables, cross-section dimensions, column height, concrete strength, yield stress, and wall thickness of steel columns. Meanwhile, existing codes, ANSI/AISC 360-22 and Eurocode-4, were used to compare with these results from preload, as shown in

Table 7. Summary of FEM results for steel columns with and without concrete filling under preloading.

FEM Specimen	% Preloadingof Steel	FEM Results				ANSI/AISC 360-22		Eurocode 4
		NFEM (kN)	NPL/NUf	NC (kN)	NCPL/NC	NAISC (kN)	NAISC/NFEM	NEC4 (kN)	NEC4/NFEM
R1-1-Without preloading	0	1685.7	1.000	623.8	1.000	1555.9	0.923	1671.4	0.991
R1-1-P40%	40	1685.7	1.000	623.8	1.000	1555.9	0.923	1671.4	0.991
R1-1-P60%	60	1685.7	1.000	623.8	1.000	1555.9	0.923	1671.4	0.991
R1-1-P70%	70	1655.5	0.982	593.6	0.952	1555.9	0.940	1671.4	1.010
R1-1-P80%	80	1619.2	0.961	557.3	0.893	1555.9	0.961	1671.4	1.032
R1-1-Only steel	---	1061.9	---	---	---	917.4	0.864	922.8	0.869
R1-L = 1500-Without preloading	0	1614.2	1.000	610.2	1.000	1514.7	0.938	1671.4	1.035
R1-L = 1500-P40%	40	1614.2	1.000	610.2	1.000	1514.7	0.938	1671.4	1.035
R1-L = 1500-P60%	60	1614.2	1.000	610.2	1.000	1514.7	0.938	1671.4	1.035
R1-L = 1500-P70%	70	1564.0	0.969	560.0	0.918	1514.7	0.968	1671.4	1.069
R1-L = 1500-P80%	80	1471.8	0.912	467.8	0.767	1514.7	1.029	1671.4	1.136
R1-L = 1500-Only steel	---	1004.0	---	---	---	895.6	0.892	922.8	0.919
C1-Without preloading	0	3971.5	1.000	2084.3	1.000	3491.5	0.879	4096.5	1.031
C1-P40%	40	3971.5	1.000	2084.3	1.000	3491.5	0.879	4096.5	1.031
C1-P60%	60	3898.1	0.982	2010.9	0.965	3491.5	0.896	4096.5	1.051
C1-P70%	70	3787.6	0.954	1900.4	0.912	3491.5	0.922	4096.5	1.082
C1-P80%	80	3367.7	0.848	1480.5	0.710	3491.5	1.037	4096.5	1.216
C1-Only steel	---	1887.2	---	---	---	1810.2	0.959	1762.6	0.934
C2-Without preloading	0	2428.5	1.000	1103.5	1.000	2138.8	0.881	2611.5	1.075
C2-P40%	40	2394.3	0.986	1069.2	0.969	2138.8	0.893	2611.5	1.091
C2-P60%	60	2332.9	0.961	1007.8	0.913	2138.8	0.917	2611.5	1.119
C2-P70%	70	2283.5	0.940	958.4	0.869	2138.8	0.937	2611.5	1.144
C2-P80%	80	2038.0	0.840	712.9	0.646	2138.8	1.049	2611.5	1.281
C2-Only steel	---	1325.1	---	---	---	1277.9	0.964	1310.5	0.989
C3-Without preloading	0	5826.4	1.000	3335.4	1.000	5060.5	0.869	5881.5	1.009
C3-P40%	40	5826.4	1.000	3335.4	1.000	5060.5	0.869	5881.5	1.009
C3-P60%	60	5826.4	1.000	3335.4	1.000	5060.5	0.869	5881.5	1.009
C3-P70%	70	5648.7	0.970	3157.7	0.947	5060.5	0.896	5881.5	1.041
C3-P80%	80	5131.8	0.881	2640.8	0.792	5060.5	0.986	5881.5	1.146
C3-Only steel	---	2491.0	---	---	---	2328.6	0.935	2425.5	0.974
C4-Without preloading	0	4041.1	1.000	2002.9	1.000	3611.4	0.894	4096.5	1.014
C4-P40%	40	4041.1	1.000	2002.9	1.000	3611.4	0.894	4096.5	1.014
C4-P60%	60	4041.1	1.000	2002.9	1.000	3611.4	0.894	4096.5	1.014
C4-P70%	70	3945.1	0.976	1906.9	0.952	3611.4	0.915	4096.5	1.038
C4-P80%	80	3635.0	0.900	1597.8	0.798	3611.4	0.993	4096.5	1.127
C4-Only steel	---	2038.2	---	---	---	1861.9	0.913	1762.6	0.865
C5-Without preloading	0	3735.5	1.000	1943.8	1.000	3343.1	0.895	4096.5	1.097
C5-P40%	40	3666.1	0.981	1874.4	0.964	3343.1	0.912	4096.5	1.117
C5-P60%	60	3615.2	0.968	1823.5	0.938	3343.1	0.925	4096.5	1.133
C5-P70%	70	3504.8	0.938	1713.1	0.881	3343.1	0.954	4096.5	1.169
C5-P80%	80	3036.1	0.813	1244.4	0.640	3343.1	1.101	4096.5	1.349
C5-Only steel	---	1791.7	---	---	---	1745.9	0.974	1762.6	0.984
C6-Without preloading	0	4891.8	1.000	1892.2	1.000	4431.6	0.906	5072.6	1.037
C6-P40%	40	4891.8	1.000	1892.2	1.000	4431.6	0.906	5072.6	1.037
C6-P60%	60	4742.0	0.969	1742.4	0.921	4431.6	0.935	5072.6	1.070
C6-P70%	70	4596.1	0.940	1596.5	0.844	4431.6	0.964	5072.6	1.104
C6-P80%	80	4122.8	0.843	1123.2	0.594	4431.6	1.075	5072.6	1.230
C6-Only steel	---	2999.6	---	---	---	2846.6	0.949	3005.6	1.002
C7-Without preloading	0	5745.3	1.000	1957.2	1.000	5029.0	0.875	5706.0	0.993
C7-P40%	40	5673.4	0.987	1885.4	0.963	5029.0	0.886	5706.0	1.006
C7-P60%	60	5459.4	0.950	1671.4	0.854	5029.0	0.921	5706.0	1.045
C7-P70%	70	5297.1	0.922	1509.0	0.771	5029.0	0.949	5706.0	1.077
C7-P80%	80	4733.9	0.824	945.8	0.483	5029.0	1.062	5706.0	1.205
C7-Only steel	---	3788.1	---	---	---	3516.4	0.928	3762.0	0.993
C8-Without preloading	0	6497.5	1.000	2022.3	1.000	5611.4	0.864	6325.4	0.974
C8-P40%	40	6306.2	0.971	1831.0	0.905	5611.4	0.890	6325.4	1.003
C8-P60%	60	6107.2	0.940	1632.0	0.807	5611.4	0.919	6325.4	1.036
C8-P70%	70	5914.9	0.910	1439.7	0.712	5611.4	0.949	6325.4	1.069
C8-P80%	80	5288.4	0.814	813.2	0.402	5611.4	1.061	6325.4	1.196
C8-Only steel	---	4475.2	---	---	---	4169.4	0.932	4466.9	0.998
C9-Without preloading	0	2551.5	1.000	664.3	1.000	2417.1	0.947	2688.6	1.054
C9-P40%	40	2451.8	0.961	564.6	0.850	2417.1	0.986	2688.6	1.097
C9-P60%	60	2355.0	0.923	467.8	0.703	2417.1	1.026	2688.6	1.142
C9-P70%	70	2281.9	0.894	394.7	0.594	2417.1	1.059	2688.6	1.178
C9-P80%	80	2042.6	0.801	155.4	0.234	2417.1	1.183	2688.6	1.316
C9-Only steel	---	1887.2	---	---	---	1810.2	0.959	1762.6	0.934
C10-Without preloading	0	3255.8	1.000	1368.6	1.000	2942.8	0.904	3374.5	1.036
C10-P40%	40	3188.9	0.979	1301.7	0.951	2942.8	0.923	3374.5	1.058
C10-P60%	60	3157.8	0.970	1270.6	0.928	2942.8	0.932	3374.5	1.069
C10-P70%	70	3050.9	0.937	1163.6	0.850	2942.8	0.965	3374.5	1.106
C10-P80%	80	2702.0	0.830	814.8	0.595	2942.8	1.089	3374.5	1.249
C10-Only steel	---	1887.2	---	---	---	1810.2	0.959	1762.6	0.934
C11-Without preloading	0	2548.1	1.000	1270.9	1.000	2403.1	0.943	2749.7	1.079
C11-P40%	40	2548.1	1.000	1270.9	1.000	2403.1	0.943	2749.7	1.079
C11-P60%	60	2507.3	0.984	1230.1	0.968	2403.1	0.958	2749.7	1.097
C11-P70%	70	2448.8	0.961	1171.6	0.922	2403.1	0.981	2749.7	1.123
C11-P80%	80	2192.8	0.861	915.5	0.720	2403.1	1.096	2749.7	1.254
C11-Only steel	---	1277.2	---	---	---	1248.7	0.978	1272.6	0.996
C12-Without preloading	0	2886.5	1.000	1336.8	1.000	2649.2	0.918	3023.5	1.047
C12-P40%	40	2886.5	1.000	1336.8	1.000	2649.2	0.918	3023.5	1.047
C12-P60%	60	2827.2	0.979	1277.9	0.956	2649.2	0.937	3023.5	1.069
C12-P70%	70	2742.5	0.950	1193.2	0.893	2649.2	0.966	3023.5	1.102
C12-P80%	80	2450.4	0.849	901.1	0.674	2649.2	1.081	3023.5	1.234
C12-Only steel	---	1549.3	---	---	---	1497.6	0.967	1491.4	0.963

.

5.1. The Behavior of Applied Load and Axial Shortening

The behavior of steel columns is directly explained through the relationship between load and axial shortening. In general, the ultimate load increases when concrete is used to fill steel columns. This increase tends to subside when there is preload on steel columns not filled with concrete. However, the decrease in the ultimate capacity of the columns does not occur at all with preload ratios or the same value, as the variables mentioned above affect the value of this effect. For example, when using preload ratios of 40%, 60%, 70%, and 80% on a column C1 with a height of 3000 mm, the load decrease was 1.00, 0.982, 0.954, and 0.848, respectively, of the ultimate capacity of the column filled with concrete without preload, as shown in Figure 8a. The value of this decrease in load entirely changes when using column C5 with a height of 5000 mm. The value of load decreases at the same preload ratios and becomes 0.982, 0.968, 0.938, and 0.813, respectively, as shown in Figure 8b.

5.2. The Effect of Variables and the Preload Ratio on the Efficiency of Columns

To obtain the effect of different variables and preload ratio on the efficiency of CFSC, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13 were drawn. Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13 show the relationship between the ultimate capacity of preloaded columns to the ultimate capacity of columns without preload and the ratios of the effect of preload for each variable separately.

5.2.1. Effect of Column Cross-Section Dimensions

Figure 9 shows this relationship regarding changing the dimensions of the cross-section of the steel column, as was changed from 150 to 250 mm. It precisely shows that the effect of the cross-section dimensions is inversely proportional to the effect of the preload ratio. As the dimensions of the column’s cross-section increase, the effect of the preload ratio on the ultimate capacity of the column decreases. In addition, not all preload ratios have the same effect when the column’s cross-section varies. With preload ratios of 40%, 60%, 70%, and 80% and a column with dimensions of 150 mm, the ratios (N_PL/N_uf) were 0.986, 0.961, 0.940, and 0.840, respectively, and through changing the column dimensions to 250 mm, they were 1.00, 1.00, 0.970, and 0.881, respectively. Through this, as the cross-section of the steel column increases, the efficiency and effect of the concrete fill increases.

Figure 9. The relationship between the ratio of the capacity with to without preload for the effect of cross-section dimensions.

Figure 9. The relationship between the ratio of the capacity with to without preload for the effect of cross-section dimensions.

5.2.2. Effect of Column Height

Figure 10 shows this relationship regarding changing the steel column height, as it was changed from 3000 to 5000 mm. It clearly shows that the effect of column height is directly proportional to the effect of the preload ratio. As the height of the column increases, the impact of the preload ratio on the ultimate capacity of the column increases. With preload ratios of 40%, 60%, 70%, and 80% and with a column height of 3000 mm, the ratios N_PL/N_uf were 1.00, 1.00, 0.976, and 0.900, respectively, and by changing the column height to 5000 mm, they were 0.981, 0.968, 0.938, and 0.813, respectively. From this, as the height of the steel column increases, the efficiency and effect of the concrete fill decreases.

Figure 10. The relationship between the ratio of the capacity with to without preload for the effect of column height.

Figure 10. The relationship between the ratio of the capacity with to without preload for the effect of column height.

5.2.3. Effect of Column Wall Thickness

Figure 11 shows this relationship regarding changing the steel column wall thickness, as it was changed from 5.0 to 12.0 mm. The effect of the column wall thickness is directly proportional to the effect of the preload ratio. As the wall thickness of the column increases, the impact of the preload ratio on the ultimate capacity increases. With preload ratios of 40%, 60%, 70%, and 80% and with a column wall thickness of 5.0 mm, the ratios N_PL/N_uf were 1.00, 0.982, 0.954, and 0.848, respectively, and by changing the column wall thickness to 12.0 mm, they were 0.971, 0.940, 0.910, and 0.814, respectively. Therefore, as the wall thickness of the steel column increases, the efficiency and effect of the concrete fill decreases.

Figure 11. The relationship between the ratio of the capacity with to without preload for the effect of column wall thickness.

Figure 11. The relationship between the ratio of the capacity with to without preload for the effect of column wall thickness.

5.2.4. Effect of Concrete Strength

Figure 12 shows this relationship regarding changing the concrete compressive strength, as it was changed from 21 to 60 MPa. Concrete compressive strength 21 MPa was chosen as it is the lowest value that can be used according to the ANSI/AISC 360-22. The effect of the concrete strength is inversely proportional to the effect of the preload ratio. As the concrete strength increases, the impact of the preload ratio on the ultimate capacity decreases. With preload ratios of 40%, 60%, 70%, and 80% and with concrete compressive strength of 21 MPa, the ratios N_PL/N_uf were 0.961, 0.923, 0.894, and 0.801, respectively, and by changing it to 60 MPa, they were 1.00, 0.982, 0.954, and 0.848, respectively. Accordingly, as the concrete compressive strength increases, the efficiency and effect of the concrete fill increases.

Figure 12. The relationship between the ratio of the capacity with and without preload for the effect of concrete strength.

Figure 12. The relationship between the ratio of the capacity with and without preload for the effect of concrete strength.

5.2.5. Effect of Steel Column Yield Stress

Figure 13 shows this relationship regarding changing the steel column yield stress, as it was changed from 334.8 to 495 MPa. The effect of the steel column yield stress is directly proportional to the effect of the preload ratio. As the steel column yield stress increases, the impact of the preload ratio on the ultimate capacity increases. With preload ratios of 40%, 60%, 70%, and 80% and with a yield stress of 334.8 MPa, the ratios N_PL/N_uf were 0.979, 0.970, 0.937, and 0.830, respectively, and by changing it to 495 MPa, they were 1.00, 0.984, 0.961, and 0.861, respectively. Thus, as the steel column yield stress increases, the efficiency and effect of the concrete fill decreases.

Figure 13. The relationship between the ratio of the capacity with to without preload for the effect of steel yield stress.

Figure 13. The relationship between the ratio of the capacity with to without preload for the effect of steel yield stress.

6. Prediction of Ultimate Axial Load Capacity under Preload

The second group of FEM analysis, which contains 84 specimens, was used to determine the effect of preload on the ultimate capacity of CFSC. By considering all of the variables taken into account, all of the results are listed in Table 7, which also contains the values calculated from existing codes (ANSI/AISC 360-22, and European-4).

First stage: Through the results of steel columns that were modeled with or without concrete fill and without preload, these results were used to verify the reliability of the existing codes, ANSI/AISC 360-22 [1] and Eurocode-4 [2], as shown in Figure 14. Through Figure 14a, where the ratio between the values calculated from the ANSI/AISC 360-22 and the results of FEM analysis, all specimens, whether columns filled or not filled with concrete, fall on the safe side of the design, where the values are less than the ultimate capacity of the columns. The average ratio N_AISC/N_FEM was equal to 0.918 with a COV of 4.05%. In Eurocode-4, the calculated values for columns filled with concrete mostly fall in the unsafe zone, i.e., the calculated values are greater than the ultimate capacity of the column, as shown in Figure 14b. The average ratio N_EC4/N_FEM was equal to 1.030 with COV of 3.71%, while in steel columns not filled with concrete, the calculated values fall on the safe side of the design. The average ratio N_EC4/N_FEM was equal to 0.947 with a COV of 5.38%. This result is completely consistent with the same result when comparing these codes with the experimental test results available from previous studies.

Second stage: Through Table 7, the ultimate capacity of the columns was obtained under the influence of preload (N_PL). Hence, the ratio (N_PL/N_uf) of decrease in this capacity was obtained relative to the CFSC without preload. It is also possible to obtain the contribution of concrete (N_C.) in increasing the load of CFSC with or without preloading. This is determined by the difference between the ultimate capacity of a CFSC and an unfilled steel column. Also, from Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13, the effect of preload is almost linear in reducing the capacity of the column up to a percentage equal to 70% of the load of the steel column that is not filled with concrete. Then, this effect suddenly decreases with a preload percentage equal to 80%. This is due to the fact that the preload percentages of up to 70% of the steel column that are not filled with concrete fall within the elastic region of the stress–strain relationship for the steel used. When the preload percentage reaches 80%, it falls within the elastic–plastic region, where the strains increase and the contribution of steel strength to increasing the column capacity decreases. Therefore, the effect of preload ratios will be divided into two groups. The first group preloads at rates from 40% to 70%. The second group is at a preload equal to 80%. Through Table 7, the percentage decrease in the contribution of concrete with preload was obtained relative to the contribution of concrete for columns without preload. Through these ratios, the effect of preload on the contribution of concrete is greater than the effect on the total capacity of CFSC. The largest percentage decrease in ultimate capacity was recorded at 80% preload for specimen C9 at a rate of 0.801, while for the same specimen, the value of the decrease in concrete contribution was equal to 0.234.

From Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13, factor K was determined to take the effect of all variables into account. This factor was basically imposed on the effect of each variable on the value of a decrease in the ultimate capacity of the column. It was found out that the effect of each of the variables, such as column height, column wall thickness, yield stress, and preload ratios, R_PL, is directly proportional to the value of the decrease in column capacity. The variables such as the cross-section dimensions and the concrete strength are inversely proportional. Therefore, all these variables are collected in one factor, K, as in Equation (19).

$$K={\displaystyle \frac{L\times t\times f_{\mathrm{y}}\times R_{\mathrm{P}\mathrm{L}}}{b\times {f\prime }_{\mathrm{c}}}}$$

(19)

The relationship between the ratios of decrease in concrete contribution resulting from preloading and the factor K was drawn as shown in Figure 15. So, this figure clearly shows that as the value of the factor K increases, the value of the concrete contribution is reduced. Through the polynomial relationship between these ratios, an obtained equation can predict the ultimate capacity of columns filled with concrete under the influence of preload on the steel column. Equation (20) is used with preload ratios not exceeding 70% of the capacity of the steel column not filled with concrete, with r equal to 0.966. Whereas, Equation (21) is used with preload ratios equal to 80% with r equal to 0.992.

$${\displaystyle \frac{\left(N_{\mathrm{P}\mathrm{L}.\mathrm{F}\mathrm{E}\mathrm{M}}-N_{\mathrm{S}.\mathrm{F}\mathrm{E}\mathrm{M}}\right)}{N_{\mathrm{C}.\mathrm{F}\mathrm{E}\mathrm{M}}}}=-0.0014K^2-0.0022K+1.00$$

(20)

$${\displaystyle \frac{\left(N_{\mathrm{P}\mathrm{L}.\mathrm{F}\mathrm{E}\mathrm{M}}-N_{\mathrm{S}.\mathrm{F}\mathrm{E}\mathrm{M}}\right)}{N_{\mathrm{C}.\mathrm{F}\mathrm{E}\mathrm{M}}}}=-0.0006K^2-0.0236K+0.9001$$

(21)

Through previous relationships, Equations (20) and (21), it is extremely difficult to perform an FEM analysis when there is a need to calculate the application of these equations. Therefore, one of the existing codes was used, and the ANSI/AISC 360-22 was selected to assist in the application. Its selection was based on previous analysis results and comparison with specimens, whether experimental or FEM results. It turns out that in all cases, these predictions fall on the safe side of the design. However, all these applications were without any preloading on steel columns. Through the results of the FEM analysis, the deficiency percentages were obtained for each preload case. The ANSI/AISC 360-22 model was used to calculate the concrete contribution according to Equation (22).

$$N_{\mathrm{c}.\mathrm{A}\mathrm{I}\mathrm{S}\mathrm{C}}=0.85{f\prime }_{\mathrm{c}}{A}_{\mathrm{c}}$$

(22)

The ultimate capacity of the steel column with or without concrete filling and without preload was calculated according to Section 2. Then, the deficiency ratios resulting from the FEM analysis were used to find the ultimate remaining capacity for these specimens. The relationship between the ratio of concrete contribution of the specimens under preloading relative to the contribution of concrete without preloading was drawn with factor K, as shown in Figure 16. By applying the same polynomial relationship, Equations (23) and (24) were obtained to be used to determine the ultimate capacity of columns under preload.

$${\displaystyle \frac{\left(N_{\mathrm{P}\mathrm{L}}-N_{\mathrm{S}.\mathrm{A}\mathrm{I}\mathrm{S}\mathrm{C}}\right)}{N_{\mathrm{C}.\mathrm{A}\mathrm{I}\mathrm{S}\mathrm{C}}}}=-0.0002K^2-0.0235K+1.00$$

(23)

$${\displaystyle \frac{\left(N_{\mathrm{P}\mathrm{L}}-N_{\mathrm{S}.\mathrm{A}\mathrm{I}\mathrm{S}\mathrm{C}}\right)}{N_{\mathrm{C}.\mathrm{A}\mathrm{I}\mathrm{S}\mathrm{C}}}}=-0.0002K^2-0.0235K+1.00$$

(24)

Equation (23) is used with preload ratios not exceeding 70% of the capacity of the steel column not filled with concrete, with r equal to 0.949. Whereas, equation 24 is used with preload ratios equal to 80% with r equal to 0.989. Through the value of the correlation coefficient, r, whether accompanying the FEM analysis equations or accompanying the results of the ANSI/AISC 360-22, these new models can predict the ultimate capacity of CFSC under preload as a percentage of the capacity of the steel column without concrete with high accuracy.

7. Conclusions

There is a high possibility of using concrete to fill an existing steel column exposed to external loads to increase the efficiency of resisting external loads resulting from structural modifications or design errors. When such columns are difficult to implement in experimental tests, FEM analysis is performed to model these types of columns under preload. First, the FEM results were verified by comparing them with specimens available in previous studies of columns without preload. The results were very accurate in simulating these columns, as the average capacity ratio reached 1.002, COV was 2.25%, and r equal to 0.999. Secondly, FEM analysis was performed on the steel columns with several variables under different preload ratios. Through the proposed new models, the ultimate axial load capacity of CFSC under preload can be predicted. In light of this research, the conclusions drawn are presented below:

• For steel columns without concrete filling, prediction values calculated from existing codes, ANSI/AISC 360-22 and Eurocode-4, were always less than the actual ultimate capacity, average ratio is 0.951, whether resulting from experimental or FEM tests. This is a result of the existing codes relying only on the elastic region of the steel, while the behavior of the columns uses the actual properties of the available steel, as it enters the elastic–plastic region;
• Through the behavior of columns under preload, some variables are directly proportional to the value of the decrease in column capacity, in terms of column height, column wall thickness, yield stress, and preload ratios, while others are inversely proportional, in terms of cross-section dimensions and concrete strength;
• With some limits in the values of the geometric properties of steel columns and with preload ratios up to 60%, they do not affect the ultimate capacity of CFSC;
• In the case of a preload ratio not exceeding 70%, the value of the decrease in column capacity is approximately linear, and in small values, where the largest decrease ratio was equal to 0.891;
• With a preload ratio equal to 80%, there is a significant decrease in the percentage of remaining capacity of the columns reaching 0.801. This obviously affects the contribution of concrete, as the decreased value reaches 0.234;
• The proposed new models, Equations (23) and (24), using the ANSI/AISC 360-22 models, can predict the ultimate capacity of the axial load of CFSC under preloading. These models have appropriate accuracy, with r of 0.949 and 0.989 for preload ratios not exceeding 70% and equal to 80%, respectively.

Future research could focus on studies that can address the drawbacks of this new model. One of the drawbacks of this new model is the lack of diversity in the cross-sectional shape, such as the fact that rectangular, circular, double-skin, and sections of steel columns stiffened internally or externally remain to be studied. The reliability and accuracy of the new model have not been verified, so experimental tests on these columns under preload should be carried out and the results compared with FEM analysis. This model also relates to axial load only, so other types of preloading, such as eccentric and cyclic loads, can be used.