Evaluation of Eccentric Compressive Behavior Between Active and Passive Preloading in CFST

Abstract

Concrete-filled steel tubes (CFSTs) are widely used in high-rise buildings and bridges, owing to their confinement effect on concrete. The confinement effect can enhance the compressive strength and ductility of the components. During the construction of high-rise buildings or bridges, CFST columns may be subject to an unforeseen preload known as a passive preload, which might impact a structure’s mechanical behavior. Additionally, a deliberate preload called an active preload is applied to a CFST column before application as a design strategy to improve the performance of the CFST. However, only a few studies have evaluated the effects of the two types of preloads on CFST performance. In this study, the eccentric compressive performances of passive and active preloading systems in a circular short CFST column were investigated using finite element numerical simulations. Four representative preloaded CFST columns were compared by analyzing their mechanical behaviors with two-stage loading (preloading and service loading). The influences of the eccentric ratio, concrete compressive strength, steel yield strength, and steel thickness on the load-bearing capacity ratio and M-P curves of the four preloaded CFST columns were evaluated. It was found that in comparison to passive preloaded CFSTs, the overall performance of the active column was satisfactory.

1. Introduction

The employment of concrete-filled steel tubes (CFSTs) is a very practical construction technique for columns and beam-column structures, and CFSTs are used extensively in high-rise buildings and bridges. There has been extensive research on CFSTs in recent decades [1,2,3,4,5,6,7,8,9]. However, some issues have yet to be addressed. For instance, the effects of preloading during construction or design on the performance of a CFST structure have yet to be fully explored.

1.1. Passive Preload

During the construction of high-rise or super high-rise buildings, it is necessary to install several layers of the structure before pumping concrete into steel tubes. Hence, steel tubes are subjected to initial gravity, which is called the preload (Figure 1a). In the construction of a CFST bridge, it is also occasionally the case that the concrete core at the end of a CFST pier is slightly above the edge of the steel tube due to field operation defects; so, the gravity of the upper beam acts on the concrete core before service loading, resulting in initial stress in the concrete (Figure 1b). Similarly, there is also a situation that is due to the shrinkage of the concrete after casting to form a tiny gap at the end of the CFST columns so that the preload is only applied to the steel tube (Figure 1c). Generally, before the service loading of members, CFSTs may be subjected to these preloads as self-weight, wet concrete weight, member weight, and temporary construction weight (Figure 1d), and this will generate pre-stress in the CFSTs.

Several researchers have focused on the influences of these undesired preloads during construction on the behavior of CFST structures. Zha et al. [12] conducted comparative tests and finite element calculations on CFST columns under axial compression with and without the preloading of steel tubes. It was reported that the existence of a steel preload reduced the bearing capacity of the compressed column. As the preload increased, the stability reduction coefficient ($\phi$) increased. Ultimately, the column lost its stability. Liew et al. [13] found that the additional deformation produced by a preload greatly affected the axial compressive capacity of intermediate and slender CFST columns because of the local buckling of steel tubes. The reduction of the axial compressive capacity was greater than 20% when the preload level (βa) was high (βa > 0.6). Therefore, Huang et al. [14] proposed the reduction of the preloading ratio during construction to minimize the effects of preloads on CFSTs. Johansson M and Gylltoft K [15] also conducted a series of experiments to compare the performances of CFST columns subjected to different axial preloads (Figure 2). It was found that the initial preload had the greatest effect on the SFS column under axial compression. Xiong et al. [16] examined the influences of different preload levels on the mechanical properties of CFST columns during eccentric compression utilizing the finite element method. The effects of the eccentricity and the slenderness ratio were taken into consideration. It was reported that the compressive ultimate capacity decreased and the deformation increased significantly due to the high preload level. Moreover, the larger eccentricity and slenderness ratio further intensified the preloading disadvantageous effect on the CFST columns. Zhang et al. [17] asserted that a high preload decreased the stability and weakened the stiffness of an eccentrically compressed CFST column. The steel tube entered the plastic state in advance during preloading, and the descending section of the load-deflection curve appeared earlier. Concrete-filled double steel tube (CFDST) columns are very similar to ordinary CFST columns. Li et al. [18] investigated the mechanical behavior of axially loaded CFDST columns with preload applied either to the outer steel tube or to both steel tubes. It is found that the strength of CFDST column may be decreased moderately when the preload was applied.

Therefore, for the abovementioned studies on the compressive behavior of CFSTs during preloading, the following inferences can be summarized: 1. the preload during building construction is neither deliberately nor actively applied. 2. Although the undesirable preload is not large, it may have a negative impact on CFSTs. Therefore, Milan et al. [11] defined this type of preload as a passive preload.

1.2. Active Preload

If a preload is intentionally imposed on a CFST column as a specific design method to improve the performance of the column, the preload is called an active preload [8]. Typically, an active preload appears in a design to improve the interaction between the steel tube and the concrete, prevent the concrete from drying out and de-hollowing, and ensure that the steel tube and concrete can always work together well. Naghipour et al. [19,20] also put forward the same concept of “active preloading”, i.e., the use of hydraulic methods to actively apply radial pre-pressure to CFST columns. It was found that an active preloaded CFST column had a higher compressive bending capacity than an ordinary CFST column. Nematzadeh et al. [21] also adopted this method to confine the concrete with a steel tube in three directions to improve the mechanical properties of a CFST column. It was also concluded that the hydraulic pre-compression increased the stiffness of the column and delayed cracking in the concrete. Ma et al. [22] developed a novel pre-stressed CFST column (Figure 3a). The key technique was to create a circumferential pretension by tightening the high-strength bolts on the exterior of the steel tube and increasing the friction force between the inner side of the steel and the concrete by planting bars. Sun [23] proposed a method for strengthening concrete with a steel jacket. Two semi-circular steel tubes were bolted together to restrain the concrete, and radial pre-compression was applied to the concrete via the bolts (Figure 3b). The experimental results of the axially compressed specimens showed that when the active circumferential pre-strain of the steel tube was 0–0.2 times the steel yield strain, the peak load increased. Chen et al. [24] used self-stressing concrete to produce active pre-stress. The results indicated that the CFST column’s deformation coordination performance was improved, but its ultimate bearing capacity with axial compression was not improved. Qi [25] proposed a novel method for applying active initial stress by first thermally expanding the steel tube, then filling in the concrete, and finally using the cooling back of the steel to produce initial extruded pre-stress on the concrete. The results of the axial compression tests on short CFST columns showed that the concrete was always in an effective three-way stress state and its ductility was better than that of an ordinary CFST. Lee et al. [26] found that thermal preloading technology is very helpful in improving the ductility of CFST. Overall, the above investigations into the performance of actively preloaded CFSTs suggested that deliberately applied preloads in design could be beneficial for the mechanical performance of CFSTs under compression.

1.3. Research Significance

It is clear from the above literature that when preloads are applied to CFST columns in various ways, the effect on the behavior of CFST columns may be significant, even though the preload values may be small. However, only a few researchers have compared the behavior of CFST columns in different preloading systems in quantitative ways. Milan et al. [11] made some progress on this issue, but their research was limited to axially compressed CFST columns. In practice, most CFST columns are eccentrically compressed. Therefore, in this study, the mechanical properties of eccentrically compressed short CFST columns with passive and active preloading systems were evaluated using finite element numerical simulation methods. First, the compressive load-carrying capacity and ductility of four representative CFST columns were compared. Then, the behavior of the concrete and the steel tubes in the preloading and service loading stages was investigated in-depth. Finally, the effects of the preloading method, eccentric ratio, concrete compressive strength, steel yield strength, and steel thickness on the load-carrying capacity and M-P curves of CFST columns were discussed.

2. Finite Element Modeling

To discuss the above issues systematically, in this study, the finite element software program Abaqus 6.14-1 was used for numerical simulation calculation and analysis. The CFST finite element model included a steel tube, a concrete core, and a rigid bottom steel plate (Figure 4). Each component was discretized using solid C3D8R elements and calculated by reducing the integration. A C3D8R element was chosen because it was more accurate and shear-locking, and a compressive bending load could not easily occur.

2.1. Uniaxial Constitutive Law for Concrete

The concrete uniaxial compressive constitutive law for circular CFSTs was described by Han LH [2]. A compressive stress-strain curve consists of two segments (branches), the initial growth segment and the descending segment (Figure 5a), as described by Equations (1) and (2), respectively.

(1)$\mathrm{For} {\epsilon }_c\le {\epsilon }_0,{\sigma }_c={\sigma }_0\left[A{\displaystyle \frac{{\epsilon }_c}{{\epsilon }_0}}-B{\left({\displaystyle \frac{{\epsilon }_c}{{\epsilon }_0}}\right)}^2\right]$

(2)$\mathrm{For} {\epsilon }_c>{\epsilon }_{0,RE},\begin{array}{c}\theta \ge 0.92, {\sigma }_c={\sigma }_0 \left(1-q\right)+{\sigma }_0 q{\left({\displaystyle \frac{{\epsilon }_c}{{\epsilon }_0}}\right)}^{0.1\theta },\\ \theta <0.92, {\sigma }_c={\sigma }_0\left({\displaystyle \frac{{\epsilon }_c}{{\epsilon }_0 }}\right){\displaystyle \frac{1}{\beta {\left(\frac{{\epsilon }_c}{{\epsilon }_0}-1\right)}^2+\frac{{\epsilon }_c}{{\epsilon }_0}}} \end{array}$

In Equations (1) and (2), σ_c and ε_c are the compressive stress and strain in concrete, respectively. In the growing segment (ε_c ≤ ε₀), σ₀ is the peak stress, ε₀ is the corresponding strain, A and B are dimensionless coefficients (A = 2 − K and B = 1 − K, where K = 0.1 θ^0.745), and θ is the ratio between the steel and concrete capacities ($\theta ={\displaystyle \frac{A_s f_y}{A_c f_{ck}}}$, where A_s and A_c are the areas of a steel tube and a concrete core, respectively).

In Equation (1), the peak stress is expressed by ${\sigma }_0=f_{ck}\left[1.194+{\left(\frac{13}{f_{ck}}\right)}^{0.45}\left(-0.07485 {\theta }^2+0.5789 \theta \right)\right]$. The peak strain is described by ${\epsilon }_0={\epsilon }_{c0}+\left[1400+800\left(\frac{f_{ck}-20}{20}\right)\right]{\theta }^{0.2}$, where ε_c0 is the peak strain of plain concrete (${\epsilon }_{c0}=1300+14.93f_{ck})$.

Equation (2) corresponds to the descending segment (ε_c > ε₀). In the top equation (θ ≥ 0.92, high confinement), q is an interpolation coefficient ($q=\frac{K}{0.2+0.1\theta }$), and in the bottom equation (θ < 0.92, moderate confinement), $\beta ={\left(2.36\times {10}^{-5}\right)}^{0.25+{\left(\theta -0.5\right)}^7 }5 {\left(f_{ck}\right)}^2{10}^{-4}.$

The fracture energy (G_F)-based approach developed by Hillerborg et al. [27] was adopted for numerical models under tension.

(3)$G_F=0.073{\left(f_{\mathrm{cm}}\right)}^{0.18},$

where $f_{\mathrm{cm}}$ is the mean concrete compressive strength (in MPa).

The material properties of preloaded CFSTs, which are presented in Table 1, were consistent with those of the models designed by Milan et al. [11].

In the concrete damage plasticity model (CDPM) [28,29], the yield surface was described by the parameters K_c and σ_b0/σ₀, where K_c is the ratio between the biaxial and triaxial isobaric compressive strengths, and σ_b0/σ₀ is the ratio between the equi-biaxial and uniaxial compressive maximum stresses. Kc was 2/3 [30] in this work, and σ_b0/σ₀ was 1.16 [25]. After yielding, the flow rule was characterized by the dilation angle and the eccentricity. The dilation angle and the eccentricity values were set to 30° and 0.1 [31], respectively. Finally, the viscosity coefficient was used to adjust the constitutive law to improve the convergence efficiency of the softening stage. The assumed value of the viscosity coefficient was close to zero [26].

2.2. Uniaxial Constitutive Laws for Steel

In order to accurately simulate the performance of steel pipes, the secondary plastic flow model is selected [32], and two sections are used to describe the tensile and compressive uniaxial stress-strain curves of steel. Its uniaxial constitutive law can be expressed by the following Formula (4):

(4)${\sigma }_{\mathrm{s}}\left\{\begin{array}{c} E_{\mathrm{s}} {\epsilon }_{\mathrm{s}} ,\left({\sigma }_{\mathrm{s}}\le f_y\right)\\ f_y+0.01E_s\left({\epsilon }_{\mathrm{s}}-{\epsilon }_{\mathrm{y}}\right) ,\left({\sigma }_{\mathrm{s}}\ge f_y\right) \end{array},\right.$

where ${\sigma }_{\mathrm{s}}$ and ${\epsilon }_{\mathrm{s}}$ are the stress and the strain of the steel, respectively. $E_s$ is the elastic modulus, and $f_{\mathrm{y}}$ and ${\epsilon }_{\mathrm{y}}$ are the yield strength and the yield strain of the steel, respectively. Figure 5b shows the curve described by Equation (4), and Table 1 also lists the steel properties.

2.3. Element Meshing

The specific meshing components of the concrete, the steel tube, and the plate are shown in Figure 6. The mesh sizes were determined using convergence studies to achieve accurate simulation results with a minimum increase in the computational cost. The basic meshing size was selected to be 25 mm. It should be noted that the steel tube thickness was discretized into three layers to avoid possible problems in the calculations.

2.4. Interface Conditions and Boundary Conditions

The Abaqus Surface-to-Surface Contact model was adopted at the interface between the concrete and the steel tube (the steel was the master surface and the concrete was the slave surface). The hard contact relationship was used between the concrete and the steel tube, that is, only the compression of the two materials was considered, and the two materials were prevented from penetrating each other. The sliding between these two materials was simulated based on the Mohr-Coulomb formulation using a penalty function, and the friction coefficient was kept constant at 0.25 [33]. Moreover, the Abaqus Tie Contact model was employed between the steel plate and the entire cross-section of the column. A rigid plate (300 mm × 300 mm × 20 mm) was constructed and tied to the bottom of the concrete column. Reference points were set on the upper surface of the steel tube and the lower surface of the rigid plate and coupled respectively. All degrees of freedom of the bottom reference point were restricted, and all degrees of freedom of the top reference point were released (Figure 4). The service loading was applied by applying an axial displacement, which was set to 35 mm.

2.5. Calculation Models

To investigate the effect of various preloads on the eccentric compressive performance of CFST columns, four representative models simplified from practice (Figure 7) were developed, with preloads applied in different directions for different objects.

First, as shown in Figure 7a, the concrete of CFST-SP relied on the hoop stresses generated in the steel tube by the steel flanges and bolts to obtain an active radial preload (Figure 3b). CFST-SP is a new structure proposed by us. Its manufacturing process is not complicated. First, the steel plate is cut according to the design size and bent into the target shape, then assembled into a tube with high-strength bolts and filled with concrete, finally, the bolts are tightened to apply preload [34]. Figure 7b, however, showed a self-stressing concrete filled steel tube column, for which the concrete had an active three-way compressive preload during its outward expansion. The application of CFST-CP is relatively mature, and many scholars have also conducted relevant research on self-stressing concrete [35,36]. In this study, the temperature was applied directly to the steel tube of CFST-SP and the concrete of CFST-CP, with reliance on the temperature difference to achieve the active preloads; so, it was not necessary to simulate the flange and bolts of CFST-SP. Similarly, as shown in Figure 7c, for the passively preloaded column CFST-CC, only the concrete was subjected to pre-compression. Additionally, as shown in Figure 7d, for CFST-SC, only the steel tubes were subjected to pre-compression. These two models were derived from the engineering cases in Figure 1b,c.

2.6. Verification of the Finite Element Model

The finite element models for ordinary CFST columns and preloaded CFST columns under compression were validated by comparing the peak loads and the load-deformation curves determined by numerical calculations with the experimental results (Table 2 and Figure 8). As shown in Table 2, D, t, and l represent the diameter of the CFST, the thickness of the steel tub, and the full length of the specimen, respectively. f_cu and f_y are the cubic compressive strength of the concrete and the yield strength of the steel, respectively. Previous studies [11,15,23,37,38,39,40] conducted ordinary CFST and experimental/numerical research on preloaded CFST in compression. In general, a column with L/D ≤ 4 is defined as a short column. The above specimens approximated short columns and were similar to the model analyzed in this study. Therefore, these specimens were suitable for validation to confirm the correctness of the model.

In Table 2, the peak loads determined from the finite element simulations (P_FEM) are compared with the experimental/numerical peak loads (P_Lit). A mean value (P_FEM/P_LIT) of 0.999 and a coefficient of variation (CoV) of 0.094 were obtained. The load-deformation responses of some typical specimens are shown in Figure 8, which includes four representative models and the abovementioned ordinary CFSTs. As can be seen from the figure, the finite element simulation results are not completely consistent with the test results. This may be because the finite element simulation is carried out under ideal conditions, while in reality there may be problems such as plastic yielding of steel bars, shrinkage creep of concrete, interface contact, and initial defects of the specimen, which lead to deviations between the simulation results and the test results. However, in general, the initial stiffness values, peak loads, and post-limit behavior (dashed lines) obtained by the finite element simulation are basically consistent with the results of the literature and this study (solid lines). Therefore, we believe that the finite element model can provide accurate calculation results.

In practice, the effect of shrinkage on solid concrete cannot be ignored. In calculations, the shrinkage deformation of concrete can be simulated by relying on its temperature drop. According to reference [41], the dry shrinkage of concrete is approximately equivalent to the shrinkage of concrete at a temperature drop of 10–15 °C. The calculated results for the model with consideration of the temperature shrinkage and the test results are shown in Figure 8. The results showed that the curves for the model with consideration of concrete shrinkage and the model without consideration of concrete shrinkage almost overlapped, indicating that concrete shrinkage had very little effect on the tested specimens. Consequently, all the subsequent analytical calculations did not need to consider concrete shrinkage.

3. Definition of the Specimens

3.1. Influencing Parameters

To quantitatively compare the performance of the preloaded CFST columns, five determining factors had to be considered, which were the preloading methods, eccentric ratio (e/r), concrete cubic compressive strength (f_cu), steel yield strength (f_y), and steel tube thickness (t). Except for the abovementioned four representative preloaded CFSTs, the remaining four categories of influencing factors were 0.2, 0.5, 0.8, and 1.1 for the eccentric ratio [42], C25, C35, and C45 for the concrete cubic compressive strength, 275 MPa, 355 MPa, and 420 MPa for the steel yield strength, and 2 mm, 4 mm, and 6 mm for the steel thickness. Additionally, consistent with Milan’s work, the diameter and the full length of the specimen were 250 mm and 1000 mm, respectively.

3.2. Application of Preloads

All four preloaded specimens were slightly deformed before the application of the service load, although the direction of the applied preload and the object to which the preload was applied differed, the initial strain had the same magnitude. For the selection of the preload value, the preload applied to the steel tube concrete should be within the yield range. In addition, this study is dedicated to discussing the performance of each preload specimen for a small value of preload, according to reference [43], the applied preload should not exceed 0.5 $f_y$. Therefore, the prestress value is assumed to be 0.2 εy. For CFST-SP, the deformation was a hoop for steel. For CFST-CP, the deformation was a three-way expansion for concrete. For CFST-CC, the deformation was longitudinal for concrete, and for CFST-SC, the deformation was longitudinal for the steel tube.

Although the direction of the applied prestress and the object of the prestressing force were different, the initial strain had the same magnitude, and because the standards of various countries limit the prestressing stress of steel pipes to 0.5–0.6 fy, it was assumed to be 0.2 ${\epsilon }_y$. For CFST-SP, the deformation is the circumferential deformation of the steel bar. For CFST-CP, the deformation is the triaxial expansion of the concrete. For CFST-CC, the deformation is the longitudinal deformation of the concrete, and for CFST-SC, the deformation is the longitudinal deformation of the steel pipe.

As far as CFST-SP was concerned, when the hoop tensile strain of the steel tube was 0.2 ε_y (Figure 9a), the steel-concrete contact pressure p₀ could be determined with the following formulas:

(a) Assuming no vertical slip between concrete and steel tube, the longitudinal strains of the concrete $\left({\epsilon }_{cz}\right)$ and the steel tube $\left({\epsilon }_{sz}\right)$ were equal; so,

(5)${\epsilon }_{cz}={\epsilon }_{sz} ,$

(b) According to equilibrium theory, the vertical internal forces in the cross-section of the steel tube and the concrete were equal in magnitude and opposite in direction. In the expressions below, A_c and A_s are the cross-sectional areas of the steel tube and the concrete, respectively, while ${\sigma }_{cz}$ and ${\sigma }_{sz}$ are the normal stresses of the cross-sections in the steel tube and the concrete, respectively.

(6)${\sigma }_{cz}{A}_c={\sigma }_{sz}{A}_s;$

(7)${\displaystyle \frac{ {\sigma }_{cz}}{{\sigma }_{sz}}}={\displaystyle \frac{A_s}{A_c}}.$

(c) According to the generalized Hooke’s Theorem, the expression for steel, is shown in Figure 9b, as follows:

(8)${\epsilon }_{sz}={\displaystyle \frac{1}{E_s}}\left({\sigma }_{sz}-{\mu }_s{\sigma }_{sh}\right);$

(9)${\epsilon }_{sh}={\displaystyle \frac{1}{E_s}}\left({\sigma }_{sh}-{\mu }_s{\sigma }_{sz}\right).$

The expression for concrete, is shown in Figure 9c, is as follows:

(10)${\epsilon }_{cz}={\displaystyle \frac{1}{E_c}}\left(\left(-{\sigma }_{cz}\right)-{\mu }_c\left(-p_0-p_0\right)\right)={\displaystyle \frac{1}{E_c}}\left(2p_0{\mu }_c-{\sigma }_{cz}\right),$

In the expression, ${\epsilon }_{sh}=0.2 {\epsilon }_y$, and D is the diameter of the specimen. $E_c$ and $E_s$ are the elastic modulus of concrete and steel, respectively, ${\mu }_c$ and ${\mu }_s$ are the elastic Poisson’s ratios of the concrete and steel, respectively, and ${\sigma }_{sh}$ is the hoop stress of the steel tube.

(d) The relationship between p₀ and σ_sh (Figure 9d) is as follows:

Equations (5)–(10) were solved to obtain the longitudinal stress of the steel tube:

(11)${\sigma }_{\mathrm{sz}}={\displaystyle \frac{\left(\frac{4E_{\mathrm{s}}t{\mu }_c}{E_{\mathrm{c}}D}+{\mu }_{\mathrm{s}}\right)E_{\mathrm{s}}{\epsilon }_{\mathrm{sh}}}{\left(1+\frac{E_{\mathrm{s}}{A}_{\mathrm{s}}}{E_{\mathrm{C}}{A}_{\mathrm{C}}}\right)-\left(\frac{4E_{\mathrm{s}}t{\mu }_{\mathrm{c}}}{E_{\mathrm{c}}D}+{\mu }_{\mathrm{s}}\right){\mu }_{\mathrm{s}}}},$

The hoop stress of the steel tube is given by

(12)${\sigma }_{sh}=E_s {\epsilon }_{sh}+{\mu }_s{\sigma }_{sz},$

The p₀ is given by

(13)$p_0={\displaystyle \frac{2{\sigma }_{sh}t}{d}},$

After substituting Equation (12) into Equation (13), p₀ = 5 MPa was obtained (Figure 9e).

In Abaqus, the hoop pre-stress was determined using a fictitious temperature reduction (∆T) of the steel tube. To avoid axial concrete-steel interaction, the steel longitudinal thermal expansion coefficient was set to zero. The required temperature reduction was obtained from a simple formulation: σ_sh = α_s∆T, where α_s and E_s are the thermal expansion coefficient and the elastic modulus of steel, respectively (α_s = 10⁻⁵ °C⁻¹). Based on the above formulas, a temperature reduction of ∆T = 60 °C was determined.

For CFST-CP, when the concrete expanded in three directions, the steel tube stretched in three directions, with the assumption of a hoop strain and longitudinal tensile strain of 0.2 ε_y for the steel tube (Figure 10). According to the above formulas, it was known that ${\epsilon }_{sh}={\epsilon }_{sz}=0.2 {\epsilon }_y$, and the steel tube and the concrete had a pre-contact pressure of 6.2 MPa. The coefficient of thermal expansion of the concrete was set to 0.8 × 10⁻⁵ °C⁻¹, and the concrete warming of 63 °C was obtained.

For CFST-CC and CFST-SC, the compressive strain of concrete and steel was 0.2 ε_sy, which meant that compressive preloads of 650 kN and 385 kN were applied to the concrete core (Figure 11a) and the steel tube (Figure 11b), respectively.

3.3. Loading Steps

In this study, as shown in Table 3, loads were applied to the models in two steps. Step 1 corresponded to the initial preloading, and Step 2 corresponded to the service loading. These two loading steps were sequential and superimposed; so, Step 2 was performed only after the completion of Step 1. Additionally, to deal with the above nonlinear problems, longitudinal displacements (ΔL) were applied instead of compressive force in order to monitor the results more accurately.

4. Finite Element Analysis and Discussions

4.1. Load-Displacement History for Different Preloading Methods

In this study, the preloaded specimens with an eccentric ratio of 0.2 were taken as an example, with a concrete cubic compressive strength of C25 (25 MPa), a steel yield strength of 275 MPa, and a steel thickness of 2 mm. To explore the longitudinal load-displacement response of CFST columns with different preloads, an ordinary CFST column was utilized as the reference for comparison. In Figure 12, the vertical coordinate is the longitudinal load, which includes longitudinal preload and service load, while the horizontal coordinate is the longitudinal deformation along the direction of the eccentric load. In the curves, “•” represents the peak load (P_u) of the curve, and “Δ” and “ο” denote 0.75 P_u, and 0.85 P_u, respectively. Moreover, the peak loads of the columns, the peak load ratios (a ratio of the peak load of a preloaded column to that of the ordinary CFST), and the ductility indexes are listed in Table 4.

According to Figure 12, all the curves included increment and decrement segments. However, each curve had a unique property due to the preloading in Step 1. As can be seen from Figure 12a and Table 4, CFST-SP had a higher peak load. This phenomenon could be ascribed to the influence of the active preload in the first step. In Step 1, the steel tube squeezed the concrete, making the steel and concrete work together in advance, while at the same time, according to equilibrium theory, CFST-SP was not loaded longitudinally at this step. Step 2 started with the respective initial stresses in the concrete and the steel tube. When the concrete in the compression bending zone was compressed by the initial radial preload and the service load, the local compressive strength of the concrete increased, which ultimately led to a slight increase in the peak load of CFST-SP compared to the ordinary CFST.

As can be seen from Figure 12b, the peak load of CFST-CP appeared earlier than that of the ordinary CFST and had a peak load ratio of 1.15, which was the highest among the specimens. This was because, in the first step, the concrete was subjected to three-way pre-pressure due to the outward expansion of the self-stress concrete, which was constrained by the steel tube. In the second step, when CFST-CP was subjected to the servicing load, the concrete in the compression bending zone of the section had higher compressive strength, resulting in the highest load-bearing capacity for CFST-CP.

Similar to CFST-CP, the concrete for CFST-CC was pre-compressed (Figure 12c). In Step 1, the preload was large and the concrete underwent early compression in three directions. In Step 2, the passive longitudinal compression of the concrete in the compression bending zone activated the confining effect of the steel tube and the concrete, ensuring that the two parts were tightly bonded from the beginning. As a result, the peak load for CFST-CC increased and reached its peak early but weakened its service load due to the excessive compressive preload.

When the longitudinal pre-compression was applied to the steel tube only, the peak load of the CFST-SC column was only 0.96 times that of the ordinary CFST column (Figure 12d and Table 4). In Step 1, only the steel tube was subjected to the longitudinal load, and its small lateral deflection caused the interface between the tube and the concrete to separate. In Step 2, although the peak load on the CFST-SC column was slightly lower than those of the other specimens, the concrete in the compression bending zone gradually expanded as the service load increased. When the deformation of the concrete increased faster than that of the steel tube, the confinement effect was enhanced. Therefore, the later curve of CFST-SC almost coincided with that of the ordinary CFST column.

To discuss the ductile properties of different preloaded CFST specimens, the ductility index (μ = ∆₂/∆₁) was introduced, as shown in Figure 13. As shown in Table 4, in comparison to the ordinary CFST column, CFST-SC had the largest ductility index because the interaction between the concrete and the steel worked later than those of the other specimens. Thus, the curve softened slowly. In contrast, the softening of the second half of the CFST-CP curve was evident, and therefore, the ductility index was the lowest.

4.2. Stress on Components

4.2.1. Step 1: Preloading Stage

The longitudinal stress cloud for the steel tube and concrete in Step 1 is shown in Figure 14. Because of the assumed low preload, all of the specimens were in the elastic phase. In addition, Figure 15 depicts the contact stresses between the concrete and the steel tube. As can be seen from the figure, the contact stress in the actively preloaded specimens CFST-SP and CFST-CP was always higher than that in the passively preloaded specimens, particularly in CFST-SP, for which the contact stresses were almost zero due to insufficient restraint. In summary, while the preload-induced stresses might have been minor, they might have had a considerable impact on the performance of the preloaded specimens in Step 2.

4.2.2. Step 2: Service Loading Stage

Concrete Stress-Strain

Figure 16 shows the longitudinal stress-strain curve for each concrete unit in the middle cross-section of the specimen, with the number of each unit in the concrete cross-section indicated. In the curve, the symbol “•” represents the peak load on the specimen. The horizontal axis represents strain and the vertical axis represents stress.

Although the active preload was not substantial for CFST-SP and CFST-CP, the concrete strength was enhanced, as seen in the graph. Furthermore, for CFST-CC, even though the pre-compression was passively applied, the concrete was subjected to an initial three-way compression, resulting in a slight increase in the concrete’s strength in the bending compression zone compared to the ordinary CFST. For CFST-SC, however, it can be seen from the diagram that the concrete initial stiffness in each CFST-SC unit was lower due to the absence of steel tubes working together, while the peak stresses in the concrete were also the lowest compared to the other specimens, even lower than those in the ordinary CFST. Finally, it is worth noting that the concrete in the CFST-SP compression bending zone reached its maximum at the same time that the specimen reached its peak load.

Steel Stress-Strain

The biaxial stresses in the steel tube in Step 2 were also influenced by the preload in Step 1. The evolution of the longitudinal and hoop stress-strain curves, as well as the Von Mises curve for the steel tube, is shown in Figs. 17 and 18. In the figures, the characters “C” and “T” denote the compressive and tensile bending zones, respectively, and the symbol “•” denotes the peak load in the curve. First, as shown in Figure 17, the steel tube started as longitudinal compressive stress in the tensile bending zone due to the small eccentric ratio and became longitudinal tensile stress as the load increased. This characteristic was consistent with the ordinary CFST. Second, at the beginning of Step 2, the hoop stresses in CFST-SP, CFST-CP, and CFST-CC were non-zero, with CFST-CP being the largest, due to the highest active radial compression in CFST-CP. In contrast, the initial hoop stress in CFST-SC was zero, which was attributed to the lag in the steel tube confinement effect caused by the compressive pre-stress in the steel tube. The von Mises evolution shown in Figure 18 could better elucidate the development of the bi-directional stresses in the steel tube. As can be seen from the graph, the Von Mises stress in the compressive bending zone of the steel tube only yielded when CFST-SP and CFST-CP reached their peak loads, while CFST-CC and CFST-SC reached their peak loads only after the Von Mises stress in the compressive bending zone yielded. Compared to the ordinary CFST, the steel tube of CFST-SC exhibited significant ductility in the compressive bending zone.

Concrete-Steel Interface Stresses

Figure 19 shows the development of contact stresses at the concrete-steel interface in the tensile and compressive bending zones in Step 2. First, it can be seen from the graphs that the stresses in both zones changed in a similar way. Second, the preloaded specimens, except for CFST-SC, started at Step 2 with non-zero interfacial stresses. As the load increased, the contact stresses in the specimens all increased. However, the stress curves of CFST-SP and CFST-CP suddenly drop and then rise. The reason for this phenomenon is that the Poisson’s ratio of steel is larger than that of concrete, so the deformation of the steel pipe is also larger than that of concrete in the early stage of service loading. However, because we applied preload, the steel pipe was already in close contact with the concrete (initial contact stress), and the deformation of the steel pipe and concrete after service loading was different, which made them less tightly combined at most, which was manifested as a decrease in contact stress, but they could still work together all the time (contact stress > 0). As the service loading increases, the two are closely combined again, and the contact stress increases.

Finally, it was evident that despite the different initial stresses in the preloaded CFSTs, the later stages (after peak load) of all the curves overlapped with the normal CFST curve and developed gently, indicating that the preload did not affect the later development of the contact stress.

5. Parametric Studies

5.1. Load-Bearing Capacity Ratio

Figure 20a–c reflect the effects of the concrete compressive strength, steel yield strength, and steel thickness on the compressive load-bearing capacity of the preloaded CFST columns, respectively. The horizontal coordinates in the figure represent the eccentricity of the specimen, and the vertical coordinates represent the load-bearing capacity ratios. P represents the peak load ratio, and S represents the maximal service load ratio, i.e., the ratio of the peak load of the preloaded CFST to the load-bearing capacity of the ordinary CFST and the ratio of the maximal service load of the preloaded CFST to the load-bearing capacity of the ordinary CFST.

As can be seen from the graph, for CFST-SP and CFST-CP, the peak load ratios of the specimen were always greater than 1.0 when the eccentric ratio increased, which meant that the load-bearing capacities of CFST-SP and CFST-CP were always higher than that of the ordinary CFST, regardless of the influences of the eccentric ratio, concrete strength, steel yield strength, and steel thickness. Additionally, the ratio values of the specimens were uniform and that of CFST-CP was slightly higher than that of CFST-SP. For CFST-CC, the peak load ratio increased significantly when the eccentricity increased, even beyond 2.0. When the concrete strength increased, the rate of change of the peak load ratio was almost the same, but for the steel tube strength and thickness, the rate of change decreased with the increase in grade, especially for the steel tube thickness. This was because the lower the steel tube strength and the steel tube thickness of the ordinary CFST were, the lower the confinement effect was. When the eccentric ratio increased, its compressive load-bearing capacity was very small. Due to the pre-three-way compressive effect, the load-bearing capacity of CFST-CC increased, and its peak load ratio with the ordinary CFST was more prominent. Finally, for CFST-SC, regardless of the grade of the influencing factor, the peak load ratio increased with the increase in the eccentric ratio, and when the eccentric ratio was greater than or equal to 0.5, the peak load ratio was greater than 1.0, with a maximum of approximately 1.20. The peak load ratios of the concrete strength, steel tube strength, and steel tube thickness followed approximately the same trend as the grade increased. However, in general, the rate of change of the peak load ratio was lower for CFST-SC than for CFST-CC. It can also be found from Figure 20 that although the peak load ratios of CFST-SC and CFST-CC were almost always greater than 1.0, i.e., the peak load was higher than that of the ordinary CFST, the maximal service loads were always lower than that of the ordinary CFST. Additionally, when the pre-strain was 0.2 ε_y, the maximal service load was always approximately 90% of the peak load of the ordinary CFST.

5.2. P-M Curves

To further evaluate the eccentric compressive performance of the preloaded CFST, the M-P envelope curves of the specimen considering the effects of different concrete strengths, steel strengths, and steel thicknesses were compared with the M-P envelope curves of the ordinary CFST. The corresponding results are shown in Figure 21, where M and P represent the bending moment and the axial force at the bottom section of the specimen, respectively. As shown in Figure 21, the M-P curves of CFST-SP and CFST-CP were more obviously convex than those of the ordinary CFST, and the carrying capacity of CFST-SC was slightly lower than that of the ordinary CFST. However, the difference between CFST-CC and the ordinary CFST was not obvious. Figure 22 interprets Figure 21 in terms of two different ratio indicators, which are given by

a₁ = (P_max − P_{max (CFST)})/P_max(CFST),(14)

a₂ = (M_max − M_max(CFST))/M_max(CFST), (15)

In the expression, a₁ represents the difference ratio of the maximum axial force between the preloaded specimen and the ordinary CFST. Similarly, a₂ represents the difference ratio of the maximum bending moment between the preloaded specimen and the ordinary CFST.

As can be seen from Figure 22, both CFST-SP and CFST-CP showed a significant increase in the maximum compressive and flexural load capacity, especially CFST-CP. Surprisingly, the difference ratios for CFST-CC were mostly positive, indicating that smaller passive preloads of concrete were not always detrimental to the carrying capacity. For CFST-SC, the restraining effect of the steel tube on the concrete lagged because the preload was only applied to the steel tube, resulting in reductions in the carrying capacity.

Figure 22a shows the effects of the concrete strength, steel tube strength, and steel thickness on a₁ for different specimens. It can be seen from the figure that except for CFST-CP, changing the parameter grades had very little effect on a₁. The variation of a₂ shown in Figure 22b was more complex compared to that of a₁. For CFST-SP and CFST-CP, the effect of the parameter grade on a₂ was small, but for CFST-SC and CFST-CC, the effect of the parameter grade on a₂ was more evident. For CFST-CC, a₂ decreased with the increasing concrete strength and even became negative. This phenomenon indicated that the greater the concrete strength was, the greater the preload was, and according to the principle of static equilibrium, the maximum bending moment became smaller instead and was even lower than that of the ordinary CFST. However, a₂ increased with the increasing steel strength and thickness, which indicated that with the increase of the confinement coefficient related to the steel strength and thickness, the CFST-CC concrete strength in the compression bending zone was improved and the maximum bending moment was enhanced. Finally, for CFST-SC, the effect of the preload on the maximum bending moment was negative for any change in the parameter grade, with concrete strength and steel tube strength being the most prominent, and the pattern of change was consistent with that of CFST-CC.

6. Conclusions

In this study, a comprehensive comparison of the compressive behavior of four representative CFST columns with active and passive preloads was carried out using the finite element method. The model we established can accurately predict the mechanical behavior of steel tube concrete columns under eccentric compression. The results show that the model is accurate and reliable and can be used for further parameter analysis. The conclusions of the study are summarized below.

(1) When the four representative preloaded CFST columns were subjected to compression loads with an eccentricity of 0.2, the peak loads of CFST-CP, CFST-SP, and CFST-CC are 3244 kN, 3020 kN and 2977 kN, which are 1.15 times, 1.04 times and 1.02 times of the peak loads of the ordinary CFST column. The CFST-SC only had 0.96 times the peak load of the ordinary CFST. In terms of ductility, CFST-SC had the highest ductility index of 9.8, and CFST-CP had the lowest ductility index of only 5.4. For the stress-strain relationship between the steel tube and the concrete, the concrete strength increased for CFST-SP and CFST-CP and increased slightly for CFST-CC compared to the concrete in the compression bending zone for the ordinary CFST, but for CFST-SC, the concrete strength was lower than that of the ordinary CFST. Additionally, for the stress-strain relationship of the steel tube, the service loading stage started with CFST- CP having the highest hoop stress and CFST-SP having zero hoop stress, but the steel tube of CFST-SC showed significant ductility in the compression bending zone. Finally, for the contact stresses between the steel tubes and the concrete, the contact stresses increased with the increasing load for all columns from the service loading stage, with only the contact stress curves for CFST-SP and CFST-CP dropping abruptly and then rising again. Furthermore, despite the different initial preloads, the later stages of all the contact stress curves (after the peak load) overlapped with and developed gently with the normal CFST curve.

(2) Different influencing parameters such as the concrete strength, steel tube strength, and thickness had a significant effect on the compressive load capacity of the preloaded CFST columns. For CFST-SP and CFST-CP, the compressive load capacity was always higher than that of the ordinary CFST, the peak load ratio is always within the range of 1.0–1.2. Moreover, no matter how the influencing parameters change, the compressive load capacity of CFST-CP was slightly higher than that of CFST-SP. For CFST-CC, when the eccentricity increased, the peak load ratio increased significantly, even beyond 2.0. The rate of change of the peak load ratio was approximately the same when the concrete strength increased, but for the steel tube strength and thickness, the rate of change decreased with the increasing grade. For CFST-SC, again, the peak load ratio increased with the increasing eccentricity, regardless of the grade of the influencing parameters, and the peak load ratio was greater than 1.0 when the eccentricity was greater than 0.5. The trend in the peak load ratios was approximately the same as the influence parameter grade increased. Finally, it was also found that although the compressive load capacity of both CFST-CC and CFST-SC is higher than that of the ordinary CFST, the actual maximal service load was always lower than that of the ordinary CFST due to the presence of the preload.

(3) The effects of the concrete strength, steel tube strength, and thickness on the M-P envelope curves of the specimens were also prominent. Regardless of the influencing parameters, the M-P curves for CFST-SP and CFST-CP were always significantly more convex than those of the ordinary CFST, and the M-P curve of CFST-SC was less convex than that of the ordinary CFST, but the difference between the curves for CFST-CC and the ordinary CFST was not significant. Additionally, a₁ and a₂ were always positive for CFST-SP and CFST-CP, indicating that the maximum compressive and flexural capacities of both CFST-SP and CFST-CP were significantly improved, especially for CFST-CP. Moreover, a₁ and a₂ were mostly positive for CFST-CC, indicating that smaller passive preloads for the concrete were not always detrimental to the load-carrying capacity. For CFST- SC, both a₁ and a₂ were negative. It is also clear that except for CFST-CP, changing the parameter grade had little effect on a₁. However, the effect of changing the parameter grade on a₂ for CFST-CC and CFST-SC was significant. For CFST-CC, a₂ decreased with the increasing concrete strength and even became negative, but a₂ increased with the increasing steel tube strength and thickness. For CFST-SC, the pattern of variation of a₂ with the influence of concrete strength and steel strength was similar to that of CFST-CC.

Author Contributions

R.D.: Conceptualization, Modeling, Calculating, Graphical Information, Reference Search, Writing—Reviewing and Editing. L.X.: Conceptualization, CFST-Related Issues, Writing—Reviewing and Editing. X.H.: Calculating, Reviewing. Z.C.: Calculating, Reviewing. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

No new data were created or analyzed in this study.

Acknowledgments

We thank our colleagues and friends for their valuable help.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. CFST columns during construction: (a) Concrete-filled steel tubes during building construction [10]; (b) Preloading on the concrete core; (c) Preloading on the steel tube; (d) Preloading on the side of the steel tube [11].

Figure 2. Comparisons of load-deformation relationships for CFST columns for different preloading schemes [11].

Figure 3. CFST with an active preload: (a) Radial preload using rebar and bolts [22]; (b) Radial preload using flanges and bolts [23].

Figure 4. Finite element model of a CFST column. (a) Elevation view; (b) Cross-sectional view.

Figure 5. Uniaxial constitutive laws: (a) concrete; (b) steel.

Figure 6. Specific meshing components: (a) General view; (b) Concrete core; (c) Steel tube; (d) Steel plate.

Figure 7. Preloaded CFST calculation models.

Figure 8. Validation based on the models from the literature: (a) CFST; (b) CFST-SP; (c) CFST-CP; (d) CFST-SC; (e) CFST-CC.

Figure 8. Validation based on the models from the literature: (a) CFST; (b) CFST-SP; (c) CFST-CP; (d) CFST-SC; (e) CFST-CC.

Figure 8. Validation based on the models from the literature: (a) CFST; (b) CFST-SP; (c) CFST-CP; (d) CFST-SC; (e) CFST-CC.

Figure 9. CFST-SP with active preloading: (a) Model; (b) Steel; (c) Concrete; (d) Cross-section of steel tube; (e) Cross-section of concrete core.

Figure 10. CFST-CP with active preloading.

Figure 11. CFST-CC and CFST-SC with passive preloading: (a) CFST-CC; (b) CFST-SC.

Figure 12. Longitudinal load versus displacement curves: (a) CFST-SP; (b) CFST-CP; (c) CFST-CC; (d) CFST-SC.

Figure 13. Ductility index.

Figure 14. Stress clouds of steel and concrete in Step 1: (a) Longitudinal stress of steel tube; (b) Longitudinal stress of concrete.

Figure 15. Concrete-steel interface stresses in Step 1.

Figure 16. Longitudinal stress versus strain curves of the concrete.

Figure 17. Stress versus strain of steel tube: (a) CFST-SP; (b) CFST-CP; (c) CFST-CC; (d) CFST-SC.

Figure 18. Von Mises yield curves: (a) CFST-SP; (b) CFST-CP; (c) CFST-CC; (d) CFST-SC.

Figure 19. Concrete-steel interface stresses in Step 2: (a) Tensile bending zone; (b) Compressive bending zone.

Figure 20. Effect of various parameters on the load-carrying capacity: (a) Effect of the concrete compressive strength; (b) Effect of the steel yield strength; (c) Effect of the steel thickness.

Figure 20. Effect of various parameters on the load-carrying capacity: (a) Effect of the concrete compressive strength; (b) Effect of the steel yield strength; (c) Effect of the steel thickness.

Figure 21. Effect of various parameters on M-P interaction diagram: (a) Effect of concrete strength; (b) Effect of steel strength; (c) Effect of steel thickness.

Figure 21. Effect of various parameters on M-P interaction diagram: (a) Effect of concrete strength; (b) Effect of steel strength; (c) Effect of steel thickness.

Figure 22. Effect of various parameters on difference ratio: (a) Difference ratio about α1; (b) Difference ratio about α2.

Table 1

Material properties of CFST specimens.

Material	Density (kN/m3)	Elastic Modulus (MPa)	Elastic Poisson’s Ratio
Concrete	23.5	2.73 × 104	0.18
Steel tube	78.5	2.0 × 105	0.29

Table 2

Comparison between FEM analysis and literature results.

Model	Specimen Label	D/t/l (mm)	Eccentricity(mm)	fcu(MPa)	fy(MPa)	PLIT(kN)	PFEM(kN)	PFEM/PLIT
Zhao XL [37]	C2	273/6/850	40	36.8	325	2504	2490	0.994
	C3	273/6/850	80	36.8	325	2161	2158	0.999
Chen BC [38]	B4	219/4/1000	75	49.3	325	986.9	1055	1.069
	C5	219/4/1000	100	54.1	325	825.2	875	1.060
Sun JP [23]	C40T20(6)	179/2/350	0	40	235	1155	1149	0.995
	C40T40(2)	183/4/350	0	40	235	1327	1511	1.139
	C40T20(2)	179/2/350	0	40	235	1072	1151	1.074
Li N [39]	t2.5-a	160/2.5/500	0	45.3	327.5	1600	1593	0.996
	t2.5-b	160/2.5/500	0	53.9	305.3	1690	1610	0.953
Johansson M and Gylltoft K [15]	SFC	650/4.5/324	0	79.4	443	2201	2240	1.018
Huang [40]	SA	108/4/324	0	54.9	336	1228	1212	0.987
Milan [11]	CFST-1-SC	250/6/1000	0	25	275	3658	3337	0.912
	CFST-1-CC	250/6/1000	0	25	275	3664	3341	0.912
Mean value	1.008
CoV	0.065

Table 3

Loading steps.

Step Number	Specimen	Load Value	Component	Direction
Step1-preloading	CFST-SP	−60 °C	Steel	Hoop tension
	CFST-CP	+63 °C	Concrete	Three-way expansion
	CFST-CC	0.2 εsy	Steel	Longitudinal compression
	CFST-SC	0.2 εsy	Concrete	Longitudinal compression
Step2-service loading	All specimens	ΔL = 35 mm	The whole section	Compression

Table 4

Load-bearing capacity ratio and ductility index (μ).

Specimen	e/r	Pu (MPa)	Peak Load Ratio	Δu (mm)	Δ1 (mm)	Δ2 (mm)	μ
CFST-SP	0.2	3020	1.04	3.2	1.0	7.1	7.1
CFST-CP		3244	1.15	2.0	1.1	5.9	5.4
CFST-CC		2977	1.02	2.1	0.8	7.5	9.4
CFST-SC		2751	0.96	3.4	0.9	8.8	9.8
CFST		2811	1.00	3.2	1.1	8.5	7.7

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