Numerical Evaluation of Embedded I-Section Strengthening in Axially Loaded Composite Concrete-Filled Stainless Steel Tubes

Abstract

To enhance the structural performance of concrete-filled steel tube (CFST) columns, various strengthening techniques have been proposed, including the use of internal steel stiffeners, external wrapping with carbon fiber-reinforced polymer (CFRP) sheets, and embedded steel elements. However, the behavior of concrete-filled stainless-steel tube (CFSST) columns remains insufficiently explored. This study numerically investigates the axial performance of square CFSST columns internally strengthened with embedded I-section steel profiles under biaxial eccentric loading. Finite element (FE) simulations were conducted using ABAQUS v. 6.2, and the developed models were validated against experimental results from the literature. A comprehensive parametric study was performed to evaluate the effects of several variables, including concrete compressive strength (f_cu), stainless-steel yield strength (f_y), the depth ratio between the stainless-steel tube and the internal I-section (D_st/D_si), biaxial eccentricities (e_x and e_y), and tube thickness (t). The results demonstrated that the axial performance of CFSST columns was most significantly influenced by increasing the D_st/D_si ratio and load eccentricities. In contrast, increasing the concrete strength and steel yield strength had relatively modest effects. Specifically, the ultimate axial capacity increased by 9.97% when the steel yield strength rose from 550 MPa to 650 MPa and by 33.72% when the tube thickness increased from 3.0 mm to 5.0 mm. A strength gain of only 10.23% was observed when the concrete strength increased from 30 MPa to 60 MPa. Moreover, the energy absorption index of the strengthened columns improved in correlation with the enhanced axial capacities.

1. Introduction

The growing demand for high-rise buildings and resilient structural systems capable of withstanding severe lateral forces from wind and seismic events has accelerated the adoption of composite steel–concrete systems [1,2]. Among these, Concrete-Filled Steel Tubular (CFST) columns have emerged as a widely used structural form, offering a combination of high compressive strength, ductility, and ease of construction [3,4]. An advanced variant of these systems is the Concrete-Filled Stainless-steel Tubular (CFSST) column, which provides additional advantages such as superior corrosion resistance, aesthetic surface finish, and improved fire performance compared to conventional carbon steel CFST members [5]. In addition to their structural advantages, CFSST members can be more economically and environmentally favorable over their service life. Despite the higher initial material cost, superior corrosion resistance reduces maintenance and repair needs, lowering lifecycle costs. Enhanced durability also minimizes replacement frequency, thereby reducing raw material consumption and construction waste generation.

Extensive research has been conducted on the behavior of CFST columns, confirming the composite interaction between the steel tube and concrete core, which enhances both the axial and flexural capacities while mitigating local buckling [6,7]. In particular, Tokgoz et al. [8] investigated the response of eccentrically loaded CFSST composite columns under combined axial compression and biaxial bending. The study involved two series of specimens composed of I- and T-shaped structural steel sections filled with either plain or steel fiber-reinforced concrete. Variations in load eccentricity and concrete strength were introduced, and a theoretical model was developed to predict strength and deformation. Results confirmed the ductile behavior of CFSST columns and the beneficial role of infill concrete and steel fibers in restraining local buckling. Manikanta et al. [9] explored the axial compressive behavior of circular CFSST stub columns using finite element (FE) analysis in ABAQUS. Their findings demonstrated that increasing the column aspect ratio significantly enhances load-bearing capacity, with failure modes characterized by inward local buckling of the steel tube. Surface cracking and the superior performance of stainless-steel indicated the suitability of CFSST columns for demanding environments and high-performance structures. Further nonlinear FE investigations were performed by Hassanein et al. [10] on circular CFSST columns. The study modeled the steel tube using S3 shell elements and the concrete core using C3D4 solid elements in ABAQUS. Rigid end plates were applied to simulate realistic boundary conditions. The analysis led to recommended refinements to the Eurocode design provisions, particularly regarding the buckling behavior of thin-walled stainless-steel tubes. Kazemzadeh Azad et al. [11] conducted a comprehensive numerical study on compact and slender CFSST box sections subjected to various loading scenarios. The columns were classified based on loading and geometric configurations, and numerical modeling was performed using S4R shell elements for the steel tube and C3D8R solid elements for the concrete. The study introduced mesh optimization techniques and provided improved design formulas for axial compression and pure bending, accounting for local buckling and member slenderness.

Recent work by Jun Chen et al. [12] provided an extensive numerical and experimental evaluation of steel–concrete composite tubes under various loading conditions. This study emphasized the influence of material grade, tube geometry, and connection detailing on the overall performance, highlighting the superior load-carrying capacity, ductility, and energy dissipation of composite tubes compared to conventional systems. Furthermore, optimization approaches for tube thickness, diameter-to-thickness ratios, and reinforcement detailing were presented, offering valuable guidance for the efficient design and practical application of composite tube systems in modern engineering.

The study by Jinan and Allawi [13] examined the structural behavior of medium–long, square, high-strength concrete-filled steel tubular columns fabricated from ultra-thin, high-strength steel tubes. The research, involving 15 test specimens, evaluated the effects of slenderness ratio, loading eccentricity, and the presence of internal steel reinforcement cages. Results revealed that ultra-thin high-strength tubes provide effective confinement to concrete; however, their restraint capacity decreases with increasing eccentricity. The introduction of a transverse steel-bar-dominated internal cage mitigated bulging and enhanced confinement, though it could not entirely prevent failure. Recognizing the limitations of existing predictive formulas, the authors proposed a modified equation for axial compression capacity, achieving accurate predictions for biaxial eccentric loading cases.

Key parameters affecting the axial performance of CFST and CFSST columns include the diameter-to-thickness ratio (D/t), concrete compressive strength (f’_c), steel tube yield strength, slenderness ratio, and the steel-to-concrete ratio. Prior research has also examined the influence of internal stiffeners, revealing that their arrangement, size, and number can significantly enhance strength, stiffness, and ductility. However, limited research has focused on CFSST columns incorporating internal carbon steel I-sections as embedded stiffeners within the concrete core. The high cost of stainless-steel has contributed to the scarcity of experimental investigations in this area. As such, finite element analysis provides a cost-effective and reliable tool for evaluating the performance of CFSST systems across a broad range of parameters. CFSST columns demonstrate excellent structural performance, especially in terms of load-carrying capacity, ductility, and durability under harsh environmental conditions. These attributes make them ideal for high-rise and infrastructure applications, where long-term performance and reduced maintenance are critical. Nevertheless, further research is needed to refine current design standards and better understand the effects of composite interaction and stiffening mechanisms. Therefore, the objective of this study is to numerically investigate the flexural performance of composite CFSST columns strengthened with embedded carbon steel I-sections under axial and biaxial loading conditions. A validated finite element model is developed based on an experimentally tested specimen. Parametric analyses are subsequently conducted to evaluate the influence of several key variables, including stainless-steel yield strength (f_y), concrete compressive strength (f_cu), the ratio of stainless-steel tube width to embedded steel depth (D_st/D_si), tube wall thickness (t), and load eccentricities (e_x and e_y).

2. Finite Element Modeling

The finite element (FE) models developed in this study are detailed in this section. As a first step, an FE model of the CFSST column was constructed using the geometric dimensions presented in Figure 1, aiming to validate the experimental results reported by Tokgoz et al. [8]. The geometric and material nonlinearity was enabled in the developed model to accurately capture large deformations, nonlinear stress–strain behavior of materials, and potential instability effects under loading.

2.1. Selected Elements and FE Mesh

The three-dimensional finite element (FE) model, along with the applied loading conditions and boundary constraints, is illustrated in Figure 2. The square CFSST column is modelled as a pin-ended member, with both ends restrained to simulate realistic support conditions.

In developing the FE models for square CFSST columns, ABAQUS/CAE provides a comprehensive Element Library under the Standard module, offering a variety of element types suitable for modeling both the infill concrete and the surrounding steel components. For this study, hexahedral elements were selected for all solid materials to ensure accuracy and convergence. The infill concrete was modelled using the 3D solid element C3D8R, which is an 8-node linear brick element with reduced integration and hourglass control, well-suited for capturing nonlinear behavior under compression. The stainless-steel tube and embedded carbon steel I-section were modelled using S4R shell elements, which are 4-node doubly curved shell elements with reduced integration and finite membrane strain capability. These elements offer reliable performance in simulating both thin and thick shell behavior. Each node possesses six degrees of freedom, and bilinear interpolation is applied for displacement and rotation fields, ensuring adequate representation of bending and membrane actions.

In the present study, the concrete and steel were modeled as homogeneous and isotropic materials, a common assumption in finite element analysis aimed at isolating the influence of the main studied parameters. While this approach neglects local variability due to manufacturing defects or environmental degradation, it ensures that the numerical trends are attributable solely to controlled parameter changes. Incorporating spatially varying or stochastic material properties would require additional experimental input and is suggested for future work.

In addition, the geometric nonlinearity was explicitly activated by setting NLGEOM = ON in Abaqus so that second-order P–Δ effects were included in all simulations. The column was modeled as a pin-ended member, as shown in Figure 2 which is represented the boundary conditions of the tested columns.

2.2. Surface Interaction Description

Accurate simulation of surface interaction between the components of the square CFSST column is essential for validating the proposed FE models. In this study, the mechanical interaction between the stainless-steel tube and the concrete core was modeled in ABAQUS using surface-to-surface contact definitions. Contact behavior was characterized by both geometric and mechanical parameters. The inner surface of the stainless-steel tube was assigned as the master surface, while the outer surface of the concrete core was designated as the slave surface, reflecting the relative stiffness of the materials.

For the normal interaction, a “hard contact” condition was applied to allow separation after contact. For the tangential interaction, the “penalty” friction formulation was used with an isotropic friction model. A friction coefficient of 0.8 was adopted for all current models, based on validation results and consistency with prior studies. For comparison, Zheng et al. [14] used coefficients of 0.25 for stainless steel–concrete interfaces and 0.6 for concrete–carbon steel interfaces, while Al Zand et al. [15] used 0.75. The adopted value in this study ensures reliable modeling of interfacial behavior under axial loading, accounting for material properties, cross-sectional geometry, and loading conditions.

The selection of a friction coefficient of 0.8 was the result of a calibration process during FE model validation, testing values within and slightly above literature-reported ranges. The adopted value provided the best agreement with experimental load–displacement results, especially in the post-yield phase. Furthermore, the higher surface roughness observed in the tested stainless-steel tubes due to manufacturing finish and surface treatment supports the physical plausibility of a slightly higher coefficient.

2.3. Constitutive Models of Materials

The constitutive behavior of the steel tube was defined using the same trilinear stress–strain relationship adopted by Al Zand et al. [15], as illustrated in Figure 3. The elastic isotropic material model was used to specify the elastic modulus and Poisson’s ratio, while the plastic isotropic model was employed to define the yield strength and corresponding plastic strain values.

Due to its brittle nature, concrete primarily fails through tensile cracking or compressive crushing. Despite these failure modes, concrete is treated as an isotropic material in the elastic range. Therefore, the elastic isotropic option was used to define its Young’s modulus and Poisson’s ratio, while the damaged plasticity model was employed to capture nonlinear behavior and define compressive strength. The same tension and compression stress–strain relationships used by Al Zand et al. [15] were adopted in this study. As shown in Figure 4, the compressive stress–strain curve assumes linear behavior up to approximately 30% of the ultimate compressive strength (f_cu), after which nonlinear behavior governs.

Table 1. Input parameters for the Concrete Damaged Plasticity (CDP) model.

Dilation Angle (ψ)	K (Shape Factor)	fbo/fco	Viscosity Parameter
35	0.667	1.16	0.00008

summarizes all input parameters used in the Concrete Damaged Plasticity (CDP) model for concrete and the constitutive model for stainless steel, including key CDP constants and other mechanical properties essential for the nonlinear analyses.

2.4. Convergence Study

Once all material properties and modeling parameters were accurately defined, a mesh convergence study was conducted to ensure the reliability of the finite element results. While a finer mesh typically improves accuracy, it also increases computational cost. Therefore, a balance between accuracy and efficiency was sought. Figure 5 presents the relationship between the ultimate load capacity (P_u) and the total number of elements used in the FE models of the square CFSST column, illustrating the effect of mesh density on the predicted structural response.

3. Results and Discussion

3.1. Verification of the FE Results

The finite element (FE) results were validated against the experimental data reported by Tokgoz et al. [8] (2021). The developed FE model, denoted as CFSST-S, was constructed using identical geometric dimensions and material properties as the corresponding tested specimen CFSSTCC-I-1. A comparison of the load–mid-span deflection responses in both the X and Y directions is presented in Figure 6 and Figure 7, respectively. The FE model predicted an ultimate axial load (P_u) of 341 kN, closely matching the experimentally measured value of 350 kN.

In addition to the ultimate load (P_u) comparison, the validation process also considered the full load–deflection response. The numerical curves showed good agreement with the experimental ones in terms of initial stiffness, post-yield slope, and deformation capacity, with deviations generally within 5–10% over the service and ultimate load ranges. This agreement confirms that the model is capable of reproducing not only the strength but also the deformation characteristics observed in the tests.

Figure 8 presents a side-by-side comparison of the buckling behavior obtained from the experimental test (Figure 8a) and the FE analysis (Figure 8b) for the tested CFSSTCC-I-3 column. In the experimental image, local and global buckling can be clearly observed in the mid-height region of the column, indicating the onset of instability under axial loading. The FE model successfully replicates this global buckling mode, with the deformation shape closely matching the experimental observation. The strong agreement between the experimental and numerical results confirms that the FE model can accurately capture the buckling pattern, deformation profile, and damage localization observed in the physical test. This correlation validates the reliability of the FE model for further parametric studies and predictive analyses.

3.2. Parametric Studies

In the present study, the ranges of the investigated parameters were selected based on common engineering practice, relevant design standards (ACI 318 [16], Eurocode 4 [17]), and previously reported experimental programs on stainless steel–concrete composite columns. For instance, the chosen yield strengths (350–650 MPa) cover commercially available stainless-steel grades, while the concrete compressive strengths (30–60 MPa) reflect normal to high-strength concretes used in practice. Similarly, the adopted tube thicknesses (2–5 mm), eccentricity values (5–100 mm), and Dst/Dsi ratios (1.25–2.0) fall within ranges observed in built structures or recommended for design optimization.

Following the validation of the FE model against experimental results, a comprehensive parametric study was conducted to investigate the influence of key parameters on the behavior of square CFSST columns that have not been thoroughly explored experimentally or numerically. The models were divided into five groups, as summarized in

Table 2. Summary of the analyzed models.

Group	Model	fy (MPa)	fcu (MPa)	t (mm)	DSt × DSi (mm)	DSi (mm)	DSt/DSi	ex and ey (mm)
1	CFSST-S-fy550 *	550	60	3	100 × 100	80	1.25	55
	CFSST-S-fy350	350	60	3	100 × 100	80	1.25	55
	CFSST-S-fy450	450	60	3	100 × 100	80	1.25	55
	CFSST-S-fy650	650	60	3	100 × 100	80	1.25	55
2	CFSST-S-fcu60 *	550	60	3	100 × 100	80	1.25	55
	CFSST-S-fcu30	550	30	3	100 × 100	80	1.25	55
	CFSST-S-fcu40	550	40	3	100 × 100	80	1.25	55
	CFSST-S-fcu50	550	50	3	100 × 100	80	1.25	55
3	CFSST-S-Dst/Dsi1.25 *	550	60	3	100 × 100	80	1.25	55
	CFSST-S-Dst/Dsi1.5	550	60	3	120 × 120	80	1.5	55
	CFSST-S-Dst/Dsi1.75	550	60	3	140 × 140	80	1.75	55
	CFSST-S-Dst/Dsi2.0	550	60	3	160 × 160	80	2	55
4	CFSST-S-t3 *	550	60	3	100 × 100	80	1.25	55
	CFSST-S-t2	550	60	2	100 × 100	80	1.25	55
	CFSST-S-t4	550	60	4	100 × 100	80	1.25	55
	CFSST-S-t5	550	60	5	100 × 100	80	1.25	55
5	CFSST-S-e55 *	550	60	3	100 × 100	80	1.25	55
	CFSST-S-e5	550	60	3	100 × 100	80	1.25	5
	CFSST-S-e25	550	60	3	100 × 100	80	1.25	25
	CFSST-S-e75	550	60	3	100 × 100	80	1.25	75
	CFSST-S-e100	550	60	3	100 × 100	80	1.25	100

* Verified control model.

. Group 1 examined the effect of varying the yield strength of the square stainless-steel tube (f_y), ranging from 350 MPa to 650 MPa. Group 2 focused on the influence of the concrete compressive strength (f_cu) of the infill material, with values ranging from 30 MPa to 60 MPa. Group 3 investigated the effect of the depth ratio between the stainless-steel tube and the embedded carbon steel section (D_st/D_si), varying from 1.25 to 2.0. Group 4 studied the impact of the steel tube wall thickness (t), with values ranging from 2.0 mm to 5.0 mm. Group 5 analyzed the influence of load eccentricities (e_x and e_y), considering a range from 5 mm to 100 mm.

These models allowed for a systematic evaluation of each parameter’s role in the axial and biaxial performance of composite square CFSST columns under realistic loading conditions.

3.2.1. Effect of the Stainless-Steel Yield Strength (f_y)

This section investigates the influence of stainless-steel tube yield strength (f_y) on the axial performance of square CFSST columns using FE modeling. The control model (CFSST-S-f_y550), with a yield strength of 550 MPa, was validated against experimental data and used as a benchmark. To assess the impact of varying f_y, three additional models were developed with yield strengths of 350 MPa, 450 MPa, and 650 MPa, designated as CFSST-S-f_y350, CFSST-S-f_y450, and CFSST-S-f_y650, respectively.

The axial load–deflection responses of these models are compared in Figure 9 and Figure 10, which illustrate the mid-span deflections along the X and Y axes. The results indicate that all models exhibit linear elastic behavior up to approximately 75–85% of their respective ultimate load (P_u). Beyond this point, the behavior transitions into an elastic–plastic regime, followed by a gradual decline in load capacity attributed to local buckling under high eccentric axial loads.

As shown in Figure 11 and summarized in

Table 3. The effects of the stainless-steel tube yield strength (f_y).

Model	Ultimate Load, Pu, kN	Change (%)
CFSST-S-fy550	341	-
CFSST-S-fy350	267	−21.7
CFSST-S-fy450	306	−10.26
CFSST-S-fy650	375	9.97

, increasing the yield strength of the stainless-steel tube led to a clear enhancement in the ultimate axial load capacity. For instance, the model with f_y = 650 MPa (CFSST-S-f_y650) reached a peak load of 375 kN, representing a 9.9% increase compared to the control model (341 kN). Conversely, reducing the yield strength to 350 MPa (CFSST-S-f_y350) resulted in a significant decrease in load capacity to 267 kN, a 21.7% reduction relative to the control model. These findings confirm that higher yield strength in the stainless-steel tube substantially improves the axial load-carrying capacity of CFSST columns.

3.2.2. Effect of the Compressive Strength of Concrete (f_cu)

This section investigates the influence of concrete compressive strength (f_cu) on the axial behavior of Concrete-Filled Stainless-steel Tube (CFSST) FE models. The reference model, designated as CFSST-S-f_cu60, uses a concrete strength of 60 MPa and was validated against corresponding experimental results. To evaluate the effect of reduced concrete strength, three additional FE models were developed with f_cu values of 50 MPa, 40 MPa, and 30 MPa, labeled as CFSST-S-f_cu50, CFSST-S-f_cu40, and CFSST-S-f_cu30, respectively.

The axial load–deflection responses of these models are presented in Figure 12 and Figure 13, showing the horizontal mid-span deflections along the X- and Y-axes. The results indicate that all models exhibited linear elastic behavior up to approximately 75–85% of their respective ultimate load capacities (P_u), beyond which an elastic–plastic response was observed until reaching Pu. Post-peak behavior involved a gradual decline in load-bearing capacity, attributed to global buckling under high eccentric axial loading.

Overall, increasing the concrete compressive strength resulted in a clear enhancement in the ultimate axial load capacity. As summarized in Figure 14 and

Table 4. The effects of the concrete compressive strength f_cu.

Model	The Ultimate Load (Pu) kN	Change (%)
CFSST-S-fcu60	341	-
CFSST-S-fcu30	331	−10.35
CFSST-S-fcu40	320	−6.56
CFSST-S-fcu50	309	−3.02

, the control model (CFSST-S-f_cu60) reached a Pu of 341 kN. Reducing f_cu to 50 MPa resulted in a minor reduction of 3.02% in P_u, yielding 309 kN. However, a further decrease in f_cu to 30 MPa led to a more significant reduction of approximately 10.35% in ultimate capacity compared to the control model.

3.2.3. The Effect of Width to Depth Ratio (D_St/D_Si)

This section examines the impact of the width-to-depth ratio of the stainless-steel tube to the embedded carbon steel section (D_st/D_si) on the axial performance of Concrete-Filled Stainless-steel Tube (CFSST) finite element (FE) models. The control model, denoted as CFSST-S-D_st/D_si 1.25, was developed with a D_st/D_si ratio of 1.25 and validated against corresponding experimental results. To assess the influence of increased D_st/D_si ratios, three additional models were analyzed with values of 1.5, 1.75, and 2.0, and labeled accordingly as CFSST-S-D_st/D_si 1.5, CFSST-S-D_st/D_si 1.75, and CFSST-S-D_st/D_si 2.0.

The axial load–deflection behavior of these models is illustrated in Figure 15 and Figure 16, representing horizontal mid-span deflections along the X- and Y-axes, respectively. The results show that all models exhibited linear elastic responses up to approximately 75–85% of their respective ultimate axial capacities (P_u). Beyond this range, the models transitioned into an elastic–plastic phase until reaching P_u, followed by a gradual reduction in load-bearing capacity due to global buckling under eccentric axial loading.

A general trend of increasing axial capacity was observed with higher D_st/D_si ratios, as shown in Figure 17 and summarized in

Table 5. The effects of the width to depth ratio (D_st/D_si).

Model	The Ultimate Load (Pu) kN	Change (%)
CFSST-S-Dst/Dsi 1.25	341	-
CFSST-S-Dst/Dsi 1.5	523	53.37
CFSST-S-Dst/Dsi 1.75	758	122.28
CFSST-S-Dst/Dsi 2.0	1062	137.85

. For instance, the control model CFSST-S-D_st/D_si 1.5 attained an ultimate load of 341 kN. Increasing the D_st/D_si ratio to 1.75 enhanced the axial capacity by approximately 53.37%, reaching 523 kN (CFSST-S-D_st/D_si 1.75). Further increasing the ratio to 2.0 led to a substantial improvement of 137.85% in Pu, achieving a peak load of 811 kN compared to the control model.

3.2.4. The Effects of the Stainless-Steel Tube Thickness (t)—Group 4

This section investigates the influence of stainless-steel tube thickness (t) on the axial performance of Concrete-Filled Stainless-steel Tube (CFSST) finite element (FE) models. The control model, denoted as CFSST-S-t 3, was developed with a tube thickness of 3 mm and validated against corresponding experimental results. To evaluate the impact of varying thicknesses, three additional models were analyzed with tube thicknesses of 2 mm, 4 mm, and 5 mm, labeled as CFSST-S-t 2, CFSST-S-t 4, and CFSST-S-t 5, respectively.

The axial load–deflection behavior of these models is presented in Figure 18 and Figure 19, which depict the horizontal mid-span deflections along the X- and Y-axes. All models exhibited a linear elastic response up to approximately 75–85% of their respective ultimate load (Pu), followed by an elastic–plastic phase leading to Pu. Beyond the peak load, the curves showed a gradual decline, indicating buckling-induced failure under eccentric axial loading.

Overall, increasing the stainless-steel tube thickness resulted in a clear enhancement of the axial load-carrying capacity, as shown in Figure 20 and summarized in

Table 6. The effect of stainless-steel tube thickness on the ultimate load, group 4.

Model	The Ultimate Load (Pu) kN	Change (%)
CFSST-S-t 3	341	-
CFSST-S-t 2	267	−19.06
CFSST-S-t 4	401	21.73
CFSST-S-t 5	456	28.67

. For instance, the control model (CFSST-S-t 3) reached a Pu of 341 kN. Increasing the tube thickness to 5 mm led to an approximate 33.72% increase in Pu, reaching 456 kN (CFSST-S-t 5). Conversely, reducing the tube thickness to 2 mm caused a decrease in Pu by approximately 19.06%, yielding 276 kN compared to the control model.

3.2.5. Effect of the Load Eccentricities (e_x and e_y)

This section explores the influence of load eccentricity (e) on the axial behavior of Concrete-Filled Stainless-steel Tube (CFSST) finite element (FE) models. The control model, designated as CFSST-S-e 55, was developed with an eccentricity of 55 mm and validated against corresponding experimental results. To investigate the effects of varying eccentricities, four additional models were analyzed with eccentricity values of 5 mm, 25 mm, 75 mm, and 100 mm, labeled as CFSST-S-e 5, CFSST-S-e 25, CFSST-S-e 75, and CFSST-S-e 100, respectively.

Figure 21 and Figure 22 present the axial load–deflection responses of these models in terms of horizontal mid-span deflections along the X- and Y-axes. All models exhibited a linear elastic behavior up to approximately 75–85% of their respective ultimate load (P_u), followed by a transition to elastic–plastic behavior until reaching Pu. Beyond this point, a gradual reduction in load-carrying capacity was observed, primarily due to global buckling under increasing eccentric axial loading.

A clear inverse relationship was observed between load eccentricity and axial capacity. As summarized in Figure 23 and

Table 7. The effect of load eccentricities on the ultimate load, Group 5.

Model	The Ultimate Load (Pu) kN	Change (%)
CFSST-S-e 55	341	-
CFSST-S-e 5	1202	252.49
CFSST-S-e 25	617	80.93
CFSST-S-e 75	262	−23.16
CFSST-S-e 100	202	−40.76

, reducing the eccentricity significantly enhanced the ultimate axial strength. For example, the control model (CFSST-S-e 55) achieved a P_u of 341 kN. Reducing the eccentricity to 5 mm resulted in a substantial increase in axial capacity, reaching 1202 kN (CFSST-S-e 5), which represents a 252.49% improvement. In contrast, increasing the eccentricity to 100 mm led to a significant reduction in strength, with P_u decreasing by approximately 40.76% compared to the control model.

To explicitly account for second-order effects, moment–curvature profiles were extracted from the FE results for five representative eccentricities (ex and ey = 5, 25, 55, 75, and 100 mm). As illustrated in Figure 24 and Figure 25 for bending about the X- and Y-axes, respectively, increasing eccentricity led to greater lateral deflections and a reduction in ultimate capacity. This reduction is attributed to the amplification of second-order moments (P–Δ effects), which become more pronounced as eccentricity increases.

Although no dedicated imperfection-sensitivity analyses were performed, geometric nonlinearity (NLGEOM = ON) was incorporated in all models to capture second-order P–Δ effects. Prior studies on short or stubby CFST and CFSST columns [18] have shown that eigenmode-affine imperfections in the range of L/2000–L/1000 typically reduce ultimate strength by only a few percent (2–5%) without changing the governing failure mode. Therefore, the primary parametric trends reported here—namely the effects of eccentricity, tube thickness, and Dst/Dsi ratio—are expected to remain valid and robust against such minor imperfections.

3.2.6. Energy Absorption

The area below the load–deflection curve can be estimated for estimating the structural member’s energy absorption index (EAI) [19]. This parameter is required to better understand the capability of CFSST columns of absorbing the amount of energy under a biaxial loading scenario for each of the suggested groups.

Figure 26 compares the Energy Absorption Index (EAI) of the Group 1 CFSST models with varying stainless-steel yield strengths (f_y). A reduction in fy from 550 MPa to 350 MPa resulted in a significant decrease in EAI from 3846 kN·mm to 2683 kN·mm, corresponding to a 30.23% reduction. Conversely, increasing f_y from 550 MPa to 650 MPa led to a notable increase in EAI to 5635 kN·mm, representing a 46.5% enhancement. These results correspond to the models CFSST-S-f_y 550 and CFSST-S-f_y 650, respectively.

Figure 27 presents a comparison of the Energy Absorption Index (EAI) for Group 2 CFSST models with varying concrete compressive strengths (f_cu). An increase in f_cu from 31 MPa to 60 MPa resulted in a corresponding rise in EAI from 3201 kN·mm to 3846 kN·mm, indicating a 16.77% improvement. Conversely, a reduction in fcu from 60 MPa to 50 MPa led to a marginal decrease in EAI, from 3846 kN·mm to 3832 kN·mm, representing a reduction of only 0.36%. These values correspond to models CFSST-S-f_cu 60 and CFSST-S-f_cu 50, respectively.

Figure 28 compares the Energy Absorption Index (EAI) of Group 3 CFSST models with varying ratios of stainless-steel tube width to carbon steel section depth (D_st/D_si). Increasing the D_st/D_si ratio from 1.25 to 2.0 led to a substantial rise in EAI, from 3846 kN·mm to 8466 kN·mm—an increase of 120.12%. Additionally, increasing the ratio from 1.25 to 1.75 resulted in a notable EAI gain of 57.02%, reaching 6039 kN·mm. These results correspond to models CFSST-S-D_st/D_si 1.25 and CFSST-S-D_st/D_si 1.75, respectively.

Figure 29 presents a comparison of the Energy Absorption Index (EAI) for Group 4 CFSST models with varying stainless-steel tube thicknesses (t). Reducing the tube thickness from 3 mm to 2 mm resulted in a decrease in EAI from 3846 kN·mm to 3233 kN·mm, representing a reduction of 18.53%. Conversely, increasing the thickness from 3 mm to 5 mm led to an increase in EAI to 4980 kN·mm, indicating a 29.48% enhancement. These results correspond to models CFSST-S-t 3 mm and CFSST-S-t 5 mm, respectively.

Figure 30 compares the Energy Absorption Index (EAI) of Group 5 CFSST models with varying load eccentricities (e). Reducing the eccentricity from 55 mm to 5 mm resulted in a significant increase in EAI, from 3846 kN·mm to 7548 kN·mm—an enhancement of 96.25%. In contrast, increasing the eccentricity from 55 mm to 100 mm led to a considerable reduction in EAI, decreasing to 2612 kN·mm, which corresponds to a 32.08% drop. These values correspond to models CFSST-S-e 55 and CFSST-S-e 100, respectively.

The structural energy dissipation efficiency of CFSST columns is most sensitive to geometric and loading parameters that directly influence stability and confinement—namely D_st/D_si ratio, load eccentricity, and tube thickness. Material strength parameters, especially stainless-steel yield strength, also play a critical role by extending the post-yield response and enhancing plastic energy absorption. These insights are vital for optimizing CFSST design in seismic and impact-prone applications where high energy dissipation is essential.

4. Conclusions

This study presented a comprehensive finite element (FE) analysis of square concrete-filled stainless-steel tube (CFSST) columns stiffened with embedded steel I-sections under biaxial eccentric loading. The analyses were conducted using ABAQUS 2020, with the FE model validated against existing experimental results. A total of 16 parametric models were developed to examine the effects of key parameters, including stainless-steel yield strength (f_y), concrete compressive strength (f_cu), the width-to-depth ratio of the stainless-steel tube to the carbon steel section (D_st/D_si), stainless-steel tube thickness (t), and biaxial load eccentricity (e_x and e_y). The key findings are summarized as follows:

• The developed FE model accurately predicted the structural behavior and ultimate load capacity of the square CFSST columns, with a deviation of approximately −2.9% compared to experimental results, demonstrating its validity and reliability.
• Both the stainless-steel yield strength (f_y) and tube thickness (t) significantly influenced the axial load capacity. Increasing f_y from 550 MPa to 650 MPa resulted in a 9.97% increase in ultimate capacity (P_u), while increasing the tube thickness from 3 mm to 5 mm led to a substantial 28.67% improvement in Pu. Specifically, increasing fy from 550 MPa to 650 MPa enhanced Pu from 341 kN to 375 kN (+9.9%), while reducing fy to 350 MPa decreased Pu to 267 kN (−21.7%). Increasing tube thickness from 3 mm to 5 mm increased Pu to 456 kN (+28.67%), whereas reducing it to 2 mm lowered Pu to 276 kN (−19.06%).
• The effect of concrete compressive strength (f_cu) on the axial capacity was relatively limited. For example, increasing f_cu from 30 MPa to 60 MPa yielded only a 10% increase in Pu, indicating that the steel components dominate the load-resisting mechanism. Increasing fcu from 30 MPa to 60 MPa raised Pu from 309 kN to 341 kN (+10.35%), while reducing it from 60 MPa to 50 MPa caused only a slight drop of 3.02%.
• A significant enhancement in axial capacity was observed with increases in the D_st/D_si ratio. Increasing this ratio from 1.25 to 2.0 led to a 137.38% increase in Pu, attributed to the larger cross-sectional area of the stainless-steel tube and the corresponding increase in confined concrete core volume. Increasing Dst/Dsi from 1.25 to 2.0 improved Pu from 341 kN to 811 kN (+137.85%), while an increase to 1.75 resulted in 523 kN (+53.37%).
• As expected, increased load eccentricity resulted in reduced axial capacity. Raising the biaxial eccentricity from 55 mm to 100 mm led to a 40.76% decrease in Pu, confirming the sensitivity of the system to second-order effects and lateral instability. Reducing e from 55 mm to 5 mm raised Pu from 341 kN to 1202 kN (+252.49%), whereas increasing it to 100 mm decreased Pu to 202 kN (−40.76%).
• Overall, the Energy Absorption Index (EAI) of the CFSST columns improved in parallel with enhancements in axial load capacity. The EAI was positively influenced by increases in f_y, f_cu, D_st/D_si, and t and was negatively affected by higher load eccentricities, reflecting their collective impact on the columns’ energy dissipation efficiency under eccentric loading conditions. For EAI, increasing fy from 550 MPa to 650 MPa improved the index from 3846 to 5635 kN·mm (+46.5%), while reducing it to 350 MPa decreased it to 2683 kN·mm (−30.23%). Similarly, increasing tube thickness from 3 mm to 5 mm enhanced EAI to 4980 kN·mm (+29.48%), whereas reducing it to 2 mm lowered it to 3233 kN·mm (−18.53%). Increasing Dst/Dsi from 1.25 to 2.0 raised EAI from 3846 to 8466 kN·mm (+120.12%), and reducing eccentricity from 55 mm to 5 mm boosted it to 7548 kN·mm (+96.25%).