Optimized Fiber Element Modeling Strategy for Concrete-Encased Steel Composite Columns: Focusing on Material Nonlinearity and Confinement Effects

Abstract

Reliable numerical simulation of concrete-encased steel (CES) composite columns remains challenging, and practical fiber-element modeling can be sensitive to confinement representation and to discretization and integration choices. Although CES columns offer superior structural performance, accurate simulation is difficult due to the complex interaction between steel and concrete under cyclic loading. Current seismic design codes, such as ASCE/SEI 41-17, often simplify modeling parameters by underestimating composite action, which can lead to uneconomical and overly conservative assessments that do not fully reflect the confining effect of the concrete encasement and the buckling restraint of the steel core. This study proposes a practical guideline for constructing an accurate analytical model for CES columns using nonlinear fiber-element analysis, with a specific focus on material constitutive laws. To validate the proposed strategy, nonlinear analyses were conducted and compared against a comprehensive database of 79 experimental specimens compiled from previous studies. The predicted-to-test peak strength ratio shows a mean of 1.02 (standard deviation of 0.058). Sensitivity studies indicate that responses stabilize beyond ~23 fibers (<1.5% error), reducing computation time by ~40% on average (from 52 to 23 fibers) compared with dense discretization while maintaining reliable hysteretic response prediction.

1. Introduction

Concrete-Encased Steel (CES) composite columns act as a unified structural member by integrating structural steel and reinforced concrete. This composite action offers significant advantages over conventional reinforced concrete or steel columns, including superior load-bearing capacity, high stiffness, and enhanced ductility [1,2]. Due to these material benefits, CES columns are increasingly adopted in high-rise buildings and long-span structures where high seismic performance is required.

Despite their favorable structural characteristics, capturing the nonlinear interaction between the steel core and surrounding concrete in CES columns remains challenging due to the complex interaction between steel and concrete. The complexity arises primarily from the nonlinear interaction between the two distinct materials: the steel section and the surrounding concrete. For reliable performance-based design, it is essential to predict the inelastic deformation capacity and governing failure modes of CES members with sufficient accuracy. Although solid finite element models can provide high accuracy, they are computationally demanding and often impractical for large-scale structural analyses.

Current seismic design guidelines, such as ASCE/SEI 41-17 [3], provide modeling parameters and acceptance criteria for composite columns. However, these code-based approaches tend to be overly conservative. They often simplify the analysis by considering only the contribution of the steel section for certain limit states, effectively ignoring the confining effect of the concrete encasement and the buckling suppression provided to the steel core. This simplification neglects the enhanced material behavior arising from composite interaction, which may result in overly conservative strength estimates and unrealistic seismic performance assessments.

To address these limitations, Fiber Element Analysis (FEA) serves as a practical alternative that balances computational efficiency with accuracy. By discretizing the cross-section into uniaxial fibers, FEA can incorporate sophisticated material constitutive laws to simulate the nonlinear behavior of concrete and steel, including confinement effects [4]. However, while general guidelines exist, an optimized discretization specifically calibrated for CES columns remains insufficiently addressed—such as the number of fibers, discretization strategy, and integration scheme—needed to ensure reliable results without excessive computational cost.

Previous studies have provided experimental and analytical evidence on CES/SRC(Steel Reinforced Concrete) column behavior under various confinement and loading conditions. Work on strength and ductility of concrete-encased composite columns has been reported through both experimental investigations and analytical studies [5,6,7]. The influence of hoop/tie reinforcement and detailing on confinement and ductility has also been examined [4,8]. Several test programs documented CES/SRC column response under monotonic and cyclic loading, including cyclic lateral loading combined with constant axial force [9,10,11,12], while other studies considered non-seismic detailing [13]. Data and observations under biaxial or eccentric demand scenarios were reported in [14,15], and additional studies addressed concentric/eccentric axial loading effects [16]. Stability- and material-regime-related aspects, such as recycled/high-strength concrete and buckling behavior, were explored in [17]. In parallel, analytical models for predicting axial capacity and member behavior have also been proposed [18,19,20]. Collectively, these studies indicate that CES column response is strongly influenced by confinement level, axial load ratio, loading path, and stability mechanisms; however, practical guidance that translates these findings into a reproducible and computationally efficient fiber-element modeling workflow (region definition, discretization density, and integration strategy) remains limited.

Recent research has further expanded the experimental and analytical boundaries of CES/SRC columns, incorporating high-strength concrete, diverse cross-sectional geometries, slenderness effects, buckling behaviors, and shear-dominated failure under low-cycle cyclic loading [21,22,23,24,25,26,27]. Analytically, approaches have evolved to include macro-modeling proposals for shear-critical short columns [22], integrated frameworks linking experiments, modeling, and design for slender members [23], and frame-level finite element applications [24]. Moreover, studies focusing on the optimization of embedded steel configurations [28] and comparative reviews of related systems—such as Concrete-Filled Steel Tubes (CFSTs) and fully encased members—have been reported [29,30]. While these contemporary studies demonstrate a broad investigation of CES columns across various materials and failure modes, there remains a notable absence of “verification-based, concise guidelines” essential for practically reproducible fiber-element modeling. Specifically, clear criteria for defining confinement regions, determining section discretization density, and selecting longitudinal integration settings are not sufficiently established. To address this demand, this study establishes a practical fiber-element modeling procedure for CES columns, substantiated by the validation of a comprehensive experimental database and numerical sensitivity analysis.

This study proposes a practical guideline for numerical modeling of CES columns using nonlinear fiber-element beam–column analysis, focusing on material nonlinearity and confinement effects. Although various experimental and analytical studies on CES/SRC columns have been reported, practically implementable and experimentally validated guidance on (i) representing multi-level confinement (including the highly confined concrete between steel flanges) and (ii) selecting efficient section discretization and numerical integration settings remains limited. The applied motivation is to support reproducible and computationally efficient component-level simulations for performance assessment and retrofit-oriented evaluation of CES columns. Therefore, the objectives of this study are to: (1) define a reproducible fiber-section modeling strategy with appropriate constitutive laws for unconfined, partially confined, and highly confined concrete and steel components; (2) identify a baseline discretization level that balances accuracy and computational efficiency; and (3) recommend an integration-point configuration consistent with plastic-hinge localization for seismic-type loading. The proposed modeling strategy is validated through comparisons with a comprehensive experimental database of 79 CES/SRC column specimens compiled from the literature [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20].

2. Experimental Database and Fiber Element Modeling in Perform-3D

2.1. Comprehensive Experimental Database

To ensure the rigorous validation of the proposed modeling guidelines, a comprehensive database of 79 Concrete-Encased Steel (CES) column specimens was compiled from existing literature [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. This database was carefully curated to encompass a wide range of critical design parameters that influence the seismic behavior of composite columns. Specimens were compiled from experimental programs on CES/SRC composite columns covering confinement detailing, cyclic response, and multi-axial loading conditions [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. Early and subsequent studies focusing on confinement (hoops/ties) and ductility provide essential context for defining confined concrete regions and calibration targets [4,5,6,7,8]. For cyclic behavior under constant axial load with lateral/bending reversals, the database relies primarily on studies explicitly reporting monotonic/cyclic or cyclic protocols [9,10,11,12,13], and also includes specimens with non-seismic detailing to broaden the validation domain [13]. To account for multi-axial demand scenarios, biaxial/eccentric loading datasets were incorporated from [14,15,16,17]. While certain references investigated extended material regimes (e.g., higher concrete strengths or recycled concrete) [2,17,21], only the specimens that fall within the parameter ranges adopted in this study were retained for the final database. The collected specimens vary significantly in terms of:

• Material Strength: Concrete compressive strength (f_c) ranging from normal to high-strength, and steel yield strength (f_y) covering standard structural steel grades.
• Geometric Parameters: A diverse range of shear span-to-depth ratios (a/d) and structural steel ratios (ρ_ss).
• Loading Conditions: Various levels of axial load ratios (P/P₀) applied during cyclic loading tests. This dataset serves as a benchmark for evaluating whether the fiber model can accurately predict key failure modes—including flexural yielding and concrete crushing—across a wide range of design conditions.

Figure 1 summarizes the overall methodology of this study, including database compilation, fiber element model construction in Perform-3D, sensitivity analyses, and validation. The key database ranges are provided in

Table 1. Summary of the experimental database and key modeling inputs used in this study.

f’c [MPa]	fys [MPa]	fyr [MPa]	ρss [%]	ρsr [%]	Vu [kN]	a/d	ALR
37.5–87.6	254–779	357–414	2.94–7.15	1.75–2.36	118–1227	0.12–0.46	0.3–989

Note: f’_c = concrete compressive strength, f_ys = yield strength of the encased structural steel section, f_yr = yield strength of longitudinal bars, ρ_ss = steel section ratio, ρ_sr = longitudinal reinforcement ratio, a/d = shear span to depth ratio, V_u = peak lateral strength measured in the experiment. ALR = axial load ratio.

.

2.2. Numerical Modeling Strategy in Perform-3D

Nonlinear finite element analyses were conducted using Perform-3D, a specialized computational tool designed for the performance-based assessment of structures. The CES columns were modeled using “Nonlinear Fiber” beam-column elements. This approach discretizes the composite cross-section into a finite number of uniaxial fibers (concrete and steel fibers), allowing for the direct calculation of moment–curvature response based on the stress–strain state of each fiber. Geometric nonlinearity (P-Δ effects) was enabled in Perform-3D for the column analyses.

2.2.1. Concrete Constitutive Model

The stress–strain relationship of concrete is the most critical factor in CES column modeling.

• Unconfined Concrete: The cover concrete was modeled using the standard inelastic constitutive law proposed by Mander et al. [31], which accounts for the softening branch after peak strength.
• Confined Concrete (Core): A distinguishing characteristic of CES columns is the additional confinement provided not only by the transverse reinforcement but also by the flanges of the embedded steel section. To capture this dual-confinement effect, a confined concrete stress–strain model was calibrated by adjusting the peak strength and ultimate strain parameters to reflect combined confinement from both transverse reinforcement and the encased steel sections. The confinement enhancement was accounted for by increasing the peak compressive strength (f’_cc) and ultimate compressive strain (ε_cu) to reflect the combined confinement provided by transverse reinforcement and the embedded steel section [32]. The calibration procedure and parameter selection are described in Section 3.2 and validated using the 79 test specimens.
• Tensile Behavior: The tensile strength of concrete was neglected to remain conservative by assuming fully cracked behavior under cyclic loading.

The concrete in an encased composite section was divided into three regions (unconfined, partially confined within hoops, and highly confined between steel flanges), and each region was assigned a different confined-concrete property set. For the highly confined concrete between steel flanges, the additional confinement effect provided by the steel flanges was incorporated following [33]. The effective confinement factor for the flange-confined zone is defined as

$$K_e^{\prime }={\displaystyle \frac{A_{bf}-A_{para}}{A_{bf}}}$$

(1)

where A_bf is the total concrete area between flanges and A_para is the area of the two parabolas used to represent ineffective confinement (Mirza and Skrabek [22] recommendation adopted in El-Tawil and Deierlein [33]). The additional confinement pressure provided by the flanges is obtained from the flange bending resistance at first yielding as

$$f_{ly}^{\prime }=K_e^{\prime }{\displaystyle \frac{t^2{f}_{ys}}{3l^2}}$$

(2)

where t is the flange thickness, l is the flange outstand length measured from the web face, and f_ys is the yield stress of the encased steel section. For the highly confined region, the total effective confinement pressure in the corresponding direction was taken as f_ly,total = f_ly + f_ly′, while the transverse-reinforcement confinement pressures (f_lx, f_ly) were computed using the effective confinement ratio approach of El-Tawil and Deierlein [33]. The resulting two-direction confinement pressures were then used to determine the confined concrete strength f_cc through the strength enhancement factor k = f_cc/f_cok per El-Tawil and Deierlein [23].

The ultimate compressive strain parameter used in Perform-3D, ε_cu, was defined on a specimen-by-specimen basis for each confined concrete region (partially confined within hoops and highly confined between steel flanges). When the source test report provided an ultimate (or termination) concrete strain, that value was adopted. Otherwise, ε_cu was computed consistently from the El-Tawil and Deierlein [33] confined-concrete stress–strain relation as the strain at which the compressive stress reaches the residual plateau level:

$$f_c\left({\epsilon }_{cu}\right)=0.3f_{cc}$$

(3)

Accordingly, ε_cu was obtained by numerically solving the descending-branch equation of the confined concrete model for f_c/f_cc = 0.3 and converting the corresponding normalized strain x to ε_cu = xε_cc for the corresponding region.

Concrete tensile strength was neglected (fully cracked assumption) to maintain a conservative and practically robust fiber element model under cyclic loading. This simplification may slightly underestimate post-cracking stiffness and affect pinching-related details; however, it reduces uncertainty associated with tensile damage/tension-stiffening parameters and is considered acceptable for the present study, which focuses on global strength and deformation-capacity prediction.

2.2.2. Steel Constitutive Model

The hysteretic behavior of the structural steel and longitudinal reinforcement bars was simulated using the Giffre–Menegotto–Pinto (GMP) model [34].

• Kinematic Hardening: Unlike simple bilinear models, the GMP model accurately represents the Bauschinger effect, which is essential for predicting energy dissipation during earthquake excitations.
• Curve Transition: The model parameters were calibrated to achieve a smooth transition from elastic to plastic behavior, thereby preventing numerical instability during load reversals.
• Perfect Bond Assumption: Following standard practice for CES columns, a perfect bond between the steel section and the surrounding concrete was assumed, meaning strain compatibility was maintained across the section.

A perfect bond (strain compatibility) between the encased steel section and the surrounding concrete is assumed, consistent with the plane-sections-remain-plane hypothesis used in fiber element beam-column formulations. This assumption may underestimate stiffness degradation and pinching effects when steel–concrete interface slip, bond deterioration, or partial composite action becomes significant under large cyclic demands. Therefore, the proposed modeling guideline is primarily intended for CES columns exhibiting stable composite action within the investigated parameter ranges; cases with pronounced interface slip may require explicit bond-slip/interface modeling. This limitation is common in practical fiber element analyses and is adopted here to balance model complexity and computational efficiency.

2.2.3. Numerical Integration and Mesh Sensitivity

Numerical integration along the element length was performed using a user-defined two-point scheme based on the plastic hinge length, L_p. Based on a preliminary sensitivity analysis conducted in this study (discussed in Section 3), the integration points were placed at the centers of the plastic hinge regions at both ends as Equation (1) [35]. Accordingly, the normalized locations were defined as x₁ = L_p/2L and x₂ = 1 − x₁, where L is the element length. For the representative column, L_p = 172.44 mm estimated using Equation (4), resulting in x₁ = 0.17 and x₂ = 0.83.

$$L_p=0.08L+0.22f_{yd}$$

(4)

3. Model Validation and Numerical Optimization

3.1. Verification Against Experimental Database

The primary validation of the proposed modeling strategy involved a direct comparison between the analytical predictions and the experimental results from the 79 CES column specimens. The validation focused on three key aspects: initial stiffness, peak strength, and post-peak ductility.

3.1.1. Hysteretic Response and Energy Dissipation

Figure 2 presents the comparison of the load–displacement hysteresis loops for representative specimens subjected to cyclic loading. The analytical results obtained from Perform-3D (red line) show close agreement with the experimental hysteresis curves (black line).

• Pinching Effect: The use of the Giffre–Menegotto–Pinto (GMP) model [34] successfully captured the “pinching” phenomenon observed in shear-critical specimens. This suggests that the model appropriately captures crack opening/closure behavior and the Bauschinger effect in the steel core.
• Stiffness Degradation: The model accurately reproduced the gradual degradation of stiffness during unloading and reloading cycles, which is critical for assessing the seismic damage accumulation.

3.1.2. Statistical Analysis of Strength Prediction

To quantitatively assess the model accuracy, the ratio between the predicted and experimental peak lateral strength, V_max,num/V_nax,exp, was calculated for all 79 specimens, where V_max was taken as the maximum actuator lateral force recorded in the cyclic load–displacement response (Figure 2).

• The comparison yielded a mean ratio (V_max,num/V_nax,exp) of 1.02 with a standard deviation of 0.058 and a COV of 0.0569 (5.7%).
• This statistical proximity to 1.0, combined with a low coefficient of variation, confirms that the proposed fiber model provides unbiased and consistent predictions across a wide range of material strengths (concrete strength up to 87.6 MPa) and geometric configurations.
• Notably, the model maintained high accuracy even for specimens with high axial load ratios (n > 0.5), a regime where conventional models often overestimate capacity due to the neglect of P-Delta effects and concrete crushing mechanisms.

Concrete crushing under high axial demands is represented by the post-peak softening of the adopted concrete compression models in the fiber section. Second-order (P-Δ) effects were included in the Perform-3D analyses, accounting for additional moments associated with axial force and lateral drift.

3.2. Mesh Sensitivity and Optimization

A central objective of this study was to establish a guideline that balances computational efficiency with numerical accuracy. To investigate the mesh sensitivity, a representative CES column cross-section was selected and idealized for the analysis, as shown in Figure 3. To this end, a rigorous sensitivity analysis was conducted focusing on section discretization and integration schemes.

3.2.1. Optimal Number of Fibers (Section Discretization)

To evaluate the impact of mesh density on accuracy, 16 different fiber discretization patterns were established, ranging from coarse to fine meshes. Among them, 10 representative meshing strategies considered in this study are illustrated in Figure 4, and the detailed specifications for all 16 cases are summarized in

Table 2. Details of the 16 section discretization methods.

No. Division	Unconfined Concrete	Partially Confined Concrete	Fully Confined Concrete	Reinforced Bar	Core Steel
21	4	4	2	8	3
23	4	4	2	8	5
25-1	4	4	4	8	5
25-2	6	4	2	8	5
26	8	4	2	8	4
27	8	4	2	8	5
29-1	8	4	4	8	5
29-2	4	8	4	8	5
31	8	8	2	8	5
33	8	4	8	8	5
34	8	8	4	8	6
37	12	4	8	8	5
38	12	4	8	8	6
42	8	12	8	8	6
52	12	12	8	8	12
60	12	12	16	8	12

.

The accuracy of fiber element analysis is theoretically dependent on the resolution of the cross-sectional mesh. This study analyzed the convergence of the moment–curvature response by varying the number of fibers from a coarse mesh (21 fibers) to a highly refined mesh (60 fibers).

The nonlinear analysis results for these 16 cases are presented in Figure 5. In the figure legends, the notation NXX-Y/Z denotes a model with XX fiber elements and integration points located at normalized lengths Y and Z. For instance, N34-0.83/0.17 indicates a section with 34 fibers using a two-point integration scheme at 0.83L and 0.17L. In addition, the notation NXX-A/B/C represents a column physically divided into three elements with normalized length ratios of A, B, and C, respectively. As observed in the graph, the predicted flexural capacity and moment–curvature response converge rapidly.

• Results: As illustrated in Figure 5 for mesh sensitivity analysis, the flexural capacity and post-peak behavior stabilized rapidly. The analysis revealed that increasing the number of fibers beyond 23 resulted in a negligible difference (less than 1.5%) in the predicted result.
• Physical Interpretation: This indicates that the strain field across the composite section does not exhibit abrupt gradients, allowing accurate predictions even with relatively coarse discretization without compromising accuracy. Therefore, an excessive subdivision of the highly confined concrete core does not contribute significantly to the global accuracy.

• Guideline: Based on this finding, a discretization of approximately 23 fibers is recommended as a balanced choice between computational efficiency and accuracy: dividing the web into 4 fibers, each flange into 4 fibers, and the concrete core/cover into an appropriate grid. This configuration reduces computational time by approximately 40% compared to dense meshing in these analyses, without compromising the reliability of seismic performance assessment.
• A discretization on the order of ~23 fibers is recommended as a practical baseline for CES columns within the investigated database ranges (f_c = 37.5–87.6 MPa, f_y ≤ 414 MPa, and ρ_ss ≤ 2.6%).
• For sections outside these ranges or with substantially different geometry/steel configuration, a brief convergence check (e.g., 23 → 34 fibers) is recommended.

3.2.2. Optimization of Numerical Integration Scheme

The selection of the numerical integration method and the location of integration points along the element length are as critical as the cross-sectional discretization. In distributed plasticity models, the element response is derived by integrating the section responses. Standard Gauss–Legendre integration, which places points within the element, often underestimates the curvature at the element extremities where the maximum moments occur in seismic applications. To address this, the Gauss–Lobatto integration rule was employed in this study. Unlike standard Gauss–Legendre integration, the Gauss–Lobatto rule places integration points at the element ends (0L and 1L), allowing for a direct and accurate capture of the peak inelastic demands at the column-beam interface. Based on the sensitivity analysis and validation against experimental data, the integration points located at 0.17L and 0.83L were identified as the optimal configuration for CES columns (Section 2.2.3). This specific configuration carries a significant physical implication: it effectively defines the plastic hinge length (L_p) of the column. By concentrating the integration weights within this region, the model can simulate the localization of damage (such as concrete crushing and steel yielding) that typically occurs at the column ends, while keeping the central portion of the element relatively elastic. This approach not only enhances the accuracy of the hysteretic response prediction but also ensures numerical stability by preventing mesh-dependent strain localization errors often encountered in softening materials.

The two-point user-defined integration locations (0.17L and 0.83L) were selected based on a plastic-hinge-length interpretation and were validated against the present experimental database. This integration scheme is therefore recommended as a practical baseline within the investigated conditions; for different boundary conditions, loading protocols, or member configurations, a brief sensitivity check is advised.

3.3. Comparison with Current Design Codes

To highlight the necessity of the proposed method, the analysis results were compared with the nominal strengths calculated using ASCE/SEI 41-17 provisions [3].

• Limitations of ASCE 41-17 [3]: The current code-based approaches often lead to conservative strength estimates because composite action is not fully considered, often underestimating the flexural capacity by 15–20%. This discrepancy is attributed to the code’s simplification which underestimates the confining effect of the concrete encasement and the composite action in the plastic range.
• Advantage of Proposed Method: By explicitly modeling the material nonlinearity and dual-confinement effect using the Mirza and Skrabek model [32], the proposed fiber element strategy recovered the “hidden” capacity reserve. This allows for a more economical design and a realistic performance evaluation, preventing unnecessary retrofitting of existing structures.

3.4. Discussion

Although constitutive models for concrete and steel and fiber-element beam–column formulations are well established, practical application to CES columns still requires several modeling decisions that can affect reproducibility and computational cost, particularly for multi-level confinement representation and plastic-hinge localization. The main contribution of this technical note is therefore not a new constitutive theory, but an implementation-oriented and experimentally validated modeling guideline for CES columns that integrates confinement region definition, baseline section discretization, and integration-point selection into a coherent workflow.

Across the compiled database of 79 CES/SRC column tests, the proposed strategy provided consistent peak strength prediction with a mean ratio of V_max,num/V_max,exp = 1.02 (SD 0.058; COV 5.7%). The model maintained good agreement even under high axial load ratios (up to n = P/P₀ = 0.989), where crushing-driven deterioration and second-order effects are critical; this is attributed to the concrete compression softening behavior in the fiber formulation together with explicit inclusion of P-Δ effects in the analyses.

From the numerical-efficiency perspective, the sensitivity study indicates that the global response stabilizes beyond a baseline discretization of approximately 23 fibers, with negligible changes (<1.5%) compared to denser discretization. In the sensitivity analyses conducted under identical analysis settings, this baseline discretization reduced the average computation time by approximately 40% relative to a 52-fiber discretization. These findings support a practical baseline modeling configuration that is sufficiently accurate for component-level performance assessment while avoiding unnecessary modeling complexity.

4. Conclusions

This study presented a practical modeling guideline for the nonlinear fiber element analysis of Concrete-Encased Steel (CES) columns. Based on the extensive validation against 79 experimental specimens, the following conclusions are drawn:

• High-Fidelity Simulation: The proposed modeling framework, integrating the Mander et al. model (modified by Mirza and Skrabek [32] for confinement) for concrete and the Giffre–Menegotto–Pinto model [34] for steel, demonstrated excellent accuracy. The statistical evaluation yielded a mean ratio of analytical-to-experimental peak lateral strength of 1.02, confirming the model’s reliability across diverse design parameters.
• Optimized Discretization: The sensitivity analysis proved that the CES column analysis exhibits mesh independence beyond a certain threshold within the investigated ranges. A cross-sectional discretization of 23 fiber elements was identified as the optimal configuration, providing precise results while significantly reducing computational cost. Refined meshing of the confined core was found to be unnecessary.
• Integration Strategy: For seismic performance assessment, defining integration points at 0.83L and 0.17L (Gauss–Lobatto rule) is recommended to accurately capture plastic hinge localization at the column ends.
• Practical Implication: Unlike conventional code-based methods (e.g., ASCE 41-17) that neglect composite action, the proposed guideline accurately accounts for the confinement effect and ductility of CES members. This allows structural engineers to achieve more rational and realistic performance-based design assessments.
• Limitations and future work: The present approach assumes perfect bond (strain compatibility) between steel and concrete and neglects concrete tensile strength, which may influence stiffness degradation and pinching under large cyclic demands. Further work is recommended to extend validation to different steel shapes/ratios and to investigate explicit interface/bond-slip modeling where partial composite action is expected.