Equivalent Constitutive Relationship of Concrete-Filled Steel Tubes Based on Strain Energy Equivalence

Literature Overview

The paper by Yuan Weibin and Jin Weiliang, published in the Journal of Zhejiang University (Engineering Science) in 2004, addresses a fundamental challenge in the structural analysis of concrete-filled steel tubes (CFST). The authors propose a new equivalent constitutive model by simplifying the composite CFST section into a transversely isotropic body of the same dimensions and applying the principle of strain energy equivalence under elastic conditions. This approach is significant because existing constitutive models for CFST often rely on empirical fitting or oversimplified assumptions that obscure the physical interaction between the steel tube and the confined concrete. The study provides a theoretically grounded framework that can be directly integrated into finite element analysis and structural design software.

Core Methodology and Technical Points

The authors first survey existing constitutive models for CFST and identify their limitations, particularly the lack of a unified theoretical basis linking the macroscopic behavior to the constituent material properties. The key innovation lies in two stages: first, under elastic conditions, the principle of strain energy equivalence is used to derive macroscopic elastic coefficients for the composite section; second, upon entering the elastic-plastic stage, the moduli are assumed to follow a quadratic parabolic degradation curve based on experimental results.

The derivation of elastic coefficients proceeds by equating the strain energy of the composite section to the sum of strain energies of the steel tube and the concrete core. For a transversely isotropic body, the elastic constants include Young's modulus in the axial direction, Young's modulus in the transverse direction, the shear modulus, and two Poisson's ratios. The steel tube contributes to the hoop stiffness and axial stiffness through its own elastic properties, while the concrete core provides the primary axial compressive resistance. The interaction between the two materials is captured through the confinement effect, which enhances the triaxial stress state of the concrete.

Elastic-Plastic Transition and Parabolic Degradation

After the elastic stage, the authors assume that the elastic moduli degrade according to a quadratic parabolic function as the material enters the plastic range. This assumption is calibrated against experimental stress-strain data from CFST compression tests. The parabolic form captures the progressive stiffness loss due to concrete cracking and steel yielding while maintaining mathematical continuity at the elastic limit. The transition stress is determined by the lower of the concrete's compressive strength and the steel's yield stress, adjusted for the confinement effect.

The study further investigates the sensitivity of the elastic moduli to variations in material strength and the steel ratio. The results show that increasing the concrete strength raises the axial modulus proportionally, while increasing the steel ratio has a more pronounced effect on the transverse modulus due to the hoop stiffness contribution of the steel tube. Comparisons with previous models demonstrate that the proposed constitutive relationship offers better agreement with experimental data across a wider range of steel ratios and material strengths.

Engineering Practice Integration and Reflections

From a practical standpoint, this constitutive model has direct applications in the finite element analysis of CFST columns and beams used in high-rise buildings, bridge piers, and offshore structures. The model's parameters can be determined from standard material tests on steel and concrete, without requiring dedicated CFST-specific testing. This reduces the cost and complexity of material characterization while improving the predictive accuracy of structural simulations. The strain energy equivalence principle is particularly elegant because it ensures that the energy balance is preserved at the macroscopic level, which is critical for convergence in nonlinear finite element analyses.

However, the model has certain limitations that warrant consideration. The transversely isotropic simplification assumes uniform material distribution around the circumference, which may not hold for CFST sections with non-circular cross-sections or with internal steel reinforcement. The parabolic degradation function, while physically motivated, may not capture the abrupt stiffness drop associated with localized buckling of the steel tube at high strain levels. Future work could extend the model to account for strain rate effects, cyclic loading behavior, and the influence of interface bonding quality between the steel tube and the concrete core.

The study by Yuan and Jin represents a significant step toward rational constitutive modeling of composite steel-concrete structures. Its theoretical clarity and practical usability make it a valuable reference for engineers engaged in the design and analysis of CFST components. The approach of using strain energy equivalence as a bridge between constituent material properties and macroscopic behavior offers a template that could be adapted to other composite structures, such as steel-reinforced concrete and steel-concrete composite slabs.