Zhuojin Pipe Fitting Co., LtdStress-Strain Relationship Model of Steel-Concrete Composite Members Under Cyclic Loading
Literature Overview
This paper by Zhang Wenfu, Hao Jinfeng, Xue Jinghong, Zhang Dan, and Che Taijie, published in Journal of Daqing Petroleum Institute (2010, Vol. 34, No. 3, pp. 104-108), establishes a stress-strain relationship model for steel-concrete composite braces under cyclic loading conditions. The research is motivated by the need to develop restoring force models for steel-concrete composite frame-brace systems, which are increasingly used in seismic-resistant structures. Funded by the Heilongjiang Provincial Education Department (10541006) and Heilongjiang Provincial Natural Science Foundation (E2008011), the work addresses a fundamental material constitutive modeling challenge.
Core Technical Framework
The authors decompose the composite member into two constituent materials—steel and concrete—and develop separate stress-strain models for each before combining them through a compatibility and equilibrium approach. For the steel component, a bilinear or multilinear elastic-plastic model is adopted, incorporating strain hardening effects. For the concrete component, the authors distinguish between constrained concrete (confined by the steel tube) and unconstrained concrete, providing separate skeleton curves for each condition.
Constitutive Model Parameters
The following table presents the key parameters of the proposed model:
| Parameter | Symbol | Typical Value | Source |
|---|---|---|---|
| Steel yield strength | f_y | 235 to 460 MPa | GB/T 1591, GB/T 700 |
| Steel elastic modulus | E_s | 206 GPa | Standard value |
| Steel hardening modulus | E_sh | 0.01 to 0.05 times E_s | Experimental calibration |
| Concrete compressive strength | f_c | 20 to 60 MPa | GB/T 50081 |
| Concrete elastic modulus | E_c | 30,000 to 40,000 MPa | GB 50010 |
| Confinement coefficient | ξ | 0.2 to 0.8 | Depends on D/t ratio |
| Concrete peak strain (constrained) | ε_cu | 0.005 to 0.012 | Function of ξ |
| Concrete peak strain (unconstrained) | ε_c0 | 0.0033 | Standard value |
Cyclic Loading Behavior and Hysteretic Rules
The most significant contribution of this paper is the establishment of concrete loading and unloading hysteretic rules. Under cyclic loading, concrete exhibits progressive damage accumulation, stiffness degradation, and strength deterioration. The authors propose a kinematic hardening model that tracks the damage state through a scalar damage variable that evolves with each loading cycle. The skeleton curve for constrained concrete is defined by a three-branch model: an initial linear elastic branch, a nonlinear hardening branch up to the peak stress, and a post-peak softening branch.
The hysteretic rules define how the stress-strain path deviates from the skeleton curve during unloading and reloading. The authors adopt a proportional loading surface concept, where the unloading stiffness decreases with increasing damage level. This approach captures the pinching effect observed in experimental hysteresis loops of steel-concrete composite columns. The model is particularly relevant for brace members, which undergo large inelastic deformations during seismic events.
Application to Steel-Concrete Composite Frame-Brace Systems
The proposed stress-strain model serves as the material foundation for developing the restoring force model of steel-concrete composite braces. The brace restoring force is obtained by integrating the stress distribution over the cross-section, accounting for the interaction between the steel tube and the confined concrete. The authors note that the model provides a reference basis for studying the restoring force characteristics of steel-concrete composite braces under low-cycle reversed loading at large deformation states.
From a practical standpoint, this constitutive model can be implemented in finite element software such as ABAQUS or OpenSees through user-defined material subroutines. The model parameters can be calibrated against experimental data from component tests, enabling engineers to predict the seismic performance of composite brace systems with reasonable accuracy. I observe that the model does not account for rate-dependent behavior, which may be relevant for high-intensity seismic events where dynamic effects become significant.
Study Insights and Implications
This paper provides a valuable constitutive modeling framework that is both physically grounded and computationally tractable. The clear separation of steel and concrete behaviors, followed by their combination through compatibility conditions, is a pedagogically sound approach that can be extended to other composite members. The hysteretic rules, while simplified, capture the essential features of cyclic behavior including stiffness degradation and strength deterioration. For engineering practice, the model enables performance-based seismic design of steel-concrete composite frame-brace systems, which is particularly relevant for critical infrastructure in high-seismic regions such as Northeast China where this research originated. The work represents a solid contribution to the understanding of material behavior under complex loading histories.