Zhuojin Pipe Fitting Co., LtdMaterial Constitutive Relations and Failure Criteria for Rectangular CFST Bent Members
Literature Overview
This paper by Yang Lv-feng, Xie Wei-wei, Rong Yan, and Jiang Li-fang from Guangxi University, published in the China Civil Engineering Journal (Vol. 52, No. 1, 2019, pp. 60–70), addresses a fundamental problem in the design of rectangular concrete-filled steel tube (CFST) flexural members: how to accurately model the material behavior of both the steel tube and the confined concrete, and how to establish a reliable failure criterion for ultimate limit state assessment. The work is supported by two National Natural Science Foundation of China grants (51738004 and 51478125), indicating its significance in the national research priority list for structural engineering.
Core Technical Content
Constitutive Model Development
The authors propose a corrected constitutive model that distinguishes between two distinct stress states experienced by the steel tube in a bent CFST member:
- Tension zone: The steel tube wall is subjected to a biaxial tensile stress state, which is favorable because the steel can develop higher strength under multiaxial tension.
- Compression zone: The steel tube wall experiences a biaxial tension-compression stress state, which is unfavorable as the compressive stress in the plane of the wall accelerates local buckling and reduces effective confinement.
The confined concrete peak stress expression is derived through regression analysis based on an experimental database of rectangular CFST axially compressed short columns. This regression approach allows the model to capture the interaction between steel confinement and concrete strength enhancement across a wide range of geometric parameters.
Failure Criterion
The proposed failure criterion is established based on the ultimate limit state of member load-bearing capacity. A key innovation is the explicit consideration of the strain hardening segment in the tension-zone steel tube, which is often neglected in simplified models. This is critical because in flexural members, the tension-zone steel can undergo significant plastic deformation before failure, and ignoring strain hardening leads to underestimation of ductility and overestimation of ultimate curvature capacity.
Fiber Model Validation
The authors employ the fiber model method to compare the accuracy and applicability of different constitutive relationships and failure criteria. The fiber model discretizes the cross-section into small area elements, each assigned a uniaxial stress-strain relationship, enabling the computation of section moment-curvature response through numerical integration.
Key Technical Parameters and Comparison
| Parameter | Traditional Model | Corrected Model |
|---|---|---|
| Steel tension zone stress state | Uniaxial assumption | Biaxial tensile (favorable) |
| Steel compression zone stress state | Uniaxial assumption | Biaxial tension-compression (unfavorable) |
| Concrete peak stress | Empirical formula without confinement correction | Regression-based with confinement correction |
| Strain hardening in tension zone | Ignored | Explicitly included |
| Failure criterion basis | Simple yield criterion | Ultimate limit state with hardening |
Engineering Practice Implications
From a practical standpoint, this work has direct relevance to the design of CFST columns under combined axial and flexural loading, which is common in multi-story buildings and bridge piers. The corrected constitutive model provides more accurate predictions of moment capacity, which directly affects the determination of plastic hinge locations and the global ductility of the structural system. For engineers involved in seismic design of CFST structures, the inclusion of strain hardening in the tension zone is particularly important because it governs the post-yield stiffness and energy dissipation capacity of the member.
The regression-based approach for confined concrete peak stress, while convenient, requires careful validation against test data from the specific project's material conditions. Engineers should verify that the regression coefficients are applicable to the concrete strength range and steel tube dimensions used in their design.
Critical Reflection
The paper's approach of using a single regression expression for confined concrete peak stress, derived from axially compressed short columns, may not fully capture the complex confinement behavior under pure bending, where the confinement effectiveness varies significantly across the cross-section depth. The transition from uniform confinement in axial compression to non-uniform confinement in bending represents a challenge that the fiber model partially addresses through element-by-element stress evaluation, but the underlying constitutive model still assumes a uniform confinement ratio. Future work should consider spatially varying confinement effects, particularly near the neutral axis where the steel tube provides minimal lateral restraint.
Additionally, the paper does not extensively discuss the effect of concrete strength grade on the model's accuracy. For high-strength concrete (fck > 60 MPa), the confinement effect is generally less pronounced, and the regression coefficients may need adjustment. Engineers applying this model to high-strength CFST members should exercise caution and perform sensitivity analyses.
Study Insights
The most valuable contribution of this paper is the systematic consideration of biaxial stress states in the steel tube walls under flexural loading. This is a physically realistic improvement over the common uniaxial assumption and has been validated through comparison with experimental data. The explicit inclusion of strain hardening in the tension zone is another significant advancement that improves the prediction of ductility and post-yield behavior.
For practical engineering applications, the proposed model should be used in conjunction with appropriate partial safety factors and should be validated against project-specific test data whenever possible. The fiber model implementation is well-suited for incorporation into finite element software, making the proposed constitutive relationships readily applicable in modern structural analysis workflows.
This work represents a meaningful step forward in the constitutive modeling of rectangular CFST flexural members, bridging the gap between simplified design formulas and rigorous numerical simulation. Engineers designing CFST structures should be aware of these refined models when performing detailed analysis, particularly for members subjected to significant bending moments where the assumptions of simpler models may lead to non-conservative results.