Zhuojin Pipe Fitting Co., LtdConstitutive Relationships and Failure Criteria for Rectangular Concrete-Filled Steel Tube Bending Members
Literature Overview
The study by Yang Lv-feng, Xie Wei-wei, Rong Yan, and Jiang Li-fang from Guangxi University, published in the China Civil Engineering Journal in 2019 (Vol. 52, No. 1, pp. 60-70), addresses a critical gap in the structural design of rectangular concrete-filled steel tube (CFST) bending members. The research is supported by the National Natural Science Foundation of China (Key Project 51738004 and General Program 51478125) and originates from the Guangxi Key Laboratory of Disaster Prevention and Mitigation and Engineering Safety. The authors propose corrected material constitutive models for both the steel tube and the confined core concrete, and establish a bearing capacity failure criterion specifically tailored for rectangular CFST bending members.
Core Technical Content
The fundamental challenge in analyzing rectangular CFST bending members lies in the biaxial stress state experienced by the steel tube walls. Unlike circular CFST members, where uniform confinement is relatively straightforward to model, rectangular sections exhibit non-uniform stress distribution across the cross-section. The authors identify two critical stress states: the favorable biaxial tensile state in the tension zone and the unfavorable biaxial tension-compression state in the compression zone of the steel tube.
Constitutive Model Development
The constitutive model for confined concrete is developed through regression analysis based on a rectangular CFST axially compressed short column test database. The peak stress expression for confined concrete accounts for the degree of confinement, which varies across different regions of the rectangular cross-section. The key innovation is the recognition that the confinement effect is not uniform: the flat walls of the rectangular tube experience different confinement pressures compared to the corner regions, and this variation must be captured in the constitutive law.
The steel tube constitutive model is corrected to reflect the actual stress-strain behavior under biaxial loading conditions. In the tension zone, the steel tube walls are subjected to a biaxial tensile stress state, which enhances ductility and strain capacity. In the compression zone, the steel tube experiences a biaxial tension-compression state, where the transverse tensile strain induced by Poisson's effect under axial compression reduces the effective compressive strength of the steel.
Failure Criterion
The bearing capacity failure criterion is established based on the ultimate limit state of member capacity, with particular attention paid to the strain hardening segment of the steel tube in the tension zone. This is a significant improvement over previous models that often neglected the strain hardening contribution, leading to underestimation of the actual flexural capacity of rectangular CFST members.
| Parameter | Description | Significance |
|---|---|---|
| Confinement coefficient | Ratio of confining pressure to concrete strength | Determines the enhancement of confined concrete strength |
| Biaxial stress ratio | Ratio of transverse to longitudinal stress | Governs the steel tube's effective stress state |
| Strain hardening ratio | Ratio of ultimate to yield stress of steel | Critical for tension zone capacity prediction |
| Width-to-thickness ratio | Geometric parameter of steel tube wall | Affects local buckling and effective width |
Interpretation of Technical Points
The use of the fiber model method for validation is particularly noteworthy. The fiber model discretizes the cross-section into small elements, each assigned its own material constitutive law, and integrates the stress-strain relationships across the depth of the section to obtain the moment-curvature relationship. By comparing different constitutive relationships and failure criteria against the experimental database, the authors demonstrate that their proposed models yield higher computational accuracy and broader applicability.
A key insight from this work is that the conventional assumption of uniform confinement in rectangular CFST sections is inadequate for accurate prediction of flexural behavior. The non-uniform confinement effect means that the effective width of the compression zone of the steel tube is less than the full width, and this reduction must be properly quantified. The authors' approach of considering the biaxial stress state provides a more physically grounded framework for this quantification.
Integration with Engineering Practice
In practical engineering design, rectangular CFST columns and beams are increasingly used in high-rise buildings, industrial structures, and bridge piers due to their high strength-to-weight ratio and compact cross-section. The corrected constitutive models and failure criteria proposed in this study can be directly applied to:
- Section design optimization for rectangular CFST bending members
- Seismic performance evaluation of CFST structural systems
- Nonlinear finite element analysis where accurate material models are essential
- Code-based design calibration for new or revised standards
The study also has implications for welding quality control in CFST fabrication. The strain hardening behavior of the steel tube in the tension zone is sensitive to the welding process used to form the rectangular tube, as welding-induced residual stresses and heat-affected zone (HAZ) properties can alter the local stress-strain response. Engineers should ensure that the welding procedures used for rectangular tube fabrication are compatible with the material behavior assumed in the design models.
Study Insights and Reflections
This research represents a significant advancement in the analytical modeling of rectangular CFST members. The recognition that the steel tube's biaxial stress state differs fundamentally between the tension and compression zones is a physically intuitive yet often overlooked aspect of CFST design. The proposed constitutive models are not merely curve-fitting exercises but are grounded in the mechanics of confined concrete and the plasticity of steel under multiaxial loading.
For practicing engineers, the most valuable takeaway is the importance of selecting appropriate material models when performing nonlinear analysis of CFST members. Using simplified models that do not account for the actual stress state can lead to either unsafe or uneconomical designs. The fiber model approach, while computationally more intensive, provides a reliable means of validating simplified design formulas.
The study's reliance on a rectangular CFST axially compressed short column test database for developing the confined concrete peak stress expression is both a strength and a potential limitation. While the database provides a solid empirical foundation, the transfer of these relationships from axial compression to bending conditions assumes that the confinement mechanism is similar in both loading scenarios. Future research should validate this assumption through dedicated bending tests on rectangular CFST members with varying geometric and material parameters.
Overall, this work provides a rigorous analytical framework that can be confidently adopted in the design and assessment of rectangular CFST bending members, contributing to safer and more efficient structural engineering practice.