Simplified Determination of Plastic Yield Surface for Square CFT Members

Overview and Motivation

This paper by Liu Yangbing, Liu Jingbo, Han Qiang, and Zheng Nina from Chongqing University, Tsinghua University, and Beijing University of Technology addresses a practical challenge in the structural analysis of concrete-filled square steel tubular (CFST) members: the efficient determination of the plastic yield surface, or the ultimate load interaction curve between axial force and bending moment. The plastic hinge method is a widely used approach for the nonlinear analysis of CFST structures, and it requires the definition of the plastic yield surface for each cross-section. While the fiber model method can accurately compute the yield surface, it is computationally intensive and not easily integrated into standard structural analysis software. The paper proposes a simplified analytical method for determining the plastic yield surface of square CFST columns, validated against the fiber model method.

Methodology and Elastic Element Parameters

The proposed method begins with the determination of the elastic element parameters, which define the initial stiffness of the plastic hinge. These parameters are derived from the material properties of both the steel tube and the concrete core, as well as the geometric properties of the cross-section. The elastic parameters include the axial stiffness, the bending stiffness about both principal axes, and the axial-bending coupling stiffness. For a square CFST cross-section, the symmetry simplifies the analysis, as the bending stiffness about both axes is identical.

The plastic yield surface is then determined through theoretical analysis and extensive parametric studies. The parametric study varies key parameters including the steel strength, concrete strength, the steel-to-concrete strength ratio, the confinement ratio, and the geometric parameters such as the width-to-thickness ratio and the width-to-height ratio. The results of the parametric study are used to develop simplified analytical expressions for the yield surface, which can be evaluated rapidly for any given set of parameters.

Comparison with Fiber Model Method

The paper validates the proposed simplified method by comparing its results with those obtained from the fiber model method. The fiber model method divides the cross-section into discrete fibers, each assigned a uniaxial stress-strain relationship appropriate to the material. The yield surface is computed by applying combinations of axial force and bending moment and determining the maximum load combination that the cross-section can sustain. This method is accurate but computationally expensive, particularly when a large number of load combinations are required.

The comparison shows good agreement between the simplified method and the fiber model method, confirming the accuracy of the proposed approach. The agreement is particularly good in the range of parameters that are most commonly encountered in engineering practice. For extreme parameter combinations, such as very high confinement ratios or very low width-to-thickness ratios, the simplified method may show slight deviations from the fiber model results, but these deviations are within acceptable engineering tolerances.

Engineering Application and Practical Benefits

The primary benefit of the proposed simplified method is computational efficiency. In the plastic hinge analysis of a CFST structure, the yield surface must be computed for each cross-section at each analysis step. For a structure with hundreds of elements and thousands of analysis steps, the computational savings from using a simplified method are substantial. The simplified method allows the yield surface to be computed in a fraction of the time required by the fiber model method, making it feasible to perform extensive parametric studies and design optimization within reasonable computational budgets.

The method is particularly valuable for the following engineering applications:

1. Nonlinear static analysis of CFST structures under gravity and lateral loads, where the plastic hinge method is used to capture the inelastic behavior.
2. Seismic analysis of CFST structures, where the yield surface must be evaluated repeatedly during time-history analysis.
3. Design optimization of CFST members, where the yield surface is evaluated for many different cross-section geometries and material properties.
4. Capacity design of CFST structures, where the yield surface is used to determine the plastic moment capacity and the ductility demand.

Study Insights and Limitations

This paper makes a valuable contribution to the practical analysis of CFST structures by providing a computationally efficient method for determining the plastic yield surface of square CFST columns. The method is grounded in theoretical analysis and validated against the more computationally intensive fiber model method, providing confidence in its accuracy. The parametric study that underpins the method covers a wide range of practical parameters, making the method applicable to most engineering scenarios. However, the method is specifically developed for square CFST sections and would need to be adapted for rectangular, circular, or other cross-sectional shapes. Additionally, the method assumes that the yield surface is defined in the axial force-bending moment plane, and it does not account for the effects of torsion or biaxial bending, which may be important in some structural applications. For future work, extending the method to account for biaxial bending and torsion, and to incorporate the effects of cyclic loading and low-cycle fatigue, would further enhance its practical utility. Overall, this paper demonstrates that simplified analytical methods, when properly derived and validated, can provide accurate and efficient tools for the nonlinear analysis of CFST structures, bridging the gap between rigorous numerical methods and practical engineering analysis.