Analytical Analysis of Local Buckling Performance of Rectangular CFST Axially Compressed Columns A Technical Study Note

Literature Overview

This 2002 paper from Xi'an University of Architecture and Technology presents a theoretical analysis of the local buckling behavior of the steel tube wall in rectangular steel tube concrete-filled (CFST) axially compressed columns. Using the energy method, the authors derived the local buckling critical stress under uniform compressive loading and obtained a local buckling coefficient k = 10 for the rectangular CFST configuration. The work provides a foundational analytical framework for understanding the interaction between the concrete core and the steel tube wall in resisting local buckling, which is a critical failure mode in CFST columns.

Technical Background and Local Buckling Mechanism

In rectangular CFST columns, the steel tube wall is subjected to compressive stresses from the axial load and lateral pressures from the confined concrete. The local buckling of the steel tube wall is a plate buckling phenomenon where the flat or slightly curved plates of the rectangular cross-section buckle under the combined action of axial compression and transverse pressure. The presence of the concrete core fundamentally alters the boundary conditions and the buckling behavior compared to hollow steel tubes, as the concrete provides lateral support and increases the effective buckling resistance.

The local buckling coefficient k is a dimensionless parameter that relates the critical buckling stress to the plate geometry and material properties. For a simply supported plate under uniform compression, the classical buckling coefficient is k = 4.0, while for a plate with one edge fixed and one edge simply supported, it increases to approximately k = 9.87. The value of k = 10 obtained in this study for rectangular CFST columns reflects the enhanced boundary conditions provided by the concrete core confinement.

Energy Method Derivation and Assumptions

The energy method (also known as the Ritz method) for buckling analysis involves assuming a displacement function that satisfies the boundary conditions and then minimizing the total potential energy with respect to the unknown coefficients. For the rectangular CFST column, the assumed displacement function for the steel tube wall must satisfy the boundary conditions at the edges where the wall connects to the adjacent wall segments and where it interfaces with the concrete core.

The key assumption in this analysis is that the concrete core exerts a uniform lateral pressure on the steel tube wall, effectively providing a continuous elastic foundation. This simplification is reasonable for columns where the concrete is well-confined and the stress distribution is relatively uniform. However, in practice, the concrete stress distribution may not be perfectly uniform, particularly near the column ends where stress concentrations occur and where the concrete may experience cracking under high loads.

The energy method derivation involves writing the strain energy of the buckled plate, the work done by the external loads (axial compression and lateral pressure), and then applying the principle of stationary potential energy. The resulting eigenvalue problem yields the critical buckling stress as a function of the plate dimensions, material properties, and boundary conditions.

Comparison with Hollow Steel Tube Behavior

The local buckling coefficient of k = 10 for rectangular CFST columns is significantly higher than the typical values for hollow rectangular steel tubes, which generally range from k = 4 to k = 8 depending on the aspect ratio and boundary conditions. This increase is attributed to the lateral confinement provided by the concrete core, which effectively increases the boundary stiffness and reduces the effective buckling length of the steel tube wall.

From a design perspective, this finding supports the well-established observation that CFST columns exhibit superior local buckling resistance compared to hollow steel tubes of the same wall thickness. The concrete core acts as an internal support that prevents the steel tube wall from buckling outward, thereby allowing the steel to reach higher stress levels before local buckling initiates. This is one of the key advantages of the CFST structural system.

Engineering Practice Implications and Design Considerations

For structural engineers designing CFST columns, the analytical framework presented in this study provides a basis for evaluating local buckling resistance. The local buckling coefficient k = 10 can be used in conjunction with material properties (yield strength, elastic modulus) and geometric parameters (plate width-to-thickness ratio) to calculate the critical buckling stress and compare it with the applied stress. If the applied stress exceeds the critical buckling stress, the column is susceptible to local buckling failure.

However, engineers should be aware of the limitations of this analytical approach. The uniform pressure assumption may not hold for all loading conditions, particularly under eccentric loading or when the concrete core experiences significant cracking. Additionally, the analysis does not account for the effects of initial imperfections, residual stresses, or the progressive degradation of concrete-steel interaction under cyclic loading. For these reasons, the analytical results should be used in conjunction with empirical design formulas and experimental validation data.

Reflections on the Analytical Approach

The energy method, while powerful for providing analytical insight, has inherent limitations when applied to complex structural systems like CFST columns. The assumption of a single displacement function for the steel tube wall may not capture the complex deformation patterns that occur during local buckling, particularly when the buckling mode involves multiple half-waves across the plate width. More advanced numerical methods, such as finite element analysis, can capture these complexities but at the cost of analytical transparency.

Nevertheless, the analytical approach provides valuable engineering insight by clearly identifying the key parameters that influence local buckling behavior. The result of k = 10 serves as a benchmark against which more complex numerical or experimental results can be compared, helping engineers understand whether their designs are reasonable and whether additional investigation is warranted.

Summary

This study provides a valuable analytical foundation for understanding the local buckling behavior of rectangular CFST axially compressed columns, deriving a local buckling coefficient of k = 10 using the energy method. The result confirms that the concrete core significantly enhances the local buckling resistance of the steel tube wall compared to hollow steel tubes, which is a fundamental advantage of the CFST structural system. For practicing engineers, this analytical framework offers a transparent and efficient method for preliminary evaluation of local buckling resistance, while also highlighting the need for empirical validation and consideration of practical factors such as initial imperfections and non-uniform loading conditions. The work remains relevant as a foundational reference for the ongoing development of CFST design methodologies.