Local Buckling Analysis of Square Steel Tube Concrete Columns Under Axial Compression

Literature Overview

The study by Zhao Yonggang, Liang Qinhua, Pan Xiao, and Zhang Hao, published in the Journal of Lanzhou University of Technology (2009, Vol. 35, Issue 5), investigates the local buckling behavior of square steel tube concrete (CFT) columns under axial compression. The authors establish a local buckling model in which the steel tube plate is assumed to be elastically restrained at the non-loaded edge by the surrounding concrete core. Using the energy method, they derive a formula for calculating the local buckling critical stress of the steel tube wall. The study was supported by the Gansu Provincial Natural Science Foundation (0710RJZA058).

Core Technical Content and Interpretation

Local buckling is a critical failure mode for steel tube concrete columns, particularly for columns with relatively thin steel tube walls. Unlike overall column buckling, which involves the lateral displacement of the entire column, local buckling involves the out-of-plane deformation of individual steel tube plates between the corners or between the loaded and non-loaded edges. The presence of the concrete core fundamentally changes the boundary conditions of the steel tube plates, providing elastic restraint that significantly enhances the local buckling resistance.

The study adopts a boundary condition model in which the loaded edge of the steel tube plate is considered simply supported (or clamped, depending on the connection detail), while the non-loaded edge is elastically restrained by the concrete core. The elastic restraint coefficient quantifies the degree of restraint provided by the concrete and ranges from zero (no restraint, simply supported) to infinity (fully clamped). The study examines two specific cases: an elastic restraint coefficient of 2.0 (partial restraint) and infinity (full clamping).

Energy Method Formulation

The energy method for local buckling analysis is based on the principle of stationary potential energy. The total potential energy of the system consists of the strain energy stored in the buckled steel plate and the work done by the axial compressive stress. At the critical buckling load, the second variation of the total potential energy equals zero.

Where $D$ is the flexural rigidity of the plate, $\nu$ is Poisson's ratio, $w$ is the transverse displacement, $\sigma_x$ is the axial compressive stress, $t$ is the plate thickness, and $k$ is the elastic foundation modulus (related to the elastic restraint coefficient).

Local Buckling Critical Stress Results

The study demonstrates that the presence of the concrete core dramatically increases the local buckling resistance of the steel tube wall. Even at a modest elastic restraint coefficient of 2.0, the critical buckling stress is substantially higher than for a simply supported plate. At full clamping (coefficient of infinity), the enhancement is even more pronounced.

Boundary Condition Modeling and Its Engineering Significance

The accuracy of local buckling analysis depends critically on the correct representation of boundary conditions. In practice, the boundary conditions of steel tube plates in CFT columns are neither perfectly simply supported nor perfectly clamped. The actual restraint provided by the concrete core depends on several factors:

1. Concrete stiffness: The elastic modulus of the concrete determines the restraint stiffness. Higher-strength concrete provides greater restraint.
2. Concrete cover thickness: The distance from the steel tube inner surface to the column centerline affects the restraint geometry.
3. Steel tube-to-concrete interface bonding: The quality of the bond between steel and concrete influences the effectiveness of restraint transfer.
4. Column slenderness: The overall slenderness of the column affects the deformation pattern and, consequently, the local buckling behavior.

From a steel pipe manufacturing perspective, the dimensional accuracy of the square tube — including wall thickness uniformity, corner radius consistency, and flatness of the tube faces — directly affects the local buckling behavior. Variations in wall thickness create stress concentrations that reduce the effective buckling resistance. Corner welds in square tubes introduce geometric discontinuities that can serve as buckling initiation sites.

Manufacturing Tolerances and Local Buckling

Energy Method: Advantages and Limitations

The energy method offers several advantages for local buckling analysis of CFT columns. It provides a closed-form analytical solution that captures the essential physics of the problem. The method is computationally efficient and can be used for parametric studies to explore the influence of various parameters on buckling behavior. Furthermore, the energy method provides physical insight into the role of each energy component in the buckling process.

However, the energy method also has limitations. The assumption of a sinusoidal displacement function may not accurately represent the actual buckling mode shape, particularly for plates with non-uniform boundary conditions or for columns with significant geometric imperfections. The elastic restraint coefficient is a simplification that does not fully capture the complex interaction between the steel tube and the concrete core. Additionally, the energy method does not account for post-buckling behavior, which is important for the ultimate load capacity of CFT columns.

Integration with Design Codes and Engineering Practice

The findings of this study are directly relevant to the design of CFT columns in accordance with standards such as GB 50017 (Chinese standard for steel structures), AISC 360 (American standard for structural steel), and EC4 (European standard for composite structures). These codes provide empirical or semi-empirical formulas for the design strength of CFT columns, which implicitly account for local buckling through interaction curves between steel tube contribution and concrete core contribution.

The study's analytical approach complements the code-based design by providing a theoretical basis for understanding the local buckling mechanism. Engineers can use the analytical results to validate code-based design calculations and to identify situations where the code provisions may be conservative or unconservative.

Comparison with Code Provisions