Local Buckling of Square Steel Tube Concrete Columns Under Axial Compression

Literature Overview

The paper by Zhao Yonggang, Liang Qinhua, Pan Xiao, and Zhang Hao, published in the Journal of Lanzhou University of Technology (2009, Vol. 35, No. 5), investigates the local buckling behavior of the steel tube wall in square steel tube concrete (STC) columns under axial compression. The research is funded by the Gansu Provincial Natural Science Foundation and employs the energy method to derive analytical expressions for the critical buckling stress of the steel tube wall, considering the elastic constraint provided by the core concrete at the unloaded edges.

Core Technical Viewpoints

The authors establish a lateral displacement function expressed as a trigonometric function to model the buckling deformation mode of the steel tube wall plate. The key assumption is that the non-loaded edges of the steel tube wall are subjected to elastic restraint from the surrounding concrete, characterized by an elastic constraint coefficient. Two limiting cases are analyzed: a finite constraint coefficient of 2.0 and an infinite constraint coefficient (representing a fixed support condition). The fundamental conclusion is that the presence of core concrete significantly enhances the resistance of the steel tube wall against local buckling.

Interpretation of Technical Points

Buckling Model Assumptions

The buckling model treats the steel tube wall as a rectangular plate under biaxial compression, with the loaded edges (in contact with the axial load application) and the unloaded edges (constrained by the core concrete) having different boundary conditions. The energy method is applied by equating the external work done by the compressive stress to the internal strain energy stored in the buckled plate.

The trigonometric displacement function takes the form:

w(x, y) = w₀ · sin(mπx/a) · sin(nπy/b)

where w₀ is the amplitude, m and n are the half-wave numbers in the x and y directions, and a and b are the plate dimensions.

Elastic Constraint Coefficient

The elastic constraint coefficient k represents the stiffness of the concrete restraint at the unloaded edge. A value of k = 2.0 corresponds to a moderate elastic support, while k = ∞ represents a fully fixed condition. The critical buckling stress increases monotonically with the constraint coefficient, confirming that stiffer concrete restraint delays local buckling.

Effect of Core Concrete

The core concrete provides three beneficial effects:

Lateral restraint against local buckling of the steel tube wall.
Confinement effect that increases the compressive strength of the concrete itself.
Reduction of the effective buckling length of the steel tube wall by providing intermediate support.

Process and Standards Analysis

Parameter	Typical Value	Influence on Buckling
Steel grade	Q235–Q460	Higher grade increases buckling resistance
Concrete strength	C30–C60	Higher strength increases restraint stiffness
Wall thickness t	4–12 mm	Thicker walls have higher buckling capacity
Side length b	200–800 mm	Larger dimensions reduce buckling stress
Constraint coefficient k	0–∞	Higher k increases critical stress
t/b ratio	0.005–0.06	Lower ratio increases buckling susceptibility

The design of square STC columns should follow the provisions of GB 50937-2013 (Code for design of concrete-filled steel tube structures), which specifies slenderness limits for the steel tube wall to prevent local buckling. The slenderness limit is typically expressed as the ratio of the plate width to thickness (b/t) and varies with the steel grade and concrete strength.

Engineering Practice Integration

In practice, local buckling of the steel tube wall is a critical failure mode for square and rectangular STC columns, particularly in buildings with large span requirements. The analytical approach presented in this paper provides engineers with a theoretical basis for checking the local buckling resistance of the steel tube wall. However, the assumption of uniform biaxial compression may not hold in practice, where stress concentrations at connection nodes and load application points can trigger premature buckling.

From a manufacturing perspective, the square steel tube used for STC columns is typically produced by cold rolling or cold drawing processes. The residual stresses introduced during cold forming can significantly reduce the actual buckling resistance below the theoretical value. Engineers should account for this by applying a reduction factor or by requiring stress-relieved material for critical applications. The welding quality at the longitudinal seam (for welded square tubes) is also critical, as any geometric imperfection at the weld can act as a buckling initiation site.

Study Insights and Implications

This paper makes a solid contribution to the theoretical understanding of local buckling in square STC columns. The energy method approach is elegant and provides clear physical insight into the buckling mechanism. The finding that core concrete dramatically improves buckling resistance validates the composite design philosophy underlying STC structures. However, the study is limited to theoretical analysis without experimental comparison, which limits its practical applicability. Future research should incorporate finite element modeling with geometric imperfections and residual stresses to provide more realistic predictions. For structural engineers, the key takeaway is that the slenderness ratio of the steel tube wall must be carefully controlled, and the concrete confinement effect should not be overestimated in design calculations.