Local Elastic Buckling Analysis of Rectangular CFST Under Non-Uniform Compression

Literature Overview

This paper by Liu Yongjian, Li Hui, and Zhang Ning, published in the Journal of Architecture and Civil Engineering in 2015 (Vol. 32, No. 4, pp. 1-8), addresses a critical yet often overlooked aspect of rectangular steel tube-confined concrete (CFST) member design: the local elastic buckling behavior of the steel plates under non-uniform compressive stress states. Funded by multiple National Natural Science Foundation projects and Ministry of Transport construction science and technology projects, this work extends classical plate buckling theory to account for the realistic stress distributions that occur in CFST members subjected to combined axial force and bending moment. The authors employed the Galerkin method to establish the governing buckling equations, utilizing different characteristic functions to describe buckling modes under non-uniform pressure, thereby resolving the asymmetry problem that arises when using triangular series as buckling functions for plates with single-sided surface constraint.

Core Technical Findings

The central contribution of this study lies in quantifying how the non-uniformity of compressive loading affects the local buckling resistance of rectangular steel plates forming the walls of CFST members. The non-uniformity gradient parameter alpha (α) is defined as the ratio characterizing the linear stress distribution across the plate width, where α = 0 corresponds to uniform compression and α = 2 corresponds to pure bending. The key findings are summarized as follows:

These results are of considerable practical significance because in real CFST structural members, such as bridge piers or building columns, the stress distribution across the steel wall is rarely uniform. The concrete core provides lateral confinement that modifies the stress state, and the combination of axial load with bending moment creates a linearly varying compressive stress distribution. Traditional design codes often conservatively assume uniform compression, which may lead to overly restrictive width-to-thickness ratio limits and unnecessary material usage.

Technical Methodology and Analysis

The authors addressed a fundamental mathematical challenge in plate buckling analysis: when a rectangular plate is subjected to non-uniform pressure, the buckling mode shape is asymmetric, and using conventional triangular Fourier series as the assumed buckling function introduces significant errors. The Galerkin method was selected as the variational approach to derive the governing equations, which ensures that the residual is orthogonal to the chosen basis functions. Different characteristic functions were employed for different boundary conditions and loading configurations to accurately capture the asymmetric buckling modes.

The analysis considered rectangular plates representing the flat walls of the steel tube, with the loaded edges representing the connections to the adjacent walls or the concrete core interface, and the unloaded edges representing the free or constrained boundaries depending on the actual structural configuration. The concrete confinement effect was implicitly accounted for through the boundary condition assumptions at the unloaded edges.

Engineering Practice Implications

From a steel pipe manufacturing and structural design perspective, this research carries several important implications. First, the finding that pure bending produces buckling coefficients approximately six times higher than uniform compression suggests that CFST members designed for predominantly flexural loading can accommodate significantly thinner steel walls than those designed for pure axial compression. This has direct bearing on the selection of steel pipe wall thickness in bridge and building applications where bending dominates.

Second, the conclusion that fixed boundary conditions at the unloaded edge produce substantially higher buckling coefficients than simply supported conditions highlights the importance of detailing at the ends of CFST members. In practice, this means that the presence of end plates, welds, or adjacent structural elements that provide rotational restraint to the steel wall can significantly enhance local buckling resistance. Engineers should carefully consider these boundary effects when evaluating the adequacy of steel wall thickness.

Third, the increasing width-to-thickness ratio limits with increasing α provide a rational basis for relaxing the geometric proportion limits in design codes for members under non-uniform compression. This could lead to more economical designs without compromising safety, particularly for CFST columns in multi-story buildings where the interaction between axial force and bending moment is significant.

Key Questions and Reflections

Several questions arise from this study that merit further investigation. The analysis assumes elastic buckling behavior, but in practice, the steel walls of CFST members may experience inelastic buckling, particularly at higher slenderness ratios or with lower-grade steels. The interaction between elastic local buckling and the post-buckling behavior of the composite member is not addressed. Additionally, the study focuses on the idealized case of linearly varying compressive stress, whereas in real CFST members, the stress distribution may be more complex due to concrete cracking, steel yielding, and geometric imperfections.

The practical application of these findings requires careful consideration of how the non-uniformity gradient α can be determined from the actual loading and member geometry. In design practice, the stress distribution at the steel wall level is typically derived from the composite section analysis, but translating this into the appropriate α value for buckling assessment requires additional engineering judgment. Furthermore, the width-to-thickness ratio limits derived from this study should be validated against experimental data from full-scale CFST member tests under combined loading to ensure that the theoretical predictions are conservative enough for design purposes.

Study Insights and Outlook

This study represents a meaningful advancement in the understanding of local buckling behavior in rectangular CFST members, moving beyond the simplifying assumption of uniform compression that has long dominated design practice. The methodology employed, combining appropriate characteristic functions with the Galerkin method, provides a robust framework that can be extended to more complex loading scenarios and boundary conditions. For steel pipe manufacturers and structural engineers, the key takeaway is that the local buckling resistance of CFST members is significantly influenced by the stress distribution, and designs that account for non-uniform compression can achieve better material efficiency. Future work should focus on extending these findings to inelastic buckling, incorporating the effects of initial geometric imperfections and residual stresses from the steel pipe manufacturing process, and validating the theoretical predictions through comprehensive experimental programs.