Local Elastic Buckling Analysis of Rectangular Concrete Filled Steel Tubes Under Non-Uniform Compression

Literature Overview

This paper by Liu Yongjian, Li Hui (Chang'an University, Shaanxi Key Laboratory of Highway, Bridge and Tunnel Engineering), and Zhang Ning (Northwest A&F University, 2015) investigates the local elastic buckling behavior of rectangular steel plates under non-uniform compressive stress distributions. Using different characteristic functions to describe the buckling modes and the Galerkin method to establish the governing equations, the study analyzes how non-uniform loading affects the local buckling performance of rectangular CFST members. The research was supported by the National Natural Science Foundation of China and Ministry of Transport construction science and technology projects.

Core Technical Content

Problem Statement and Methodology

The local buckling of steel plates in CFST members is a critical design consideration, as it governs the effective cross-sectional capacity and the composite action between the steel tube and concrete core. Traditional buckling analysis often assumes uniform compressive stress distributions, which may not represent the actual stress states in practical CFST members subjected to bending, eccentric loading, or combined loading conditions.

The study addresses the asymmetry problem that arises when using trigonometric series as buckling functions to simulate the buckling modes of rectangular plates with one-sided surface constraints under non-uniform loading. By employing different characteristic functions tailored to specific boundary and loading conditions, more accurate buckling mode shapes and critical loads are obtained.

Key Findings

The research reveals several important relationships:

Parameter	Effect on Buckling	Engineering Implication
Load gradient α increases	Buckling coefficient increases	Non-uniform loading is beneficial for buckling resistance
α = 2 (pure bending)	Buckling load ~6x that of uniform compression	Bending-dominated members have higher local buckling capacity
Width-thickness ratio limit	Increases with α	More generous slenderness limits under non-uniform loading
Fixed boundary (non-loaded edge)	Significantly higher buckling coefficient	Boundary conditions have major influence on buckling resistance

Buckling Coefficient Analysis

The buckling coefficient is a dimensionless parameter that relates the critical buckling stress to the material properties and plate geometry. The study demonstrates that:

Under uniform compression (α = 0), the buckling coefficient reaches its minimum value, representing the most unfavorable loading condition.
As the load gradient α increases (representing more non-uniform loading), the buckling coefficient increases significantly.
Under pure bending (α = 2), the elastic buckling load characteristic value is approximately six times that under uniform axial compression.
The width-thickness ratio limit (a critical geometric parameter for steel plate buckling) increases with the load gradient, indicating that more slender plates can be used under non-uniform loading conditions.

Boundary Condition Effects

The study specifically examines the effect of boundary conditions on the non-loaded edge of the plate. Fixed (clamped) boundary conditions on the non-loaded edge produce significantly higher buckling coefficients compared to simply supported conditions. This has direct implications for the design of CFST members where the concrete core provides partial restraint to the steel plate edges.

Engineering Practice Implications

Steel Plate Slenderness Limits

For the design of rectangular CFST members, the width-thickness ratio of the steel plates is a critical parameter. The study's findings suggest that:

Current design codes that use uniform compression buckling coefficients may be overly conservative for members primarily subjected to bending.
The actual buckling capacity of steel plates in CFST members is significantly enhanced by the concrete core, which provides lateral restraint and modifies the stress distribution.
More accurate buckling analysis considering the actual stress distribution can lead to more efficient and economical designs.

Quality Control for Steel Plate Fabrication

From a steel pipe and plate fabrication perspective, the following quality considerations are important:

Plate flatness - Local buckling is sensitive to initial imperfections. The flatness tolerance of steel plates used for CFST fabrication should be tightly controlled.
Wall thickness uniformity - Variations in wall thickness affect the width-thickness ratio and thus the buckling resistance. Thickness measurement at multiple points along the plate length is recommended.
Edge quality - The condition of the plate edges (particularly the loaded edge) affects the buckling behavior. Edge defects such as burrs, notches, or thickness reductions should be avoided.
Weld quality - In box-type CFST members fabricated from plates, the weld quality at the edges affects the effective boundary conditions. Poor welds may reduce the effective restraint, lowering the buckling resistance.

Application to CFST Column and Beam Design

The study's findings have direct applications in the design of:

CFST columns subjected to eccentric loading (non-uniform stress distribution)
CFST beams under bending (pure bending stress distribution)
CFST members at connection zones with complex stress states
Rectangular CFST members in bridge and building structures

Study Insights and Critical Reflection

This research contributes significantly to the understanding of local buckling in rectangular CFST members by moving beyond the simplifying assumption of uniform compression. The use of appropriate characteristic functions and the Galerkin method provides a rigorous analytical framework that captures the essential physics of the buckling problem.

The finding that pure bending produces approximately six times the buckling load compared to uniform compression is particularly significant for practical design. Many CFST members in real structures are subjected to combined axial and bending loads, where the stress distribution is non-uniform. Using uniform compression buckling coefficients for such members would be unconservative in terms of safety but overly conservative in terms of material efficiency.

For steel pipe and plate suppliers, this study underscores the importance of providing accurate material and geometric property data. The buckling resistance is sensitive to both the material properties (Young's modulus, Poisson's ratio) and the geometric properties (plate width, thickness, initial imperfections). High-quality steel plates with tight dimensional tolerances and controlled surface quality are essential for achieving the predicted buckling performance.

The boundary condition findings highlight the importance of connection design in CFST members. The concrete core provides partial restraint to the steel plates, but the degree of restraint depends on the concrete-steel bond quality, which is influenced by surface preparation, concrete mix design, and placement quality. Engineers should ensure that the assumed boundary conditions in the design analysis are consistent with the actual construction details and quality control measures.