Constitutive Relationship of Confined Concrete in Square Steel Tube Columns

Literature Overview

This paper by Cai Jian and Sun Gang from the South China University of Technology addresses the constitutive behavior of concrete confined by square steel tubes under axial compression. Published in the Journal of South China University of Technology (Natural Science Edition) in 2008 (Vol. 36, No. 1, pp. 105-109), the study was supported by the Guangdong Provincial Natural Science Foundation.

The authors analyze the load-bearing mechanism of square steel tube concrete (SRC) under axial compression, equating the confining action of the steel tube to an effective lateral confining stress. Drawing on typical confined concrete constitutive models, they propose an equivalent uniaxial compressive constitutive relationship for the core concrete confined by a square steel tube. Based on experimental results, they determine several key parameters: peak strain modification coefficient, effective lateral confining stress coefficient of the steel tube, and the lateral stress of the steel tube at the peak.

Core Technical Framework

The fundamental concept is that the steel tube provides lateral confinement to the core concrete, which increases both the compressive strength and the ductility of the concrete. The authors' approach of representing this confinement as an equivalent lateral stress is a well-established methodology, but its application to square cross-sections presents unique challenges compared to circular sections.

Technical Analysis of Confinement Mechanism

The confinement mechanism in square steel tube concrete columns differs fundamentally from that in circular sections. In a circular section, the confining pressure is uniformly distributed around the perimeter. In a square section, the stress distribution is non-uniform: the corners experience different confinement conditions than the flat faces, and the confinement effect is strongest at the center of the section and weakest near the corners.

This non-uniformity is a direct consequence of the geometry. The steel tube walls of a square section are flat plates that tend to buckle inward under the outward pressure of the expanding concrete. The effective confining stress is therefore a function of the width-to-thickness ratio (D/t) of the steel tube wall, the material properties of both the steel and the concrete, and the interaction between the steel tube and the concrete.

From a welding and fabrication standpoint, square steel tubes are typically manufactured by cold-bending flat steel plates and welding the longitudinal seam. The weld seam location relative to the flat faces is critical: if the seam is at the center of a face, it experiences the highest compressive stress from the concrete; if it is at a corner, the stress state is more complex. The weld quality directly affects the effective confining stress because any weld defect reduces the effective wall thickness and compromises the ability of the steel tube to maintain its shape under the confining action.

The proposed constitutive model was validated by calculating the full load-strain curves of square SRC short columns under axial compression, with good agreement between calculated and experimental results. This validation confirms that the equivalent lateral stress approach is suitable for evaluating the ultimate load-bearing capacity and ductility of square SRC short columns.

Process and Quality Considerations

For engineers specifying and fabricating square steel tube concrete columns, several quality control points emerge from this study:

1. Wall Thickness Uniformity: The confining stress is highly sensitive to wall thickness. Variations in wall thickness due to rolling or bending tolerances can lead to non-uniform confinement. The wall thickness should be controlled within tight tolerances, and ultrasonic thickness measurement should be performed at regular intervals along the tube length.
2. Weld Seam Quality: The longitudinal weld in cold-bent square tubes is a potential weak point. Penetration testing (PT) and magnetic particle testing (MT) should be applied to all longitudinal welds, and for thicker sections, radiographic testing (RT) or phased array ultrasonic testing (PAUT) should be used to detect volumetric defects.
3. Steel Grade Selection: The yield strength and elongation of the steel tube material directly affect the confining stress coefficient. Higher-strength steels provide greater confinement but may have reduced ductility, which could affect the overall ductility of the SRC column. A balance must be struck between strength and ductility requirements.

Study Insights and Reflections

This paper makes a valuable contribution to the understanding of confined concrete behavior in square SRC columns, which are increasingly used in high-rise buildings and special structures where architectural constraints favor square or rectangular cross-sections. The proposed constitutive model provides a practical tool for engineers to predict the behavior of these columns under axial compression.

However, I note that the model is primarily validated for short columns under axial compression. In practical structures, SRC columns are subjected to combined axial and bending loads, and the confinement effect may be different due to the non-uniform stress distribution across the section. Furthermore, the model does not explicitly account for the effect of welding residual stresses, which can be significant in cold-bent square tubes and can influence both the initial stress state and the ultimate load capacity. Future work should extend the constitutive model to account for these practical considerations, particularly for columns fabricated from welded steel tubes where the residual stress distribution is a function of the welding process and sequence.