Zhuojin Pipe Fitting Co., LtdCalculation of Axial Compression Capacity of Concrete-Filled Steel Tube Columns Based on Unified Strength Theory
Literature Overview
This paper by Shi Qingxuan, Rong Chong, Ren Hao, and Zhang Ting from Xi'an University of Architecture and Technology was published in the Chinese Quarterly of Mechanics in 2015 (Volume 36, Issue 4, pages 690-696). The study is supported by the National Natural Science Foundation of China (Grants 51478382 and 51178380) and the Doctoral Program Special Research Fund (Grant 20116120110004). The research focuses on deriving a more accurate axial compression load-bearing capacity formula for concrete-filled steel tube (CFST) columns using the Von Mises yield criterion and the double-shear unified strength theory (UST), with particular attention to the confinement effect on the core concrete.
Core Technical Approach
The fundamental challenge in CFST column design lies in accurately capturing the interaction between the steel tube and the core concrete under axial compression. The authors adopt a dual approach: the Von Mises criterion describes the steel tube's yielding behaviour, while the double-shear unified strength theory characterises the triaxial stress state of the confined core concrete. The key innovation is the derivation of a confinement coefficient formula for the core concrete based on extensive experimental data, which quantifies the lateral confining pressure exerted by the steel tube on the core concrete.
The unified strength theory provides a continuous yield surface in principal stress space that interpolates between the Mohr-Coulomb criterion (representing the lower bound) and the Von Mises criterion (representing the upper bound) through a material parameter b, where 0 ≤ b ≤ 1. This allows the model to account for the intermediate principal stress effect, which is particularly significant for the core concrete under the complex stress state within a CFST column.
Confinement Coefficient Derivation
The confinement coefficient represents the ratio of the lateral confining pressure on the core concrete to the compressive strength of the unconfined concrete. The authors derive this coefficient by considering the equilibrium of forces at the steel-concrete interface and calibrating against a large body of experimental data from published literature. The resulting formula improves upon previous models by incorporating geometric parameters (column diameter, steel tube thickness, length-to-diameter ratio) and material properties (steel yield strength, concrete compressive strength) in a more physically consistent manner.
| Parameter | Symbol | Typical Range | Influence on Capacity |
|---|---|---|---|
| Column outer diameter | D | 100-400 mm | Larger D increases capacity but may reduce confinement effectiveness per unit area |
| Steel tube wall thickness | t | 4-12 mm | Thicker tube provides greater confinement pressure |
| Concrete compressive strength | f_c | 20-80 MPa | Higher f_c increases capacity but confinement ratio may decrease |
| Steel yield strength | f_y | 235-460 MPa | Higher f_y increases steel contribution to total capacity |
| Length-to-diameter ratio | L/D | 2-20 | Higher L/D reduces capacity due to buckling effects |
Comparison with Existing Formulas
The authors compare their proposed formula against several widely used design equations, including those from GB 50017, Eurocode 4, and the Mander model. The comparison demonstrates that the unified strength theory-based formula achieves better agreement with experimental results across a wider range of geometric and material parameters. The average error between calculated and experimental values is notably reduced, particularly for columns with high confinement ratios and high-strength concrete.
From a practical standpoint, the improved formula offers engineers a more reliable tool for designing CFST columns in high-rise buildings, bridges, and industrial structures where accurate prediction of ultimate capacity is critical for both safety and economy. The physical basis of the model—grounded in the unified strength theory—also provides greater confidence in extrapolating results to parameter combinations not directly covered by existing test databases.
Key Insights and Engineering Implications
The study highlights two primary factors influencing CFST column capacity: geometric dimensions and material strength. Among geometric factors, the diameter-to-thickness ratio (D/t) is particularly critical because it governs both the local buckling resistance of the steel tube and the confinement effectiveness on the core concrete. A smaller D/t ratio generally provides better confinement but may be uneconomical for large-diameter columns.
From a materials perspective, the study confirms that increasing concrete strength beyond approximately 60 MPa yields diminishing returns in terms of confinement effectiveness, because the confinement ratio (lateral pressure divided by concrete strength) decreases as concrete strength increases. This insight is directly relevant to the selection of high-strength concrete for CFST applications, suggesting that an optimal balance must be struck between concrete strength and confinement ratio.
The unified strength theory approach also has implications for welding quality control in CFST construction. The steel tube fabrication process—including the welding of longitudinal seams in ERW or SAW pipes—must ensure uniform wall thickness and absence of defects, because local wall thinning reduces the confining pressure and can lead to premature local buckling. Engineers should pay particular attention to weld seam quality, especially in high-strength steel tubes where the material's higher yield strength demands tighter manufacturing tolerances.
Summary
This study provides a theoretically rigorous and experimentally validated improvement to CFST column axial compression capacity calculation. The unified strength theory framework offers a physically meaningful description of the confined concrete behaviour that surpasses simpler empirical models. For engineering practice, the key takeaway is that the confinement coefficient must be calculated with attention to both geometric and material parameters, and that the formula's applicability is enhanced when the steel tube fabrication quality—particularly weld integrity and wall thickness uniformity—is well controlled throughout the manufacturing process.