Ultimate Bearing Capacity Calculation of Square Steel Tube Concrete Axially Compressed Short Members

Literature Overview

The paper by Wu Jianbin, Zhao Hongtie, Xue Jianyang, Ge Hongpeng, and Kang Xiliang, published in Building Structures (2007, Vol. 37, Issue 10, pp. 72-73), presents a theoretical analysis of the load-bearing mechanism of square steel tube concrete (STC) short columns under axial compression. The authors propose fundamental assumptions for the bearing capacity calculation and derive an analytical expression for the ultimate load capacity at steel tube yielding using the limit equilibrium method. Funded by the National Natural Science Foundation of China (50478044), this work contributes to the theoretical foundation of STC member design.

Core Technical Points

The authors begin with a theoretical analysis of the stress-strain behavior of square STC short members under axial compression. The key assumptions include:

Plane sections remain plane before yielding of the steel tube
The concrete core is confined by the steel tube, with the confinement effect characterized by a confinement effectiveness coefficient
The steel tube yields uniformly at the ultimate state
The stress distribution in the concrete follows a modified constitutive model that accounts for lateral confinement

Using the limit equilibrium method, the authors derive a closed-form analytical expression for the ultimate bearing capacity of the member at the point of steel tube yielding. This analytical solution is then validated against experimental data from both domestic and international test programs, demonstrating good agreement.

Key Design Parameters and Their Influence

Parameter	Symbol	Typical Range	Influence on Capacity
Steel tube width	b	100-600 mm	Proportional increase in capacity
Steel tube wall thickness	t	4-20 mm	Increases confinement and capacity
Concrete strength	f_c	20-80 MPa	Proportional increase in capacity
Steel yield strength	f_y	235-460 MPa	Moderate increase in capacity
Confinement effectiveness coefficient	η	0.3-0.9	Higher η means better confinement
Steel tube slenderness ratio	b/t	10-100	Lower ratio gives higher confinement

Confinement Effectiveness and Steel Tube Geometry

The confinement effectiveness coefficient is a critical parameter in the analytical model, and it depends heavily on the geometric properties of the square steel tube. For square tubes, the confinement is less effective than for circular tubes because the corners of the square section do not provide uniform lateral pressure to the concrete. The authors' analytical approach accounts for this geometric effect through the confinement effectiveness coefficient, which is a function of the b/t ratio and the relative dimensions of the concrete core.

From a steel pipe manufacturing perspective, the b/t ratio directly influences the forming process and weld quality of square tubes. For square tubes with high b/t ratios (thin-walled sections), the corner radius becomes a critical parameter. According to EN 10219 and GB/T 6728, the minimum internal corner radius should not be less than 1.5 times the wall thickness. For thin-walled square tubes used in STC applications, the corner radius affects both the forming process (cold bending or roll forming) and the weld quality at the longitudinal seam.

Welding Considerations for Square STC Columns

Square steel tubes used in STC columns are typically manufactured by cold bending of hot-rolled strip followed by longitudinal welding. The welding process must be carefully controlled to ensure:

Full penetration of the longitudinal weld with no lack of fusion or incomplete penetration
Controlled heat input to prevent excessive distortion of the tube profile
Residual stress management through proper welding sequence and, if necessary, stress-relieving treatment
Surface quality of the weld seam meeting the requirements for concrete pouring (smooth, no undercut that could trap air during concrete placement)

The recommended welding processes for square tube longitudinal seams include:

Tube Wall Thickness	Recommended Process	Filler Metal	Shielding Gas
3-6 mm	GMAW (MAG)	ER50-6 or equivalent	CO₂ + 5% O₂
6-12 mm	SAW (single or double)	SAl-Fe-50 or equivalent	Flux + CO₂
12-25 mm	SAW (double) or FCAW	SAl-Fe-50 or equivalent	Flux + CO₂
> 25 mm	SAW (double) with preheating	SAl-Fe-50 or equivalent	Flux + CO₂

Validation and Engineering Application

The analytical expression derived in this paper has been validated against experimental data from multiple research programs, demonstrating its reliability for design purposes. The approach provides a more transparent and physically meaningful basis for capacity calculation compared to empirical formulas, as it explicitly accounts for the interaction between the steel tube and the confined concrete.

For engineering practice, this analytical method can be used to:

Verify the design capacity of existing STC columns under retrofitting scenarios
Optimize the steel tube geometry (b, t) for a given concrete strength and load requirement
Evaluate the effect of material degradation (steel corrosion, concrete carbonation) on remaining capacity
Develop design charts and simplified formulas for routine engineering use

Study Insights and Implications

This research contributes a rigorous theoretical framework for the design of square STC short columns, bridging the gap between empirical design codes and fundamental mechanics. The explicit consideration of the confinement effectiveness coefficient allows engineers to quantify the contribution of the steel tube to concrete confinement and make informed decisions about section geometry and material selection.

From a manufacturing and quality control standpoint, the analytical model reinforces the importance of maintaining tight dimensional tolerances on square steel tubes, particularly the wall thickness uniformity and corner radius consistency. Variations in these parameters directly affect the confinement effectiveness and, consequently, the load-bearing capacity of the STC member. Quality assurance programs for square tube supply should include dimensional inspection (wall thickness at multiple locations, corner radius measurement), visual inspection of weld seams, and non-destructive testing as specified in relevant standards.