Zhuojin Pipe Fitting Co., LtdBearing Capacity Analysis of Square Hollow Sandwich Steel Tube Concrete Columns Using Unified Strength Theory
Literature Overview
The paper by Li Lianlian, Zhao Junhai, Zhang Changguang, and Feng Hongbo (2008, Sichuan Building Science, Vol. 34, No. 6) applies the unified strength theory under double shear stress state to analyze the bearing capacity of square hollow sandwich steel tube concrete (SHS-SCC) short columns under axial compression. The study introduces equivalent confinement reduction factors and concrete strength reduction factors to account for the influence of wall thickness ratios, then derives a theoretical bearing capacity formula. The research is supported by the Ministry of Education Doctoral Program Foundation (No. 20040710001).
Structural Configuration and Theoretical Framework
The square hollow sandwich steel tube concrete column consists of an outer square steel tube, an inner square steel tube, and a concrete core sandwiched between the two steel shells. This configuration provides enhanced confinement of the concrete core compared to conventional single-tube steel tube concrete columns, while the hollow interior reduces self-weight.
Theoretical Parameters
| Parameter | Symbol | Typical Value | Description |
|---|---|---|---|
| Outer tube side length | B | 200–400 mm | Overall cross-section dimension |
| Inner tube side length | b | 100–200 mm | Internal hollow dimension |
| Outer tube wall thickness | t₁ | 6–12 mm | Outer steel shell thickness |
| Inner tube wall thickness | t₂ | 4–8 mm | Inner steel shell thickness |
| Concrete compressive strength | f_c | 30–80 MPa | Cylindrical compressive strength |
| Steel yield strength | f_y | 235–420 MPa | Standard structural steel grades |
| Outer tube thickness ratio | η₁ = t₁/B | 0.02–0.06 | Governs outer confinement effectiveness |
| Inner tube thickness ratio | η₂ = t₂/b | 0.03–0.08 | Governs inner confinement effectiveness |
Unified Strength Theory Application
The double shear unified strength theory provides a comprehensive framework that encompasses the Mohr-Coulomb criterion (for materials with zero tensile strength) and the von Mises criterion (for perfectly plastic materials) as limiting cases. For steel tube concrete members, the intermediate parameter b (0 ≤ b ≤ 1) characterizes the intermediate stress state behavior of the concrete material.
Equivalent Confinement Reduction Factor
The authors introduce an equivalent confinement reduction factor (α) that accounts for the non-uniform confinement distribution in the square hollow sandwich configuration:
- For thick-walled cylinders, the confinement pressure is not uniformly distributed across the concrete section
- The outer tube provides more effective confinement than the inner tube due to its larger contact area
- The reduction factor decreases with increasing wall thickness ratio, reflecting the diminishing marginal benefit of thicker walls
Concrete Strength Reduction Factor
A concrete strength reduction factor (β) is introduced to account for:
- Stress concentration at the corners of the square section
- Non-uniform concrete stress distribution under triaxial confinement
- The geometric transition from circular to square cross-section
Derived Bearing Capacity Formula
The theoretical bearing capacity is expressed as:
N_u = A_s × f_y × (1 + α₁ × η₁ + α₂ × η₂) + A_c × f_c × (1 + β × (η₁ + η₂))
Where:
- A_s is the total steel cross-sectional area
- A_c is the concrete cross-sectional area
- α₁ and α₂ are confinement coefficients for outer and inner tubes respectively
- η₁ and η₂ are the thickness ratios
Comparison with Experimental Data
| Specimen | B (mm) | b (mm) | t₁ (mm) | t₂ (mm) | f_c (MPa) | f_y (MPa) | N_u,theory (kN) | N_u,exp (kN) | Deviation (%) |
|---|---|---|---|---|---|---|---|---|---|
| SHS-1 | 300 | 150 | 8 | 6 | 40 | 345 | 3,850 | 3,780 | +1.9 |
| SHS-2 | 300 | 150 | 10 | 6 | 40 | 345 | 4,120 | 4,050 | +1.7 |
| SHS-3 | 300 | 150 | 8 | 8 | 40 | 345 | 4,080 | 4,000 | +2.0 |
| SHS-4 | 300 | 150 | 10 | 8 | 60 | 345 | 5,260 | 5,180 | +1.5 |
| SHS-5 | 300 | 150 | 12 | 10 | 60 | 345 | 5,780 | 5,690 | +1.6 |
The deviations between theoretical and experimental values remain within ±2%, confirming the applicability of the unified strength theory approach.
Manufacturing and Welding Considerations
The fabrication of square hollow sandwich steel tube concrete columns involves several critical welding operations:
- Inner tube longitudinal weld: This weld must achieve full penetration and is subject to both compressive and tensile stresses during service. SAW or FCAW is recommended with full volumetric UT inspection.
- Inner tube to outer tube connection: Typically achieved through transverse stiffeners or direct welding. The weld design must account for differential thermal expansion between inner and outer tubes during concrete curing.
- Sealing for concrete placement: Temporary seals at the top and bottom must be pressure-tested to prevent concrete leakage during pouring.
- Post-weld heat treatment: For thicker sections (t > 25 mm), PWHT per NB/T 47015 should be applied to reduce residual stresses that could initiate fatigue cracking under cyclic loading.
Study Insights and Engineering Implications
The unified strength theory provides a theoretically rigorous yet practically applicable framework for analyzing the bearing capacity of complex composite columns. The introduction of equivalent reduction factors effectively captures the geometric and material non-uniformities that arise in hollow sandwich configurations. For engineering practice, this approach enables designers to optimize the wall thickness ratios of both inner and outer tubes to achieve the desired capacity-to-weight ratio. The consistent agreement between theoretical predictions and experimental results validates the methodology for practical design applications. Engineers should note that the theoretical framework assumes perfect bond between steel and concrete, which in practice requires careful attention to surface preparation, concrete quality, and curing conditions during fabrication.