Zhuojin Pipe Fitting Co., LtdConstitutive Relationship of Steel Tube Concrete Under Axial Tension
Literature Overview
Published in Industrial Construction in 1990 by Pan Youguang and Zhong Shantong from Harbin Institute of Architecture and Civil Engineering, this paper analyzes the constitutive relationship of steel tube concrete (STC) members under axial tension. Supported by the National Natural Science Foundation of China, the study uses the compatibility of deformation conditions to analyze the load-bearing behavior of STC members under axial tension. The key finding is that the lateral constraint provided by the core concrete on the steel tube increases the proportional limit and yield point of the steel tube by approximately 10% within the commonly used STC range.
Core Technical Analysis
Deformation Compatibility Approach
The analytical approach adopted by the authors is based on the fundamental principle of deformation compatibility between the steel tube and the core concrete under axial tension. When an STC member is subjected to axial tension, both the steel tube and the concrete core experience the same axial strain (assuming perfect bond). However, the Poisson's ratio effects differ between the two materials, leading to a complex interaction.
Under axial tension, the steel tube tends to contract laterally (Poisson effect), while the concrete core, being in tension, also tends to contract laterally. However, the key insight is that the concrete core, being in tension, exerts a radial inward force on the steel tube through the interface bond. This radial constraint effectively puts the steel tube wall in a state of biaxial stress (axial tension plus radial compression), which raises the effective yield strength of the steel tube compared to its uniaxial yield strength.
| Parameter | Symbol | Description | Effect Under Tension |
|---|---|---|---|
| Axial strain | ε | Common to steel and concrete | Increases with load |
| Steel tube yield strength (uniaxial) | f_y | Specified yield strength | Baseline value |
| Steel tube yield strength (confined) | f_y' | Effective yield strength under confinement | f_y' ≈ 1.10 × f_y |
| Concrete tensile strength | f_ct | Tensile strength of concrete | Relatively low |
| Poisson's ratio (steel) | ν_s | Lateral contraction ratio | ≈ 0.3 |
| Poisson's ratio (concrete) | ν_c | Lateral contraction ratio | ≈ 0.2 |
Constitutive Relationship Derivation
The derivation of the constitutive relationship involves several key steps:
- Equilibrium equations: Establishing the force balance in the axial and radial directions for a differential element of the STC member.
- Compatibility conditions: Enforcing the condition that the axial strains in the steel tube and concrete core are equal at all points.
- Constitutive laws: Applying the appropriate stress-strain relationships for both materials, including the biaxial stress state in the steel tube.
- Interface conditions: Modeling the bond-slip behavior at the steel-concrete interface, which governs the load transfer between the two materials.
The resulting constitutive relationship describes the overall stress-strain behavior of the STC member under axial tension, incorporating the enhanced yield strength of the steel tube due to the radial confinement from the concrete core.
Engineering Practice Implications
The finding that the steel tube's yield point increases by approximately 10% under axial tension has direct implications for the design and quality control of STC members:
| Design Consideration | Impact of 10% Yield Strength Increase | Engineering Action |
|---|---|---|
| Tensile capacity calculation | Higher design capacity | Use f_y' = 1.10 × f_y in calculations |
| Steel tube selection | Lower grade steel may suffice | Optimize material selection for cost |
| Safety factor | Enhanced safety margin | Maintain standard safety factors |
| Quality control | Verify actual yield strength | Mill test certificates, tensile testing |
| Welding procedure | Account for enhanced yield strength | Adjust preheat and heat input |
For steel pipe manufacturing, the quality of the steel tube directly influences the accuracy of the constitutive relationship prediction. The yield strength of the steel tube must be accurately known from mill test certificates, and any deviation from the specified grade (e.g., due to heat treatment variations or chemical composition fluctuations) will affect the predicted 10% enhancement.
The interface bond between the steel tube and the concrete core is critical to the validity of the constitutive relationship. In practice, the bond strength depends on several factors:
- Surface preparation: Ribbed or deformed steel tubes provide better bond than smooth tubes.
- Concrete mix design: The aggregate size, cement content, and water-cement ratio affect the bond strength.
- Placement quality: Proper compaction ensures intimate contact between the concrete and the tube inner surface.
- Curing conditions: Proper curing is essential for achieving the specified concrete strength and bond.
Key Questions and Reflections
The paper's analysis is theoretically sound and provides valuable insight into the tensile behavior of STC members. However, several questions merit further investigation. First, the 10% enhancement in yield strength is stated to apply within the "commonly used STC range," but the specific range of parameters (tube dimensions, concrete grades, steel grades) over which this enhancement is valid should be explicitly defined. Second, the effect of concrete cracking under tension on the bond strength and the composite action should be considered, as cracking may reduce the radial constraint on the steel tube. Third, the long-term behavior under sustained tensile loading, considering creep and shrinkage of the concrete, should be investigated.
The analytical approach adopted by the authors is elegant in its simplicity, relying on fundamental principles of equilibrium and compatibility rather than complex numerical methods. This approach is well-suited for deriving closed-form constitutive relationships that can be directly incorporated into design codes and hand calculations.
Study Insights
This literature, though published in 1990, remains relevant to contemporary engineering practice because it addresses a fundamental aspect of STC member behavior that is often overlooked in design codes. The finding that the steel tube's yield strength is enhanced by approximately 10% under axial tension due to the radial constraint from the concrete core has direct implications for the design of STC tension members, such as those used in bridge stay cables, tensile bracing, and suspended structures. For steel pipe engineers, the key takeaway is that the mechanical properties of the steel tube—particularly the yield strength and the Poisson's ratio—are critical parameters in the constitutive relationship, and their accurate determination through quality control testing is essential for reliable design. The analytical framework presented here can serve as a foundation for more advanced studies that incorporate additional factors such as strain rate effects, temperature effects, and cyclic loading effects.