Zhuojin Pipe Fitting Co., LtdCreep Analysis of Axially Compressed Steel-Concrete Composite Short Columns
Overview of the Study
This paper by Han Bing and Wang Yuanfeng from the School of Civil Engineering and Architecture, Northern Jiaotong University, published in the Journal of the China Railway Society in 1999 (Volume 21, Issue 6, pages 87-90), addresses the time-dependent deformation behavior of steel-concrete composite columns under sustained axial compression. The study employs the hereditary flow theory to develop a simplified one-dimensional creep calculation model specifically tailored to the mechanics of confined concrete within steel tubes. This work is foundational for the long-term design and assessment of composite column structures in railway bridges, buildings, and infrastructure where sustained loading conditions prevail.
Theoretical Framework
The hereditary flow theory, also known as the age-dependent creep theory, provides a rigorous mathematical framework for describing the time-dependent strain of concrete under sustained stress. Unlike simpler approaches that assume constant creep coefficients, the hereditary flow theory accounts for the age at which the stress is applied, the duration of loading, and the nonlinear interaction between elastic and creep deformations.
Key Theoretical Elements
| Element | Description | Relevance to Steel-Concrete Composite |
|---|---|---|
| Hereditary integral | Integral formulation of time-dependent strain | Captures the loading history effect on creep |
| Creep compliance function | Time-dependent strain per unit stress | Modified for confined concrete behavior |
| Elastic modulus of confined concrete | Increased due to lateral confinement by steel tube | Steel tube provides radial restraint |
| Poisson's ratio of composite section | Effective ratio for the composite cross-section | Governs the interaction between steel and concrete |
| One-dimensional simplification | Reduction of 3D problem to 1D axial model | Valid for short columns under axial load |
The authors' key insight is that the steel tube in a steel-concrete composite column provides lateral confinement to the concrete core, which fundamentally alters the creep behavior compared to unconfined concrete. Under sustained axial load, the concrete tends to expand laterally due to creep, but the steel tube restrains this expansion. This restraint introduces a confining pressure that increases with time, which in turn reduces the creep strain of the concrete. This coupled interaction between the steel tube and concrete core is the central mechanical feature that the authors' model captures.
Simplified One-Dimensional Creep Model
The authors propose a one-dimensional creep calculation formula by exploiting the symmetry and simplicity of the composite column cross-section. For a short column under axial compression, the deformation is predominantly axial, and the radial equilibrium between the steel tube and concrete core can be expressed in a closed-form relationship.
The derivation proceeds as follows:
- Concrete creep strain: Expressed using the hereditary flow integral, which depends on the stress history and the concrete's age at loading.
- Steel tube deformation: Governed by elastic behavior with consideration of the Poisson effect and the confining pressure interaction.
- Compatibility condition: The radial strain of the steel tube equals the radial strain of the concrete core at the interface.
- Equilibrium condition: The sum of axial forces in the steel tube and concrete equals the applied load.
By solving these coupled equations, the authors obtain a simplified formula that predicts the time-dependent axial shortening of the composite column. The model is then compared with experimental-based regression formulas from the literature, demonstrating reasonable agreement.
Comparison with Experimental Approaches
| Approach | Method | Strengths | Limitations |
|---|---|---|---|
| Hereditary flow theory (this paper) | Analytical model based on fundamental mechanics | Physically rigorous, accounts for confinement | Requires accurate material parameters |
| Empirical regression (literature [5]) | Statistical fitting to experimental data | Simple to apply | Limited to specific test conditions |
| Finite element analysis | Numerical simulation | Captures complex interactions | Computationally intensive |
Engineering Significance and Practice
Steel-concrete composite columns are widely used in railway bridges, high-rise buildings, and industrial structures where high load-bearing capacity and compact cross-sections are required. The long-term behavior of these columns is critical for serviceability assessment, as excessive creep can lead to:
- Differential settlement: In bridge structures, time-dependent shortening of composite columns can cause uneven deck deflection.
- Cracking of adjacent elements: Excessive creep in composite columns may induce cracking in connected structural members.
- Loss of prestress: In prestressed composite systems, creep-induced shortening reduces the effective prestress force.
For design practice, the following recommendations emerge from this study:
- Material characterization: Accurate determination of the creep compliance function for the specific concrete mix is essential. Standard concrete with high water-cement ratios exhibits significantly higher creep than low-w/c ratio concrete.
- Steel tube specification: The steel grade and wall thickness influence the confinement effectiveness. Thicker walls provide greater restraint but may over-constrain the concrete, leading to potential cracking under thermal effects.
- Loading history: The age of concrete at the time of loading is a critical parameter. Creep is substantially reduced when loading is applied at a later age, as the concrete has already undergone significant self-desiccation shrinkage.
Study Insights and Implications
This paper contributes a physically grounded analytical tool for predicting the long-term deformation of steel-concrete composite columns. The hereditary flow theory approach, while mathematically more complex than empirical methods, provides superior predictive capability for varying loading histories and material conditions. For railway bridge engineers, where composite columns may be subjected to sustained loads for decades, this type of analysis is essential for ensuring long-term serviceability. The one-dimensional simplification is a practical compromise that retains the essential physics while remaining computationally tractable for routine design applications. Future work should extend this framework to eccentrically loaded columns and consider the interaction between creep and other time-dependent effects such as shrinkage and thermal cycling.