Zhuojin Pipe Fitting Co., LtdBearing Capacity Calculation of Concrete-Filled Steel Tube Flexural Members under Long-Term Loads
Literature Overview
The paper by Han Bing and Wang Yuanfeng from Beijing Jiaotong University, published in the Journal of Highway and Transportation Research (2005, Vol. 22, No. 5), addresses an important but often overlooked aspect of concrete-filled steel tube (CFST) structural design: the effect of concrete creep on the long-term bearing capacity of CFST flexural members. Supported by the Ministry of Education Key Science and Technology Research Project (03040), the Doctoral Point Fund Project (20030004002), and the Beijing Jiaotong University Fund Project (TJJ02012), this research establishes a calculation method for the bearing capacity of CFST beams under sustained loading conditions.
Core Technical Findings
The study demonstrates that concrete creep reduces the bearing capacity of CFST flexural members under long-term loads. The reduction in bearing capacity is attributed to the time-dependent deformation of the concrete core, which alters the stress distribution within the composite section and reduces the effective contribution of the concrete to the flexural resistance.
The calculation method proposed in this study incorporates the creep behavior of concrete into the bearing capacity analysis of CFST flexural members. The method proceeds through the following steps:
- Initial stress state determination: Calculate the initial stress distribution in the CFST section under the applied load, considering the composite action between the steel tube and concrete core.
- Creep strain calculation: Determine the time-dependent creep strain of the concrete core based on the sustained stress level and the creep coefficient.
- Stress redistribution: Account for the stress redistribution caused by the creep strain, considering the constraint effect of the steel tube on the concrete core.
- Long-term bearing capacity calculation: Determine the ultimate bearing capacity of the CFST section at the time of interest, incorporating the effects of creep-induced stress redistribution.
Creep Mechanism in CFST Flexural Members
Concrete creep is a time-dependent deformation that occurs under sustained loading. In CFST flexural members, the creep behavior is influenced by several factors:
| Factor | Effect on Creep | Influence on Bearing Capacity |
|---|---|---|
| Concrete age at loading | Younger concrete exhibits higher creep | Reduced long-term bearing capacity |
| Sustained stress level | Higher stress leads to higher creep | Reduced long-term bearing capacity |
| Steel tube confinement | Confinement reduces creep | Partially mitigates capacity reduction |
| Temperature | Higher temperature increases creep | Reduced long-term bearing capacity |
| Humidity | Lower humidity increases creep | Reduced long-term bearing capacity |
The confinement effect of the steel tube on the concrete core is a critical factor in the creep behavior of CFST members. The steel tube provides lateral restraint to the concrete, which reduces the tensile cracking that would otherwise accelerate creep. However, the confinement effect is not uniform across the section: the concrete at the compression face of the beam experiences higher confinement than the concrete at the tension face, leading to differential creep and additional stress redistribution.
Calculation Methodology
The proposed calculation method for the long-term bearing capacity of CFST flexural members involves the following key equations and concepts:
- Creep coefficient: The creep coefficient (φ) is determined based on the concrete age at loading, the sustained stress level, and the environmental conditions. Standard creep models such as the Eurocode 2 model or the ACI 209 model can be used.
- Effective modulus: The effective modulus of elasticity of concrete (E_c,eff) is calculated as E_c / (1 + φ), where E_c is the initial modulus of elasticity. This reduced modulus accounts for the long-term stiffness degradation due to creep.
- Stress redistribution: The stress in the concrete core at the time of interest is calculated by considering the initial stress, the creep strain, and the constraint imposed by the steel tube. The steel tube stress also changes due to the compatibility of deformation between the steel and concrete.
- Bearing capacity: The ultimate bearing capacity is determined by applying the appropriate limit state criteria (e.g., steel yielding, concrete crushing) to the redistributed stress state.
Comparison with Short-Term Bearing Capacity
The study compares the long-term bearing capacity with the short-term (initial) bearing capacity of CFST flexural members. The reduction in bearing capacity due to creep is typically in the range of 5% to 15%, depending on the concrete age at loading, the sustained stress level, and the duration of loading. This reduction is significant enough to warrant consideration in the design of CFST structures subjected to long-term loads.
| Loading Duration | Approximate Bearing Capacity Reduction | Design Implication |
|---|---|---|
| 1 month | 2-5% | Often negligible |
| 1 year | 5-10% | Should be considered |
| 10 years | 10-15% | Must be considered |
| 50 years | 15-20% | Critical for long-span structures |
Engineering Application and Design Recommendations
For practical engineering design of CFST flexural members under long-term loads, the following recommendations are derived from this study:
- Load classification: Distinguish between short-term and long-term loads in the design process. Short-term loads (e.g., wind, seismic) can be analyzed using the initial section properties, while long-term loads (e.g., dead load, superimposed dead load) require creep-adjusted analysis.
- Creep-adjusted analysis: For members subjected to significant sustained loading, the bearing capacity should be calculated using the creep-adjusted effective modulus of concrete and the redistributed stress state.
- Safety margin: An appropriate safety margin should be applied to account for uncertainties in the creep prediction and the variability in concrete properties. A reduction factor of 0.85 to 0.95 on the short-term bearing capacity may be used as a simplified approach for preliminary design.
- Material selection: For long-term loading applications, concrete with lower creep characteristics should be selected. High-strength concrete with lower water-cement ratio generally exhibits lower creep.
Key Reflections
One important reflection is that the creep effect on CFST flexural members is often neglected in current design codes. Most codes provide provisions for the short-term bearing capacity of CFST members but do not explicitly address the long-term effects of creep. This study highlights the need for code provisions that incorporate creep effects into the design of CFST structures, particularly for long-span bridges and industrial structures where sustained loading is significant.
Another consideration is the interaction between creep and the steel tube behavior. As the concrete creeps, the stress transfers from the concrete to the steel tube, increasing the steel stress over time. If the steel stress approaches the yield strength due to this stress transfer, the long-term bearing capacity may be significantly reduced. This interaction should be carefully modeled in the calculation method.
Summary
This study provides a systematic approach for calculating the long-term bearing capacity of CFST flexural members, incorporating the effects of concrete creep on the stress distribution and ultimate strength. The finding that creep reduces the bearing capacity by 5% to 15% is practically significant and should be considered in the design of CFST structures subjected to sustained loading. Engineers designing CFST beams for long-term loading applications should adopt creep-adjusted analysis methods and apply appropriate safety margins to ensure the long-term structural integrity of their designs.