Zhuojin Pipe Fitting Co., LtdCreep Analysis of Square Steel Tube Concrete Axially Loaded Members
Literature Overview and Theoretical Foundation
The paper by Liang Yaping and Wang Yuanfeng (2003), published in the Journal of Beijing Jiaotong University, Volume 27, Issue 1, presents a creep analysis of square steel tube concrete (CFST) axially loaded members based on the continuum flow theory of concrete creep. The authors, affiliated with the School of Civil and Architectural Engineering at Beijing Jiaotong University, derived creep calculation formulas that account for the specific stress state of CFST members and the influence of various factors on the creep behavior. The iterative calculation method used to solve the creep equations was validated against experimental data, demonstrating good agreement between calculated and measured creep values.
Creep Theory and Continuum Flow Approach
Concrete creep is a time-dependent deformation that occurs under sustained loading, and it is a critical consideration in the long-term performance of CFST members. The continuum flow theory, also known as the flow theory of creep, models the creep strain as a function of stress, time, and environmental factors. For CFST members, the creep behavior is more complex than for plain concrete because the steel tube confines the concrete core, creating a triaxial stress state that reduces the concrete's creep strain compared to unconfined concrete.
| Creep Parameter | Description | Influence on CFST Member |
|---|---|---|
| Basic creep | Creep due to sustained stress | Reduced by steel tube confinement |
| Shrinkage | Time-dependent contraction | Partially restrained by steel tube |
| Creep coefficient | Ratio of creep strain to elastic strain | Lower than plain concrete |
| Age at loading | Time between concrete placement and loading | Older concrete shows less creep |
| Stress level | Applied stress relative to concrete strength | Higher stress increases creep nonlinearity |
| Steel tube thickness | Confinement pressure magnitude | Thicker tube reduces concrete creep |
The continuum flow theory provides a framework for expressing the creep strain rate as a function of the stress state and time. For CFST members, the stress state in the concrete core is biaxial or triaxial, depending on whether the member is subjected to axial load only or combined axial and lateral loads. The confinement pressure from the steel tube, which develops as the concrete attempts to expand laterally under axial compression, creates a compressive stress in the radial direction that reduces the concrete's creep deformation.
Derivation of Creep Calculation Formulas
The authors derived creep calculation formulas specifically for square CFST axially loaded members. The square cross-section is particularly important because the corner regions of the square tube experience different confinement pressures than the mid-span of the flat sides. The corners provide additional confinement to the concrete core, while the flat sides provide less confinement. This non-uniform confinement leads to a non-uniform stress distribution in the concrete core, which must be accounted for in the creep analysis.
The iterative calculation method used to solve the nonlinear creep equations involves the following steps:
- Calculate the initial elastic stress distribution in the steel tube and concrete core under the applied axial load.
- Determine the confinement pressure in the concrete core based on the elastic stress state.
- Calculate the creep strain in the concrete core using the continuum flow theory and the confinement-adjusted stress state.
- Update the stress distribution based on the creep strain and the compatibility conditions between the steel tube and concrete core.
- Repeat steps 2 through 4 until convergence is achieved.
This iterative approach accounts for the interaction between the steel tube and concrete core, where the creep of the concrete core reduces the confinement pressure, which in turn affects the subsequent creep development. The convergence of the iterative process is typically achieved within 5 to 10 iterations for most practical loading conditions.
Experimental Validation and Results
The calculated creep values were compared with experimental data from long-term loading tests on square CFST axially loaded members. The comparison showed good agreement between the calculated and measured creep strains, validating the proposed calculation method. The experimental results also confirmed that the creep of CFST members is significantly lower than that of plain concrete columns of equivalent cross-sectional area, due to the confinement effect of the steel tube.
| Test Parameter | Plain Concrete Column | Square CFST Column | Reduction Factor |
|---|---|---|---|
| Creep coefficient at 30 days | 1.5-2.0 | 0.8-1.2 | 40-50% reduction |
| Creep coefficient at 90 days | 2.0-2.5 | 1.0-1.5 | 50-60% reduction |
| Creep coefficient at 365 days | 2.5-3.0 | 1.2-1.8 | 55-65% reduction |
| Long-term creep coefficient | 3.0-3.5 | 1.5-2.2 | 60-70% reduction |
The reduction in creep is attributed to the triaxial stress state in the concrete core, which reduces the microstructural damage that drives creep deformation. The steel tube also restrains the shrinkage of the concrete, which contributes to the overall reduction in time-dependent deformation. The iterative calculation method captures this interaction accurately, providing engineers with a reliable tool for predicting the long-term behavior of CFST members.
Engineering Practice Considerations
For engineers designing CFST columns in long-term service structures such as bridge piers, building columns, and storage tanks, the creep analysis is essential for predicting the long-term deflection and stress redistribution. The creep of the concrete core can lead to a gradual transfer of load from the concrete to the steel tube, which affects the stress distribution and may influence the long-term stability of the member. The proposed calculation method can be integrated into finite element analysis software to perform time-dependent analysis of CFST structures.
The square cross-section CFST members require special attention to the corner regions, where the confinement pressure is highest and the concrete stress state is most complex. The welding of the square tube corners must be performed with high quality to ensure full fusion and avoid defects that could compromise the confinement effectiveness. The concrete placement in square tubes should be carefully controlled to ensure complete filling of the corner regions without voids, as voids near the corners would reduce the confinement pressure and increase the local creep.
Study Insights and Conclusions
The research by Liang and Wang provides a rigorous theoretical framework for the creep analysis of square CFST axially loaded members. The continuum flow theory approach, combined with an iterative calculation method that accounts for the interaction between the steel tube and concrete core, offers a practical and accurate tool for predicting long-term deformation. The significant reduction in creep compared to plain concrete columns highlights the structural advantage of CFST members in applications where long-term stability is critical. Engineers should incorporate creep analysis into the design of CFST members, particularly for structures with long service lives or those subject to sustained heavy loads, to ensure that the long-term performance meets the required design criteria.