Creep Analysis of CFST Members under Large Eccentric Compression - Technical Study Note

Literature Overview

The paper by Guo Weiwei, Wang Yuanfeng, and Han Bing (Engineering Mechanics, 2003, Vol. 20, No. 1, pp. 91-95) investigates the creep behavior of concrete-filled steel tube (CFST) members subjected to large eccentric compression. The research is supported by the Ministry of Railways Science and Technology Development Fund (J99Z071) and the Northern Jiaotong University Fund (2002SM011). The authors employ the hereditary flow theory for creep analysis under continuously unloading conditions, extending the conventional creep models to account for the complex stress history experienced by CFST members.

Core Technical Content

Creep Phenomenon in CFST Members

In CFST members under eccentric compression, the stress distribution across the cross-section is non-uniform. The concrete on the compression side experiences sustained compressive stress, leading to time-dependent deformation (creep), while the concrete on the tension side may experience unloading as the steel tube takes on more of the tensile force. This unloading condition is particularly challenging for creep analysis because conventional creep models assume monotonic loading.

Hereditary Flow Theory Application

The hereditary flow theory (also known as the hereditary integral or Boltzmann superposition principle) expresses the creep strain as a convolution integral of the stress history and the creep compliance function:

ε_creep(t) = ∫₀ᵗ S(t-τ) · dσ(τ)

where S(t-τ) is the creep compliance function and dσ(τ) represents the stress increment at time τ. This formulation is particularly suitable for CFST members because it can handle the continuously varying stress state caused by the redistribution of internal forces between the steel tube and the core concrete over time.

Key Findings

1. Steel ratio effect: Increasing the steel ratio (ρ = A_s·f_y / (A_c·f'c)) significantly reduces the creep deformation. This is because the steel tube provides greater confinement to the core concrete, delaying the onset of micro-cracking and reducing the creep compliance.
2. Eccentricity effect: Higher eccentricity ratios lead to larger tension zones in the concrete, where unloading occurs. The unloading creep (recovery) partially compensates for the compression-side creep, but the net effect is still an increase in total creep deformation due to the non-linearity of concrete creep.
3. Confinement stress effect: The lateral confinement provided by the steel tube reduces the creep of the core concrete. The confinement stress increases with the axial load and is highest at the interface between the steel tube and the concrete. This confinement effect is most pronounced for members with lower D/t ratios (thicker walls).
4. Time-dependent behavior: The creep deformation increases with time, but the rate of increase decreases as the member ages. The hereditary flow theory captures this aging effect through the time-dependent compliance function.

Interpretation of Technical Points

Creep Model Selection

The selection of the hereditary flow theory over simpler models (such as the effective modulus method or the age-adjusted effective modulus method) is justified by the complex stress history in CFST members under large eccentric compression. The effective modulus method assumes that the stress is constant throughout the loading period, which is not the case for eccentrically loaded CFST members where the stress redistributes over time.

Engineering Implications for Pipe Design

From a pipe fabrication and design perspective, the creep analysis has several important implications:

1. Long-term deflection control: The creep deformation contributes to the long-term deflection of CFST columns and frames. For slender members, the creep-induced second-order effects (P-Δ effects) can significantly amplify the total deflection. The design must account for this by either increasing the member stiffness or reducing the eccentricity.
2. Stress redistribution: Over time, the creep of the concrete core causes a redistribution of stresses between the steel tube and the concrete. The steel tube gradually takes on more of the load, which can lead to increased stress in the weld joints connecting the steel tube to other structural elements. This stress redistribution should be considered in the fatigue assessment of welded connections.
3. D/t ratio optimization: The creep analysis suggests that members with lower D/t ratios (thicker walls) exhibit less creep because the confinement stress is higher. However, thicker walls increase material cost and weight. An optimal D/t ratio must be found that balances creep performance with economic considerations. For railway applications, a D/t ratio of 60-80 is commonly recommended.

Process and Standards Analysis

The creep analysis methodology presented in this paper aligns with the principles established in major design codes:

• GB 50017-2017 (Chinese Code for Design of Steel Structures): Provides creep coefficients for concrete-filled steel tubes based on the effective modulus method, but does not explicitly address the stress redistribution effects in eccentrically loaded members.
• Eurocode 4 (EN 1994-1-2): Uses a time-dependent analysis approach that is conceptually similar to the hereditary flow theory, but with simplified compliance functions.
• ACI 318: Provides creep factors for reinforced concrete members but does not specifically address CFST members.

The hereditary flow theory used in this paper represents a more rigorous approach that could be incorporated into future revisions of these codes. The iterative method used to simulate the time-dependent nature of creep is particularly valuable for long-term performance prediction, which is essential for the design of railway bridges and other infrastructure with a 100-year design life.

Integration with Engineering Practice

In practical engineering, the creep analysis of CFST members is most relevant for the following scenarios:

1. Long-term serviceability assessment: For railway bridges, the long-term deflection must be controlled to ensure track geometry is maintained. The creep analysis provides the tools to predict deflections at various time intervals (1 year, 5 years, 25 years, 50 years, 100 years) and to verify that they remain within acceptable limits.
2. Weld joint fatigue assessment: The stress redistribution caused by creep can lead to cyclic stress variations in weld joints, particularly at the connections between the steel tube and the end plates or stiffeners. These cyclic stresses must be evaluated against the fatigue design curve (e.g., FAT 90 or FAT 112 per EN 1993-1-9) to ensure adequate fatigue life.
3. Construction sequencing: The creep analysis can inform the construction sequencing decisions. For example, if the concrete is placed at a young age (e.g., 3 days), the creep will be significantly larger than if placed at a mature age (e.g., 28 days). This has implications for the timing of welding operations and the application of prestress.

Key Questions and Reflections

• The paper focuses on the creep of the concrete core, but what about the creep of the steel tube itself? At elevated temperatures or under sustained high stresses, the steel can also exhibit time-dependent deformation (creep or relaxation). This is particularly relevant for CFST members in fire conditions or in high-temperature environments.
• How does the creep analysis interact with the fracture mechanics assessment of weld defects? A pre-existing weld crack can grow under the sustained stresses caused by creep, and the combined effect of creep and crack growth should be evaluated for critical members.
• The paper uses a linear creep model, but concrete creep is inherently non-linear, especially at high stress levels. How does the non-linearity affect the accuracy of the hereditary flow theory predictions?

Study Insights and Implications

This paper makes a significant contribution to the understanding of time-dependent behavior in CFST members. The use of the hereditary flow theory represents a rigorous and physically meaningful approach that captures the complex stress history experienced by eccentrically loaded CFST members. The findings have direct implications for the design and fabrication of CFST structures, particularly in terms of long-term deflection control and weld joint fatigue assessment.

For pipe fabricators, the key message is that the creep behavior of the concrete core affects the long-term stress state of the steel tube, which in turn affects the fatigue performance of weld joints. Therefore, the creep analysis should be an integral part of the design process, and the results should be communicated to the fabrication team to ensure that the weld details are designed for the appropriate fatigue category. The paper also highlights the importance of the steel ratio and the D/t ratio in controlling creep, which are parameters that are directly determined during the pipe selection and fabrication stage.