Creep Analysis of Long-Span Concrete-Filled Steel Tube Arch Bridges

Literature Overview

The paper by Zhang Zhicheng (2007), published in Engineering Mechanics (Vol. 24, No. 5, pp. 151–160), addresses a critical and often underappreciated aspect of long-span CFST arch bridge design: the long-term deformation behavior of the core concrete under sustained loading. The author introduces the "age-adjusted effective modulus method" to derive a transformed elastic modulus formula for the core concrete within a steel tube, which simultaneously accounts for concrete creep and steel-concrete interaction. The method is then applied to a 308-meter span CFST arch bridge using ANSYS finite element software, and the results are validated against conventional approaches.

Core Technical Method

The fundamental challenge in creep analysis of CFST arch bridges lies in the coupled behavior between the steel tube and the core concrete. Unlike plain concrete structures, the steel tube imposes a lateral confining pressure on the core concrete, which alters the stress-strain history and consequently modifies the creep and shrinkage response. Traditional creep analysis methods, such as the simple effective modulus method, tend to underestimate long-term deformations because they do not account for the time-varying stress redistribution between steel and concrete.

The age-adjusted effective modulus method, originally proposed by Bažant and others, introduces an age-adjustment factor ρ that modifies the effective modulus to reflect the progressive change in stress during the loading period. The transformed elastic modulus E_eq for the core concrete is expressed as:

E_eq = E_c(t_0) / (1 + ρ × φ(t, t_0))

where E_c(t_0) is the instantaneous elastic modulus of concrete at the time of loading t_0, φ(t, t_0) is the creep coefficient from time t_0 to time t, and ρ is the age-adjustment factor that depends on the loading age and the creep model used.

The key insight of this paper is that by using the transformed modulus in a standard linear elastic finite element model, the nonlinear time-dependent behavior is effectively captured without requiring iterative incremental analyses. This dramatically simplifies the computational workflow while maintaining engineering accuracy.

Application to the 308 m Span Bridge

The case study bridge is a 308 m span CFST arch bridge, representative of the large-scale infrastructure projects undertaken in China during the 2000s. The finite element model in ANSYS employs shell elements for the steel tube and solid elements for the core concrete, with appropriate contact conditions to model the steel-concrete interface. The construction process is simulated in stages: steel tube erection, concrete infilling, and application of permanent and live loads.

The results demonstrate that the proposed method produces creep deformation predictions within approximately 5–8% of more rigorous time-step analyses, which is well within acceptable engineering tolerances for design purposes. Furthermore, the author compares the effects of different creep coefficient patterns recommended by the old and new Chinese bridge codes (JTG D60), finding that the newer code's pattern generally predicts larger long-term deflections, leading to more conservative design outcomes.

Engineering Practice Implications

For engineers involved in the design and construction of long-span CFST arch bridges, this paper offers several practical takeaways:

• The transformed modulus method provides a computationally efficient alternative to full time-dependent analyses, making it suitable for preliminary design and sensitivity studies.
• The choice of creep coefficient pattern significantly influences predicted long-term deflections; engineers should verify which code edition is adopted and consider the implications for deflection limits.
• The construction sequence must be carefully modeled, as the loading age of the core concrete at each stage directly affects the creep contribution.
• The steel-concrete interaction, particularly the confining effect, should not be neglected in creep analysis, as it can reduce the effective creep strain of the core concrete.

Study Insights and Reflections

Having reviewed this paper with a metallurgical and welding engineering perspective, I find the treatment of steel-concrete interaction particularly relevant. In my experience with pipe fitting fabrication, the interaction between different materials under sustained loading is a recurring theme, whether in dissimilar metal welds or in composite structures. The concept of a transformed modulus that lumps together time-dependent and interaction effects is analogous to the approach used in welding residual stress prediction, where equivalent elastic properties are sometimes employed to simplify thermo-mechanical coupling.

One limitation I would note is that the paper focuses on linear creep behavior and does not address potential nonlinear effects such as concrete cracking or steel yielding under extreme loading. For bridges subjected to severe environmental conditions or fatigue loading, a more comprehensive constitutive model may be warranted. Nevertheless, for the majority of service-level design cases, the method presented here represents a pragmatic and reliable tool.

In summary, this paper makes a valuable contribution to the structural engineering community by providing a simplified yet accurate framework for creep analysis of CFST arch bridges. The methodology is directly transferable to other composite structures involving steel and concrete, and its implementation in mainstream finite element software ensures broad accessibility to practicing engineers.