Out-of-Plane Creep Stability Analysis of Steel Tube Concrete Arches

Literature Overview

Jiang Wei, Lü Dagang, and Yang Dawei (2013), published in Journal of Harbin Institute of Technology (Vol. 45, No. 10, pp. 1–6), present a novel numerical method for analyzing the out-of-plane creep stability of steel tube concrete (CFST) arches. Supported by the National Science and Technology Support Program (2013BAJ08B01) and multiple National Natural Science Foundation grants (51178150, 50978080, 50678057), this research addresses a critical but under-studied aspect of CFST arch structural performance.

Core Methodology

Modified Effective Modulus Method (AEMM)

The proposed method combines the Modified Age-Effective Modulus Method (AEMM) for concrete creep analysis with the Finite Element Method (FEM). The key innovation is the introduction of time-varying initial geometric imperfections to describe the creep deformation of CFST arches at any given time, which are then incorporated into the FEM model to solve for out-of-plane creep stability bearing capacity.

Methodological Framework

Step	Description	Key Parameter
1. Material characterization	Define steel and concrete constitutive models including creep	Age-Effective Modulus
2. Initial imperfection generation	Define initial geometric imperfection function	Imperfection amplitude
3. Time-stepping analysis	Advance creep deformation at each time step	Time increment
4. Imperfection update	Update geometric imperfection based on accumulated creep	Deformation history
5. Stability analysis	Solve eigenvalue problem for out-of-plane buckling	Critical load
6. Iteration	Repeat steps 3–5 until convergence	Convergence criterion

Parametric Study Results

Influence of Key Parameters

The parametric study reveals the following sensitivity rankings for out-of-plane creep stability bearing capacity:

Parameter	Influence Level	Trend
Slenderness ratio	High	Decreases capacity significantly
Steel ratio (section steel content)	High	Increases capacity
Concrete loading age	High	Increases capacity (older concrete = less creep)
Span-rise ratio	Low	Minor effect
Lateral disturbance force	Low	Minor effect
Load level	Moderate	Higher sustained load = more creep deformation

Quantitative Findings

The creep effect reduces the out-of-plane stability bearing capacity of CFST arches by up to 13.8%. This is a substantial reduction that must be accounted for in design, particularly for long-span arches subjected to sustained loads over extended periods.

Engineering Practice Integration

Design Recommendations

Slenderness ratio control: Limit the slenderness ratio of CFST arch ribs to minimize sensitivity to creep-induced instability.
Steel ratio optimization: Increase the steel ratio in arch ribs to enhance both initial stiffness and long-term stability.
Loading age consideration: Account for the concrete loading age in design calculations, as younger concrete exhibits more significant creep deformation.
Imperfection sensitivity: Include realistic initial geometric imperfections in stability analysis rather than relying on idealized perfect geometry.

Comparison with Existing Design Codes

Design Approach	Creep Consideration	Out-of-Plane Stability	Adequacy for CFST Arches
Current Chinese codes (GB 50017)	Not explicitly addressed	Elastic buckling only	Inadequate for long-term assessment
Eurocode 3 (EN 1993-1-5)	Partial creep consideration	Limited	Partially adequate
Proposed AEMM-FEM method	Full time-dependent creep	Time-varying stability	Comprehensive

Key Questions and Reflections

The study raises several important questions for practical application. First, how should the initial imperfection amplitude be determined for design purposes? The study uses experimentally calibrated values, but in practice, construction tolerances and erection procedures determine the actual imperfection profile. Second, the method assumes uniform creep behavior across the cross-section, which may not hold for heterogeneous or partially filled CFST sections.

Additionally, the study focuses on elastic out-of-plane buckling. In practice, inelastic buckling may govern for stockier arches, and the interaction between in-plane and out-of-plane buckling modes requires further investigation.

Study Insights and Implications

This research makes a significant contribution to the understanding of long-term structural behavior of CFST arches. The finding that creep can reduce out-of-plane stability capacity by up to 13.8% is a critical design consideration that has been largely overlooked in current practice. Engineers designing CFST arch bridges and long-span structures should incorporate time-dependent stability analysis into their design process, using the AEMM-FEM framework or equivalent methods. The parametric sensitivity analysis provides clear guidance on which design parameters most effectively enhance long-term stability, enabling rational and economical structural design.