Zhuojin Pipe Fitting Co., LtdCreep Effect Analysis on Steel Tube Concrete Arch Bridges
Literature Overview
The paper by Han Bing, Du Jinsheng, and Wang Yuanfeng (2005), published in the Journal of Highway and Transportation Research, investigates the long-term creep behavior of steel tube concrete (STC) arch bridges using the effective creep theory combined with finite element analysis. The study was funded by the Ministry of Education Key Science and Technology Research Project (03040) and the University Doctoral Point Foundation (20030004002). This research addresses a critical but often overlooked aspect of STC bridge engineering: the time-dependent deformation of the concrete core under sustained loading, which can significantly affect the structural performance and serviceability of arch bridges over their design life.
Theoretical Framework: Effective Creep Theory
The effective creep theory, also known as the age-adjusted effective modulus method, is a widely used approach for analyzing time-dependent behavior of concrete structures. The fundamental equation relates the stress increment due to creep to the initial elastic stress through an age-adjusted effective modulus:
The effective modulus E_eff is defined as:
E_eff = E_c / (1 + ϕ·χ)
where E_c is the instantaneous elastic modulus of concrete, ϕ is the creep coefficient, and χ is the aging coefficient that accounts for the effect of time-varying loading on creep development.
Creep Coefficient Parameters
The creep coefficient ϕ depends on multiple factors:
| Factor | Influence on Creep | Typical Range |
|---|---|---|
| Concrete age at loading | Higher age reduces creep | 0.5-1.5 (depending on loading age) |
| Duration of loading | Longer duration increases creep | 2.0-4.0 (at 50 years) |
| Concrete strength | Higher strength reduces creep | 1.5-3.5 (depending on grade) |
| Environmental conditions | Dry conditions increase creep | 0.8-1.2 (relative humidity factor) |
| Member size | Larger members reduce creep | 0.9-1.1 (size effect) |
The aging coefficient χ typically ranges from 0.7 to 0.9 for sustained loading conditions, reflecting the fact that creep develops more slowly as concrete ages and gains strength over time.
Structural Analysis of STC Arch Bridges
Finite Element Modeling Approach
The finite element model of the STC arch bridge incorporates the following key elements:
- Steel tube elements: Modeled with elastic material properties, accounting for temperature effects but not creep (as steel does not exhibit significant creep at service temperatures).
- Concrete core elements: Modeled with time-dependent material properties using the effective creep theory, with age-adjusted effective modulus applied at each time step.
- Interface elements: Representing the bond between steel tube and concrete, with potential for slippage under sustained loading.
- Support conditions: Accurately modeling the boundary conditions of the arch, including settlement and rotation constraints.
The analysis is performed in time increments, with the effective modulus updated at each step to reflect the progressive development of creep. This time-stepping approach captures the interaction between the steel tube (which does not creep) and the concrete core (which does), resulting in stress redistribution over time.
Key Findings from Numerical Analysis
The numerical results demonstrate several important phenomena:
| Parameter | Effect of Creep | Magnitude |
|---|---|---|
| Arch deformation | Increased deflection | 20-40% increase over elastic prediction |
| Internal forces | Redistribution between steel and concrete | Significant stress transfer |
| Concrete stress | Reduced (creep relief) | 10-25% reduction |
| Steel stress | Increased (load transfer) | 10-25% increase |
| Thrust line position | Shift toward extrados | Moderate to significant |
The most critical finding is that creep significantly affects the structural behavior during the aging stage of the bridge's service life. The deformation increase due to creep can be substantial, potentially affecting the geometric configuration of the arch and the distribution of internal forces. This is particularly important for STC arch bridges, where the interaction between the non-creeping steel tube and the creeping concrete core creates a complex time-dependent behavior.
Engineering Practice Implications
Design Considerations
For the design of STC arch bridges, the following considerations should be incorporated:
- Long-term deflection predictions: Design deflections should account for creep and shrinkage effects, not just elastic deformations. The total long-term deflection may be 1.5 to 2.5 times the initial elastic deflection.
- Stress redistribution: The stress in the steel tube will increase over time as the concrete creeps, potentially leading to higher steel stresses than predicted by elastic analysis. This should be verified against allowable stress limits.
- Serviceability checks: Creep-induced deformations should be checked against serviceability limit states, including deflection limits, crack width limits, and geometric compatibility requirements.
- Construction sequencing: The timing of concrete placement and the duration of sustained loading during construction (e.g., during cable-stayed construction or temporary support removal) significantly affect the final creep response.
Construction Monitoring Recommendations
For STC arch bridges under construction, the following monitoring parameters should be tracked:
- Arch crown deflection over time
- Strain gauges on steel tube (to monitor stress redistribution)
- Concrete strain gauges (to verify creep predictions)
- Settlement of arch supports
- Temperature measurements (to separate thermal effects from creep)
Key Reflections and Insights
The study by Han Bing and colleagues highlights a fundamental characteristic of composite structures: the time-dependent behavior of one component (concrete) interacts with the elastic behavior of another (steel), creating a complex evolution of internal forces over time. This interaction is particularly pronounced in STC arch bridges, where the arch action creates sustained compressive stresses in the concrete core that drive significant creep deformation.
From a practical standpoint, the effective creep theory provides a computationally efficient framework for long-term behavior prediction. While more sophisticated approaches (such as the multi-linear nonlinear viscoelastic model or the Bazant-Baweja B3 model) exist, the effective modulus method offers a good balance between accuracy and computational efficiency for engineering design purposes. The key is to properly calibrate the creep parameters to the specific concrete mix, environmental conditions, and loading history.
A critical insight from this research is that the aging stage of the bridge's life (typically 10-50 years after construction) is when creep effects become most pronounced. Many bridges are designed and inspected based on initial elastic predictions, without adequate consideration of long-term deformation. This can lead to unexpected serviceability issues, including increased deflections, cracking, and stress concentrations that may not be apparent during construction.
Reference Value and Outlook
This research provides a valuable methodology for analyzing the long-term behavior of STC arch bridges. The combination of effective creep theory with finite element analysis is a practical and reliable approach for engineering applications. Future research should extend this methodology to include shrinkage effects (which are often comparable in magnitude to creep), temperature effects, and the interaction between creep and fatigue in the steel tube. Additionally, the development of simplified analytical methods for preliminary design, based on the detailed finite element results, would be valuable for practical engineering applications where computational resources are limited.
The findings of this study should be incorporated into the design guidelines for STC arch bridges, ensuring that long-term deformation and stress redistribution are adequately considered in the design process. Engineers should adopt a time-dependent analysis approach for all critical STC arch bridge designs, rather than relying solely on elastic analysis.