Creep Effect Analysis on Steel Tube Concrete Arch Bridges

Literature Overview

The paper by Han Bing, Du Jinsheng, and Wang Yuanfeng (2005), published in Journal of Highway and Transportation Research, Vol. 22, No. 6, pp. 75–77, investigates the influence of concrete creep on steel tube concrete (STC) arch bridges. Funded by the Ministry of Education Key Science and Technology Research Project (03040) and the Doctoral Fund of Higher Education Institutions (20030004002), this study employs the successive flow theory to analyze the time-dependent deformation behavior of STC arch bridges. The research was conducted by the Beijing Jiaotong University School of Civil Engineering and the Ministry of Transport Highway Research Institute.

Core Technical Content

Creep Analysis Methodology

The successive flow theory (also known as the age-adjusted effective modulus method) is employed to account for the time-dependent stress redistribution in STC members under sustained loading. The theory introduces an age-adjusted effective modulus that combines the elastic modulus and the creep coefficient, allowing the time-dependent behavior to be incorporated into standard finite element analysis frameworks.

The key equations governing the creep analysis include:

• The age-adjusted effective modulus: $E_{ae}(t, t_0) = E_c(t_0) \cdot \frac{1 + \varphi(t, t_0)}{1 + \theta \cdot \varphi(t, t_0)}$
• Where $\varphi(t, t_0)$ is the creep coefficient, $E_c(t_0)$ is the elastic modulus at loading age $t_0$, and $\theta$ is the age-adjustment coefficient

Influence of Creep on Structural Behavior

Technical Interpretation

Mechanism of Creep in STC Arch Bridges

In an STC arch bridge, the concrete and steel tube are bonded together and share the applied loads. However, the concrete exhibits significant time-dependent deformation (creep) under sustained compressive stress, while the steel tube does not. This differential deformation causes a gradual transfer of load from the concrete to the steel tube over time.

The consequences of this load transfer are significant:

1. The concrete stress decreases over time, which is beneficial as it reduces the risk of concrete crushing and delays the onset of micro-cracking.
2. The steel tube stress increases over time, which may approach or exceed the yield stress if the initial design does not account for creep.
3. The overall deflection of the arch increases, potentially affecting the clearance requirements for roadways or waterways beneath the bridge.
4. The thrust at the arch haunches increases, which must be accommodated by the foundation design.

Creep Coefficient and Its Influencing Factors

The magnitude of creep is governed by the creep coefficient $\varphi(t, t_0)$, which depends on:

• Age of concrete at loading ($t_0$): Younger concrete exhibits higher creep
• Time since loading ($t - t_0$): Creep increases with time, approaching an asymptotic value
• Concrete composition: Higher water-cement ratio increases creep
• Environmental conditions: Higher humidity and temperature reduce creep
• Stress level: Creep is approximately linear for stresses below 0.4 times the compressive strength

Engineering Practice Implications

Design Considerations

1. The initial design of STC arch bridges must include a creep analysis to determine the time-dependent redistribution of internal forces. The design loads should be based on the maximum values that occur at the end of the creep period (typically 50–100 years for bridge design life).
2. The camber of the arch should be set based on the total deflection (elastic + creep) to ensure that the final geometry meets the design profile.
3. The foundation design must account for the increased thrust at the arch haunches due to creep-induced load redistribution.
4. The steel tube should be designed to accommodate the increased stress levels that develop over time, with an appropriate safety margin against yielding.

Construction Considerations

• The concrete should be placed at a mature age (typically 7–14 days) to minimize the initial creep contribution.
• The steel tube should be pre-installed and properly aligned before concrete placement to ensure uniform load sharing.
• The construction sequence should be planned to minimize the duration of sustained loading during the early age of the concrete.

Quality Control for Creep-Sensitive Structures

• Concrete strength testing should be performed at multiple ages (7, 28, 56, 90 days) to monitor the strength development and estimate the creep behavior.
• The concrete mix design should be optimized to minimize creep: low water-cement ratio, use of supplementary cementitious materials (fly ash, silica fume), and proper curing.
• Long-term monitoring of deflection and internal forces should be implemented to verify that the actual creep behavior matches the design predictions.

Study Insights and Reflections

This study highlights a critical aspect of STC bridge engineering that is often overlooked in preliminary design: the long-term time-dependent behavior of the composite section. While the elastic analysis provides a reasonable estimate of the initial structural response, the creep-induced redistribution of internal forces can be significant enough to affect the safety and serviceability of the bridge over its design life.

The use of the successive flow theory is appropriate for this analysis, as it provides a computationally efficient method for incorporating time-dependent effects into standard finite element models. However, the accuracy of the predictions depends on the quality of the creep coefficient data used. Engineers should use creep data specific to the concrete mix and environmental conditions of the project, rather than relying on generic values from standards.

The finding that creep significantly affects both the deformation and internal force state of STC arch bridges has direct implications for the design of bearings, expansion joints, and foundation elements. These components must be designed to accommodate the long-term movement and force changes induced by creep, otherwise premature failure may occur.