Impact Coefficient Analysis of Concrete-Filled Steel Tube Tied-Arch Bridge Based on Vehicle-Bridge Coupled Vibration

Literature Overview

This research paper by Chen Xuyong, Tang Jie, Yang Hongyin, Song Tengting, and Yi Bei from Wuhan Institute of Technology, Wenzhou Municipal Engineering Construction and Development Company, and CCCC Second Highway Consultants, published in the Journal of Wuhan Institute of Technology (2018, Vol. 40, Issue 2, pp. 197-202), investigates the impact coefficient of a concrete-filled steel tube (CFST) tied-arch bridge using vehicle-bridge coupled vibration analysis. The study employs finite element modeling and transient dynamic analysis to examine the dynamic response under various traffic conditions.

Methodology and Modeling Approach

The study employs a rigorous numerical approach to analyze the dynamic behavior of the CFST tied-arch bridge:

The use of constraint equations to enforce displacement compatibility between the wheels and the bridge contact points is a critical modeling detail. This approach ensures that the vehicle-bridge interaction is properly captured, which is essential for accurate impact coefficient prediction. The APDL (ANSYS Parametric Design Language) command stream enables automated batch processing of multiple analysis scenarios.

Key Dynamic Response Findings

The study examines the influence of several traffic parameters on the bridge's dynamic response and impact coefficient:

Bridge Surface Roughness:

The roughness of the bridge deck surface significantly affects the dynamic response. Rougher surfaces generate larger dynamic wheel loads, which increase the impact coefficient. This finding is consistent with general bridge dynamics principles but is specifically validated for CFST tied-arch bridge configurations.

Vehicle Speed:

An interesting finding is that the maximum dynamic displacement of the bridge changes very little with increasing vehicle speed. This suggests that the bridge's natural frequencies and mode shapes are such that the dynamic amplification does not vary significantly over the typical vehicle speed range. However, the impact coefficient does vary with speed, following a trend similar to that of simply supported beam bridges.

Number of Vehicles:

Multiple vehicles on the bridge simultaneously increase the dynamic response, but the effect is not simply proportional to the number of vehicles. The phase relationship between vehicles and the bridge's natural modes plays a significant role in determining the combined dynamic response.

Vehicle Spacing:

The spacing between vehicles affects the dynamic response through the superposition of individual vehicle effects. When vehicle spacing corresponds to the bridge's natural wavelength, constructive interference can occur, leading to amplified dynamic response.

Impact Coefficient Characteristics

The impact coefficient (μ) is defined as the ratio of the maximum dynamic response to the static response, and it is a critical parameter in bridge design for determining the dynamic load factor. The study finds that:

1. The impact coefficient for the CFST tied-arch bridge varies with vehicle speed, following a trend similar to simply supported beam bridges. This suggests that the fundamental dynamic characteristics governing impact coefficient behavior are consistent across different bridge types.
2. The impact coefficient is influenced by all four investigated parameters: bridge surface roughness, vehicle speed, number of vehicles, and vehicle spacing. This multi-parameter dependence underscores the complexity of dynamic bridge response.
3. The maximum dynamic displacement remains relatively stable with increasing vehicle speed, indicating that the bridge's stiffness and mass distribution provide effective dynamic filtering.

Engineering Practice Implications

For bridge design engineers, the findings of this study have several practical implications:

• Dynamic load factor selection: The impact coefficient values obtained from this study should be used in the design of CFST tied-arch bridges, particularly for determining the dynamic load factor applied to traffic loads.
• Surface condition maintenance: Since bridge surface roughness significantly affects dynamic response, proper maintenance of the bridge deck surface is essential for ensuring the designed dynamic performance.
• Traffic management: Understanding the effects of vehicle speed, number, and spacing on dynamic response can inform traffic management strategies to minimize dynamic loading.
• Modeling validation: The study demonstrates the importance of proper vehicle-bridge interaction modeling, including displacement compatibility constraints, for accurate dynamic analysis.

Study Insights and Reflections

This study provides valuable insights into the dynamic behavior of CFST tied-arch bridges under realistic traffic conditions. The finding that maximum dynamic displacement is relatively insensitive to vehicle speed is practically significant, as it suggests that the bridge's dynamic performance is robust across normal operating conditions. The similarity of impact coefficient trends between CFST tied-arch bridges and simply supported beam bridges suggests that existing design guidelines for impact coefficients may be applicable with appropriate adjustments. The rigorous numerical methodology employed, including proper vehicle-bridge interaction modeling, sets a benchmark for dynamic bridge analysis. Engineers should note that the study focuses on a specific bridge configuration, and the results should be validated against site-specific conditions before application to design. The emphasis on multi-parameter analysis reflects the complex reality of bridge dynamics, where multiple factors interact to determine the overall dynamic response.