Hanger Force Calculation and Tension Adjustment in CFST Tied-Arch Bridges

Literature Overview

This paper by Li Jie, Chen Huai, Jiang Yingying, and Zhou Mingkun, published in Railway Construction (2014, Vol. 54, Issue 1), presents a systematic approach to calculating and adjusting hanger forces in concrete-filled steel tube (CFST) tied-arch bridges. The study employs an analytical method based on the lever principle for hanger force calculation and proposes improvements to the influence matrix method commonly used in engineering practice for post-construction tension adjustment. The research originates from the School of Civil Engineering at Zhengzhou University.

Analytical Method for Hanger Force Calculation

The paper proposes using the lever principle to calculate the hanger tension forces in CFST tied-arch bridges. This analytical approach is based on the static equilibrium of the arch rib and the deck structure, treating the hangers as tension members that transfer the deck load to the arch rib through vertical force components.

The lever principle method offers several advantages over numerical methods:

1. Simplicity: The calculation can be performed with basic structural mechanics knowledge, without requiring specialized bridge analysis software.
2. Speed: Results are obtained almost instantaneously, which is valuable during the design and construction phases when rapid iteration is needed.
3. Transparency: The physical basis of the calculation is clear, making it easy to verify and explain to other engineers.

However, the lever principle method has limitations in accuracy for complex bridge geometries or when the structural interaction between the arch rib, deck, and hangers is significant. The method assumes a simplified structural model that may not capture all the nonlinear interactions present in a real CFST tied-arch bridge.

Influence Matrix Method and Its Improvement

The influence matrix method is the standard approach used in engineering practice for adjusting hanger tensions after bridge construction. The method involves:

1. Establishing a structural analysis model of the completed bridge using specialized bridge analysis software.
2. Computing the influence matrix, which describes how the tension in each hanger affects the tension in all other hangers and the structural geometry.
3. Using the influence matrix to determine the required tension adjustments for each hanger to achieve the target cable forces and structural profile.

The paper identifies limitations in the conventional influence matrix method and proposes an improved approach that better reflects the actual construction sequence of hanger tension adjustment. The key improvement is that the method accounts for the sequential nature of hanger tensioning, where each hanger is adjusted one at a time rather than all simultaneously.

Tension Adjustment Strategy

The paper establishes two key principles for hanger tension adjustment:

1. The target value for the active tension of each hanger at completion should be the cable force produced by the permanent dead load of the completed structure. This ensures that the hangers are properly stressed to carry their design share of the dead load.
2. The adjustment of hanger forces should prioritize the structural profile (line shape) of the bridge. This means that the geometric configuration of the arch rib and deck is the primary control objective, with hanger tension values being adjusted to achieve the desired profile.

Engineering Practice Considerations

From a steel pipe manufacturing and welding perspective, the hanger force calculation and adjustment process has direct implications for the design and fabrication of CFST arch bridge components:

1. Steel tube chord members: The arch rib and deck longitudinal beams are typically fabricated from steel tubes. The hanger forces impose specific stress states on these members, and the welding connections at the tube joints must be designed to accommodate the actual force distribution.
2. Hanger anchor connections: The hangers are connected to the arch rib and deck through anchor plates and welded connections. The tension adjustment process may impose cyclic loading on these connections, which must be designed for fatigue resistance.
3. Weld quality assurance: The accuracy of hanger force calculations depends on the structural model, which assumes idealized material properties and connection stiffness. Any deviation in weld quality or steel tube properties from the design assumptions will affect the actual hanger force distribution.

Study Insights and Engineering Implications

This paper provides a practical and rigorous framework for hanger force calculation and tension adjustment in CFST tied-arch bridges. The lever principle method offers a quick and transparent analytical tool for preliminary design, while the improved influence matrix method provides a more accurate approach for post-construction adjustment that accounts for the sequential nature of the tensioning process. The emphasis on structural profile as the primary control objective is a pragmatic approach that recognizes the importance of geometric accuracy in ensuring the long-term performance and aesthetics of the bridge. For engineers involved in the fabrication and assembly of CFST arch bridge components, understanding the hanger force distribution and adjustment strategy is essential for ensuring that the welded connections and steel tube members are designed and fabricated to accommodate the actual service loads. The study reinforces the principle that structural analysis and construction methodology must be integrated throughout the design and construction process to achieve optimal performance.