Geometric Nonlinear Analysis of Large-Span Steel Tube Concrete Arch Bridges

Literature Overview

The paper by Hu Dalin, Aif Haime, and Huang Anlu, published in China Journal of Highway and Transport in 1998 (Volume 11, Issue 2, pp. 45–51), presents a three-dimensional geometric nonlinear analysis of large-span steel tube concrete (STC) arch bridges. The authors employed an average axial strain model in a Lagrange-SR coordinate system to develop a three-dimensional beam element tangent stiffness matrix for the nonlinear analysis. The study demonstrates that deformation verification governs the design of large-span STC arch bridges, and that material nonlinear effects must be accounted for in precise deformation analysis.

Core Technical Framework

The Average Axial Strain Model

The average axial strain model is a key element formulation approach for geometric nonlinear analysis of curved members. Unlike the traditional Euler-Bernoulli beam theory, which assumes that plane sections remain plane and normal to the deformed axis, the average axial strain model accounts for the coupling between axial and bending deformations in curved members. This is particularly important for arch structures, where large rotations and axial forces interact significantly.

The tangent stiffness matrix in the Lagrange-SR (Spatially Rotated) coordinate system is derived by considering:

1. The initial curvature of the arch member
2. The large rotations of the cross-section
3. The coupling between axial deformation and bending
4. The material constitutive relationship (elastic-plastic for steel tubes and concrete)

Three-Dimensional Beam Element Formulation

The three-dimensional beam element used in the study incorporates:

The Lagrange-SR system is advantageous because it maintains a consistent spatial reference frame throughout the deformation, avoiding the complications of large rotations in the local coordinate system. The average axial strain model is particularly suitable for arch members because it captures the membrane-bending coupling that is inherent in curved geometry.

Key Technical Findings

Deformation-Governed Design

The numerical examples in the study demonstrate that for large-span STC arch bridges, the deformation (deflection and displacement) governs the design rather than the strength. This is a critical finding that has implications for the design philosophy of STC arch bridges. In conventional steel or reinforced concrete arches, strength typically governs, but the composite action of the steel tube and concrete fill in STC members provides sufficient strength that deformation becomes the limiting factor.

Material Nonlinear Effects on Deformation

The study shows that precise analysis of STC arch bridge deformation requires accounting for material nonlinear effects. As the arch loads increase, the concrete core enters the cracking and crushing regime, and the steel tube may yield locally. These material nonlinearities redistribute stresses and strains, leading to larger deformations than predicted by purely elastic analysis. This finding is consistent with the behavior observed in STC columns and beams, where the composite action changes with increasing load level.

Comparison with Linear Analysis

The study implicitly compares the results of geometric nonlinear analysis with those of linear elastic analysis. The key differences include:

Engineering Practice Implications

Design Considerations for STC Arch Bridges

The findings of this study have several important implications for the design and construction of large-span STC arch bridges:

1. Deformation Control: The design must include explicit checks for deformation limits, particularly for the arch rib displacement and the overall bridge deflection. The allowable deformation should be based on serviceability criteria, including aesthetic considerations and long-term durability.
2. Material Nonlinear Modeling: Design software must incorporate material nonlinear models for both the steel tube and the concrete fill. The steel tube should be modeled with an elastic-perfectly plastic or bilinear constitutive law, while the concrete should use a nonlinear model that accounts for cracking, crushing, and confinement effects.
3. Construction Sequence Effects: The construction sequence of STC arch bridges (typically involving temporary supports, steel tube erection, and concrete filling) introduces additional deformations that must be accounted for in the nonlinear analysis. The temporary support removal stage is particularly critical, as it introduces large geometric changes.
4. Steel Tube Thickness Selection: The thickness of the steel tube in an STC arch rib affects both the strength and the stiffness of the member. A thicker steel tube provides greater confinement to the concrete, which improves the concrete's compressive strength and ductility. However, a thicker steel tube also increases the weight and cost of the structure.

Connection to Steel Pipe Manufacturing

From a steel pipe manufacturing perspective, the study highlights the importance of producing steel tubes with consistent mechanical properties and geometric accuracy. The steel tubes used in STC arch bridges are typically large-diameter welded or seamless tubes, and their properties directly affect the structural performance. Key manufacturing considerations include:

The geometric accuracy of the steel tube is particularly important for the assembly of arch ribs, where precise alignment is required to avoid eccentric loading. Any deviation from the design geometry can lead to additional bending moments and reduced load-carrying capacity.

Key Questions and Reflections

A significant question arising from this study is the accuracy of the average axial strain model for STC arch members with varying cross-sections. Large-span arch bridges often have variable cross-sections along the span, with thicker ribs at the crown and thinner ribs at the springing. The average axial strain model may not accurately capture the local stress concentrations at cross-section transitions. Further research is needed to validate the model against experimental data for variable-section arch ribs.

Another reflection concerns the long-term behavior of STC arch bridges. The study focuses on the initial loading response, but STC structures are subject to creep and shrinkage of the concrete core over time. These time-dependent effects can significantly alter the deformation behavior of the arch, particularly for long-term serviceability assessment. The ACI creep and shrinkage model, which is used in related research on STC columns, should be incorporated into the nonlinear analysis for long-term predictions.

Study Insights and Implications

This study provides a solid theoretical foundation for the geometric nonlinear analysis of large-span STC arch bridges. The use of the average axial strain model in the Lagrange-SR coordinate system is a robust approach that captures the essential physics of curved member behavior. The finding that deformation governs the design is a valuable insight for engineers, as it shifts the focus from strength-based design to stiffness-based design. For steel pipe manufacturers, the study underscores the importance of producing high-quality, dimensionally accurate steel tubes for large-diameter applications. The integration of geometric and material nonlinear analysis is essential for the reliable design of STC arch bridges, and the methods presented in this study provide a practical framework for such analysis.