Ultimate Bearing Capacity Analysis of Steel Tube Concrete Arch Bridges

Literature Overview

This paper, published in Central-South Highway Engineering (2004, Vol. 29, No. 4, pp. 24-28) by Zhang Jianmin, Zheng Jialian, and Xiao Rucheng from Tongji University and the Guangxi Department of Transportation, presents a nonlinear analysis of the ultimate bearing capacity of a large-span steel tube concrete (CFST) arch bridge. The research was supported by the China Postdoctoral Science Foundation (Grant No. 2003034279). The study focuses on the Nanning Yonghe Bridge, a representative large-span CFST arch bridge in China.

Analytical Methodology

The analytical approach employed in this study is notable for its treatment of both material and geometric nonlinearity, which are critical for predicting the ultimate behavior of CFST arch bridges. The key methodological choices are:

1. Beam element formulation: An unlayered circular cross-section Timoshenko beam element is used, which accounts for shear deformation effects that are significant in CFST members with relatively short spans and deep sections.
2. Composite material constitutive model: A combined constitutive relationship for the CFST material is developed that captures the interaction between the steel tube and the concrete core under compressive loading.
3. Geometric nonlinearity: Large displacement effects, including the P-Δ effect and arch action changes due to deformation, are incorporated through a displacement-based nonlinear analysis framework.

The use of the Timoshenko beam element is particularly appropriate for CFST arch ribs because the steel tube-concrete composite action creates a member with a relatively high shear-to-bending stiffness ratio, especially in shorter arch segments. Euler beam theory, which neglects shear deformation, would underestimate the deflections and overestimate the stiffness of such members.

Material Nonlinearity: CFST Constitutive Model

The composite constitutive model for CFST material must capture several important phenomena:

• Concrete confinement effect: The steel tube provides lateral confinement to the concrete core, which increases the concrete's compressive strength and ductility beyond its unconfined values.
• Steel tube degradation: As the concrete core expands laterally under compression, it exerts outward pressure on the steel tube, causing the tube to yield in the hoop direction and reducing its axial load capacity.
• Strain hardening and softening: The CFST material exhibits strain hardening after initial yielding, followed by strain softening at large deformations as the concrete crushes and the steel tube buckles.

The constitutive model is typically formulated in terms of the equivalent stress-strain relationship for the CFST composite section, derived from the individual stress-strain relationships of the steel and concrete components and the confinement interaction.

Geometric Nonlinearity and Instability

The geometric nonlinearity of CFST arch bridges manifests in several ways:

1. Large displacements: As the arch deforms under increasing load, the geometry changes significantly, altering the force distribution and potentially leading to snap-through or snap-back behavior.
2. P-Δ effects: The axial compression in the arch ribs creates additional bending moments proportional to the lateral displacement, which amplifies the deformation and can lead to instability.
3. Arch action modification: The deformation of the arch changes the thrust line, potentially shifting the resultant force outside the cross-section and causing local instability.
4. Buckling: The arch ribs are susceptible to both local buckling of the steel tube and overall buckling of the arch system.

The analysis must track the equilibrium path through the nonlinear range, identifying limit points, bifurcation points, and the ultimate load at which the structure can no longer sustain additional loading.

Verification Against Model Tests

The analytical results were validated against model test data for the CFST arch bridge. This verification is essential because nonlinear analysis of complex structural systems is sensitive to modeling assumptions, constitutive parameters, and boundary conditions. The model test provides an independent check on the analytical predictions.

The comparison between analytical and experimental results typically examines:

• Ultimate load ratio (analytical to experimental)
• Load-deflection curve shape
• Deformation pattern at ultimate load
• Location of critical failure sections

Engineering Practice Considerations

The analysis of CFST arch bridge ultimate capacity has direct implications for several practical aspects of bridge engineering:

Fabrication and Welding Quality

The ultimate capacity of a CFST arch bridge depends critically on the quality of the steel tube fabrication and welding:

• Longitudinal welds: In large-diameter CFST arch ribs, the steel tube is typically fabricated from rolled plates joined by longitudinal butt welds. These welds must achieve full structural continuity, as any defect can initiate buckling under compressive loading.
• Circumferential welds: The tube is assembled from segments joined by circumferential butt welds. These welds must be radiographically tested to ensure full penetration and absence of porosity or lack of fusion.
• Weld residual stresses: The welding of large steel plates introduces residual stresses that can reduce the local buckling resistance of the tube. Post-weld stress relief or controlled welding sequences are recommended.

Concrete Placement Quality

The quality of concrete placement inside the steel tube directly affects the CFST composite action:

• Void-free fill: Air voids or incomplete fill reduce the effective cross-sectional area and weaken the confinement interaction.
• Compaction: Adequate compaction of the concrete inside the tube is essential to achieve design strength. Internal vibrators are typically used, with careful control to avoid damaging the tube interior.
• Curing: Proper curing of the concrete inside the tube is challenging but essential. Curing compounds or temporary moisture barriers may be required.

Key Questions and Reflections

The study raises important questions about the applicability of the analytical model to different CFST arch bridge geometries and loading conditions. The Nanning Yonghe Bridge serves as the basis for the analysis, but the model's predictions for bridges with different rise-to-span ratios, arch rib cross-sections, or loading configurations require careful validation.

Another important consideration is the influence of construction sequence on the ultimate capacity. CFST arch bridges are typically constructed using temporary support structures that are removed after the arch is completed. The removal of temporary support introduces a redistribution of forces that can significantly affect the stress state and ultimate capacity of the arch. The analytical model must account for the construction sequence to provide accurate predictions.

Study Insights and Implications

The most valuable contribution of this research is the demonstration that a nonlinear analysis incorporating both material and geometric nonlinearity can accurately predict the ultimate bearing capacity of CFST arch bridges. This capability is essential for the rational design of large-span CFST arch bridges, where the ultimate limit state governs the structural safety assessment.

For bridge engineers, the study reinforces the importance of using appropriate constitutive models and nonlinear analysis methods in the design of CFST arch bridges. Linear elastic analysis is inadequate for predicting the ultimate behavior, and simplified design codes may not capture the complex interaction between the steel tube and concrete core under large deformations.

For welding engineers, the study highlights the critical role of weld quality in determining the ultimate capacity of CFST arch bridge ribs. The steel tube is a primary load-bearing component, and weld defects can significantly reduce the buckling resistance and ultimate strength of the arch. Rigorous quality control of all welds, including full radiographic testing of critical welds and strict adherence to qualified welding procedures, is essential for the safety and serviceability of CFST arch bridges.