Elastoplastic Ultimate Bearing Capacity Analysis of Steel Tube Concrete Arch Bridges Using Section Internal Force Plasticity Coefficient Method

Literature Overview

This 2003 paper by Li Dejian, Dai Gonglian, and Zeng Qingyuan, published in the Journal of Central South University of Technology, presents a nonlinear analysis method for the elastoplastic ultimate bearing capacity of steel tube concrete (STC) arch bridges. The method employs a section internal force plasticity coefficient approach based on the modified Lagrangian formulation, incorporating both material and geometric nonlinearities. The study is validated through comparison with experimental data for STC compression members and applied to the analysis of the Yiyang Zijiang No. 3 Bridge main arch during construction and service stages.

Research Background and Engineering Context

Steel tube concrete arch bridges have gained increasing popularity for medium to large span applications due to their structural efficiency, rapid construction, and aesthetic appeal. The composite action between the steel tube and concrete core provides superior load-bearing capacity compared to either material alone. However, the nonlinear behavior of STC arches under loading—particularly the interaction between material yielding and geometric deformation—requires sophisticated analysis methods to accurately predict ultimate bearing capacity and stability safety factors.

Traditional linear elastic analysis methods, which consider only geometric nonlinearity, tend to overestimate the critical buckling load of STC arches. The inclusion of material nonlinearity (elastoplastic behavior) is essential for accurate prediction of ultimate capacity, as the progressive yielding of the composite section reduces the effective stiffness and alters the load path.

Methodology: Section Internal Force Plasticity Coefficient Method

The proposed method is based on the following theoretical framework:

1. Modified Lagrangian formulation: The equilibrium equations are expressed in the current deformed configuration, accounting for geometric nonlinearity through the updated reference configuration at each load increment.
2. Element incremental equilibrium: The stiffness matrix for each arch element is derived using the incremental equilibrium equation, which includes both material stiffness and geometric stiffness contributions.
3. Section internal force plasticity coefficient: A plasticity coefficient is defined for each section to characterize the transition from elastic to plastic behavior based on the section's internal force state (axial force, bending moment, and shear force). This coefficient is used to modify the element stiffness matrix at each load step.
4. Current stiffness parameter method: Material nonlinearity and geometric nonlinearity are analyzed simultaneously using the current stiffness parameter approach, which updates the stiffness matrix at each increment based on the current stress-strain state.

The method also incorporates the initial internal force method to account for system transitions between construction stages and the transfer of elastic internal forces between stages.

Validation and Application

The method was validated through comparison with experimental results for STC axial compression members and eccentric compression members. The elastoplastic ultimate bearing capacity predictions showed good agreement with test data, confirming the accuracy and reliability of the proposed approach.

The method was then applied to the Yiyang Zijiang No. 3 Bridge, a steel tube concrete arch bridge spanning the Zijiang River. The analysis covered both construction stages (during arch installation) and the completed bridge service stage, considering the different structural systems and load conditions at each stage.

Key findings from the application:

1. The elastoplastic ultimate bearing capacity is significantly lower than the elastic critical buckling load that considers only geometric nonlinearity, confirming that material yielding must be accounted for in stability analysis.
2. The stability safety factor based on elastoplastic analysis is more conservative than that based on elastic analysis, providing a more realistic assessment of structural safety.
3. Construction stage analysis revealed that the arch structure during installation may have lower stability margins than the completed bridge, highlighting the importance of construction sequence analysis.
4. The section internal force plasticity coefficient method provides a computationally efficient approach that captures the essential nonlinear behavior without requiring full constitutive integration at every Gauss point.

Welding and Steel Pipe Quality Implications

From a steel pipe manufacturing and welding quality perspective, the findings of this research have several important implications:

• Weld integrity and ultimate capacity: The elastoplastic analysis assumes continuous, homogeneous material behavior across the steel tube cross-section. Weld defects such as lack of fusion, porosity, or cracks effectively reduce the cross-sectional area and create stress concentrations that can initiate premature yielding. Therefore, rigorous weld inspection and quality control are essential to ensure that the actual structural capacity matches the analytical predictions.
• Steel tube geometric tolerances: The analysis assumes ideal geometric properties. In practice, ovality, wall thickness variation, and local deformations in steel tubes reduce the actual moment of inertia and section modulus, potentially lowering the ultimate capacity below predicted values.
• Material property consistency: The constitutive model used in the analysis requires accurate material properties. Steel grade certification, mechanical property testing, and chemical composition verification should be performed on the actual steel pipe material to ensure that design assumptions are valid.
• Construction stage welding: During arch bridge construction, temporary welding connections and erection welds may have different quality characteristics than final production welds. The analysis should account for the actual connection quality at each construction stage.

Study Insights and Practical Recommendations

This research demonstrates that the section internal force plasticity coefficient method is a powerful and practical tool for the nonlinear analysis of steel tube concrete arch bridges. The method provides more accurate predictions of ultimate bearing capacity and stability safety factors compared to linear elastic approaches that neglect material yielding.

For engineering practice, the following recommendations emerge:

1. Elastoplastic analysis should be mandatory for the design of STC arch bridges with spans exceeding 100 meters, where material yielding is likely to influence stability.
2. Construction stage analysis should be performed for all STC arch bridges, as the structural system during installation may have different stability characteristics than the completed structure.
3. Weld quality control should be elevated to a critical level for STC arch bridges, with full-penetration welds and comprehensive non-destructive testing at all longitudinal and circumferential welds.
4. Material testing should include high-temperature and cyclic loading tests to validate the constitutive models used in nonlinear analysis.

This study provides a rigorous analytical framework for the design of steel tube concrete arch bridges, bridging the gap between theoretical nonlinear analysis and practical engineering design requirements.