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

Literature Overview

The paper by Li Dejian, Dai Gonglian, and Zeng Qingyuan (2003), published in the Journal of Central South University of Technology, presents a nonlinear analysis method for steel tube concrete (STC) arch bridges. The method employs a section internal force plasticity coefficient approach to establish the elastic-plastic stiffness matrix of spatial arch elements, considering both material nonlinearity and geometric nonlinearity. The analysis was applied to the Yiyang Zijiang River No. 3 Bridge, a steel tube concrete arch bridge, evaluating ultimate bearing capacity during both construction and operational stages.

Methodology Description

The core of the method is the use of plasticity coefficients to modify the section internal forces (axial force, bending moment) at each element node, reflecting the progressive yielding of the composite section. The procedure is as follows:

1. Establish the constitutive relationship model for steel tube concrete, accounting for the confinement effect of the steel tube on the concrete.
2. Derive the element incremental equilibrium equation using the modified Lagrangian formulation.
3. Construct the elastic-plastic stiffness matrix using the section internal force plasticity coefficient method.
4. Perform nonlinear analysis using the current stiffness parameter method to capture material nonlinearity and geometric nonlinearity simultaneously.
5. Apply the initial internal force method to account for system conversion between construction stages and elastic internal force transfer.

Key Technical Parameters and Constitutive Models

The steel tube concrete constitutive model used in the study accounts for the triaxial stress state of confined concrete. The confinement pressure exerted by the steel tube increases the concrete's compressive strength and ductility. The key parameters include:

• Concrete compressive strength (f_c): determines the unconfined strength baseline
• Steel tube yield strength (f_y): determines the transition to plastic behavior
• Confinement ratio (A_steel / A_concrete): governs the degree of confinement enhancement
• Elastic modulus ratio (E_steel / E_concrete): affects the load distribution between steel and concrete

The plasticity coefficients are derived from the stress-strain relationships of both steel and concrete, modified for the confined state. As loading increases, these coefficients decrease, reflecting the progressive loss of stiffness in the yielding regions of the section.

Verification Against Experimental Data

The method was validated against experimental results for several STC axially compressed and eccentrically compressed members. The elastic-plastic ultimate bearing capacity predictions showed good agreement with test results, confirming the accuracy and reliability of the method. The comparison demonstrated that considering only geometric nonlinearity overestimates the ultimate bearing capacity, particularly for members with higher slenderness ratios or eccentricity ratios.

Application to Yiyang Zijiang River No. 3 Bridge

The practical application to the Yiyang Zijiang River No. 3 Bridge arch demonstrates the method's engineering utility. The analysis covered:

• Construction stage: The arch ribs are erected and progressively loaded. The initial internal force method captures the system conversion from temporary support to self-supporting arch structure.
• Operational stage: Full dead load plus live load (traffic) is applied. The elastic-plastic analysis reveals the actual load redistribution as yielding progresses in critical sections.

The results showed that the elastic-plastic stability safety factor was significantly lower than the elastic stability safety factor obtained from geometric nonlinearity analysis alone. This difference highlights the importance of material nonlinearity in the ultimate limit state assessment of STC arch bridges.

Engineering Practice Integration

For engineers involved in the design and assessment of STC arch bridges, this paper provides a rigorous analytical tool that goes beyond the simplified methods typically used in preliminary design. The key engineering implications are:

• Design safety: Elastic analysis alone may provide a false sense of safety. The elastic-plastic method reveals the true reserve capacity and identifies the actual failure mechanism.
• Construction monitoring: The method can predict critical load levels during construction, enabling proactive monitoring and intervention if measured deformations exceed predictions.
• Retrofit assessment: For existing STC arch bridges, the elastic-plastic method can evaluate remaining capacity after damage or degradation, supporting informed retrofit decisions.

The method's computational demands are higher than linear analysis, but modern finite element software can implement the plasticity coefficient approach efficiently. Engineers should ensure that the constitutive models used are calibrated for the specific steel and concrete grades employed in the bridge, as material property variations can significantly affect predictions.

Key Questions and Reflections

• How sensitive are the results to the choice of steel tube concrete constitutive model? Different models (Mander, Park, Usami) may yield different confinement enhancement predictions.
• Can the method be extended to consider fatigue and creep effects, which are relevant for long-term bridge performance?
• What are the limitations when the steel tube exhibits significant local buckling before overall instability?

The paper represents a significant advancement in the analytical capabilities for STC arch bridges. The method bridges the gap between simplified elastic analysis and full nonlinear finite element analysis, providing engineers with a practical yet rigorous tool for ultimate limit state assessment.

Study Insights and Implications

The most important insight is that material nonlinearity cannot be neglected in the ultimate bearing capacity assessment of STC arch bridges. The elastic-plastic safety factor is consistently lower than the elastic safety factor, meaning that designs based solely on elastic stability may be unconservative. Engineers should adopt elastic-plastic analysis methods for the final design verification of STC arch bridges, particularly for long-span structures where the consequences of underestimating the ultimate load are severe. The section internal force plasticity coefficient method offers a computationally efficient approach that captures the essential nonlinear behavior without the complexity of full incremental-iterative analysis.