Dual Nonlinear Finite Element Analysis of Steel Tube Concrete Truss Arch

Literature Overview

This paper by Chen Youjie and Chen Baochun from Fuzhou University, published in 2003 in the Journal of Fuzhou University (Natural Science Edition), presents a computational method for in-plane force analysis of steel tube concrete truss arch bridges that accounts for both material and geometric nonlinearity. The authors developed a dedicated finite element program using spatial beam elements, applying a composite method for the constitutive relationship of steel tube concrete (SRC) and a mixed method for dual nonlinearity. The work was funded by the Fuzhou University Science and Technology Development Fund (XKJ(YM)-0113).

Core Technical Approach

The fundamental challenge in analyzing SRC truss arches lies in capturing the complex interaction between steel tube confinement and concrete core behavior under progressive loading. The authors address this through a systematic methodology:

Spatial beam element formulation — The truss arch is discretized using three-dimensional beam elements that can capture axial, bending, and torsional responses simultaneously, which is essential for the three-dimensional force state in arch structures.
Composite constitutive method — The SRC column behavior is modeled by combining the individual stress-strain relationships of steel and concrete, accounting for the confinement effect that the steel tube exerts on the concrete core.
Mixed method for dual nonlinearity — Material nonlinearity (yielding, hardening, concrete crushing) and geometric nonlinearity (P-Δ effects, large displacements) are coupled through a mixed solution strategy, allowing analysis through the entire loading process including post-peak behavior.

Technical Parameters and Modeling Details

Parameter	Description	Relevance
Element type	Spatial beam element	Captures 3D force state in arch
Material model	Composite SRC constitutive law	Steel-concrete interaction
Solution method	Mixed method (dual nonlinearity)	Material + geometric nonlinearity
Analysis scope	Full loading process	Pre-peak, peak, post-peak
Application	Truss arch bridge	In-plane force analysis

The composite constitutive method is particularly significant because it avoids the computational complexity of full three-dimensional continuum modeling while still capturing the essential mechanics of confined concrete. The steel tube provides lateral confinement pressure on the concrete core, which increases the concrete's compressive strength and ductility. This confinement effect is a function of the steel tube's hoop stress, which depends on the steel tube's diameter-to-thickness ratio and yield strength.

Connection with Engineering Practice

From a steel pipe manufacturing and welding perspective, this analysis has direct implications for the design of steel tubes used in SRC structural members:

The confinement effectiveness depends on the steel tube's diameter-to-thickness ratio (D/t). Thinner-walled tubes provide better confinement but may be more susceptible to local buckling. Typical D/t ratios for SRC applications range from 10 to 80.
The welding quality at tube joints (welded end caps, longitudinal weld seams for welded tubes) directly affects the confinement integrity. Defects such as incomplete fusion, porosity, or lack of penetration at weld seams can compromise the tube's ability to confine the concrete core.
Residual stresses from welding can influence the buckling behavior of the steel tube under compressive loading, which is critical in arch members where axial compression dominates.

Key Insights and Reflections

The use of a mixed method for dual nonlinearity is a pragmatic engineering approach. Full Newton-Raphson methods with geometric stiffness matrices can be computationally expensive, especially for large-scale structures with hundreds of truss members. The mixed method offers a balance between accuracy and computational efficiency, which was particularly important in 2003 when computational resources were more limited.

However, several limitations should be noted. The spatial beam element approach does not capture local buckling of the steel tube walls, which can be a critical failure mode for slender tubes under high compressive stress. Additionally, the in-plane analysis does not address out-of-plane stability, which is equally important for arch structures. Engineers applying this methodology should supplement it with stability analysis (as discussed in Topic 2) and local buckling checks.

The conclusions drawn from the full-process analysis provide valuable insights into the failure sequence and load redistribution capacity of SRC truss arches. The progressive yielding pattern and the ultimate load-carrying capacity relative to the elastic prediction are critical for understanding the safety margin of these structures.

Reference Value and Outlook

This paper represents an important contribution to the computational modeling of SRC structures at a time when such analyses were still relatively specialized. The methodology can be extended to more complex structural forms, including spatial truss arches and hybrid steel-concrete systems. For steel pipe manufacturers and welders, the key takeaway is that the mechanical performance of SRC members is intimately linked to the quality of the steel tube itself — its geometry, material properties, and weld integrity — making quality control at the fabrication stage a critical factor in structural safety.