Zhuojin Pipe Fitting Co., LtdNonlinear Analysis of Circular Steel Tube Concrete Structures Using Combined Element Method
Literature Overview
This 2009 paper published in the Journal of Shenzhen University (Science and Engineering Edition) presents a nonlinear finite element analysis method for circular steel tube concrete structures based on the combined element approach. Funded by the National Natural Science Foundation Key Program (50808180) and the Ministry of Education Doctoral Program Foundation (200805331064), the research was conducted by researchers from Central South University and Shenzhen University. The study develops a practical computational method that directly utilizes the axial force-strain relationship and the axial force-bending moment-curvature relationship of the composite cross-section, eliminating the need for layered section analysis and significantly improving computational efficiency.
Combined Element Methodology and Theoretical Foundation
The combined element method presented in this paper is based on the fundamental relationships between the axial force, bending moment, and curvature of a circular steel tube concrete composite cross-section. These relationships are derived from the constitutive behavior of the steel tube and the concrete core under various stress states, and they encapsulate the combined effect between the two materials.
The key innovation of this method is the direct use of the cross-sectional axial force-bending moment-curvature relationship to determine the section stiffness, rather than decomposing the cross-section into discrete layers and computing the stiffness of each layer individually. This approach is particularly advantageous for circular cross-sections where the layered method requires a large number of layers to accurately represent the curved geometry and the non-uniform stress distribution.
The following table compares the combined element method with the traditional layered beam element method:
| Feature | Combined Element Method | Layered Beam Element Method |
|---|---|---|
| Section stiffness calculation | Direct from N-M-kappa relationship | Layer-by-layer integration |
| Number of layers required | Not applicable | 100 to 500+ for circular sections |
| Computational efficiency | High | Moderate to low |
| Accuracy for circular sections | High | Depends on layer number |
| Implementation complexity | Moderate | Moderate to high |
| Applicable cross-section shapes | Any shape with known N-M-kappa relationship | Primarily rectangular and circular |
The nonlinear analysis employs the Updated Lagrangian (U.L.) formulation, which is well-suited for problems involving large deformations and geometric nonlinearity. The incremental equilibrium equations are solved using an iterative procedure that updates the element stiffness matrix at each load increment based on the current configuration of the structure.
Verification and Application to Structural Systems
The combined element method was verified against experimental results for several types of steel tube concrete structural members, including:
- Axially loaded eccentric compression columns, where the load eccentricity ratio was varied to cover the range from pure compression to significant bending.
- Unequal end moment eccentric compression columns, where the bending moment distribution was asymmetric, creating a more complex stress state in the cross-section.
- Compression-bending members, where the interaction between axial compression and bending was the primary design consideration.
- Steel tube concrete model arch ribs, where the structural behavior involved significant geometric nonlinearity due to the curved geometry and the large deformations under load.
The load-deformation curves and ultimate bearing capacities obtained from the combined element method were in close agreement with the experimental results, confirming the accuracy of the method. When compared with the layered beam element method, the combined element method produced results of comparable accuracy while requiring significantly less computational time. The speed improvement was particularly pronounced for circular cross-sections, where the layered method requires a large number of layers to achieve acceptable accuracy.
The practical significance of the computational speed improvement cannot be overstated. In structural design practice, nonlinear analysis is often performed for multiple load combinations and multiple design scenarios, and the total computational time can be a significant constraint. The combined element method reduces this constraint by orders of magnitude, making nonlinear analysis feasible for routine design work rather than being reserved for special research applications.
Engineering Practice and Design Code Implications
The combined element method has direct implications for the development of design codes and practical design procedures for steel tube concrete structures. The method provides a computationally efficient tool for:
- Generating interaction curves for steel tube concrete columns under combined axial compression and bending, which are essential for the design of moment-resisting frames.
- Performing pushover analysis of steel tube concrete structures to evaluate the seismic performance and identify the mechanism of failure.
- Conducting parametric studies to optimize the section properties of steel tube concrete members for specific design objectives.
- Developing simplified design formulas that are based on the combined element method results but can be applied without the need for a full finite element analysis.
From a manufacturing and quality control perspective, the accurate prediction of structural behavior provided by the combined element method enables engineers to specify appropriate acceptance criteria for steel tube concrete members. The method can be used to determine the maximum allowable residual stress in the steel tube, the minimum required bond strength between the steel tube and the concrete core, and the acceptable range of geometric tolerances for the steel tube fabrication.
This literature represents a significant methodological advancement in the computational analysis of steel tube concrete structures, providing a practical and efficient tool for structural engineers. The combined element method bridges the gap between detailed research-grade finite element models and simplified design formulas, offering a middle ground that is both accurate and computationally tractable for routine engineering applications. The method is particularly valuable for the design of large-scale steel tube concrete structures such as bridge piers, offshore platforms, and high-rise building columns where nonlinear behavior must be considered in the design.