Nonlinear Analysis of Circular Steel Tube Concrete Structures Using Composite Unit Method

Literature Overview and Methodological Innovation

The paper by Liu Wei, Ding Faxing, and Xing Feng, published in the Journal of Shenzhen University (Science and Engineering) (2009, Vol. 26, No. 3, pp. 301–304), presents a composite unit method for the nonlinear finite element analysis of circular steel tube concrete (CSTC) structures. Supported by the National Natural Science Foundation of China (50808180) and the Ministry of Education Doctoral Fund (200805331064), this research was conducted at Central South University and Shenzhen University.

The key innovation is the development of a composite unit method that directly computes section stiffness from end forces without the need for layered section discretization, thereby accelerating computational efficiency while maintaining accuracy. This method is based on the practical calculation methods for axial force-strain and axial force-bending moment-curvature relationships of circular CSTC composite sections.

Theoretical Framework and U.L. Formulation

The composite unit method employs the Updated Lagrangian (U.L.) formulation, which updates the reference configuration at each load increment. This is particularly suitable for problems involving large geometric nonlinearity, such as CSTC columns under eccentric compression where significant lateral deflections develop.

The method introduces a plane beam element nonlinear analysis framework that incorporates the material nonlinearity of both steel and concrete through the composite section's axial force-strain and moment-curvature relationships. The incremental equilibrium equation is established in the U.L. formulation, allowing for the simultaneous consideration of geometric and material nonlinearities.

Comparison of Analysis Methods

Validation Cases and Results

The authors validated the composite unit method against experimental data for several CSTC structural components:

• CSTC eccentric compression columns
• CSTC columns with unequal end moments
• CSTC compression-bending members
• CSTC model arch ribs

The load-deformation curves and ultimate bearing capacities obtained from the composite unit method were found to be in close agreement with experimental results. When compared with the layered beam element method, both approaches yielded similar results, confirming the accuracy of the composite unit method while highlighting its computational advantages.

The model arch rib analysis is particularly noteworthy because arch ribs are common in bridge and long-span structures, and their nonlinear behavior involves complex interactions between axial compression, bending, and geometric nonlinearity. The successful simulation of arch rib behavior demonstrates the versatility of the composite unit method beyond simple column analysis.

Engineering Practice Implications

From a pipe manufacturing and welding perspective, the composite unit method has practical value in the design verification of CSTC structures that incorporate welded steel tubes. The method's computational efficiency makes it suitable for parametric studies during the design phase, allowing engineers to optimize tube dimensions, wall thickness, and material grades before detailed fabrication drawings are issued.

The accuracy of the analysis depends critically on the constitutive models used for steel and concrete. For steel tubes, the material should conform to relevant standards such as GB/T 8162 (seamless tubes) or GB/T 3091 (welded tubes), with verified yield strength, tensile strength, and elongation. Welding defects such as cracks, lack of fusion, or excessive distortion can significantly reduce the effective section properties assumed in the analysis. Therefore, rigorous non-destructive testing (NDT) including ultrasonic testing (UT) and magnetic particle testing (MT) of welds is essential to ensure the structural integrity assumed in the nonlinear analysis.

Study Insights and Reflection

The composite unit method represents a pragmatic approach to nonlinear analysis that balances accuracy with computational efficiency. In an era where high-performance computing is increasingly available, the speed advantage may seem less critical, but for routine design checks and parametric optimization, efficiency remains valuable. The method's direct use of section N-M-φ relationships also provides a clearer physical interpretation of the structural behavior, as engineers can directly examine how axial force and moment interact within the composite section.

One limitation is that the method assumes a plane section remains plane, which may not hold under severe local buckling of the steel tube. For ultra-thin wall tubes or cases with significant local deformation, a full three-dimensional shell-solid model may be more appropriate. Engineers should exercise judgment in selecting the appropriate level of modeling fidelity.

Reference Value and Outlook

This paper contributes a computationally efficient and physically transparent method for the nonlinear analysis of CSTC structures. Its validation against multiple structural forms—columns, beams, and arch ribs—demonstrates broad applicability. Future extensions could incorporate temperature-dependent material properties for fire analysis, cyclic loading for seismic assessment, and explicit consideration of welding residual stresses and defects. For pipe manufacturers and welding engineers, the method provides a tool to evaluate how variations in tube wall thickness, material grade, and weld quality affect the overall structural performance, enabling more informed quality control decisions during fabrication.