Homogeneous Generalized Yield Function for Rectangular CFST and Truss Ultimate Load Capacity

Literature Overview

Published in 2017 in the China Civil Engineering Journal (土木工程学报), Volume 50, Issue 11, this paper by Yang Lufeng, Jiang Lifang, Zheng Jian, and Xie Weiwei from Guangxi University presents a theoretical framework for the ultimate load capacity analysis of concrete-filled steel tube (CFST) truss structures. The work is supported by the National Natural Science Foundation of China (51478125) and introduces two key innovations: a homogeneous generalized yield function (HGYF) for rectangular CFST sections and an elastic modulus reduction method (EMRM) for structural analysis.

Theoretical Framework

The HGYF is developed as a unified yield criterion applicable to rectangular CFST sections of varying proportions. The confinement effect coefficient serves as the independent variable, and higher-order polynomial fitting is used to determine the HGYF coefficients for different section geometries. This approach creates a continuous mathematical surface that encompasses the entire range of rectangular CFST cross-sections, from nearly square to highly elongated shapes.

The EMRM is then built upon the HGYF. The method identifies high-stress elements in the structure based on an adaptive criterion derived from the HGYF, and progressively reduces the elastic modulus of these elements to simulate stiffness degradation. This process continues until the structure reaches its ultimate load capacity. The adaptive nature of the method ensures that only the critical elements are modified, maintaining computational efficiency.

Technical Advantages and Validation

The HGYF offers several advantages over existing yield criteria for CFST sections. Traditional approaches often require separate formulations for different section shapes or rely on numerical integration that is computationally expensive. The homogeneous formulation provides a single, continuous expression that can be applied across the entire design space, simplifying both analytical and numerical implementations.

The EMRM provides a significant computational efficiency advantage over full nonlinear finite element analysis. By operating within a linear elastic framework and modifying stiffness rather than solving nonlinear equilibrium equations iteratively, the method can achieve results comparable to incremental nonlinear FEA at a fraction of the computational cost. This makes it practical for structural optimization and parametric studies involving large truss structures.

Validation was performed at two levels: component-level comparison with model tests and structural-level comparison with incremental nonlinear FEA results. The agreement in both cases confirms the accuracy and applicability of the proposed methods.

Engineering Practice Implications

CFST truss structures are widely used in large-span roof structures, sports arenas, airport terminals, and industrial facilities. The ultimate load capacity of these structures is a critical design parameter, and the ability to efficiently and accurately predict this capacity has direct economic implications. The EMRM enables engineers to rapidly evaluate multiple design alternatives, optimize material usage, and identify critical members that govern structural capacity.

For steel pipe manufacturers and structural engineers, the HGYF provides a more refined understanding of the interaction between steel confinement and concrete core behavior in rectangular sections. The confinement effect coefficient, which quantifies the degree of lateral restraint provided by the steel tube, is a fundamental parameter in CFST design. The polynomial fitting approach allows this coefficient to be accurately related to section geometry, steel properties, and concrete properties, providing a quantitative basis for design decisions.

The method is particularly relevant for the design of CFST truss structures in seismic regions, where the inelastic behavior of members governs the structure's capacity to dissipate seismic energy. By identifying high-stress elements and simulating stiffness degradation, the EMRM captures the progressive nature of structural failure, which is essential for evaluating seismic resilience.

Study Insights and Reflections

The polynomial fitting approach used to develop the HGYF introduces an approximation error that depends on the polynomial order and the range of section geometries covered. For extreme section proportions — such as very thin-walled or very elongated rectangular sections — the fitting accuracy may degrade. Engineers applying this method should verify the fit quality for their specific section proportions before relying on the results for design.

The EMRM, while efficient, is fundamentally a stiffness-based approach that does not capture all aspects of nonlinear behavior. It does not account for geometric nonlinearity (P-Δ effects), material softening after peak strength, or shear deformation. For structures where these effects are significant, the EMRM results should be used as a preliminary estimate, with detailed nonlinear analysis performed for final design verification.

The work represents a significant advancement in CFST structural analysis methodology. The combination of a rigorous yield function with an efficient analysis method addresses the practical need for fast, accurate structural evaluation tools. Future research should extend the HGYF to include more complex loading conditions — such as combined axial, flexural, and torsional loads — and develop design-oriented formulations that can be directly incorporated into structural design software.