Flexural Rigidity of Steel Tube Concrete Members and Frame Structure Analysis Applications

Literature Overview and Historical Context

The paper by Zha Xiaoxiong, Tang Jiaxiang, and Zhong Shantong (1998), published in the Journal of Harbin University of Architecture, Volume 31, Issue 5, presents a theoretical and experimental investigation of the flexural rigidity of steel tube concrete (CFST) columns. The authors, affiliated with the Postdoctoral Research Station, Huazhong University of Science and Technology, and Harbin University of Architecture, treated the CFST member as a composite material and derived theoretical expressions for the flexural rigidity of the composite section. This work was conducted during a period of rapid growth in the use of CFST members in high-rise and long-span structures in China, making the accurate determination of flexural rigidity a critical design parameter.

Theoretical Framework for Flexural Rigidity

The flexural rigidity of a structural member, expressed as EI where E is the elastic modulus and I is the moment of inertia, is a fundamental parameter in structural analysis that governs the member's resistance to bending deformation. For a CFST member, the effective flexural rigidity is not simply the sum of the flexural rigidities of the steel tube and concrete core, because the two materials deform together under bending and the concrete core is confined by the steel tube, leading to a triaxial stress state that enhances the concrete's compressive strength and elastic modulus.

The authors derived a theoretical expression for the flexural rigidity that accounts for the composite action of the steel tube and concrete core. The key insight is that the steel tube confines the concrete core, creating a lateral pressure that increases the concrete's effective elastic modulus under compression. This confinement effect means that the composite flexural rigidity is greater than the simple sum of the individual flexural rigidities of the steel tube and the unconfined concrete core. The theoretical model also considers the effect of axial load on the flexural rigidity, recognizing that the P-Delta effect and the axial stress state influence the bending behavior of the column.

Experimental Validation

The theoretical predictions were validated through experimental tests on CFST columns subjected to bending loads. The experimental program included measuring the deflection at various load levels and comparing the measured flexural rigidity with the theoretical predictions. The results showed good agreement between the theoretical and experimental values, confirming the validity of the proposed theoretical model. The comparison with the flexural rigidity calculated from the original section dimensions revealed that the composite approach yields higher rigidity values, reflecting the beneficial interaction between the steel tube and concrete core.

The experimental results also highlighted the effect of slenderness ratio on the flexural rigidity. For slender CFST columns, the effective flexural rigidity is reduced due to the increased influence of second-order effects. The authors noted that the ratio of the composite flexural rigidity to the steel tube flexural rigidity alone increases with the concrete fill ratio, indicating that the concrete core contributes significantly to the overall bending resistance, particularly in the elastic range.

Application to High-Rise Frame Structure Analysis

The paper extends the flexural rigidity analysis to the preliminary analysis of high-rise frame structures using CFST columns. The accurate determination of column flexural rigidity is essential for calculating the lateral stiffness of the frame, which directly affects the building's natural frequency, drift under wind and seismic loads, and the distribution of internal forces among frame members. The authors demonstrated that using the composite flexural rigidity values in frame analysis leads to more accurate predictions of structural response compared to using the steel tube flexural rigidity alone.

For practical design, the composite flexural rigidity should be used in the elastic analysis phase, while the nonlinear behavior of the CFST member should be considered in the ultimate limit state design. The transition from elastic to inelastic behavior in CFST columns is gradual due to the composite action, and the flexural rigidity decreases progressively as the concrete core cracks and the steel tube yields. Engineers should use the appropriate flexural rigidity values for each analysis stage to ensure accurate structural predictions.

Study Insights and Engineering Recommendations

This research from 1998 remains highly relevant to contemporary CFST design practice. The concept of treating CFST as a composite material and deriving an effective flexural rigidity is now well-established in international codes such as Eurocode 4 and the AISC specification for composite construction. However, the paper's emphasis on the interaction between axial load and flexural rigidity is particularly important for column design in tall buildings, where the axial load ratio can significantly influence the bending behavior. Engineers should ensure that the flexural rigidity values used in structural analysis accounts for the confinement effect, the axial load level, and the time-dependent behavior of the concrete. The work by Zha et al. provides a solid foundation for the rational design of CFST frame structures and continues to inform current design methodologies.