Bending Performance and Bearing Capacity Calculation of Elliptical Steel Tube Concrete Members

Literature Overview

This research paper by Jiang Han, Wang Jingfeng, and Shen Qihan (Hefei University of Technology, published in 2018 in Progress in Steel Building Structures) investigates the bending performance and bearing capacity of elliptical steel tube concrete (CFST) members through numerical analysis using ABAQUS. Supported by the National Natural Science Foundation of China (Grant 51478158) and the Ministry of Education New Century Talent Support Program (NCET-12-0838), the study develops a simplified calculation formula for the bending bearing capacity of elliptical CFST members, filling a gap in the design methodology for this non-circular cross-section type.

Research Background and Motivation

Elliptical steel tube concrete members are used in structural applications where the advantages of elliptical geometry are beneficial:

• Aesthetic requirements in architectural applications
• Structural efficiency in specific loading conditions (bending about the major or minor axis)
• Space constraints that require non-circular cross-sections
• Aerodynamic considerations in certain applications

However, the non-circular cross-section of elliptical CFST members creates challenges for structural analysis and design:

• Complex contact behavior between the steel tube and concrete
• Non-uniform confinement effect around the cross-section perimeter
• Different bending behavior about the major and minor axes
• Lack of established design formulas and code provisions

The absence of reliable design formulas for elliptical CFST members has limited their application in practice, despite their potential structural and aesthetic advantages.

Numerical Analysis Methodology

Model Development

The authors developed a finite element model using ABAQUS that accounts for:

• Complex contact behavior: The contact between the steel tube and concrete is modeled with a penalty contact algorithm that captures the non-uniform confinement effect around the elliptical perimeter.
• Elliptical cross-section geometry: The elliptical shape is accurately represented in the model, with appropriate element density near the steel tube wall where stresses are concentrated.
• Material nonlinearity: Both steel and concrete are modeled with their full stress-strain relationships, including strain hardening for steel and confined concrete behavior.
• Geometric nonlinearity: Large deformations are considered, which is important for capturing the post-buckling behavior of the steel tube.

Model Validation

The numerical model was validated against six experimental tests on elliptical CFST members under pure bending. The validation results showed good agreement between the numerical predictions and experimental results, confirming the accuracy of the model for parametric studies.

Parametric Analysis Results

Parameters Studied

Key Findings

1. Steel strength effect: Higher steel yield strength increases the ultimate bending moment. The relationship is approximately linear, with the contribution of steel to the total capacity being proportional to f_y.
2. Concrete strength effect: Higher concrete compressive strength increases the ultimate bending moment, but the effect is less pronounced than for steel strength. The confined concrete contribution is enhanced by the steel tube.
3. D/t ratio effect: Smaller D/t ratios (thicker walls) increase the ultimate bending moment. This is because thicker walls provide better confinement and resist local buckling more effectively.
4. Axis ratio effect: The major-to-minor axis ratio affects the bending behavior differently depending on the bending direction:

• Bending about the major axis: Higher a/b ratio increases the moment capacity due to the larger section modulus
• Bending about the minor axis: Higher a/b ratio may decrease the moment capacity due to the reduced confinement effect on the minor axis

Failure Modes

The numerical analysis revealed distinct failure modes for elliptical CFST members under pure bending:

• Steel tube local buckling: The primary failure mode for thin-walled members, occurring on the compression side of the section
• Concrete crushing: The secondary failure mode, occurring at the extreme compression fiber
• Composite failure: A combination of steel buckling and concrete crushing, occurring for intermediate D/t ratios

The failure mode is influenced by the D/t ratio, with thinner walls (higher D/t) failing by steel buckling and thicker walls (lower D/t) failing by concrete crushing or composite failure.

Proposed Simplified Calculation Formula

Based on the parametric analysis results, the authors propose a simplified formula for the bending bearing capacity of elliptical CFST members:

The formula follows the principle of superposition with enhancement factors:

• The steel tube contribution is calculated based on the section modulus and yield strength
• The concrete contribution is enhanced by a confinement factor that accounts for the non-uniform confinement effect of the elliptical steel tube
• The enhancement factor is calibrated against the numerical analysis results and validated against experimental data

Formula Characteristics

Engineering Practice Implications

Steel Tube Manufacturing for Elliptical Sections

The research highlights several manufacturing considerations for elliptical steel tubes used in CFST applications:

1. Forming process: Elliptical steel tubes are typically formed from circular tubes through controlled deformation. The forming process must maintain wall thickness uniformity and avoid excessive thinning at the minor axis.
2. Dimensional accuracy: The major and minor axis dimensions must be manufactured to tight tolerances to ensure the actual cross-section matches the design assumptions.
3. Surface quality: The inner surface of the elliptical tube must be smooth to promote good concrete-steel bonding and uniform confinement.
4. Welding of elliptical tubes: When elliptical tubes are fabricated from plates, the welding process must account for the elliptical geometry. Welding distortions can alter the elliptical shape, affecting the structural performance.

Design Considerations

For engineers designing with elliptical CFST members:

• The bending capacity about the major axis is generally higher than about the minor axis due to the larger section modulus
• The confinement effect is non-uniform around the elliptical perimeter, with stronger confinement at the major axis and weaker confinement at the minor axis
• The D/t ratio should be limited to prevent premature local buckling, with recommended limits similar to those for circular CFST members
• The proposed simplified formula provides a practical tool for preliminary design, but detailed FEA should be used for critical applications

Study Insights and Reflections

The research makes a significant contribution to the field of elliptical CFST structural design by providing a validated numerical analysis methodology and a practical simplified calculation formula. The parametric analysis reveals the relative importance of different design parameters and identifies the critical failure modes.

The most important finding is that the bending capacity of elliptical CFST members can be predicted with reasonable accuracy using a simplified formula that accounts for the non-uniform confinement effect. This provides engineers with a practical design tool that was previously unavailable.

However, several limitations should be noted:

• The study focuses on pure bending, which is a simplified loading condition. In practice, elliptical CFST members are often subjected to combined bending and axial compression.
• The numerical model, while validated against six tests, may not capture all failure modes, particularly those involving complex interaction between steel buckling and concrete crushing.
• The study does not address the effect of shear force on the bending capacity, which is important for members with short spans or high shear demands.
• The long-term behavior (creep, shrinkage, fatigue) of elliptical CFST members is not investigated.

Future research should extend the investigation to combined loading conditions, include more experimental validation, and develop design provisions for practical engineering applications. The proposed simplified formula should be further validated against a broader database of test results before being adopted in design codes.

The research demonstrates the value of numerical analysis in filling gaps in structural design knowledge, particularly for non-standard cross-sections where experimental data is limited. The combination of numerical analysis, parametric studies, and formula development provides a rigorous and practical approach to structural design methodology development.