Zhuojin Pipe Fitting Co., LtdFinite Element Analysis of Fire Resistance for Bidirectionally Eccentrically Loaded Square Steel Tube Concrete Columns under Three-Side Fire
Literature Overview and Problem Formulation
The paper by Zhang Bo, Xu Guangpeng, Ren Qingxin, and Liu Xiangyu (2023, Journal of Shenyang Jianzhu University, Vol. 39, No. 1, pp. 9-16), supported by the National Natural Science Foundation of China (Grant 51808351), investigates the fire resistance of bidirectionally eccentrically loaded square steel tube concrete (SRC) columns subjected to three-side fire exposure. The study employs ABAQUS finite element modelling to establish coupled thermal-mechanical analysis models and systematically examines the influence of load eccentricity angle, load ratio, slenderness ratio, cross-sectional side length, and eccentricity ratio on the fire resistance limit.
Thermal and Mechanical Modelling Approach
The finite element model comprises two coupled analyses: a thermal analysis to determine the temperature distribution within the column under the three-side fire exposure scenario, and a mechanical analysis to evaluate the structural response under combined thermal and mechanical loading. The three-side fire condition represents a realistic fire scenario in which one face of the column is shielded (typically by an adjacent wall or partition), while the remaining three faces are exposed to the standard ISO 834 fire curve or an equivalent temperature-time relationship.
Key modelling assumptions and parameters include:
| Modelling Parameter | Typical Values or Approach |
|---|---|
| Fire temperature curve | ISO 834 standard fire curve: T = 345 log10(8t + 1) + 20 °C |
| Steel tube material model | Temperature-dependent constitutive law (yield strength, elastic modulus, thermal expansion coefficient) |
| Concrete material model | Temperature-dependent stress-strain relationship with consideration of spalling and cracking |
| Interface behaviour | Bond-slip model between steel tube and concrete core |
| Mesh type | 8-node solid elements (C3D8) for both steel and concrete |
| Boundary conditions | Fixed at base, eccentric axial load applied at top |
Key Findings and Parametric Analysis Results
The study identifies five primary parameters influencing the fire resistance limit of the column:
- Load eccentricity angle: A larger eccentricity angle reduces the fire resistance limit, as the combined bending moments from thermal expansion and mechanical eccentricity create a more severe stress state.
- Load ratio: Higher load ratios (applied load divided by the ambient temperature compressive capacity) reduce fire resistance, as the column has less reserve capacity to accommodate thermal degradation.
- Slenderness ratio: Higher slenderness ratios reduce fire resistance due to increased susceptibility to thermal buckling and second-order effects.
- Cross-sectional side length: Smaller cross-sectional dimensions reduce fire resistance because the fire-exposed perimeter to cross-sectional area ratio is higher, leading to more rapid temperature rise in the core.
- Eccentricity ratio: The eccentricity ratio (e/b, where e is the eccentricity and b is the section dimension) exhibits a non-monotonic effect. Within the range of 0 to 0.3, there exists an optimal eccentricity ratio that maximises the fire resistance limit, with an improvement of more than 80% compared to the concentrically loaded case.
The finding regarding the optimal eccentricity ratio is particularly noteworthy and counter-intuitive. The authors explain that a moderate eccentricity induces a biaxial bending moment that, combined with the thermal gradient from three-side fire exposure, can create a more favourable stress distribution in the cross-section. Specifically, the mechanical eccentricity moment can partially counteract the thermal bending moment, resulting in a net reduction of the combined bending effect. This is analogous to the concept of prestressing in reinforced concrete design, where an intentional eccentricity is used to improve performance under specific loading conditions.
Simplified Design Formula and Verification
The paper proposes a simplified calculation formula for the fire resistance limit that shows good agreement with the finite element results within the studied parameter range. This simplified formula is valuable for practical engineering design, as it avoids the need for detailed finite element analysis during the design phase while still capturing the essential physics of the three-side fire scenario.
Engineering Practice and Code Compliance
For engineers designing steel tube concrete columns in fire-exposed structures, the following considerations are relevant:
- Fire resistance classification: According to GB 50016 (Code for Fire Protection Design of Buildings), structural elements in multi-storey buildings typically require fire resistance ratings of 1.0 to 3.0 hours depending on building height and occupancy. The three-side fire scenario is a recognised condition in fire engineering design, as it represents a common configuration where one face of a column is protected by a wall.
- Material protection: In cases where the inherent fire resistance of the SRC column is insufficient, additional fire protection measures such as intumescent coatings, gypsum board encasement, or fire-resistant concrete overlays may be applied.
- Slenderness limitation: The study highlights the importance of limiting the slenderness ratio of SRC columns in fire design. Excessive slenderness can lead to premature thermal buckling, which is a ductile failure mode that may not be adequately captured by simplified design formulas.
Key Questions and Study Insights
The non-monotonic behaviour of the eccentricity ratio is a fascinating finding that warrants further investigation. The optimal eccentricity ratio is likely dependent on the specific combination of load ratio, cross-sectional dimensions, and fire exposure duration. In practical design, engineers should not assume that any eccentricity will improve fire resistance; rather, the optimal eccentricity must be determined through analysis for the specific structural configuration.
Another important consideration is the potential for concrete spalling under fire exposure. The finite element model should include a spalling criterion based on the temperature gradient through the concrete section. If spalling occurs, the effective cross-sectional area is reduced, and the steel tube may be directly exposed to the fire, leading to rapid temperature rise and loss of strength.
Summary and Conclusions
This study provides a rigorous finite element-based investigation of the fire resistance of bidirectionally eccentrically loaded square SRC columns under three-side fire exposure. The identification of the optimal eccentricity ratio range (0 to 0.3) and the associated 80% improvement in fire resistance limit represent significant and practically useful findings. The proposed simplified formula offers a viable design tool for engineers. However, the results should be applied with awareness of the modelling assumptions, and additional experimental validation under realistic fire conditions would strengthen the confidence in these findings for critical structural applications.