Simplified Calculation Method for Cross-Section Temperature Field of Steel Pipe Concrete Columns under Fire

Literature Overview

This paper by Han Jinsheng, Dong Yuli, Cong Shuping, Sun Huangsheng, and Sun Yuedong from Shandong University of Science and Technology and Harbin Institute of Technology, published in the Journal of Shandong University of Science and Technology (Natural Science Edition) in 2009 (Vol. 28, No. 3, pp. 34-39), presents a simplified calculation method for determining the cross-sectional temperature distribution of steel pipe concrete columns under fire conditions. The study was supported by the National "Eleventh Five-Year" Science and Technology Support Program Key Project (Grant No. 2006BAJ13B03) and the Shandong University of Science and Technology "Spring Bud Program" (Grant No. 2008AZZ111).

Core Viewpoints and Technical Approach

The research addresses the practical challenge of calculating temperature distributions in steel pipe concrete columns during fire, which is essential for fire resistance design but is typically computationally intensive. The authors developed a simplified method through the following systematic approach:

Development of a finite difference numerical calculation program for the cross-sectional temperature field of steel pipe concrete columns under fire.
Validation of the numerical program against experimental results, confirming good agreement.
Analysis of the influence of key parameters including steel pipe wall thickness, steel pipe diameter, and concrete aggregate type on the cross-sectional temperature field.
Simplification of the main influencing factors and development of a fitted simplified calculation method.

Parameter	Influence on Temperature Field	Simplification Approach
Steel pipe wall thickness	Thicker walls provide better thermal insulation	Linear correction factor applied
Steel pipe diameter	Larger diameters result in higher core temperatures	Geometric scaling factor
Concrete aggregate type	Different aggregates have different thermal properties	Aggregate-specific coefficient
Fire duration	Longer exposure leads to higher temperatures	Time-dependent function
Fire temperature	Higher fire temperatures increase core temperatures	Nonlinear temperature function

Interpretation of Technical Points

Finite Difference Method Validation

The finite difference numerical program developed by the authors serves as the foundation for the simplified method. The program solves the heat conduction equation for the axisymmetric cross-section of the steel pipe concrete column, accounting for the different thermal properties of the steel pipe, the concrete core, and the fire environment. The validation against experimental results demonstrates that the numerical approach accurately captures the complex heat transfer mechanisms, including conduction through the steel pipe wall, conduction within the concrete, and the convective and radiative heat transfer from the fire gases to the steel pipe outer surface.

Key Factors and Their Interactions

The analysis of the temperature field reveals that the steel pipe wall thickness has a significant influence on the thermal insulation provided to the concrete core. Thicker steel pipe walls act as a thermal barrier, slowing the rate of heat transfer to the concrete and resulting in lower core temperatures for a given fire duration. However, the relationship is not strictly linear because the steel pipe itself heats up, and the thermal conductivity of steel decreases at elevated temperatures, creating a non-linear insulation effect.

The steel pipe diameter influences the temperature field through the ratio of the heat transfer path length to the cross-sectional area. Larger diameter columns have a greater distance from the heated outer surface to the center of the concrete core, which results in lower core temperatures. However, larger columns also have a greater surface area exposed to the fire, which can partially offset the benefit of the increased heat transfer path length.

The concrete aggregate type affects the temperature field primarily through the thermal conductivity and specific heat capacity of the aggregate. Aggregates with lower thermal conductivity, such as lightweight aggregates, provide better thermal insulation and result in lower core temperatures. The aggregate type also affects the thermal expansion behavior of the concrete, which is important for assessing the risk of concrete spalling under fire conditions.

Simplified Calculation Method

The simplified calculation method developed by the authors reduces the complex finite difference analysis to a set of practical formulas that can be applied in engineering design without the need for specialized computational tools. The method incorporates correction factors for the key parameters identified in the parametric study, and the accuracy of the simplified method has been verified to meet the precision requirements for engineering practice. This is a significant contribution because it makes fire resistance assessment of steel pipe concrete columns accessible to practicing engineers who may not have access to or expertise in finite element analysis.

Integration with Engineering Practice

In fire resistance design, the temperature distribution within a steel pipe concrete column is critical for determining the residual load-bearing capacity at various fire durations. The simplified calculation method provides a practical tool for engineers to estimate the temperature field without resorting to full finite element analysis, which can significantly reduce the time and cost of fire resistance assessment.

The method is particularly useful for preliminary design stages where rapid evaluation of different column configurations is needed. Engineers can quickly assess how changes in steel pipe wall thickness, diameter, or concrete mix design affect the fire resistance performance, and select the most economical configuration that meets the required fire resistance rating.

For detailed design and code compliance, the simplified method can be used as a screening tool to identify configurations that require more detailed analysis. Columns that show adequate fire resistance according to the simplified method can be accepted without further analysis, while columns that are marginal or insufficient can be refined with more detailed numerical analysis.

Key Questions and Reflections

The accuracy of the simplified method is stated to meet engineering practical requirements, but it is important to understand the range of applicability and the magnitude of the error. For critical applications where precise fire resistance assessment is required, such as in nuclear facilities or high-rise buildings, engineers should verify the results of the simplified method with full numerical analysis. The simplified method is best suited for routine applications where the temperature field is within the range covered by the parametric study.

Another consideration is the effect of fire duration on the accuracy of the simplified method. Fire resistance ratings are typically specified for discrete durations such as 1 hour, 2 hours, and 3 hours. The simplified method should be validated for each of these durations to ensure that the correction factors are appropriate across the full range of fire exposure times.

Study Insights and Implications

This paper makes a valuable contribution to the practical fire resistance design of steel pipe concrete columns by providing a simplified calculation method that balances accuracy with computational efficiency. The systematic approach of developing a numerical model, validating it against experimental data, identifying key parameters, and developing a simplified method is a model for engineering research that bridges the gap between fundamental analysis and practical application. For practicing engineers, the simplified method provides a practical tool for fire resistance assessment that can be readily incorporated into design workflows, reducing the barrier to performing fire resistance calculations and improving the overall safety of steel pipe concrete structures.