Simplified Calculation Method for Cross-Sectional Temperature Field of Steel Tube Concrete Columns Under Fire

Literature Overview

The paper by Han Jinsheng, Dong Yuli, and colleagues (2009), published in the Journal of Shandong University of Science and Technology, presents a simplified calculation method for determining the cross-sectional temperature field of steel tube concrete (STC) columns subjected to fire loading. Funded by the National Science and Technology Support Program of China and Shandong University of Science and Technology research grants, this study addresses a critical gap in fire engineering practice: the need for practical yet accurate methods to evaluate the thermal response of STC columns, which are widely used in high-rise buildings, industrial structures, and bridges.

Core Technical Methodology

Finite Difference Numerical Model

The study begins by developing a finite difference numerical calculation program to compute the cross-sectional temperature field of STC columns under standard fire conditions. The numerical model accounts for the coupled heat transfer between the steel tube and the concrete core, including the effects of thermal conductivity variation with temperature, heat capacity changes, and the convective and radiative heat flux from the fire environment to the steel tube outer surface. The validation of the numerical model against experimental data showed good agreement, establishing the reliability of the computational framework.

Parametric Analysis of Influencing Factors

Based on both experimental results and extensive numerical simulations, the study systematically analyzed the influence of three primary geometric and material parameters on the cross-sectional temperature field:

Parameter	Effect on Temperature Field	Engineering Significance
Steel tube wall thickness	Thicker walls delay heat transfer to concrete core	Primary factor in fire resistance rating
Steel tube outer diameter	Larger diameters increase the concrete core thermal mass	Affects temperature gradient distribution
Concrete aggregate type	Aggregate type influences concrete thermal conductivity	Determines heat transfer rate within concrete

The steel tube wall thickness was identified as the most influential parameter, which is consistent with the fundamental principle that the steel tube acts as a thermal barrier between the fire environment and the concrete core. Thicker steel tubes provide greater thermal resistance, slowing the rate of temperature rise in the concrete core and thereby enhancing the overall fire resistance of the column.

Simplified Calculation Method Development

The simplified method was developed by fitting analytical expressions to the parametric study results, reducing the complex two-dimensional heat conduction problem to a set of practical formulas that can be evaluated using standard engineering calculations. The accuracy of the simplified method was verified against both experimental and numerical results, demonstrating that it meets the precision requirements for practical engineering applications.

Engineering Practice Applications

Fire Resistance Design

The simplified calculation method has direct application in the fire resistance design of STC columns. Designers can use the method to rapidly evaluate the fire resistance rating of proposed column cross-sections, comparing different steel tube thicknesses and diameters to identify the most cost-effective configuration that meets the required fire resistance duration. This is particularly valuable during the early design stages when rapid iteration between design options is necessary.

Comparison with Existing Methods

Method	Accuracy	Computational Complexity	Applicability
Full finite element thermal analysis	High	Very high	Research and detailed design
Existing code methods (Eurocode 4)	Moderate	Moderate	General STC members
Simplified method (this study)	Good	Low	STC columns specifically

The simplified method occupies a practical middle ground between the high accuracy of full numerical analysis and the limited applicability of existing code methods. It is specifically tailored for STC columns, incorporating the unique thermal behavior of the steel tube-concrete interface that generic methods may not capture accurately.

Integration with Structural Fire Analysis

The cross-sectional temperature field is the essential input for structural fire analysis, which determines the residual load-bearing capacity of the column at elevated temperatures. The simplified temperature calculation method can be integrated into a two-step fire analysis procedure: first, the temperature field is computed using the simplified method, and then the structural response is evaluated using temperature-dependent material properties and section analysis procedures. This two-step approach is widely accepted in fire engineering practice and is adopted by major international codes including Eurocode 4.

Critical Reflection

The simplified calculation method represents a valuable contribution to practical fire engineering, but its applicability is bounded by the parametric range of the underlying study. Engineers should verify that the steel tube thickness, diameter, and concrete aggregate type of their specific project fall within the validated range before applying the method. Additionally, the study focuses on standard fire conditions, which represent a specific temperature-time relationship. Real fire scenarios may involve different temperature profiles, including fast fires in industrial settings or slow fires in large compartments, which could affect the accuracy of the simplified method. The method also assumes uniform temperature distribution around the steel tube circumference, which is reasonable for isolated columns but may not hold for columns in close proximity to other structural elements or where fire compartment geometry creates non-uniform heat flux distributions. Engineers should exercise professional judgment when applying the simplified method and consider full numerical analysis for critical or complex structural configurations.