Nonlinear Finite Element Analysis of Temperature Field in Square-Section Steel Tube Concrete Members

Literature Overview

The paper by Xu Lei and Han Linhai, published in the Journal of Harbin University of Architecture in 1999 (Vol. 32, No. 5, pp. 34-38), presents a nonlinear finite element analysis of the temperature field in square-section steel tube concrete (SC) members under fire conditions. This research was conducted at the Metal Structure Research Laboratory of Harbin University of Architecture and was supported by the National Natural Science Foundation. The work addresses the critical issue of fire resistance performance of steel tube concrete structures and provides a methodology for predicting the temperature distribution within these composite members during fire exposure.

Core Technical Content

The study focuses on determining the temperature field distribution within square-section steel tube concrete members when subjected to standard fire curves. The analysis begins with the reasonable determination of the surface temperature of the steel tube concrete member under fire conditions, which serves as the boundary condition for the subsequent finite element analysis. The nonlinear finite element method is then employed to calculate the temperature field distribution throughout the cross-section, considering the nonlinear thermal properties of both the steel tube and the concrete core.

The key aspects of this analysis include:

Surface Temperature Determination: The surface temperature of the steel tube concrete member is determined based on the fire curve and the heat transfer conditions at the exposed surface. This includes consideration of radiation and convection heat transfer mechanisms.
Thermal Property Nonlinearity: Both steel and concrete exhibit temperature-dependent thermal properties, including thermal conductivity, specific heat, and thermal expansion coefficient. These nonlinear relationships are incorporated into the finite element formulation.
Fire Protection Layer Effects: The study considers the influence of different fire protection layer thicknesses, including concrete cover and fire-resistant coatings, on the temperature field distribution within the steel tube concrete member.

Thermal Parameters and Boundary Conditions

Parameter	Steel Tube	Concrete Core	Fire Protection Coating
Thermal conductivity at 20°C	50-60 W/(m·K)	1.4-2.5 W/(m·K)	0.04-0.15 W/(m·K)
Thermal conductivity at 800°C	40-45 W/(m·K)	1.0-1.5 W/(m·K)	0.03-0.10 W/(m·K)
Specific heat at 20°C	460-500 J/(kg·K)	880-1000 J/(kg·K)	1000-1500 J/(kg·K)
Density	7850 kg/m³	2400 kg/m³	500-800 kg/m³
Temperature-dependent	Yes	Yes	Yes

The finite element model employs solid elements with temperature-dependent material properties. The boundary conditions include:

Convective and radiative heat transfer at the external surface
Adiabatic condition at the symmetry planes (for quarter-symmetric modeling)
Initial uniform temperature distribution at ambient temperature

Parametric Study Results

The parametric analysis reveals several important trends regarding the temperature field in square-section steel tube concrete members:

Effect of Fire Protection Layer Thickness: Increasing the thickness of the fire protection layer (both concrete cover and fire-resistant coating) significantly reduces the peak temperature reached by the steel tube. A fire-resistant coating thickness of 25-50 mm can delay the steel tube from reaching critical temperatures (650°C) by 30-60 minutes under standard fire conditions.
Effect of Steel Tube Dimensions: Larger steel tube dimensions (wall thickness and section size) result in lower internal temperatures at the steel tube inner surface due to the greater thermal mass of the steel tube wall. However, the effect diminishes beyond a certain thickness due to the relatively high thermal conductivity of steel.
Temperature Gradient Distribution: The temperature gradient within the concrete core is relatively steep near the steel tube inner surface and becomes more uniform toward the center of the cross-section. This non-uniform temperature distribution creates thermal stresses that must be considered in the structural assessment.
Time-Temperature Relationship: The temperature at critical locations (steel tube inner surface, concrete center) follows a predictable time-dependent pattern that can be correlated with the fire duration and protection layer characteristics.

Engineering Practice Integration

For pipeline engineering and structural applications, the findings of this paper have several important implications:

Fire Protection Design: The analysis provides a quantitative basis for determining the required fire protection layer thickness for steel tube concrete members. For critical pipeline support structures, the fire protection design should ensure that the steel tube temperature does not exceed 550°C (for structural steel) or 650°C (for high-temperature steel) during the required fire resistance duration.

Material Selection for Fire Protection: The study demonstrates that the thermal properties of the fire protection material are critical. Materials with low thermal conductivity (such as intumescent coatings, ceramic fiber boards, or vermiculite boards) are most effective. The thermal conductivity of the fire protection material should be evaluated at elevated temperatures, as it typically decreases with temperature, providing additional insulation benefit.

Quality Control Considerations: During the fabrication and installation of steel tube concrete members:

The fire protection coating application must be uniform and of consistent thickness.
Any gaps or defects in the fire protection layer can create thermal bridges that significantly reduce fire resistance.
The concrete cover thickness must be verified to ensure adequate protection of the steel tube.

Key Findings and Validation

The finite element results show good agreement with experimental data, validating the accuracy of the nonlinear thermal analysis approach. The maximum deviation between predicted and measured temperatures is within acceptable engineering limits (typically ±20-30°C), which is sufficient for fire resistance assessment purposes.

The study establishes that the temperature field in square-section steel tube concrete members is governed by:

The thermal conductivity and heat capacity of the constituent materials
The geometry of the cross-section (section size, wall thickness, cover thickness)
The fire protection layer characteristics
The fire curve and duration

Study Insights and Implications

This paper provides a valuable methodology for fire engineering analysis of steel tube concrete structures. From a practical standpoint, the nonlinear finite element approach allows for the evaluation of complex geometries and varied fire protection configurations that would be prohibitively expensive to test experimentally.

I find the parametric study particularly useful for design optimization. The clear identification of the key parameters affecting the temperature field enables engineers to make informed decisions regarding section design, material selection, and fire protection specifications. The approach can be directly extended to other cross-section shapes (circular, rectangular) and different fire scenarios (hydrocarbon fire, pool fire).

One area for future improvement is the incorporation of the thermal-structural coupling effects. The temperature field affects the mechanical properties of both steel and concrete, and the resulting thermal stresses can influence the crack patterns in concrete, which in turn affects the heat transfer. A fully coupled thermal-structural analysis would provide more accurate predictions for critical applications.