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Background to thermal analysis


To introduce a basic background of thermal analysis for fire situations.


Thermal models are presented and simple rules are given for calculating the transient thermal response of steel elements, with or without a protective coating. The concept of the section factor of the steel section is introduced. Composite steel-concrete elements (columns and slabs) are also discussed.


Fire is a very complex phenomenon which can take many forms and involves different kinds of chemical reactions.

From a structural point of view, only the fires that can cause structural damage are of interest and, in this case, fire can be regarded as an accidental situation.

Design criteria for structural fire safety require some assumptions both for the structural and heating models.

Fire is usually represented by a temperature-time curve which gives the average temperature reached during fire in a small size compartment or in the furnaces used for fire resistance tests. International standards are based on the standard fire defined by the heat exposure given by the ISO 834 curve (see Figure 1) for buildings. For other applications, e.g. tunnels, other curves should be used. Reference can also be made to natural fires which have different temperature-time relationships depending on fire load density and ventilation conditions (see Figures 2a and 2b).


In more complex analyses, different heating models can be considered to represent the temperature development in different zones of the fire compartment or in the neighbourhood of it. This is the case, for instance, for many large industrial buildings or for external columns near the windows of a building.

The response of a structural member exposed to fire is governed by the rate that it is heated because the mechanical properties of materials decrease as temperature rises and, likewise, the structural resistance of a member reduces with temperature rise.

Collapse occurs at the time when the structural resistance reduces to the applied action effects. This fire resistance time can happen in a very short time when the increase of temperature is rapid. Steel elements have an quite unfavourable behaviour in this respect due to the very high thermal conductivity of the steel. A rapid heating of the whole profile takes place as a result. In comparison, composite elements have a favourable behaviour due to the great thermal inertia of the elements and the lower thermal conductivity of the concrete.

In this lecture, some basic aspects of thermal analysis are discussed. The general equation for heat transfer is presented, followed by the simplified method, which may be adopted for steel members. Thermal gradients across the section and along the member are neglected.

In a fire, the temperature of the steel increases similarly but with some delay compared to the gas temperature of the fire (see Figure 3). The delay depends on the thermal inertia of the element as well as on the intensity of heat flow passing through its external surface. If the element has an applied protective coating, this delay is longer. For bare elements, the delay depends on the section factor of the element.


In Figure 3, the temperature rise in three different cases is compared for the same element. Curve (a) represents the delay for the bare element, while curves (b) and (c) apply to the cases of some protective coating, without and with moisture content.

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