Design Formulae

There are only a few of design formulae for calculating the temperature response of steel and concrete members. It should be noted that the formulae are only valid for the prediction of thermal response to the heating conditions upon which the formulae are derived. In most cases, the formulae have been empirically derived from the standard fire tests. As a result, designers are often unable to apply the formulae to their particular design with different heating conditions, for example in case of a natural fire.

The main assumption in the design formulae for calculating the temperature response of structural members is that the member boundaries are not subject to any possible changes during the fire exposure, except for a partial or total loss of the insulation for steelwork. The temperature rise of steelwork is normally calculated at small time steps and the temperature rises are accumulated after each time step until the end of fire exposure. The loss of insulation can easily be considered in the analytical procedure by changing the boundary conditions at any specified time step and onwards.

However, to date, the spalling of concrete cannot be incorporated in any simple calculation formulae since the mechanism of spalling is very complicated and difficult to be quantified. For concrete members, spalling of concrete cover can occur during a fire exposure reducing the cross section of the member and exposing the reinforcement to the fire, resulting in a greater loss in strength. Without considering spalling, the calculation of the thermal response will tend to be less conservative and may lead to unsafe design in the structural response.

There are simple design formulae available for calculating the thermal response of the following structural members:

• Unprotected steel members
• Protected steel members
• Unprotected composite slabs
• Concrete members