Simplifications of Differential Equations
The aim of structural fire engineering design is to ensure that structures do not collapse when subjected to high temperatures in fire. Design of structures for fire still relies on single element behavior in the fire resistance test. The future of structural fire engineering design has to be evaluated in terms of the whole performance based design of structures for fire. This should include natural fire exposures, heat transfer calculations, and whole structural system behavior, recognizing the interaction of all elements of the structure in the region of the fire and any cooler elements outside the boundary of the compartment. Prescriptive fire grading and design methods based on heating single elements in the fire resistance test over-simplify the whole fire design process. The real problem can be addressed by performance based design methods where possible fire scenarios are investigated and fire temperatures are calculated based on the compartment size, shape, ventilation, assumed fire load and thermal properties of the fuel itself. The temperatures achieved by the connected structure can then be determined by heat transfer analysis. Traditionally steel and reinforced concrete fire design has been based upon fire resistance testing although fire resistance by calculation has also been implemented for many years.
Analysis of a small number of room fire tests revealed that fire load was an important factor in determining fire severity. It has been suggested that fire severity could be related to the fire load of a room and expressed as an area under the temperaturetime curve. The severities of two fires were equal if the area under the temperature-time curves were equal (above a base line of 300°C). Thus any fire temperature-time history could be compared to the standard curve. This approach obviously has limited applicability with respect to structural design.
The structural engineer is obviously interested to know not only the temperature-time relationship, but the second derivative of such function, which creates the acceleration and therefore the dynamic forces that are acting on structural system on top of static forces due to temperature elongations. The real fire test normally is presented by the double-curvature temperature-time function, while the standard test is presented by a singlecurvature function, and that makes a whole difference for structural design. On top of that, the real fire computer simulations of the temperaturetime curves have “small” oscillations along the curve, which are creating additional dynamic forces. The area under the temperature-time curve obviously doesn’t provide the answer to all these questions.
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Text by LEO Razdolsky, LR Structural Engineering Inc., Lincolnshire, Illinois, USA , Professor at Northwestern University, Evanston, Illinois, USA