Differential Equations And Assumtions

Fire is a very complex chemical process influenced by many factors that affect its growth, spread, and development. Structural Fire Load establishment requires a basic understanding of the chemical and physical nature of fire. This includes information describing sources of heat energy, composition and characteristics of fuels, and environmental conditions necessary to sustain the combustion process. It is important first to define curtain terms and conditions that will be used in this book, since some definitions differ from one source to another.

For example, the definition of “flashover” in fire compartment (room) development has qualitative and quantitative differences in different reference sources. The “flashover” defined by different authors in the literature are as follows: [1]: “The transition from the fire growth period to the fully developed stage in the enclosure fire development.” [2]: “A dramatic event in a room fire that rapidly leads to full room involvement; an event that can occur at a smoke temperature of 500 to 600 C°.” [3]: “The transition from a localized fire to the general conflagration within the compartment when all fuel surfaces are burning”

The latest definition given by the NFPA 921-2004 [4] is as follows: “A transitional phase in the development of a compartment fire in which surfaces exposed to thermal radiation reach ignition temperature more or less simultaneously and fire spreads rapidly throughout the space resulting in full room involvement or total involvement of the compartment or enclosed area.” It is important to underline here that the latest NFPA definition has a reference to thermal radiation as a main source of energy that creates the flashover conditions and as a consequence leads to the fully developed compartment fire.

The design values of a Structural Fire Load in most practical cases are based on fully developed stage in the enclosure fire development, therefore simplification can be made in conservation energy equation with respect to other sources of energy, such as conduction and convection (see below). For all practical purposes in structural engineering analyses and design the Structural Fire Load is temperature-time function that is obtained from conservation of energy, mass and momentum equations.

As it has been indicated in previous Chapter 02, this function is presented by a double-convex curve, therefore the “mathematical” definition of a flashover point could be done as follows: the point, where the curvature sign is changing (second derivation is 0 or first derivation is maximum at this point). First derivation of temperature with respect to time multiplied by specific heat and density is the Heat Release Rate (HRR). Therefore the definition of a flashover point could be stated also as a point on the temperature-time curve where HRR reaches the maximum.

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Text by Dr. Leo Razdolsky , LR Structural Engineering Inc., Professor at Northwestern University, Evanston, IL., USA