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Temperature development

Following temperature curves are used for the description of the gas temperature according to EN 1991-1-2.

Standard temperature curve

The fundamental nominal curve, the temperature of gas in the fire compartment is given by the expression

Where is:

θg

  • The gas temperature in the fire compartment in °C

t

  • The time in minutes

External fire curve

The external fire curve is defined by the expression

Where is"

θg

  • The gas temperature in the fire compartment in °C

t

  • The time in minutes

The gas temperature is limited by the value 680°C. Therefore, the critical temperature won't be achieved in certain cases.

Hydrocarbon fire curve

The hydrocarbon curve is defined by the expression

Where is:

θg

  • The gas temperature in the fire compartment in °C

t

  • The time in minutes

Also this curve is limited, the limiting value is 1100°C.

Parametric temperature curve

This curve is valid for fire compartments up to 500m2, without openings in the roof and for a maximum compartment height of 4m. The curve consists of two phases: heating phase and cooling phase. Following parameters describe the geometry of the curve:

  • The time tlim for maximum gas temperature in case of fuel controlled fire
  • The thermal absorptivity for the total enclosure b given by the expression

Where is:

ρ

  • The density of boundary of enclosure in kg/m3

c

  • The specific heat of boundary of enclosure in J/(kg K)

λ

  • thermal conductivity of boundary of enclosure in W/(m K)
  • The opening factor O given by the expression

Where is:

Av

  • The total area of vertical openings on all walls in m2

heq

  • The weighted average of window heights on all walls in m

At

  • The total area of enclosure (walls, ceiling and floor, including openings) in m2
  • The design value of the fire load density qt,d related to the total surface area At of the enclosure.

Temperature development

The temperature development differs for protected and unprotected fire details.

Following expression is used for unprotected members:

Where is:

Δθa,t

  • The increment of temperature in an unprotected steel member

Am/V

  • The section factor for unprotected steel members

ca

  • The specific heat of steel

ρa

  • The unit mass of steel

hnet

  • The design value of the net heat flux

Δt

  • The time period

The specific heat of steel differs according to the temperature in accordance with the chapter 3.4.1.2 of EN 1993-1-2. The net heat flux hnet is given according to the chapter 3.1 of EN 1991-1-2. The temperature of steel member is checked with the help of temperature increments, the time period specified for the temperature increment Δt is 5 seconds.

The temperature development for protected members is defined by following expression:

where

Where is:

Δθa,t

  • The increment of temperature in a protected steel member

λp

  • The thermal conductivity of the fire protection system

Ap/V

  • The section factor for steel members insulated by fire protection material

dp

  • The thickness of the fire protection material

ca

  • The specific heat of steel

ρa

  • The unit mass of steel

θg,t

  • The ambient gas temperature at time t

θa,t

  • The steel temperature at time t

Δt

  • The time period

Δθg,t

  • The increase of the ambient gas temperature during the time interval Δt

cp

  • The temperature independent specific heat of the fire protection material

ρp

  • The unit mass of the fire protection material

The specific heat of steel differs according to the temperature in accordance with the chapter 3.4.1.2 of EN 1993-1-2. The temperature of steel member is checked with the help of temperature increments, the time period specified for the temperature increment Δt is 30 seconds.

The critical time is given as a sum of time increments Δt, that reach the critical temperature. The critical temperature is calculated in advance with the help of utilization of the member.

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