Eurocode 1-1-2

BS EN 1991-1-2:2002 - General Actions: Actions on structures exposed to fire.

BS EN 1991-1-2 provides general rules for the determination of thermal actions on structures exposed to fire and their application for structural analysis. The standard specifies:

  • Temperature-time curves for standard fire exposure (including the standard temperature-time curve)

  • Natural fire models for compartment fires

  • Thermal material properties for structural materials at elevated temperatures

  • Methods for determining temperature distributions in structural members

  • Thermal actions for structural fire design

Section 3 - Thermal actions for temperature analysis

Section 3 - Thermal actions for temperature .

This section contains equations for thermal actions on structural elements exposed to fire.

Equation Modules

Equation 3.1 - Net Heat Flux

Equation 3.1 - Net heat flux per unit area of the surface.

ofire.eurocode_1_1_2.section_3.equation_3_1.net_heat_flux_surface(h_net_c, h_net_r)

Net heat flux per unit area of the surface.

This equation determines the total net heat flux to a surface by combining convective and radiative components.

\[\dot{h}_{net} = \dot{h}_{net,c} + \dot{h}_{net,r}\]

where:

  • \(\dot{h}_{net}\) is the net heat flux per unit area (W/m²)

  • \(\dot{h}_{net,c}\) is the net convective heat flux per unit area (W/m²)

  • \(\dot{h}_{net,r}\) is the net radiative heat flux per unit area (W/m²)

Parameters:
  • h_net_c (float) – Net convective heat flux per unit area (W/m²)

  • h_net_r (float) – Net radiative heat flux per unit area (W/m²)

Returns:

Net heat flux per unit area (W/m²)

Return type:

float

Assumptions:

To be completed

Limitations:

To be completed

Example

>>> import ofire
>>> result = ofire.eurocode_1_1_2.section_3.equation_3_1.net_heat_flux_surface(15000.0, 25000.0)

Equation 3.2 - Net convective heat flux

Equation 3.2 - Net convective heat flux per unit area of the surface.

ofire.eurocode_1_1_2.section_3.equation_3_2.net_convective_heat_flux_surface(alpha_c, theta_g, theta_m)

Net convective heat flux per unit area of the surface.

This equation calculates the net convective heat flux to a surface based on the heat transfer coefficient and temperature difference.

\[\dot{h}_{net,c} = \alpha_c (\theta_g - \theta_m)\]

where:

  • \(\dot{h}_{net,c}\) is the net convective heat flux per unit area (W/m²)

  • \(\alpha_c\) is the coefficient of heat transfer by convection (W/m²K)

  • \(\theta_g\) is the gas temperature in the vicinity of the fire exposed surface (°C)

  • \(\theta_m\) is the surface temperature of the member (°C)

Parameters:
  • alpha_c (float) – Heat transfer coefficient (W/m²K)

  • theta_g (float) – Gas temperature in the vicinity of the exposed member (°C)

  • theta_m (float) – Member surface temperature (°C)

Returns:

Net convective heat flux per unit area (W/m²)

Return type:

float

Assumptions:

None stated in the document

Limitations:

None stated in the document

Example

>>> import ofire
>>> result = ofire.eurocode_1_1_2.section_3.equation_3_2.net_convective_heat_flux_surface(50.0, 650.0, 150.0)

Equation 3.3 - Net radiative heat flux

Equation 3.3 - Net radiative heat flux per unit area of the surface.

ofire.eurocode_1_1_2.section_3.equation_3_3.net_radiative_heat_flux_surface(phi, epsilon_m, epsilon_f, sigma, theta_r, theta_m)

Net radiative heat flux per unit area of the surface.

This equation calculates the net radiative heat flux to a surface considering configuration factor, material properties, and temperature difference.

\[\dot{h}_{net,r} = \Phi \cdot \varepsilon_m \cdot \varepsilon_f \cdot \sigma \cdot \left[ (\theta_r + 273)^4 - (\theta_m + 273)^4 \right]\]

where:

  • \(\dot{h}_{net,r}\) is the net radiative heat flux per unit area (W/m²)

  • \(\Phi\) is the configuration factor (dimensionless)

  • \(\varepsilon_m\) is the surface emissivity of the member (dimensionless)

  • \(\varepsilon_f\) is the emissivity of the fire (dimensionless)

  • \(\sigma\) is the Stefan-Boltzmann constant (W/m²K⁴)

  • \(\theta_r\) is the effective radiation temperature of the fire environment (°C)

  • \(\theta_m\) is the surface temperature of the member (°C)

Parameters:
  • phi (float) – Configuration factor (dimensionless)

  • epsilon_m (float) – Surface emissivity of the member (dimensionless)

  • epsilon_f (float) – Emissivity of the fire (dimensionless)

  • sigma (float) – Stefan-Boltzmann constant (W/m²K⁴)

  • theta_r (float) – Effective radiation temperature of the fire environment (°C)

  • theta_m (float) – Surface temperature of the member (°C)

Returns:

Net radiative heat flux per unit area (W/m²)

Return type:

float

Assumptions:

None stated in the document

Limitations:

None stated in the document

Example

>>> import ofire
>>> result = ofire.eurocode_1_1_2.section_3.equation_3_3.net_radiative_heat_flux_surface(0.8, 0.8, 0.9, 5.67e-8, 650.0, 150.0)

Equation 3.4 - Standard temperature-time curve

Equation 3.4 - Standard temperature-time curve calculation.

ofire.eurocode_1_1_2.section_3.equation_3_4.standard_temp_time_curve(t)

Standard temperature-time curve calculation.

\[\theta_g = 20 + 345 \cdot \log_{10}(8 \cdot t + 1)\]

where:

  • \(\theta_g\) is the gas temperature (°C)

  • \(t\) is the time (minutes)

Parameters:

t (float) – Time (minutes)

Returns:

Temperature (°C)

Return type:

float

Assumptions:

None stated in the document

Limitations:

None stated in the document

Example

>>> import ofire
>>> result = ofire.eurocode_1_1_2.section_3.equation_3_4.standard_temp_time_curve(10.0)

Equation 3.5 - External fire curve

Equation 3.5 - External temperature-time curve calculation.

ofire.eurocode_1_1_2.section_3.equation_3_5.external_temp_time_curve(t)

External temperature-time curve calculation.

\[\theta_g = 660 \cdot \left( 1 - 0.687 \cdot e^{-0.32t} - 0.313 \cdot e^{-3.8t} \right) + 20\]

where:

  • \(\theta_g\) is the gas temperature (°C)

  • \(t\) is the time (minutes)

Parameters:

t (float) – Time (minutes)

Returns:

Temperature (°C)

Return type:

float

Assumptions:

None stated in the document

Limitations:

None stated in the document

Example

>>> import ofire
>>> result = ofire.eurocode_1_1_2.section_3.equation_3_5.external_temp_time_curve(10.0)

Equation 3.6 - Hydrocarbon temperature-time curve

Equation 3.6 - Hydrocarbon temperature-time curve calculation.

ofire.eurocode_1_1_2.section_3.equation_3_6.hydrocarbon_temp_time_curve(t)

Hydrocarbon temperature-time curve calculation.

\[\theta_g = 1080 \cdot \left( 1 - 0.325 \cdot e^{-0.167t} - 0.675 \cdot e^{-2.5t} \right) + 20\]

where:

  • \(\theta_g\) is the gas temperature (°C)

  • \(t\) is the time (minutes)

Parameters:

t (float) – Time (minutes)

Returns:

Temperature (°C)

Return type:

float

Assumptions:

None stated in the document

Limitations:

None stated in the document

Example

>>> import ofire
>>> result = ofire.eurocode_1_1_2.section_3.equation_3_6.hydrocarbon_temp_time_curve(10.0)