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:
- Returns:
Net heat flux per unit area (W/m²)
- Return type:
- 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:
- Returns:
Net convective heat flux per unit area (W/m²)
- Return type:
- 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:
- 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)
- 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)
- 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)
- 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)