# Temperature distribution

The temperature distribution is a Nationally Determined Parameter (NDP) according to EN 1992-1-2 4.1(1)P.

The table below has been compiled with how the distribution can be chosen in PRE-Stress.

Advanced calculation method (Finite element method) | Danish Standard DS/EN 1992-1-2, Annex A | Note | |

Eurocode | ✔ | ✔ | |

British annex | ✔ | ✔ | |

Cypriotic annex | ✔ | ✔ | Annex not available in PRE-Stress |

Danish annex | - | ✔ | Advanced method (FEM) will not be available due to national annex |

Finnish annex | ✔ | ✔ | |

Luxembourg annex | ✔ | ✔ | Annex not available in PRE-Stress |

Norwegian annex | ✔ | ✔ | |

Swedish annex | ✔ | ✔ |

Currently only the method given in Danish Standard DS/EN 1992-1-2, Annex A is available in PRE-Stress

# Temperature distribution according to Danish Standard DS/EN 1992-1-2, Annex A

## Rectangular cross-section

Ordering of sides:

• T: Top

• B: Bottom

• L: Left

• R: Right

Definition of exposure to fire:

As for the definition of, origo (0,0) is located at the center of the cross-section, with the x-axis positive to the right side and the y-axis positive towards the bottom).

The temperature at the point (x, y) of a rectangular cross-section (for t minutes' worth of exposure) considering the custom sides is calculated by

where

.

where

θ_{1} is the temperature of an exposed one-sided cross-section

θ_{2} the temperature of an exposed two-sided cross-section

x, y is the distance from the center of the cross-section to the current point of calculation

t is time in minutes

ρ is the density in kg/m^{3}

c_{p} is the specific heat capacity

λ is the thermal conductivity

θ=500°C is used as an approximation.

For concrete according to DS2426

## Variable rectangular cross-section

We use the same calculation method as for the rectangular cross-section. However, the width **b** now depends on y-coordinate.

## Cross-section with flange(s)

We use the same calculation method as for rectangular cross-sections, with the following approximation:

During the calculation, the cross-section is divided according Control theory > Section properties, into a body of width **b** (body width) and height **h** (original cross-section height) and a flange with width **b _{f}** and height

**h**.

_{f}In the common area between the body and flanges, the temperatures are defined as the minimum value of the values of the body and the flange.

## Cross-sections with flange(s) and variable height of flange

Uses the same calculation method as Cross-section with flange(s). However, the height of flange **h _{f}** depends on x-coordinate.

## Plates

Uses the same calculation method as for the rectangular cross-section, but with δR = δL = 0. In addition, we use an assumed width **b** of 1000 mm.

## Circular cross-section

In the following, R = D / 2 is the radius of the circular cross-section. When calculating the temperature in a circular cross-section r to the middle of the cross-section set,

δT = δB = δL = δR = 1

b = D

θ_{4,b,h}(r, 0, t) is then calculated as described for a rectangular cross-section.

## Hollowcore cross-section

The same methods are used as for rectangular / plate cross-section. The lower flange (from the bottommost fiber up to the a_{50}-value) is assumed as a rectangular plate. And the temperature is then interpolated to the top of the slab where a temperature of 160°C according to EN 1168 is assumed. There is also another check for If the temperature is higher than 160°C temperature at the top then no further calculation will be performed and the calculation aborted.

# References

EN 1992-1-2:2004/NA:2005 (United Kingdom)

CYS EN 1992-1-2:2004

DS/EN 1992-1-2/NA:2011

SFS-EN 1992-1-2/NA:2007

EN 1992-1-2:2004/AN-LU:2011

NS-EN 1992-1-2:2004/NA:2010

SS-EN 1992-1-2:2004, BFS 2019:1 - EKS 11