# 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

θ1 is the temperature of an exposed one-sided cross-section

θ2 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/m3

cp is the specific heat capacity

λ is the thermal conductivity θ=500°C is used as an approximation.

### Danish Annex

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 bf and height hf.

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 hf 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 θ4,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. However, areas where the holes occupy more than 50% of the width of the cross-section have a temperature lower than 160°C according to EN 1168. If the temperature is higher than 160°C temperature, no further calculation will be performed.

# 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 2015:6 - EKS 10

EN 1168:2005+A3

Created by Fredrik Lagerström on 2020/06/11 10:39