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.
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. The lower flange (from the bottommost fiber up to the a50-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