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2.3.2 Reduction of Cross-Section
Reduction of Cross-Section
After the cross-section's subdivision into zones, the temperature θi in the center of each i zone is determined. This occurs based on the temperature courses according to EN 1992-1-2, Annex A, which are based on the following assumptions:
- The specific heat of concrete corresponds to the specifications according to EN 1992-1-2, clause 3.2.2.
- The moisture is 1.5 % (the specified temperatures are on the safe side for moistures > 1.5 %).
- The thermal conductivity of concrete is the lower limit value mentioned in EN 1992-1-2, clause 3.3.3.
- The emission value for the concrete surface is 0.7.
- The convective heat-transmission coefficient is 25 W/m2K.
The reduction factor kc (θi) is determined for the temperature found in the i zone's center in order to take the decrease of the characteristic concrete compressive strength fck into account. This reduction factor kc (θi) depends on the concrete's aggregates:
According to EN 1992-1-2, Figure 4.1, graph 1 is to be used for normal concrete with aggregates containing quartz, and graph 2 for normal concrete with aggregates containing limestone.
The cross-section damaged by fire is represented by a reduced cross-section. Consequently, a damaged zone of thickness az on the sides exposed to fire is not taken into account for the ultimate limit state design.
The calculation of the damaged zone thickness az depends on the structural component type:
- Beams, plates
- Columns, walls, and other structural components for which effects due to the second-order analysis must be taken into account
half the width of the equivalent wall
mean reduction coefficient for a specific cross-section
n : number of parallel zones in w
The temperature change in each zone is taken into account with the factor (1 - 0.2/n).
reduction coefficient for concrete at point M (see Figure 2.9)