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2.3.2 Reduction of Cross-Section

Reduction of Cross-Section

Determination of temperature θi in center of zone

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 concrete's specific heat 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 concrete's thermal conductivity 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.
Determination of reduction factor kci)

The reduction factor kci) 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. The reduction factor kci) 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.

Figure 2.9 Factor kci) for considering decrease of concrete compressive strength according to , Figure 4.1
Determination of damaged zone with thickness az

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.

Figure 2.10 Reduction of strength and cross-section in case of fire according to , Figure B.3

The calculation of the damaged zone thickness az depends on the structural component type:

  • Beams, plates

az = w · 1 - kc,mkcθM 

  • Columns, walls, and other structural components for which effects due to second-order analysis must be taken into account

az = w · 1 - kc,mkcθM1.3 

where

Table 2.4

w

: half the width of equivalent wall

kc,m

: mean reduction coefficient for a specific cross-section

n : number of parallel zones in w

The change of temperature in each zone is taken into account with the factor (1 - 0.2/n).

kcM)

: reduction coefficient for concrete at point M (see Figure 2.9)