2.3.2 Reduction of Cross-Section

Reduction of Cross-Section

After the cross-section's subdivision into zones, the temperature θ_i 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 k_c (θ_i) is determined for the temperature found in the i zone's center in order to take the decrease of the characteristic concrete compressive strength f_ck into account. This reduction factor k_c (θ_i) 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 a_z on the sides exposed to fire is not taken into account for the ultimate limit state design.

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

• Beams, plates

$a_z = w · \left[1 - \frac{k_{c,m}}{k_c\left({\theta }_M\right)}\right]$

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

$a_z = w · \left[1 - {\left(\frac{k_{c,m}}{k_c\left({\theta }_M\right)}\right)}^{1.3}\right]$

where