004573

0001-01-01

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Overview

1 Introduction

2 Theoretical Background

2.3.2 Reduction of Cross-Section

Reduction of Cross-Section

Determination of temperature θ_i in center of zone

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.

Determination of reduction factor k_c (θ_i)

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.

Figure 2.9 Factor k_c (θ_i) for considering decrease of concrete compressive strength according to [2] Figure 4.1

Determination of damaged zone with thickness a_z

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.

Figure 2.10 Reduction of strength and cross-section in case of fire exposure according to [2] Figure B.3

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

Beams, plates

$a_{z} = w \cdot [1 - \frac{k_{c, m}}{k_{c} (θ_{M})}]$

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

$a_{z} = w \cdot [1 - {(\frac{k_{c, m}}{k_{c} (θ_{M})})}^{1.3}]$

where

Table 2.4
w	half the width of the equivalent wall
k_c,m	mean reduction coefficient for a specific cross-section
	$k_{c, m} = \frac{1 - \frac{0.2}{n}}{n} \sum_{i = 1}^{n} k_{c} (θ_{i})$
	n : number of parallel zones in w
	The temperature change in each zone is taken into account with the factor (1 - 0.2/n).
k_c(θ_M)	reduction coefficient for concrete at point M (see Figure 2.9)

Literature

[2]	Eurocode 2: Design of concrete structures - Part 1-2: Structural fire design; EN 1992-1-2:2010-12

Parent section

2.3 Fire Resistance Design