2.3.3 Stress-Strain Curve of Concrete

Stress-Strain Curve of Concrete

Point M, a point on the central line of the equivalent wall (cf. Figure 2.8), is governing for the reduction of the concrete's material properties. It is used to determine the reduction factor k_c (θ_M). The concrete's reduced material properties are to be used for the entire reduced cross-section (without damaged zone a_z) for the ultimate limit state design in case of fire.

The stress-strain curve for the concrete's compressive strength is determined depending on the temperature in point M and the type of aggregates. The values of the compressive strain ε_cu1,θ for the compression strength f_c,θ can be found in EN 1992-1-2, Table 3.1.

$f_{c,\theta } = k_c\left({\theta }_M\right) · f_{ck }$

where

• k_c(θ_M) : reduction coefficient for concrete at point M (see Figure 2.9)
• f_ck : characteristic compressive strength of concrete at normal temperature

The diagram (Figure 2.12) shows how the stress-strain relation of normal concrete with aggregates containing limestone changes depending on the temperature. The graph's descending branch is not taken into account for the fire resistance design.

The concrete's reduced modulus of elasticity is determined for the fire protection design according to the following equation:

$E_{cd,\theta } = {\left[k_c\left({\theta }_M\right)\right]}^2 · E_{c }$

where

• k_c(θ_M) : reduction coefficient for concrete at point M (see Figure 2.9)
• E_c : modulus of elasticity of concrete at normal temperature (20 °C)

Being on the safe side, the concrete's tensile strength is not applied for either the cross-section design or the fire protection design. For the sake of completeness, however, the values can be found in the description of the material properties (cf. Chapter 3.2).

According to [2] Figure 3.2, the tensile strength of concrete is generally to be reduced for the fire resistance design:

$f_{ck,t}\left(\theta \right) = k_{c,t}\left({\theta }_M\right) · f_{ck,t }$

where

• k_c,t (θ_M) : reduction coefficient for concrete tensile strength according to Figure 2.13
• f_ck,t : characteristic tensile strength of concrete at normal temperature (20 °C)