2.3.4 Stress-Strain Curve of Reinforcing Steel

Stress-Strain Curve of Reinforcing Steel

To determine the reduction factor k_s (θ), the temperature in the center of the most unfavorable reinforcing member must be determined first. Depending on how the reinforcing steel is produced and classified (class N or class X), and how much it is strained, the reduction factor k_s (θ) is determined.

The stress-strain relation of reinforcing steel is defined by the following parameters:

• slope in linear-elastic range E_s,θ
• proportionality limit f_sp,θ
• maximum stress level f_sy,θ

The maximum reinforcing steel strength to be applied in the fire design is determined as follows:

$f_{sy,\theta } = k_s\left(\theta \right) · f_{yk }$

where

• k_s (θ) : reduction coefficient for reinforcing steel (see Figure 2.14 or Figure 2.15)
• f_yk : characteristic strength of reinforcing steel at normal temperature

If the reinforcing steel can be assigned to graph 1 or graph 2 of Figures 4.2a or 4.2b in EN 1992-1-2 (cf. Figure 2.14 and Figure 2.15), it is possible to take the reduced modulus of elasticity of the reinforcing steel depending on the reinforcing steel temperature and the steel's type of production from EN 1992-1-2, Table 3.2a or 3.2b. They are displayed in the following figures.

For reinforcing steels assigned to graph 3 according to EN 1992-1-2, Figure 4.2a, the reduced modulus of elasticity is calculated as follows:

$E_{sy,\theta } = k_s\left(\theta \right) · E_{s }$

where

• k_s (θ) : reduction coefficient for reinforcing steel (see Figure 2.14 or Figure 2.15)
• E_s : modulus of elasticity of reinforcing steel at normal temperature (20 °C)