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2.3.4 Stress-Strain Curve of Reinforcing Steel

Stress-Strain Curve of Reinforcing Steel

Reduction factor ks (θ) for tensile strength of steel

To determine the reduction factor ks (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 X), and how much it is strained, the reduction factor ks (θ) is determined.

Figure 2.14 Class N -- reduction factor ks (θ) according to [5], Figure 4.2a
Figure 2.15 Class X -- reduction factor ks (θ) according to [5], Figure 4.2b
Reduction of reinforcing steel strength fsy,θ

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

  • slope in linear-elastic range Es,θ
  • proportionality limit fsp,θ
  • maximum stress level fsy,θ

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

fsy,θ = ksθ · fyk 

where

    • ks (θ) : reduction coefficient for reinforcing steel (see Figure 2.14 or Figure 2.15)
    • fyk : characteristic strength of reinforcing steel at normal temperature
Determination of reduced modulus of elasticity Es,θ of reinforcing steel

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. Sie sind in den folgenden Bildern dargestellt.

Figure 2.16 Class N -- parameters of stress-strain relation of steel according to , Table 3.2a
Figure 2.17 Class X -- parameters of stress-strain relation of steel according to , Table 3.2b

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:

Esy,θ = ksθ · Es 

where

    • ks (θ) : reduction coefficient for reinforcing steel (see Figure 2.14 or Figure 2.15)
    • Es : modulus of elasticity of reinforcing steel at normal temperature (20 °C)
Literatur
[5] Quast, Ulrich. Zum nichtlinearen Berechnen im Stahlbeton- und Spannbetonbau. Beton und Stahlbetonbau, Heft 9 und Heft 10, 1994.