Limitation of reinforcing steel stress

In window 1.3 Surfaces, the tension stresses of the reinforcing steel reinforcement are limited to σ_s,max = 0.8 ⋅ f_yk according to EN 1992-1-1, clause 7.2(5) (see Figure 2.90). For BSt 500 S (B), the maximum steel stress σ_s,max is thus determined as:

${\sigma }_{s,\text{max}} = 0.8 · f_{yk} = 0.8 · 500 = 400 {\text{N/mm}}^2$

The maximum stress σ_s,max is to be compared with the provided tension stress for both reinforcement directions.

The provided tension stress σ_s is determined as follows:

${\sigma }_s = \frac{{\alpha }_E · m_{Ed} · \left(d - x\right)}{I_{i,II}}$

avec

With the values calculated in chapter 2.6.4.6, the provided tension stresses σ_s,u,φ1 and σ_s,u,φ2 in the two reinforcement directions φ₁ and φ₂ can be determined as follows:

${\sigma }_{s,u,{\varphi }_1} = \frac{6.061 · 3 674 · \left(17 - 4.19\right)}{13 701} = 208.18 {\text{N/mm}}^2$

${\sigma }_{s,u,{\varphi }_2} = \frac{6.061 · 2 733 · \left(15.8 - 4.02\right)}{11 677} = 167.09 {\text{N/mm}}^2$

The existing tension stresses σ_s,-z,φ1 and σ_s,-z,φ2 are therefore smaller than the maximum steel stress σ_s,max (see Figure 2.90). The governing quotient of existing to allowable steel stress is available in the reinforcement direction φ₁. The design is fulfilled.