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Overview

1 Introduction

2 Theoretical Background

2.6.4.8 Limitation of reinforcing steel stress

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:

$σ_{s, max} = 0.8 \cdot f_{y k} = 0.8 \cdot 500 = 400 {N/mm}^{2}$

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:

$σ_{s} = \frac{α_{E} \cdot m_{E d} \cdot (d - x)}{I_{i, I I}}$

where

Table 2.2
α_E		relation of elastic moduli (E_s / E_cm)
m_Ed		applied moment
d		effective depth
$x = \frac{α_{E} \cdot a_{s}}{b} \cdot (- 1.0 + \sqrt{1.0 + \frac{2.0 \cdot b \cdot d}{α_{E} \cdot α_{s}}})$		depth of concrete neutral axis
	b	width of element (always 1m for plates)
	a_s	provided tension reinforcement
$I_{i, I I} = \frac{1}{3} \cdot b \cdot x^{3} + α_{e} \cdot α_{s} \cdot {(d - x)}^{2}$		ideal moment of inertia in state II

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:

$σ_{s, u, ϕ_{1}} = \frac{6.061 \cdot 3 674 \cdot (17 - 4.19)}{13 701} = 208.18 {N/mm}^{2}$

$σ_{s, u, ϕ_{2}} = \frac{6.061 \cdot 2 733 \cdot (15.8 - 4.02)}{11 677} = 167.09 {N/mm}^{2}$

Image 2.94 Maximum steel stresses in reinforcement direction 1 and 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.

Image 2.95 Analysis of reinforcing steel stress

Parent section

2.6.4 Serviceability Limit State Designs