# RF-CONCRETE Surfaces – Online Manual Version 5

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## RF-CONCRETE Surfaces – Online Manual Version 5

# 2.6.4.7 Limitation of concrete compressive stress

#### Limitation of concrete compressive stress

In window 1.3 *Surfaces*, the concrete compressive stress is limited to σ_{c,max} = 0.45 ⋅ f_{ck} and the steel stress to σ_{s,max} = 0.80 ⋅ f_{yk}.

For concrete C30/37, the maximum (negative) concrete stress σ_{c,max} is thus determined:

- σ
_{c,max}= 0.45 ∙ f_{ck}= 0.45 ∙ (-30.0) = -13.5 N/mm^{2}

The provided concrete compressive stress is determined under the assumption of a linear stress distribution because the multitude of iterations for determining the suitable direction of the concrete compression strut would be too time-consuming. A linear distribution is sufficiently accurate because in the serviceability state, there are normally concrete compressive strains of at most 0.3 to 0.5 ‰.

The maximum stress σ_{c,max} is to be compared with the provided stress of the concrete compression zone for both reinforcement directions.

The provided concrete compressive stress σ_{c} is determined as follows:

${\sigma}_{c}=\frac{{m}_{Ed}}{{I}_{i,II}}\xb7x$

where

m |
| applied moment |

| ideal moment of inertia in state II | |

| b | width of element (always 1 m for plates) |

| α | ratio of elastic moduli |

| a | provided tension reinforcement |

| d | effective depth |

| depth of concrete neutral axis |

For the reinforcement direction φ_{1}, the following neutral axis depth x_{-z,φ1} is thus obtained:

${x}_{-z,{\varphi}_{1}}=\frac{6.061\xb711.31}{100}\xb7\left(-1.0+\sqrt{1.0+\frac{2.0\xb7100\xb717}{6.061\xb711.31}}\right)=4.19\text{cm}$

The same value and the related intermediate values can also be found in the details table.

For the reinforcement direction φ_{2}, the neutral axis depth x_{-z,φ2} is obtained:

${x}_{-z,{\varphi}_{2}}=\frac{6.061\xb711.31}{100}\xb7\left(-1.0+\sqrt{1.0+\frac{2.0\xb7100\xb715.8}{6.061\xb711.31}}\right)=4.02\text{cm}$

This value and the related intermediate values can also be found in the details.

For the two directions of reinforcement, the ideal moments of inertia I_{i,II} in state II (cracked section) are determined as follows:

${I}_{i,II,-z,{\varphi}_{1}}=\frac{1}{3}\xb7100.0\xb74.{19}^{3}+6.061\xb711.31\xb7{\left(17-4.19\right)}^{2}=13701{\text{cm}}^{4}$

${I}_{i,II,-z,{\varphi}_{2}}=\frac{1}{3}\xb7100.0\xb74.{02}^{3}+6.061\xb711.31\xb7{\left(15.8-4.02\right)}^{2}=11678{\text{cm}}^{4}$

Thus, according to Equation 2.69, the following concrete compressive stresses σ_{c} are obtained in the concrete compression zone (i.e. at the top side of the surface) for the two reinforcement directions φ_{1} and φ_{2}:

${\sigma}_{c,o,{\varphi}_{1}}=\frac{3676\xb74.19}{13701}=-11.24{\text{N/mm}}^{2}$

${\sigma}_{c,o,{\varphi}_{2}}=\frac{2773\xb74,02}{11678}=-9.41{\text{N/mm}}^{2}$

These values are also shown in Figure 2.92 (the program takes more decimal places into account).

The existing compressive stresses σ_{c,+z,φ1} and σ_{c,+z,φ2} are therefore smaller than the maximum concrete stress σ_{c,max} (see Figure 2.90).
The governing quotient of existing and allowable concrete compressive stress is available in the reinforcement direction φ_{1}.
The design is fulfilled.