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188.8.131.52 Limitation of concrete compressive stress
Limitation of concrete compressive stress
In window 1.3 Surfaces, the concrete compressive stress is limited to σc,max = 0.45 ⋅ fck and the steel stress to σs,max = 0.80 ⋅ fyk.
For concrete C30/37, the maximum (negative) concrete stress σc,max is thus determined:
- σc,max = 0.45 ∙ fck = 0.45 ∙ (-30.0) = -13.5 N/mm2
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 σc,max is to be compared with the provided stress of the concrete compression zone for both reinforcement directions.
The provided concrete compressive stress σc is determined as follows:
ideal moment of inertia in state II
width of element (always 1 m for plates)
ratio of elastic moduli
provided tension reinforcement
depth of concrete neutral axis
For the reinforcement direction φ1, the following neutral axis depth x-z,φ1 is thus obtained:
The same value and the related intermediate values can also be found in the details table.
For the reinforcement direction φ2, the neutral axis depth x-z,φ2 is obtained:
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 Ii,II in state II (cracked section) are determined as follows:
Thus, according to Equation 2.69, the following concrete compressive stresses σc are obtained in the concrete compression zone (i.e. at the top side of the surface) for the two reinforcement directions φ1 and φ2:
These values are also shown in Figure 2.92 (the program takes more decimal places into account).
The existing compressive stresses σc,+z,φ1 and σc,+z,φ2 are therefore smaller than the maximum concrete stress σc,max (see Figure 2.90). The governing quotient of existing and allowable concrete compressive stress is available in the reinforcement direction φ1. The design is fulfilled.