RF-CONCRETE Surfaces – Online Manual Version 5

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RF-CONCRETE Surfaces – Online Manual Version 5

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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 σc,max = 0.45 ⋅ fck and the steel stress to σs,max = 0.80 ⋅ fyk.

Figure 2.90 Limiting the concrete compressive and steel stresses in the Stress Check tab of window 1.3 Surfaces

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:

σc = mEdIi,II ·x 

where

Table 2.2

mEd

applied moment

ideal moment of inertia in state II

b

width of element (always 1 m for plates)

αE

ratio of elastic moduli

as

provided tension reinforcement

d

effective depth

depth of concrete neutral axis

For the reinforcement direction φ1, the following neutral axis depth x-z,φ1 is thus obtained:

x-z,ϕ1 = 6.061 · 11.31100 · -1.0 + 1.0 + 2.0 · 100 · 176.061 ·11.31 = 4.19 cm 

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

Figure 2.91 Depth of concrete compression zone for reinforcement direction 1

For the reinforcement direction φ2, the neutral axis depth x-z,φ2 is obtained:

x-z, ϕ2 = 6.061 · 11.31100 · -1.0 + 1.0 + 2.0 · 100 · 15.86.061 · 11.31 = 4.02 cm 

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

Figure 2.92 Depth of concrete compression zone for reinforcement direction 2

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

Ii,II,-z,ϕ1 = 13 · 100.0 · 4.193 + 6.061 · 11.31 · 17 - 4.192 = 13701 cm4 

Ii,II,-z,ϕ2 = 13 · 100.0 · 4.023 + 6.061 · 11.31 · 15.8 - 4.022 = 11 678 cm4 

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:

σc,o,ϕ1 = 3 676 · 4.1913 701 = -11.24 N/mm2

σc,o,ϕ2 = 2 773 · 4,0211 678 = -9.41 N/mm2

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.

Figure 2.93 Analysis of concrete compressive stress