Assumptions for the effective tensile strength in connection with the determination of the minimum reinforcement according to DIN EN 1992-1-1 7.3.2
Figure 01 - Strength Development fct, eff - Factor βcc
Figure 02 - Logarithmic representation of factor βcc
Figure 03 - Input of factor for reduction fct, eff, As, min
Figure 04 - Check box for slow-curing concrete
Technical Article
When determining the minimum reinforcement for the serviceability limit state according to 7.3.2, the applied effective tensile strength fct, eff has a significant influence on the determined amount of reinforcement. The following section provides an overview for determining the effective tensile strength fct, eff and the input options in RF-CONCRETE.
Dependency on type of imposed load
To determine the effective tensile strength fct, eff, it is necessary to define whether restraint should be considered only earlier or later.
Former restraint is caused, for example, by the flow of hydration heat.
Subsequent restraint is caused, for example, by temperature stress. It is a late restraint when the concrete has reached the strength required by the standard.
If only the early restraint is taken into account and there are no other specifications regarding the tensile strength, the effective early tensile strength can be assumed according to [1] as follows:
- After 3 days (simplified for thin components h ≤ 0.30 m)
fct, eff ≈ 0.65 fctm - After 5 days (simplified for medium-thick components)
fct, eff ≈ 0.75 fctm - After 7 days (simplified for thick structural components h> 0.80 m)
fct, eff ≈ 0.85 fctm
The specifications apply to common concretes with medium strength development (N).
Mean tensile strength as a function of time
With the formula EN 1992-1-1 3.1.2 (5) (3.4), it is possible to assume the tensile strength depending on the concrete age. Using the formula, you can set up the following functions for strength development:
Figure 01 - Strength Development fct, eff - Factor βcc
Figure 02 - Logarithmic representation of factor βcc
Slow and fast setting concrete
For concretes hardening slowly (L) or rapidly (R), the value of the tensile strength must be reduced or increased by 0.15 fctm .
Input in the program
In RF-CONCRETE, you can factorize the effective tensile strength in the input:
Figure 03 - Input of factor for reduction fct, eff, As, min
For slow-curing concrete, the tensile strength can or the minimum reinforcement As,s, min be reducedmin via a check box in the input A to 0.85.
Figure 04 - Check box for slow-curing concrete
Note
The determination of the effective tensile strength has a considerable influence on the result of the minimum reinforcement because it directly reduces it. It is therefore worth considering whether early restraint alone is taken into account. A simplified assumption as in DIN 1045-1 that the effective tensile strength can be reduced to 50% is not found in the Eurocode.
Keywords
Tensile strength Initial cracking Effects due to Restraint Restraint forces
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