Assumptions for the Effective Tensile Strength Connected with Determining the Minimum Reinforcement According to DIN EN 1992-1-1 7.3.2
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 article gives an overview about determining the effective tensile strength fct,eff and the input options in RF-CONCRETE.
Depending on the Type of Effects Due to Restraint
To determine the effective tensile strength fct,eff, it is necessary to define if restraints should be considered sooner or later.
Early restraint is caused, for example, by the flow of hydration heat.
Late 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 structural components h ≤ 0.30 m)
fct,eff ≈ 0.65 fctm - After 5 days (simplified for medium structural 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 concrete with medium strength development (N).
Mean Tensile Strength in Relation to 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 Diagram 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.
Entering in the Program
In RF-CONCRETE, you can factorize the effective tensile strength when entering it in the program:
Figure 03 - Entering Factor to Reduce fct,eff,As,min
For slowly hardening concrete, the tensile strength or the minimum reinforcement As,min can be reduced via a check box during the input to 0.85 As,min.
Figure 04 - Checkbox for Slowly Hardening Concrete
Please Note
Determining the effective tensile strength has a significant influence on the result of the minimum reinforcement, because it directly reduces it. It is therefore worth considering if you consider only early restraint. The Eurocode gives no simplified assumption that the effective tensile strength can be reduced to 50% as it is stated in DIN 1045-1.
Author
Dipl.-Ing. (FH) Adrian Langhammer
Product Engineering & Customer Support
Mr. Langhammer is responsible for the development of the add-on modules for reinforced cocrete, and provides technical support for our customers.
Keywords
Tensile strength First cracking Effects due to restraint Restraint forces
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Structural engineering software for finite element analysis (FEA) of planar and spatial structural systems consisting of plates, walls, shells, members (beams), solids and contact elements
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