Limiting Crack Widths According to DIN EN 1992-1-1 with and Without Direct Calculation in RF-CONCRETE

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Technical Article

Eurocode 2 provides two ways to perform a crack width design. On the one hand, the crack width design according to 7.3.3 can be performed without direct calculation by means of tables for the limitation of the member spacing and diameter. On the other hand, the crack width wk can be determined directly according to 7.3.4 and compared with a limit value.

Theoretical Background

The designs 7.3.4 and 7.3.4 are usually performed for the external load. Both designs are based on the formulas (7.9) and (7.11).

The crack width design is performed in the modules if the existing concrete stress is σc > fct,eff,wk and the concrete is cracked. You can adjust the value fct,eff,wk in the modules.

Figure 01 - Effective Concrete Tensile Strength at Time of Cracking in RF-CONCRETE Surfaces

The table 7.2DE used for the indirect calculation is based on the limit values of (7.9) and (7.11) and on assumptions for the tensile strength fct,eff and for the modulus of elasticity Es. Based on these assumptions, the maximum allowable diameters depending on the steel stress are shown in Table 7.2.DE and the maximum values of the member spacings in 7.3N. Both tables are set up for an allowable crack width of 0.2 to 0.4 mm. Using a modified limit diameter, the values of the system to be considered are transferred to the values specified in Table 7.2DE.

Figure 02 - DIN EN 1992-1-1 Tab. 7.2DE and 7.3N

For the direct calculation, there are no limits for the allowable crack width because the crack width wk is always calculated directly. This also allows you to apply a limit value of the crack width < 0.2 mm.

Utilizing in RF-CONCRETE

Both methods are available in the RF-CONCRETE Members and RF-CONCRETE Surfaces add-on modules. According to the default setting, both methods are active. Theoretically, it is not necessary to perform both designs. It is sufficient if one of the two designs is fulfilled. Nevertheless, there is a specific reason why both designs are activated by default. In the following, this point, the economic reinforcement for the crack width design, will be described.

Figure 03 - Method of Limiting Crack Width

Find Economical Reinforcement for Crack Width Design

In RF-CONCRETE Members and RF-CONCRETE Surfaces, the option "Find the most economical reinforcement for crack width design" is available. The reason for this option is as follows.

According to DIN EN 1992 7.3.3 (2), exceeding the crack widths is unlikely if the minimum reinforcement according to 7.3.2 is met and at the same time

  • for cracks due to predominant restraint, the member diameter according to Table 7.2N is observed. In this case, you have to use the value immediately after cracking for the steel stress (i.e. use σs in Equation (7.1)).

  • for cracks due to predominantly direct actions, the conditions according to Table 7.2N or Table 7.3N are met. The steel stresses are usually determined on the basis of cracked cross-sections under the governing action combination.

This means that not all parts of the indirect calculation have to be fulfilled if it is ensured at the same time that the minimum reinforcement is met. This may result in the required reinforcement determined in the course of the direct calculation not being the most economical reinforcement. This is also the reason why both designs are active by default.

Figure 04 - RF-CONCRETE Surfaces: Finding Economical Reinforcement for the Crack Width Design

Crack Width Design for Allowable Crack Width < 0.2 mm

Due to the situation of the presetting mentioned above, there may be a problem in the design of an allowable crack width < 0.2 mm. For the range wk < 0.2 mm, the tables on which the indirect calculation is based are not relevant. In this context, the indirect calculation must be deactivated for such a situation and only be verified with the direct calculation.

Figure 05 - Crack Width Less Than 0.2 mm

Calculation Performance

Especially with regard to the situation that both designs are performed according to the default setting, the question of the computing speed sometimes arises. In this regard, the additionally performed design has no major influence on the calculation. The determination of the required reinforcement for the crack width design is performed iteratively. If a design is not fulfilled, an additional rebar is assigned to the required reinforcement and the design is performed again. This is done until either no more members can be inserted into the cross-section or the applied design criteria are fulfilled.

Crack Width Design for Restraint

The RF-CONCRETE add-on modules are designed in such a way that the minimum reinforcement according to 7.3.2 is determined for the imposed stress. Insofar as it is feasible that the loading due to restraint can be displayed on the load side, the crack width design for the restraint can also be performed by means of the crack width calculation.

Author

Dipl.-Ing. (FH) Adrian Langhammer

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

Crack width Restraint Direct crack width calculation Indirect crack width calculation WU guideline FD concrete

Reference

[1]   Eurocode 2: Design of concrete structures - Part 1‑1: General rules and rules for buildings; EN 1992‑1‑1:2004 + AC:2010
[2]   Manual RF-CONCRETE Surfaces. (2017). Tiefenbach: Dlubal Software.

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  • Updated 11/10/2020

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