RF-CONCRETE Members Version 5

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RF-CONCRETE Members Version 5

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3.6.7 Serviceability Limit State

Serviceability Limit State

This tab is displayed if at least one load case or load combination is selected for the serviceability limit state design in the 1.1 General Data window.

Figure 3.40 Window 1.6 Reinforcement, tab Serviceability

For information on the theoretical background of serviceability limit state designs, see chapter 2.2.

For the serviceability limit state design, you can specify various criteria concerning stress design and crack width analysis. The following table gives an overview of the relevant clauses in the standard.

Table 3.3 Stress designs and crack width analyses
Standard Normative specifications in
EN 1992-1-1

Limitation of concrete stress σc

7.2 (1)

Limitation of steel stress σs

7.2 (4)

Limitation of crack widths wk

7.3.1 (5) and 7.3.4

Limit diameter limit ds

Table 7.2 (see Figure 2.3)

Maximum rebar spacing limit sl

Table 7.3 (see Figure 2.4)

Minimum reinforcement min As

7.3.2 (2)

Not all of these designs have to be fulfilled. The design of concrete and steel stresses, for example, can be dispensed with, if the internal forces are determined according to the elasticity theory, not more than 15 % are redistributed in the ULS design, and the rules according to EN 1992-1-1, clause 9 are followed.

By deactivating individual designs (stress designs, for example), they are not considered for the determination of the longitudinal reinforcement. The available results (concrete and steel stresses under loading in serviceability limit state, for example), however, are still displayed in the results windows 4.1 to 4.4.

Concrete Stress Analysis

EN 1992-1-1, 7.2 (1) requires the Limitation of concrete compressive stress σc in order to avoid function-affecting longitudinal cracks, micro cracks, or strong creep.

The concrete compressive stresses can be reduced according to clause 7.2 (2) and 7.2 (3) with the factors k1 (0.6 recommended) and k2 (0.45 recommended), or a user-defined factor α.

Design of Crack Width Control

The Limit value for allowable crack width wk,max can be defined for the top and bottom side of the member according to EN 1992-1-1, 7.3.1 (5). The [Info] button opens a dialog box with information about the surrounding conditions.

Figure 3.41 Crack widths depending on exposure class according to EN 1992-1-1

It is also possible to specify the crack widths individually for the top and bottom reinforcement.

Three possibilities are available for the limitation of crack widths according to which the reinforcement is designed:

Table 3.4 Crack width designs
Standard Normative specifications in
EN 1992-1-1

Limit diameter limit ds

Table 7.2 (see Figure 2.3)

Maximum rebar spacing limit sl

Table 7.3 (see Figure 2.4)

Direct calculation of crack width wk

7.3.1 (5) and 7.3.4

These design criteria are described in chapter 2.2.4.

Generally, only one of the limit ds, limit sl, or wk criteria must be fulfilled for the crack width design!

With the option Find the most economical reinforcement for crack width design in the Determination of Longitudinal Reinforcement section (see below), you can check which one of the three criteria can be covered by the least necessary reinforcement area. The program will add individual rebars to the provided reinforcement until the design is successfully fulfilled.

For the direct crack width calculation of wk, you can define an upper limit for the maximum crack spacing sr,max according to EN 1992-1-1, Eq. (7.14) (see chapter 2.2.4).

The effective concrete tensile strength fct,eff,wk at the moment of cracking used for the crack width analysis can be influenced by a factor for the mean concrete tensile strength fctm. The effective concrete tensile strength fct,eff,wk is also used in the analytical serviceability limit state design to analyze whether the cross-section is cracked or uncracked. The general settings in the Serviceability tab of the Details dialog box also allow you to analyze the crack width on the uncracked cross-section, meaning fct,eff,wk is not reached (see Figure 4.2).

Deflection Analysis

If the check box is selected, the additional module window 1.7 Deflection Data is available for entering the member parameters (see chapter 3.7).

Steel Stress Analysis

EN 1992-1-1, 7.2 (4) requires a Limitation of steel stress σs in order to avoid non-elastic strains, unallowable crack formations, and deformations.

The steel stresses can be reduced according to clause 7.2 (5) by the factors k3 (0.8 recommended) and k4 (1.0 recommended), or by a user-defined factor α.

Minimum Reinforcement for Effects Due to Restraint
Figure 3.42 Window section Minimum Reinforcement for Effects Due to Restraint (for NA DIN and ÖNORM)

When designing the limitation of crack widths, you have to distinguish between load actions and effects due to restraint. An effect due to restraint is considerably reduced by crack formation in the structural component. A sufficiently dimensioned minimum reinforcement As,min provides for an allocation of the entire component reduction to several cracks with accordingly small crack widths. The crack widths due to load actions, however, depend on the available steel stress and the reinforcement layout.

For effects due to restraint, it is necessary for the criterion of the minimum reinforcement As,min to always be fulfilled.

The Stress distribution within the section prior to cracking affects the factor kc according to EN 1992-1-1, Eq. (7.1). Several options are available in the list. kc = 1.0 is applied to centric restraint with pure tension load. In the case of bending restraint with pure bending load, σc is equal to zero in the component axis, and thus kc = 0.4 according to Eq. (7.2). Alternatively, it is possible to determine kc according to Eq. (7.2) or (7.3) dependent on the loading, whereas the mean concrete stress σc is determined from the loads. In addition to the stress distribution, the factor kc approximatively considers the increase of the inner lever arm for crack formation.

The As,min layout list defines the reinforcement layer the minimum reinforcement is assigned to.

If you expect a Crack formation in the first 28 days, you should reduce the effective concrete tensile strength fct,eff according to EN 1992-1-1, 7.3.2 (2). You can enter the appropriate reduction factor into the input field. The German National Annex recommends to use fct,eff = 0.50 ⋅ fctm (28d). If you cannot determine a definite point of time for crack formation within the first 28 days, in accordance with the National Annex for Germany, a tensile strength of 3 N/mm2 for normal concrete should be assumed.

The National Annex for Germany for EN 1992-1-1, clause 7.3.2 (2) distinguishes for the factor k used to consider nonlinearly distributed self-equilibrating stresses between the types of effect due to restraint. You have to specify whether tensile stresses are caused due to

  • restraint caused in the structural component itself (from drain of hydration heat, for example) or
  • restraint caused outside of the structural component (e.g. column settlement).

  

In RF-CONCRETE Members, the crack width is calculated directly for the respective load action according to EN 1992-1-1, 7.3.4. For effects due to restraint, the program designs the minimum reinforcement for limiting the specified crack width according to EN 1992-1-1, clause 7.3.2.

The check box 0.85 As,min for slowly hardening concrete allows you to reduce the minimum reinforcements for concretes with r ≤ 0.3 according to the National Annex for Germany or Austria. You can find further information about this in the following article:
https://www.dlubal.com/en/support-and-learning/support/knowledge-base/000889

Determination of Longitudinal Reinforcement
Figure 3.43 Window section Determination of Longitudinal Reinforcement

The check box Increase the required longitudinal reinforcement automatically for serviceability limit state design allows you to design the longitudinal reinforcement so that the design for serviceability is fulfilled. If this option is deactivated, the program uses the provided reinforcement resulting from the ultimate limit state design or from manually defined specifications for the SLS design.

The reinforcement's dimensioning for the SLS design is determined by increasing the reinforcement iteratively. The required ULS reinforcement serves as initial value for iterations. The program analyzes whether it is sufficient to resist the characteristic load. If not, it is increased gradually. The dimensioning process ends without results if the rebar spacing sl of the reinforcement is as large as the rebar diameter dsl. The results windows will indicate that the respective point cannot be designed.

For the design according to EN 1992-1-1, it is possible to Find the most economical reinforcement for crack width design. Click the [Info] button to display information about this procedure. The Information dialog box describes in which case a crack width check can be considered as fulfilled.

Figure 3.44 Information dialog box for determining most economical reinforcement

Clause 7.2 of EN 1992-1-1 describes under which conditions the stresses shall be limited. This means that not all design ratios shown in window 4.1 have to be less than 1 in order to fulfill the serviceability limit state design!

The following article on our website describes how the program determines the most economic reinforcement for the crack width analysis:
https://www.dlubal.com/en/support-and-learning/support/knowledge-base/000506

If the check box to Consider As,min acc. to 7.3.2 also for the direct calculation of crack width acc. to 7.3.4 is selected, As,min is also considered if the crack width design is performed in the most economical way by using direct calculation according to 7.3.4. Hence, if the check box is clear, the reinforcement will only be considered if the crack width design is carried out without direct calculation.

Details

The [Details] button opens the Details dialog box. In the Serviceability tab, you can specify additional settings for the SLS designs.

Figure 3.45 Details dialog box, Serviceability tab

This dialog tab is described in chapter 4.1.2.