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 Window 1.1 General Data.

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. Table 3.3 provides an overview of the relevant clauses in the standard.

Table 3.3 Stress designs and crack width analyses

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

EN 1992-1-1, 7.2 (1) requires the Limitation of concrete compressive stress σ_c 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.

The Limit value for allowable crack width w_k,max can be specified 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.

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

For the limitation of crack widths, three different criteria are available according to which the reinforcement is designed:

Table 3.4 Crack width designs

Design	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 d_s, limit s_l, or w_k criteria must be fulfilled for the crack width design!

With the Find the most economical reinforcement for crack width design option in the Determination of Longitudinal Reinforcement section (see below), you can check, which 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 w_k, you can define an upper limit for the maximum crack spacing s_r,max according to EN 1992-1-1, Eq. (7.14) (see Chapter 2.2.4).

The effective concrete tensile strength f_ct,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 f_ctm. The effective concrete tensile strength f_ct,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 f_ct,eff,wk is not reached (see Figure 4.2).

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).

EN 1992-1-1, 7.2 (4) requires a Limitation of steel stress σ_s 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.

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 A_s,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 A_s,min to always be fulfilled.

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

The A_s,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 f_ct,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 f_ct,eff = 0.50 ⋅ f_ctm (28d). If you cannot determine a definite point of time for crack formation within the first 28 days, a tensile strength of at least 3 N/mm² for normal concrete should be assumed in accordance with the German National Annex.

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

• restraint caused in the structural component itself (e.g. from drain of hydration heat) 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 0.85 A_s,min for slowly hardening concrete check box 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-US/support-and-learning/support/knowledge-base/000889

The Increase the required longitudinal reinforcement automatically for serviceability limit state design check box 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 for the SLS design that results from the ultimate limit state design or from manually defined specifications.

The reinforcement's dimensioning for the SLS design is determined by increasing the reinforcement iteratively. The required ULS reinforcement serves as the 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 s_l of the reinforcement is as large as the rebar diameter d_sl. The result 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 when the check of crack width can be considered as being fulfilled.

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-US/support-and-learning/support/knowledge-base/000506

If the check box to Consider A_s,min acc. to 7.3.2 also for the direct calculation of crack width acc. to 7.3.4 is selected, A_s,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.

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

This dialog tab is described in Chapter 4.1.2.