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1 Introduction
2 Theoretical Background
3 Input Data
4 Calculation
5 Results
6 Result Evaluation
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8 General Functions
9 Examples
10 Literature

2.4.8 Serviceability Limit State

Serviceability Limit State

With EN 1992-1-1, more detailed designs for the serviceability limit state have found their way into engineering offices.

The serviceability limit state is divided into three groups:

  • Limitation of stresses (EN 1992-1-1, clause 7.2)
  • Limitation of crack widths (EN 1992-1-1, clause 7.3)
  • Limitation of deformations (EN 1992-1-1, clause 7.4)

Hereafter, only the limitation of deformations is described, also taking the influence of creep and shrinkage into account.

The reason for the more detailed analysis of deformations can be found again in the nonlinear behavior of reinforced concrete as a composite material. As a result of crack formation, the stiffness is reduced significantly in particular areas compared to the pure state I (uncracked sections). If the cracking is not taken into account, occurring deformations will be underestimated. By considering creep and shrinkage, the deformation may be three to eight times larger, depending on the stress state and boundary conditions.

The governing curvatures are determined as basis for deformations. It is important not to forget the concrete's effectiveness for tension between the cracks, otherwise unrealistic results are to be expected.

A correct interpretation of results from nonlinear calculations requires knowledge of the most important factors. Therefore, we compare the most important parameters that affect the stiffnesses in uncracked sections (state I) and cracked sections (state II) in the table below:

Table 2.5 Influence values and their impact in uncracked and cracked state
Influencing value State I (uncracked) State II (cracked)

Creep
(here as reduction of elastic modulus for concrete)

The stiffness is mainly controlled by concrete.
Thus, a reduced modulus of elasticity leads to a considerable reduction of stiffness.

Minor influence

Reinforcement ratio

Minor influence
(see Creep for reasons)

The stiffness in state II is mainly controlled by the reinforcement.
The influence is therefore enormous.

Axial force

Influence hardly given
(In case of simplified linear-elastic analyses, there is no influence at all.)

A tensile force reduces the stiffness significantly.
This must be considered when modeling the shrinkage, as it leads to tension stresses in the concrete.

Material properties

Generally, the mean material properties are used to calculate the deformation. The effectiveness of concrete on tension between cracks (Tension Stiffening) must also be taken into account by appropriate approaches (see Chapter 2.4.3) because otherwise no realistic deformation analysis is possible.

The mean material properties according to DIN 1045-1 and EN 1992-1-1 for determining the deformations do not differ from each other (or only marginally).

Calculational mean values of material strengths

-- Stress-strain curve for steel according to EN 1992-1-1, Figure NA.3.8.1

  • fy = fyk
  • ft = fyk for serviceability considerations
  • Esm = 200 000 N/mm2 mean modulus of elasticity for steel

-- Stress-strain curve for concrete according to EN 1992-1-1, 3.1.5 and 5.7

  • fcm mean concrete compressive strength
  • Ecm mean modulus of elasticity for concrete (secant)
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