Online manuals, introductory examples, tutorials, and other documentation.
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, 7.2 or DIN 1045-1, 11.1)
- Limitation of crack widths (EN 1992-1-1, 7.3 or DIN 1045-1, 11.2)
- Limitation of deformations (EN 1992-1-1, 7.4 or DIN 1045-1, 11.3)
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 affecting the stiffnesses in uncracked sections (state I) and cracked sections (state II) in the table below:
|Influencing value||State I (uncracked)||State II (cracked)|
Creep (here as reduction of elastic modulus for concrete)
The stiffness is mainly controlled by concrete.
The stiffness in state II is mainly controlled by the reinforcement.
Influence hardly given
A tensile force reduces the stiffness significantly.
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).
-- 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)