# RF-CONCRETE Surfaces – Online Manual Version 5

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# 2.8.4.2 Taking shrinkage into account

#### Taking shrinkage into account

Shrinkage describes a time-dependent change of volume without the effect of external loads or temperature. This manual will not go into details regarding the shrinkage problems and their individual types (drying shrinkage, autogenous shrinkage, plastic shrinkage, and carbonation shrinkage).

Significant influence values of shrinkage are relative humidity, effective thickness of structural components, aggregate, concrete strength, water-cement ratio, temperature, as well as the type and duration of curing. The shrinkage-determining value is the total shrinkage strain εcs at the considered point of time t.

According to EN 1992-1-1, clause 3.1.4, the total shrinkage strain εcs is composed of the components for drying shrinkage εcd and autogenous shrinkage εca:

Equation 2.101 [7] Eq. (3.8)

The component from drying shrinkage εcd is determined as follows.

Equation 2.102 [7] Eq. (3.9)

where

Equation 2.103 [7] Eq. (3.10)

 t age of concrete at relevant point of time in days ts age of concrete when shrinkage starts in days effective component thickness [mm] (for surfaces: h0 = h)Ac  cross-section areau    cross-section perimeter kh coefficient according to [4] Table 3.3 depending on the effective cross-section thickness h0 εcd,0 basic value according to [4] Table 3.2 or Annex B, Eq. (B.11):

 αds1, αds2 factors for considering the type of cement (see Table 2.3) fcm mean cylinder compressive strength of concrete in [N/mm2] fcmo = 10 N/mm2

 RH relative humidity of environment [%] RH0 100 %
Table 2.3 Factors αds1 and αds2 depending on the type of cement
Cement Class Property αds1 αds2

32,5 N

S

slow-hardening

3

0.13

32,5 R; 42,5 R

N

normal-hardening

4

0.12

42,5 R; 52,5 N/R

R

rapid-hardening

6

0.11

The autogenous shrinkage strain εca is determined as follows.

 [7] Eq. (3.11)

where

 βas (t) = 1 - e-0.2√t [7] Eq. (3.12) εca (∞) = 2.5 ∙ (fck - 10) ∙ 10-6 [7] Eq. (3.13) t   in days
Taking shrinkage in RF-CONCRETE NL into account (while considering the reinforcement)

The data for the shrinkage strain is entered in window 1.3 Surfaces. In it, you can specify the age of concrete at the relevant point of time and at the beginning of shrinkage, the relative air humidity, and the type of cement. Based on these specifications, RF-CONCRETE NL determines the shrinkage strain εcs.

The shrinkage strain εcs (t,ts) can also be specified manually, independent of standards.

The shrinkage strain is only applied to the concrete layers; the reinforcement layers remain unconsidered. Thus, there is a difference from the classical temperature loading, which also affects the reinforcement layers. Therefore, the model for shrinkage used in RF-CONCRETE NL considers the restraint of the shrinkage strain εsh that is exerted by the reinforcement or the cross-section curvature for an unsymmetrical reinforcement. The resulting loads from the shrinkage strain are automatically applied to the surfaces as virtual loads and calculated. Depending on the structural system, the shrinkage strain results in additional stresses (statically indeterminate system) or additional deformations (statically determinate system). For shrinkage, RF-CONCRETE NL therefore considers the influence of the structural boundary conditions in different ways.

The loads resulting from shrinkage are automatically assigned to the loading for serviceability defined in window 1.1 General Data and are therefore included in the nonlinear calculation.

The shrinkage depends on the correct distribution of the stiffness in the cross-section. Therefore, the consideration of tension stiffening (residual tensile strength of concrete according to Quast) as well as a small value for damping are recommended for the concrete's tension zone.

The 1D model shown in Figure 2.148 illustrates how shrinkage is considered in the program.