RFCONCRETE Surfaces – Online Manual Version 5
Online manuals, introductory examples, tutorials, and other documentation.
RFCONCRETE Surfaces – Online Manual Version 5
2.8.4.2 Taking shrinkage into account
Taking shrinkage into account
Shrinkage describes a timedependent 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, watercement ratio, temperature, as well as the type and duration of curing. The shrinkagedetermining value is the total shrinkage strain ε_{cs} at the considered point of time t.
According to EN 199211, clause 3.1.4, the total shrinkage strain ε_{cs} is composed of the components for drying shrinkage ε_{cd} and autogenous shrinkage ε_{ca}:
${\epsilon}_{cs}={\epsilon}_{cd}+{\epsilon}_{ca}$
Equation 2.101 [7] Eq. (3.8)
The component from drying shrinkage ε_{cd} is determined as follows.
${\epsilon}_{cd}\left(t\right)={\beta}_{ds}\left(t,{t}_{s}\right)\xb7{k}_{h}\xb7{\epsilon}_{cd,0}$
Equation 2.102 [7] Eq. (3.9)
where
${\beta}_{ds}\left(t,{t}_{s}\right)=\frac{\left(t{t}_{s}\right)}{\left(t{t}_{s}\right)+0.4\xb7\sqrt{{h}_{0}^{3}}}$
Equation 2.103 [7] Eq. (3.10)
t  age of concrete at relevant point of time in days 
t_{s}  age of concrete when shrinkage starts in days 
effective component thickness [mm] (for surfaces: h_{0} = h)  
k_{h}  coefficient according to [4] Table 3.3 depending on the effective crosssection thickness h_{0} 
ε_{cd,0}  basic value according to [4] Table 3.2 or Annex B, Eq. (B.11): 
${\epsilon}_{cd,0}=0.85\xb7\left[\left(220+110\xb7{\alpha}_{ds1}\right)\xb7exp\left({\alpha}_{ds2}\xb7\frac{{f}_{cm}}{{f}_{cmo}}\right)\right]\xb7{10}^{6}\xb7{\beta}_{RH}$
α_{ds1}, α_{ds2}  factors for considering the type of cement (see Table 2.3) 
f_{cm}  mean cylinder compressive strength of concrete in [N/mm^{2}] 
f_{cmo}  = 10 N/mm^{2} 
${\beta}_{RH}=1.55\xb7\left[1{\left(\frac{RH}{R{H}_{0}}\right)}^{3}\right]$
RH  relative humidity of environment [%] 
RH_{0}  100 % 
Cement  Class  Property  α_{ds1}  α_{ds2} 

32,5 N  S  slowhardening  3  0.13 
32,5 R; 42,5 R  N  normalhardening  4  0.12 
42,5 R; 52,5 N/R  R  rapidhardening  6  0.11 
The autogenous shrinkage strain ε_{ca} is determined as follows.
[7] Eq. (3.11) 
where
β_{as} (t) = 1  e^{0.2√t }  [7] Eq. (3.12) 
ε_{ca} (∞) = 2.5 ∙ (f_{ck}  10) ∙ 10^{6}  [7] Eq. (3.13) 
t in days 

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, RFCONCRETE NL determines the shrinkage strain ε_{cs}.
The shrinkage strain ε_{cs }(t,t_{s}) 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 RFCONCRETE NL considers the restraint of the shrinkage strain ε_{sh} that is exerted by the reinforcement or the crosssection 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, RFCONCRETE 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 crosssection. 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.