2.8.4.2 Vliv smršťování

Vliv smršťování

Shrinkage describes a time-dependent change of the volume without the effect of external loads or temperature. Další rozčlenění smršťování do jednotlivých podob výskytu (smršťování vysycháním, autogenní smršťování, plastické smršťování a karbonatační smršťování) zde není blíže pojednáno.

Důležitými vlivovými faktory smršťování jsou relativní vlhkost vzduchu, efektivní tloušťka dílce, granulace kameniva, pevnost betonu, hodnota hydraulického cementu, teplota, způsob a trvání následné péče. The shrinkage-determining value is the total shrinkage strain ε_cs at the considered point of time t.

According to EN 1992-1-1, 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:

${\epsilon }_{cs} = {\epsilon }_{cd} + {\epsilon }_{ca}$

Rovnice 2.101 [7] Eq. (3.8)

The component from drying shrinkage ε_cd is determined as follows.

${\epsilon }_{cd}\left(t\right) = {\beta }_{ds} \left(t,t_s\right) · k_h · {\epsilon }_{cd,0}$

Rovnice 2.102 [7] Eq. (3.9)

S

${\beta }_{ds }\left(t,t_s\right) = \frac{\left(t - t_s\right)}{\left(t - t_s\right) + 0.4 · \sqrt{h_0^3}}$

Rovnice 2.103 [7] Eq. (3.10)

${\epsilon }_{cd,0} = 0.85 · \left[\left(220 + 110 · {\alpha }_{ds1}\right) · exp \left(-{\alpha }_{ds2} · \frac{f_{cm}}{f_{cmo}}\right)\right] · {10}^{-6} · {\beta }_{RH }$

${\beta }_{RH} = 1.55 · \left[1 - {\left(\frac{RH}{R{H}_0}\right)}^3 \right]$

The autogenous shrinkage strain ε_ca is determined as follows.

S

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 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 RF-CONCRETE NL considers the restraint of the shrinkage strain ε_sh 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.

As a simplification, four layers are considered: The dark orange layers represent the concrete with little damage, the light orange layers the more heavily damaged concrete. The blue layer corresponds to the reinforcement. Each concrete layer is characterized by the actual modulus of elasticity E_c,i and each cross-sectional area by A_c,i. The reinforcement is characterized by the actual modulus of elasticity E_s and the cross-sectional area A_s. Each layer is described by means of the coordinate z_i.

Shrinkage strain can also be applied as an external load in RFEM: In the New Surface Load dialog box of RFEM, you can open the Generate Surface Load Due to Shrinkage dialog box by clicking the button shown on the left.

In this dialog box, you can enter the parameters for determining the shrinkage strain. To transfer the determined shrinkage value as a load magnitude into the initial dialog box, New Surface Load, click [OK]. The load type is automatically set to Axial strain. Please note that the shrinkage strain acts on the entire cross-section and that possible restraints or cross-section curvatures are not taken into account by the reinforcement.