2.7.5.2 Shrinkage

Shrinkage

In the deformation calculation according to EN 1992-1-1, there are two areas that are influenced by shrinkage effects.

The material stiffness in each reinforcement direction Φ is reduced by the so-called coefficient of shrinkage influence κ_sh,Φ,c. For the two crack states c (cracked/uncracked), the axial forces n_sh,Φ,c and bending moments m_sh,Φ,c can be calculated from the free shrinkage strain ε_sh:

$$\begin{gathered} n_{sh,\varphi } = -{\epsilon }_{sh} · E_s · (a_{s1} + a_{s2}) \\ {m}_{sh,\varphi } = n_{sh} · e_{sh} \end{gathered}$$

where

With these internal forces from shrinkage, the additional curvature κ_sh,Φ,c induced by shrinkage is calculated in the analyzed point – without influence of the surrounding model. Subsequently, the new coefficient of shrinkage influence κ_sh,Φ,c is calculated according to:

${\kappa }_{sh,\varphi ,c} = \frac{{\kappa }_{sh,\varphi ,c} + {\kappa }_{\varphi }}{{\kappa }_{\varphi }}$

where

The coefficient κ_sh,Φ,c is limited to the interval κ_sh,Φ,c ∈ (1, 100): Therefore, κ_sh,Φ,c may not reduce the stiffness by more than 100 times for numerical and physical reasons. Furthermore, the minimum value κ_sh,Φ,c = 1 means that it is not possible to consider the influence of shrinkage if the influence of shrinkage has an orientation opposite to the loading-induced curvature κ_d.

The influence of shrinkage on the membrane stiffness is not considered.

The second influence of shrinkage lies in the calculation of the distribution coefficient ζ according to EN 1992-1-1, clause 7.4.3, Equation (7.18). The following chapter describes the distribution coefficient in detail.