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Overview

1 Introduction

2 Theoretical Background

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.

Reduction of material stiffness

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:

$n_{s h, ϕ} = - ε_{s h} \cdot E_{s} \cdot (a_{s 1} + a_{s 2}) m_{s h, ϕ} = n_{s h} \cdot e_{s h}$

where

Table 2.2
n_sh,Φ	additional axial force from shrinkage in reinforcement direction φ
m_sh,Φ	additional moment from shrinkage in the centroid of the ideal cross-section in reinforcement direction Φ
a_s1	bottom reinforcement surface
a_s2	top reinforcement surface
E_s	modulus of elasticity of reinforcing steel
ε_sh	shrinkage strain
e_sh	eccentricity of shrinkage forces (state I and state II) from the center of gravity of the ideal cross-section

Image 2.115 Internal forces n_sh,Φ and m_sh,Φ

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:

$κ_{s h, ϕ, c} = \frac{κ_{s h, ϕ, c} + κ_{ϕ}}{κ_{ϕ}}$

where

Table 2.2
κ_Φ	curvature induced by external loading without shrinkage influence in reinforcement direction Φ
κ_sh,Φ,c	curvature induced by shrinkage (and reinforcement arrangement) without influence of creep in reinforcement direction Φ

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.

Calculation of distribution coefficient

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.

Parent section

2.7.5 Considering Long-Term Effects