RF-CONCRETE Surfaces – Online Manual Version 5

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RF-CONCRETE Surfaces – Online Manual Version 5

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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 κsh,Φ,c. For the two crack states c (cracked/uncracked), the axial forces nsh,Φ,c and bending moments msh,Φ,c can be calculated from the free shrinkage strain εsh:

nsh,ϕ = -εsh · Es · (as1 + as2)msh,ϕ = nsh · esh 

where

Table 2.2

nsh,Φ

additional axial force from shrinkage in reinforcement direction φ

msh,Φ

additional moment from shrinkage in the centroid of the ideal cross-section in reinforcement direction Φ

as1

bottom reinforcement surface

as2

top reinforcement surface

Es

modulus of elasticity of reinforcing steel

εsh

shrinkage strain

esh

eccentricity of shrinkage forces (state I and state II) from the center of gravity of the ideal cross-section

Figure 2.115 Internal forces nsh,Φ and msh,Φ

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

κsh,ϕ,c = κsh,ϕ,c + κϕκϕ 

where

Table 2.2

κΦ

curvature induced by external loading without shrinkage influence in reinforcement direction Φ

κsh,Φ,c

curvature induced by shrinkage (and reinforcement arrangement) without influence of creep in reinforcement direction Φ

The coefficient κsh,Φ,c is limited to the interval κsh,Φ,c ∈ (1, 100): Therefore, κsh,Φ,c may not reduce the stiffness by more than 100 times for numerical and physical reasons. Furthermore, the minimum value κsh,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 κd.

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.