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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 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:
additional axial force from shrinkage in reinforcement direction φ
additional moment from shrinkage in the centroid of the ideal cross-section in reinforcement direction Φ
bottom reinforcement surface
top reinforcement surface
modulus of elasticity of reinforcing steel
eccentricity of shrinkage forces (state I and state II) from the center of gravity of the ideal cross-section
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:
curvature induced by external loading without shrinkage influence in reinforcement direction Φ
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.
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.