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2.7.7 Cross-Section Properties for Deformation Analysis
Cross-Section Properties for Deformation Analysis
For the material stiffness matrix D needed for the deformation analysis, the program requires the cross-section properties dependant on the cracked state that are available in every direction of reinforcement. These are the following:
- moment of inertia to the ideal center of gravity IΦ,
- moment of inertia to the geometric center of the cross-section I0,Φ,
- cross-section area AΦ,
- eccentricity of the ideal center of gravity eΦ to the geometric center.
The mean strain εΦ and the mean curvature ΚΦ are interpolated between a cracked and an uncracked state according to EN 1992-1-1, Equation (7.18):
The strains in the cracked state c (state I and II) are calculated according to the following equations:
Thus, the influence of shrinkage is considered by using the factor ksh,φ,c.
If no axial forces nΦ act (e.g. in the type of model 2D - XY (uZ / φX / φY), only those ideal cross-section properties are relevant that relate to the ideal center of the cross-section:
If axial forces are available, the cross-section properties are related to the geometric center of the cross-section:
Equation 2.88 (2.88)
In the course of the calculation of the cross-section properties, the initial value of the poisson's ratio νinit is reduced according to the following equation: