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2.7.4 Cross-Section Properties
The cross-section properties are calculated for both reinforcement directions Φ and both cross-section states c (cracked/uncracked). A linear-elastic behavior of the concrete on the tension side is applied for state I (uncracked cross-section) and the concrete tensile strength is not considered for state II (cracked cross-section).
If no axial forces nΦ act as is the case for the model type 2D - XY (uZ / φX / φY), for example, this part of the calculation is independent of the internal forces and a direct calculation of the cross-section properties is possible. In the remaining cases, the compression zone depth is calculated by means of an iterative method of calculation, the so-called "binary method". For numerical reasons, the program uses the minimum value for the reinforcement ratio ρmin = 10-4 in every iteration step, meaning that if there is no reinforcement, a virtual minimum reinforcement area is applied. This small value has no noticeable influence on the results (stiffnesses).
The calculated ideal cross-section properties (related to the concrete cross-section) in a reinforcement direction φ and the crack state c are
- the moment of inertia to the ideal center of gravity IΦ,c,
- the moment of inertia to the geometric center of the cross-section I0.Φ,c,
- the cross-section area AΦ,c,
- the eccentricity of the ideal center of gravity eΦ,c.