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2.4.4 Mean Moment-Curvature Relation

Mean Moment-Curvature Relation

The mean moment-curvature relation describes the relation between moment and curvature by taking the concrete's tension stiffening effect into account. By means of discrete conditions of strain (curvatures), it is possible to determine a corresponding moment. On the basis of the ultimate strain at failure, the ultimate curvature is generally divided varyingly depending on the task. The disadvantage of this approach is that it requires a very fine division in order to also represent the transition zones for significant yield points. By connecting the respective single points, you get a continuous (polygonal) line representing the characteristic moment-curvature diagram. The diagram curve is also affected by or dependent on the acting axial force. However, in most practical situations, it is sufficient to apply a moment-curvature relation linearized in particular areas.

RF-CONCRETE Members determines the stiffness in a process-related way (double bending, no constant axial force) on every element node directly from the internal force of the previous iteration. One of the differences between the two approaches of Tension Stiffening is that in the approach by Quast, the mean stiffness arises directly from the stress calculation. In contrast, in the approach with the modified characteristic steel curve, the mean curvature is to be determined separately once more, which may lead to certain losses in velocity depending on geometry and system.

For compression elements, we generally have to use the model by Quast [7] to consider the concrete's effectiveness. The reason is the simplified calculation in the uncracked state for the model via the modified characteristic steel curve (see chapter and chapter 4.2.2).

Figure 2.25 Examplary diagram of a moment-curvature relation
[7] Deutscher Ausschuss für Stahlbetonbau (Hrsg.) Heft 415 – Programmgesteuerte Berechnung beliebiger Massivbauquerschnitte unter zweiachsiger Biegung mit Längskraft. Beuth Verlag GmbH, Berlin, 1990.

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