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9.2.6.4 Mean Curvatures

Mean Curvatures

The mean curvatures arising with the selected Tension-Stiffening approach are determined from the calculations for pure state I and pure state II.

The underlying Tension Stiffening model described in book 525 [6] considers the concrete's tension stiffening effect between the cracks by means of a reduction of the steel strain. The required parameters are determined as follows.

Governing state of crack formation
 Steel stress in state II for crack formation: σsr1,II = 166.12 N/mm2 Steel stress in state II: σs1,II = 242.27 N/mm2

Hence, we will have a closer look at the final crack state.

Average steel strain
• εsm = εs2,II - βt ∙ (εsr,II - εsr,I)
• εsm = 1.211 - 0.306 ∙ (0.8306 - 0.199) = 1.0177 ‰

where

• εs2,II = 1.211 ‰ : steel strain in state II
• εsr1,II = 0.8306 : steel strain for crack internal force in state II
• εsr1,I = 0.199 ‰ : steel strain for crack internal force in state I
• βt = 0.306 : load duration factor of available action
Mean curvature

Mean bending stiffness

From the mean curvature (1/r)z,m and the relation

the secant stiffness in the corresponding node results.

where

• My = 17.64 kNm : available moment
• (1/r)z,m = 1.226 ⋅ 10-2m-1 : steel strain for crack internal force in state II
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Literatur
 [6] Deutscher Ausschuss für Stahlbeton (Hrsg.): Heft 525 – Erläuterungen zu DIN 1045-1. Beuth Verlag GmbH, 2003.