RF-CONCRETE Members – Online Manual Version 5

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RF-CONCRETE Members – Online Manual Version 5

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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
Table 9.0

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

   σs1,II = 242.27 N/mm2  1.3 · σsr1,II = 215.96 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

1rz,m = εsm - εcd = 1.0177 + 0.63780.135 = 12.26 mmm = 1.226 · 10-2 m-1  

Mean bending stiffness

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

1rz,m = MIy,m · E  

the secant stiffness in the corresponding node results.

Iy,m · E = My1/rz,m = 0.017641.226 · 10-2 = 1.43883 MNm2 = 1438.83 kNm2  

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
Results of RF-CONCRETE Members
Figure 9.27 Detailed results of mean curvatures
Literatur
[6] Deutscher Ausschuss für Stahlbeton (Hrsg.): Heft 525 – Erläuterungen zu DIN 1045-1. Beuth Verlag GmbH, 2003.

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