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9.1.4 Curvature for Cracked Sections (State II)

Curvature for Cracked Sections (State II)

Curvature due to loading

When characteristic loads are applied, concrete shows linear elastic behavior. The concrete stress distributed over the compression zone is assumed to be triangular.

The depth of the concrete compression area can be determined as follows:

x = ρ · αe · d · -1 + 1 + 2ρ · αe =    = 0.0026 · 20.0 ·17 cm · -1 + 1 + 20.0026 · 20.0 = 4.68 cm

The tension stress in the reinforcement is determined with MEd = 18.50 kNm as follows:

σs = MAs · d - x3 = 18.5 · 10-34.45 · 10-4 · 0.17 - 0.04683  = 269.60 N/mm2 

The curvature in the final crack state is determined as follows:

1rM,II  = εsd - x = 1.346 · 10-3170 - 46.8 = 0.010931 m-1 

where

εs = σsEs = 269.26200 000 = 1.346 · 10-3 

Curvature due to shrinkage

The curvature for cracked sections (state II) is determined in manual calculations by means of a table from [13] (see Figure 9.2).

ω1 = αe · Asb · d = 20.0 · 4.45 cm2100 cm · 17 cm = 0.052       β = 1.10 

1rcs,II = εcs · αe ·SIIIII = εcs · β ·1d = 0.0005 · 1.10 · 10.17 m = 0.00324 m-1 

Total curvature

1rtot,II = 1rM,II = 1rcs,II = 0.01093 + 0.00324 = 0.01417 m-1 

Figure 9.2 Calculation table for cracked sections only (state II) from [13]
Literatur
[13] Noakowski, Piotr u. Schäfer, Horst. Steifigkeitsorientierte Statik im Stahlbetonbau. Ernst & Sohn Verlag, 2003.

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