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| ====Querkraftbemessung====
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| ::{|
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| |<math> C_{Rdc} = \frac{0,15}{\gamma_{c}} </math>||<math>| mit: \gamma_{c} = 1,5</math>
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| |<math> C_{Rdc} = \frac{0,15}{1,5} </math>||
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| |<math> C_{Rdc} = 0,1 </math>||
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| |<math> k=1+\sqrt{\frac{200}{d}} </math>|| <math>\begin{cases}
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| \ge 1,0 \\
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| \le 2,0
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| \end{cases}</math>
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| | || <math>| mit: d = 177 mm </math>
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| |<math>k=1+\sqrt{\frac{200}{177}}</math> ||
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| |<math>k=2,06</math> || <math>\begin{cases}
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| \ge 1,0 \\
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| \ge 2,0
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| \end{cases}</math>
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| |<math>k=2</math> ||
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| |}
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| |<math> \rho_{l} = \frac{A_{sl}}{b_{w} \cdot d} </math>||<math> \le 0,02 </math>
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| | || <math>| mit: A_{sl} = 1,88 \frac{cm^{2}}{m} </math>
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| | || <math>| mit: b_{w} = 100 cm </math>
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| | || <math>| mit: d = 17,7 cm</math>
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| |<math> \rho_{l} = \frac{1,88 \frac{cm^{2}}{m} }{100 cm \cdot 17,7 cm }</math>||
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| |<math> \rho_{l} =1,06 \cdot 10^{-3} </math>||<math> \le 0,02 </math>
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| |}
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| |<math> \sigma_{cp}=\frac{ N_{Ed} }{ A_{c} } </math> || <math>| mit: N_{Ed} = extr n = \pm 11,56 \frac{kN}{m} </math>
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| | || <math>| mit: A_{c} = 1,0 m \cdot 0,17 m</math>
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| |}
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| ====== Querkrafttragfähigkeit ohne Querkraftbewehrung ======
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| \sigma_{cp}=\frac{ N_{Ed}}{A_{c}}
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| \frac{50000}{\left( 300\cdot 800 \right)-1571}=0,21N/mm{}^\text{2}\end{array}</math>
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| <math>\begin{array}{l}{{V}_{Rd,c}}=\left[ {{C}_{Rdc}}\cdot k\cdot {{\left( 100\cdot {{\rho }_{l}}\cdot {{f}_{ck}} \right)}^{\frac{1}{3}}}+0,12\cdot {{\sigma }_{cp}} \right]\cdot {{b}_{w}}\cdot d\\\quad \ \ \ =\left[ 0,1\cdot 1,52\cdot {{\left( 100\cdot 0,007\cdot 35 \right)}^{\frac{1}{3}}}+0,12\cdot 0,21 \right]\cdot 300\cdot 740\\\quad \quad =103,6kN\quad \le \quad 500kN\end{array}</math>
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| Anordnung senkrechter Bügel<br />
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| === Winkel der Betondruckstrebe ===
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| <math>\begin{array}{l}{{V}_{Rd,cc}}=0,5\cdot 0,48\cdot f_{ck}^{\frac{1}{3}}\cdot \left( 1-1,2\cdot \frac{{{\sigma }_{cd}}}{{{f}_{cd}}} \right)\cdot {{b}_{w}}\cdot z=0,5\cdot 0,48\cdot {{35}^{\frac{1}{3}}}\cdot \left( 1-1,2\cdot \frac{0,21}{0,85\cdot \frac{35}{1,5}} \right)\cdot 300\cdot 0,9\cdot 740\\\quad \quad =154,861kN\\\cot \Theta =\frac{1,2-1,4\cdot \frac{{{\sigma }_{cp}}}{{{f}_{cd}}}}{1-\frac{{{V}_{Rd,cc}}}{{{V}_{Ed}}}}=\frac{1,2-1,4\cdot \frac{0,21}{0,85\cdot \frac{35}{1,5}}}{1-\frac{154,861}{500}}=1,72\end{array}</math>
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| === Nachweis der Betondruckstrebe ===
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| <math>\begin{array}{l}{{\nu }_{1}}=0,75\cdot \left( 1,1-\frac{{{f}_{ck}}}{500} \right)\le 0,75\\\quad =0,75\cdot \left( 1,1-\frac{35}{200} \right)=0,69\\{{V}_{Rd,\max }}={{\nu }_{1}}\cdot {{f}_{cd}}\cdot {{b}_{w}}\cdot z\cdot \frac{\cot \Theta }{1+\cot {}^\text{2}\Theta }=0,69\cdot \left( 0,85\cdot \frac{35}{1,5} \right)\cdot 300\cdot \left( 0,9\cdot 740 \right)\cdot \frac{1,72}{1+1,72{}^\text{2}}\\\quad \quad \ \ \ =1188kN\ge 500kN\end{array}</math>
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| === Nachweis der Zugstrebe ===
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| <math>\begin{array}{l}{{V}_{Rd,s}}={{a}_{sw}}\cdot {{f}_{yd}}\cdot \sin \alpha \cdot z\cdot (\cot \Theta +\cot \alpha )\\{{a}_{sw}}\ge \frac{{{V}_{Ed}}}{{{f}_{yd}}\cdot \sin \alpha \cdot z\cdot \left( \cot \Theta +\cot \alpha \right)}\\\quad \,\,\ge \frac{500}{\frac{50}{1,15}\cdot \sin 90\cdot 0,9\cdot 74\cdot \left( 1,72 \right)}=0,10039cm{}^\text{2}/cm=10,04cm{}^\text{2}/m\end{array}</math>
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| gewählt: zweischnittig ø10/15cm, <math>{{a}_{sw}}=12,56cm{}^\text{2}/m</math>
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| ==''Quellen''==
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| :''Normen''
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| <references group="N" /><br />
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| <br />
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| :''Fachliteratur''
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| <references group="F" /><br />
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| <br />
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| :''Links''
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| <references group="L" />
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| <br />
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| {{Seiteninfo
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| |Quality-flag = [[File:quality-flag-white.gif|right|70px]]
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| |Status = Seite in Bearbeitung}}
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| [[Kategorie:Grundlagen/Begriffe-Stahlbetonbau]]-Stahlbetonbau]]
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