Benutzer:Sneumann

Querkraftbemessung

$C_{Rdc}={\frac {0,15}{\gamma _{c}}}$	$|mit:\gamma _{c}=1,5$
$C_{Rdc}={\frac {0,15}{1,5}}$
$C_{Rdc}=0,1$

$k=1+{\sqrt {\frac {200}{d}}}$	${\begin{cases}\geq 1,0\\\leq 2,0\end{cases}}$
	$|mit:d=177mm$
$k=1+{\sqrt {\frac {200}{177}}}$
$k=2,06$	${\begin{cases}\geq 1,0\\\geq 2,0\end{cases}}$
$k=2$

$\rho _{l}={\frac {A_{sl}}{b_{w}\cdot d}}$	$\leq 0,02$
	$|mit:A_{sl}=1,88{\frac {cm^{2}}{m}}$
	$|mit:b_{w}=100cm$
	$|mit:d=17,7cm$
$\rho _{l}={\frac {1,88{\frac {cm^{2}}{m}}}{100cm\cdot 17,7cm}}$
$\rho _{l}=1,06\cdot 10^{-3}$	$\leq 0,02$

$\sigma _{cp}={\frac {N_{Ed}}{A_{c}}}$	$|mit:N_{Ed}=extrn=\pm 11,56{\frac {kN}{m}}$
	$|mit:A_{c}=1,0m\cdot 0,17m$

Querkrafttragfähigkeit ohne Querkraftbewehrung

\sigma_{cp}=\frac{ N_{Ed}}{A_{c}}

\frac{50000}{\left( 300\cdot 800 \right)-1571}=0,21N/mm{}^\text{2}\end{array}</math>

${\begin{array}{l}{{V}_{Rd,c}}=\left[{{C}_{Rdc}}\cdot k\cdot {{\left(100\cdot {{\rho }_{l}}\cdot {{f}_{ck}}\right)}^{\frac {1}{3}}}+0,12\cdot {{\sigma }_{cp}}\right]\cdot {{b}_{w}}\cdot d\\\quad \ \ \ =\left[0,1\cdot 1,52\cdot {{\left(100\cdot 0,007\cdot 35\right)}^{\frac {1}{3}}}+0,12\cdot 0,21\right]\cdot 300\cdot 740\\\quad \quad =103,6kN\quad \leq \quad 500kN\end{array}}$

Anordnung senkrechter Bügel

Winkel der Betondruckstrebe

${\begin{array}{l}{{V}_{Rd,cc}}=0,5\cdot 0,48\cdot f_{ck}^{\frac {1}{3}}\cdot \left(1-1,2\cdot {\frac {{\sigma }_{cd}}{{f}_{cd}}}\right)\cdot {{b}_{w}}\cdot z=0,5\cdot 0,48\cdot {{35}^{\frac {1}{3}}}\cdot \left(1-1,2\cdot {\frac {0,21}{0,85\cdot {\frac {35}{1,5}}}}\right)\cdot 300\cdot 0,9\cdot 740\\\quad \quad =154,861kN\\\cot \Theta ={\frac {1,2-1,4\cdot {\frac {{\sigma }_{cp}}{{f}_{cd}}}}{1-{\frac {{V}_{Rd,cc}}{{V}_{Ed}}}}}={\frac {1,2-1,4\cdot {\frac {0,21}{0,85\cdot {\frac {35}{1,5}}}}}{1-{\frac {154,861}{500}}}}=1,72\end{array}}$

Nachweis der Betondruckstrebe

${\begin{array}{l}{{\nu }_{1}}=0,75\cdot \left(1,1-{\frac {{f}_{ck}}{500}}\right)\leq 0,75\\\quad =0,75\cdot \left(1,1-{\frac {35}{200}}\right)=0,69\\{{V}_{Rd,\max }}={{\nu }_{1}}\cdot {{f}_{cd}}\cdot {{b}_{w}}\cdot z\cdot {\frac {\cot \Theta }{1+\cot {}^{\text{2}}\Theta }}=0,69\cdot \left(0,85\cdot {\frac {35}{1,5}}\right)\cdot 300\cdot \left(0,9\cdot 740\right)\cdot {\frac {1,72}{1+1,72{}^{\text{2}}}}\\\quad \quad \ \ \ =1188kN\geq 500kN\end{array}}$

Nachweis der Zugstrebe

${\begin{array}{l}{{V}_{Rd,s}}={{a}_{sw}}\cdot {{f}_{yd}}\cdot \sin \alpha \cdot z\cdot (\cot \Theta +\cot \alpha )\\{{a}_{sw}}\geq {\frac {{V}_{Ed}}{{{f}_{yd}}\cdot \sin \alpha \cdot z\cdot \left(\cot \Theta +\cot \alpha \right)}}\\\quad \,\,\geq {\frac {500}{{\frac {50}{1,15}}\cdot \sin 90\cdot 0,9\cdot 74\cdot \left(1,72\right)}}=0,10039cm{}^{\text{2}}/cm=10,04cm{}^{\text{2}}/m\end{array}}$

gewählt: zweischnittig ø10/15cm, ${{a}_{sw}}=12,56cm{}^{\text{2}}/m$

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