Bemessung bei zweiachsiger Biegung und Längskraft (Bsp.)

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Handrechnung

Einwirkungen

Querschnitts-, Systemabmessungen und Betongüte

${\begin{array}{l}b/h=25/25cm\\{{d}_{1}}=5,4cm\\C25/30\\l=2m\end{array}}$

Schnittgrößen (angreifende Horizontalkräfte in 1m Höhe)

${\begin{array}{l}{{N}_{Ed}}=-150kN\\{{M}_{y,Ed}}={{H}_{z}}\cdot l\cdot {\frac {1}{4}}=60\cdot 2\cdot 0,25=30kNm\\{{M}_{z,Ed}}={{H}_{y}}\cdot l\cdot {\frac {1}{4}}=40\cdot 2\cdot 0,25=20kNm\end{array}}$

Schlankheitskriterium

${\begin{array}{l}{{l}_{0}}=\beta \cdot {{l}_{col}}=1\cdot 2=2m\\\lambda ={\frac {{l}_{0}}{i}}={\frac {{l}_{0}}{\sqrt {\frac {I}{A}}}}={\frac {200}{\sqrt {\frac {{{25}^{4}}/12}{{25}^{2}}}}}=27,7\end{array}}$

$n={\frac {{N}_{Ed}}{{{A}_{c}}\cdot {{f}_{cd}}}}={\frac {-150}{{{25}^{2}}\cdot 0,85\cdot {\frac {2,5}{1,5}}}}=-0,17$

${{\lambda }_{\lim }}={\frac {16}{\sqrt {n}}}={\frac {16}{\sqrt {0,17}}}=38,9$

Nachweis nach Theorie I. Ordnung legitimiert.

Bezogene Schnittgrößen

${\begin{array}{l}{{\nu }_{Ed}}={\frac {{N}_{Ed}}{b\cdot h\cdot {{f}_{cd}}}}={\frac {-150}{{{25}^{2}}\cdot 0,85\cdot {\frac {2,5}{1,5}}}}=-0,17\\{{\mu }_{y,Ed}}={\frac {{M}_{y,Ed}}{b\cdot h{}^{\text{2}}\cdot {{f}_{cd}}}}={\frac {3000}{25{}^{\text{3}}\cdot 0,85\cdot {\frac {2,5}{1,5}}}}=0,14\\{{\mu }_{z,Ed}}={\frac {{M}_{Ed}}{b{}^{\text{2}}\cdot h\cdot {{f}_{cd}}}}={\frac {2000}{25{}^{\text{3}}\cdot 0,85\cdot {\frac {2,5}{1,5}}}}=0,09\end{array}}$

Bemessung

${\begin{array}{l}{\frac {{d}_{1}}{h}}={\frac {{b}_{1}}{b}}={\frac {0,054}{0,25}}=0,22\approx 0,2\\\end{array}}$

${\begin{array}{l}{{\mu }_{1}}=\max\{{{\mu }_{Ed,y}};{{\mu }_{Ed,z}}\}=\max\{0,14;0,09\}=0,14\\{{\mu }_{2}}=\min\{{{\mu }_{Ed,y}};{{\mu }_{Ed,z}}\}=\min\{0,14;0,09\}=0,09\end{array}}$

${{\nu }_{Ed}}\approx -0,2$

${\begin{array}{l}{{\omega }_{tot}}=0,5\\{{A}_{s,tot}}={{\omega }_{tot}}\cdot {\frac {b\cdot h}{{{f}_{yd}}/{{f}_{cd}}}}=0,5\cdot {\frac {25{}^{\text{2}}}{{\frac {50}{1,15}}/0,85\cdot {\frac {2,5}{1,5}}}}=10,2cm{}^{\text{2}}\end{array}}$