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| =====Bereich der Arbeitsfuge Fußpunkt=====
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| ======Vorbemessung======
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| ::{|
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| | <math> z_{est} = 0,75 \cdot h </math>||<math>| mit: h = h_{L} = 20 cm </math>
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| | <math> z_{est} = 0,75 \cdot 20 cm </math>||
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| | <math> z_{est} = 15 cm </math>||
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| |}
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| <br />
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| <br />
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| ::{|
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| | <math> M_{Ed,est} = M_{Ed} - N_{Ed} \cdot z_{s1,est} </math>||<math>| mit: z_{s1,est} = 15 cm </math>
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| | ||<math>| mit: N_{Ed} = extr n = 11,56 \frac{kN}{m}</math>
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| | ||<math>| mit: M_{Ed} = M_{Ed,S} =6.63 \frac{kNm}{m} </math>
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| | <math> M_{Ed,est} = 6.63 \frac{kNm}{m} - 11,56 \frac{kN}{m} \cdot 0,15 m </math>||
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| |-
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| | <math> M_{Ed,est} = 4.9 \frac{kNm}{m}</math>||
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| |}
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| <br />
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| ::{|
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| | <math> a_{s,est} = \frac{M_{Ed,est}}{z_{s1,est} \cdot f_{yd} } + \frac{N_{Ed}}{f_{yd}} </math>||<math>| mit: z_{s1,est} = 15 cm </math>
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| | ||<math>| mit: f_{yd} = 43,5 \frac{kN}{cm^{2}} </math>
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| | ||<math>| mit: N_{Ed} = extr n = 11,56 \frac{kN}{m} </math>
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| | ||<math>| mit: M_{Ed,est} = 4.9 \frac{kNm}{m} </math>
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| | <math> a_{s,est} = \frac{490 \frac{kNcm}{m}}{15 cm \cdot 43,5 \frac{kN}{cm^{2}} } + \frac{11,56 \frac{kN}{m}}{43,5 \frac{kN}{cm^{2}}} </math>||
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| |-
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| | <math> a_{s,est} \approx 1,02 \frac{kNcm}{m} </math>||
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| |}
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| gewählt: R188 ø6/15cm, <math>{{a}_{s}}= 1,88 \frac{cm^{2}}{m} </math>
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| ======Querschnittsgeometrie======
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| :<math>c_{v}=\mathrm{max}\begin{cases}
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| C_{nom,dur} \\
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| C_{nom,b,Bü} \\
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| C_{nom,b,L}
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| \end{cases}</math><br /><br />
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| <br />
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| ::{|
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| | <math> C_{nom,dur} = C_{min,dur} + \Delta C_{dev} </math>|| <math>| mit: C_{min,dur} = 10 mm </math> für XC1
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| | || <math>| mit: \Delta C_{dev} = 10 mm </math>
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| | <math> C_{nom,dur} = 10 mm + 10 mm </math>||
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| | <math> C_{nom,dur} = 20 mm </math>||
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| |}
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| <br />
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| ::{|
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| | <math> C_{nom,b,Bü} = C_{min,b,Bü} + \Delta C_{dev} </math>|| <math>| mit: C_{min,b,Bü} = 0 mm </math>
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| | ||<math>| mit: \Delta C_{dev} = 10 mm </math>
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| | <math> C_{nom,b,Bü} = 0 mm + 10 mm </math>||
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| | <math> C_{nom,b,Bü} = 10 mm </math>||
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| |}
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| ::{|
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| | <math> C_{nom,b,L} = C_{min,b,L} - \varnothing bue + \Delta C_{dev} </math>|| <math>| mit: C_{min,b,L} = 7 mm </math>
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| | ||<math>| mit: \Delta C_{dev} = 10 mm </math>
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| | ||<math>| mit: \varnothing bue = 0 mm </math>
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| | <math> C_{nom,b,L} = 6 mm - 0 mm + \Delta 10 mm </math>||
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| | <math> C_{nom,b,L} = 16 mm </math>||
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| |}
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| :<math>c_{v}=\mathrm{max}\begin{cases}
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| 20 mm \\
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| 10 mm \\
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| 16 mm
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| \end{cases}</math><br /><br />
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| ::{|
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| | <math> d_{1} = c_{v} + \varnothing bue + \frac{\varnothing L}{2}</math>|| <math>| mit: c_{v} = 20 mm </math>
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| | || <math>| mit: \varnothing bue = 0 mm </math>
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| | || <math>| mit: \varnothing L = 6 mm </math>
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| | <math> d_{1} = 20 mm + 0 mm + \frac{6 mm}{2} </math>||
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| | <math> d_{1} = 23,0 mm</math>||
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| |}
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| ::{|
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| | <math> d = h_{L} - d_{1} </math>|| <math>| mit: d_{1} = 23 mm </math>
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| | || <math>| mit: h_{L} = 200 mm </math>
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| | <math> d = 200 mm - 23,0 mm </math>||
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| | <math> d = 177 mm = 17,7 cm </math>||
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| |}
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| =====Bemessung mit dem ω-Verfahren=====
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| ::{|
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| |<math> z_{s} = d - \frac{h_{L} }{2} </math>|| <math>| mit: d = 17,7 cm </math>
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| | || <math>| mit: h_{L} = 20 cm </math>
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| |<math> z_{s} = 17,7 cm - \frac{20 cm}{2} </math>||
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| |-
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| |<math> z_{s} = 7,7 cm </math>||
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| |}
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| ::{|
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| |<math> M_{Eds} = M_{Ed,S} - extr n \cdot z_{s} </math>|| <math>| mit: z_{s} = 7,7 cm </math>
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| | || <math>| extr n = 11,56 \frac{kN}{m} </math>
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| | ||<math>| mit: M_{Ed,S} =663 \frac{kNcm}{m} </math>
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| |<math> M_{Eds} = 663 \frac{kNcm}{m} - 11,56 \frac{kN}{m} \cdot 7,7 cm </math>||
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| |<math> M_{Eds} = 573.988 \frac{kNcm}{m} </math>||
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| |}
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| ::{|
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| |<math> \mu_{Eds} = \frac{M_{Eds}}{b\cdot d^{2} \cdot f_{cd}} </math>|| <math>| mit: d = 17,7 cm </math>
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| | || <math>| mit: b = 100 cm </math>
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| | || <math>| mit: f_{cd} = 1,42 \frac{kN}{cm^{2}}</math>
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| | || <math>| mit: M_{Eds} = 573.988 \frac{kNcm}{m} </math>
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| |<math> \mu_{Eds} = \frac{ 573.988 \frac{kNcm}{m}}{100 cm \cdot (17,7 cm)^{2} \cdot 1,42 \frac{kN}{cm^{2}} } </math>||
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| |<math> \mu_{Eds} = 0,0169 </math>||
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| |}
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| <br />
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| <br />
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| ::{|
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| |<math> \omega = \omega_{1} + \frac{ \omega_{2} - \omega_{1} } { \mu_{Eds,2} - \mu_{Eds,1}} \cdot ( \mu_{Eds} - \mu_{Eds,1} ) </math>||
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| <math>| mit: \omega_{1} = 0,0101 </math>
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| | || <math>| mit: \omega_{2} = 0,0203 </math>
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| | || <math>| mit: \mu_{Eds} = 0,0169 </math>
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| | || <math>| mit: \mu_{Eds,1} = 0,01 </math>
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| | || <math>| mit: \mu_{Eds,2} = 0,02 </math>
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| |<math> \omega = 0,0101 + \frac{ 0,0203 - 0,0101 } { 0,02 - 0,01 } \cdot ( 0,0169 - 0,01 ) </math>||
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| |<math> \omega = 0,01714 </math>||
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| |}
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| <br />
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| <br />
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| ::{|
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| |<math> a_{s,1} = \frac{1}{ \sigma_{sd}} \cdot ( \omega \cdot b \cdot d \cdot f_{cd} + N_{Ed} ) </math>|| <math>| mit: \omega = 0,01714 </math>
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| | || <math>| mit: f_{cd} = 1,42 \frac{kN}{cm^{2}} </math>
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| | || <math>| mit: d = 17,7 cm </math>
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| | || <math>| mit: b = 100 cm </math>
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| | || <math>| mit: N_{Ed} = extr n = (-11,56) \frac{kN}{m} </math>
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| |<math> a_{s,1} = \frac{1}{ 43,5 \frac{kN}{cm^{2}}} \cdot ( 0,0151 \cdot 100 cm \cdot 17,7 cm \cdot 1,42 \frac{kN}{cm^{2}} + (-11,56) \frac{kN}{m} ) </math>||
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| |<math> a_{s,1} = 0,61 \frac{cm^{2}}{m} </math>||
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| |}
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| gewählt: R188 ø6/15cm, <math>{{a}_{s}}= 1,88 \frac{cm^{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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