-Abstand Momentennullpunkt und Momentenmaximum:
x = V A , C ( g d + q d ) = 231 , 81 88 , 8 = 2 , 61 m {\displaystyle x={\cfrac {V_{A,C}}{(g_{d}+q_{d})}}={\cfrac {231,81}{88,8}}=2,61m}
⇒ Δ x = 2 , 61 2 = 1 , 305 m _ {\displaystyle \Delta x={\cfrac {2,61}{2}}={\underline {1,305m}}}
-Moment im Abstand Δ x {\displaystyle \Delta x} vom Momentennullpunkt:
Δ M E d = V A , C ⋅ Δ x − ( g d + q d ) ⋅ Δ x 2 2 = 231 , 81 ⋅ 1 , 31 − 88 , 8 ⋅ 1 , 31 2 2 = 227 , 48 k N m {\displaystyle \Delta M_{Ed}=V_{A,C}\cdot \Delta x-(g_{d}+q_{d})\cdot {\cfrac {\Delta x^{2}}{2}}=231,81\cdot 1,31-88,8\cdot {\cfrac {1,31^{2}}{2}}=227,48kNm}
z ≈ 0 , 475 m {\displaystyle z\approx 0,475m}
Δ F c d = Δ M E d z ⋅ b a b e f f = 227 , 48 0 , 475 ⋅ 79 , 25 188 , 5 = 201 , 98 k N _ {\displaystyle \Delta F_{cd}={\cfrac {\Delta M_{Ed}}{z}}\cdot {\cfrac {b_{a}}{b_{eff}}}={\cfrac {227,48}{0,475}}\cdot {\cfrac {79,25}{188,5}}={\underline {201,98kN}}}
-Vereinfachung Druckgurt: c o t θ = 1 , 2 {\displaystyle cot\theta =1,2} ⇒ θ ≈ 40 {\displaystyle \theta \approx 40} °
-Druckstrebennachweis:
V R d , m a x = 0 , 492 ⋅ ν 1 ⋅ f c d ⋅ h f ⋅ Δ x = 0 , 492 ⋅ 0 , 75 ⋅ 19 , 8 ⋅ 0 , 2 ⋅ 1 , 31 = 1 , 914 M N = 1914 k N _ > Δ F c d = 201 , 98 k N {\displaystyle V_{Rd,max}=0,492\cdot \nu _{1}\cdot f_{cd}\cdot h_{f}\cdot \Delta x=0,492\cdot 0,75\cdot 19,8\cdot 0,2\cdot 1,31=1,914MN={\underline {1914kN}}>\Delta F_{cd}=201,98kN~}
-Zugstrebennachweis:
a s f = Δ F c d ( f y d ⋅ Δ x ⋅ 1 , 2 ) = 0 , 20198 ( 435 ⋅ 1 , 31 ⋅ 1 , 2 ) = 2 , 95 ⋅ 10 − 4 = 2 , 95 c m 2 / m _ _ {\displaystyle a_{sf}={\cfrac {\Delta F_{cd}}{(f_{yd}\cdot \Delta x\cdot 1,2)}}={\cfrac {0,20198}{(435\cdot 1,31\cdot 1,2)}}=2,95\cdot 10^{-4}={\underline {\underline {2,95cm^{2}/m}}}~}
⇒ gewählt: ∅ 10 {\displaystyle \varnothing 10} s = 30 c m {\displaystyle s=30cm} a s w , v o r h = 5 , 24 c m 2 / m _ _ {\displaystyle a_{sw,vorh}={\underline {\underline {5,24cm^{2}/m}}}~}
V R d , s = a s f ⋅ f y d ⋅ Δ x ⋅ c o t θ = 5 , 24 ⋅ 43 , 5 ⋅ 1 , 31 ⋅ 1 , 2 = 358 , 32 k N _ > Δ F c d = 201 , 98 k N {\displaystyle V_{Rd,s}=a_{sf}\cdot f_{yd}\cdot \Delta x\cdot cot\theta =5,24\cdot 43,5\cdot 1,31\cdot 1,2={\underline {358,32kN}}>\Delta F_{cd}=201,98kN~}
-Ergebnis MB_Baustatik:
vom Momentennullpunkt:
⇒ 
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