1. November 2024

Berechnung der Stablast

q = 1.00 kN / m^{2}

h_{1} = 4.00 m

h_{2} = 6.00 m

b_{ges} = 12.00 m

α = \arctan (\frac{h_{2} - h_{1}}{b_{ges}}) = \arctan (\frac{6.000 - 4.000}{12.000}) = 9.46 °

b_{1} = \tan (α) \cdot h_{1} = \tan (9.46 °) \cdot 4.000 = 0.667 m

l_{1} = \sqrt{b_{1}^{2} + h_{1}^{2}} = \sqrt{0 . 667^{2} + 4 . 000^{2}} = 4.055 m

l_{2} = \cos (α) \cdot h_{2} = \cos (9.46 °) \cdot 6.000 = 5.918 m

A_{R} = \frac{b_{1} \cdot h_{1}}{2} = \frac{0.667 \cdot 4.000}{2} = 1.335 m^{2}

l_{ges} = \sqrt{b_{ges}^{2} + {(h_{2} - h_{1})}^{2}} = \sqrt{12 . 000^{2} + {(6.000 - 4.000)}^{2}} = 12.166 m

q_{c} = \frac{q \cdot A_{R}}{l_{ges}} = \frac{1.00 \cdot 1.333}{12.166} = 0.110 kN / m

q_{2} = q_{c} + l_{1} \cdot q = 0.110 + 4.055 \cdot 1.000 = 4.165 kN / m

q_{5} = q_{c} + l_{2} \cdot q = 0.110 + 5.918 \cdot 1.000 = 6.028 kN / m

q_{4} = q_{c} = 0.110 kN / m

q	Lastgröße Flächenlast
A_R	Restfläche (im Bild 4 rot markiert)
q_c	konstanter Lastanteil auf belasteten Stab
q₂	Stablast Knoten 2
q₅	Stablast Knoten 5
q₄	Stablast Knoten 4

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