Metoda analityczna

1) Obliczam wysokość, powierzchnie ściany:

H = 4 + 3 + 6 + 2 = 15 m

A = 15 x 10 = 150 m²

N_x = ρ x g x y_s x A

y_s = ½ H = ½ x 15 = 7,5 m

ρ x g = 1050 x 9,81 = 10300,5 kg/m² x s²

N_x = 10300,5 x 7,5 x 150 = 11588063 N

Y_n = 2/3 H = 2/3 x 15 = 10,0 m

2) Obliczam składowe sił:

N_y = ∑ N_yi

N_y1 = ρ x g x V₁

V₁ = 0,2146 x R² x 10 = 0,2146 x 16 x 10 = 34,34 m ³

N_y1 = 10300,5 x 34,34 = 353719,17 N

N_y2 = ρ x g x V₂

V₂ = 4 x 13 x 10 -½ (4 x 6 x 10)= 400 m³

N_y2 = 10300,5 x 400 = 4120200 N

N_y3 = ρ x g x V₃

V₃ = ½ x 8 x 6 x 10 = 240 m³

N_y3 = 10300,5 x 240 = 2472120 N

N_y4 = ρ x g x V₄

V₄ = 15 x 8 x 10 - 2 x 8 x 10 - ½ (6 x 8 x 10)= 800 m³

N_y4 = 10300,5 x 800 = 8240400 N

3)

N_y = N_y1 + N_y2 + N_y3 + N_y4 = ρ x g ( -34,34 + 400 - 240 + 800) = 10300,5 x 925,66 = 9534761 N

4)

N = Ny² + Nx² = √(9534761² + 11588063² ) = 15006498,59

Tgα = N_y/N_x = 0,82281

α = 39^o

N_y*x= N_y1*x₁ + N_y2*x₂ + N_y3*x₃ + N_y4*x₄ = -353719,17 *2,122 + 4120200 *2,5 - 2472120 *3,33 + 8240400 *4 = 34279348 N

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