Laboratorium Wytrzymałość materiałów	Ćwiczenie nr 1	Temat: Projekt kratownicy płaskiej.
	Grupa M 22	Ocena końcowa

Dane:

a = 3 [m]

P1 = 6000 [N]	P2 = 13000 [N]	P3 = 4500 [N]
G = 180^0	D = 270^0	E = 45^0

Obliczenia.

p = 2w - 3,

w = 7,

p = 11.

ΣMi_A = P₂ ⋅ 3a + P₃ ⋅ cos 45⁰ ⋅ a - P₃ ⋅ sin 45⁰ ⋅ 2a - R_F ⋅ a - P₁ ⋅ a = 0,

R_F = 29818 [N] .

Σx = R_Ax + P₁ - P₃ ⋅ cos 45⁰ = 0,

R_Ax = - 2818 [N] .

Σy = R_Ay - P₂ + R_F + P₃ ⋅ sin 45⁰ = 0,

R_Ay = -20000 [N] .

Wêze³ D:

Σy = - S₄ ⋅ sin 45⁰ - P₂ = 0,

S₄ = - 18384 [N] .

Σx = - S₃ - S₄ ⋅ sin 45⁰ = 0,

S₃ = -13000 [N] .

Węzeł C:

Σx = S₃ - S₂ = 0,

S₂ = -13000 [N] .

Σy = S₁₁ = 0,

S₁₁ = 0 [N] .

Węzeł E:

Σy = S₁₁ + S₁₀ ⋅ sin 45⁰ + S₄ ⋅ cos 45⁰ + P₃ ⋅ sin 45⁰ = 0,

S₁₀ = 13885 [N] .

Σx = S₄ ⋅ cos 45⁰ - S₁₀ ⋅ cos 45⁰ - S₅ - P₃ ⋅ cos 45⁰ = 0,

S₅ = -26000 [N] .

Wêze³ B:

Σy = - S₉ - S₁₀ ⋅ sin 45⁰ = 0,

S₉ = -9818 [N] .

Σx = S₂ - S₁ - S₁₀ ⋅ cos 45⁰ = 0,

S₁ = 22818 [N] .

Wêze³ A:

Σx = S₁ + R_Ax + S₈ ⋅ cos 45⁰ = 0,

S₈ = - 28284 [N] .

Σy = R_Ay - S₇ - S₈ ⋅ sin 45⁰ = 0,

S₇ = 0 [N] .

Węzeł G:

Σx = P₁ + S₆ = 0,

S₆ = -6000 [N] .

Σy = S₇ = 0,

S₇ = 0 .

Wyniki:

S1 = 22818 [N]	pręt rozciągany	S7 = 0 [N]
S2 = -13000 [N]	pręt ściskany	S8 = - 28284 [N]	pręt ściskany
S3 = -13000 [N]	pręt ściskany	S9 = - 9818 [N]	pręt ściskany
S4 = - 18384 [N]	pręt ściskany	S10 = 13885 [N]	pręt rozciągany
S5 = -26000 [N]	pręt ściskany	S11 = 0 [N]
S6 = -6000 [N]	pręt ściskany

Sprawdzenie.

Węzeł F:

Σx = S₅ - S₆ - S₈ ⋅ cos 45⁰ = 0,

0 = 0.

Σy = S₉ + R_F + S₈ ⋅ sin 45⁰ = 0,

0 = 0.

Obliczenia są wykonane prawidłowo.

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