Rysunek ;

Dane :

P₁ = 5000 [ N ]

P2 = 5500 [N]

P1w = 0 [N]

P2w = 2200 [N]

P1r = 1820 [N]

Pr2 = 2000 [N]

Ms = 425000 [Nmm ]

a = 50 [mm]

b = 100 [mm]

c = 180 [mm]

d = 100 [mm]

r₁= 80 [mm]

r₂ = 150 [mm]

α = 90°

Obliczam reakcje :

ΣMA = - P1r ⋅b - P2 ⋅( b+c ) + R_Bx (c + b + d) = 0

ΣM_A = R_AX ⋅ ( b + c + d ) - P_1r ⋅ (c + d ) - P₂ ⋅ d = 0

ΣPiz = P_2w - R_BZ

R_BZ = - P_2w

R_BZ = 2200 [N]

Mg = P_2w ⋅ r₂

ΣMiA = - P1 ⋅ b - P_2r ( b + c ) - Mg + R_B ( b + c + d ) = 0

= 3657.8 [N]

ΣMiB = R_AY ⋅ (b+ c + d ) - P1 ⋅ ( c + d ) - P_2r ⋅ d + Mg = 0

ΣPiz = R_BZ - P_2w = 0 Mg = P_2r ⋅ r₂

R_BZ = 2200 [N]

Wartości momentów na osi X - Z :

0 ≤ z ≤ a

M.(z). = 0

a ≤ z ≤ (a + b )

M.(z). = R_AX ⋅ ( z - a )

M_{.(z = a).} = R_AX ⋅ ( a - a ) = 0

M_{.(z = a + b )}. = R_AX ⋅ ( a - a + b ) = R_AX ⋅ b = 2788.42 ⋅ 100 = 278842 [ Nm ]

( a + b ) ≤ z ≤ (a + b + c )

M.(z). = R_AX ⋅ ( z - a ) - P_1r [ z - ( a + b )]

M_{.(z = a + b )}. = R_AX ⋅ ( a - a + b ) = R_AX ⋅ b = 2788.42 ⋅ 100 = 278842 [ Nm ]

M_{.(z = a + b + c )}. = R_AX ⋅ [( a + b + c) - a ] - P_1r [ ( a + b + c) - ( a + b )] =

= 2788.42 ⋅ 280 - 1820 ⋅ 180 = 453157.6 [ Nm ]

( a + b + c ) ≤ z ≤ (a + b + c + d )

M.(z). = R_AX ⋅ ( z - a ) - P_1r [ z - ( a + b )] - P₂ [ z - ( a+ b + c )]

M_{.(z = a + b + c )}. = R_AX ⋅ [( a + b + c) - a ] - P_1r [ ( a + b + c) - ( a + b )] =

= 2788.42 ⋅ 280 - 1820 ⋅ 180 = 453157.6 [ Nm ]

M_{.(z = a + b + c + d )}. = R_AX ⋅ [( a + b + c + d ) - a ] - P_1r [ ( a + b + c + d ) - ( a + b )] -

- P₂ [ ( a + b + c + d ) - ( a + b + c )] = 1059599.6 - 5096000 - 550000 = 0 [Nm ]

Wartości momentów na osiach Y - Z

Mg = P_2r ⋅ r₂

0 ≤ z ≤ a

M.(z). = 0

a ≤ z ≤ (a + b )

M.(z). = - R_AY ⋅ ( z - a )

M_{.(z = a).} = - R_AY ⋅ ( a - a ) = 0

M_{.(z = a + b )}. = - R_AY ⋅ ( a - a + b ) = - R_AY ⋅ b = - 3342.1052 ⋅ 100 = - 334210.52 [ Nm ]

( a + b ) ≤ z ≤ (a + b + c )

M.(z). = - R_AY ⋅ ( z - a ) + P₁ [ z - ( a + b )]

M_{.(z = a + b )}. = - R_AY ⋅ ( a - a + b ) = R_AX ⋅ b = - R_AY ⋅ b = 3342.1052 ⋅ 100 = - 334210.52 [ Nm ]

M_{.(z = a + b + c )}. = - R_AY ⋅ [( a + b + c) - a ] + P₁ [ ( a + b + c) - ( a + b )] =

= - 3342.1052 ⋅ 280 + 5000 ⋅ 180 = - 35788 [ Nm ]

( a + b + c ) ≤ z ≤ (a + b + c + d )

M.(z). = - R_AY ⋅ ( z - a ) + P₁ [ z - ( a + b )] - Mg

M_{.(z = a + b + c )}. = - R_AY ⋅ [( a + b + c) - a ] + P₁ [ ( a + b + c) - ( a + b )] - Mg =

= - 3342.1052 ⋅ 280 + 5000 ⋅ 180 - 330000 = - 365788 [ Nm ]

M_{.(z = a + b + c + d )}. = - R_AY ⋅ [( a + b + c + d ) - a ] + P₁ [ ( a + b + c + d ) - ( a + b )] +

+ P2r [(a + b + c + d ) - ( a + b + c )]- Mg = - 3342.1052 ⋅ 380 + 5000 ⋅ 280 - 330000 +

2000 ⋅ 100 = 0 [ Nm ]

Momenty skręcające :

ΣMs = Ms - P₁ ⋅ r₁ + P₂ ⋅ r₂ = 0

Ms = P₁ ⋅ r₁ - P₂ ⋅ r₂

Ms = 5000 ⋅ 80 - 5500 ⋅ 150 [ Nmm ]

Ms₁ = - 425000 ; (425000 )

Wykresy momentów :

0 ≤ z ≤ a + b

Ms = Ms₁ = 425000 [Nmm ]

( a + b ) ≤ z ≤ (a + b + c )

Ms = Ms₁ + P₁ ⋅ r₁ = 825000 [Nmm ]

( a + b + c ) ≤ z ≤ (a + b + c + d )

Ms = Ms₁ + P₁ ⋅ r₁ - P₂ ⋅ r₂ = 425000 + 400000 - 825000 = 0 [Nmm ]

Momenty wypadkowe:

Momenty zastępcze :

Mzc =

• ≤ z ≤ a + b

Mz =
= 355580,5 [Nmm]

W punkcie 1 moment zastępczy wynosi :

W punkcie 2 moment zastępczy wynosi :

W punkcie 3 moment zastępczy wynosi :

M_Z3 = 0

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