同济大学理论力学课件
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[ AB ] FA A [ BC ] C FC
FB1 B F B FB1
FB2
[铰 B ]
B FB2
7
P3 习题:3(a)
A P1 B P2 C A FAx FAy [ 整体 ] P1 B P2 C FC D FD D
P3 习题:3(a)
A FAx FAy [ AB ] P1 FBy F Bx B FBx B FBy P2 C FC [ BD ] D FD
γ α
FR'
β
H C
y
B
FR' = 5 i + 10 j + 5 k (kN) MOx = 0 MOy = - F1·OA + M34 = 0 MOz = F2·OA - F5·OC = 0
x
A
'= 5 FR √6 kN
—
MO = 0
FR = FR'
11
P4 习题:2 F2 z
M h MO
z
y
b
O
MOy = F2·h - M = 20 N·m α ' = 90° MOz = F1·l - F2·b = 10 N·m β ' = 26.57° MO = 10 √5 N·m
—
γ ' = 63.43°
z
z
y
M'
MOy
⊥
M⊥ M∥ O
x
y
' M⊥
MOz
x
O
12
P4 习题:2 z
M⊥
y
O M∥ =
' FR M∥
Mz My O Mx
— Mx = -Fy l = -25√2 N·m — Mz = Fy l = 25√2 N·m z
MO γ′
y x
α′ O
β′
O
y
x
— — MO = - 25 √2 ( i + j - k )(N·m) MO = 25√6 N·m 1 cosα′= - — — √3 1 cosβ′= - — — √3 1 cosγ′= — — √3
E G O F1 A F2 D H F F3 C 4 F5 y B G
z
E H C B D M34 F5 y
O F1 A F2
x
x
M34 = F3·OA j = 6 j (kN·m)
P4 习题:1
向O点简化:
' = F = 5 kN FRx 5
z
cosα = — — √6
2 G O 1 E D
' = F = 10 kN cosβ = — FRy — 2 √6 1 ' = F = 5 kN cosγ = — FRz — 1 √6
5
P2 习题:2(b)
[ AB ] B F1 C FA A B F1 C A E C D FA A E B F1 FD O F2 D FE FC FC C E FD O F2 D FE [ 轮O ]
O F2
[ 整体 ]
6
P2 习题:2(c)
A C FA A C FC [ 整体 ]
B F
B F
P2 习题:2(c)
2
P1 习题:3 z
z
A
F l1 y l3 O x l=
MOA l MO
A
F l1 y
l3 O x Mx = Fl2 l2 My = Mz = 0
α
l2
MO = Mx = Fl2 i
MOA = MOcosα =
l122+ + l22b +2 l32 a + cosα = l1/ l Fl1l2 a l122+ + l22b +2 l32 a +
8
P3 习题:3(b)
P A D O1 O2 O3 C B
[ AO1 ] FA A FD O1 FO1 D O3 FO3 [ DO3 ]
P A FA C F Cx FCy B [ AB ] A FA
P C FCy B
P3 习题:3(b)
F FCx Cy FCy C D FD [ CO2 ] FO2 O2 C D FD
l
x F1
y
MOy O
MOz ' FR
x
' = F = 100 N FRx 2
FR' = 100 i + 100 j (N)
' = 100 FR √2 N
向O点简化:
' = F = 100 N FRy 1 ' =0 FRz
—
α = β = 45° γ = 90°
P4 习题:2
MOx = 0
MO = 20 j + 10 k (N·m)
P2 习题:1(a)
O A B O
FNA
A
PB
FNB
[圆O]
3
P2 习题:1(b)
[ 整体 ] F
B C C A O C C
F
B
O A
FO FA [ AB ] F
B C
C
O
FC
A
FC [ OC ]
FO FA
P2 习题:1(b)
[ 整体 ] F
B C C A O C C
F
B
O A
FAx
FO [ AB ]
FD D [ 整体 ] [ BCD ]
P3 习题:3(c)
FE E FAx [ AB ] A FAy E FE B FBy FBx FBx FBy F1 B FB
[铰 B ] O FO2 A [ OE ] FO1 [ OD ] O D FD [铰 O ] FO2 FOx
FO1
O F Oy
10
P4 习题:1 z
P1 习题:1 sinϕ = 3/ 5 cosϕ = 4/ 5
sinθ = 4/ 5 cosθ = 3/ 5
F D k
Fx = Fcosϕ sinθ = 64 N Fy = Fcosϕ cosθ = 48 N Fz = Fsinϕ = 60 N
F D Fz Fx C Fy A
ϕ
l2
B
ϕ
B
θ
i j l1
A
θ
l3
C
F = Fx i + Fy j + Fz k = 64 i + 48 j + 60 k (N)
P1 习题:1
ϕ
l2
B FAB α
F D
l=
l122+ + l22b +2 l32 a += 25 cm
θ
l
γ
A
cosα = l1/ l = 15/ 25 cosβ = l2/ l = 16/ 25 cosγ = l3/ l = 12/ 25
FO2x
O2 FO2y P
P C B A D O3 [ 整体 ] O1 FO2 FO3 FO1 O2 O3 FO3 C B
A D O1 FO1 FO2x O2 FO2y
9
P3 习题:3(c)
A E B
F1
F2 C
O D A FAx FAy E B F1 F2 C FB B F2 C
O FOx FOy D
F
B C
FAy
C O
FC
A
FC [ OC ]
FO FAy
FAx
4
P2 习题:2(a)
A F1 O A F1 FOx P O FOy [ 整体 ] B FB F2 P B F2
P2 习题:2(a)
FAB A
[ AB ]
B FBA A F1 FOx P O FOy [ 轮O ] FAB FB [ 滑块 ] FBA B F2
l3
C
β
l1
FAB = Fxcosα + Fycosβ + Fzcosγ = 97.92 N
1
P1 习题:2 z
F O Fx Fy
z
y
O
y
x — √2 √2 N Fx = - — F = - 50 2 —
x — — 2 √ Fy = — F = 50√2 N 2
Fz = 0
P1 习题:2 — My = -|Fx|l = -25√2 N·m z
x
— — 2 √ ' — MOy = 10 2 N·m = M⊥ √ 2 — 2 )2 +( M2' )2 = 10 3 N·m M √ ( Oz a + b ⊥ +
M⊥ =
最终结果: 力螺旋
√6 a= — = — m = 12.25 cm ' 20 F
M⊥
R
—
13
ຫໍສະໝຸດ Baidu
FB1 B F B FB1
FB2
[铰 B ]
B FB2
7
P3 习题:3(a)
A P1 B P2 C A FAx FAy [ 整体 ] P1 B P2 C FC D FD D
P3 习题:3(a)
A FAx FAy [ AB ] P1 FBy F Bx B FBx B FBy P2 C FC [ BD ] D FD
γ α
FR'
β
H C
y
B
FR' = 5 i + 10 j + 5 k (kN) MOx = 0 MOy = - F1·OA + M34 = 0 MOz = F2·OA - F5·OC = 0
x
A
'= 5 FR √6 kN
—
MO = 0
FR = FR'
11
P4 习题:2 F2 z
M h MO
z
y
b
O
MOy = F2·h - M = 20 N·m α ' = 90° MOz = F1·l - F2·b = 10 N·m β ' = 26.57° MO = 10 √5 N·m
—
γ ' = 63.43°
z
z
y
M'
MOy
⊥
M⊥ M∥ O
x
y
' M⊥
MOz
x
O
12
P4 习题:2 z
M⊥
y
O M∥ =
' FR M∥
Mz My O Mx
— Mx = -Fy l = -25√2 N·m — Mz = Fy l = 25√2 N·m z
MO γ′
y x
α′ O
β′
O
y
x
— — MO = - 25 √2 ( i + j - k )(N·m) MO = 25√6 N·m 1 cosα′= - — — √3 1 cosβ′= - — — √3 1 cosγ′= — — √3
E G O F1 A F2 D H F F3 C 4 F5 y B G
z
E H C B D M34 F5 y
O F1 A F2
x
x
M34 = F3·OA j = 6 j (kN·m)
P4 习题:1
向O点简化:
' = F = 5 kN FRx 5
z
cosα = — — √6
2 G O 1 E D
' = F = 10 kN cosβ = — FRy — 2 √6 1 ' = F = 5 kN cosγ = — FRz — 1 √6
5
P2 习题:2(b)
[ AB ] B F1 C FA A B F1 C A E C D FA A E B F1 FD O F2 D FE FC FC C E FD O F2 D FE [ 轮O ]
O F2
[ 整体 ]
6
P2 习题:2(c)
A C FA A C FC [ 整体 ]
B F
B F
P2 习题:2(c)
2
P1 习题:3 z
z
A
F l1 y l3 O x l=
MOA l MO
A
F l1 y
l3 O x Mx = Fl2 l2 My = Mz = 0
α
l2
MO = Mx = Fl2 i
MOA = MOcosα =
l122+ + l22b +2 l32 a + cosα = l1/ l Fl1l2 a l122+ + l22b +2 l32 a +
8
P3 习题:3(b)
P A D O1 O2 O3 C B
[ AO1 ] FA A FD O1 FO1 D O3 FO3 [ DO3 ]
P A FA C F Cx FCy B [ AB ] A FA
P C FCy B
P3 习题:3(b)
F FCx Cy FCy C D FD [ CO2 ] FO2 O2 C D FD
l
x F1
y
MOy O
MOz ' FR
x
' = F = 100 N FRx 2
FR' = 100 i + 100 j (N)
' = 100 FR √2 N
向O点简化:
' = F = 100 N FRy 1 ' =0 FRz
—
α = β = 45° γ = 90°
P4 习题:2
MOx = 0
MO = 20 j + 10 k (N·m)
P2 习题:1(a)
O A B O
FNA
A
PB
FNB
[圆O]
3
P2 习题:1(b)
[ 整体 ] F
B C C A O C C
F
B
O A
FO FA [ AB ] F
B C
C
O
FC
A
FC [ OC ]
FO FA
P2 习题:1(b)
[ 整体 ] F
B C C A O C C
F
B
O A
FAx
FO [ AB ]
FD D [ 整体 ] [ BCD ]
P3 习题:3(c)
FE E FAx [ AB ] A FAy E FE B FBy FBx FBx FBy F1 B FB
[铰 B ] O FO2 A [ OE ] FO1 [ OD ] O D FD [铰 O ] FO2 FOx
FO1
O F Oy
10
P4 习题:1 z
P1 习题:1 sinϕ = 3/ 5 cosϕ = 4/ 5
sinθ = 4/ 5 cosθ = 3/ 5
F D k
Fx = Fcosϕ sinθ = 64 N Fy = Fcosϕ cosθ = 48 N Fz = Fsinϕ = 60 N
F D Fz Fx C Fy A
ϕ
l2
B
ϕ
B
θ
i j l1
A
θ
l3
C
F = Fx i + Fy j + Fz k = 64 i + 48 j + 60 k (N)
P1 习题:1
ϕ
l2
B FAB α
F D
l=
l122+ + l22b +2 l32 a += 25 cm
θ
l
γ
A
cosα = l1/ l = 15/ 25 cosβ = l2/ l = 16/ 25 cosγ = l3/ l = 12/ 25
FO2x
O2 FO2y P
P C B A D O3 [ 整体 ] O1 FO2 FO3 FO1 O2 O3 FO3 C B
A D O1 FO1 FO2x O2 FO2y
9
P3 习题:3(c)
A E B
F1
F2 C
O D A FAx FAy E B F1 F2 C FB B F2 C
O FOx FOy D
F
B C
FAy
C O
FC
A
FC [ OC ]
FO FAy
FAx
4
P2 习题:2(a)
A F1 O A F1 FOx P O FOy [ 整体 ] B FB F2 P B F2
P2 习题:2(a)
FAB A
[ AB ]
B FBA A F1 FOx P O FOy [ 轮O ] FAB FB [ 滑块 ] FBA B F2
l3
C
β
l1
FAB = Fxcosα + Fycosβ + Fzcosγ = 97.92 N
1
P1 习题:2 z
F O Fx Fy
z
y
O
y
x — √2 √2 N Fx = - — F = - 50 2 —
x — — 2 √ Fy = — F = 50√2 N 2
Fz = 0
P1 习题:2 — My = -|Fx|l = -25√2 N·m z
x
— — 2 √ ' — MOy = 10 2 N·m = M⊥ √ 2 — 2 )2 +( M2' )2 = 10 3 N·m M √ ( Oz a + b ⊥ +
M⊥ =
最终结果: 力螺旋
√6 a= — = — m = 12.25 cm ' 20 F
M⊥
R
—
13
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