Расчетно-графические работы по статике. Божкова Л.В - 39 стр.

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МАМИ | Москва

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39
Составим уравнение равновесия:
∑
=
k
kx
F ;0 ,0sincoscos
1
=
⋅
⋅
−
⋅
−
+
β
α
γ
TPXX
AB
(1)
∑
=
k
ky
F ;0 ,0coscos
=
⋅
⋅
−
β
α
TY
A
(2)
∑
k
kz
F ;0 ,0sinsin
21
=
⋅
+
−
⋅
+
+
α
γ
TPPZZ
BA
(3)
(
)
∑
=
k
kx
Fm ;0
r
,0sin
2
2
=⋅⋅+⋅+⋅−
aTaZ
a
P
A
α
(4)
(
)
;0=
∑
k
k
y
Fm
r
,0sin
2
sin
21
=⋅⋅−⋅+⋅⋅−
bT
b
PbP
αγ
(5)
(
)
∑
=
k
kz
Fm ;0
r
.0sincoscoscos
=
⋅
⋅
⋅
+
⋅
⋅
⋅
−
⋅
−
aTbTaXM
A
β
α
β
α
(6)
Решая систему уравнений
(
)
(
)
,61
−
определим:
из (5)
( )
,35sin
2sin
1
1
2
HP
P
T =
⋅−⋅= γ
α
из (6)
( )
,7,46sincoscoscos HTT
a
b
a
M
X
A
=⋅⋅+⋅⋅⋅−= βαβα
из (4)
( )
,1,20sin
2
2
HT
P
Z
A
−=⋅−= α
из (2)
(
)
,0,15coscos HTY
A
=
⋅
⋅
=
β
α
из (3)
(
)
HTZPPZ
AB
3sinsin
12
=
⋅
−
−
⋅
−
=
α
γ
,
из (1)
(
)
,45,48sincoscos
1
HXTPX
AB
−
=
−
⋅
⋅
+
⋅
=
β
α
γ
                                       39
         Составим уравнение равновесия:

         ∑ Fkx = 0;            X B + X A − P1 ⋅ cos γ − T ⋅ cosα ⋅ sin β = 0,               (1)
         k


         ∑ Fky = 0;           YA − T ⋅ cosα ⋅ cos β = 0,                                    (2)
         k


         ∑ Fkz = 0;           Z A + Z B + P1 ⋅ sin γ − P2 + T ⋅ sin α = 0,                  (3)
         k



         ∑ mx (Fk ) = 0;
                r                      a
                              − P2 ⋅     + Z A ⋅ a + T ⋅ sin α ⋅ a = 0,                     (4)
         k                             2


               ( )
             r                                          b
         ∑ y k = 0;
          m F                 − P1 ⋅ sin γ ⋅ b + P2 ⋅
                                                        2
                                                          − T ⋅ sin α ⋅ b = 0,              (5)
         k


               ( )
             r
         ∑ z k = 0;
          m F                 M − X A ⋅ a − T ⋅ cosα ⋅ cos β ⋅ b + T ⋅ cosα ⋅ sin β ⋅ a = 0. (6)
         k


Решая систему уравнений (1) − (6 ), определим:

                      1  P2               
из (5)          T=        ⋅  − P1 ⋅ sin γ  = 35(H ),
                    sin α  2              
                          − ⋅ T ⋅ cos α ⋅ cos β + T ⋅ cos α ⋅ sin β = 46,7(H ),
                      M b
из (6)          XA =
                       a a
                Z A = 2 − T ⋅ sin α = −20,1(H ),
                      P
из (4)
                      2
из (2)          YA = T ⋅ cos α ⋅ cos β = 15,0(H ),

из (3)          Z B = P2 − P1 ⋅ sin γ − Z A − T ⋅ sin α = 3(H ) ,

из (1)          X B = P1 ⋅ cos γ + T ⋅ cos α ⋅ sin β − X A = −48,45(H ),

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