ZADANIE 2
Dane :
a = 2,5 m
b = 3,5 m
c = 4,8 m
P = 5 kN
M = 1 kNm
q = 6 kN/m
EI = const.
1.
Schemat układu statycznie niewyznaczalnego.
2.
Stopień statycznej niewyznaczalności.
SSN = w – 3t
SSN = 6 -3 = 3
3.
Układ podstawowy
4.
Obciążenie układu podstawowego
a)
siłami rzeczywistymi
b)
siłami jednostkowymi w miejscu odrzuconych więzów
5.
Obliczenie elementów układu równań kanonicznych metodą sił – przemieszczenia w
miejscu i kierunku odrzuconych więzów
EI
EI
EI
EI
EI
EI
EI
EI
EI
EI
EI
EI
EI
EI
EI
EI
ds
EI
M
M
ds
EI
M
M
ds
EI
M
M
ds
EI
M
M
ds
EI
M
M
P
P
P
P
P
P
31
,
573
2
16
,
188
23
,
479
6
,
9
3
1
8
,
4
3
2
5
,
3
8
,
4
2
1
8
,
4
3
1
6
,
9
3
2
5
,
3
6
,
9
2
1
2
1
8
,
4
3
2
8
,
4
8
,
4
2
1
6
,
9
8
,
4
6
,
9
1
92
,
10260
2
79
,
3641
03
,
8440
8
,
4
2
1
6
,
9
2
1
5
,
3
8
5
,
3
1
3
2
6
,
9
3
1
8
,
4
3
2
5
,
3
12
,
69
2
1
8
,
4
3
1
6
,
9
3
2
5
,
3
67
,
206
2
1
2
1
6
,
9
8
,
4
92
,
164
2
1
6
,
9
8
,
4
92
,
188
2
1
8
,
4
2
1
8
,
4
8
8
,
4
1
3
2
8
,
4
3
1
8
,
4
12
,
69
2
1
1
93
,
1925
8
,
4
3
1
8
,
4
92
,
164
2
1
8
,
4
3
2
8
,
4
92
,
188
2
1
8
,
4
3
2
42
,
5
75
,
17
2
1
8
,
4
3
1
42
,
5
1
2
1
1
59
,
110
6
,
9
8
,
4
8
,
4
2
1
1
489
,
78
8
,
4
3
2
8
,
4
8
,
4
2
1
8
,
4
3
2
42
,
5
8
,
4
2
1
1
22
2
2
2
1
21
12
11
2
2
22
2
2
1
1
2
1
21
12
1
1
11
=
+
=
⋅
+
⋅
⋅
⋅
⋅
+
⋅
+
⋅
⋅
⋅
⋅
+
+
⋅
⋅
⋅
⋅
+
⋅
⋅
=
−
=
−
−
=
=
⋅
+
⋅
⋅
⋅
⋅
⋅
+
+
⋅
+
⋅
⋅
⋅
⋅
−
⋅
+
⋅
⋅
⋅
⋅
−
+
+
⋅
⋅
⋅
−
⋅
⋅
⋅
−
⋅
⋅
⋅
⋅
⋅
−
⋅
⋅
⋅
⋅
−
=
−
=
⋅
⋅
⋅
⋅
−
⋅
⋅
⋅
⋅
−
−
⋅
⋅
⋅
⋅
+
⋅
⋅
⋅
⋅
=
=
⋅
⋅
⋅
=
=
=
⋅
⋅
⋅
⋅
+
⋅
⋅
⋅
⋅
=
⋅
=
⋅
=
⋅
=
⋅
=
=
⋅
=
∑ ∫
∑ ∫
∑ ∫
∑ ∫
∑ ∫
δ
δ
δ
δ
δ
δ
δ
δ
δ
δ
δ
δ
kN
X
kN
X
X
X
X
X
EI
X
EI
X
EI
EI
X
EI
X
EI
X
X
X
X
P
P
08
,
31
25
,
19
0
92
,
10260
31
,
573
59
,
110
0
93
,
1925
59
,
110
489
,
78
0
92
,
10260
31
,
573
59
,
110
0
93
,
1925
59
,
110
489
,
78
0
0
2
1
2
1
2
1
2
1
2
1
2
2
22
1
21
1
2
12
1
11
=
−
=
=
−
⋅
+
⋅
=
−
⋅
+
⋅
=
−
⋅
+
⋅
=
−
⋅
+
⋅
=
+
⋅
+
⋅
=
+
⋅
+
⋅
δ
δ
δ
δ
δ
δ
6.
Rozwiązanie układu równań kanonicznych i obliczenie rzeczywistych wartości sił w
miejscu odrzuconych więzów.
08
,
31
)
25
,
19
(
08
,
31
)
25
,
19
(
08
,
31
)
25
,
19
(
2
1
2
1
2
1
2
2
1
1
2
2
1
1
2
2
1
1
⋅
+
−
⋅
+
=
⋅
+
−
⋅
+
=
⋅
+
−
⋅
+
=
⋅
+
⋅
+
=
⋅
+
⋅
+
=
⋅
+
⋅
+
=
N
N
N
N
T
T
T
T
M
M
M
M
X
N
X
N
N
N
X
T
X
T
T
T
X
M
X
M
M
M
p
n
p
p
n
p
p
n
p
p
n
p
p
n
p
p
n
p
w punkcie A
kN
N
kN
T
kNm
M
n
p
n
p
n
p
66
,
8
08
,
31
0
)
25
,
19
(
)
45
,
0
(
0
94
,
16
08
,
31
0
)
25
,
19
(
)
88
,
0
(
0
1
08
,
31
0
)
25
,
19
(
0
1
=
⋅
+
−
⋅
−
+
=
=
⋅
+
−
⋅
−
+
=
=
⋅
+
−
⋅
+
=
w punkcie D
kN
N
kN
T
M
n
p
n
p
n
p
5
08
,
31
0
)
25
,
19
(
0
5
08
,
31
08
,
31
)
1
(
)
25
,
19
(
0
0
0
08
,
31
0
)
25
,
19
(
0
0
−
=
⋅
+
−
⋅
+
−
=
−
=
⋅
−
+
−
⋅
+
=
=
⋅
+
−
⋅
+
=
7.
Wykres sił wewnętrznych w układzie rzeczywistym statycznie niewyznaczalnym.
8.
Obliczam kąt obrotu w punkcie B – wpływ M.
EI
EI
ds
EI
M
M
k
n
p
k
2
,
361
1
8
,
4
05
,
17
2
1
1
8
,
4
45
,
133
2
1
1
0
=
⋅
⋅
⋅
+
⋅
⋅
⋅
=
⋅
=
∑∫
ϕ
ϕ
dla I 360
E = 205 GPa
I = 19610 cm
4
0
00898
,
0
10
19610
10
205
2
,
361
8
6
≅
−
=
⋅
⋅
⋅
−
=
−
k
ϕ
9.
Sprawdzenie kinematyczne:
-
układ do sprawdzenia
-
sporządzam wykresy sił jednostkowych od X1, X2 dla M
-
obliczam wartości na kierunkach X1 i X2
0
0
0
404
0
2
64
,
120
36
,
344
0
57
,
0
2
1
1
2
1
5
,
3
8
5
,
3
6
3
2
57
,
0
3
1
1
3
2
5
,
3
7
,
91
2
1
2
1
8
,
4
5
,
0
45
,
133
1
8
,
4
05
,
17
2
1
57
,
0
2
1
8
,
4
8
8
,
4
6
3
2
1
0
0
0
0
09
,
187
0
8
,
4
5
,
0
42
,
5
8
42
,
5
6
3
2
8
,
4
3
2
42
,
5
65
,
74
2
1
8
,
4
3
1
8
,
4
45
,
133
2
1
8
,
4
3
2
8
,
4
05
,
17
2
1
1
0
2
2
2
2
1
=
≅
−
=
−
−
=
⋅
+
⋅
⋅
⋅
⋅
⋅
+
⋅
+
⋅
⋅
⋅
⋅
−
+
+
⋅
⋅
−
⋅
⋅
⋅
−
⋅
⋅
⋅
⋅
⋅
=
⋅
=
=
=
⋅
⋅
⋅
⋅
⋅
+
⋅
⋅
⋅
⋅
−
⋅
⋅
⋅
⋅
+
⋅
⋅
⋅
⋅
=
⋅
∑∫
∑∫
EI
EI
EI
EI
EI
ds
EI
M
M
EI
EI
ds
EI
M
M
n
p
X
n
p
X