Dr inż. Janusz Dębiński
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
1. Charakterystyki geometryczne przekroju pręta
1.1. Zadania 1
−
16
W tabeli 1.1 przedstawiono położenie punktu A o zadanych współrzędnych w układzie YZ.
Tabela 1.1. Położenie punktu A w układzie współrzędnych
Nr
Układ współrzędnych
1
Y
Z
A
2
Y
Z
A
3
Y
Z
A
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−
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−
Charakterystyki ...
2
Nr
Układ współrzędnych
4
Y
Z
A
5
Y
Z
A
6
Y
Z
A
7
Y
Z
A
8
Y
Z
A
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−
Charakterystyki ...
3
Nr
Układ współrzędnych
9
Y
Z
A
10
Y
Z
A
11
Y
Z
A
12
Y
Z
A
13
Y
Z
A
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−
Charakterystyki ...
4
Nr
Układ współrzędnych
14
Y
Z
A
15
Y
Z
A
16
Y
Z
A
1.2. Zadania 17
−
32
W tabeli 1.2 przedstawiono współrzędne punktu A położonego w układzie współrzędnych YZ.
Tabela 1.2. Współrzędne punktu A
Nr
Współrzędne punktu A
Nr
Współrzędne punktu A
17
A(3,2)
18
A(3,
−
2)
19
A(
−
3,
−
2)
20
A(
−
3,2)
21
A(2,3)
22
A(
−
2,3)
23
A(
−
2,
−
3)
24
A(2,
−
3)
25
A(3,2)
26
A(
−
3,2)
27
A(
−
3,
−
2)
28
A(3,
−
2)
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Nr
Współrzędne punktu A
Nr
Współrzędne punktu A
29
A(2,3)
30
A(
−
2,3)
31
A(
−
2,
−
3)
32
A(2,
−
3)
1.3. Zadania 33
−
36
W tabeli 1.3 przedstawiono wartości momentów statycznych przekrojów prostokątnych w układzie
współrzędnych YZ.
Tabela 1.3. Momenty statyczne przekrojów prostokątnych
Nr
Momenty statyczne w układzie współrzędnych YZ
33
S
Y
=
4,0⋅3,0⋅3,0=36,0 cm
3
S
Z
=
4,0⋅3,0⋅4,0=48,0 cm
3
34
S
Y
=
4,0⋅3,0⋅
−
3,0
=−
36,0 cm
3
S
Z
=
4,0⋅3,0⋅4,0=48,0 cm
3
35
S
Y
=
4,0⋅3,0⋅
−
3,0
=−
36,0 cm
3
S
Z
=
4,0⋅3,0⋅
−
4,0
=−
48,0 cm
3
36
S
Y
=
4,0⋅3,0⋅3,0=36,0 cm
3
S
Z
=
4,0⋅3,0⋅
−
4,0
=−
48,0 cm
3
1.4. Zadania 37
−
52
W tabeli 1.4 przedstawiono wartości momentów statycznych przekrojów będących trójkątami równora-
miennymi w układzie współrzędnych YZ.
Tabela 1.4. Momenty statyczne przekrojów będących trójkątami równoramiennymi
Nr
Momenty statyczne w układzie współrzędnych YZ
37
S
Y
=
1
2
⋅
6,0⋅3,0⋅3,0=27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅5,0=45,0 cm
3
38
S
Y
=
1
2
⋅
6,0⋅3,0⋅
−
2,0
=−
18,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅5,0=45,0 cm
3
39
S
Y
=
1
2
⋅
6,0⋅3,0⋅
−
2,0
=−
18,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅
−
5,0
=−
45,0 cm
3
40
S
Y
=
1
2
⋅
6,0⋅3,0⋅3,0=27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅
−
5,0
=−
45,0 cm
3
41
S
Y
=
1
2
⋅
6,0⋅3,0⋅2,0=18,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅5,0=45,0 cm
3
42
S
Y
=
1
2
⋅
6,0⋅3,0⋅
−
3,0
=−
27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅5,0=45,0 cm
3
43
S
Y
=
1
2
⋅
6,0⋅3,0⋅
−
3,0
=−
27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅
−
5,0
=−
45,0 cm
3
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−
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−
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−
Charakterystyki ...
6
Nr
Momenty statyczne w układzie współrzędnych YZ
44
S
Y
=
1
2
⋅
6,0⋅3,0⋅2,0=18,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅
−
5,0
=−
45,0 cm
3
45
S
Y
=
1
2
⋅
6,0⋅3,0⋅3,0=27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅4,0=36,0 cm
3
46
S
Y
=
1
2
⋅
6,0⋅3,0⋅
−
3,0
=−
27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅4,0=36,0 cm
3
47
S
Y
=
1
2
⋅
6,0⋅3,0⋅
−
3,0
=−
27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅
−
6,0
=−
54,0 cm
3
48
S
Y
=
1
2
⋅
6,0⋅3,0⋅3,0=27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅
−
6,0
=−
54,0 cm
3
49
S
Y
=
1
2
⋅
6,0⋅3,0⋅3,0=27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅6,0=54,0 cm
3
50
S
Y
=
1
2
⋅
6,0⋅3,0⋅
−
3,0
=−
27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅6,0=54,0 cm
3
51
S
Y
=
1
2
⋅
6,0⋅3,0⋅
−
3,0
=−
27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅
−
4,0
=−
36,0 cm
3
52
S
Y
=
1
2
⋅
6,0⋅3,0⋅3,0=27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅
−
4,0
=−
36,0 cm
3
1.5. Zadania 53
−
68
W tabeli 1.5 przedstawiono wartości momentów statycznych przekrojów będących trójkątami prosto -
kątnymi w układzie współrzędnych YZ.
Tabela 1.5. Momenty statyczne przekrojów będących trójkątami prostokątnymi
Nr
Momenty statyczne w układzie współrzędnych YZ
53
S
Y
=
1
2
⋅
6,0⋅3,0⋅3,0=27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅4,0=36,0 cm
3
54
S
Y
=
1
2
⋅
6,0⋅3,0⋅
−
2,0
=−
28,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅4,0=36,0 cm
3
55
S
Y
=
1
2
⋅
6,0⋅3,0⋅
−
2,0
=−
28,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅
−
6,0
=−
54,0 cm
3
56
S
Y
=
1
2
⋅
6,0⋅3,0⋅3,0=27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅
−
6,0
=−
54,0 cm
3
57
S
Y
=
1
2
⋅
6,0⋅3,0⋅2,0=18,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅4,0=36,0 cm
3
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Wytrzymałość materiałów
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−
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−
Charakterystyki ...
7
Nr
Momenty statyczne w układzie współrzędnych YZ
58
S
Y
=
1
2
⋅
6,0⋅3,0⋅
−
3,0
=−
27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅4,0=36,0 cm
3
59
S
Y
=
1
2
⋅
6,0⋅3,0⋅
−
3,0
=−
27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅
−
6,0
=−
54,0 cm
3
60
S
Y
=
1
2
⋅
6,0⋅3,0⋅2,0=18,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅
−
6,0
=−
54,0 cm
3
61
S
Y
=
1
2
⋅
6,0⋅3,0⋅3,0=27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅6,0=54,0 cm
3
62
S
Y
=
1
2
⋅
6,0⋅3,0⋅
−
2,0
=−
18,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅6,0=54,0 cm
3
63
S
Y
=
1
2
⋅
6,0⋅3,0⋅
−
2,0
=−
18,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅
−
4,0
=−
36,0 cm
3
64
S
Y
=
1
2
⋅
6,0⋅3,0⋅3,0=27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅
−
4,0
=−
36,0 cm
3
65
S
Y
=
1
2
⋅
6,0⋅3,0⋅2,0=18,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅6,0=54,0 cm
3
66
S
Y
=
1
2
⋅
6,0⋅3,0⋅
−
3,0
=−
27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅6,0=54,0 cm
3
67
S
Y
=
1
2
⋅
6,0⋅3,0⋅
−
3,0
=−
27,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅
−
4,0
=−
36,0 cm
3
68
S
Y
=
1
2
⋅
6,0⋅3,0⋅2,0=18,0 cm
3
S
Z
=
1
2
⋅
6,0⋅3,0⋅
−
4,0
=−
36,0 cm
3
1.6. Zadania 69
−
72
W tabeli 1.6 przedstawiono przybliżone położenie środka ciężkości przekrojów prętów zbudowanych
z dwóch lub trzech prostokątów.
Tabela 1.6. Położenie środka ciężkości przekrojów prętów
Nr
Położenie środka ciężkości przekroju pręta
69
sc
1
sc
2
sc
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−
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8
Nr
Położenie środka ciężkości przekroju pręta
70
sc
1
sc
2
sc
71
sc
1
sc
2
sc
3
sc
72
sc
1
sc
2
sc
3
sc
1.7. Zadania 73
−
74
W tabeli 1.7 przedstawiono położenie środka ciężkości przekrojów prostokątnego oraz będącego trójką-
tem prostokątnym.
Tabela 1.7. Położenie środka ciężkości przekrojów prostokątnego oraz będącego trójkątem prostokątnym
Nr
Położenie środka ciężkości przekroju
73
a
k
sc
k
2
a
2
a
2
k
2
74
a
k
sc
k
3
2
3
⋅k
a
3
2
3
⋅
a
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−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
9
1.8. Zadania 75
−
76
W tabeli 1.8 przedstawiono momenty bezwładności w układach osi środkowych przekrojów prostokąt-
nego oraz będącego trójkątem prostokątnym.
Tabela 1.8. Momenty bezwładności przekrojów prostokątnego oraz będącego trójkątem prostokątnym
Nr
Momenty bezwładności
75
J
Y
=
J
Ygl
=
a⋅k
3
12
J
Z
=
J
Zgl
=
k⋅a
3
12
76
J
Y
=
J
Ygl
=
a⋅k
3
36
J
Z
=
J
Zgl
=
k⋅a
3
36
1.9. Zadania 77
−
84
W tabeli 1.9 przedstawiono dewiacyjne momenty bezwładności przekrojów będących trójkątami prosto -
kątnymi.
Tabela 1.9. Dewiacyjne momenty bezwładności przekrojów będących trójkątami prostokątnymi
Nr
Dewiacyjny moment bezwładności
Nr
Dewiacyjny moment bezwładności
77
J
YZ
=
J
Y0Z0
=
a
2
⋅
k
2
72
78
J
YZ
=
J
Y0Z0
=−
a
2
⋅
k
2
72
79
J
YZ
=
J
Y0Z0
=−
a
2
⋅
k
2
72
80
J
YZ
=
J
Y0Z0
=
a
2
⋅
k
2
72
81
J
YZ
=
J
Y0Z0
=−
a
2
⋅
k
2
72
82
J
YZ
=
J
Y0Z0
=
a
2
⋅
k
2
72
83
J
YZ
=
J
Y0Z0
=
a
2
⋅
k
2
72
84
J
YZ
=
J
Y0Z0
=−
a
2
⋅
k
2
72
1.10. Zadania 85
−
102
W tabeli 1.10 przedstawiono wartości momentów bezwładności przekrojów prętów walcowanych
w układzie współrzędnych YZ.
Tabela 1.10. Wartości momentów bezwładności przekrojów prętów walcowanych
Nr
Momenty bezwładności
85
J
Y
=
J
Ygl
=
23130 cm
4
J
Z
=
J
Zgl
=
1320cm
4
86
J
Y
=
J
Ygl
=
1320cm
4
J
Z
=
J
Zgl
=
23130 cm
4
87
J
Y
=
J
Ygl
=
605 cm
4
J
Z
=
J
Zgl
=
62,7cm
4
88
J
Y
=
J
Ygl
=
605 cm
4
J
Z
=
J
Zgl
=
62,7 cm
4
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−
odpowiedzi
−
Charakterystyki ...
10
Nr
Momenty bezwładności
89
J
Y
=
J
Ygl
=
62,7 cm
4
J
Z
=
J
Zgl
=
605cm
4
90
J
Y
=
J
Ygl
=
62,7 cm
4
J
Z
=
J
Zgl
=
605cm
4
91
J
Y
=
J
Ygl
=
289 cm
4
J
Z
=
J
Zgl
=
110cm
4
92
J
Y
=
J
Ygl
=
289 cm
4
J
Z
=
J
Zgl
=
110cm
4
93
J
Y
=
J
Ygl
=
110 cm
4
J
Z
=
J
Zgl
=
289 cm
4
94
J
Y
=
J
Ygl
=
110 cm
4
J
Z
=
J
Zgl
=
289 cm
4
95
J
Y
=
J
Ygl
=
289 cm
4
J
Z
=
J
Zgl
=
210 cm
4
96
J
Y
=
J
Ygl
=
289 cm
4
J
Z
=
J
Zgl
=
110cm
4
97
J
Y
=
J
Ygl
=
289 cm
4
J
Z
=
J
Zgl
=
110cm
4
98
J
Y
=
J
Ygl
=
289 cm
4
J
Z
=
J
Zgl
=
110cm
4
99
J
Y
=
J
Ygl
=
110 cm
4
J
Z
=
J
Zgl
=
289 cm
4
100
J
Y
=
J
Ygl
=
110 cm
4
J
Z
=
J
Zgl
=
289 cm
4
101
J
Y
=
J
Ygl
=
110 cm
4
J
Z
=
J
Zgl
=
289 cm
4
102
J
Y
=
J
Ygl
=
110 cm
4
J
Z
=
J
Zgl
=
289 cm
4
1.11. Zadania 103
−
110
W tabeli 1.11 przedstawiono wartości dewiacyjnego momentu bezwładności kątowników nierównora-
miennych w układzie współrzędnych YZ.
Tabela 1.11. Wartości dewiacyjnego momentu bezwładności kątowników nierównoramiennych
Nr
Dewiacyjny moment bezwładności
Nr
Dewiacyjny moment bezwładności
103
J
YZ
=
J
Y0Z0
=−
335,2 cm
4
104
J
YZ
=
J
Y0Z0
=
335,2 cm
4
105
J
YZ
=
J
Y0Z0
=
335,2 cm
4
106
J
YZ
=
J
Y0Z0
=−
335,2 cm
4
107
J
YZ
=
J
Y0Z0
=
335,2 cm
4
108
J
YZ
=
J
Y0Z0
=−
335,2 cm
4
109
J
YZ
=
J
Y0Z0
=−
335,2 cm
4
110
J
YZ
=
J
Y0Z0
=
335,2 cm
4
Dr inż. Janusz Dębiński
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Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
11
1.12. Zadania 111
−
142
W tabeli 1.12 przedstawiono wartości momentów bezwładności przekrojów prostokątnych w układzie
współrzędnych YZ.
Tabela 1.12. Wartości momentów bezwładności przekrojów prostokątnych
Nr
Momenty bezwładności
111
J
Y
=
6,0⋅2,0
3
12
3,0
2
⋅
6,0⋅2,0
J
Z
=
2,0⋅6,0
3
12
5,0
2
⋅
6,0⋅2,0
J
YZ
=
0,03,0⋅5,0⋅6,0⋅2,0
112
J
Y
=
6,0⋅2,0
3
12
−
3,0
2
⋅
6,0⋅2,0
J
Z
=
2,0⋅6,0
3
12
5,0
2
⋅
6,0⋅2,0
J
YZ
=
0,0
−
3,0
⋅
5,0⋅6,0⋅2,0
113
J
Y
=
6,0⋅2,0
3
12
−
3,0
2
⋅
6,0⋅2,0
J
Z
=
2,0⋅6,0
3
12
−
5,0
2
⋅
6,0⋅2,0
J
YZ
=
0,0
−
3,0
⋅
−
5,0
⋅
6,0⋅2,0
114
J
Y
=
6,0⋅2,0
3
12
3,0
2
⋅
6,0⋅2,0
J
Z
=
2,0⋅6,0
3
12
−
5,0
2
⋅
6,0⋅2,0
J
YZ
=
0,03,0⋅
−
5,0
⋅
6,0⋅2,0
115
J
Y
=
6,0⋅2,0
3
12
1,0
2
⋅
6,0⋅2,0
J
Z
=
2,0⋅6,0
3
12
5,0
2
⋅
6,0⋅2,0
J
YZ
=
0,01,0⋅5,0⋅6,0⋅2,0
116
J
Y
=
6,0⋅2,0
3
12
−
1,0
2
⋅
6,0⋅2,0
J
Z
=
2,0⋅6,0
3
12
5,0
2
⋅
6,0⋅2,0
J
YZ
=
0,0
−
1,0
⋅
5,0⋅6,0⋅2,0
117
J
Y
=
6,0⋅2,0
3
12
−
3,0
2
⋅
6,0⋅2,0
J
Z
=
2,0⋅6,0
3
12
3,0
2
⋅
6,0⋅2,0
J
YZ
=
0,0
−
3,0
⋅
3,0⋅6,0⋅2,0
118
J
Y
=
6,0⋅2,0
3
12
−
3,0
2
⋅
6,0⋅2,0
J
Z
=
2,0⋅6,0
3
12
−
3,0
2
⋅
6,0⋅2,0
J
YZ
=
0,0
−
3,0
⋅
−
3,0
⋅
6,0⋅2,0
119
J
Y
=
6,0⋅2,0
3
12
1,0
2
⋅
6,0⋅2,0
J
Z
=
2,0⋅6,0
3
12
−
5,0
2
⋅
6,0⋅2,0
J
YZ
=
0,01,0⋅
−
5,0
⋅
6,0⋅2,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
12
Nr
Momenty bezwładności
120
J
Y
=
6,0⋅2,0
3
12
−
1,0
2
⋅
6,0⋅2,0
J
Z
=
2,0⋅6,0
3
12
−
5,0
2
⋅
6,0⋅2,0
J
YZ
=
0,0
−
1,0
⋅
−
5,0
⋅
6,0⋅2,0
121
J
Y
=
6,0⋅2,0
3
12
3,0
2
⋅
6,0⋅2,0
J
Z
=
2,0⋅6,0
3
12
3,0
2
⋅
6,0⋅2,0
J
YZ
=
0,03,0⋅3,0⋅6,0⋅2,0
122
J
Y
=
6,0⋅2,0
3
12
3,0
2
⋅
6,0⋅2,0
J
Z
=
2,0⋅6,0
3
12
−
3,0
2
⋅
6,0⋅2,0
J
YZ
=
0,03,0⋅
3,0
⋅
6,0⋅2,0
123
J
Y
=
6,0⋅2,0
3
12
3,0
2
⋅
6,0⋅2,0
J
Z
=
2,0⋅6,0
3
12
0,0
2
⋅
6,0⋅2,0
J
YZ
=
0,03,0⋅0,0⋅6,0⋅2,0=0
124
J
Y
=
6,0⋅2,0
3
12
0,0
2
⋅
6,0⋅2,0
J
Z
=
2,0⋅6,0
3
12
5,0
2
⋅
6,0⋅2,0
J
YZ
=
0,00,0⋅5,0⋅6,0⋅2,0=0
125
J
Y
=
6,0⋅2,0
3
12
−
3,0
2
⋅
6,0⋅2,0
J
Z
=
2,0⋅6,0
3
12
0,0
2
⋅
6,0⋅2,0
J
YZ
=
0,0
−
3,0
⋅
0,0⋅6,0⋅2,0=0
126
J
Y
=
6,0⋅2,0
3
12
0,0
2
⋅
6,0⋅2,0
J
Z
=
2,0⋅6,0
3
12
−
5,0
2
⋅
6,0⋅2,0
J
YZ
=
0,00,0⋅
−
5,0
⋅
6,0⋅2,0=0
127
J
Y
=
2,0⋅3,0
3
12
2,5
2
⋅
2,0⋅3,0
J
Z
=
3,0⋅2,0
3
12
5,0
2
⋅
2,0⋅3,0
J
YZ
=
0,02,5⋅5,0⋅2,0⋅3,0
128
J
Y
=
2,0⋅3,0
3
12
2,5
2
⋅
2,0⋅3,0
J
Z
=
3,0⋅2,0
3
12
−
5,0
2
⋅
2,0⋅3,0
J
YZ
=
0,02,5⋅
−
5,0
⋅
2,0⋅3,0
129
J
Y
=
2,0⋅3,0
3
12
−
2,5
2
⋅
2,0⋅3,0
J
Z
=
3,0⋅2,0
3
12
5,0
2
⋅
2,0⋅3,0
J
YZ
=
0,0
−
2,5
⋅
5,0⋅2,0⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
13
Nr
Momenty bezwładności
130
J
Y
=
2,0⋅3,0
3
12
−
2,5
2
⋅
2,0⋅3,0
J
Z
=
3,0⋅2,0
3
12
−
5,0
2
⋅
2,0⋅3,0
J
YZ
=
0,0
−
2,5
⋅
−
5,0
⋅
2,0⋅3,0
131
J
Y
=
2,0⋅3,0
3
12
1,5
2
⋅
2,0⋅3,0
J
Z
=
3,0⋅2,0
3
12
5,0
2
⋅
2,0⋅3,0
J
YZ
=
0,01,5⋅5,0⋅2,0⋅3,0
132
J
Y
=
2,0⋅3,0
3
12
−
1,5
2
⋅
2,0⋅3,0
J
Z
=
3,0⋅2,0
3
12
5,0
2
⋅
2,0⋅3,0
J
YZ
=
0,0
−
1,5
⋅
5,0⋅2,0⋅3,0
133
J
Y
=
2,0⋅3,0
3
12
−
2,5
2
⋅
2,0⋅3,0
J
Z
=
3,0⋅2,0
3
12
1,0
2
⋅
2,0⋅3,0
J
YZ
=
0,0
−
2,5
⋅
1,0⋅2,0⋅3,0
134
J
Y
=
2,0⋅3,0
3
12
−
2,5
2
⋅
2,0⋅3,0
J
Z
=
3,0⋅2,0
3
12
−
1,0
2
⋅
2,0⋅3,0
J
YZ
=
0,0
−
2,5
⋅
−
1,0
⋅
2,0⋅3,0
135
J
Y
=
2,0⋅3,0
3
12
−
1,5
2
⋅
2,0⋅3,0
J
Z
=
3,0⋅2,0
3
12
−
5,0
2
⋅
2,0⋅3,0
J
YZ
=
0,0
−
1,5
⋅
−
5,0
⋅
2,0⋅3,0
136
J
Y
=
2,0⋅3,0
3
12
1,5
2
⋅
2,0⋅3,0
J
Z
=
3,0⋅2,0
3
12
−
5,0
2
⋅
2,0⋅3,0
J
YZ
=
0,01,5⋅
−
5,0
⋅
2,0⋅3,0
137
J
Y
=
2,0⋅3,0
3
12
2,5
2
⋅
2,0⋅3,0
J
Z
=
3,0⋅2,0
3
12
−
1,0
2
⋅
2,0⋅3,0
J
YZ
=
0,02,5⋅
−
1,0
⋅
2,0⋅3,0
138
J
Y
=
2,0⋅3,0
3
12
2,5
2
⋅
2,0⋅3,0
J
Z
=
3,0⋅2,0
3
12
1,0
2
⋅
2,0⋅3,0
J
YZ
=
0,02,5⋅5,0⋅2,0⋅3,0
139
J
Y
=
2,0⋅3,0
3
12
2,5
2
⋅
2,0⋅3,0
J
Z
=
3,0⋅2,0
3
12
0,0
2
⋅
2,0⋅3,0
J
YZ
=
0,02,5⋅0,0⋅2,0⋅3,0=0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
14
Nr
Momenty bezwładności
140
J
Y
=
2,0⋅3,0
3
12
−
2,5
2
⋅
2,0⋅3,0
J
Z
=
3,0⋅2,0
3
12
0,0
2
⋅
2,0⋅3,0
J
YZ
=
0,0
−
2,5
⋅
0,0⋅2,0⋅3,0=0
141
J
Y
=
2,0⋅3,0
3
12
0,0
2
⋅
2,0⋅3,0
J
Z
=
3,0⋅2,0
3
12
5,0
2
⋅
2,0⋅3,0
J
YZ
=
0,00,0⋅5,0⋅2,0⋅3,0=0
142
J
Y
=
2,0⋅3,0
3
12
0,0
2
⋅
2,0⋅3,0
J
Z
=
3,0⋅2,0
3
12
−
5,0
2
⋅
2,0⋅3,0
J
YZ
=
0,00,0⋅
−
5,0
⋅
2,0⋅3,0=0
1.13. Zadania 143
−
222
W tabeli 1.13 przedstawiono wartości momentów bezwładności przekrojów będących trójkątami prosto-
kątnymi w układzie współrzędnych YZ.
Tabela 1.13. Wartości momentów bezwładności przekrojów będących trójkątami prostokątnymi
Nr
Momenty bezwładności
143
J
Y
=
6,0⋅3,0
3
36
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
3,0⋅4,0⋅
1
2
⋅
6,0⋅3,0
144
J
Y
=
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
2,0
⋅
4,0⋅
1
2
⋅
6,0⋅3,0
145
J
Y
=
6,0⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
3,0
⋅
−
6,0
⋅
1
2
⋅
6,0⋅3,0
146
J
Y
=
6,0⋅3,0
3
36
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
3,0⋅
−
6,0
⋅
1
2
⋅
6,0⋅3,0
147
J
Y
=
6,0⋅3,0
3
36
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
6,0
2
⋅
1
2
⋅
6,0⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
15
Nr
Momenty bezwładności
147
J
YZ
=−
3,0
2
⋅
6,0
2
72
3,0⋅6,0⋅
1
2
⋅
6,0⋅3,0
148
J
Y
=
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
2,0
⋅
6,0⋅
1
2
⋅
6,0⋅3,0
149
J
Y
=
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
2,0
⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
150
J
Y
=
6,0⋅3,0
3
36
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
3,0⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
151
J
Y
=
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
2,0⋅6,0⋅
1
2
⋅
6,0⋅3,0
152
J
Y
=
6,0⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
3,0
⋅
6,0⋅
1
2
⋅
6,0⋅3,0
153
J
Y
=
6,0⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
3,0
⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
154
J
Y
=
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
2,0⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
155
J
Y
=
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
2,0⋅4,0⋅
1
2
⋅
6,0⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
16
Nr
Momenty bezwładności
156
J
Y
=
6,0⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
3,0
⋅
4,0⋅
1
2
⋅
6,0⋅3,0
157
J
Y
=
6,0⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
3,0
⋅
−
6,0
⋅
1
2
⋅
6,0⋅3,0
158
J
Y
=
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
2,0⋅
−
6,0
⋅
1
2
⋅
6,0⋅3,0
159
J
Y
=
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
2,0⋅4,0⋅
1
2
⋅
6,0⋅3,0
160
J
Y
=
6,0⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
1,0
⋅
4,0⋅
1
2
⋅
6,0⋅3,0
161
J
Y
=
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
2,0
⋅
2,0⋅
1
2
⋅
6,0⋅3,0
162
J
Y
=
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
2,0
⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
163
J
Y
=
6,0⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
1,0
⋅
−
6,0
⋅
1
2
⋅
6,0⋅3,0
164
J
Y
=
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
6,0
2
⋅
1
2
⋅
6,0⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
17
Nr
Momenty bezwładności
164
J
YZ
=
3,0
2
⋅
6,0
2
72
2,0⋅
−
6,0
⋅
1
2
⋅
6,0⋅3,0
165
J
Y
=
6,0⋅3,0
3
36
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
3,0⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
166
J
Y
=
6,0⋅3,0
3
36
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
3,0⋅2,0⋅
1
2
⋅
6,0⋅3,0
167
J
Y
=
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
2,0⋅6,0⋅
1
2
⋅
6,0⋅3,0
168
J
Y
=
6,0⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
1,0
⋅
6,0⋅
1
2
⋅
6,0⋅3,0
169
J
Y
=
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
2,0
⋅
4,0⋅
1
2
⋅
6,0⋅3,0
170
J
Y
=
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
2,0
⋅
−
2,0
⋅
1
2
⋅
6,0⋅3,0
171
J
Y
=
6,0⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
1,0
⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
172
J
Y
=
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
2,0⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
18
Nr
Momenty bezwładności
173
J
Y
=
6,0⋅3,0
3
36
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
3,0⋅
−
2,0
⋅
1
2
⋅
6,0⋅3,0
174
J
Y
=
6,0⋅3,0
3
36
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
3,0⋅4,0⋅
1
2
⋅
6,0⋅3,0
175
J
Y
=
6,0⋅3,0
3
36
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
1,0⋅6,0⋅
1
2
⋅
6,0⋅3,0
176
J
Y
=
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
2,0
⋅
6,0⋅
1
2
⋅
6,0⋅3,0
177
J
Y
=
6,0⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
3,0
⋅
4,0⋅
1
2
⋅
6,0⋅3,0
178
J
Y
=
6,0⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
3,0
⋅
−
2,0
⋅
1
2
⋅
6,0⋅3,0
179
J
Y
=
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
2,0
⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
180
J
Y
=
6,0⋅3,0
3
36
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
1,0⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
181
J
Y
=
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
19
Nr
Momenty bezwładności
181
J
YZ
=
3,0
2
⋅
6,0
2
72
2,0⋅
−
2,0
⋅
1
2
⋅
6,0⋅3,0
182
J
Y
=
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
2,0⋅4,0⋅
1
2
⋅
6,0⋅3,0
183
J
Y
=
6,0⋅3,0
3
36
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
1,0⋅4,0⋅
1
2
⋅
6,0⋅3,0
184
J
Y
=
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
2,0
⋅
4,0⋅
1
2
⋅
6,0⋅3,0
185
J
Y
=
6,0⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
3,0
⋅
2,0⋅
1
2
⋅
6,0⋅3,0
186
J
Y
=
6,0⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
3,0
⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
187
J
Y
=
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
2,0
⋅
−
6,0
⋅
1
2
⋅
6,0⋅3,0
188
J
Y
=
6,0⋅3,0
3
36
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
1,0⋅
−
6,0
⋅
1
2
⋅
6,0⋅3,0
189
J
Y
=
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
2,0⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
20
Nr
Momenty bezwładności
190
J
Y
=
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
2,0⋅2,0⋅
1
2
⋅
6,0⋅3,0
191
J
Y
=
6,0⋅3,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
0,0⋅4,0⋅
1
2
⋅
6,0⋅3,0
192
J
Y
=
6,0⋅3,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
0,0⋅
−
6,0
⋅
1
2
⋅
6,0⋅3,0
193
J
Y
=
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
2,0
⋅
0,0⋅
1
2
⋅
6,0⋅3,0
194
J
Y
=
6,0⋅3,0
3
36
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
3,0⋅0,0⋅
1
2
⋅
6,0⋅3,0
195
J
Y
=
6,0⋅3,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
0,0⋅6,0⋅
1
2
⋅
6,0⋅3,0
196
J
Y
=
6,0⋅3,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
0,0⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
197
J
Y
=
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
2,0
⋅
0,0⋅
1
2
⋅
6,0⋅3,0
198
J
Y
=
6,0⋅3,0
3
36
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
21
Nr
Momenty bezwładności
198
J
YZ
=−
3,0
2
⋅
6,0
2
72
3,0⋅0,0⋅
1
2
⋅
6,0⋅3,0
199
J
Y
=
6,0⋅3,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
0,0⋅6,0⋅
1
2
⋅
6,0⋅3,0
200
J
Y
=
6,0⋅3,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
0,0⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
201
J
Y
=
6,0⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
3,0
⋅
0,0⋅
1
2
⋅
6,0⋅3,0
202
J
Y
=
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
2,0⋅0,0⋅
1
2
⋅
6,0⋅3,0
203
J
Y
=
6,0⋅3,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
0,0⋅4,0⋅
1
2
⋅
6,0⋅3,0
204
J
Y
=
6,0⋅3,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
0,0⋅
−
6,0
⋅
1
2
⋅
6,0⋅3,0
205
J
Y
=
6,0⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
3,0
⋅
0,0⋅
1
2
⋅
6,0⋅3,0
206
J
Y
=
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
2,0⋅0,0⋅
1
2
⋅
6,0⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
22
Nr
Momenty bezwładności
207
J
Y
=
6,0⋅3,0
3
36
0,5
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
0,5⋅4,0⋅
1
2
⋅
6,0⋅3,0
208
J
Y
=
6,0⋅3,0
3
36
0,5
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
0,5⋅
−
6,0
⋅
1
2
⋅
6,0⋅3,0
209
J
Y
=
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
2,0
⋅
−
1,0
⋅
1
2
⋅
6,0⋅3,0
210
J
Y
=
6,0⋅3,0
3
36
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
3,0⋅
−
1,0
⋅
1
2
⋅
6,0⋅3,0
211
J
Y
=
6,0⋅3,0
3
36
0,5
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
0,5⋅6,0⋅
1
2
⋅
6,0⋅3,0
212
J
Y
=
6,0⋅3,0
3
36
0,5
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
0,5⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
213
J
Y
=
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
2,0
⋅
1,0⋅
1
2
⋅
6,0⋅3,0
214
J
Y
=
6,0⋅3,0
3
36
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
3,0⋅1,0⋅
1
2
⋅
6,0⋅3,0
215
J
Y
=
6,0⋅3,0
3
36
−
0,5
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
6,0
2
⋅
1
2
⋅
6,0⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
23
Nr
Momenty bezwładności
215
J
YZ
=
3,0
2
⋅
6,0
2
72
−
0,5
⋅
6,0⋅
1
2
⋅
6,0⋅3,0
216
J
Y
=
6,0⋅3,0
3
36
−
0,5
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
0,5
⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
217
J
Y
=
6,0⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
−
3,0
⋅
1,0⋅
1
2
⋅
6,0⋅3,0
218
J
Y
=
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
3,0
2
⋅
6,0
2
72
2,0⋅1,0⋅
1
2
⋅
6,0⋅3,0
219
J
Y
=
6,0⋅3,0
3
36
−
0,5
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
0,5
⋅
4,0⋅
1
2
⋅
6,0⋅3,0
220
J
Y
=
6,0⋅3,0
3
36
−
0,5
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
6,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
0,5
⋅
−
6,0
⋅
1
2
⋅
6,0⋅3,0
221
J
Y
=
6,0⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
−
3,0
⋅
−
1,0
⋅
1
2
⋅
6,0⋅3,0
222
J
Y
=
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
3,0⋅6,0
3
36
−
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=−
3,0
2
⋅
6,0
2
72
2,0⋅
−
1,0
⋅
1
2
⋅
6,0⋅3,0
1.14. Zadania 223
−
302
W tabeli 1.14 przedstawiono wartości momentów bezwładności przekrojów będących trójkątami prosto-
kątnymi w układzie współrzędnych YZ.
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
24
Tabela 1.14. Wartości momentów bezwładności przekrojów będących trójkątami prostokątnymi
Nr
Momenty bezwładności
223
J
Y
=
1,5⋅3,0
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
3,0⋅2,5⋅
1
2
⋅
1,5⋅3,0
224
J
Y
=
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
−
2,0
⋅
2,5⋅
1
2
⋅
1,5⋅3,0
225
J
Y
=
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
−
2,0
⋅
−
3,0
⋅
1
2
⋅
1,5⋅3,0
226
J
Y
=
1,5⋅3,0
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
3,0⋅
−
3,0
⋅
1
2
⋅
1,5⋅3,0
227
J
Y
=
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
2,0⋅3,0⋅
1
2
⋅
1,5⋅3,0
228
J
Y
=
1,5⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
−
3,0
⋅
3,0⋅
1
2
⋅
1,5⋅3,0
229
J
Y
=
1,5⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
−
3,0
⋅
−
2,5
⋅
1
2
⋅
1,5⋅3,0
230
J
Y
=
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
2,0
⋅
−
2,5
⋅
1
2
⋅
1,5⋅3,0
231
J
Y
=
1,5⋅3,0
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
25
Nr
Momenty bezwładności
231
J
YZ
=−
1,5
2
⋅
3,0
2
72
3,0⋅3,0⋅
1
2
⋅
1,5⋅3,0
232
J
Y
=
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
2,0
⋅
3,0⋅
1
2
⋅
1,5⋅3,0
233
J
Y
=
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
2,0
⋅
−
2,5
⋅
1
2
⋅
1,5⋅3,0
234
J
Y
=
1,5⋅3,0
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
3,0⋅
−
2,5
⋅
1
2
⋅
1,5⋅3,0
235
J
Y
=
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
2,0⋅2,5⋅
1
2
⋅
1,5⋅3,0
236
J
Y
=
1,5⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
3,0
⋅
2,5⋅
1
2
⋅
1,5⋅3,0
237
J
Y
=
1,5⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
3,0
⋅
−
3,0
⋅
1
2
⋅
1,5⋅3,0
238
J
Y
=
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
2,0⋅
−
3,0
⋅
1
2
⋅
1,5⋅3,0
239
J
Y
=
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
2,0⋅2,5⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
26
Nr
Momenty bezwładności
240
J
Y
=
1,5⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
−
1,0
⋅
2,5⋅
1
2
⋅
1,5⋅3,0
241
J
Y
=
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
−
2,0
⋅
0,5⋅
1
2
⋅
1,5⋅3,0
242
J
Y
=
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
−
2,0
⋅
−
1,0
⋅
1
2
⋅
1,5⋅3,0
243
J
Y
=
1,5⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
−
1,0
⋅
−
3,0
⋅
1
2
⋅
1,5⋅3,0
244
J
Y
=
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
2,0⋅
−
3,0
⋅
1
2
⋅
1,5⋅3,0
245
J
Y
=
1,5⋅3,0
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
3,0⋅
−
1,0
⋅
1
2
⋅
1,5⋅3,0
246
J
Y
=
1,5⋅3,0
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
3,0⋅0,5⋅
1
2
⋅
1,5⋅3,0
247
J
Y
=
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
1,0⋅3,0⋅
1
2
⋅
1,5⋅3,0
248
J
Y
=
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
27
Nr
Momenty bezwładności
248
J
YZ
=
1,5
2
⋅
3,0
2
72
−
2,0
⋅
3,0⋅
1
2
⋅
1,5⋅3,0
249
J
Y
=
1,5⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
−
3,0
⋅
1,0⋅
1
2
⋅
1,5⋅3,0
250
J
Y
=
1,5⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
−
3,0
⋅
−
0,5
⋅
1
2
⋅
1,5⋅3,0
251
J
Y
=
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
−
2,0
⋅
−
2,5
⋅
1
2
⋅
1,5⋅3,0
252
J
Y
=
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
1,0⋅
−
2,5
⋅
1
2
⋅
1,5⋅3,0
253
J
Y
=
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
2,0⋅
−
0,5
⋅
1
2
⋅
1,5⋅3,0
254
J
Y
=
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
2,0⋅1,0⋅
1
2
⋅
1,5⋅3,0
255
J
Y
=
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
2,0⋅3,0⋅
1
2
⋅
1,5⋅3,0
256
J
Y
=
1,5⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
1,0
⋅
3,0⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
28
Nr
Momenty bezwładności
257
J
Y
=
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
2,0
⋅
1,0⋅
1
2
⋅
1,5⋅3,0
258
J
Y
=
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
2,0
⋅
−
0,5
⋅
1
2
⋅
1,5⋅3,0
259
J
Y
=
1,5⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
1,0
⋅
−
2,5
⋅
1
2
⋅
1,5⋅3,0
260
J
Y
=
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
2,0⋅
−
2,5
⋅
1
2
⋅
1,5⋅3,0
261
J
Y
=
1,5⋅3,0
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
3,0⋅
−
0,5
⋅
1
2
⋅
1,5⋅3,0
262
J
Y
=
1,5⋅3,0
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
3,0⋅1,0⋅
1
2
⋅
1,5⋅3,0
263
J
Y
=
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
1,0⋅2,5⋅
1
2
⋅
1,5⋅3,0
264
J
Y
=
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
2,0
⋅
2,5⋅
1
2
⋅
1,5⋅3,0
265
J
Y
=
1,5⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
29
Nr
Momenty bezwładności
265
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
3,0
⋅
0,5⋅
1
2
⋅
1,5⋅3,0
266
J
Y
=
1,5⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
3,0
⋅
−
1,0
⋅
1
2
⋅
1,5⋅3,0
267
J
Y
=
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
2,0
⋅
−
3,0
⋅
1
2
⋅
1,5⋅3,0
268
J
Y
=
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
1,0⋅
−
3,0
⋅
1
2
⋅
1,5⋅3,0
269
J
Y
=
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
2,0⋅
−
1,0
⋅
1
2
⋅
1,5⋅3,0
270
J
Y
=
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
2,0⋅0,5⋅
1
2
⋅
1,5⋅3,0
271
J
Y
=
1,5⋅3,0
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
0,0⋅2,5⋅
1
2
⋅
1,5⋅3,0
272
J
Y
=
1,5⋅3,0
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
0,0⋅
−
3,0
⋅
1
2
⋅
1,5⋅3,0
273
J
Y
=
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
−
2,0
⋅
0,0⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
30
Nr
Momenty bezwładności
274
J
Y
=
1,5⋅3,0
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
3,0⋅0,0⋅
1
2
⋅
1,5⋅3,0
275
J
Y
=
1,5⋅3,0
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
0,0⋅3,0⋅
1
2
⋅
1,5⋅3,0
276
J
Y
=
1,5⋅3,0
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
0,0⋅
−
2,5
⋅
1
2
⋅
1,5⋅3,0
277
J
Y
=
1,5⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
−
3,0
⋅
0,0⋅
1
2
⋅
1,5⋅3,0
278
J
Y
=
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
2,0⋅0,0⋅
1
2
⋅
1,5⋅3,0
279
J
Y
=
1,5⋅3,0
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
0,0⋅3,0⋅
1
2
⋅
1,5⋅3,0
280
J
Y
=
1,5⋅3,0
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
0,0⋅
−
2,5
⋅
1
2
⋅
1,5⋅3,0
281
J
Y
=
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
2,0
⋅
0,0⋅
1
2
⋅
1,5⋅3,0
282
J
Y
=
1,5⋅3,0
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
31
Nr
Momenty bezwładności
282
J
YZ
=−
1,5
2
⋅
3,0
2
72
3,0⋅0,0⋅
1
2
⋅
1,5⋅3,0
283
J
Y
=
1,5⋅3,0
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
0,0⋅2,5⋅
1
2
⋅
1,5⋅3,0
284
J
Y
=
1,5⋅3,0
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
0,0⋅
−
3,0
⋅
1
2
⋅
1,5⋅3,0
285
J
Y
=
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
2,0⋅0,0⋅
1
2
⋅
1,5⋅3,0
286
J
Y
=
1,5⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
3,0
⋅
0,0⋅
1
2
⋅
1,5⋅3,0
287
J
Y
=
1,5⋅3,0
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
0,5⋅2,5⋅
1
2
⋅
1,5⋅3,0
288
J
Y
=
1,5⋅3,0
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
0,5⋅
−
3,0
⋅
1
2
⋅
1,5⋅3,0
289
J
Y
=
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
0,25
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
−
2,0
⋅
−
0,25
⋅
1
2
⋅
1,5⋅3,0
290
J
Y
=
1,5⋅3,0
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
0,25
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
1,5
2
⋅
3,0
2
72
3,0⋅
−
0,25
⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
32
Nr
Momenty bezwładności
291
J
Y
=
1,5⋅3,0
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
0,5⋅3,0⋅
1
2
⋅
1,5⋅3,0
292
J
Y
=
1,5⋅3,0
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
0,5⋅
−
2,5
⋅
1
2
⋅
1,5⋅3,0
293
J
Y
=
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
0,25
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
2,0
⋅
0,25⋅
1
2
⋅
1,5⋅3,0
294
J
Y
=
1,5⋅3,0
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
0,25
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
3,0⋅0,25⋅
1
2
⋅
1,5⋅3,0
295
J
Y
=
1,5⋅3,0
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
0,5
⋅
3,0⋅
1
2
⋅
1,5⋅3,0
296
J
Y
=
1,5⋅3,0
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
2,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
0,5
⋅
−
2,5
⋅
1
2
⋅
1,5⋅3,0
297
J
Y
=
1,5⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
0,25
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
3,0
⋅
0,25⋅
1
2
⋅
1,5⋅3,0
298
J
Y
=
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
0,25
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
2,0⋅0,25⋅
1
2
⋅
1,5⋅3,0
299
J
Y
=
1,5⋅3,0
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
2,5
2
⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
33
Nr
Momenty bezwładności
299
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
0,5
⋅
2,5⋅
1
2
⋅
1,5⋅3,0
300
J
Y
=
1,5⋅3,0
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
0,5
⋅
−
3,0
⋅
1
2
⋅
1,5⋅3,0
301
J
Y
=
1,5⋅3,0
3
36
−
3,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
0,25
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
−
3,0
⋅
−
0,25
⋅
1
2
⋅
1,5⋅3,0
302
J
Y
=
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
3,0⋅1,5
3
36
−
0,25
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=−
1,5
2
⋅
3,0
2
72
2,0⋅
−
0,25
⋅
1
2
⋅
1,5⋅3,0
1.15. Zadania 303
−
318
W tabeli 1.15 przedstawiono wartości momentów bezwładności przekrojów prętów w układzie współ-
rzędnych YZ.
Tabela 1.15. Wartości momentów bezwładności przekrojów prętów
Nr
Momenty bezwładności
303
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
−
3,0
2
⋅
6,0
2
72
1,0⋅2,0⋅
1
2
⋅
6,0⋅3,0
304
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
−
3,0
2
⋅
6,0
2
72
−
2,0
⋅
2,0⋅
1
2
⋅
6,0⋅3,0
305
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
−
3,0
2
⋅
6,0
2
72
−
2,0
⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
306
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
34
Nr
Momenty bezwładności
306
J
YZ
=
0,0 −
−
3,0
2
⋅
6,0
2
72
1,0⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
307
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
3,0
2
⋅
6,0
2
72
1,0⋅4,0⋅
1
2
⋅
6,0⋅3,0
308
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
3,0
2
⋅
6,0
2
72
−
2,0
⋅
4,0⋅
1
2
⋅
6,0⋅3,0
309
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
3,0
2
⋅
6,0
2
72
−
2,0
⋅
−
2,0
⋅
1
2
⋅
6,0⋅3,0
310
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
3,0
2
⋅
6,0
2
72
1,0⋅
−
2,0
⋅
1
2
⋅
6,0⋅3,0
311
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
−
3,0
2
⋅
6,0
2
72
2,0⋅4,0⋅
1
2
⋅
6,0⋅3,0
312
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
−
3,0
2
⋅
6,0
2
72
−
1,0
⋅
4,0⋅
1
2
⋅
6,0⋅3,0
313
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
−
3,0
2
⋅
6,0
2
72
−
1,0
⋅
−
2,0
⋅
1
2
⋅
6,0⋅3,0
314
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
−
2,0
2
⋅
1
2
⋅
6,0⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
35
Nr
Momenty bezwładności
314
J
YZ
=
0,0 −
−
3,0
2
⋅
6,0
2
72
2,0⋅
−
2,0
⋅
1
2
⋅
6,0⋅3,0
315
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
3,0
2
⋅
6,0
2
72
2,0⋅2,0⋅
1
2
⋅
6,0⋅3,0
316
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
3,0
2
⋅
6,0
2
72
−
1,0
⋅
2,0⋅
1
2
⋅
6,0⋅3,0
317
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
3,0
2
⋅
6,0
2
72
−
1,0
⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
318
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
2,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
−
4,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
3,0
2
⋅
6,0
2
72
2,0⋅
−
4,0
⋅
1
2
⋅
6,0⋅3,0
1.16. Zadania 319
−
334
W tabeli 1.16 przedstawiono wartości momentów bezwładności przekrojów prętów w układzie współ-
rzędnych YZ.
Tabela 1.16. Wartości momentów bezwładności przekrojów prętów
Nr
Momenty bezwładności
319
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
1,5
2
⋅
3,0
2
72
2,0⋅0,5⋅
1
2
⋅
1,5⋅3,0
320
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
1,5
2
⋅
3,0
2
72
−
1,0
⋅
0,5⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
36
Nr
Momenty bezwładności
321
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
1,5
2
⋅
3,0
2
72
−
1,0
⋅
−
1,0
⋅
1
2
⋅
1,5⋅3,0
322
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
1,5
2
⋅
3,0
2
72
2,0⋅
−
1,0
⋅
1
2
⋅
1,5⋅3,0
323
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
1,5
2
⋅
3,0
2
72
1,0⋅1,0⋅
1
2
⋅
1,5⋅3,0
324
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
1,5
2
⋅
3,0
2
72
−
2,0
⋅
1,0⋅
1
2
⋅
1,5⋅3,0
325
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
1,5
2
⋅
3,0
2
72
−
2,0
⋅
−
0,5
⋅
1
2
⋅
1,5⋅3,0
326
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
1,5
2
⋅
3,0
2
72
1,0⋅
−
0,5
⋅
1
2
⋅
1,5⋅3,0
327
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
−
1,5
2
⋅
3,0
2
72
2,0⋅1,0⋅
1
2
⋅
1,5⋅3,0
328
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
−
1,5
2
⋅
3,0
2
72
−
1,0
⋅
1,0⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
37
Nr
Momenty bezwładności
329
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
−
1,5
2
⋅
3,0
2
72
−
1,0
⋅
−
0,5
⋅
1
2
⋅
1,5⋅3,0
330
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
1,5
2
⋅
3,0
2
72
2,0⋅
−
0,5
⋅
1
2
⋅
1,5⋅3,0
331
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
−
1,5
2
⋅
3,0
2
72
1,0⋅0,5⋅
1
2
⋅
1,5⋅3,0
332
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
−
1,5
2
⋅
3,0
2
72
−
2,0
⋅
0,5⋅
1
2
⋅
1,5⋅3,0
333
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
−
1,5
2
⋅
3,0
2
72
−
2,0
⋅
−
1,0
⋅
1
2
⋅
1,5⋅3,0
334
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
−
1,5
2
⋅
3,0
2
72
1,0⋅
−
1,0
⋅
1
2
⋅
1,5⋅3,0
1.17. Zadania 335
−
350
W tabeli 1.17 przedstawiono wartości momentów bezwładności przekrojów prętów w układzie współ-
rzędnych YZ.
Tabela 1.17. Wartości momentów bezwładności przekrojów prętów
Nr
Momenty bezwładności
335
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
−
3,0
2
⋅
6,0
2
72
0,0⋅0,0⋅
1
2
⋅
6,0⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
38
Nr
Momenty bezwładności
336
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
3,0
2
⋅
6,0
2
72
0,0⋅0,0⋅
1
2
⋅
6,0⋅3,0
337
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
−
3,0
2
⋅
6,0
2
72
0,0⋅0,0⋅
1
2
⋅
6,0⋅3,0
338
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
0,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
3,0
2
⋅
6,0
2
72
0,0⋅0,0⋅
1
2
⋅
6,0⋅3,0
339
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
0,5
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
−
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
3,0
2
⋅
6,0
2
72
0,5⋅
−
1,0
⋅
1
2
⋅
6,0⋅3,0
340
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
0,5
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
−
3,0
2
⋅
6,0
2
72
0,5⋅1,0⋅
1
2
⋅
6,0⋅3,0
341
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
−
0,5
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
−
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
−
3,0
2
⋅
6,0
2
72
−
0,5
⋅
−
1,0
⋅
1
2
⋅
6,0⋅3,0
342
J
Y
=
14,0⋅8,0
3
12
−
6,0⋅3,0
3
36
−
0,5
2
⋅
1
2
⋅
6,0⋅3,0
J
Z
=
8,0⋅14,0
3
12
−
3,0⋅6,0
3
36
1,0
2
⋅
1
2
⋅
6,0⋅3,0
J
YZ
=
0,0 −
3,0
2
⋅
6,0
2
72
−
0,5
⋅
1,0⋅
1
2
⋅
6,0⋅3,0
343
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
−
1,5
2
⋅
3,0
2
72
0,0⋅0,0⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
39
Nr
Momenty bezwładności
344
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
1,5
2
⋅
3,0
2
72
0,0⋅0,0⋅
1
2
⋅
1,5⋅3,0
345
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
−
1,5
2
⋅
3,0
2
72
0,0⋅0,0⋅
1
2
⋅
1,5⋅3,0
346
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
0,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
1,5
2
⋅
3,0
2
72
0,0⋅0,0⋅
1
2
⋅
1,5⋅3,0
347
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
−
0,25
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
1,5
2
⋅
3,0
2
72
0,5⋅
−
0,25
⋅
1
2
⋅
1,5⋅3,0
348
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
0,25
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
−
1,5
2
⋅
3,0
2
72
0,5⋅0,25⋅
1
2
⋅
1,5⋅3,0
349
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
−
0,25
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
−
1,5
2
⋅
3,0
2
72
−
0,5
⋅
0,25
⋅
1
2
⋅
1,5⋅3,0
350
J
Y
=
6,0⋅8,0
3
12
−
1,5⋅3,0
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
8,0⋅6,0
3
12
−
3,0⋅1,5
3
36
0,25
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0 −
1,5
2
⋅
3,0
2
72
−
0,5
⋅
0,25⋅
1
2
⋅
1,5⋅3,0
1.18. Zadania 351
−
382
W tabeli 1.18 przedstawiono wartości momentów bezwładności przekrojów prętów w układzie współ-
rzędnych YZ.
Tabela 1.18. Wartości momentów bezwładności przekrojów prętów
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
40
Nr
Momenty bezwładności
351
J
Y
=
9,0⋅6,0
3
36
−
2,0⋅1,5
3
12
0,75
2
⋅
1,5⋅2,0
J
Z
=
6,0⋅9,0
3
36
−
1,5⋅2,0
3
12
1,0
2
⋅
1,5⋅2,0
J
YZ
=
6,0
2
⋅
9,0
2
72
−
0,00,75⋅1,0⋅1,5⋅2,0
352
J
Y
=
9,0⋅6,0
3
36
−
2,0⋅1,5
3
12
0,75
2
⋅
1,5⋅2,0
J
Z
=
6,0⋅9,0
3
36
−
1,5⋅2,0
3
12
−
1,0
2
⋅
1,5⋅2,0
J
YZ
=
6,0
2
⋅
9,0
2
72
−
0,00,75⋅
−
1,0
⋅
1,5⋅2,0
353
J
Y
=
9,0⋅6,0
3
36
−
2,0⋅1,5
3
12
−
0,75
2
⋅
1,5⋅2,0
J
Z
=
6,0⋅9,0
3
36
−
1,5⋅2,0
3
12
−
1,0
2
⋅
1,5⋅2,0
J
YZ
=
6,0
2
⋅
9,0
2
72
−
0,0
−
0,75
⋅
−
1,0
⋅
1,5⋅2,0
354
J
Y
=
9,0⋅6,0
3
36
−
2,0⋅1,5
3
12
0,75
2
⋅
1,5⋅2,0
J
Z
=
6,0⋅9,0
3
36
−
1,5⋅2,0
3
12
1,0
2
⋅
1,5⋅2,0
J
YZ
=−
6,0
2
⋅
9,0
2
72
−
0,00,75⋅1,0⋅1,5⋅2,0
355
J
Y
=
9,0⋅6,0
3
36
−
2,0⋅1,5
3
12
−
0,75
2
⋅
1,5⋅2,0
J
Z
=
6,0⋅9,0
3
36
−
1,5⋅2,0
3
12
1,0
2
⋅
1,5⋅2,0
J
YZ
=−
6,0
2
⋅
9,0
2
72
−
0,0
−
0,75
⋅
1,0⋅1,5⋅2,0
356
J
Y
=
9,0⋅6,0
3
36
−
2,0⋅1,5
3
12
0,75
2
⋅
1,5⋅2,0
J
Z
=
6,0⋅9,0
3
36
−
1,5⋅2,0
3
12
−
1,0
2
⋅
1,5⋅2,0
J
YZ
=−
6,0
2
⋅
9,0
2
72
−
0,00,75⋅
−
1,0
⋅
1,5⋅2,0
357
J
Y
=
9,0⋅6,0
3
36
−
2,0⋅1,5
3
12
−
0,75
2
⋅
1,5⋅2,0
J
Z
=
6,0⋅9,0
3
36
−
1,5⋅2,0
3
12
−
1,0
2
⋅
1,5⋅2,0
J
YZ
=
6,0
2
⋅
9,0
2
72
−
0,0
−
0,75
⋅
−
1,0
⋅
1,5⋅2,0
358
J
Y
=
9,0⋅6,0
3
36
−
2,0⋅1,5
3
12
−
0,75
2
⋅
1,5⋅2,0
J
Z
=
6,0⋅9,0
3
36
−
1,5⋅2,0
3
12
1,0
2
⋅
1,5⋅2,0
J
YZ
=
6,0
2
⋅
9,0
2
72
−
0,0
−
0,75
⋅
1,0⋅1,5⋅2,0
359
J
Y
=
9,0⋅6,0
3
36
−
2,0⋅1,5
3
12
0,75
2
⋅
1,5⋅2,0
J
Z
=
6,0⋅9,0
3
36
−
1,5⋅2,0
3
12
1,0
2
⋅
1,5⋅2,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
41
Nr
Momenty bezwładności
359
J
YZ
=
6,0
2
⋅
9,0
2
72
−
0,00,75⋅1,0⋅1,5⋅2,0
360
J
Y
=
9,0⋅6,0
3
36
−
2,0⋅1,5
3
12
−
0,75
2
⋅
1,5⋅2,0
J
Z
=
6,0⋅9,0
3
36
−
1,5⋅2,0
3
12
1,0
2
⋅
1,5⋅2,0
J
YZ
=−
6,0
2
⋅
9,0
2
72
−
0,0
−
0,75
⋅
1,0⋅1,5⋅2,0
361
J
Y
=
9,0⋅6,0
3
36
−
2,0⋅1,5
3
12
−
0,75
2
⋅
1,5⋅2,0
J
Z
=
6,0⋅9,0
3
36
−
1,5⋅2,0
3
12
−
1,0
2
⋅
1,5⋅2,0
J
YZ
=−
6,0
2
⋅
9,0
2
72
−
0,0
−
0,75
⋅
−
1,0
⋅
1,5⋅2,0
362
J
Y
=
9,0⋅6,0
3
36
−
2,0⋅1,5
3
12
0,75
2
⋅
1,5⋅2,0
J
Z
=
6,0⋅9,0
3
36
−
1,5⋅2,0
3
12
−
1,0
2
⋅
1,5⋅2,0
J
YZ
=−
6,0
2
⋅
9,0
2
72
−
0,00,75⋅
−
1,0
⋅
1,5⋅2,0
363
J
Y
=
4,5⋅6,0
3
36
−
1,0⋅1,5
3
12
−
0,75
2
⋅
1,0⋅1,5
J
Z
=
6,0⋅4,5
3
36
−
1,5⋅1,0
3
12
−
0,5
2
⋅
1,0⋅1,5
J
YZ
=
4,5
2
⋅
6,0
2
72
−
0,0
−
0,75
⋅
−
0,5
⋅
1,0⋅1,5
364
J
Y
=
4,5⋅6,0
3
36
−
1,0⋅1,5
3
12
0,75
2
⋅
1,0⋅1,5
J
Z
=
6,0⋅4,5
3
36
−
1,5⋅1,0
3
12
−
0,5
2
⋅
1,0⋅1,5
J
YZ
=
4,5
2
⋅
6,0
2
72
−
0,00,75⋅
−
0,5
⋅
1,0⋅1,5
365
J
Y
=
4,5⋅6,0
3
36
−
1,0⋅1,5
3
12
0,75
2
⋅
1,0⋅1,5
J
Z
=
6,0⋅4,5
3
36
−
1,5⋅1,0
3
12
0,5
2
⋅
1,0⋅1,5
J
YZ
=
4,5
2
⋅
6,0
2
72
−
0,00,75⋅0,5⋅1,0⋅1,5
366
J
Y
=
4,5⋅6,0
3
36
−
1,0⋅1,5
3
12
0,75
2
⋅
1,0⋅1,5
J
Z
=
6,0⋅4,5
3
36
−
1,5⋅1,0
3
12
0,5
2
⋅
1,0⋅1,5
J
YZ
=−
4,5
2
⋅
6,0
2
72
−
0,00,75⋅0,5⋅1,0⋅1,5
367
J
Y
=
4,5⋅6,0
3
36
−
1,0⋅1,5
3
12
−
0,75
2
⋅
1,0⋅1,5
J
Z
=
6,0⋅4,5
3
36
−
1,5⋅1,0
3
12
0,5
2
⋅
1,0⋅1,5
J
YZ
=−
4,5
2
⋅
6,0
2
72
−
0,0
−
0,75
⋅
0,5⋅1,0⋅1,5
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
42
Nr
Momenty bezwładności
368
J
Y
=
4,5⋅6,0
3
36
−
1,0⋅1,5
3
12
0,75
2
⋅
1,0⋅1,5
J
Z
=
6,0⋅4,5
3
36
−
1,5⋅1,0
3
12
−
0,5
2
⋅
1,0⋅1,5
J
YZ
=−
4,5
2
⋅
6,0
2
72
−
0,00,75⋅
−
0,5
⋅
1,0⋅1,5
369
J
Y
=
4,5⋅6,0
3
36
−
1,0⋅1,5
3
12
−
0,75
2
⋅
1,0⋅1,5
J
Z
=
6,0⋅4,5
3
36
−
1,5⋅1,0
3
12
−
0,5
2
⋅
1,0⋅1,5
J
YZ
=−
4,5
2
⋅
6,0
2
72
−
0,0
−
0,75
⋅
−
0,5
⋅
1,0⋅1,5
370
J
Y
=
4,5⋅6,0
3
36
−
1,0⋅1,5
3
12
−
0,75
2
⋅
1,0⋅1,5
J
Z
=
6,0⋅4,5
3
36
−
1,5⋅1,0
3
12
0,5
2
⋅
1,0⋅1,5
J
YZ
=−
4,5
2
⋅
6,0
2
72
−
0,0
−
0,75
⋅
0,5⋅1,0⋅1,5
371
J
Y
=
4,5⋅6,0
3
36
−
1,0⋅1,5
3
12
0,75
2
⋅
1,0⋅1,5
J
Z
=
6,0⋅4,5
3
36
−
1,5⋅1,0
3
12
−
0,5
2
⋅
1,0⋅1,5
J
YZ
=−
4,5
2
⋅
6,0
2
72
−
0,00,75⋅
−
0,5
⋅
1,0⋅1,5
372
J
Y
=
4,5⋅6,0
3
36
−
1,0⋅1,5
3
12
−
0,75
2
⋅
1,0⋅1,5
J
Z
=
6,0⋅4,5
3
36
−
1,5⋅1,0
3
12
−
0,5
2
⋅
1,0⋅1,5
J
YZ
=
4,5
2
⋅
6,0
2
72
−
0,0
−
0,75
⋅
−
0,5
⋅
1,0⋅1,5
373
J
Y
=
4,5⋅6,0
3
36
−
1,0⋅1,5
3
12
−
0,75
2
⋅
1,0⋅1,5
J
Z
=
6,0⋅4,5
3
36
−
1,5⋅1,0
3
12
0,5
2
⋅
1,0⋅1,5
J
YZ
=
4,5
2
⋅
6,0
2
72
−
0,0
−
0,75
⋅
0,5⋅1,0⋅1,5
374
J
Y
=
4,5⋅6,0
3
36
−
1,0⋅1,5
3
12
0,75
2
⋅
1,0⋅1,5
J
Z
=
6,0⋅4,5
3
36
−
1,5⋅1,0
3
12
0,5
2
⋅
1,0⋅1,5
J
YZ
=
4,5
2
⋅
6,0
2
72
−
0,00,75⋅0,5⋅1,0⋅1,5
375
J
Y
=
9,0⋅6,0
3
36
−
2,0⋅1,5
3
12
0,0
2
⋅
1,5⋅2,0
J
Z
=
6,0⋅9,0
3
36
−
1,5⋅2,0
3
12
0,0
2
⋅
1,5⋅2,0
J
YZ
=
6,0
2
⋅
9,0
2
72
−
0,00,0⋅0,0⋅1,5⋅2,0
376
J
Y
=
9,0⋅6,0
3
36
−
2,0⋅1,5
3
12
0,0
2
⋅
1,5⋅2,0
J
Z
=
6,0⋅9,0
3
36
−
1,5⋅2,0
3
12
0,0
2
⋅
1,5⋅2,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
43
Nr
Momenty bezwładności
376
J
YZ
=−
6,0
2
⋅
9,0
2
72
−
0,00,0⋅0,0⋅1,5⋅2,0
377
J
Y
=
9,0⋅6,0
3
36
−
2,0⋅1,5
3
12
0,0
2
⋅
1,5⋅2,0
J
Z
=
6,0⋅9,0
3
36
−
1,5⋅2,0
3
12
0,0
2
⋅
1,5⋅2,0
J
YZ
=
6,0
2
⋅
9,0
2
72
−
0,00,0⋅0,0⋅1,5⋅2,0
378
J
Y
=
9,0⋅6,0
3
36
−
2,0⋅1,5
3
12
0,0
2
⋅
1,5⋅2,0
J
Z
=
6,0⋅9,0
3
36
−
1,5⋅2,0
3
12
0,0
2
⋅
1,5⋅2,0
J
YZ
=−
6,0
2
⋅
9,0
2
72
−
0,00,0⋅0,0⋅1,5⋅2,0
379
J
Y
=
4,5⋅6,0
3
36
−
1,0⋅1,5
3
12
0,0
2
⋅
1,0⋅1,5
J
Z
=
6,0⋅4,5
3
36
−
1,5⋅1,0
3
12
0,0
2
⋅
1,0⋅1,5
J
YZ
=
4,5
2
⋅
6,0
2
72
−
0,00,0⋅0,0⋅1,0⋅1,5
380
J
Y
=
4,5⋅6,0
3
36
−
1,0⋅1,5
3
12
0,0
2
⋅
1,0⋅1,5
J
Z
=
6,0⋅4,5
3
36
−
1,5⋅1,0
3
12
0,0
2
⋅
1,0⋅1,5
J
YZ
=−
4,5
2
⋅
6,0
2
72
−
0,00,0⋅0,0⋅1,0⋅1,5
381
J
Y
=
4,5⋅6,0
3
36
−
1,0⋅1,5
3
12
0,0
2
⋅
1,0⋅1,5
J
Z
=
6,0⋅4,5
3
36
−
1,5⋅1,0
3
12
0,0
2
⋅
1,0⋅1,5
J
YZ
=−
4,5
2
⋅
6,0
2
72
−
0,00,0⋅0,0⋅1,0⋅1,5
382
J
Y
=
4,5⋅6,0
3
36
−
1,0⋅1,5
3
12
0,0
2
⋅
1,0⋅1,5
J
Z
=
6,0⋅4,5
3
36
−
1,5⋅1,0
3
12
0,0
2
⋅
1,0⋅1,5
J
YZ
=
4,5
2
⋅
6,0
2
72
−
0,00,0⋅0,0⋅1,0⋅1,5
1.19. Zadania 383
−
414
W tabeli 1.19 przedstawiono wartości momentów bezwładności przekrojów prętów w układzie współ-
rzędnych YZ.
Tabela 1.19. Wartości momentów bezwładności przekrojów prętów
Nr
Momenty bezwładności
383
J
Y
=
7,0⋅6,0
3
12
1,0
2
⋅
6,0⋅7,0−
3,0⋅1,5
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
44
Nr
Momenty bezwładności
383
J
Z
=
6,0⋅7,0
3
12
0,5
2
⋅
6,0⋅7,0−
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,01,0⋅0,5⋅6,0⋅7,0−
−
1,5
2
⋅
3,0
2
72
0,5⋅1,0⋅
1
2
⋅
1,5⋅3,0
384
J
Y
=
7,0⋅6,0
3
12
1,0
2
⋅
6,0⋅7,0−
3,0⋅1,5
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
6,0⋅7,0
3
12
0,5
2
⋅
6,0⋅7,0−
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,01,0⋅0,5⋅6,0⋅7,0−
1,5
2
⋅
3,0
2
72
0,5⋅2,0⋅
1
2
⋅
1,5⋅3,0
385
J
Y
=
7,0⋅6,0
3
12
1,0
2
⋅
6,0⋅7,0−
3,0⋅1,5
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
6,0⋅7,0
3
12
0,5
2
⋅
6,0⋅7,0−
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,01,0⋅0,5⋅6,0⋅7,0−
−
1,5
2
⋅
3,0
2
72
1,0⋅2,0⋅
1
2
⋅
1,5⋅3,0
386
J
Y
=
7,0⋅6,0
3
12
1,0
2
⋅
6,0⋅7,0−
3,0⋅1,5
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
6,0⋅7,0
3
12
0,5
2
⋅
6,0⋅7,0−
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,01,0⋅0,5⋅6,0⋅7,0−
1,5
2
⋅
3,0
2
72
1,0⋅1,0⋅
1
2
⋅
1,5⋅3,0
387
J
Y
=
7,0⋅6,0
3
12
−
1,0
2
⋅
6,0⋅7,0−
3,0⋅1,5
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
6,0⋅7,0
3
12
0,5
2
⋅
6,0⋅7,0−
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0
−
1,0
⋅
0,5⋅6,0⋅7,0−
1,5
2
⋅
3,0
2
72
−
0,5
⋅
1,0⋅
1
2
⋅
1,5⋅3,0
388
J
Y
=
7,0⋅6,0
3
12
−
1,0
2
⋅
6,0⋅7,0−
3,0⋅1,5
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
6,0⋅7,0
3
12
0,5
2
⋅
6,0⋅7,0−
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0
−
1,0
⋅
0,5⋅6,0⋅7,0−
−
1,5
2
⋅
3,0
2
72
−
0,5
⋅
2,0⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
45
Nr
Momenty bezwładności
389
J
Y
=
7,0⋅6,0
3
12
−
1,0
2
⋅
6,0⋅7,0−
3,0⋅1,5
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
6,0⋅7,0
3
12
0,5
2
⋅
6,0⋅7,0−
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0
−
1,0
⋅
0,5⋅6,0⋅7,0−
1,5
2
⋅
3,0
2
72
−
1,0
⋅
2,0⋅
1
2
⋅
1,5⋅3,0
390
J
Y
=
7,0⋅6,0
3
12
−
1,0
2
⋅
6,0⋅7,0−
3,0⋅1,5
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
6,0⋅7,0
3
12
0,5
2
⋅
6,0⋅7,0−
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0
−
1,0
⋅
0,5⋅6,0⋅7,0−
−
1,5
2
⋅
3,0
2
72
−
1,0
⋅
1,0⋅
1
2
⋅
1,5⋅3,0
391
J
Y
=
7,0⋅6,0
3
12
−
1,0
2
⋅
6,0⋅7,0−
3,0⋅1,5
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
6,0⋅7,0
3
12
−
0,5
2
⋅
6,0⋅7,0−
1,5⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0
−
1,0
⋅
−
0,5
⋅
6,0⋅7,0−
−
1,5
2
⋅
3,0
2
72
−
0,5
⋅
−
1,0
⋅
1
2
⋅
1,5⋅3,0
392
J
Y
=
7,0⋅6,0
3
12
−
1,0
2
⋅
6,0⋅7,0−
3,0⋅1,5
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
6,0⋅7,0
3
12
−
0,5
2
⋅
6,0⋅7,0−
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0
−
1,0
⋅
−
0,5
⋅
6,0⋅7,0−
1,5
2
⋅
3,0
2
72
−
0,5
⋅
−
2,0
⋅
1
2
⋅
1,5⋅3,0
393
J
Y
=
7,0⋅6,0
3
12
−
1,0
2
⋅
6,0⋅7,0−
3,0⋅1,5
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
6,0⋅7,0
3
12
−
0,5
2
⋅
6,0⋅7,0−
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0
−
1,0
⋅
−
0,5
⋅
6,0⋅7,0−
−
1,5
2
⋅
3,0
2
72
−
1,0
⋅
−
2,0
⋅
1
2
⋅
1,5⋅3,0
394
J
Y
=
7,0⋅6,0
3
12
−
1,0
2
⋅
6,0⋅7,0−
3,0⋅1,5
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
6,0⋅7,0
3
12
−
0,5
2
⋅
6,0⋅7,0−
1,5⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
46
Nr
Momenty bezwładności
394
J
YZ
=
0,0
−
1,0
⋅
−
0,5
⋅
6,0⋅7,0−
1,5
2
⋅
3,0
2
72
−
1,0
⋅
−
1,0
⋅
1
2
⋅
1,5⋅3,0
395
J
Y
=
7,0⋅6,0
3
12
1,0
2
⋅
6,0⋅7,0−
3,0⋅1,5
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
6,0⋅7,0
3
12
−
0,5
2
⋅
6,0⋅7,0−
1,5⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,01,0⋅
−
0,5
⋅
6,0⋅7,0−
1,5
2
⋅
3,0
2
72
0,5⋅
−
1,0
⋅
1
2
⋅
1,5⋅3,0
396
J
Y
=
7,0⋅6,0
3
12
1,0
2
⋅
6,0⋅7,0−
3,0⋅1,5
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
6,0⋅7,0
3
12
−
0,5
2
⋅
6,0⋅7,0−
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,01,0⋅
−
0,5
⋅
6,0⋅7,0−
−
1,5
2
⋅
3,0
2
72
0,5⋅
−
2,0
⋅
1
2
⋅
1,5⋅3,0
397
J
Y
=
7,0⋅6,0
3
12
1,0
2
⋅
6,0⋅7,0−
3,0⋅1,5
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
6,0⋅7,0
3
12
−
0,5
2
⋅
6,0⋅7,0−
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,01,0⋅
−
0,5
⋅
6,0⋅7,0−
1,5
2
⋅
3,0
2
72
1,0⋅
−
2,0
⋅
1
2
⋅
1,5⋅3,0
398
J
Y
=
7,0⋅6,0
3
12
1,0
2
⋅
6,0⋅7,0−
3,0⋅1,5
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
6,0⋅7,0
3
12
−
0,5
2
⋅
6,0⋅7,0−
1,5⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,01,0⋅
−
0,5
⋅
6,0⋅7,0−
−
1,5
2
⋅
3,0
2
72
1,0⋅
−
1,0
⋅
1
2
⋅
1,5⋅3,0
399
J
Y
=
5,0⋅5,5
3
12
1,25
2
⋅
5,0⋅5,5−
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
5,5⋅5,0
3
12
0,5
2
⋅
5,0⋅5,5−
3,0⋅1,5
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,01,25⋅0,5⋅5,0⋅5,5−
1,5
2
⋅
3,0
2
72
1,0⋅1,0⋅
1
2
⋅
1,5⋅3,0
400
J
Y
=
5,0⋅5,5
3
12
1,25
2
⋅
5,0⋅5,5−
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
47
Nr
Momenty bezwładności
400
J
Z
=
5,5⋅5,0
3
12
0,5
2
⋅
5,0⋅5,5−
3,0⋅1,5
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,01,25⋅0,5⋅5,0⋅5,5−
−
1,5
2
⋅
3,0
2
72
1,0⋅0,5⋅
1
2
⋅
1,5⋅3,0
401
J
Y
=
5,0⋅5,5
3
12
1,25
2
⋅
5,0⋅5,5−
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
5,5⋅5,0
3
12
0,5
2
⋅
5,0⋅5,5−
3,0⋅1,5
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,01,25⋅0,5⋅5,0⋅5,5−
1,5
2
⋅
3,0
2
72
1,0⋅0,5⋅
1
2
⋅
1,5⋅3,0
402
J
Y
=
5,0⋅5,5
3
12
1,25
2
⋅
5,0⋅5,5−
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
5,5⋅5,0
3
12
0,5
2
⋅
5,0⋅5,5−
3,0⋅1,5
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,01,25⋅0,5⋅5,0⋅5,5−
−
1,5
2
⋅
3,0
2
72
2,0⋅1,0⋅
1
2
⋅
1,5⋅3,0
403
J
Y
=
5,0⋅5,5
3
12
−
1,25
2
⋅
5,0⋅5,5−
1,5⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
5,5⋅5,0
3
12
0,5
2
⋅
5,0⋅5,5−
3,0⋅1,5
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0
−
1,25
⋅
0,5⋅5,0⋅5,5−
1,5
2
⋅
3,0
2
72
−
1,0
⋅
0,5⋅
1
2
⋅
1,5⋅3,0
404
J
Y
=
5,0⋅5,5
3
12
−
1,25
2
⋅
5,0⋅5,5−
1,5⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
5,5⋅5,0
3
12
0,5
2
⋅
5,0⋅5,5−
3,0⋅1,5
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0
−
1,25
⋅
0,5⋅5,0⋅5,5−
−
1,5
2
⋅
3,0
2
72
−
1,0
⋅
1,0⋅
1
2
⋅
1,5⋅3,0
405
J
Y
=
5,0⋅5,5
3
12
−
1,25
2
⋅
5,0⋅5,5−
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
5,5⋅5,0
3
12
0,5
2
⋅
5,0⋅5,5−
3,0⋅1,5
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0
−
1,25
⋅
0,5⋅5,0⋅5,5−
1,5
2
⋅
3,0
2
72
−
2,0
⋅
1,0⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
48
Nr
Momenty bezwładności
406
J
Y
=
5,0⋅5,5
3
12
−
1,25
2
⋅
5,0⋅5,5−
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
5,5⋅5,0
3
12
0,5
2
⋅
5,0⋅5,5−
3,0⋅1,5
3
36
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0
−
1,25
⋅
0,5⋅5,0⋅5,5−
−
1,5
2
⋅
3,0
2
72
−
2,0
⋅
0,5⋅
1
2
⋅
1,5⋅3,0
407
J
Y
=
5,0⋅5,5
3
12
−
1,25
2
⋅
5,0⋅5,5−
1,5⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
5,5⋅5,0
3
12
−
0,5
2
⋅
5,0⋅5,5−
3,0⋅1,5
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0
−
1,25
⋅
−
0,5
⋅
5,0⋅5,5−
−
1,5
2
⋅
3,0
2
72
−
1,0
⋅
−
0,5
⋅
1
2
⋅
1,5⋅3,0
408
J
Y
=
5,0⋅5,5
3
12
−
1,25
2
⋅
5,0⋅5,5−
1,5⋅3,0
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
5,5⋅5,0
3
12
−
0,5
2
⋅
5,0⋅5,5−
3,0⋅1,5
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0
−
1,25
⋅
−
0,5
⋅
5,0⋅5,5−
1,5
2
⋅
3,0
2
72
−
1,0
⋅
−
1,0
⋅
1
2
⋅
1,5⋅3,0
409
J
Y
=
5,0⋅5,5
3
12
−
1,25
2
⋅
5,0⋅5,5−
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
5,5⋅5,0
3
12
−
0,5
2
⋅
5,0⋅5,5−
3,0⋅1,5
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0
−
1,25
⋅
−
0,5
⋅
5,0⋅5,5−
−
1,5
2
⋅
3,0
2
72
−
2,0
⋅
−
1,0
⋅
1
2
⋅
1,5⋅3,0
410
J
Y
=
5,0⋅5,5
3
12
−
1,25
2
⋅
5,0⋅5,5−
1,5⋅3,0
3
36
−
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
5,5⋅5,0
3
12
−
0,5
2
⋅
5,0⋅5,5−
3,0⋅1,5
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,0
−
1,25
⋅
−
0,5
⋅
5,0⋅5,5−
1,5
2
⋅
3,0
2
72
−
2,0
⋅
−
0,5
⋅
1
2
⋅
1,5⋅3,0
411
J
Y
=
5,0⋅5,5
3
12
1,25
2
⋅
5,0⋅5,5−
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
5,5⋅5,0
3
12
−
0,5
2
⋅
5,0⋅5,5−
3,0⋅1,5
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
Wytrzymałość materiałów
−
zadania sprawdzające
−
odpowiedzi
−
Charakterystyki ...
49
Nr
Momenty bezwładności
411
J
YZ
=
0,01,25⋅
−
0,5
⋅
5,0⋅5,5−
1,5
2
⋅
3,0
2
72
1,0⋅
−
0,5
⋅
1
2
⋅
1,5⋅3,0
412
J
Y
=
5,0⋅5,5
3
12
1,25
2
⋅
5,0⋅5,5−
1,5⋅3,0
3
36
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
5,5⋅5,0
3
12
−
0,5
2
⋅
5,0⋅5,5−
3,0⋅1,5
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,01,25⋅
−
0,5
⋅
5,0⋅5,5−
−
1,5
2
⋅
3,0
2
72
1,0⋅
−
1,0
⋅
1
2
⋅
1,5⋅3,0
413
J
Y
=
5,0⋅5,5
3
12
1,25
2
⋅
5,0⋅5,5−
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
5,5⋅5,0
3
12
−
0,5
2
⋅
5,0⋅5,5−
3,0⋅1,5
3
36
−
1,0
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,01,25⋅
−
0,5
⋅
5,0⋅5,5−
1,5
2
⋅
3,0
2
72
2,0⋅
−
1,0
⋅
1
2
⋅
1,5⋅3,0
414
J
Y
=
5,0⋅5,5
3
12
1,25
2
⋅
5,0⋅5,5−
1,5⋅3,0
3
36
2,0
2
⋅
1
2
⋅
1,5⋅3,0
J
Z
=
5,5⋅5,0
3
12
−
0,5
2
⋅
5,0⋅5,5−
3,0⋅1,5
3
36
−
0,5
2
⋅
1
2
⋅
1,5⋅3,0
J
YZ
=
0,01,25⋅
−
0,5
⋅
5,0⋅5,5−
−
1,5
2
⋅
3,0
2
72
2,0⋅
−
0,5
⋅
1
2
⋅
1,5⋅3,0
Dr inż. Janusz Dębiński
BNS-I
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