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Wytrzymałość materiałów II
ZAD 4
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Dane:
γ
35
=
α
26
=
β
31
=
E
92.21 GPa
=
Temat
13
=
εa 571
=
εb 422
=
εc
118
−
=
ν
0.19
=
φa γ
=
φa 35
=
φb 180 β
−
γ
+
=
φb 184
=
φc γ α
+
=
φc 61
=
2
φa
⋅
70
=
2
φb
⋅
368
=
2
φc
⋅
122
=
sin 2
φa
⋅
dec
⋅
(
)
0.94
=
sin 2
φc
⋅
dec
⋅
(
)
0.848
=
cos 2
φa
⋅
dec
⋅
(
)
0.342
=
cos 2
φc
⋅
dec
⋅
(
)
0.53
−
=
sin 2
φb
⋅
dec
⋅
(
)
0.139
=
Nie pisać w nawiasach "dec"
cos 2
φb
⋅
dec
⋅
(
)
0.99
=
1
2
εx εy
+
(
)
1
2
εx εy
−
(
)
⋅
cos 2
φa
⋅
dec
⋅
(
)
⋅
+
1
2
γxy
⋅
sin 2
φa
⋅
dec
⋅
(
)
⋅
+
εa
=
1
2
εx εy
+
(
)
1
2
εx εy
−
(
)
⋅
cos 2
φb
⋅
dec
⋅
(
)
⋅
+
1
2
γxy
⋅
sin 2
φb
⋅
dec
⋅
(
)
⋅
+
εb
=
1
2
εx εy
+
(
)
1
2
εx εy
−
(
)
⋅
cos 2
φc
⋅
dec
⋅
(
)
⋅
+
1
2
γxy
⋅
sin 2
φc
⋅
dec
⋅
(
)
⋅
+
εc
=
Napisać że układ równań obliczony za pomocą jakiego programu, lub samemu obliczyć.
εx 323
=
εy
1097
−
=
γxy 1522
=
Wyznaczenie kierunków odkształceń głównych
tg2
α
γxy
εx εy
−
1522
323
1097
−
(
)
−
=
=
tg2
α 1.072
=
α
atan tg2
α
(
)
180
π
⋅
2
=
α
23.49
=
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Wyznaczenie wartości odkształceń głównych
ε1
1
2
εx εy
+
(
)
1
2
εx εy
−
(
)
2
γxy
2
+
⋅
+
1
2
323
1097
−
(
)
+
[
]
⋅
1
2
323
1097
−
(
)
−
[
]
2
1522
2
+
⋅
+
=
=
ε2
1
2
εx εy
+
(
)
1
2
εx εy
−
(
)
2
γxy
2
+
⋅
−
1
2
323
1097
−
(
)
+
[
]
⋅
1
2
323
1097
−
(
)
−
[
]
2
1522
2
+
⋅
−
=
=
ε1 653.78
=
ε2
1427.78
−
=
Wyznaczenie wartości naprężeń
G
E
2 1
ν
+
(
)
⋅
=
σx
E
1
ν
2
−
εx ν εy
⋅
+
(
)
10
6
−
⋅
92.21 GPa
⋅
1
0.19
2
−
323
0.19
1097
−
(
)
⋅
+
[
]
⋅
10
6
−
⋅
=
=
σx 10.96 MPa
=
σy
E
1
ν
2
−
εy ν εx
⋅
+
(
)
10
6
−
⋅
92.21 GPa
⋅
1
0.19
2
−
1097
−
(
)
0.19 323
⋅
+
[
]
⋅
10
6
−
⋅
=
=
σy
99.07
−
MPa
=
τxy G γxy
⋅
10
6
−
⋅
92.21 GPa
⋅
2 1
0.19
+
(
)
⋅
1522
⋅
10
6
−
⋅
=
=
τxy 58.97 MPa
=
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