SKRIPTA RIJEÅ ENIH ZADATAKA IZ OTPORNOSTI MATERIJALA

∆D
( 1)
1 ( 1−ν
)
1
1
∆D
2
= ε D
2
1
2
1
1
= ε D
pD
⎯⎯→
E
D
≅ D
p =
1600
0,
7 ⋅10
2
5
=
pD
E
1
1
1
( 1−ν
)
2
2
pD
=
2tE
2
≅ 1600mm
1,
1
( 1−
0,
34)
1
2
2
pD
+
2tE
2
= 1,
1 → p =
D
E
2
1600
+
2 ⋅5
⋅ 2 ⋅10
5
=
1
1
0,
85
1,
1
( 1−ν
)
N
mm
2
1
2
2
D
+
2tE
= σ
Naprezanje u prstenu (homogeno stanje naprezanja) :
( 2)
pD2
0,
85⋅1600
N
σ 1 = = = 136,
0 2
2t 2 ⋅5
mm
Sila u prstenu :
( 2)
1
S = t ⋅ h ⋅σ
= 5⋅
200 ⋅136,
0 = 136kN
Kontrola :
∆D
2
∆D
1
( 2)
1
σ
= D2
E
pD1
=
E
1
1
2
136,
0
= 1600 = 1,
087mm
5
2 ⋅10
0,
85⋅1600
5
0,
7 ⋅10
( 1−ν
) = ( 1−
0,
34)
∆D
= ∆D
+ ∆D
= 1,
087 +
2
1
0,
013
= 1,
1mm
= 0,
013mm
2
( 1)
( 1)
1 = σ 2
41