SKRIPTA RIJEÅ ENIH ZADATAKA IZ OTPORNOSTI MATERIJALA
SKRIPTA RIJEÅ ENIH ZADATAKA IZ OTPORNOSTI MATERIJALA SKRIPTA RIJEÅ ENIH ZADATAKA IZ OTPORNOSTI MATERIJALA
74 47. Zadatak Odrediti to����������������������������������������������������������������������������� m cm a m l kN F 2 , 0 20 5 10 = = = = ( ) 4 2 2 ' 4 2 2 3 2 2 3 ' 4 2 2 3 2 2 3 ' 2 2 2 2 2 2 2 2 3 1 6 5 6 7 2 3 2 0 6 5 2 6 7 2 0 12 11 6 5 2 12 2 6 5 2 12 12 11 6 7 2 3 2 12 2 6 7 2 12 6 7 3 2 3 2 2 6 5 3 2 2 3 2 a a a a a a a a a a a I a a a a a a a a a a a I a a a a a a a a a a a I a a a a a a z a a a a a a y a a a a A yz z y T T = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⋅ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⋅ + + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⋅ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⋅ + = = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⋅ + ⋅ + ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⋅ + ⋅ = = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⋅ + ⋅ + ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⋅ + ⋅ = = ⋅ + ⋅ = = ⋅ + ⋅ = = + ⋅ = Glavne osi momenata površine drugog reda : ( ) ( ) ( ) 0 12 7 3 1 12 11 4 5 3 1 12 11 3 1 12 11 3 1 2 2 1 12 11 2 2 1 4 2 1 2 1 45 90 2 0 3 1 2 12 11 12 11 3 1 2 2 2 4 4 2 4 4 1 4 4 4 2 ' 2 ' ' ' ' 2 , 1 4 4 4 4 ' ' ' = = = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = = = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ± = ⋅ ± ⋅ ⋅ = + − ± + = ° = → ° = → ∞ = ⋅ − = − ⋅ − = − − = yz z y yz z y z y z y yz I I a a I I a a I a a a I I I I I I a a a a I I I tg α α α
75 Položaj neutralne osi : ° − = → − = − = ° − = − = 65 14286 , 2 7 15 45 12 7 4 5 4 4 ϕ α ϕ tg a a tg I I tg z y Ekstremna naprezanja su u to�kama B i D : MPa a Fl a Fl a a a a Fl y I z I M MPa a Fl a Fl a a a a Fl y I z I M D D z D y D B B z B y B 78 , 6 2 , 0 5 10 10 35 38 35 38 7 2 5 4 12 7 6 2 4 5 2 2 2 45 sin 45 cos 21 , 3 2 , 0 5 10 10 35 18 35 18 7 2 5 4 12 7 6 2 4 5 2 2 2 45 sin 45 cos 3 3 3 3 4 4 3 3 3 3 4 4 = ⋅ ⋅ = = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ° + ° = − = ⋅ ⋅ − = − = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − = ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + − = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ° + ° = σ σ σ σ a a a a a y a a a a a z a a a a a y a a a a a z D D B B 6 2 2 2 6 5 2 2 6 7 45 sin 6 5 45 cos 6 7 2 2 2 6 7 2 2 6 5 45 sin 6 7 45 cos 6 5 6 2 2 2 6 7 2 2 6 5 45 sin 6 7 45 cos 6 5 2 2 2 6 5 2 2 6 7 45 sin 6 5 45 cos 6 7 = − = ° − ° = = + = ° + ° = = + − = ° − − ° − = − = − + − = ° − + ° − =
- Page 23 and 24: 17. Zadatak Plo�a je izložena dj
- Page 25 and 26: 20. Zadatak U to�ki A napregnutog
- Page 27 and 28: 22. Zadatak Pravokutna plo�ica di
- Page 29 and 30: 24. Zadatak Odrediti glavna napreza
- Page 31 and 32: 27. Zadatak Za optere�enje na tla
- Page 33 and 34: t 29. Zadatak Odrediti potreban bro
- Page 35 and 36: 31. Zadatak Metalna vilica i plo�
- Page 37 and 38: 37 33. Zadatak Odrediti potrebnu du
- Page 39 and 40: 39 Moment od sile FMi s obzirom na
- Page 41 and 42: ∆D ( 1) 1 ( 1−ν ) 1 1 ∆D 2 =
- Page 43 and 44: 43 b) Nosivost zakovice ( ) ( ) 2 m
- Page 45 and 46: 45 ( ) ( ) Nmm kNm U U I G M I G M
- Page 47 and 48: 47 ( ) ( ) ° − = → ° − =
- Page 49 and 50: ( 2) ⎛ M A − ⎜ ⎝ GI pI M A
- Page 51 and 52: 41. Zadatak Odrediti potrebne dimen
- Page 53 and 54: 42. Zadatak Za nosa� oblika I-pro
- Page 55 and 56: 55 Iz kriterija �vrsto�e za mak
- Page 57 and 58: 43. Zadatak Za nosa� zadan i opte
- Page 59 and 60: II. podru�je: 2.2 m < x < 4 m III
- Page 61 and 62: c) dimenzioniranje nosa�a -��
- Page 63 and 64: - tangencijalno naprezanje 63
- Page 65 and 66: Maksimalni moment savijanja na udal
- Page 67 and 68: 45. Zadatak Za zadani nosa� i opt
- Page 69 and 70: 69 Posmi���������
- Page 71 and 72: Momenti savijanja na pojedinim segm
- Page 73: 73 Kut zaokreta u to�ki D : ( ) (
- Page 77 and 78: 77 ( ) ( ) ( ) ( ) ( ) ( ) T T y y
- Page 79 and 80: 79 To�ka 1 : MPa mm N b I S T MPa
74<br />
47. Zadatak<br />
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10<br />
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4<br />
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3<br />
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2<br />
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3<br />
2<br />
0<br />
6<br />
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Glavne osi momenata površine drugog reda :<br />
( ) ( ) ( )<br />
0<br />
12<br />
7<br />
3<br />
1<br />
12<br />
11<br />
4<br />
5<br />
3<br />
1<br />
12<br />
11<br />
3<br />
1<br />
12<br />
11<br />
3<br />
1<br />
2<br />
2<br />
1<br />
12<br />
11<br />
2<br />
2<br />
1<br />
4<br />
2<br />
1<br />
2<br />
1<br />
45<br />
90<br />
2<br />
0<br />
3<br />
1<br />
2<br />
12<br />
11<br />
12<br />
11<br />
3<br />
1<br />
2<br />
2<br />
2<br />
4<br />
4<br />
2<br />
4<br />
4<br />
1<br />
4<br />
4<br />
4<br />
2<br />
'<br />
2<br />
'<br />
'<br />
'<br />
'<br />
2<br />
,<br />
1<br />
4<br />
4<br />
4<br />
4<br />
'<br />
'<br />
'<br />
=<br />
=<br />
=<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎝<br />
⎛<br />
−<br />
=<br />
=<br />
=<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎝<br />
⎛<br />
+<br />
=<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎝<br />
⎛<br />
±<br />
=<br />
⋅<br />
±<br />
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⋅<br />
=<br />
+<br />
−<br />
±<br />
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=<br />
°<br />
=<br />
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°<br />
=<br />
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∞<br />
=<br />
⋅<br />
−<br />
=<br />
−<br />
⋅<br />
−<br />
=<br />
−<br />
−<br />
=<br />
yz<br />
z<br />
y<br />
yz<br />
z<br />
y<br />
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y<br />
z<br />
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yz<br />
I<br />
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a<br />
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I<br />
I<br />
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I<br />
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