SKRIPTA RIJEÅ ENIH ZADATAKA IZ OTPORNOSTI MATERIJALA

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46. Zadatak Koriste�i analiti�ki postupak odre�ivanja elasti�ne linije nosa�a odrediti kut zaokreta u to�kama D i F te progib u to�ki E. a = 5m kN q = 10 m b = 2m P = 50kN c = d = 1m EI 5 2 = 8⋅10 Nm Ekvivalentni sustav Reakcije u osloncima ∑ M ∑ M ∑ F z d D A = 0 → F = 0 → q ⋅ 7 ⋅3, 5 + P ⋅8 − F ⋅5 − F ⋅9 = 0 → F = 0 → F A F y ⋅ 2 − P ⋅1 = 0 → F − q ⋅ 7 − P + F F C + F C F = P 50 = = 25kN 2 2 F = 0 → F A C = 11kN = 420 = 84kN 5 70
Momenti savijanja na pojedinim segmentima : ( I ) 0 ≤ x ≤ a → M ( x) = F A 2 x ⋅ x − q ⋅ 2 ( II ) a ≤ x ≤ ( a + b) → M ( x) = F ⋅ x − q ⋅ + F ⋅ ( x − 5) A ( III )( a + b) ≤ x ≤ ( a + b + c) → M ( x) = F ⋅ x − q ⋅ + F ⋅ ( x − 5) ( IV )( a + b + c) ≤ x ≤ ( a + b + c + d ) → M ( x) = F ⋅ x − q ⋅ + F ⋅ ( x − 5) 2 x 2 A C A 2 x 2 C 2 x 2 C + q ⋅ ( x − 7) 2 2 + q ⋅ Iz diferencijalne jednadžbe elasti�ne linije nosa�a slijedi za moment savijanja : 2 d w EI = −M 2 dx 2 d w EI = −F 2 dx 2 d w 2 dx ( I ) ( x) 2 x ⋅ x + q ⋅ 2 2 x 2 ( II ) EI = −F ⋅ x + q ⋅ − F ⋅ ( x − 5) 2 d w 2 dx 2 x 2 ( III ) EI = −F ⋅ x + q ⋅ − F ⋅ ( x − 5) 2 d w 2 dx A A A 2 x 2 ( IV ) EI = −F ⋅ x + q ⋅ − F ⋅ ( x − 5) Za kut zaokreta : 2 3 dw x x ( I ) EI = −FA ⋅ + q ⋅ + C dx 2 6 ( II ) ( III ) ( IV ) ( II ) ( III ) ( IV ) A 2 3 dw x x EI = −FA ⋅ + q ⋅ − FC ⋅ dx 2 6 2 3 dw x x EI = −FA ⋅ + q ⋅ − FC ⋅ dx 2 6 2 3 dw x x EI = −FA ⋅ + q ⋅ − FC ⋅ dx 2 6 Za progib nosa�� : 3 4 x x ( I ) EIw = −FA ⋅ + q ⋅ + C1 ⋅ x + D 6 24 3 4 x x EIw = −FA ⋅ + q ⋅ − FC ⋅ 6 24 3 4 x x EIw = −FA ⋅ + q ⋅ − FC ⋅ 6 24 3 4 x x EIw = −FA ⋅ + q ⋅ − FC ⋅ 6 24 1 C C C ( x − 5) 2 − q ⋅ − q ⋅ 2 ( x − 7) 2 ( x − 7) 2 2 ( x − 5) ( x − 7) 2 2 2 2 + P ⋅ ( x − 8) 2 3 ( x − 5) ( x − 7) ( x − 8) 1 2 ( x − 5) 6 3 + C − q ⋅ − q ⋅ 6 6 3 ( x − 5) ( x − 7) 6 2 3 + C 3 + P ⋅ 3 4 ( x − 5) ( x − 7) ( x − 8) 6 + C − q ⋅ − q ⋅ ⋅ x + D 24 24 2 4 + C 3 + P ⋅ 6 2 ⋅ x + D 3 3 2 + C + C 4 4 ⋅ x + D ( x − 7) 4 2 2 − P ⋅ ( x − 8) 71
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GRA�EVINSKI FAKULTET SVEU�ILIŠ
Page 3 and 4:
2. Zadatak Odrediti naprezanja u š
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9 cm m A E l S l cm m A E l S l MPa
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11 9. Zadatak ( ) ( ) ( ) ( ) MPa m
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11. Zadatak Cilindri�ni stup prom
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15 Sile u štapovima : ( ) ( ) ( )
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17 Iz uvjeta ravnoteže sila : ( )
Page 19 and 20: 15. Zadatak Za zadano stanje naprez
Page 21 and 22: 16. Zadatak Za zadano stanje naprez
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: 69 Posmi��
Page 73 and 74: 73 Kut zaokreta u to�ki D : ( ) (
Page 75 and 76: 75 Položaj neutralne osi : ° −
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
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SKRIPTA RIJEÅ ENIH ZADATAKA IZ OTPORNOSTI MATERIJALA

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