SKRIPTA RIJEÅ ENIH ZADATAKA IZ OTPORNOSTI MATERIJALA

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Uvjeti kompatibilnosti deformacija : ϕ ϕ w w w ( I ) ( II ) ( a) = ϕ ( a) → C ( III ) ( IV ) ( a + b + c) = ϕ ( a + b + c) ( I ) ( II ) ( a) = w ( a) → D = D 1 1 = C 2 2 ( II ) ( III ) ( a + b) = w ( a + b) → C ⋅ 7 + D = C ⋅ 7 + D K( 1) 2 → C ( III ) ( IV ) ( a + b + c) = w ( a + b + c) → C3 ⋅8 + D3 = C4 ⋅8 + D4 → D3 = D4 Rubni uvjeti : w w w ( 0) ( I ) ( a) = w ( x = 5) ( IV ) ( l) = w ( x = 9) 3 2 = C + 9 ⋅C 4 + D4 = 0K( 2) ( 1) ⇒ −6, 25⋅ 7 + 0 = C4 ⋅ 7 + D4 → D4 = −43, 75 − 7 ⋅C 4 K( 3) ( 3) → ( 2) ⇒ C = −229, 58 = C 502, 917 D 4 = 0 → D = 1563, 31 = D Progib u to�ki E : w w w E E E = w 1 4 = 0 → D 3 2 = D 1 = 0 3 4 9 9 = 0 → −11⋅ + 10 ⋅ − 84 ⋅ 6 24 3 4 3 3 4 5 5 = 0 → −11 + 10 + C1 ⋅5 = 0 → C1 = −6, 25 = C 6 24 ( III ) ( IV ) ( x = 8) = w ( x = 8) 3 10 = 8⋅10 6 3 4 ⎡ 8 8 ⎢−11⋅ + 10 ⋅ − 84 ⋅ ⎣ 6 24 −3 = 14, 53⋅10 m = 14, 53mm Kut zaokreta u to�ki F : ϕ = ϕ ϕ ϕ F F F ( IV ) ( x = 9) 3 10 = 8 ⋅10 = 6 −15, 05 ⋅10 1 = EI y ⎡ ⎢− F ⎣ 2 3 ⎡ 9 9 ⎢−11⋅ + 10 ⋅ − 84 ⋅ ⎣ 2 6 −3 rad = −0, 01505rad A 3 3 4 ( 9 − 5) ( 9 − 7) ( 9 − 8) 6 3 ( 8 − 5) ( 8 − 7) 6 −10 ⋅ 24 −10 ⋅ 3 4 1 ⎡ x x = ⎢− FA ⋅ + q ⋅ − FC ⋅ EI y ⎣ 6 24 2 3 x x ⋅ + q ⋅ − FC ⋅ 2 6 4 − 24 2 + 50 ⋅ 6 3 ( x − 5) ( x − 7) 6 − q ⋅ 24 ⎤ 229, 58⋅ 8 + 1563, 31⎥ ⎦ 2 3 ( x − 5) ( x − 7) ( x − 8) − q ⋅ 2 3 ( 9 − 5) ( 9 − 7) ( 9 − 8) 2 −10 ⋅ 2 6 + 50 ⋅ 6 2 + P ⋅ 2 2 3 4 2 ⎤ − 229, 58⎥ ⎦ + C 4 ⋅9 + D ⎤ + C3 ⋅ x + D3 ⎥ ⎦ ⎤ + C4 ⎥ ⎦ 4 = 0 72
73 Kut zaokreta u to�ki D : ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) rad rad rad rad C x q x F x q x F EI C x F x q x F EI x x D d D d D l D l D C A y d D C A y l D III II d D l D D 00406 , 0 01193 , 0 01599 , 0 01193 , 0 10 93 , 11 58 , 229 6 7 7 10 2 5 7 84 6 7 10 2 7 11 10 8 10 01599 , 0 10 99 , 15 25 , 6 2 5 7 84 6 7 10 2 7 11 10 8 10 6 7 2 5 6 2 1 2 5 6 2 1 7 7 3 3 2 3 2 6 3 3 2 3 2 6 3 3 3 2 3 2 2 2 3 2 = − = − = ⋅ − = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − ⋅ − − ⋅ − ⋅ + ⋅ − ⋅ = = ⋅ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − ⋅ − ⋅ + ⋅ − ⋅ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + − ⋅ − − ⋅ − ⋅ + ⋅ − = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + − ⋅ − ⋅ + ⋅ − = = + = = + = − − ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ
Page 1 and 2:
GRA�EVINSKI FAKULTET SVEU�ILIŠ
Page 3 and 4:
2. Zadatak Odrediti naprezanja u š
Page 5 and 6:
Page 7 and 8:
Page 9 and 10:
9 cm m A E l S l cm m A E l S l MPa
Page 11 and 12:
11 9. Zadatak ( ) ( ) ( ) ( ) MPa m
Page 13 and 14:
11. Zadatak Cilindri�ni stup prom
Page 15 and 16:
15 Sile u štapovima : ( ) ( ) ( )
Page 17 and 18:
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 and 70: 69 Posmi��
Page 71: Momenti savijanja na pojedinim segm
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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