SKRIPTA RIJEÅ ENIH ZADATAKA IZ OTPORNOSTI MATERIJALA
SKRIPTA RIJEÅ ENIH ZADATAKA IZ OTPORNOSTI MATERIJALA SKRIPTA RIJEÅ ENIH ZADATAKA IZ OTPORNOSTI MATERIJALA
49. Zadatak Za zadani nosa� i optere�enje odrediti mjerodavan koeficijent sigurnosti prema teoriji najve�ih normalnih naprezanja u to�kama 1 i 2 presjeka I-I ako je zadano kriti�no naprezanje materijala �K. P = 30kN H = 25kN q = 15kN / m σ ΣF R ΣM 1 1, 5 − q ⋅1⋅ + q ⋅ 2 2 ΣF = 0 : R x Ax Ay y − H = 0 ⇒ R A = 0 : = + R 0 : B Presjek I – I : N = −25kN T = −18, 125kN 2 Ax M = 27, 1875kNm I I = H = 25kN + P ⋅1, 5 − R ⋅3 = 0 ⇒ R − q ⋅ 2, 5 − P = 0 ⇒ R 3 70 ⋅10 = + 70 ⋅10 ⋅ 12 6 4 = 5, 83⋅10 mm B Ay B = 49, 375kN 10 ⋅100 12 3 = 18, 125kN 10 ⋅ 70 ⋅5 + 10 ⋅100 ⋅ 60 + 20 ⋅ 40 ⋅120 159500 yT = = ⇒ y 10 ⋅ 70 + 10 ⋅100 + 20 ⋅ 40 2500 2 A = 2500mm S y y W K y max y max = 320MPa = z I y max = 40 ⋅ 20 ⋅ 5, 83⋅10 = 66, 2 T = 63, 8mm 40 ⋅ 20 12 2 2 ( 63, 8 − 5) + + 10 ⋅100 ⋅ ( 63, 8 − 60) + + 40 ⋅ 20 ⋅ ( 66, 2 −10) 6 ⇒ W y max 3 = 88, 1⋅10 mm 3 3 ( 66, 2 −10) + ( 66, 2 − 20) ⋅10 ⋅ ⇒ S = 55, 6 ⋅10 mm 3 66, 2 − 20 2 y y max T 40 2 1 30 10 30 70 mm z 3 20 100 10 130 2 78
79 To�ka 1 : MPa mm N b I S T MPa mm N A N xz y y xz x x 29 , 17 29 , 17 10 10 83 , 5 10 6 , 55 10 125 , 18 10 10 2500 10 25 1 2 6 3 3 max 1 1 2 3 1 = ⇒ = ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅ ⋅ = − = ⇒ − = ⋅ − = = τ τ σ σ To�ka 2 : 0 0 0 40 10 83 , 5 0 10 125 , 18 6 , 318 6 , 318 10 6 , 308 2500 10 25 10 1 , 88 10 1875 , 27 2 2 6 3 2 2 2 2 3 3 6 2 = = ⇒ = ⋅ ⋅ ⋅ ⋅ = ⋅ ⋅ = − = ⇒ − = − − = ⋅ − + ⋅ ⋅ − = + = y xz y y xz x y x S b I S T MPa mm N A N W M τ τ σ σ Provjera po teoriji najve�ih normalnih naprezanja (1. teorija �vrsto�e) : To�ka 1 : ( ) ( ) ( ) ( ) ( ) 6 , 24 13 320 00 , 13 29 , 17 4 10 5 , 0 10 5 , 0 4 5 , 0 5 , 0 1 1 1 1 2 2 1 2 1 2 1 1 1 = ⇒ = = = ⇒ ⋅ + − ⋅ + − ⋅ = ⋅ + ⋅ + ⋅ = k k MPa ek K ek ek xz x x ek σ σ σ σ τ σ σ σ To�ka 2 : ( ) ( ) ( ) ( ) ( ) 0 , 1 6 , 318 320 6 , 318 0 4 6 , 318 5 , 0 6 , 318 5 , 0 4 5 , 0 5 , 0 2 2 2 2 1 2 2 1 2 2 2 2 2 2 = ⇒ = = − = = ⇒ ⋅ + − ⋅ + − ⋅ = ⋅ + ⋅ + ⋅ = k k MPa ek K x ek ek xz x x ek σ σ σ σ σ τ σ σ σ
- 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 and 74: 73 Kut zaokreta u to�ki D : ( ) (
- Page 75 and 76: 75 Položaj neutralne osi : ° −
- Page 77: 77 ( ) ( ) ( ) ( ) ( ) ( ) T T y y
79<br />
To�ka 1 :<br />
MPa<br />
mm<br />
N<br />
b<br />
I<br />
S<br />
T<br />
MPa<br />
mm<br />
N<br />
A<br />
N<br />
xz<br />
y<br />
y<br />
xz<br />
x<br />
x<br />
29<br />
,<br />
17<br />
29<br />
,<br />
17<br />
10<br />
10<br />
83<br />
,<br />
5<br />
10<br />
6<br />
,<br />
55<br />
10<br />
125<br />
,<br />
18<br />
10<br />
10<br />
2500<br />
10<br />
25<br />
1<br />
2<br />
6<br />
3<br />
3<br />
max<br />
1<br />
1<br />
2<br />
3<br />
1<br />
=<br />
⇒<br />
=<br />
⋅<br />
⋅<br />
⋅<br />
⋅<br />
⋅<br />
=<br />
⋅<br />
⋅<br />
=<br />
−<br />
=<br />
⇒<br />
−<br />
=<br />
⋅<br />
−<br />
=<br />
=<br />
τ<br />
τ<br />
σ<br />
σ<br />
To�ka 2 :<br />
0<br />
0<br />
0<br />
40<br />
10<br />
83<br />
,<br />
5<br />
0<br />
10<br />
125<br />
,<br />
18<br />
6<br />
,<br />
318<br />
6<br />
,<br />
318<br />
10<br />
6<br />
,<br />
308<br />
2500<br />
10<br />
25<br />
10<br />
1<br />
,<br />
88<br />
10<br />
1875<br />
,<br />
27<br />
2<br />
2<br />
6<br />
3<br />
2<br />
2<br />
2<br />
2<br />
3<br />
3<br />
6<br />
2<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 />
y<br />
xz<br />
y<br />
y<br />
xz<br />
x<br />
y<br />
x<br />
S<br />
b<br />
I<br />
S<br />
T<br />
MPa<br />
mm<br />
N<br />
A<br />
N<br />
W<br />
M<br />
τ<br />
τ<br />
σ<br />
σ<br />
Provjera po teoriji najve�ih normalnih naprezanja (1. teorija �vrsto�e) :<br />
To�ka 1 :<br />
( ) ( )<br />
( ) ( ) ( )<br />
6<br />
,<br />
24<br />
13<br />
320<br />
00<br />
,<br />
13<br />
29<br />
,<br />
17<br />
4<br />
10<br />
5<br />
,<br />
0<br />
10<br />
5<br />
,<br />
0<br />
4<br />
5<br />
,<br />
0<br />
5<br />
,<br />
0<br />
1<br />
1<br />
1<br />
1<br />
2<br />
2<br />
1<br />
2<br />
1<br />
2<br />
1<br />
1<br />
1<br />
=<br />
⇒<br />
=<br />
=<br />
=<br />
⇒<br />
⋅<br />
+<br />
−<br />
⋅<br />
+<br />
−<br />
⋅<br />
=<br />
⋅<br />
+<br />
⋅<br />
+<br />
⋅<br />
=<br />
k<br />
k<br />
MPa<br />
ek<br />
K<br />
ek<br />
ek<br />
xz<br />
x<br />
x<br />
ek<br />
σ<br />
σ<br />
σ<br />
σ<br />
τ<br />
σ<br />
σ<br />
σ<br />
To�ka 2 :<br />
( ) ( )<br />
( ) ( ) ( )<br />
0<br />
,<br />
1<br />
6<br />
,<br />
318<br />
320<br />
6<br />
,<br />
318<br />
0<br />
4<br />
6<br />
,<br />
318<br />
5<br />
,<br />
0<br />
6<br />
,<br />
318<br />
5<br />
,<br />
0<br />
4<br />
5<br />
,<br />
0<br />
5<br />
,<br />
0<br />
2<br />
2<br />
2<br />
2<br />
1<br />
2<br />
2<br />
1<br />
2<br />
2<br />
2<br />
2<br />
2<br />
2<br />
=<br />
⇒<br />
=<br />
=<br />
−<br />
=<br />
=<br />
⇒<br />
⋅<br />
+<br />
−<br />
⋅<br />
+<br />
−<br />
⋅<br />
=<br />
⋅<br />
+<br />
⋅<br />
+<br />
⋅<br />
=<br />
k<br />
k<br />
MPa<br />
ek<br />
K<br />
x<br />
ek<br />
ek<br />
xz<br />
x<br />
x<br />
ek<br />
σ<br />
σ<br />
σ<br />
σ<br />
σ<br />
τ<br />
σ<br />
σ<br />
σ
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