SKRIPTA RIJEÅ ENIH ZADATAKA IZ OTPORNOSTI MATERIJALA
SKRIPTA RIJEÅ ENIH ZADATAKA IZ OTPORNOSTI MATERIJALA SKRIPTA RIJEÅ ENIH ZADATAKA IZ OTPORNOSTI MATERIJALA
12. Zadatak Dimenzionirati �eli�nu zategu kružnog pore�nog presjeka (A1) i drveni kosnik pravokutnog popre�nog presjeka (h=2b) površine A2 = 10A1 ako je F=155 kN a dopušteni naponi za �elik 12 ·10 7 N/m 2 i drvo 6·10 6 N/m 2 . 7 N σ 1dop = 12 ⋅10 m 6 N σ 2dop = 6 ⋅10 2 m 11 N E1 = 2 ⋅10 2 m 10 N E2 = 1⋅10 2 m E = 20E A 1 2 = 10 A h = 2b 2 1 Plan pomaka : 2 l / 2 3 sinα = = 5l / 6 5 2l / 3 4 cosα = = 5l / 6 5 l l 2 1 2 = l 3 5 = l 6 sin β = cos β = 14 2 2
15 Sile u štapovima : ( ) ( ) ( ) ( ) kN S kN S F F F S S S S l A E l A E S S l A E l A E S A E l S A E l S A E l S l A E l S l l l l S l S Fl M D C C D D c A 4 , 353 ; 9 , 58 38 , 0 2 6 1 5 12 sin 4 sin 3 1 1 6 2 5 2 6 10 2 3 3 5 20 2 sin sin 2 sin 2 sin 2 sin sin ; sin sin 2 2 3 2 3 1 1 0 3 1 sin 3 2 sin 0 1 2 2 2 1 2 1 2 1 2 1 2 1 2 2 2 1 1 1 2 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 = = → = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = + = ⇒ ⇒ → = ⇒ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = = → = ⇒ = ∆ = = ∆ = = → = = − − → = ∑ α β β α β α α α δ β β δ δ δ δ δ β α K K Dimenzioniranje : cm h cm b cm A b cn b h b A cm A A cm d cm m d S d S d A A S dop dop dop 74 , 27 87 , 13 87 , 13 2 8 , 384 2 8 , 384 2 8 , 384 48 , 38 10 10 7 6 06 , 0 10 12 10 4 , 353 4 4 4 2 2 2 2 2 1 2 7 3 1 1 1 1 2 1 1 1 1 1 = = = = = ⇒ = = ⋅ = = ⋅ = = = → = ≥ ⋅ ⋅ ⋅ ⋅ = ≥ → ≥ = → ≤ = π πσ σ π σ σ Kontrola napona : MPa MPa A S MPa MPa A S dop dop 6 53 , 1 10 87 , 13 2 10 9 , 58 120 84 , 91 4 10 7 10 4 , 353 2 4 2 3 2 2 2 1 4 2 3 1 1 1 = ≤ = ⋅ ⋅ ⋅ = = = ≤ = ⋅ ⋅ = = − − σ σ σ π σ
- Page 1 and 2: GRA�EVINSKI FAKULTET SVEU�ILIŠ
- Page 3 and 4: 2. Zadatak Odrediti naprezanja u š
- Page 5 and 6: 4. Zadatak Odrediti naprezanja u š
- Page 7 and 8: 6. Zadatak Odrediti naprezanja u š
- 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: 11. Zadatak Cilindri�ni stup prom
- 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
15<br />
Sile u štapovima :<br />
( )<br />
( )<br />
( )<br />
( )<br />
kN<br />
S<br />
kN<br />
S<br />
F<br />
F<br />
F<br />
S<br />
S<br />
S<br />
S<br />
l<br />
A<br />
E<br />
l<br />
A<br />
E<br />
S<br />
S<br />
l<br />
A<br />
E<br />
l<br />
A<br />
E<br />
S<br />
A<br />
E<br />
l<br />
S<br />
A<br />
E<br />
l<br />
S<br />
A<br />
E<br />
l<br />
S<br />
l<br />
A<br />
E<br />
l<br />
S<br />
l<br />
l<br />
l<br />
l<br />
S<br />
l<br />
S<br />
Fl<br />
M<br />
D<br />
C<br />
C<br />
D<br />
D<br />
c<br />
A<br />
4<br />
,<br />
353<br />
;<br />
9<br />
,<br />
58<br />
38<br />
,<br />
0<br />
2<br />
6<br />
1<br />
5<br />
12<br />
sin<br />
4<br />
sin<br />
3<br />
1<br />
1<br />
6<br />
2<br />
5<br />
2<br />
6<br />
10<br />
2<br />
3<br />
3<br />
5<br />
20<br />
2<br />
sin<br />
sin<br />
2<br />
sin<br />
2<br />
sin<br />
2<br />
sin<br />
sin<br />
;<br />
sin<br />
sin<br />
2<br />
2<br />
3<br />
2<br />
3<br />
1<br />
1<br />
0<br />
3<br />
1<br />
sin<br />
3<br />
2<br />
sin<br />
0<br />
1<br />
2<br />
2<br />
2<br />
1<br />
2<br />
1<br />
2<br />
1<br />
2<br />
1<br />
2<br />
1<br />
2<br />
2<br />
2<br />
1<br />
1<br />
1<br />
2<br />
2<br />
2<br />
2<br />
1<br />
1<br />
1<br />
1<br />
1<br />
1<br />
1<br />
1<br />
1<br />
2<br />
2<br />
2<br />
2<br />
2<br />
2<br />
1<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 />
=<br />
∆<br />
=<br />
=<br />
∆<br />
=<br />
=<br />
→<br />
=<br />
=<br />
−<br />
−<br />
→<br />
=<br />
∑<br />
α<br />
β<br />
β<br />
α<br />
β<br />
α<br />
α<br />
α<br />
δ<br />
β<br />
β<br />
δ<br />
δ<br />
δ<br />
δ<br />
δ<br />
β<br />
α<br />
K<br />
K<br />
Dimenzioniranje :<br />
cm<br />
h<br />
cm<br />
b<br />
cm<br />
A<br />
b<br />
cn<br />
b<br />
h<br />
b<br />
A<br />
cm<br />
A<br />
A<br />
cm<br />
d<br />
cm<br />
m<br />
d<br />
S<br />
d<br />
S<br />
d<br />
A<br />
A<br />
S<br />
dop<br />
dop<br />
dop<br />
74<br />
,<br />
27<br />
87<br />
,<br />
13<br />
87<br />
,<br />
13<br />
2<br />
8<br />
,<br />
384<br />
2<br />
8<br />
,<br />
384<br />
2<br />
8<br />
,<br />
384<br />
48<br />
,<br />
38<br />
10<br />
10<br />
7<br />
6<br />
06<br />
,<br />
0<br />
10<br />
12<br />
10<br />
4<br />
,<br />
353<br />
4<br />
4<br />
4<br />
2<br />
2<br />
2<br />
2<br />
2<br />
1<br />
2<br />
7<br />
3<br />
1<br />
1<br />
1<br />
1<br />
2<br />
1<br />
1<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 />
⋅<br />
⋅<br />
=<br />
≥<br />
→<br />
≥<br />
=<br />
→<br />
≤<br />
=<br />
π<br />
πσ<br />
σ<br />
π<br />
σ<br />
σ<br />
Kontrola napona :<br />
MPa<br />
MPa<br />
A<br />
S<br />
MPa<br />
MPa<br />
A<br />
S<br />
dop<br />
dop<br />
6<br />
53<br />
,<br />
1<br />
10<br />
87<br />
,<br />
13<br />
2<br />
10<br />
9<br />
,<br />
58<br />
120<br />
84<br />
,<br />
91<br />
4<br />
10<br />
7<br />
10<br />
4<br />
,<br />
353<br />
2<br />
4<br />
2<br />
3<br />
2<br />
2<br />
2<br />
1<br />
4<br />
2<br />
3<br />
1<br />
1<br />
1<br />
=<br />
≤<br />
=<br />
⋅<br />
⋅<br />
⋅<br />
=<br />
=<br />
=<br />
≤<br />
=<br />
⋅<br />
⋅<br />
=<br />
=<br />
−<br />
−<br />
σ<br />
σ<br />
σ<br />
π<br />
σ
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