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1/11

Univerzitet u Tuzli

RGGF

Odsjek: Graevinski

Otpornost materijala sa teorijom elastinosti II

Autor: Mutapi Elmir Recenzent: Dobrnji Elvedin

2015


2/11

ZADATAK 1

Dimenzionisati gredu optereenu na koso savijanje ako je zadato:

-Optereenje grede kao na slici:

-Presjek grede:

-Doputeni napon: =14 kN/cm2


3/11

DIO 1:

tt

ttttttY

tt

ttttttX

tttttttA

T

T

3226,16310

5,27100161265,384

919,9310

151005,8126684

310205718127

2

222

2

222

2

1

DIO 2: (upljina)

t

t

ttttttY

tt

ttttttX

tttttttA

T

T

9804,15

204

5,2754161005,350

6078,9204

15545,8100650

204183520105

2

222

2

222

1


4/11

Teite cijelog presjeka:

tt

ttttY

t

t

ttttX

tttA

T

T

983,16106

98,15204323,16310

52,10

106

608,920492,9310

106204310

2

22

2

22

222

Momenti inercije:

Za dio 1:

4

222

4444

223

223

223

4444

223

223

223

035,10081

)48,4()517,10(100)02,2()983,0(126)52,4()483,13(84

157,9093373,534063,10281536,2724

)48,4(10012

205)02,2(126

12

718)52,4(84

12

127

28,30406062,1126975,3523468,15613

)517,10(10012

520)983,0(126

12

187)483,13(84

12

712

tI

tttttttI

ttttI

tttt

tttt

tttt

I

ttttI

tttt

tttt

tttt

I

XY

XY

Y

Y

X

X

Za dio 2:

4

222

4444

223

223

223

4444

22

3

22

3

22

3

996,5789

)48,4()517,10(54)02,2()983,0(100)52,4()483,13(50

36,45968016,25413733,6161866,1438

)48,4(5412

183)02,2(100

12

520)52,4(50

12

105

98,18636293,601396,3429731,9193

)517,10(5412318)983,0(100

12205)483,13(50

12510

tI

tttttttI

ttttI

tttt

tttt

tttt

I

ttttI

ttttttttttttI

XY

XY

Y

Y

X

X

Ukupni momenti inercije za cijeli presjek:

444

444

444

04,4291996,5789035,10081

797,449636,4596157,9093

3,1176998,1863628,30406

tttI

tttI

tttI

XY

Y

X


5/11

Momenti savijanja:

kNmM

kNmM

kNRkNRRM ABBA

13503450

18004450

450450046007300100

2

1

2

)()(

496,8392,62cos

245,15922,62sin

1800

XYYX

XYXXYXYYYX

Y

X

MAX

III

xIMIMyIMIM

kNmMM

kNmMM

kNmM

Koordinate najoptereenije take (x,y)

A(-10,52t ; -16,983t)

Pomou pravila desne ruke odreujemo predznak momenta.Na slici je prikazan pozitivan smijer

momenta,palac treba da otijentisan u smijeru ose,a ostali prsti pokazuju smijer momenta.


6/11

cmtt

kNm

tt

tt

ttt

ttt

ttt

ttt

675,214

1006798,26798,214

6798,2

65,34511128

39,3206383784,60420276

)04,4291(797,44963,11769

)52,10())04,4291245,1592(3,11769496,839(

)04,4291(797,44963,11769

)983,16()04,4291496,839797,4496245,1592(

33

38

55

2444

44

2444

44


7/11

ZADATAK 2

Odrediti:

-Napone u presjeku ako sila F=10000kN ima koordinate (30,15) u odnosu na teini koordinatni

sistem

-Jezgro presjeka

-Uporediti dobijene napone sa naponima kada je sila u teitu presjeka


8/11

Povrina presjeka:

Teite presjeka:

Momenti inercije:

25,47023012022

45122

2

755,7

cmA

cmcmXT 6198,605,4702

603600210527022525,281

423

23

23

43

23

23

25,6334571)1360012

12030(2)44270

36

4512(2)3625,281

36

755,7(

44,64328312

301202)19270

36

1245(2)5,1725,281

36

5,775(

cmI

cmI

Y

X


9/11

Poluprenici inercije:

cmA

Ii

cm

A

Ii

YY

XX

7,36

7,11

Neutralna osa:

cm

Y

iN

cmX

iN

F

XY

F

YX

13,9

15

7,11

9,4430

7,36

22

22

Naponi u presjeku:

2

22

2

22

/00,6))61(7,36

30)5,22(

7,11

151(

5,4702

10000

/21,11)597,36

3027

7,11

151(

5,4702

10000

cmkN

cmkN

ZB

ZA


10/11

Jezgro presjeka:

Neutralne ose 1 i 2 nam sijeku X osu na velikoj udaljenosti.To moemo odrediti na sledei nain:

cm

XX

cm

66159720

7200375,0

27270375,0

0375,0120

5,45,45,2227

Koordinate jezgre presjeka:

0

08,2261

7,36

0

83,2259

7,36

52,58,24

7,11

04,2

52,58,24

7,11

04,2661

7,36

2

4

22

4

2

3

22

3

22

2

2

2

22

1

22

1

Y

iY

cmX

iX

Y

iY

cmX

iX

cmY

iY

cmX

iX

cmY

iY

cmX

iX

X

Y

X

Y

X

Y

X

Y


11/11

)(/126,25,4702

10000 2 PRITISAKcmkNA

FZ

Vei je pritiskujui napon kada je presjek ekscentrino optereen: -11,21kN/cm2

> -2,126kN/cm2

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