Proračun Ab Grede-Anvelope

IV. Proraun grede pozicija 207 208 207

IV.I Analiza optereenja: Na gredu djeluje optereenje od ploe pozicija 202-203-203-202. Greda je T presijeka.

Stalno optereenje : Vlastita teina grede : mkNgvt /66,225,0125028,0 Stalno optereenje od ploe pozicija 202-203-203-202 :

-3 ,7 3 k N /m -3 ,7 3 k N /m -3 ,7 3 k N /m -3 ,7 3 k N /m

3 ,9 3 5 m 3 ,9 3 5 m 3 ,9 3 5 m 3 ,9 3 5 mC 3 5 /4 5 C 3 5 /4 5 C 3 5 /4 5 C 3 5 /4 5

-5,7

7 kN

7,87

kN

-6,8

1 kN

8,91

kN

5,77

kN

-7,8

7 kN

-6,8

1 kN8,91

kN

mkNl

gR yg /78,16287,773,3143,1

2143,1

Ukupno stalno optereenje : /203202 /44,1978,1666,2 mkNRgg gvt

Pokretno optereenje : Pokretno optereenje od ploe pozicija 202-203-203-202 :

C 3 5 /4 5C 3 5 /4 5C 3 5 /4 53 ,9 3 5 m 3 ,9 3 5 m C 3 5 /4 53 ,9 3 5 m 3 ,9 3 5 m

- 6 ,2 3 k N - 6 ,2 3 k N - 6 ,2 3 k N

15,2

2 kN

-14,

78 k

N

10,8

4 kN

13,6

8 kN

9,73

kN

-9,2

9 kN

0,98

kN

mkNl

qR yq /98,29287,723,6223,1

2223,1

IV.II Statiki proraun Stalno optereenje :

3 0 x 5 03 0 x 5 0 3 0 x 5 0

-1 9 ,4 4 k N /m

120,

10 k

Nm

120,

10 k

Nm

120,

10 k

Nm

120,

10 k

Nm

-1 9 ,4 4 k N /m -1 9 ,4 4 k N /m

7 ,8 6 m 7 ,8 6 m 7 ,8 6 mC 3 5 /4 5 C 3 5 /4 5 C 3 5 /4 5

-9 6 ,0 8 k N m

-3 0 ,0 2 k N m

-9 6 ,0 8 k N m

kNmlgM xg 08,9686,744,1908,008,0

22207 kNmlgM xg 02,3086,744,19025,0025,0

22208 kNmlgM xg 10,12086,744,191,01,0

22208207

30x5030x50 30x50

-19 ,44kN /m -19 ,44kN /m -19 ,44kN /m

91,6

8 kN

-61,

12 k

N

-76,

40 k

N

7 ,86 m 7 ,86 m 7 ,8 6 mC 35 /45 C 35 /45 C 35 /45

-61,

12 k

N

76,4

0 kN

91,6

8 kN

08,16886,744,191,11,1208207 xg lgR Polje 207 : Pokretno optereenje

7 ,8 6 m3 0 x 5 0

C 3 5 /4 5C 3 5 /4 5C 3 5 /4 53 0 x 5 0

7 ,8 6 m3 0 x 5 0

7 ,8 6 m

92,6

1 kN

m

92,6

1 kN

m

92,6

1 kN

m

- 2 9 ,9 8 k N /m -2 9 ,9 8 k N /m

-1 8 7 ,0 7 k N m -1 8 7 ,0 7 k N m

kNmlqM xq 07,18786,798,29101,0101,022207

Polje 208 : Pokretno optereenje

7 ,86 m30x50

C 35 /45C 35 /45C 35 /4530x50

7 ,86 m30x50

7 ,86 m

92,6

1 kN

m

92,6

1 kN

m

92,6

1 kN

m

92,6

1 kN

m

2 9 ,98kN /m

-138 ,91 kN m

kNmlqM xq 91,13886,798,29075,0075,022208

Leaj 207-208 : Pokretno optereenje

7,86 m30x50

C35/45C35/45C35/4530x50

7,86 m30x50

7,86 m

29,98kN /m 29,98kN /m

-135,76 kNm -98,72 kNm

61,1

2 kN

m

61,1

2 kN

m

216,

70 k

Nm

216,

70 k

Nm

7,86 m30x50

C35/45C35/45C35/4530x50

7,86 m30x50

7,86 m

-29,98kN/m -29,98kN/m

145,

39 k

N

-90,25 kN 137,38 kN

-98,

03 k

N

7,78

kN

kNmlqM xq 70,21686,798,29117,0117,022208207 kNmlqR xq 77,28286,798,292,12,1

208207 Raunski moment savijanja u polju pozicija 207 :

7,86 m30x50

C35/45C35/45C35/4530x50

7,86 m30x50

7,86 m

-410,33 kNm -410,33 kNm

kNmMMM qgsd 33,41008,1875,108,9635,15,135,1207207207

Raunski moment savijanja u polju pozicija 208 :

7,86 m30x50

C35/45C35/45C35/4530x50

7,86 m30x50

7,86 m

-248,89 kNm

kNmMMM qgsd 89,24891,1385,102,3035,15,135,1

208208208 Raunski moment savijanja na leaju pozicija 207-208 :

7,86 m30x50

C35/45C35/45

487,

19 k

Nm

487,

19 k

Nm

C35/4530x50

7,86m30x50

7,86 m

kNmMMM qgsd 19,48770,2165,110,12035,15,135,1 208207208207208207 Raunski poprena sila na leaju pozicija 207-208 :

kNmRRR qgsd 06,65177,2825,108,16835,15,135,1208207208207208207

IV.III. Dimenzioniranje armature Materijal : C35/45 Armatura : S-400 (RA 400/500)

pretpostavka: mma 22 mmv 8 cmh 50 cmc 0.2 - suhi okoli

udaljenost do teita armature :

cmcd av 9.322,28,02

21

statika visina :

cmdhd 10,4690,3501 Raunska vrsto betona : 22 /33,2/0,20

5,135 cmkNmmN

ff

c

ckcd

Raunska vrstoa armature : 22 /783,34/83,347

15,1400 cmkNmmkN

ff

s

ykyd

Dimenzioniranje armature u polju poz. 207 Sudjelujua irina ploe : cmlbb weff 62,1615

78685,028585,01

cmbblb

l

bb

l

bbbb wwy

wy

w

wy

weff 5,393282282787

22

22

22

2 21

Bezdimenzionalni koeficijent armiranja :

0252,0051,033,210,4662,161

4103322

207

cdeffsd

sd fdbM

odabrano za : 053,0 ; 964,0 ; 095,0 poloaj neutralne osi : cmdx 38,410,46095,0 < 12 cm

Potrebna armatura :

2207

1 55,26783,3410,46964,041033 cm

fdMA

yd

sds

Minimalna armatura :

2min 94,140010,46286,06,0 cm

fdbA

yk

ws

Maksimalna armatura :

2max 23,42410,4662,161783,3433,285,085,0 cmdb

ffA effyd

cds

ODABRANA ARMATURA: 21 64,26227 cmAods

udaljenost od teita armature:

ns

sa

aavsa

v

A

AncAncd

11

11

122

cmd 79,580,37

80,3322,22,22,28,00,280,34

22,28,00,2

1

statika visina:

cmdhd 21,4479,5501

Odreivanje sudjelujue irine ploe : cmlbb weff 62,1615

78685,028585,0


0252,0056,033,221,4462,161

4103322

207

cdeffsd

sd fdbM


Potrebna armatura :

2207

1 74,27783,3421,44962,041033 cm

fdMA

yd

sds

ODABRANA ARMATURA: 21 77,2713,164,26121227 cmAods

Dimenzioniranje armature u polju poz. 208

Odreivanje sudjelujue irine ploe : cmlbb weff 04,1385

7867,02857,0


252.0036.033,210,4604,138

2488922

208

cdeffsd

sd fdbM


Potrebna armatura : 2208

1 95,15783,3410,46973,024889 cm

fdMA

yd

sds

ODABRANA ARMATURA: 21 34,1613,121,15121224 cmAods

Dimenzioniranje armature leaja poz. 207-208

Smanjenje momenta nad leajem :

kNmtRM sd 55,328

40,006,6518

208207

/208207 /64,45455,3219,487 mkNmMMM sdlezajsd


252,0328,033,210,4628

4546422 cdw

lezajsd

sd fdbM

Dvostruko armirani leaj :

1) 252,0250,033,2

64010,4628

45464

6

22

cdw

leajsd

ftdb

M

2) 252,0304,033,210,4628

32554546422

cdw

sdleajsd

fdbMM

Granini moment savijanja : kNmfdbM cdwsdsd 3493933,210,4628252,0 22lim, cmcd av 90,32

2,28,0222

Vlana armatura :

2

2

lim,lim,1

82,3195,487,26783,3490,310,46

34939325545464783,3410,46811,0

34939 cm

fddMMM

fdM

Ayd

sdleajsd

yd

sds

Gdje je : 811.0lim Tlana armatura :

22lim,

2 95,4783,3490,310,4634939325545464

)(cm

fddMMM

Ayd

sdleajsd

s

ODABRANA ARMATURA: Vlana armatura: 21,342291 odsA Tlana armatura: 21 67,5192 cmAods

Dimenzioniranje armature rubnog leaja

Uzima se kNmM sd 58,10233,41025,025,0

207 Bezdimenzionalni koeficijent armiranja :

252,0074,033.210,4628

1025825,022

207

cdw

sdsd fdb

M

odabrano za : 076,0 ; 951,0 ; 123,0 Potrebna armatura :

2207

1 73,6783,3410,46951,01025825,0 cm

fdMA

yd

sds

ODABRANA ARMATURA: 21 60.7222 cmAods

KOMBINACIJE POTREBNE ZA CRTANJE ANVELOPE MOMENTA SAVIJANJA

1. Stalno optereenje :

kNmlgmmm

kNmlgMM

ggg

gC

gB

12,1508

86,744,198

10,12086,744,191,01,022

312111

22

3 0 x 5 03 0 x 5 0 3 0 x 5 0

-1 9 ,4 4 k N /m

120,

10 k

Nm

120,

10 k

Nm

120,

10 k

Nm

120,

10 k

Nm

-1 9 ,4 4 k N /m -1 9 ,4 4 k N /m

7 ,8 6 m 7 ,8 6 m 7 ,8 6 mC 3 5 /4 5 C 3 5 /4 5 C 3 5 /4 5

-9 6 ,0 8 k N m

-3 0 ,0 2 k N m

-9 6 ,0 8 k N m 2. Pokretno optereenje : * 1. kombinacija :

kNmlqm

kNmlqMM

g

qC

q

52,2318

86,798,298

61,9205,022

11

211

7 ,8 6 m3 0 x 5 0

C 3 5 /4 5C 3 5 /4 5C 3 5 /4 53 0 x 5 0

7 ,8 6 m3 0 x 5 0

7 ,8 6 m

92,6

1 kN

m

92,6

1 kN

m

92,6

1 kN

m

- 2 9 ,9 8 k N /m -2 9 ,9 8 k N /m

- 1 8 7 ,0 7 k N m -1 8 7 ,0 7 k N m * Anvelopa :

kNmmmm

kNmmmmmkNmMMMMM

qgsd

qgsdsd

qB

gB

gB

Csd

Bsd

66,20205,112,15035,15,135,1

94,54952,2315,112,15035,15,135,1

05,301)61,92(5,1)10,120(35,15,15,135,1

212121,

111131,11,

* 2. kombinacija :

kNmlqm

kNmlqMM

g

qC

q

52,2318

86,798,298

61,9205,022

11

211

7 ,86 m30x50

C 35 /45C 35 /45C 35 /4530x50

7 ,86 m30x50

7 ,86 m

92,6

1 kN

m

92,6

1 kN

m

92,6

1 kN

m

92,6

1 kN

m

2 9 ,98kN /m

-138 ,91 kN m *Anvelopa :

kNmmmm

kNmmmmmkNmMMMMM

qgsd

qgsdsd

qB

gB

gB

Csd

Bsd

94,54952,2315,112,15035,15,135,1

66,20205,112,15035,15,135,1

05,301)61,92(5,1)10,120(35,15,15,135,1

212121,

111131,11,

* 3. kombinacija :

kNmlqmm

kNmlqMkNmlqMM

qg

qC

qC

qB

52,2318

86,798,298

12,61033,0;70,216117,022

2111

22

7,86 m30x50

C35/45C35/45C35/4530x50

7,86 m30x50

7,86 m

29,98kN /m 29,98kN /m

-135,76 kNm -98,72 kNm

61,1

2 kN

m

61,1

2 kN

m

216,

70 k

Nm

216,

70 k

Nm

* Anvelopa :

* 4. kombinacija :

kNmlqmm

kNmlqMkNmlqM

qq

qB

qC

52,2318

86,798,298

12,61033,0;70,216117,022

3121

22

29,98kN /m216,

70 k

Nm

216,

70 k

Nm

29,98kN /m

61,1

2 kN

m

61,1

2 kN

m

30x507,86 m

-135,76 kNm

C 35/45C35/45

-98,72 kN m

30x507,86 mC 35/457,86 m

30x50

* Anvelopa :

kNmmmm

kNmmmm

kNmmmmkNmMMM

kNmMMMM

qgsd

qgsd

qgsd

qC

gC

Csd

qB

gB

gB

Bsd

66,20205,112,15035,15,135,1

94,54952,2315,112,15035,15,135,1

94,54952,2315,112,15035,15,135,1

82,253)12,61(5,1)10,120(35,15,135,1

19,487)70,216(5,1)10,120(35,15,15,135,1

313131,

212121,

111111,

kNmmmm

kNmmmm

kNmmmmkNmMMM

kNmMMMM

qgsd

qgsd

qgsd

qC

gC

Csd

qB

gB

gB

Bsd

94,54952,2315,112,15035,15.135.1

94,54952,2315,112,15035,15,135,1

66,20205,112,15035,15,135,1

19,487)70,216(5,1)10,120(35,15,135,1

82,253)12,61(5.1)10,120(35,15,15,135,1

313131,

212121,

111111,

* 5. kombinacija :

7 ,8 6 m3 0 x 5 0

C 3 5 /4 5C 3 5 /4 5C 3 5 /4 53 0 x 5 0

7 ,8 6 m3 0 x 5 0

7 ,8 6 m

-2 9 ,9 8 k N /m -2 9 ,9 8 k N /m -2 9 ,9 8 k N /m

185,

22 k

Nm

185,

22 k

Nm

185,

22 k

Nm

185,

22 k

Nm

- 1 4 8 ,1 7 k N m -1 4 8 ,1 7 k N m

-2 7 ,7 8 k N m

* Anvelopa :

kNmmmmmmkNmMMMM

qgsdsdsd

qB

gB

Bsd

Csd

94,54952,2315,112,15035,15,135,1

97,439)22,185(5,1)10,120(35,15,135,1

111131,21;11,

kNmlqmmm

kNmlqMM

qqg

qC

qB

52,2318

86,798,298

22,1851,022

312111

2

* 6. kombinacija :

kNmlqm

kNmlqMkNmlqM

q

qC

qB

52,2318

86,798,298

49,31017,0;09,124067,022

11

22

31x50 31x50 31x50

124,09

kNm

124,09

kNm

-31,49

kNm

-31,49

kNm

-166,69kNm

-29,98kN/m

7,86m 7,86m 7,86mC35/45 C35/45 C35/45

* Anvelopa :

kNmmmmm

kNmmmmkNmMMMkNmMMM

qgsdsd

qgsd

qC

gC

Csd

qB

gB

Bsd

66,20205,112,15035,15,135,1

94,54952,2315,112,15035,15,135,1

37,20949,315,1)10,120(35,15,135,1

27,348)09,124(5,1)10,120(35,15,135,1

212131,21,

111111,

* 7. kombinacija :

kNmlqm

kNmlqMkNmlqM

q

qC

qB

52,2318

86,798,298

09,124067,0

49,31017,0

22

31

2

2

31x50

-166,69kNm

7,86mC35/45

-29,98kN/m

124,09

kNm

124,09

kNm

C35/457,86m

-31,49

kNm

-31,49

kNm

31x50

7,86mC35/4531x50

* Anvelopa :

kNmmmmm

kNmmmmkNmMMM

kNmMMM

qgsdsd

qgsd

qC

gC

Csd

qB

gB

Bsd

66,20205,112,15035,15,135,1

94,54952,2315,112,15035,15,135,1

27,348)09,124(5,1)10,120(35,15,135,1

37,209)49,31(5,1)10,120(35,15,135,1

212121,11,

111131,

ANVELOPA MOMENTA SAVIJANJA

DULJINA SIDRENJA ARMATURE

min,,

,, b

provs

regsbanetb IA

AlI

gdje su:

a=1.0 - za ravne ipke Ib,min - minimalna duljina sidrenja

As,reg - potrebna povrina armature

lb - duljina prianjanja

Duljina prianjanja se dobije iz uvjeta da sila kojom se odupire prionjivost betona i armature

bude vea od sile koja djeluje u armaturi ( vidi sliku ) :

bd

ydb

bdydb

ydbbd

sydbbd

bd

ff

l

ffl

flf

AflfPP

4

14

42

2

Minimalna duljina prianjanja : cmll bb 10153,0min, vrstou prianjanja uzimamo iz tablice na str. 493 za odreenu klasu betona:

- za C 35/45 22 /34,0/4,3 cmkNmmNfbd

Duljinu sidrenja raunamo za svaki profil armature koji smo odabrali kod prorauna : Profil = 22cm:

227,5634,0783,34

42,2

4cm

ff

lbd

ydb

2, 28,31 cmA regS ; 2, 21,34 cmA provS

2

,

,, 45,5121,34

28,3127,560,1 cmAA

lIprovs

regsbanetb

cmcmcmll bb 100,332,21513,1927,5634,034,0min,

mjerodavno lb,net=52cm

Profil = 19cm:

259,4834,0783,34

49,1

4cm

ff

lbd

ydb


2

,

,, 42,4267,5

95,459,480,1 cmAA

lIprovs

regsbanetb

cmcmcmll bb 105,289,11552,1659,4834,034,0min,


Profil = 12cm:

269,3034,0783,34

42,1

4cm

ff

lbd

ydb


2

,

,, 59,3064,26

55,2669,300,1 cmAA

lIprovs

regsbanetb

cmcmcmll bb 100,182,11543,1069,3034,034,0min,


Horizontalni pomak anvelope momenata savijanja 1) PBABcmda 69.3425.4675.075.0 2) 27.253925.469.05.09.05.05.0 ECcmctgctgdctgza mjerodavno a = 26cm

PODACI POTREBNI ZA POKRIVANJE MOMENTNOG DIJAGRAMA

Odabrana armatura slA ydslsl fAF dz zFM sl*sl *sls MkomM sdM redSdM

Polje 207

722 112

3.80 1.13

132.18 39.30 0.964 42.62

5633.51 1674.97

39434.57 1674.97 41033

Polje 208

422 112

2.84 1.13

98.78 39.30 0.973 44.86

4431.27 1763.00

17725.08 1763.00 24889

Leaj 207-208 922 3.80 132.18 0.811 34.22 4523.20 40708.80 45464 42209 Rubni leaj 222 3.80 132.18 0.951 43.84 5794.77 11589.54 10258

4Proraun grede 207-208-2075Anvelope

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Proračun Ab Grede-Anvelope