15 - Greda Sa Prepustom

1

1

BETONSKE KONSTRUKCIJE 1

Vežba br.15

2

g = 30 kN/m MB 30

p = 20 kN/m RA 400/500

2

3

4

336

420

252

672

378

3

5

URØ8/204RØ22

5RØ22

2RØ12

B-B2RØ22

2RØ12

2RØ22

2RØ22

URØ10/20

4RØ22C-C

Presek u polju: Presek nad osloncem:

6

336

420

252

672Osiguranje glavnih napona zatezanja:

2l,Cn

l,Cmu cm/kN252.0

7.4735420kN420T =×

=τ⇒=

2An

Amu cm/kN201.0

7.4735336kN336T =×

=τ⇒=

2An

d,Cmu cm/kN151.0

7.4735252kN252T =×

=τ⇒=

4

7

τAn =2.01

τC,ln =2.52

τn

MB30 ⇒ τr=1.1 MPa

8

kN5.657.47352

252.011.03Tbu =××−×

=

kN5.3545.65420TTT bumuRu =−=−=

2RuRu cm/kN212.0

7.47355.354

zbT

=×

=×

=τ

( ) cm45.8a76.1011040212.035785.02e )1(

uu =×=×+××××

=

2C,l C,l 2 rmu n 2

r

0.11 kN / cm420T 420 kN 0.252 kN / cm35 47.7 3 0.33 kN / cm

> τ == ⇒ τ = = × < τ =

pp. URØ10; aa(1)=0.785cm2; m=2

Presek C levo:

5

9

( )θ×α+α×σ×××

=τ ctgsincosebam

vu

)1(u)1(

u,u

cm4.22102.035

785.02b

ame 2.min,uz

)1(u

u =××

×=

µ××

≤ −

cm20e.usvcm25

cm5.262hcm35b

.mine uu =⇒

==

≤

( ) 2)1(u,u cm/kN090.011040

2035785.02

=×+×××

×=τ

Usvojimo: URØ10/20

10

τn

τu,u

6

11

cm11912.290.04.281l,C

Ru

)1(u,u

2 =×=ττ

×λ

MPa22.190.012.2)1(u,u

l,Cmax,Ru

l,CRu =−=τ−τ=τ∆

cm4.1621194.2812 =−=λ∆

pp. URØ12; aa(1)=1.13 cm2; m=2

u2 1.13e 40 21.17 cm

35 0.122×

= × =×

(1) 2u,u

2 1.13 40 0.129 kN / cm35 20

×τ = × =

×

Ukupno usvojeno: URØ10/20 + URØ12/20(1) 2u,u 0.09 0.129 0.219 kN / cmτ = + =

URØ12/20

12

(URØ10/20)

7

13

kN5.348354.1622

090.0212.0H k,vu =×

×

−=

( )θ×α+α×σ=

ctgsincosH

Akkv

k,vuk,a

( )2

a,k348.5 348.5A 6.16 cm

40 0.707 0.707 1.0 40 2= = =

× + × ×

bAH k,vu ×= τ

αk=45o ; θ=90o

Usvojeno 2RØ22 (7.60cm2)

14

τRu-τu,u

8

15

τRu-τu,u τRu-τu,u

16

τRu-τu,u

KOSIM PROFILIMADUŽINA OSIGURANJA DUŽINA OSIGURANJA

KOSIM PROFILIMA

τRu-τu,u

9

17

18

kN5.1077.47352

201.011.03TAbu =××

−×=

2A A 2 rmu n 2

r


> τ == ⇒ τ = = × < τ =

kN5.2285.107336TTT bumuRu =−=−=

2Ru cm/kN137.0

7.47355.228

=×

=τ

( ) cm1.13a7.1611040137.035785.02e )1(

uu =×=×+××××

=

pp. URØ10; aa(1)=0.785cm2; m=2

Presek A:

10

19

τAn =2.01

τARu=1.37

τ(1)

u,u

= 0.

90

τ(2)

u,u

= 1.

47

τn

τu,u

τRu

20

cm11937.190.04.181A

Ru

)1(u,u

1 =×=ττ

×λ

MPa047.090.037.1)1(u,u

Amax,Ru

ARu =−=τ−τ=τ∆

cm4.621194.1811 =−=λ∆

u2 0.50e 40 24.3 cm

35 0.047×

= × =×

pp. URØ8; aa(1)=0.50cm2; m=2

(1) 2u,u

2 0.5 40 0.057 kN / cm35 20

×τ = × =

×

Ukupno usvojeno URØ10/20 + URØ8/20

(1) 2u,u 0.09 0.057 0.147 kN / cmτ = + =

URØ8/20

11

21

τnτC,d

n =1.51

τC,dRu =0.61

Presek C desno:

22

kN5.1497.47352

151.011.03T d,Cbu =××

−×=

2C,d A 2 rmu n 2

r


> τ == ⇒ τ = = × < τ =

kN5.1025.149252TTT bumuRu =−=−=

2Ru cm/kN061.0

7.47355.102

=×

=τ

(1)u u

2 0.785e 40 37.2 a35 0.061

×= × = ×

×

ue 29.2 cm=

pp. URØ10; aa(1)=0.785cm2

Usvojeno URØ10/20

12

23

ub

auvaau N

zMAZ −=σ×=

aub au u

Mz 0.9 h Z N

0.9 h≈ × ⇒ ≈ −

×

−×+=×+= 1uu1auuau a

2dNMyNMM

au378gornja zona : Z 792.5 kN

0.9 53≈ =

×

au672donja zona : Z 1408.8 kN

0.9 53≈ =

×

Za Nu=0: auau

MZ

0.9 h≈

×

LINIJA ZATEŽUĆIH SILA:

24

C DBA

13

25A B DC

v=40

v=40

v=40v=40

POMERANJE LINIJE ZATEŽUCIH SILA:v = 0.75×h = 0.75×53 = 39.75 ≈ 40 cm

( )( )armaturakosauzengijeh50.0vuzengijeh75.0v

+×=×=

26

6×Z(1

)au

Z(1)

auZ(1

)au

Z(1)

auZ(1

)au

Z(1)

auZ(1

)au

v=40

v=40

v=40

v=40

C DBA

usvojeno u polju: 9RØ22

usvojeno nad osloncem: 6RØ22

14

27

Z(1)

auZ(1

)au

Z(1)

auZ(1

)au

Z(1)

auZ(1

)au

6×Z(1

)au

A B DC

v=40

v=40

v=40

v=40

5

Ls1

UKUPNA DUŽINA ŠIPKE

STATICKI POTREBNA DUŽINA ŠIPKE Ls1


Ls2Ls2 STATICKI POTREBNADUŽINA ŠIPKE

DUŽINA SIDRENJA:Ls1 = 70 cm (dobra adhezija)Ls2 = 105 cm (loša adhezija)

28

p

v

pu

vs 8.14

Ø4ØL

τ×σ

×=τ×γ

σ×=

2.802.452.101.751.401.20RA0.980.920.850.760.670.60GA605040302015MB

pprianjanjanaponaVrednosti τ

cm708.6975.18.1

40042.2L 1s ≈=

××=

cm105L5.1L 1s2s =×= (Za uslove loše adhezije sračunato sa 2/3τp)

15

29

DUŽINA SIDRENJA:Ls1 = 70 cm (dobra adhezija)Ls2 = 105 cm (loša adhezija)

POMERANJE LINIJE ZATEŽUCIH SILA:v = 0.75×h = 0.75×53 = 39.75 ≈ 40 cm


Ls2Ls2 STATICKI POTREBNA DUŽINA ŠIPKE

Ls1


STATICKI POTREBNA DUŽINA ŠIPKE Ls1

C DBA

6

7

8

1

2

3

4

8

1

2

3

4

5

v=40

v=40

v=40

v=40

5

30P O S 1 - G R ED A SA P R E PU S T O M08 .10 .1998 . L ist 1 /1

16

31

32

POMERENA LINIJA ZATEŽUĆ IH SILA

LINIJA ZATEŽUĆ IH SILA

1

3

5

4

9

8

6

10

6

v = 40

40 40

1Ø22

2Ø22

2Ø22

2Ø22

2Ø22

2Ø22

3 2RØ22

2RØ225

2RØ22108 2RØ22 7 2RØ22 2RØ22711 2RØ12 11 2RØ12

13 6.5

9URØ10/2012

3URØ8/2013

20URØ8/2013 15URØ10/2012 5URØ10/2012 10URØ8/2013

960

45

885

45

1 2RØ22 L=1005

1RØ22 L=9302

2RØ22 L=1026832

325

64105

45.5

45.5

2RØ22 L=6205620654.5

2RØ22 L=360335

9

A1...840x594R 1:20MB 30 RA 400/500

GODIŠNJI ZADATAK - LIST br.6

PLAN ARMATURE POS 1

KOLICINE MATERIJALA

25

16025 25 20 380 28020 80 20 180 5

4.5

2RØ12 L=65011630

55

10

30

3010

55

29URØ10 L=19012

30

33URØ8 L=190

55 55

10

30

10

132

2 3

31

1

6.54.5 4.513 6.5

4.5

35

25.5

60

4.5

4.5 26

5.5

204.

5

URØ10/20

48

2RØ22

9 9

2RØ12

2RØ22

12

37

68

37

68

PRESEK 3-3 R 1:10

4RØ22

3 3

REKAPITULACIJA ARMATURESPECIFIKACIJA ARMATURE

ΣG[kg]

g[m]

LΣ[kg/m]

1g[mm]

Ø

UKUPNO:

25.462.70

23.7

34.9

129.12

26.00

55.10

478.8

394.8

0.4058

3.058

0.911

0.63310

12

22

gL gLΣ

20.10

[m]

n

2

[kom.]

Ø

22

[mm] [cm]

1005

9.30

20.52

15.20

7.10

12.40

1

2

22

22 1026

930

2

2

2

22

22

22

760

355

620

9.40

17.90

7.20

26.00

10.00

2

2

22

22 895

470

2

4

2

22

12

22 500

360

650

2

3

4

6

5

7

8

9

11

10

1

55.10

62.70

29

33

19010

1908

12

13

BETON (MB 30):

ARMATURA (RA 400/500): 478.8

2.573

kg

m3

kg/m478.82.573 = 186.13 3 betona

OPLATA: 16.468 m2

30

1225

86050

63.4

CBA D

4.5

5.5

204.

525

.5

26

4.5 4.5

60

PRESEK 1-1 R 1:10

4x6.5=26

4.54.5

4812

2RØ12

2RØ22

URØ8/204RØ22

5RØ22

PRESEK 2-2 R 1:10

1

4812

60

30

30 285

35

CO

NFI

DEN

TIA

L!

435

2 35

14

10 10

25.5

4.5

205.

54.

5

60

35

6.5

4.5 4.5

88

1 1

67 7

6

4812

2RØ22

2RØ22

26

4.5 4.5

4RØ22

2RØ12URØ10/20

17

33

4.5

5.5

204.

525

.5

26

4.5 4.5

60

PRESEK 1-1 R 1:10

4x6.5=26

4.54.5

4812

2RØ12

2RØ22

URØ8/204RØ22

5RØ22

1

35

435

2 35

14

10 10

34

13 6.5

3 3

PRESEK 2-2 R 1:10

25.5

4.5

205.

54.

5

60

35

6.5

4.5 4.5

88

1 1

67 7

6

4812

2RØ22

2RØ22

26

4.5 4.5

4RØ22

2RØ12URØ10/20

18

35

6.54.5 4.513 6.5

4.5

35

25.5

60

4.5

4.5 26

5.5

204.

5

URØ10/20

482RØ22

9 9

2RØ12

2RØ22

12

37

68

37

68

PRESEK 3-3 R 1:10

4RØ22

Documents

15 - Greda Sa Prepustom