# Vodjenje Armature Duz Nosaca

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16-Jul-2016

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• 1Konstrukcija linije zateuih sila

-

z

s=

s-

s= = u

au

vv

u

v

aua Nh

M1NzMA)0N(

uau

vaau NhMAZ -

z=s=

-+=+= 1uu1auuau a2dNMyNMM

va1aaauv1a AAZ s=s=s=s

• 2.min

uvaau h9.0

MAZ

s=

.min.min h9.0z

9.0.consthh

z==

uauu MM0N ==

u.min

auvaau Nh9.0

MAZ -

s=

Konstrukcija linije zateuih sila

isto savijanje:

• 3L = 12.0 m

Reakcije oslonaca

Bg = (30122/2)/9 = 240 kNAg = 3012 240 = 120 kN

Ap1 = Bp1 = 409/2 = 180 kN

Bp2 = [(603(9+3/2)]/9Bp2 = 210 kNAp2 = 603 210 = -30 kN

• 4Dijagrami momenata savijanjaoslonac:Mg = 3032/2 = 135 kNmpolje:xmax = 120/30 = 4.0 mMg = 1204 3042/2Mg = 240 kNm

polje:Mp1 = 4092/2 = 405 kNm

oslonac:Mp2 = 6032/2 = 270 kNm

• 5Anvelopa momenata savijanja

( )

( )212

1

21

2

1

PP8.1G0.1P8.1G0.1P8.1G0.1

G1.0

PP8.1G6.1P8.1G6.1P8.1G6.1

G6.1

++

+

+

++

++

• 6Anvelopa momenata savijanja

9.0 m

Mu

= 11

09.4

kN

m Mu

= 70

2.0

kNm

4.3 m1.6G+1.8P1

1.6G+1.8P2

3.0 m

• 7Anvelopa momenata savijanja

1.0 m8.0 m

1.0 m8.0 m

1.0G+1.8P1

Mu

= 11

09.4

kN

m Mu

= 70

2.0

kNm

4.3 m 1.6G+1.8P1

1.0G+1.8P21.6G+1.8P2

1.6G+1.8P1 1.0G+1.8P1

1.0G+1.8P2 1.6G+1.8P2

• 8Anvelopa momenata savijanja

1.0G+1.8P21.6G+1.8P2

1.0G+1.8P1

1.6G+1.8P1

nu

lta t

acka

dijagra

ma M

g

MG i MP istog znaka

MG i MP istog znaka MG i MP razlicitog znaka

MG i MP razlicitog znaka

• 9Anvelopa momenata savijanja

1.0 m8.0 m

1.0 m8.0 m

4.3 m

Mu

= 11

09.4

kN

m Mu

= 70

2.0

kNm

1.6G+1.8P1 1.0G+1.8P1

1.0G+1.8P2 1.6G+1.8P2

• 10

Dimenzionisanje - presek u polju

aI = 2.5 + 1.0 + 2.5/2 = 4.75 cmaII = 4.75 + 3.0 + 2.5 = 10.25 cm

a1 = (54.75 + 410.25)/9a1 = 7.19 cm

h = 75 - 7.19 = 67.81 cmh 68 cm = hra.

40

21.7

5

4.75

4.75

5.5

4.75

4.75

5R25

4R25

U10/30

30.5

16.2

5

1560

75

2R25

2R12

22 2R12

• 11

Dimenzionisanje - oslonac

aI = 2.5 + 1.0 + 2.5/2 = 4.75 cmaII = 4.75 + 3.0 + 2.5 = 10.25 cm

a1 = (44.75 + 210.25)/6a1 = 6.58 cm

h = 75 - 6.58 = 68.42 cmh 68 cm = hra.

40

21.7

5

4.75

4.75

5.5

4.75

4.75

4R25

2R25

U10/15

30.5

16.2

5

1560

75

2R25

22

2R12

2R12

• 12

Analitiki izrazi za momente savijanja

2)xL(gM:lx

2xgxAM:lx

2

g

2

gg

--=

-=

0M:lx2

xpxAM:lx

1p

21

1p1p

=

-=

2)xL(pM:lx

xAM:lx2

22p

2p2p

--=

=

• 13Vrednosti momenata savijanja - Excelx Mg Mp1 Mp2

1.6G+1.8P1

1.6G+1.8P2

1.0G+1.8P1

1.0G+1.8P2 MAX MIN

0 0 0 0 0 0 0 0 0 00.5 56.25 85 -15 243 63 209.3 29.3 243 0

1 105 160 -30 456 114 393 51 456 01.5 146.3 225 -45 639 153 551.3 65.3 639 0

2 180 280 -60 792 180 684 72 792 02.5 206.3 325 -75 915 195 791.3 71.3 915 0

3 225 360 -90 1008 198 873 63 1008 03.5 236.3 385 -105 1071 189 929.3 47.3 1071 0

4 240 400 -120 1104 168 960 24 1104 04.5 236.3 405 -135 1107 135 965.3 -6 .8 1107 -6 .8

5 225 400 -150 1080 90 945 -45 1080 -455.5 206.3 385 -165 1023 33 899.3 -90 .8 1023 -90 .8

6 180 360 -180 936 -36 828 -144 936 -1446.5 146.3 325 -195 819 -117 731.3 -204.8 819 -204.8

7 105 280 -210 672 -210 609 -273 672 -2737.5 56.25 225 -225 495 -315 461.3 -348.8 495 -348.8

8 0 160 -240 288 -432 288 -432 288 -4328.5 -63 .8 85 -255 51 -561 89.3 -522.8 89.3 -561

9 -135 0 -270 -216 -702 -135 -621 0 -7029.5 -93 .8 0 -188 -150 -487.5 -93 .8 -431.3 0 -487.5

10 -60 0 -120 -96 -312 -60 -276 0 -31210.5 -33 .8 0 -67 .5 -54 -175.5 -33 .8 -155.3 0 -175.5

11 -15 0 -30 -24 -78 -15 -69 0 -7811.5 -3 .75 0 -7 .5 -6 -19 .5 -3 .8 -17 .3 0 -19 .5

12 0 0 0 0 0 0 0 0 0

• 14

-800

-400

0

400

800

12000 1 2 3 4 5 6 7 8 9 10 11 12

Mu

[kN

m]

1.6G+1.8P11.6G+1.8P2G+1.8P1G+1.8P2

Anvelopa momenata savijanja - Excel

• 15

Mu

= 11

09.4

kN

m Mu

= 70

2.0

kNm

Z au

18

12.8 Zau 1109.4/(0.90.68) = 1812.8 kN

Z au

11

47.1

Zau 702/(0.90.68) = 1147.1

.min

uu

.min

auvaau h9.0

MNh9.0

MAZ

=-

s=

M/z linija

• 16

• 17

• 18

• 19

• 20

Tg

Tp1

Tp2

1,6Tg+1,8(Tp1+Tp2)

• 21

• 22

M/z linija

kN3.1964091.4aZ v)1(

a)1(

au ==s=

Z au

18

12.8

Z au

11

47.1

Z(1) au

=196

.3

• 23

Linija zateuih silaZ a

u

1812

.8

Z au

11

47.1

9Z(

1) au=1

767.

1

• 24

M/z linija

z = 0.964Aa,potr. = 42.33 cm2 (usv. 44.18 cm2)

z = 0.894Aa,potr. = 28.85 cm2 (usv. 29.45 cm2)

Z au

18

12.8

Z au

11

47.1

9Z(

1) au=1

767.

1 6Z(

1) au=1

178.

1

• 25

Linija zateuih silaZ a

u

1812

.8

Z au

11

47.1

v=0.51

v=0.51

v=0.51v=0.51

POMERANJE LINIJE ZATEUCIH SILA:v = 0.75h = 0.7568 = 51 cm

M/z linije

• 26

Linija pokrivanja armaturom

5R25

2R25

4R25

725

225

425

225

>425 >425

>725 >725

• 27

Linija pokrivanja armaturom

5R25

2R25

525

225

225

>425 >425

>725 >725

225

225

225

>5 >5

>2>2

• 28

Linija pokrivanja armaturom

3R25

2R25

325

225

225

>425 >425

>725 >725

225

225

225

>5 >5

>2>2

>3 >3

225

• 29

Linija pokrivanja armaturomZ a

u

1812

.8Z a

u

1147

.1

A B

POMERENA LINIJA ZATEUCIH SILA LINIJA ZATEUCIH SILA

LINIJA POKRIVANJA ARMATUROM

v=51

v=51

v=51v=51

POMERANJE LINIJE ZATEUCIH SILA:v = 0.75h = 0.7568 = 51 cm

(M, N)(M, N, T)

• 30Z a

u

1812

.8Z a

u

1147

.1

A

B

3

1

1

POMERENA LINIJA ZATEUCIH SILA LINIJA ZATEUCIH SILA

LINIJA POKRIVANJA ARMATUROM

v=51

v=51

v=51v=51

UKUPNA DUINA IPKE (700 cm)

STATICKI POTREBNA DUINA IPKE (460 cm)

2

1

5

225

125

225

225

225

69

35

65

125

205

25

85

165

180280

DUINA SIDRENJA:

Ls1 = 79.4 80 cm (dobra adhezija)Ls2 = 119 120 cm (loa adhezija)

POMERANJE LINIJE ZATEUCIH SILA:v = 0.75h = 0.7568 = 51 cm

NOSIVOST JEDNE IPKE ARMATURE:

Z(1)au = a(1)a sv = 4.9140 = 196.3 kN

Zau Mau / (0.9h) - NuMau = Mu + Nu (d 2 - a1)Nu = 0: Mau = Mu ; Zau Mu / (0.9h)

(M, N, T) (M, N)M/Z linija

• 31

• 32

• 33

Sidrenje armature

75.3175.18.1

4004

8.14L

p

vs =

=t

s=

22...cm70cm8.692.275.31L 1s ==25...cm80cm4.795.275.31L 1s ==

22...cm105cm705.1L 2s ==

1s1s2p

1p2s1p2p L5.1LL3

2=

tt

=t=t

25...cm120cm805.1L 2s ==

• 34

Sidrenje armature1

25v=51 v=51

L.Z.S. LINIJA M z

v=51 v=51 305205

L25s1 = 80STATICKI POTREBNA

DUINA IPKE (390 cm)

UKUPNA DUINA IPKE (550 cm)

L25s1 = 80

5 5

A B

p

vs 8.14

Lt

s=

• 35

• 36

• 37

• 38

• 39

1215

6015

5

15 15

BA

1

1

1-1

3

3

3-32-2

2

2

75

• 40

1215

6015

5

15 15

BA

1

1

1-1

3

3

5

75

5 54x7.5=30

40

15

5 530

40

3-3

5

75

15 15

5 530

40

2-2

5

75

2

2

1 2R25 6 2R25

6 2R25

35

1

1 2R25

6

75

1 2R251 2R25

• 41

1215

6015

5

15 15

BA

1

1

1-1

3

3

5

75

5 54x7.5=30

40

15

5 530

40

3-3

5

75

15 15

5 530

40

2-2

5

75

2

2

1 2R25 6 2R253 2R25

6 2R25

3 2R25 L=925 (2)

35

890

35

1

2

1 2R25, 3 2R25

6

1 2R25

75

1 2R25

3

2 1R25 L=860 (1)

35

825

2 1R251 2R25

3 2R25

2

3

2 1R25

• 42

1215

6015

55

15 15

BA

1

1

1-1

3

3

5.5

5

75

5 54x7.5=30

40

15

5 530

4