09 - Mali Ekscentricitet_ Konstrukcija Dijagrama Interakcije

1

Mogu dilata cija pr eseka a  stanja dilatacija ZATEZANJE

2

εb2 εa2

2 a

Aa2 2

a d h

PRITISAK

a

a'

d

7 3

b c

e f C

d

g h

Aa1 1

a

b

10‰

εa1 εb1

3.5

3 εv

0

2

d

7 4

3.5

γ u,i

2

Mali eks cen tric itet - si la p ritis ka εb2 0

2

3.5

σb=f B

a

Aa2

2 d

M u

a d h

N u

εa2

2 d

Gb

y -

d

7 3

εb=2‰

σb=f B C

d x

d

7 4

Aa1 εa1

a

b

d x

εb1

Dbu

2 d

Da2u a h

d y

2 d

Da1u a

2‰ NEUTRALNA LINIJA

εb1

a

d

14 − 4 × εb 2 = ; 2 ‰ ≤ εb2 ≤ 3.5 ‰ 3

3

Mali eks cen tric itet - si la p ritis ka εb1

14 − 4 × εb2 = ; 2 ‰ ≤ εb 2 ≤ 3.5 ‰ 3

Dbu

= αd × b × d × f B

125 + 64 × εb2 − 16 × ε2 b 2 αd = 189

y d = k d × d 40 (εb2 − 2 )2 × k d = 7 125 + 64 × εb 2 − 16 × ε2 b 2

4

Mu

Aa2 =2Ø25

Aa2 =0

MALI EKS. (ZATEZANJE)

VELIK I EKSCEN TRICITET TRICITET

MALI EKS. (PRITISAK)

Nu

5

Nos iv os t pr eseka u za zavis vis no st i od pojedi nih param eta etara ra UTICAJ KVALITETA CELIKA Mu

Mu

540

780

500

750

480

720

460

690

440

660

420

RA 400/500

GA 240/360

630

400

600

380

570

360

540

340

510

320

480

300

450

280

420

260

390

240

360

220

330

200

300

180

270

160

240

140

210

120 100

sigv 4 00 00 2 40 40

55 57 7 44 42 2

120 90

sigv 40 00 0 24 40 0

84 45 5 61 15 5

60

Nu

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 7 6 5 4 3 2 1 0 9 8 7 6 5 4 3 2 1 0 9 8 7 6 5 0 8 7 6 5 4 3 2 1 0 9 0 1 2 3 4 5 6 7 8 8 9 0 1 2 3 4 5 6 7 7 8 9 0 1 9 1 2 3 4 5 6 7 8 9 9 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3

a. jednostruko armiran presek

GA 240/360

150

60

20

RA 400/500

180

80

40

0 0 7 8 0 0 0 0 0 0 0 0 0 0 1 0 9 0 1 2 3 4 5 6 7 8 0 1 - 1 - 9 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 - 9 -

840 810

520

Nu

30

0 0 8 1 -

0 0 6 1 -

0 0 4 1 -

0 0 2 1 -

0 0 0 1 -

0 0 8 -

0 0 6 -

0 0 4 -

0 0 2 -

0 0 2

0 0 4

0 0 6

0 0 8

0 0 0 1

0 0 2 1

0 0 4 1

0 0 6 1

0 0 8 1

0 0 0 2

0 0 2 2

0 0 4 2

0 0 6 2

0 0 8 2

0 0 0 3

0 0 2 3

0 0 4 3

0 0 6 3

b. simetricno armiran presek

0 0 8 3

0 0 0 4

0 0 2 4

0 0 4 4

6

Nos iv os t pr eseka u za zavis vis no st i od pojedi nih param eta etara ra UTICAJ KVALITETA BETONA Mu

Mu

500

680 660

480

640

460

620 600

440

580

420

560

400

540 520

380

500

360

480

340

460 440

320

420

300

400

280

380 360

260

340

240

320

220

300

MB40 MB35 MB30

280 200

260

180

240

160

220 200

140 120 100 80

fb 25.5 23.0 20.5

180

MB40 508 475 442

140

MB30

120 100

60

0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 - 6 - 5 - 4 - 3 - 2 - 1 -

60 40

Nu

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3


681 648 615

80

40 20

fb 25.5 23.0 20.5

160

MB35

Nu

20 0 0 4 1 -

0 0 2 1 -

0 0 0 1 -

0 0 8 -

0 0 6 -

0 0 4 -

0 0 2 -

0 0 2

0 0 4

0 0 6

0 0 8

0 0 0 1

0 0 2 1

0 0 4 1

0 0 6 1

0 0 8 1

0 0 0 2

0 0 2 2

0 0 4 2

0 0 6 2

0 0 8 2

0 0 0 3

0 0 2 3

0 0 4 3

0 0 6 3

0 0 8 3


0 0 0 4

0 0 2 4

0 0 4 4

0 0 6 4

7

Nos iv os t pr eseka u za zavis vis no st i od pojedi nih param eta etara ra UTICAJ POLOŽAJA ARMATURE Mu

Mu 440

620 600

420

580 560

400

540 380

520

360

a/d=0.125

340

a/d=0.100

320

a/d=0.075

a/d=0.125

500 480

a/d=0.100

460

a/d=0.075

440 420

300

400 280

380 360

260

340

240

320

220

300 280

200

260 180

240 220

160

200

140

180

120 100 80

160 a1 4 ..5 5 6 ..0 0

4 53 4 42

7 ..5 5

4 31

140 120 100

40

Nu

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 0 8 6 4 2 0 8 6 4 2 0 8 6 4 2 0 8 6 4 2 0 8 6 4 2 0 0 6 4 2 0 8 6 4 2 0 8 6 0 1 2 2 3 4 5 6 6 7 8 9 0 0 1 2 3 4 4 5 6 7 8 8 9 0 1 2 8 1 2 3 4 4 5 6 7 8 8 9 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3


6 04

60

40

0 0 0 0 0 0 0 0 2 4 6 8 0 2 4 6 0 7 - 6 - 5 - 4 - 4 - 3 - 2 - 1 - 8 -

6 26 6 15

7 ..5 5

80

60

20

a1 4 ..5 5 6 ..0 0

Nu

20

0 0 4 1 -

0 0 2 1 -

0 0 0 1 -

0 0 8 -

0 0 6 -

0 0 4 -

0 0 2 -

0 0 2

0 0 4

0 0 6

0 0 8

0 0 0 1

0 0 2 1

0 0 4 1

0 0 6 1

0 0 8 1

0 0 0 2

0 0 2 2

0 0 4 2

0 0 6 2

0 0 8 2

0 0 0 3


0 0 2 3

0 0 4 3

0 0 6 3

0 0 8 3

8

Nos iv os t pr eseka u za zavis vis no st i od pojedi nih param eta etara ra

UTIC UTICAJ AJ KOLI KOLICI CIN NE ZAT ZATEG EGNU NUTE TE ARM ARMATUR ATURE E

UTIC UTICAJ AJ KOLI KOLICI CINE NE PRIT PRITIS ISNU NUTE TE ARM ARMATUR ATURE E

Mu

Aa1=60 Aa1=50 Aa1=40

Mu 600

600

580

580

560

560

540

540

520

520

500

500

480

480

460

460

440

440

420

420

400

400

380

380

360

360

340

340

320

320

300

300

280

280

260

260

240

240

220

220

200

160 140

Aa1=20

120 100 80

Aa1=10

60 40 20

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 3 2 1 0 0 0 0 0 0 0 0 0 0 1 - 1 - 1 - 1 - 1 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 -

200

b=30cm d=60cm Aa2=0 a1=6cm MB30, GA 240/360

180

Aa1=30

Aa1=0

Aa2=30

160 140 120 100 80 60

Aa2=10 Aa2=0

40

Nu

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 1 2 3 4 5 6 7 8 9 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3

Aa2=20

b=30cm d=60cm Aa1=30cm2 a1=6cm MB30, GA 240/360

180

Nu

20

0 0 4 1 -

0 0 2 1 -

0 0 0 1 -

0 0 8 -

0 0 6 -

0 0 4 -

0 0 2 -

0 0 2

0 0 4

0 0 6

0 0 8

0 0 0 1

0 0 2 1

0 0 4 1

0 0 6 1

0 0 8 1

0 0 0 2

0 0 2 2

0 0 4 2

0 0 6 2

0 0 8 2

0 0 0 3

0 0 2 3

0 0 4 3

0 0 6 3

0 0 8 3

9

Nos iv os t pr eseka u za zavis vis no st i od pojedi nih param eta etara ra

UTICAJ ŠIRINE B 960

UTICAJ DEBLJINE PLOCE dp

Mu

840

930 900

780

870

750

840 810

720

780

690

750

660

720

630

690

600

660

570

B/b=4

630

540

600

480

540

480

420

B/b=3

450

360

390

330

360

b=30cm d=60cm

330 300

240

270 240 210

Aa1=30cm2,Aa2=0 Aa1=30cm2,Aa2=0 a1=6cm MB30, GA 240/360

210 180 150 120

180 150 120

B/b=1

90 60

90

0 0 4

0 0 6

0 0 8

0 0 0 1

0 0 2 1

0 0 4 1

0 0 6 1

0 0 8 1

0 0 0 2

0 0 2 2

0 0 4 2

0 0 6 2

0 0 8 2

0 0 0 3

0 0 2 3

0 0 4 3

60

Nu

B/b=0.5

30

0 0 6 3

dp/d=0.10

B=90cm b=30cm d=60cm Aa1=30cm2,Aa2=0 Aa1=30cm2,Aa2=0 a1=6cm MB30, GA 240/360

300

B/b=2 dp=12cm

270

0 0 2

dp/d=0.15

390

420

0 0 2 -

dp/d=0.20

450

510

0 0 4 -

dp/d=0.25

510

570

0 0 6 -

Mu

810

0 0 8 3

0 0 0 4

0 0 2 4

0 0 4 4

0 0 6 4

0 0 8 4

0 0 0 5

0 0 2 5

0 0 4 5

Nu

30

0 0 6 -

0 0 4 -

0 0 2 -

0 0 2

0 0 4

0 0 6

0 0 8

0 0 0 1

0 0 2 1

0 0 4 1

0 0 6 1

0 0 8 1

0 0 0 2

0 0 2 2

0 0 4 2

0 0 6 2

0 0 8 2

0 0 0 3

0 0 2 3

0 0 4 3

0 0 6 3

0 0 8 3

0 0 0 4

0 0 2 4

0 0 4 4

0 0 6 4

0 0 8 4

0 0 0 5

10 N u ×d×f B 0.1 2.6

0.2

0.3

0.4

0.5

0.6

0.7

εb2/εb1 = 2/2‰

0.8 2.6

LINIJA "h"

2.4

2.4

2.2

2.2

2.0

2.0

εb2/ εb1 = 3.5/0‰

LINIJA "g"

1.8 1.6

1.8

εb2/εa1 = 3.5/0‰

MALI EKSCENTRICITET SILA PRITISKA

LINIJA "f"

1.6

1.4

1.4

εb2/ εa1 = 3.5/-1‰ 1.2

1.2

.0

1.0

LINEARNA INTERPOLACIJA KOEFICIJENATA SIGURNOSTI

3.5/ εv

LINIJA "e"

0.8

0.8

0.6

0.6

0.4

0.4

0

= µ 1

0.2

0

0.6

LINIJA "c"

5 0.

MALI EKSC. SILA ZATEZANJA

-0.4

εb2/ εa1 = 3.5/-10‰

4 0.

1.0

-0.2

3.5/-3‰ LINIJA "d"

3 0.

0.8

M u b×d 2 ×

3.5/-2‰ 2 0 .

0.4

-0.6

6 0.

-0.8 . 0 7

-1.0

8 0. = 1

µ

1.2 1.4

-1.2 -1.4

εb2/ εa1 = 0/-10‰

LINIJA "b"

1.6 0

(dij agr am 2.4.10, 2.4.10, st r.135 PBA B-2)

0.2

1 0.

0.2

RA 400/ 400/500 500 ; Aa2=Aa1 ; a/d=0.10 ; sve MB

0.1 0.2 εa2/εa1 = -10/-10‰

-1.6 0.3

0.4

0.5

0.6

0.7

0.8

11

ZATEZANJE

PRITISAK

2

εb2 εa2

a

a'

b c

12

3.5

e f C

d

g h “ c ”

10‰

“ b ” “ a ”

εa1 εb1

3 εv

0

2

3.5 3. 5

ZATEZANJE

13

PRITISAK

2

εb2 εa2

d

e f

3.5

C

g h εa1 εb1

3

“ d ” “ f ”

“ h ”

εv

0

2

3.5

6 . 1 8 . 0

4 . 1 -

2 . 1 -

0 . 1 -

8 . 0 -

6 . 0 -

4 . 0 -

M u b×d 2 ×f B

2 . 0 -

2 . 0

14 4 . 0

6 . 0

6 . 0

0 . 1

" e " v A J ε I / 5 N . I 3 L

‰ ‰ 2 0 / " 1 5 - " d . c / ‰ " " 3 3 5 . - A / 3 A J J 5 . I = I N N 3 I 1 I a L ε L /

7 . 0

8 . 0

2 . 1

4 . 1

6 . 1

8 . 1

0 . 2

2 . 2

4 . 2

6 . 2 8 . 0

7 . 0

‰ 1 / 5 . 3 =

6 . 0

1 a

2 b

ε /

ε

2 b

ε

I T A S J I O C N A L R U O G P I S R E T A T N A I N A E N J I R C A I F E E N I L O K

5 . 0

4 . 0

3 . 0

2 . 0

‰ 0 " a 1 - " / 0 A J 1 - I N = I 1 L 1 . a

ε /

‰ 0 " b 1 - " / 0 A J = I N 1 I a ε L /

8 . 0 =

µ 1

2 b

ε

0

2 a

ε

0 6 . 1 -

4 . 1 -

2 . 1 -

7 . 0

6 . 0

A J . N C A S Z K E E T I A L Z A A M L I S

0 . 1 -

8 . 0 -

5 . 0

4 . 0

3 . 0

2 . 0 1 . 0

6 . 0 -

4 . 0 -

2 . 0 -

b

0

6 . 0

8 . 0

0 . 1

3 . 0

T E T I A C I K S R I T T N I E R C P S A K L E I S I L A M

µ 1

4 . 0

4 . 0

ε

0 =

2 . 0

5 . 0

‰ 0 " / f 5 . " 3 A J = I N ‰ 1 I a ε L 0 " / / g 2 5 b . " ε 3 A J = I 1 N b I ε / L 2

2 . 1

4 . 1

6 . 1

8 . 1

‰ 2 " h / 2 " A = I J 1 b N ε I / 2 L b ε

0 . 2

2 . 2

4 . 2

2 . 0

1 . 0

6 . 2

N u b×d×f B

15

N u b×d×f B 0.1 2.6 2.4 2.2

0.2

0.3

0.4

PRITISAK

εb2/εb1 = 2/2‰

LINIJA "h"

2

MALI EKSCENTRICITET SILA PRITISKA

3.5 d

7 3

2.0 1.8 1.6

εb2/εb1 = 3.5/0‰

LINIJA "g"

C

εb2/εa1 = 3.5/0‰

g

LINIJA "f"

d

h

7 4

1.4 1.2

1.0 0.8

0

2

3.5

16

N u b×d×f B

εb2/εa1 = 3.5/0‰

LINIJA "f"

1.6

1.6

LINEARNA INTERPOLACIJA KOEFICIJENATA SIGURNOSTI

1.4

1.4

εb2/εa1 = 3.5/-1‰ 1.2

1.2

1.0

1.0

3.5/εv

LINIJA "e"

0.8

0.8

0.6

0.6

0.4

0.4

3.5/-2‰

0

= µ 1

0.2

0

0.2

3.5/-3‰

M u b×d 2 ×f B

1 0. 1

-0.2 0

2 0.

0.1

-0.2 0.2

0.3

0.4

0.5

0.6

0.7

0.8

17

18

19

20

21

22

09 - Mali Ekscentricitet_ Konstrukcija Dijagrama Interakcije

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