06 - moment loma.pdf

1Odreivanje Mu - bez uzimanja u obzir nosivosti Aa2

( )11buuaubu1a ayNMMzD:0M -+===

sNZD:0N uaubu =-=

Mu=?

b

Aa1

x=s

h

Zau

Dbu

z=z

hh

xa 1

NuGb

y b2

hd

a 1

y b1

ea1

h - x

eb sb

2v

u

v

B11a

NfhbA:0Ns

-s

m==

kfhbN+As=B

uv1ab1

s=am

( )

--

=-- a2

dNfbkh

ayNM=M 11 uB2

1buauu

fbkh= M:0M B

2

au1a

=

Odreivanje Mu - bez uzimanja u obzir nosivosti Aa2

3Primer 11a (materijal za vebe, str. 24)

MB 40RA 400/500Nu = 800 kN

aI = 4.5 cmaII = 10 cma1 = (54.5 + 310)/8a1 = 6.56 cm

h = 80 - 6.56 = 73.44 cm

Aa1 = 39.27 cm2 (8R25)15

40

24

80

4.5

234.

55.

54.

5

4.5

5R25

3R25

2R25

2R12

U8/25

8 8

2R12

18.5

4942.1k 31.65% 0.316555.244.7340

800+4027.391 ===

=m

kNm3.14581055.240942.1

44.73M 22

au =

= -

MB 40 fB = 25.5 MPa = 2.55 kN/cm2

RA 400/500 sv = 400 MPa = 40 kN/cm2

0.416h

0.810ab

3.5eb

1.94231.6570.8370.3915.45km1M %zsea

kNm7.11901056.62

808003.1458=M 2u =

-- -

Primer 11a (materijal za vebe, str. 24)

5Odreivanje Mu - uzimanje u obzir nosivosti Aa2

( ) ( )11buuau2aubu1a ayNMMahDzD:0M -+==-+=

=-+= sNZDD:0N uauaubu

Mu=?

b

Aa1

x=s

h

Zau

Dbu

z=z

hh

xa 1

NuGb

y b2

hd

a 1

y b1

ea1

Aa2ea2

a 2x-

a 2

h - a

2

h - x

Dau

eb sb

6Bbbu fhbsD a=

5.32za3

23b

b

bb ee

-e=a

b1a

b

ss1

5.3259.0s

e-

=e

=e

1ab

1a

s1s10

259.0se

-=e

=e

Odreivanje Mu - uzimanje u obzir nosivosti Aa2

( ) 2za612 bb

bb ee-

e=a

7105.3

1a

b

=e=e

1ab

bse+e

e=

259.0277

105.35.3s ==+

=

ea1 = 10

Aa1

eb = 3.5

x=0.

259

h

hOdreivanje Mu - uzimanje u obzir nosivosti Aa2

simultani lom

8b1a

b

ss1

5.3

259.0s

e-

=e

=e

25.55.34.0

4.01

5.3259.04.0s

1a

b

=-

=e

=e>=

Aa1

eb = 3.5

x=0.

4h

ea1 = 5.25

10

> 3.5

0.25

9h


lom po betonu

91ab

1a

s1s

10

259.0s

e-

=e

=e

210167.01

167.0

10259.0167.0s

b

1a

=-

=e

=e 10

3.5

0.25

9h


lom po armaturi

10

2a2aau AD s=

1a1aau AZ s=

va2a2a E se=s

va1a1a E se=s

b2

b2

2a ss

xax

ea-

=e-

=e

s0NZDD:0N uauaubu =--+=x

= s

h

eb

ea2

a 2x-

a 2

ea

sa

10ev

sv

ha2

2 =a


11

Primer 11b (materijal za vebe, str. 24)

MB 40RA 400/500Nu = 800 kN

a1 = 6.56 cmh = 80 - 6.56 = 73.44 cm

a2 = 4.5 cm

Aa1 = 39.27 cm2 (8R25)Aa2 = 9.82 cm2 (2R25)15

40

24

80

4.5

234.

55.

54.

5

4.5

5R25

3R25

2R25

2R12

U8/25

8 8

2R12

18.5

12

17.85.33.0

3.015.3259.03.0s 1ab =-

=e=e>=

pretp. s = 0.3

810.05.33

25.332 bb =-

=ae

Dbu = 0.810 0.3 40 73.44 2.55 = 1819.2 kN

0.416h

0.810ab

3.5eb

2.16824.3200.8750.3008.15km1M %zsea

Bbbu fhbsD a=

ili:


13

Dau = 9.82 40 = 392.7 kNx

= s

h

eb

ea2

a 2x-

a 2

2a2aau AD s=

061.044.735.4

ha2

2 ===a

785.25.33.0

061.03.02a =

-=e

905.110210

400E 3a

vv =

=s

=e

2v2av2a cmkN40=s=se>e

ea

sa

10ev

sv

2.78

5

8.17


14

Zau = 39.27 40 = 1570.8 kN

1a1aau AZ s=

2v1av1a cmkN4017.8 =s=se>=e

0NZDD:0N uauaubu =--+=SN = 1819.2 + 392.7 1570.8 800 = -158.9 kN

SN < 0 s > 0.3


15

uauaubu NDZD:0N +-==

Kako je s > 0.3, sledi:ea2 > 2.785 > ev sa2 = svDau = 392.7 kN = Aa2 svZau = 1570.8 kN = Aa1 sv

Dbu = 1570.8 392.7 + 800 = 1978.1 kNeb = 3.5 ab = 0.810

326.055.244.7340810.0

1.1978fhb

DsBb

bu =

=a

=


16

s = 0.326 ; Dau = 392.7 kN

0.416h

0.810ab

3.5eb

2.09526.3570.8650.3267.25km1M %zsea

kNcm152430)5.444.73(7.39255.240095.244.73M

2

au =-+

=

kNm8.1256kNcm12568056.62

80800152430=Mu ==

--

( )2auB2

au ahDfbkhM -+

=

v1av1a 25.7 s=se>=e


17

229.75.3326.0

326.015.3259.0326.0s 1ab =-

=e=e>=

( )( ) 416.025.335.32

245.335.32b =-+-

=he

( ) ( ) cm47.63326.0416.0144.73s1hz =-=h-=

( )

---+= 1u2aubuu a2dNahDzDM

( )

---+= 56.6

2808005.444.737.39247.631.1978Mu

Mu = 125880 kNcm = 1258.8 kNm pri Nu = 800 kN


18

Mu

Aa1

xII x

M

ZM,Nau = ZMau

DM,Nbu > DMbu

Nu M,N

M

Poloaj neutralne linije u zavisnosti od Nu

06 - moment loma.pdf

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