zadatak kontinuirana greda

INstrukcije AB kontinuirana greda

INstrukcije 1

Zadatak 2: AB KONTINUIRANA GREDA

Za zadati nosac i opterecenje na skici:

• Nacrtati dijagrame presjecnih sila M,T,N (sopstvena tezina grede uracunata u

opterecenje g)

• Odrediti potrebnu kolicinu atrmature i nacrtati karakteristicne poprecne presjeke u

razmjeri R1:10

• Rasporediti armaturu i nacrtati poprecni presjek armature prema liniji zatzuch sila i liniji

pokrivanja armature

• Napraviti tabelu specifikacije armature

• Podaci:

o MB 25

o GA 240/360

o Poprecni presjek grede d/35cm

o gu=40kN/m

o Pu=34 kN/m

1. ANALIZA OPTEREĆENJA

qu= gu + pu =40 kN/m+34 kN/m=74 kN/m


INstrukcije 2

SHEMA 1:polje I i polje III

“B”

2MB(l1+l2)+MCl2=-6(RBL+ RB

D)

RBL=��∗�� RB

D=��∗��

2MB(4,2+5,7)+MC5,7=-6(�∗�,�� + � ∗�,�

�� )

19,8MB+5,7 Mc=-6(228,44+308,65)

19,8 MB+5,7 Mc=-3222,58 => MC=(-3222,57

-19,8 MB)/5,7

MC=-565,36 -3,47 MB

“C”

MBl2+2MC(l2+l3)=-6(RCL+ RC

D)

RCL=��∗�� RC

D=��∗��

MB5,7+2MC(5,7+4,2)=-6(� ∗�,�� + �∗�,��

�� )

5,7 MB+19,8 Mc=-6(308.65+228,44)

5,7 MB+19,8 Mc =-3222,56

5,7 MB+19,8 (-565,36 -3,47 MB) =-3222.56

-63 MB =7971.59

MB =-126.37KNm Mc =-126.37Nm


INstrukcije 3

POLJE I

Sile reakcije

ΣMA=0

YB*4,2-qu*4,2*2,1- MB=0

YB=��,��,�

�,� YB=185,48 KN

ΣMB=0

-YA*4.2+qu*4.2*2.1- MB=0

YA=��,��,�

�,� YA=125.31KN

Tx=0KN

Tx=YA-qu*X=0→X=�� = ��,��

�

X=1,69m

Momenti

MA= 0 KNm

Mx=Mmax= YA *X-qu *X*X/2=106.09KNm

MB=-126.


4

POLJE II

Sile reakcije

ΣMB=0

YC*5,7-gu*5,7*2,85+MB- MC =0

YC=��,��,��,�

�, YC=114 KN

ΣMC=0

-YB*5,1+gu*5,1*2,55- MC +MB =0

YB=��,��,��,�

�,

Tx=0KN

Tx=YB-gu*X=0 X=YB/gu=114/40 X=2,85m

Momenti

MB= -126.37KNm

Mx=Mmax=YB*X-gu*X*X/2-MB=36.07 KNm

MC=-126.37KNm

YB=114 KN


5

POLJE III

Sile reakcije

ΣMD=0

YC*4,2-qu*4,2*2,1- MC=0

YC=��,��,�

�,� YC=185,48 KN

ΣMC=0

-YD*4.2+qu*4.2*2.1- MC =0

YD= ��,��,�

�,� YD=125.31KN

Tx=0KN

Tx=YC-qu*X=0→ X=�� = ��,��

�

X=2,50m

Momenti

MA= 0 KNm

Mx=Mmax= YC *X-qu *X*X/2- MC =106.09KNm

MB=-126.37KNm


INstrukcije 6

SHEMA 2:polje II

“B”


D)


D=��∗��

2MB(4,2+5,7)+MC5,7=-6(� ∗�,�� + �∗�,�

�� )

19,8MB+5,7 Mc=-6(123,48+571,01)

19,8 MB+5,7 Mc=-4166,94

MC=(-4166,94 -19,8 MB)/5,7

MC=-731,04 -3,47 MB

“C”


D)


D=��∗��

MB5,7+2MC(5,7+4,2)=-6(�∗�,�� + � ∗�,��

�� )

5,7 MB+19,8 Mc=-6(571,01+123,48)

5,7 MB+19,8 Mc =-4166,95

5,7 MB+19,8 (-731,04 -3,47 MB) =- 4166,95

-63 MB =10307.72

MB =-163.40KNm Mc =-163.40KNm


7

POLJE I

Sile reakcije

ΣMB=0

YA*4,2-gu*4,2*2,1+MB=0

YA= ��,��,�

�,� YA=45.09 KN

ΣMA=0

-YB*4,2+qu*4,2*2,1+MB=0

YB= ��,��,�

�,� YB=122,90 KN

Tx=0KN

Tx=YA-gu*X=0→ X=�� = ��, �

� X=1,12m

Moment inercije

MA= 0 KNm

Mx=Mmax=YA *X-gu*X*X/2=25,41 KNm

MB=-163.4KNm


8

POLJE II

Sile reakcije

ΣMB=0

YC*5,7-qu*5,7*2,85+MB- MC =0

YC=�� ,��,� ��,�

�, YC=210,9 KN

ΣMC=0

-YB*5,7+qu*5,7*2,85 +MB - MC =0

YC=�� ,��,� ��,�

�, YB=210,9 KN

Tx=0KN

Tx=YB-qu*X=0 X=�� = �� ,�

� X=2,85m

Momenti

MB= -163.4 KNm

Mx= Mmax= YB *X-qu *X*X/2-MB

Mmax =137.12 KNm

MC=-163.4KNm


9

POLJE III

Sile reakcije

ΣMC=0

YD*4,2-gu*4,2*2,1+MC=0

YD= ��,��,�

�,� YD=45.09 KN

ΣMD=0

-YC*3,8+qu*3,8*1,9+MC=0

Tx=0KN

Tx=YC-gu*X=0→ X=�� = ��,�

� X=3.07m

Momenti

MC=-163.40KNm

Mx=Mmax=YD*X-gu*X*X/2=25,41 KNm

MD= 0 KNm

YC=��,��,�

�,� YC=122.9 KN


INstrukcije 10

SHEMA 3:oslonac I

“B”


D)


D=��∗��

2MB(4,2+5,7)+MC5,7=-6(�∗�,�� + �∗�,�

�� )

19,8MB+5,7 Mc=-6(228,43+571,01)

19,8 MB+5,7 Mc=-4796,69

MC=(-4796,68 -19,8 MB)/5,7

MC=-841,52 -3,47 MB

“C”


D)


D=��∗��

MB5,7+2MC(5,7+4,2)=-6(�∗�,�� + � ∗�,��

�� )

5,7 MB+19,8 Mc=-6(571,01+123,48)

5,7 MB+19,8 Mc =-4166,95

5,7 MB+19,8 (-841,52 -3,47 MB) =-4166,94

-63 MB =12495,27

MB =-198,08KNm Mc=-153,42KNm


INstrukcije 11

OSLONAC Ilijevp

Sile reakcije

ΣMB=0

YA*4,2-qu*4,2*2,1+MB =0

YA=��,��, �

�,� YA=108.23KN

ΣMA=0

-YB*4,2+qu*4,2*2,1 + MB

Tx=0KN

Tx=YA-qu*X=0→ X=�� = � �,��

� X=1.46 m

Momenti

MA= 0KNm

Mx= Mmax= YA *X-qu *X*X/2= 79.15KNm

MBl=-198,08KNm

YB=��,��, �

�,� YB=202,56 KN


12

OSLONAC Idesno

Sile reakcije

ΣMB=0

YC*5,7-qu*5,7*2,85+MB- MC =0

YC=�� ,��, ��,��

�, YC=203.06 KN

ΣMC=0

-YB*5,7+qu*5,7*2,85 +MB - MC =0

YB=�� ,��, ��,��

�, YB=218.73 KN

Tx=0KN

Tx=YB-qu*X=0→X=�� = ��,�

� X=2.95m

Momenti

MB= -198,08 KNm

Mx= Mmax= YB *X-qu *X*X/2-MB

Mmax= 125.18KNm

MC=-153,42KNm


13

POLJE III

Sile reakcije

ΣMC=0

YD*4.2-gu*4.2*2.1+MC=0

YD=��,��,��

�,� YD=47.46 KN

ΣMD=0

-YC*3,8+qu*3,8*1,9+MC=0

YC=��,��,��

�,�

YC=120.53 KN

Tx=0KN

Tx=YC-gu*X=0→X=�� = �� ,��

�

X=YC/gu=120.53/40 X=3,01m

Momenti

MC= -153,42KNm

Mx= Mmax= YC *X-gu *X*X/2-MC

Mmax= 28.16 KNm

MD=0KN


INstrukcije 14

SHEMA 4:oslonac II

“B”


D)


D=��∗��

2MB(4,2+5,7)+MC5,7=-6(� ∗�,�� + �∗�,�

�� )

19,8MB+5,7 Mc=-6(123,48+571,01)

19,8 MB+5,7 Mc=-4166,94

MC=(-4166,94 -19,8 MB)/5,7

MC=-731,04 -3,47 MB

“C”


D)


D=��∗��

MB5,7+2MC(5,7+4,2)=-6(�∗�,�� + �∗�,��

�� )

5,7 MB+19,8 Mc=-6(571,01+228,43)

5,7 MB+19,8 Mc =-4796,68

5,7 MB+19,8 (-731,04 -3,47 MB) =-4796,68

-63 MB =9677.97

MB =-153,42KNm Mc =-198,08KNm


INstrukcije 15

POLJE I

Sile reakcije

ΣMA=0

YB*4.2-gu*4.2*2.1- MB=0

YA= ��,��,��

�,� YB=120,53 KN

ΣMB=0

-YA*4,2+qu*4,2*2,1- MB=0

YA=��,��,��

�,� YA=47,46 KN

Tx=0KN

Tx=YA-gu*X=0→ X==�� = �,��

�

X=1,18m

Momenti

MA= 0 KNm

Mx= Mmax= YA *X-gu *X*X/2=28,16 KNm

MB=-153.42 KNm


INstrukcije 16

OSLONAC IIlijevo

Sile reakcije

ΣMB=0

YC*5,7-qu*5,7*2,85-Mc+MB =0

YC=�� ,��,��, �

�, YB=218.73 KN

ΣMC=0

-YB*5,7+qu*5,7*2,85-MC+ MB =0

Tx=0KN

Tx=YB-qu*X=0→ X=�� = ��,�

� X=2.74m

Momenti

MB= -153,42 KNm

Mx= Mmax= YB *X-qu *X*X/2-MB=125.18 KNm

MC=-198,08KNm

YB=�� ,��,��, �

�, YC=203.06 KN


INstrukcije 17

OSLONAC IIdesno

ΣMC=0

YD*4,2-qu*4,2*2,1-MC=0

YD=��,��, �

�,� YD=108.23 KN

ΣMD=0

-YC*3,8+qu*3,8*1,9-MD=0

YC=��,��, �

�,� YC=202.56 KN

Tx=0KN

Tx=YC-qu*X=0→ X=�� = � �,��

�

X=2.73m

Momenti

MC= -198,33KNm

Mx= Mmax= YD *X-qu *X*X/2=79.15KNm

MD=0KNm


18

DIMENZIONISANJE

OSLONAC I

MB=-198,08KNm

MB25 fb=17.25MPa

GA 240/360 σv=240MPa

b=35cm= 0.35m

Pretpostavka:

Lom po betonu, a dilatacija armature εb/a=3,5/9,6‰

k=2,281 μ=21,629%

� = � ∗ � � !∗"!=2,281 ∗ � ��, �&'(

,��(∗�,��)*+

h=2,281*0,181=0,413m

h=41,31cm

,- = ! ∗ � ∗ "!./ ∗ 1233%

Aa=1446.09*0.0718*0.216

Aa=22.48cm2

d=h+a0+øu+ø/2= 41.3+2,5+1+1,25 d=46,06cm d=50cm

1. USVAJANJE ARMATURE

Glavna armature:

5ø25________24,54cm2

Aausv

=

24,54 cm2

a=(35-2*2,5-2*1-5*2,5)/4=3,87˃3cm

Uzengije: øu=1/3ø=1/3*28=9,33cm

øu10/30

e= 2/3*d=33.333cm e=30cm

PODUŽNI RASPORED ARMATURE

Linija pokrivanja:

V=0,5*h=0,5*41,3cm

V=20,65cm

Z=0,9*h=0,9*0,413m

Z=0,371m

Z=Mu/z=198.08KNm/0.371m

Z=532.71KN

Zmax=Aausv*σv=24,54cm2*240MPa=

=24.54 *10-4*240*106

Zmax=588.96KN


19

OSLONAC II

Mc=-198,08

MB20→fb=17,25MPa

GA 240/360→σv=240MPa

b=35cm

h=41,31 cm

� = �� 5"!∗!

= ,��6

� �78,98:;<9,�=<∗�>,=∗�999:?@

= ,��6 ,��6

k = 2,281 kusv=2,281, εb/a=3,5/9,6‰→ μ=21,629%

,- = ! ∗ � ∗ "!./ ∗ 1233%

AC = 35cm ∗ 41,31cm ∗ 17,25MPa240MPa ∗ 21,629%100%

Aa=1446,08cm2*0,0718*0,216 Aa=22,48 cm2


Glavna armature:

5ø25________24,54cm2

Aausv

= 24,54 cm

2

2. PODUŽNI RASPORED ARMATURE

Linija pokrivanja:

Z=0,9*h=0,9*0,413m

Z=0,371m

Z=)�P = ��, �&'(

,��(

Z=532,71KN


=24,54*10-4*240*106

Zmax=588,96KN


20

POLJE I

MA-B=106.09 KNm

MB25 fb=17.25MPa

GA 240/360 σv=240MPa

b=35cm

h=41,31cm

� = �� 5"!∗!

= ,��6

� 23Q,3RSTU2V,WXYZ[∗3,\XU

= ,��6 ,��6

K= 3.116 kusv=3.118 εb/a=1.98/10‰ μ=10.963%

,- = ! ∗ � ∗ "!./ ∗ 1233%

Aa=30cm*41.31cm*17.25MPa/240MPa*10.963/100

Aa=1446.09*0.0718*0.1096 Aa=11.39cm2

USVAJANJE ARMATURE

Glavna armature:

1ø25________4,91cm2

2ø22________7,60cm2

Aausv

= 12,51 cm

2

Uzengije:

øu10/30


Linija pokrivanja:

Z=0,9*h=0,9*0,413m

Z=0,371m

Z=Mu/z=106.9KNm/0.371m

Z=285.32KN


=12.51 *10-4*240*106

Zmax=300.24KN


21

POLJE II

MA-B=137,12KNm

MB20→fb=17,25MPa

GA 240/360→σv=240MPa

b=35cm

h=41,31cm

� = �� 5"!∗!

= ,��6

� ��>,�:;<9,�=<∗�>,=∗�999:?@

= ,��6 ,�� 6

k = 2,741→kusv=2,744, εb/a=2,46/10‰→ μ=14,393%

,- = ! ∗ � ∗ "!./ ∗ 1233%

AC = 30cm ∗ 41,31cm ∗ 17,25MPa240MPa ∗ 14,393%100%

Aa=1265,1cm2*0,0583*0,143 Aa=14,95 cm2


Glavna armature:

2ø25 → 9,82cm2

2ø20 → 6,28 cm2

Aausv

= 16,10 cm

2

Uzengije: øu=1/3ø=1/3*22=7,33cm

øu8/25

e= ] ��^ = 27,33_`30_`a

4. PODUŽNI RASPORED ARMATURE

Linija pokrivanja:

Z=0,9*h=0,9*0,4217m

Z=0,371m

Z=)�P = ��,��&'(

,��(

Z=368,75KN


=16,10*10-4*240*106

Zmax=386,40KN


22

POLJE III

MA-B=106.09 KNm

MB25 fb=17.25MPa

GA 240/360 σv=240MPa

b=35cm

h=41,31cm

� = �� 5"!∗!

= ,��6

� 23Q,3RSTU2V,WXYZ[∗3,\XU

= ,��6 ,��6

K= 3.116 kusv=3.118 εb/a=1.98/10‰ μ=10.963%

,- = ! ∗ � ∗ "!./ ∗ 1233%

Aa=30cm*41.31cm*17.25MPa/240MPa*10.963/100

Aa=1446.09*0.0718*0.1096 Aa=11.39cm2

USVAJANJE ARMATURE

Glavna armature:

1ø25________4,91cm

2ø22________7,60cm

Aausv

= 12,51 cm

2

Uzengije:

øu10/30


Linija pokrivanja:

Z=0,9*h=0,9*0,413m

Z=0,371m

Z=Mu/z=106.9KNm/0.371m

Z=285.32KN


=12.51 *10-4*240*106

Zmax=300.24KN


23

DUŽINA SIDRENJA:

b = � �� =471 ø22 → ls=k* ø=47*2,2cm=103,4cm

los =2/3*lsef=2/3*(c* ls*

dedf)= 2/3* 2/3* 103,4cm= 45,95cm→46cm

ø22 → ls=1,5*k* ø=1,5*47*2,2cm=155,1cm

lsef=2/3*(c* ls*

dedf)= 2/3* 3/5* 155,1cm= 62,04cm→63cm

2 ø25 → ls=k* ø=47*2,5cm=114,88cm

0,6 ls= 0,6*114,88cm= 68,98cm→69cm

ø25 → ls=1,5*k* ø=1,5*47*2,5cm=176,25cm

lsef=c* ls*

dedf=2/3*3/5* 176,25cm= 70,5cm→71cm

3 ø25 → ls=1,5*k* ø=1,5*47*2,5cm=176,25cm

los =2/3*lsef=2/3*(c* ls*

dedf)= 2/3* 2/3* 116,25cm= 78,336cm→79cm

4 ø25 → ls=1,5*k* ø=1,5*47*2,5cm=176,25cm

lsef=c* ls*

dedf=2/3*2/5* 176,25cm= 82,063cm→83cm

5 ø22 → ls=k* ø=47*2cm=102,12cm

lsef=2/3*(c* ls*

dedf)= 2/3* 102,12cm= 48,63cm→49cm


24

SPECIFIKACIJA

1 l=420+2*(15-2,5)+2*29=453cm

za ø˃20 → k=13ø=28,6=29cm

2 l=k+0,6ls+s√2+248+ s√h+115+ls+k=29+69+58+248+58+115+69+29=675cm

s√2=(50-5-2*1-2,5/2-2,2/2)√2=57,48=58cm

za ø˃20 → k=13ø=28,6=29cm

3 l=420+570+420+2*(15-2,5)+2*29=1493cm

4 l=2*(k+106+ lsef +s√2)+370=922cm

s√2=(50-2*(2,5+0,8+2,2/2))√2=58,26=58cm

za ø˃20 → k=13ø=28,6=29cm

5 l=570+2*49+2*29=726cm

za ø˃20 → k=13ø=28,6=29cm

6 l=2*(k+44+29) =162cm

50-2*2,5-2* øu/2=44cm/24cm

za ø<10 → k=8cm


25


26

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