zadatak kontinuirana greda
DESCRIPTION
rjesenje zadatkaTRANSCRIPT
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 AB kontinuirana greda
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 AB kontinuirana greda
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.
INstrukcije AB kontinuirana greda
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
INstrukcije AB kontinuirana greda
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 AB kontinuirana greda
INstrukcije 6
SHEMA 2:polje II
“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(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”
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(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
INstrukcije AB kontinuirana greda
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
INstrukcije AB kontinuirana greda
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
INstrukcije AB kontinuirana greda
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 AB kontinuirana greda
INstrukcije 10
SHEMA 3:oslonac I
“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(228,43+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”
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(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 AB kontinuirana greda
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
INstrukcije AB kontinuirana greda
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
INstrukcije AB kontinuirana greda
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 AB kontinuirana greda
INstrukcije 14
SHEMA 4:oslonac II
“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(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”
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(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 AB kontinuirana greda
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 AB kontinuirana greda
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 AB kontinuirana greda
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
INstrukcije AB kontinuirana greda
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
INstrukcije AB kontinuirana greda
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
1. USVAJANJE ARMATURE
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
Zmax=Aausv*σv=24,54cm2*240MPa=
=24,54*10-4*240*106
Zmax=588,96KN
INstrukcije AB kontinuirana greda
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
PODUŽNI RASPORED ARMATURE
Linija pokrivanja:
Z=0,9*h=0,9*0,413m
Z=0,371m
Z=Mu/z=106.9KNm/0.371m
Z=285.32KN
Zmax=Aausv*σv=12,51cm2*240MPa=
=12.51 *10-4*240*106
Zmax=300.24KN
INstrukcije AB kontinuirana greda
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
3. USVAJANJE ARMATURE
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
Zmax=Aausv*σv=16,10cm2*240MPa=
=16,10*10-4*240*106
Zmax=386,40KN
INstrukcije AB kontinuirana greda
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
PODUŽNI RASPORED ARMATURE
Linija pokrivanja:
Z=0,9*h=0,9*0,413m
Z=0,371m
Z=Mu/z=106.9KNm/0.371m
Z=285.32KN
Zmax=Aausv*σv=12,51cm2*240MPa=
=12.51 *10-4*240*106
Zmax=300.24KN
INstrukcije AB kontinuirana greda
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
INstrukcije AB kontinuirana greda
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
INstrukcije AB kontinuirana greda
25
INstrukcije AB kontinuirana greda
26